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Structure-Property Relationships

2010-01-18T17:44:15Z

67.183.23.184: /* Electric Field Perturbation of Structure */

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Bond order alternation (BOA) and bond length alternation (BLA) are useful concepts that can be correlated to α the linear polarizability and β the first hyperpolarizability of molecules. The effect of applied electrical fields on BOA and BLA can be predicted by understanding the chemical structure and how charge distribution and dipole moment will shift.

=== Applying theory to relate structure to properties ===

Material chemists help bring theory to play with the rational design of molecules.
[[Image:Sumoverstate.png|thumb|900px|center|Sum over state expression for β]]
The sum over states expression for β describes the factors for building a molecule with high β. This can be translated into an optimized molecule, which can then be incorporated into an optimized material.

See Meyers 1994 <ref>F. Meyers, S. R. Marder, B. M. Pierce, J. L. Bredas
J. Am. Chem. Soc., 1994, 116 (23), pp 10703–10714 Electric Field Modulated Nonlinear Optical Properties of Donor-Acceptor Polyenes: Sum-Over-States Investigation of the Relationship between Molecular Polarizabilities (.alpha., .beta., and .gamma.) and Bond Length Alternation http://pubs.acs.org/doi/abs/10.1021/ja00102a040?journalCode=jacsat&quickLinkVolume=116&quickLinkPage=10703&volume=116</ref>

=== Bond Length Alternation ===
[[Image:Bla.png|thumb|300px|Bond Length Alternation (BLA) in a polymethine chain]]
Bond length alternation is a construct that can be used to monitor the amount of polarization in a molecule. Bond-length alternation (BLA) is defined as the average of the difference in the length between adjacent carbon-carbon bonds in a polymethine ((CH)n) chain. A polymethine dye is a series of CH units connected by double or single bonds.

Bond-length alternation (BLA) is defined as the average of the difference in the length between adjacent carbon-carbon bonds in a polymethine ((CH)n) chain. Polyenes (such as ethylene) have alternating C-C double (1.34 Å), the carbon bond in ethane (1.54 Å) and single bonds between two sp2 hybridized carbons in a polyene is (1.45 Å). As you move from butadiene to polyacetylene the double bonds a bit longer and the single bonds become a little shorter. The average difference between single and double bond lengths is the bond length alternation (BLA), for polyenes show a high degree of BLA (+ 0.11 Å). If instead of a structural view we wish to consider an electronic or molecular orbital related parameter we can consider bond order. A double bond has a bond order of 2 and single bond has a bond order of one. The bond order alternation is -1 (1-2=-1). If you attach a donor and acceptor group to opposite ends of the molecule donor will attempt to transfer electrons to the acceptor by pushing electrons into the chain.

A simple model has been proposed recently where α, β and γ are correlated with the degree of ground-state polarization.
The degree of ground-state polarization, or in other words the degree of charge separation in the ground state, depends primarily on the chemical structure (for example, the structure of the π-conjugated system, or the strength of the donor and acceptor substituents), but also on its surroundings (for example, the polarity of the medium).
In donor-acceptor polyenes, this variable is related to a geometrical parameter, the bond-length alternation (BLA)

=== Resonance Structures and BLA ===
[[Image:Resonance_bla.png|thumb|300px|Resonance structures trends. As the two structures contribute more equally to the ground-state structure of the molecule the BLA decreases]]
It is illustrative to discuss the wave function of the ground state in terms of a linear combination of the two limiting resonance structures:
#a neutral form characterized by a positive BLA and
#a charge-separated form characterized by a negative BLA (since the double and single bond pattern is now reversed relative to the neutral form).

From an energetic standpoint the two resonance structures can be treated as having two potential wells separated by a nuclear coordinate. The first resonance structure on the left has a BLS of .11. Using the same carbon numbering scheme first molecule on the right would have a BLA of -.11 because the double bonds in the center are shifted right one carbon atom. The neutral molecule has a lower potential energy and therefore will the more favored state. The potential energy diagram shows a higher energy curve for the charge separated resonance structure and a dotted line shows the mixing state. The ground of this is a resonance structure that looks more like the neutral molecule. For substituted polyenes with weak donors and acceptors, the neutral resonance form dominates the ground-state wave function, and the molecule has a high degree of BLA.

This is visualized by the relative size of the two balloons over the equilibrium arrow, (this is not a representation of the molecule itself).

By adding a donor group on the right and acceptor on the left you decrease the energy difference between the two forms thus stabilizing the molecule. The relative contribution of the two forms to the resonance structure becomes more equal. The bond length alternation will decrease and the molecule will look less polyene like and more zwitterionic (charge separated). With stronger donors and acceptors, the contribution of the charge-separated resonance form to the ground state increases and simultaneously, BLA decreases.

In the bottom structure we replace the C=O with a C=N+ (an iminium group) which is a stronger charge acceptor. The electrons move from one side to the other. The structure on the right is an identical to the structure on the left. The charge will be equally distributed between the two nitrogens resulting in 1.5 bonds between all carbons. The two forms have the same energy. When the two resonance forms contribute equally to the ground-state structure, the molecule exhibits essentially no BLA. This zero BLA limit is the so-called cyanine limit. The position of the electron will be more sensitive to the electric field in the cyanine case; this is also known as polarizability.

Second order optical materials requires asymmetrical polarizability. Neither the first case with total transfer (polyene limit) and or the last case with equal transfer (cyanine limit) will have asymmetry; they will not have no β. The middle molecule will has some asymmetrical polarizability. Starting at the polyene limit or the cyanine limit you can add weak acceptors and thereby increase the asymmetry, and the β increases. The curve of β vs bond length alternation will start at zero, go up to a peak and then go back down to zero. For example, with stilbene and paranitroaniline and add stronger donors and acceptor groups, or make the molecules longer, you can increase the β. However, past a certain point stronger donors and acceptors simply results in a zwitterion and the polarizability decreases. The optimal point can be described and predicted this using quantum mechanics and four orbitals.

=== Electric Field Perturbation of Structure ===
[[Image:BOA_perturb.png|thumb|500px|BLA as a function of Electric Field]]
To move electrons from one end to another it requires a very large electric field (10<sup>7</sup> volts per cm) on the order of the energy that holds the molecule together. These fields are about 100 larger than are typically used in a laboratory. You can plot the BLA and the Bond order alternation (BOA) as well as the induced dipole moment. This molecule does not start at the polyene limit for BLA of .11 because there first molecule already has a donor and acceptor groups. The BLA starts at .08 and as the field is increase it goes down to zero and then becomes negative. The bond order alternative (BOA) starts negative, goes to zero and then becomes positive. The change with respect to electric field is greatest in the center of the curve near zero BLA or BOA. An electric field can increase charge separation in the ground –state of molecules. This in turn modifies the BLA, the Bond Order Alternation (BOA) and the dipole moment.

[[Image:Appliedfield_distribution.png|thumb|500px|center|Effect of Applied field on pi-Charge Distribution]]

As you move from no electric field to a large electric field (shown as 0, 5 and 8 x 10<sup>7</sup> V/cm) there is an increase in positive charge on one end (the nitrogen end) and an increase in negative charge on the other end (the oxygen end).

<div id="Flash">'''Induced Polarization Animation'''</div>

<swf width="550" height="400">http://depts.washington.edu/cmditr/media/boa.swf</swf>

In the above animation see what happens to the electron density distribution as you apply an electric field using the bar on the right.

=== Dipole Moment vs. Field and BOA ===
[[Image:Dipole_vs_BOA.png|thumb|400px|dipole versus electric field and dipole versus BOA]]
As a consequence of the charge redistribution, the dipole moment increases as a function of the applied electric field. Since the BOA is a function of field and the dipole moment is a function of field one can now correlate the dipole with the BOA to develop our first structure (BOA)- property (dipole moment) relationship.

The dipole moment versus electric field goes up and then saturates. The mathematical definition of polarizability is
Dμ DE; the slope of any function at any given point. The slope increases and then decreases. The slope is highest around 30-40 μ

A plot of dipole vs BOA going from a polyene to a cyanine is approximately a straight line because both the dipole and the BOA are sigmoidal curves. Around zero BOA (the cyanine limit) the polarizability is largest. The second derivative of this curve is the first hyperpolizability.

=== Linear Polarizability and BOA ===
[[Image:Linearpolarize_boa.png|thumb|500px|Linear polarizability as a function of BOA]]

:<math>\alpha \propto \left ( \frac {\mu^{2}_{ge}}{E_{ge}}\right )\,\!</math>

A linear polarizablity α(alpha) vs BOA curve starts small, increases to a maximum and then goes down. A graph of polarizability vs charge is a sigmoidal curve so the maximum slope of such a curve occurs near the inflection point where BOA is zero. The polarizability is highest at the cyanine limit, and the hyperpolarizability is zero at the cyanine limit. Rate of change of polarizability is zero at the cyanine limit and from a particle- in-a-box perspective the molecule does not have an asymmetrical polarizability. Thus without any sum-over-states calculations you can draw conclusions about the linear polarizability and hyperpolarizability using only ground state dipole moment calculations.

In a sum-over-states calculation the linear polarizability is defined as the sum over the square of all of the transition dipole moments, between the ground and any of the excited states, divided by the energy gap. The result is the red curve which peaks at the cyanine limit. Spectroscopically molecules like these usually have a single strong peak which has a transition dipole moment that is larger than others and that peak tends to be the lowest energy, resulting in a larger energy gap.

In a two state model we choose to ignore the contribution from all terms except the one that give rise to the strong peak. α is the transition dipole moment squared between the ground and one excited state, over the energy gap between these two states results in the blue open circles. This matches the red curve very well so the two state model seems to capture the essence of the relationship. The question is which term is responsible for the peak; is it the transition dipole moment (blue triangle) or one over the energy gap (blue square)? Calculating and plotting these two terms shows that both peak near the cyanine limit. As a result the polarizabilty peaks at the cyanine limit.

=== First Hyper-polarizability and BOA ===

[[Image:First_hyperpole.png|thumb|400px|β versus BOA- (Oudar, Chemla, Garito and Lalama)]]
By calculating β (beta) for each electric field and differing BOA and taking into account all the states it shows that β goes up, peaks about halfway between the polyene and the cyanine limit, goes down to zero and then goes negative. In the two level model for β is related to the transition dipole moment squared, the change in the dipole moment and divided by the energy gap. Most aromatic molecules tend to be near polyene limit with a small β.

:<math>\beta \propto \left( \frac {\mu^{2} _{ge} ( \mu _ {ee} - \mu _{gg})} {E^{2}_{ge}}\right)\,\!</math>

Where:
:<math>\mu_{ge}\,\!</math> is the transition dipole moment
:<math>\mu_{ee}\,\!</math> is the dipole moment of the excited state
:<math>\mu_{gg}\,\!</math> is the dipole moment of the ground state
:<math>E_{ge}\,\!</math> is the energy gap between the states - or ω<sub>ge</sub> the frequency corresponding to the excited state energy.

Considering only the two states the β model (blue circles) matches the experimental values (red dots) well. So the two state model looks good for β as well as α. The energy gap squared peaks at the cyanine limit as does the transition dipole moment.

A polyene that has no dipole moment (eg it is symmetrical) in the ground state will have no dipole moment in the excited state. The change in dipole moment (blue plus symbol) peaks closer to the polyene limit. Most aromatic molecules tend to be near polyene limit with a small beta. The beginning portion of the β curve looks almost linear, this led researchers to believe that they just had to add stronger donors and acceptors to the molecule in order to increase β. But they were not seeing the whole picture.

=== Factors Affecting Charge Separation ===
[[Image:Chargeseparaton.png|thumb|400px|Effect of aromaticity on charge distribution in resonance structures]]

The relative contribution of each limiting resonance structure to the ground-state structure of a molecule is related to their relative energies. When the two resonance forms are very different in energy the ground-state structure will be dominated by the lower energy form and the molecules will exhibit a large degree of BLA.

In organic molecules there are two factors that dominate the energetics of the resonance structures to a first approximation.

First, there is a Coulombic term that is destabilizing when charge is separated. Adding donors and acceptors does encourage separation of charge but this also costs energy. Increasing the strength of the donor and acceptor end groups, and/or placing the molecule in a more polar solvent to the molecule can each lead to stabilization of the charge separated form.

In addition, there is also an energy consideration associated with the topology of the molecule.If a molecule has 6 π-electrons in a ring the molecule has an additional resonance stabilization and is referred to as aromatic. In the case of stilbene with added donor and acceptors there is a loss of aromaticity, (a loss of 36kcal/mol). This favors the molecule that is aromatic.

For molecules whose neutral forms are aromatic, charge separation will interrupt the aromaticity and yield structure with a higher energy quinoidal resonance form.

This disruption of the aromaticity results in additional destabilization due to the loss of aromatic stabilization and in such systems the molecule will be further biased towards the neutral resonance form

If, on the other hand, the neutral form is quinoidal, then the molecule will gain aromatic stabilization in the charge-separated resonance form. Aromaticity can be used as a driving force to get past the cyanine limit. The groups can used to tune the molecules for particular desired polarization characteristics.

'''Tuning Bond Length Alternation Leads to Optimization of β'''

We can tune aromaticity and charge separation.

Therefore we can tune energetics of resonance structures.

Therefore we can tune bond length alternation across a wide range.

If βis a peaked function, we can tune the bond length alternation so as to be at the peak and optimize β.

'''Evolution of Dipole Moments'''
[[Image:Dipole_evolution.png|thumb|400px|Dipole Moments and Bond Order Alternation]]
Note that both the ground- and the excited-state dipole moments increase as BOA becomes more positive.
However note also that the past the cyanine-limit (0 BOA) the excited-state dipole moment(μ<sub>ee</sub>) is less than the ground-state dipole moment(μ<sub>gg</sub>) so Δ μ becomes negative. The excited state dipole moment vs BOA has a flat slope, while the groundstate dipole is going up, therefore the ground state is going to exhibit more polarizability.

<br clear='all'>
=== Manipulation of BLA Through Topology ===
[[Image:Topology.png|thumb|300px|Tuning Aromaticity to Optimize β ]]
Until recently, most molecules that had been examined for NLO, such as donor-acceptor substituted stilbenes or diphenyl polyenes, had a very large BLA, typically greater than 0.10 Å. The calculations above, for example, predict that β is maximized at a value of ~0.04 Å; thus, these molecules with large BLA are not sufficiently polarized to give the correct BLA needed to maximize β. It was hypothesized that the high magnitude of BLA observed in the central polyene bridge of donor-acceptor substituted stilbenes and related molecules is indicative of an insufficient contribution of the charge-separated resonance forms to the ground-state configurations of the molecules and is a consequence of the loss of aromatic stabilization in the charge-separated forms.

We can tune aromaticity and charge separation. There first molecule is called an phenylisoxazimone. Aromatic groups must have 4n+2 electrons in a ring. The benzene has 4n+2. In the charge separated form there is a somewhat aromatic ring which offsets the loss of aromaticity from benzene.

In the second example there single bonds that are cross conjugated to a fully conjugated form when in the charge separated form.

In the third example of heterocycles such as thiophenes we start with neutral molecules that lack the full benzene aromaticity. You still lose aromaticity on both sides but not a full benzenes’ worth.

Using these techniques we can tune energetics of resonance structures therefore we can tune bond length alternation across a wide range. If β is a peaked function, we can tune the bond length alternation so as to be at the peak and optimize β.

== References ==
<references/>
[[category:second order NLO]]
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Structure-Property Relationships

2010-01-18T17:43:41Z

67.183.23.184: /* Electric Field Perturbation of Structure */

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Bond order alternation (BOA) and bond length alternation (BLA) are useful concepts that can be correlated to α the linear polarizability and β the first hyperpolarizability of molecules. The effect of applied electrical fields on BOA and BLA can be predicted by understanding the chemical structure and how charge distribution and dipole moment will shift.

=== Applying theory to relate structure to properties ===

Material chemists help bring theory to play with the rational design of molecules.
[[Image:Sumoverstate.png|thumb|900px|center|Sum over state expression for β]]
The sum over states expression for β describes the factors for building a molecule with high β. This can be translated into an optimized molecule, which can then be incorporated into an optimized material.

See Meyers 1994 <ref>F. Meyers, S. R. Marder, B. M. Pierce, J. L. Bredas
J. Am. Chem. Soc., 1994, 116 (23), pp 10703–10714 Electric Field Modulated Nonlinear Optical Properties of Donor-Acceptor Polyenes: Sum-Over-States Investigation of the Relationship between Molecular Polarizabilities (.alpha., .beta., and .gamma.) and Bond Length Alternation http://pubs.acs.org/doi/abs/10.1021/ja00102a040?journalCode=jacsat&quickLinkVolume=116&quickLinkPage=10703&volume=116</ref>

=== Bond Length Alternation ===
[[Image:Bla.png|thumb|300px|Bond Length Alternation (BLA) in a polymethine chain]]
Bond length alternation is a construct that can be used to monitor the amount of polarization in a molecule. Bond-length alternation (BLA) is defined as the average of the difference in the length between adjacent carbon-carbon bonds in a polymethine ((CH)n) chain. A polymethine dye is a series of CH units connected by double or single bonds.

Bond-length alternation (BLA) is defined as the average of the difference in the length between adjacent carbon-carbon bonds in a polymethine ((CH)n) chain. Polyenes (such as ethylene) have alternating C-C double (1.34 Å), the carbon bond in ethane (1.54 Å) and single bonds between two sp2 hybridized carbons in a polyene is (1.45 Å). As you move from butadiene to polyacetylene the double bonds a bit longer and the single bonds become a little shorter. The average difference between single and double bond lengths is the bond length alternation (BLA), for polyenes show a high degree of BLA (+ 0.11 Å). If instead of a structural view we wish to consider an electronic or molecular orbital related parameter we can consider bond order. A double bond has a bond order of 2 and single bond has a bond order of one. The bond order alternation is -1 (1-2=-1). If you attach a donor and acceptor group to opposite ends of the molecule donor will attempt to transfer electrons to the acceptor by pushing electrons into the chain.

A simple model has been proposed recently where α, β and γ are correlated with the degree of ground-state polarization.
The degree of ground-state polarization, or in other words the degree of charge separation in the ground state, depends primarily on the chemical structure (for example, the structure of the π-conjugated system, or the strength of the donor and acceptor substituents), but also on its surroundings (for example, the polarity of the medium).
In donor-acceptor polyenes, this variable is related to a geometrical parameter, the bond-length alternation (BLA)

=== Resonance Structures and BLA ===
[[Image:Resonance_bla.png|thumb|300px|Resonance structures trends. As the two structures contribute more equally to the ground-state structure of the molecule the BLA decreases]]
It is illustrative to discuss the wave function of the ground state in terms of a linear combination of the two limiting resonance structures:
#a neutral form characterized by a positive BLA and
#a charge-separated form characterized by a negative BLA (since the double and single bond pattern is now reversed relative to the neutral form).

From an energetic standpoint the two resonance structures can be treated as having two potential wells separated by a nuclear coordinate. The first resonance structure on the left has a BLS of .11. Using the same carbon numbering scheme first molecule on the right would have a BLA of -.11 because the double bonds in the center are shifted right one carbon atom. The neutral molecule has a lower potential energy and therefore will the more favored state. The potential energy diagram shows a higher energy curve for the charge separated resonance structure and a dotted line shows the mixing state. The ground of this is a resonance structure that looks more like the neutral molecule. For substituted polyenes with weak donors and acceptors, the neutral resonance form dominates the ground-state wave function, and the molecule has a high degree of BLA.

This is visualized by the relative size of the two balloons over the equilibrium arrow, (this is not a representation of the molecule itself).

By adding a donor group on the right and acceptor on the left you decrease the energy difference between the two forms thus stabilizing the molecule. The relative contribution of the two forms to the resonance structure becomes more equal. The bond length alternation will decrease and the molecule will look less polyene like and more zwitterionic (charge separated). With stronger donors and acceptors, the contribution of the charge-separated resonance form to the ground state increases and simultaneously, BLA decreases.

In the bottom structure we replace the C=O with a C=N+ (an iminium group) which is a stronger charge acceptor. The electrons move from one side to the other. The structure on the right is an identical to the structure on the left. The charge will be equally distributed between the two nitrogens resulting in 1.5 bonds between all carbons. The two forms have the same energy. When the two resonance forms contribute equally to the ground-state structure, the molecule exhibits essentially no BLA. This zero BLA limit is the so-called cyanine limit. The position of the electron will be more sensitive to the electric field in the cyanine case; this is also known as polarizability.

Second order optical materials requires asymmetrical polarizability. Neither the first case with total transfer (polyene limit) and or the last case with equal transfer (cyanine limit) will have asymmetry; they will not have no β. The middle molecule will has some asymmetrical polarizability. Starting at the polyene limit or the cyanine limit you can add weak acceptors and thereby increase the asymmetry, and the β increases. The curve of β vs bond length alternation will start at zero, go up to a peak and then go back down to zero. For example, with stilbene and paranitroaniline and add stronger donors and acceptor groups, or make the molecules longer, you can increase the β. However, past a certain point stronger donors and acceptors simply results in a zwitterion and the polarizability decreases. The optimal point can be described and predicted this using quantum mechanics and four orbitals.

=== Electric Field Perturbation of Structure ===
[[Image:BOA_perturb.png|thumb|500px|BLA as a function of Electric Field]]
To move electrons from one end to another it requires a very large electric field (10<sup>7</sup> volts per cm) on the order of the energy that holds the molecule together. These fields are about 100 larger than are typically used in a laboratory. You can plot the BLA and the Bond order alternation (BOA) as well as the induced dipole moment. This molecule does not start at the polyene limit for BLA of .11 because there first molecule already has a donor and acceptor groups. The BLA starts at .08 and as the field is increase it goes down to zero and then becomes negative. The bond order alternative (BOA) starts negative, goes to zero and then becomes positive. The change with respect to electric field is greatest in the center of the curve near zero BLA or BOA. An electric field can increase charge separation in the ground –state of molecules. This in turn modifies the BLA, the Bond Order Alternation (BOA) and the dipole moment.

[[Image:Appliedfield_distribution.png|thumb|500px|center|Effect of Applied field on pi-Charge Distribution]]

As you move from no electric field to a large electric field (shown as 0, 5 and 8 x 10<sup>7</sup> V/cm) there is an increase in positive charge on one end (the nitrogen end) and an increase in negative charge on the other end (the oxygen end).

<div id="Flash">Induced polarization Animation</div>

<swf width="550" height="400">http://depts.washington.edu/cmditr/media/boa.swf</swf>

In the above animation see what happens to the electron density distribution as you apply an electric field using the bar on the right.

=== Dipole Moment vs. Field and BOA ===
[[Image:Dipole_vs_BOA.png|thumb|400px|dipole versus electric field and dipole versus BOA]]
As a consequence of the charge redistribution, the dipole moment increases as a function of the applied electric field. Since the BOA is a function of field and the dipole moment is a function of field one can now correlate the dipole with the BOA to develop our first structure (BOA)- property (dipole moment) relationship.

The dipole moment versus electric field goes up and then saturates. The mathematical definition of polarizability is
Dμ DE; the slope of any function at any given point. The slope increases and then decreases. The slope is highest around 30-40 μ

A plot of dipole vs BOA going from a polyene to a cyanine is approximately a straight line because both the dipole and the BOA are sigmoidal curves. Around zero BOA (the cyanine limit) the polarizability is largest. The second derivative of this curve is the first hyperpolizability.

=== Linear Polarizability and BOA ===
[[Image:Linearpolarize_boa.png|thumb|500px|Linear polarizability as a function of BOA]]

:<math>\alpha \propto \left ( \frac {\mu^{2}_{ge}}{E_{ge}}\right )\,\!</math>

A linear polarizablity α(alpha) vs BOA curve starts small, increases to a maximum and then goes down. A graph of polarizability vs charge is a sigmoidal curve so the maximum slope of such a curve occurs near the inflection point where BOA is zero. The polarizability is highest at the cyanine limit, and the hyperpolarizability is zero at the cyanine limit. Rate of change of polarizability is zero at the cyanine limit and from a particle- in-a-box perspective the molecule does not have an asymmetrical polarizability. Thus without any sum-over-states calculations you can draw conclusions about the linear polarizability and hyperpolarizability using only ground state dipole moment calculations.

In a sum-over-states calculation the linear polarizability is defined as the sum over the square of all of the transition dipole moments, between the ground and any of the excited states, divided by the energy gap. The result is the red curve which peaks at the cyanine limit. Spectroscopically molecules like these usually have a single strong peak which has a transition dipole moment that is larger than others and that peak tends to be the lowest energy, resulting in a larger energy gap.

In a two state model we choose to ignore the contribution from all terms except the one that give rise to the strong peak. α is the transition dipole moment squared between the ground and one excited state, over the energy gap between these two states results in the blue open circles. This matches the red curve very well so the two state model seems to capture the essence of the relationship. The question is which term is responsible for the peak; is it the transition dipole moment (blue triangle) or one over the energy gap (blue square)? Calculating and plotting these two terms shows that both peak near the cyanine limit. As a result the polarizabilty peaks at the cyanine limit.

=== First Hyper-polarizability and BOA ===

[[Image:First_hyperpole.png|thumb|400px|β versus BOA- (Oudar, Chemla, Garito and Lalama)]]
By calculating β (beta) for each electric field and differing BOA and taking into account all the states it shows that β goes up, peaks about halfway between the polyene and the cyanine limit, goes down to zero and then goes negative. In the two level model for β is related to the transition dipole moment squared, the change in the dipole moment and divided by the energy gap. Most aromatic molecules tend to be near polyene limit with a small β.

:<math>\beta \propto \left( \frac {\mu^{2} _{ge} ( \mu _ {ee} - \mu _{gg})} {E^{2}_{ge}}\right)\,\!</math>

Where:
:<math>\mu_{ge}\,\!</math> is the transition dipole moment
:<math>\mu_{ee}\,\!</math> is the dipole moment of the excited state
:<math>\mu_{gg}\,\!</math> is the dipole moment of the ground state
:<math>E_{ge}\,\!</math> is the energy gap between the states - or ω<sub>ge</sub> the frequency corresponding to the excited state energy.

Considering only the two states the β model (blue circles) matches the experimental values (red dots) well. So the two state model looks good for β as well as α. The energy gap squared peaks at the cyanine limit as does the transition dipole moment.

A polyene that has no dipole moment (eg it is symmetrical) in the ground state will have no dipole moment in the excited state. The change in dipole moment (blue plus symbol) peaks closer to the polyene limit. Most aromatic molecules tend to be near polyene limit with a small beta. The beginning portion of the β curve looks almost linear, this led researchers to believe that they just had to add stronger donors and acceptors to the molecule in order to increase β. But they were not seeing the whole picture.

=== Factors Affecting Charge Separation ===
[[Image:Chargeseparaton.png|thumb|400px|Effect of aromaticity on charge distribution in resonance structures]]

The relative contribution of each limiting resonance structure to the ground-state structure of a molecule is related to their relative energies. When the two resonance forms are very different in energy the ground-state structure will be dominated by the lower energy form and the molecules will exhibit a large degree of BLA.

In organic molecules there are two factors that dominate the energetics of the resonance structures to a first approximation.

First, there is a Coulombic term that is destabilizing when charge is separated. Adding donors and acceptors does encourage separation of charge but this also costs energy. Increasing the strength of the donor and acceptor end groups, and/or placing the molecule in a more polar solvent to the molecule can each lead to stabilization of the charge separated form.

In addition, there is also an energy consideration associated with the topology of the molecule.If a molecule has 6 π-electrons in a ring the molecule has an additional resonance stabilization and is referred to as aromatic. In the case of stilbene with added donor and acceptors there is a loss of aromaticity, (a loss of 36kcal/mol). This favors the molecule that is aromatic.

For molecules whose neutral forms are aromatic, charge separation will interrupt the aromaticity and yield structure with a higher energy quinoidal resonance form.

This disruption of the aromaticity results in additional destabilization due to the loss of aromatic stabilization and in such systems the molecule will be further biased towards the neutral resonance form

If, on the other hand, the neutral form is quinoidal, then the molecule will gain aromatic stabilization in the charge-separated resonance form. Aromaticity can be used as a driving force to get past the cyanine limit. The groups can used to tune the molecules for particular desired polarization characteristics.

'''Tuning Bond Length Alternation Leads to Optimization of β'''

We can tune aromaticity and charge separation.

Therefore we can tune energetics of resonance structures.

Therefore we can tune bond length alternation across a wide range.

If βis a peaked function, we can tune the bond length alternation so as to be at the peak and optimize β.

'''Evolution of Dipole Moments'''
[[Image:Dipole_evolution.png|thumb|400px|Dipole Moments and Bond Order Alternation]]
Note that both the ground- and the excited-state dipole moments increase as BOA becomes more positive.
However note also that the past the cyanine-limit (0 BOA) the excited-state dipole moment(μ<sub>ee</sub>) is less than the ground-state dipole moment(μ<sub>gg</sub>) so Δ μ becomes negative. The excited state dipole moment vs BOA has a flat slope, while the groundstate dipole is going up, therefore the ground state is going to exhibit more polarizability.

<br clear='all'>
=== Manipulation of BLA Through Topology ===
[[Image:Topology.png|thumb|300px|Tuning Aromaticity to Optimize β ]]
Until recently, most molecules that had been examined for NLO, such as donor-acceptor substituted stilbenes or diphenyl polyenes, had a very large BLA, typically greater than 0.10 Å. The calculations above, for example, predict that β is maximized at a value of ~0.04 Å; thus, these molecules with large BLA are not sufficiently polarized to give the correct BLA needed to maximize β. It was hypothesized that the high magnitude of BLA observed in the central polyene bridge of donor-acceptor substituted stilbenes and related molecules is indicative of an insufficient contribution of the charge-separated resonance forms to the ground-state configurations of the molecules and is a consequence of the loss of aromatic stabilization in the charge-separated forms.

We can tune aromaticity and charge separation. There first molecule is called an phenylisoxazimone. Aromatic groups must have 4n+2 electrons in a ring. The benzene has 4n+2. In the charge separated form there is a somewhat aromatic ring which offsets the loss of aromaticity from benzene.

In the second example there single bonds that are cross conjugated to a fully conjugated form when in the charge separated form.

In the third example of heterocycles such as thiophenes we start with neutral molecules that lack the full benzene aromaticity. You still lose aromaticity on both sides but not a full benzenes’ worth.

Using these techniques we can tune energetics of resonance structures therefore we can tune bond length alternation across a wide range. If β is a peaked function, we can tune the bond length alternation so as to be at the peak and optimize β.

== References ==
<references/>
[[category:second order NLO]]
<table id="toc" style="width: 100%">
<tr>
<td style="text-align: left; width: 33%">[[Second-order Processes|Previous Topic]]</td>
<td style="text-align: center; width: 33%">[[Main_Page#Second-order Processes, Materials & Characterization |Return to Second-order Processes, Materials & Characterization Menu]]</td>
<td style="text-align: right; width: 33%">[[Second-order NLO Materials| Next Topic]]</td>
</tr>
</table>

Photonics Wiki Showcase

2010-01-18T17:37:34Z

67.183.23.184: /* Flash Simulations */

Here are some examples from the Photonics Wiki that are useful for a quick tour.

=== Basic Features ===

*[[Main Page | Table of contents show structure of information on the page.]]

*[[Acronyms and Unit Abbreviations]]

*[[Organic Heterojunctions in Solar Cells | Adobe Acrobat for slide sequences]]

*[[Electromagnetic_Radiation | Latex for Math Formulas - (go to page and edit to see the source)]]

*[[Solar_Technologies#External_Links | External Links and References]]

*[[Organic Photovoltaic Fabrication and Test Apparatus | Flash Video for Lab Training]]

*[[How to Give a Research Presentation]]

*[[Electromagnetic_Spectrum#Knowledge_Check | Knowledge Check - Wiki Quiz]]

=== Flash Simulations ===

*[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]

*[[Second-order_NLO_Materials#Flash | Poling Simulation]]

*[[Second-order_NLO_Materials#Flash2 | Interactions]]

*[[Second-order_Processes#Flash | Electro-optical effect animation]]

*[[Introduction_to_Third-order_Processes_and_Materials#Flash |Phase Conjugate Mirror]]

*[[Attenuated Total Reflectance#Flash |Attenuated Total Reflectance]]

*[[Polarization_and_Polarizability#Flash | Four types of polarization animation]]

Photonics Wiki Showcase

2010-01-18T17:36:29Z

67.183.23.184: /* Flash Simulations */

Here are some examples from the Photonics Wiki that are useful for a quick tour.

=== Basic Features ===

*[[Main Page | Table of contents show structure of information on the page.]]

*[[Acronyms and Unit Abbreviations]]

*[[Organic Heterojunctions in Solar Cells | Adobe Acrobat for slide sequences]]

*[[Electromagnetic_Radiation | Latex for Math Formulas - (go to page and edit to see the source)]]

*[[Solar_Technologies#External_Links | External Links and References]]

*[[Organic Photovoltaic Fabrication and Test Apparatus | Flash Video for Lab Training]]

*[[How to Give a Research Presentation]]

*[[Electromagnetic_Spectrum#Knowledge_Check | Knowledge Check - Wiki Quiz]]

=== Flash Simulations ===

*[[Organic Heterojunctions in Solar Cells#Flash | Flash Simulation of Exciton Diffusion]]

*[[Second-order_NLO_Materials#Flash | Poling Simulation]]

*[[Second-order_NLO_Materials#Flash2 | Interactions]]

*[[Second-order_Processes#Flash | Electro-optical effect animation]]

*[[Introduction_to_Third-order_Processes_and_Materials#Flash |Phase Conjugate Mirror]]

*[[Attenuated Total Reflecton#Flash |Attenuated Total Reflecton]]

*[[Polarization_and_Polarizability#Flash | Four types of polarization animation]]

Attenuated Total Reflectance

2010-01-18T17:35:38Z

67.183.23.184: /* Technique */

=== Overview ===
Attenuated Total Reflection or ATR is a technique used together with Teng Mann to measure the R33 of electro-optic materials. A beam of IR light is directed through a prism at an angle exceeding the critical angle for internal reflection. This produces an evanescent wave at the prism surface. If a EO polymer is pressed in intimate contact with the prism they can be coupled so that he evanescent wave stimulates emission from the sample. This emission is measured with a photodiode. An electric field applied to an EO polymer changes its index of refraction which alters the critical angle.

=== Technique ===
<div id="Flash">Attenuated Total Reflection simulation</div>

<swf width="720" height="480">http://depts.washington.edu/cmditr/media/atr.swf</swf>

The above simulation allows you visualize what is happening during ATR measurement.

The EO material sample is pressed against the prism by the pneumatic plunger. The angle of the prism with respect to the laser is controlled with the slide bar. 0 degrees means the edge of the prism is normal to the laser beam and the sample is 45 degrees from the beam.

The photodiode produces a current when there is reflection from the sample. At certain critical angles the sample traps light due to total internal reflection and its reflectance is attenuated.

The field strength to the sample is controlled with the other slide 0-10 volts. This controls the EO effect in the sample.

Click Auto graph to record the diode current and the sample lockin voltage across a range of angles from -12 to 0 ( -2800 to 0 microsteps). Repeat this measurement at various field strengths to see the effect on the diode current.

=== Significance ===
The electro-optic coefficient for a poled polymer film can be calculated as follows<ref>J. Phys. Chem. C, 2008, 112 (21), pp 7983–7988
DOI: 10.1021/jp712154g.</ref>

:<math>r_{33} = \frac {2d\Delta R} {n^3_{TM} V_m} \frac {\delta n_{eff}} {\delta \theta} \left /( \frac {\delta R \delta n_{eff} } {\delta \theta \delta n_{TM} } \right ) \,\!</math>

where
:<math>R\,\!</math> is the DC reflected signal

:<math>V_m\,\!</math> is the AC modulation voltage

:<math>n_{eff}\,\!</math> is the ordinary index of refraction

:<math>n_{TM}\,\!</math> is the film refractive index

=== References ===
<references/>

Attenuated Total Reflectance

2010-01-18T17:35:10Z

67.183.23.184: /* Technique */

=== Overview ===
Attenuated Total Reflection or ATR is a technique used together with Teng Mann to measure the R33 of electro-optic materials. A beam of IR light is directed through a prism at an angle exceeding the critical angle for internal reflection. This produces an evanescent wave at the prism surface. If a EO polymer is pressed in intimate contact with the prism they can be coupled so that he evanescent wave stimulates emission from the sample. This emission is measured with a photodiode. An electric field applied to an EO polymer changes its index of refraction which alters the critical angle.

=== Technique ===
<div id="Flash">Attenuated Total Reflection simulation</div>

<swf width="720" height="480">http://depts.washington.edu/cmditr/media/atr.swf</swf>

The above simulation allows you visualize what is happening during ATR measurement.

The EO material sample is pressed against the prism by the pneumatic plunger. The angle of the prism with respect to the laser is controlled with the slide bar. 0 degrees means the edge of the prism is normal to the laser beam and the sample is 45 degrees from the beam.

The photodiode produces a current when there is relfection from the sample. At certain critical angles the sample traps light due to total internal reflection and its reflectance is attenuated.

The field strength to the sample is controlled with the other slide 0-10 volts. This controls the EO effect in the sample.

Click Auto graph to record the diode current and the sample lockin voltage across a range of angles from -12 to 0 ( -2800 to 0 microsteps). Repeat this measurement at various field strengths to see the effect on the diode current.

=== Significance ===
The electro-optic coefficient for a poled polymer film can be calculated as follows<ref>J. Phys. Chem. C, 2008, 112 (21), pp 7983–7988
DOI: 10.1021/jp712154g.</ref>

:<math>r_{33} = \frac {2d\Delta R} {n^3_{TM} V_m} \frac {\delta n_{eff}} {\delta \theta} \left /( \frac {\delta R \delta n_{eff} } {\delta \theta \delta n_{TM} } \right ) \,\!</math>

where
:<math>R\,\!</math> is the DC reflected signal

:<math>V_m\,\!</math> is the AC modulation voltage

:<math>n_{eff}\,\!</math> is the ordinary index of refraction

:<math>n_{TM}\,\!</math> is the film refractive index

=== References ===
<references/>

Introduction to Third-order Processes and Materials

2009-09-28T22:25:41Z

67.183.23.184: /* Hyperpolarizability */

<table id="toc" style="width: 100%">
<tr>

<td style="text-align: center; width: 33%">[[Main_Page#Third-order Processes, Materials & Characterization |Return to Third-order Processes, Materials & Characterization Menu]]</td>
<td style="text-align: right; width: 33%">[[Two Photon Absorption | Next Topic]]</td>
</tr>
</table>

Third order non linear optical (NLO) materials change their polarization based on the intensity of the applied light. This gives rise to a variety of useful properties such as self-focusing, two photon absorption, and third harmonic generation.

== Hyperpolarizability ==

Nonlinear polarization becomes more important with increasing field strength, since it scales with higher powers of the field. This relates to χ<sup>(3)</sup>, which is a materials property. χ <sup>(3)</sup> and γ can exist in all materials and all molecules, even those which are centrosymmetric materials. (χ<sup>(2)</sup> can only happen in non centrosymmetric materials).

=== Taylor Expansion for Polarization ===
Under normal conditions,

:<math>\alpha_{ij}E .> \beta_{ijk}/2 E·E > \gamma_{ijkl} /6 E·E·E.\,\!</math>

Where
:<math>j\,\!</math> is the coordinate system for the applied field

:<math>i\,\!</math> is the coordinate system for the induced polarization in the molecule

:<math>\alpha\,\!</math> is 3 x 3 tensor

:<math>\beta\,\!</math> is 3 x 3 x 3 tensor with 27 components

:<math>\gamma\,\!</math> is a 3 x 3 x 3 x 3 tensor with 81 components

Thus, there were few observations of NLO effects before the invention of the laser with its associated large electric fields.

Just as α is the linear polarizability, the higher order terms β and γ (equation (7)) are called the first and second hyperpolarizabilities respectively.

=== Taylor Expansion for Polarization ===

Or when all the fields are identical there is a Taylor expansion for bulk polarization:

:<math>P = P_0 + \chi^{(1)}·E + 1/2\chi^{(2)}·· E^2 + 1/6\chi^{(3)}···E^3+ ...\,\!</math> (9)

Some materials such as polyvinylene difluoride when polled can have a bulk polarization in the absence of an applied field.

Just as a molecule can only have a b if it is noncentrosymmetric, a material can only have a χ<sup>(2)</sup> if the material is noncentrosymmetric (i.e., a centrosymmetry arrangement of noncentrosymmetric molecules lead to zero χ<sup>(2)</sup>) .

=== Third-order Nonlinear Polarization of Matter and Third-order NLO Effects ===
[[Image:Harmonic_quartic.png|thumb|300px|Deviation from simple harmonic plot with + or - quartic terms]]

Remember that in χ<sup>(2)</sup> NLO the harmonic potential has a cubic term that makes one side of the potential somewhat more steep and other side flattened.

With χ<sup>(3)</sup> we add a restoring force that scales as a displacement to the 4th power. This is an even function. If the correction is added in a positive way the well becomes steeper, adding the correction in a negative way the potential well is more shallow. These curves shown are greatly exaggerated, in reality the deviation would be less than the thickness of the lines as they are drawn. For the most part during normal oscillations the electrons are held within a quadratic potential. Only when there is a large electric field is there deviation of the electron from their resting position to the point where these terms (terms which account for anharmonicity) are manifested in any significant way. When a restoring force of x4 is added to a molecule the polarization deviates from the harmonic potential. A greater displacement means that it is getting harder to polarize the molecule and the greater the difference between the harmonic potential and the quartic potential. A material with a greater susceptibility has a higher refractive index (and a higher dielectric constant). As you polarize this material more and more it becomes harder to polarize and its susceptibility decreases and its refractive index decreases. If when you polarize a material it becomes easier to polarize then the refractive index will decrease.

=== Non linear self focusing process ===

When a beam of light passes into a NLO material with a higher refractive index it will have an intensity distribution that is higher in the center than at the edge. The material that is in the highest intensity will have generate a high refractive index than the material at the edge where there is low intensity. The refractive index changes because the intensity of light changes the polarizability, the susceptibility, and therefore the refractive index. This is essentially a lens that focuses light closer to the interface between materials. In a focusing beam the cross-sectional area of the beam decreases as you approach the focal point and the intensity increases (because there are more photons in a unit area). If the polarizability and susceptibility is proportional to the cube of the electric field then the refractive index will increase. So as a beam becomes focused the added intensity increases the refractive index, causing even more concentrated focus, more intensity and more change in refractive index. This process is called “non linear self focusing”.

All materials (including glass and air) have third order non-linear optical effects. Sometimes these effects can lead to catastrophic self-focusing, leading to the destruction of the materials. This can cause an extremely high intensity of light that can actually damage a laser (it will blow apart). The more perfect the material the less likely you are to blow it apart. When are doing experiments involving frequency tripling researchers use perfect defect free crystals. In laser fusion crystals are used that are as big as a person.

In the case where the polarization decreases with intensity the condition is called self-defocusing. The beam passing through a material has a tendency to spread.

A molecule with a negative β or a negative χ<sup>(2)</sup> has a axis or the plane of the molecule has been flipped so that the donor and acceptors are opposite. There will still be an asymmetric polarizability in response to a static electric field. Positive and negative β lead to the same effects but with opposite signs. However positive and negative γ and positive and negative χ<sup>(3)</sup> lead to different effects. Specifically, negative χ<sup>(3)</sup> leads to self-defocusing, and positive χ<sup>(3)</sup> leads to self-focusing.

The quartic contribution to the potential has mirror symmetry with respect to the distortion coordinate; as a result both centrosymmetric and noncentrosymmetric materials will have third-order optical nonlinearities.

=== Third order polarization ===

If we reconsider equation (14) for the expansion of polarization of a molecule as a function of electric field and assume that the even-order terms are zero (i.e., that the molecule is centrosymmetric) we see that:

:<math>\mu = \mu_0+ \alpha E_0cos(\omega t) + \gamma/6E_{0}^{3}cos3(\omega t) + ...\,\!</math> (22)

If a single field, E(omega,t), is acting on the material, we know from trigonometry that:

:<math>\mu/6E_{0}^{3}cos3(\omega t) = \gamma/6E_{0}^{3}[(3/4)cos(\omega t) + (1/4)cos(3\omega t)]\,\!</math> (23)

These leads to process of frequency tripling in that you can shine light on the molecule and get light at the third harmonic.

thus,

:<math>\mu = \mu_0+ \alpha E_0 cos(omega t) + \gamma /6 E03(3/4)cos(\omega t) + \gamma /6 E03(1/4)cos(3\omega t)\,\!</math> (24)
or:

:<math>\mu= \mu_0+ [\alpha + \gamma /6 E_{0}^{2}(3/4)]E_0cos(\omega t) + \gamma /6 E03(1/4)cos(3\omega t)\,\!</math> (25)

This is an effective polarizability that is related to E<sub>0</sub><sup>2</sup> (the maximum deviation of the sinusoidal electric field) and γ. E<sub>0</sub><sup>2</sup> is always positive. γ can be either positive or negative. Thus by increasing the magnitude of the electric field (light) shining on the materials (with a positive γ) increase the polarizability as the square of the field or decrease the polarizability ( if the γ is negative). So due to the third order effect the linear polarizability can be changed simply by modifying the intensity of the applied light.

=== Third Harmonic Generation and the Optical Kerr Effect ===

Thus, the interaction of light with third-order NLO molecules will create a polarization component at its third harmonic.

In addition, there is a component at the fundamental, and we note that the :<math>[\alpha + \gamma /6 E_{0}^{2}(3/4)]\,\!</math> term of equation (25) is similar to the term leading to the linear electrooptic effect or the pockels effect.

Likewise the induced polarization for a bulk material, would lead to third harmonic generation through chi(3), the material susceptibility analogous to γ.

There are two kinds of Kerr effects. In an optical frequency Kerr effect a very high intensity beam is applied that changes the refractive index of a material.

The quadratic electro-optic effect involves a low intensity beam combined with an applied voltage that can modulate the refractive index.

== Four Wave Mixing ==

Third harmonic generation is a four wave mixing process. Three waves (electric 1, 2 and 3) interact in material to create a fourth wave. In the case of third harmonic generation with single beam of light the three fields are degenerate; electric field 1 has the same frequency, phase and momentum (k-vect) as electric field 2 and three.

This does not have to be case. There could be three beams with different phases at arbitrary directions, polarizations and frequency components that can all mix and give sums and differences of frequency leading to all kinds of output light.

:<math>\omega 1 + \omega 2 + \omega 3\,\!</math> : this is third harmonic generation

or

:<math>\omega 1 + \omega 2 - \omega 3\,\!</math> : this gives light out at the same frequency (degenerate four wave mixing) as the input leading to the self-focusing effect.

Another interesting manifestation of third-order NLO effect is degenerate four wave mixing in which two beams of light interacting within a material create an interference pattern that will lead to a spatially periodic variation in light intensity across the material. As we have noted before the induced change in refractive index of a third-order nonlinear optical material is proportional to the intensity of the applied field. Thus, if two beams are interacting with a third-order NLO material, the result will be a refractive index grating because of constructive and destructive interference. The diffraction pattern creates areas of high and low light intensity on an NLO material. The areas that are brightest will have an increased refractive index (with a positive χ<sup>(3)</sup>). At the darkest point the refractive index will have zero change. So if the intensity is changing periodically then the refractive index will have a periodic variation as well. When a third beam is incident on this grating a fourth beam, called the phase conjugate, is diffracted from the grating. This process is called four wave mixing: two writing beams and a probe beam result in a fourth phase conjugate beam.

=== Degenerate Four-wave Mixing ===
[[Image:4wavemixing.png|thumb|200px|Phase Congugate Optics]]
A potential use of Degenerate Four-wave Mixing (DFWM) is in phase conjugate optics.

If two beams are directed on a material they create a diffractive index grating. A beam of light has a momentum determined by the direction it is traveling. If the beams of light mix and do not transfer energy to the material the momentum must be conserved. Two counter propagating beams (with the same phase) have a momentum sum of zero.

Phase conjugate optics takes advantage of a special feature of the diffracted beam: its path exactly retraces the path of one of the writing beams.

*As a result, a pair of diverging beams impinging on a phase conjugate mirror will converge after "reflection".

*In contrast, a pair of diverging beams reflected from an ordinary mirror will continue to diverge.

Thus, distorted optical wavefronts can be reconstructed using phase conjugate optical systems.

=== Phase Conjugation ===

Thus, distorted optical wavefronts can be reconstructed using phase conjugate optical systems.

A diverging set of beams reflected off of a normal mirror continues to diverge. (left)
A diverging set of beams reflected off of a phase conjugate mirror exactly retrace their original path and are recombined at their point of origin. (right)

=== Phase Conjugate Mirror ===
[[Image:Phaseconjugate_mirror.png|thumb|300px|Reflection from phase conjugate retraces exactly same path and alterations as incoming wave.]]
A planar wave (a) passes through a distorting material (b) that introduces an aberration and the light interacts with a phase conjugate mirror (c) creating the phase conjugate wavefront. (d)
Phase conjugate wave passes through the distorting material on the reverse path canceling the original aberation thus producing an undistorted wavefront.

A wavefront made up a lot of beams is travelling in direction a through a medium. Some aberration (with lower refractive index) in the material allows a portion of the light to go faster causing a bump in the wavefront. When the wavefront hits the phase conjugate mirror all parts are reversed. The part of the beam that comes into the mirror first ends up leaving last; there is a time reversal. When the reversed beam travel back and encounters the original aberration the distortion is removed.

There are applications for this when looking at distant objects that have passed through a material that is scattering. If you bounce the light off a phase conjugate in two passes and you can get back the original undistorted image. This is useful for targeting applications and for looking at images on the Earth from a satellite where there are distortions due to inhomogeneities the atmosphere. This is a third order non linear optical effect.

See wikipedia http://en.wikipedia.org/wiki/Nonlinear_optics#Optical_phase_conjugation

== Second Hyper-polarizability and BOA ==
[[Image:Secondpolarizability_boa.png|thumb|500px|Contributions to γ from various terms]]
The curve in red shows γ as a function of BOA as it goes from a polyene limit, through cyanine-like limit, up to a zwitterionic polyene limit. γ is calculated using perturbation theory. It starts positive, goes up, goes through zero and has negative peak at the cyanine-like limit and then comes back up and is positive.

The simplified perturbation expression for γ that involves three expressions, dubbed '''n''' (negative), '''tp''' (two photon) and '''d''' (dipolar because it only comes into effect when there is a change in dipole between the ground and the excited state.)

:<math>\gamma \propto - \left ( \frac {\mu^{4}_{ge}} {E^{3}_{ge}} \right) + \sum_{e^\prime} \left( \frac {\mu^{2}_{ge} \mu^{2}_{ee^\prime}} {E^{2}_{ge} E_{ge^\prime}} \right ) + \left ( \frac {\mu^{2}_{ge} (\mu_{ee} - \mu_{gg})^{2}} {E^{3}_{ge}} \right )\,\!</math>

N the transition dipole moment between the ground and the initial site (coming in at the 4th power) divided by the energy gap between those two states.

Ge is the transition dipole moment between and the excited state squared, and between the excited state and a higher lying excited state squared.

Two energy terms goes between the ground and the excited state squared and the other between the ground and the higher excited state.

The final term should look a lot like β. The difference in dipole moment is squared so that it always positive, the energy term is cubed. It starts at the zero, increases to maximum and then return to zero.

The calculation gives γ using this model which is plotted as open blue circle. These look a lot like the red dots.

Each term contributes to the resulting curve for γ.

=== Third-order Nonlinear Optical Properties of Polarized Polyenes ===
[[Image:Betacarotene_NLO.png|thumb|400px|Effect on γ when various acceptors are added to beta-carotene]]
Beta carotene is the pigment found in margarine. By adding stronger and stronger acceptors it be polarized. Lambda max increases by a factor of 45.

The real part of the refractive index is related to how light is diffracted, the imaginary part is related to absorption of light.

The same is true about γ. The real part refers to how the refractive index is changed as light of a given intensity goes through it. The imaginary part is related to two photon absorption. Molecules will have both real and imaginary parts.
In order to make useful devices like the Mach Zehnder interferometer you want the index of refraction to change but don’t want to lose light in the material. ELO materials can lose transparency due to absorption or scattering. They can also lose transparency at a high intensity is due to the process of two photon absorption. Dipolar molecules tend to have large positive γ but also tend to have high two photon absorption cross sections.

Recently we have discovered that molecules with negative γ that have verge large real parts that lead to interesting optical effects and that in certain spectral regions their imaginary part is almost zero so there is no light lost due to two photon absorption. These are good candidates for all optical switching applications because until now molecules with high χ(3) have had a high a loss due to two photon absorption.

<table id="toc" style="width: 100%">
<tr>

<td style="text-align: center; width: 33%">[[Main_Page#Third-order Processes, Materials & Characterization |Return to Third-order Processes, Materials & Characterization Menu]]</td>
<td style="text-align: right; width: 33%">[[Two Photon Absorption | Next Topic]]</td>
</tr>
</table>

External Education Links

2009-07-20T22:15:47Z

67.183.23.184: /* Hands On Demos and Activity Ideas */

==Photonics Topics==
These external links may be useful for your research

=== Optoelectronics ===

[http://www.succeed.ufl.edu/content/optical/ Optoelectronics module UNC]

[http://plc.case.edu/tutorial/enhanced/main.htm Liquid Crystals at CWRU]

=== Organic Light Emitting Diodes ===

[http://mrsec.wisc.edu/Edetc/nanolab/oLED/index.html Building a simple OLED]

[http://mrsec.wisc.edu/Edetc/nanolab/index.html Nanotechnology and Photonics Lab videos]

[http://www.google.com/url?sa=t&source=web&ct=res&cd=11&url=http%3A%2F%2Fwww.rsc.org%2Fimages%2FRSCelectro_tcm18-87773.pdf&ei=Pss_SqmnMJLIsQOb_63yCg&usg=AFQjCNHYreUEQKtkqQ20uV-euD3wRBbYdA&sig2=b_UxdYbTo5MT-rxTaMqA0A Royal Society of Chemistry OLED lesson plan]

=== Photovoltaics ===

[http://www1.eere.energy.gov/solar/pv_important.html National Renewable Energy Laborartory]

===Engineering===
[http://www.engineeringpathway.com/ep/ Engineering Pathway]

===Nanotechnology===
[http://www.nclt.us/ National Center for Learning and Teaching in Nanoscale Science and Engineering]

[https://nanohub.org/home Nanotechnology education hub]

==Reference Sources==

[http://www.cope.gatech.edu/ COPE: Center for Organic Photonics & Electronics at Georgia Tech]

[http://www.isiwebofknowledge.com/index.html ISI Science Citation Index]

[http://msds.ehs.cornell.edu/msdssrch.asp Material Safety Data Sheets Search from Cornell University]

[http://webbook.nist.gov/chemistry/ NIST Chemistry Webbook]

[http://physics.nist.gov/cuu/index.html NIST Physics Database]

[http://www.colby.edu/chemistry/cmp/cmp.html Organic Compounds Database]

[http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng Spectral Database System for Organic Compounds]

[http://www.bioscience.org/atlases/jourabbr/list.htm Abbreviations for Journal Names]

[http://www.chem.wisc.edu/areas/organic/index-chem.htm Useful Compilation of Information About Organic Chemistry]

[http://www.unl.edu/CMRAcfem/em.htm Electron Microscopy Overview]

[http://www.ux1.eiu.edu/%7Ecfthb/research/handbook/TLCstains.htm TLC Staining]

[http://www.chem.uky.edu/research/grossman/text/ans1sted/ Answer Keys for Problems from Grossman's Book]

[http://www.chem.ucalgary.ca/shmo/ Simple Program for Huckel MOs, easy to use!]

[http://www.chem.wisc.edu/areas/reich/handouts/NameReagents/namedreag-cont.htm A Broad List of Named Reagents that you may come across]

[http://www.chem.qmul.ac.uk/iupac/gtpoc/ IUPAC Glossary of Physical Organic Chemistry]

==K-12 Educational Resources==
[http://www.physicsclassroom.com/ The Physics Classroom - Tutorials, demonstrations and manipulatives]

[http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ Flash Animations for Physics]

[http://www.micro.magnet.fsu.edu/optics/index.html Molecular Expressions- Science Optics and You]

[http://www.teachersdomain.org/ Teacher domain- K12 resource with lots of media]

[http://www.curriki.org Curriki- K-12 Lessons]

[http://undsci.berkeley.edu/index.php How Science Works - UC Berkeley program gives an excellent overview of scientific process(es)]

[http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html#hph Hyperphysics Georgia State University- concept maps and explanations]

[http://www.pathwaystoscience.org/ Pathyways to Science]

=== Hands On Demos and Activity Ideas ===
Note: this is a brainstorming area that GPAC can use to help collaborate on the science demo kits.

[http://projectsol.aps.com/inside/inside_pv.asp APS Project Sol- Animation explains silicon solar solar cells]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.informalscience.org/research/resources Informal Science Education - Good resource to see what museums are doing with outreach activities.]

[http://www.astc.org/ Association of Science and Technology Centers- Main clearinghouse for museum exhibit and demo technologies.]

== E-learning ==
===General Info===
[http://www.nsf.gov/pubs/2008/nsf08204/nsf08204.pdf Fostering E-learning in the Networked World- NSF]

[http://www.ecornell.com/about/approach/whitepaperV2_1.pdf Cornell Learning Molecule Concept]

[http://creativecommons.org/about/licenses/ Creative Commons Content Licenses]

[http://commons.carnegiefoundation.org/ The Carnegie Commons - Technology, teaching and learning]

===Digital Libraries===
[http://www.nsdl.org National Science Digital Library - NSDL]

[http://amser.org/ Applied Math and Science Education Respository]

[http://www.chemeddl.org/ Chemical Education Digital Library]

[http://www.merlot.org/merlot/index.htm MERLOT Multimedia Educational Resource for Learning and Online Teaching]

[http://www.chemcollective.org/ The Chem Collective- Online resources for Teaching and Learning Chemistry]

[http://www.smete.org/smete/ SMETE Digital Library Science Mathematics Engineering and Technology Education ]

===Other Wikis===
[http://thzpolymers.pbwiki.com/ Special wiki from the Thz group at UMBC]

[http://en.wikipedia.org/wiki/Main_Page Wikipedia]

[http://en.wikibooks.org/wiki/Wikibooks:Community_Portal Wikibooks]

[http://commons.wikimedia.org Wikimedia]

[http://en.wikiversity.org/wiki/Wikiversity:Main_Page Wikiversity]

===Open Courseware===
[http://ocw.mit.edu/OcwWeb/web/home/home/index.htm MIT Open Courseware]

[http://www.oercommons.org/ Open Educational Commons]

[http://www.cmu.edu/oli/index.shtml Open Learning Initiative]

==Tools==

[http://exelearning.org/ eXe xhtml authoring software for building modules with SCORM output.]

[http://jmol.sourceforge.net/ JMOL molecular 3D manipulation tool and plugin]

[http://www.openscience.org/links/ Open Science Project - software tools for scientists]

[http://www.chemspider.com/Search.aspx Chem Spider Chemical Structures Database]

[http://moodle.org Moodle Course Management System]

[http://www.sakaiproject.org/portal Sakai Collaboration tools for Higher Ed]

[http://freemind.sourceforge.net/wiki/index.php/Main_Page Freemind Concept Mapping Software]

[http://www.wordle.net/ Wordle- create snazzy graphics from vocabulary, or text]

External Education Links

2009-07-20T22:14:09Z

67.183.23.184: /* Hands On Demos and Activity Ideas */

==Photonics Topics==
These external links may be useful for your research

=== Optoelectronics ===

[http://www.succeed.ufl.edu/content/optical/ Optoelectronics module UNC]

[http://plc.case.edu/tutorial/enhanced/main.htm Liquid Crystals at CWRU]

=== Organic Light Emitting Diodes ===

[http://mrsec.wisc.edu/Edetc/nanolab/oLED/index.html Building a simple OLED]

[http://mrsec.wisc.edu/Edetc/nanolab/index.html Nanotechnology and Photonics Lab videos]

[http://www.google.com/url?sa=t&source=web&ct=res&cd=11&url=http%3A%2F%2Fwww.rsc.org%2Fimages%2FRSCelectro_tcm18-87773.pdf&ei=Pss_SqmnMJLIsQOb_63yCg&usg=AFQjCNHYreUEQKtkqQ20uV-euD3wRBbYdA&sig2=b_UxdYbTo5MT-rxTaMqA0A Royal Society of Chemistry OLED lesson plan]

=== Photovoltaics ===

[http://www1.eere.energy.gov/solar/pv_important.html National Renewable Energy Laborartory]

===Engineering===
[http://www.engineeringpathway.com/ep/ Engineering Pathway]

===Nanotechnology===
[http://www.nclt.us/ National Center for Learning and Teaching in Nanoscale Science and Engineering]

[https://nanohub.org/home Nanotechnology education hub]

==Reference Sources==

[http://www.cope.gatech.edu/ COPE: Center for Organic Photonics & Electronics at Georgia Tech]

[http://www.isiwebofknowledge.com/index.html ISI Science Citation Index]

[http://msds.ehs.cornell.edu/msdssrch.asp Material Safety Data Sheets Search from Cornell University]

[http://webbook.nist.gov/chemistry/ NIST Chemistry Webbook]

[http://physics.nist.gov/cuu/index.html NIST Physics Database]

[http://www.colby.edu/chemistry/cmp/cmp.html Organic Compounds Database]

[http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng Spectral Database System for Organic Compounds]

[http://www.bioscience.org/atlases/jourabbr/list.htm Abbreviations for Journal Names]

[http://www.chem.wisc.edu/areas/organic/index-chem.htm Useful Compilation of Information About Organic Chemistry]

[http://www.unl.edu/CMRAcfem/em.htm Electron Microscopy Overview]

[http://www.ux1.eiu.edu/%7Ecfthb/research/handbook/TLCstains.htm TLC Staining]

[http://www.chem.uky.edu/research/grossman/text/ans1sted/ Answer Keys for Problems from Grossman's Book]

[http://www.chem.ucalgary.ca/shmo/ Simple Program for Huckel MOs, easy to use!]

[http://www.chem.wisc.edu/areas/reich/handouts/NameReagents/namedreag-cont.htm A Broad List of Named Reagents that you may come across]

[http://www.chem.qmul.ac.uk/iupac/gtpoc/ IUPAC Glossary of Physical Organic Chemistry]

==K-12 Educational Resources==
[http://www.physicsclassroom.com/ The Physics Classroom - Tutorials, demonstrations and manipulatives]

[http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ Flash Animations for Physics]

[http://www.micro.magnet.fsu.edu/optics/index.html Molecular Expressions- Science Optics and You]

[http://www.teachersdomain.org/ Teacher domain- K12 resource with lots of media]

[http://www.curriki.org Curriki- K-12 Lessons]

[http://undsci.berkeley.edu/index.php How Science Works - UC Berkeley program gives an excellent overview of scientific process(es)]

[http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html#hph Hyperphysics Georgia State University- concept maps and explanations]

[http://www.pathwaystoscience.org/ Pathyways to Science]

=== Hands On Demos and Activity Ideas ===

[http://projectsol.aps.com/inside/inside_pv.asp APS Project Sol- Animation explains silicon solar solar cells]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.exploratorium.edu/snacks/index.html Exploratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

[http://www.informalscience.org/research/resources Informal Science Education - Good resource to see what museums are doing with outreach activities.]

[http://www.astc.org/ Association of Science and Technology Centers- Main clearinghouse for museum exhibit and demo technologies.]

== E-learning ==
===General Info===
[http://www.nsf.gov/pubs/2008/nsf08204/nsf08204.pdf Fostering E-learning in the Networked World- NSF]

[http://www.ecornell.com/about/approach/whitepaperV2_1.pdf Cornell Learning Molecule Concept]

[http://creativecommons.org/about/licenses/ Creative Commons Content Licenses]

[http://commons.carnegiefoundation.org/ The Carnegie Commons - Technology, teaching and learning]

===Digital Libraries===
[http://www.nsdl.org National Science Digital Library - NSDL]

[http://amser.org/ Applied Math and Science Education Respository]

[http://www.chemeddl.org/ Chemical Education Digital Library]

[http://www.merlot.org/merlot/index.htm MERLOT Multimedia Educational Resource for Learning and Online Teaching]

[http://www.chemcollective.org/ The Chem Collective- Online resources for Teaching and Learning Chemistry]

[http://www.smete.org/smete/ SMETE Digital Library Science Mathematics Engineering and Technology Education ]

===Other Wikis===
[http://thzpolymers.pbwiki.com/ Special wiki from the Thz group at UMBC]

[http://en.wikipedia.org/wiki/Main_Page Wikipedia]

[http://en.wikibooks.org/wiki/Wikibooks:Community_Portal Wikibooks]

[http://commons.wikimedia.org Wikimedia]

[http://en.wikiversity.org/wiki/Wikiversity:Main_Page Wikiversity]

===Open Courseware===
[http://ocw.mit.edu/OcwWeb/web/home/home/index.htm MIT Open Courseware]

[http://www.oercommons.org/ Open Educational Commons]

[http://www.cmu.edu/oli/index.shtml Open Learning Initiative]

==Tools==

[http://exelearning.org/ eXe xhtml authoring software for building modules with SCORM output.]

[http://jmol.sourceforge.net/ JMOL molecular 3D manipulation tool and plugin]

[http://www.openscience.org/links/ Open Science Project - software tools for scientists]

[http://www.chemspider.com/Search.aspx Chem Spider Chemical Structures Database]

[http://moodle.org Moodle Course Management System]

[http://www.sakaiproject.org/portal Sakai Collaboration tools for Higher Ed]

[http://freemind.sourceforge.net/wiki/index.php/Main_Page Freemind Concept Mapping Software]

[http://www.wordle.net/ Wordle- create snazzy graphics from vocabulary, or text]

External Education Links

2009-07-20T22:13:41Z

67.183.23.184: /* Hands On Demos and Activity Ideas */

==Photonics Topics==
These external links may be useful for your research

=== Optoelectronics ===

[http://www.succeed.ufl.edu/content/optical/ Optoelectronics module UNC]

[http://plc.case.edu/tutorial/enhanced/main.htm Liquid Crystals at CWRU]

=== Organic Light Emitting Diodes ===

[http://mrsec.wisc.edu/Edetc/nanolab/oLED/index.html Building a simple OLED]

[http://mrsec.wisc.edu/Edetc/nanolab/index.html Nanotechnology and Photonics Lab videos]

[http://www.google.com/url?sa=t&source=web&ct=res&cd=11&url=http%3A%2F%2Fwww.rsc.org%2Fimages%2FRSCelectro_tcm18-87773.pdf&ei=Pss_SqmnMJLIsQOb_63yCg&usg=AFQjCNHYreUEQKtkqQ20uV-euD3wRBbYdA&sig2=b_UxdYbTo5MT-rxTaMqA0A Royal Society of Chemistry OLED lesson plan]

=== Photovoltaics ===

[http://www1.eere.energy.gov/solar/pv_important.html National Renewable Energy Laborartory]

===Engineering===
[http://www.engineeringpathway.com/ep/ Engineering Pathway]

===Nanotechnology===
[http://www.nclt.us/ National Center for Learning and Teaching in Nanoscale Science and Engineering]

[https://nanohub.org/home Nanotechnology education hub]

==Reference Sources==

[http://www.cope.gatech.edu/ COPE: Center for Organic Photonics & Electronics at Georgia Tech]

[http://www.isiwebofknowledge.com/index.html ISI Science Citation Index]

[http://msds.ehs.cornell.edu/msdssrch.asp Material Safety Data Sheets Search from Cornell University]

[http://webbook.nist.gov/chemistry/ NIST Chemistry Webbook]

[http://physics.nist.gov/cuu/index.html NIST Physics Database]

[http://www.colby.edu/chemistry/cmp/cmp.html Organic Compounds Database]

[http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng Spectral Database System for Organic Compounds]

[http://www.bioscience.org/atlases/jourabbr/list.htm Abbreviations for Journal Names]

[http://www.chem.wisc.edu/areas/organic/index-chem.htm Useful Compilation of Information About Organic Chemistry]

[http://www.unl.edu/CMRAcfem/em.htm Electron Microscopy Overview]

[http://www.ux1.eiu.edu/%7Ecfthb/research/handbook/TLCstains.htm TLC Staining]

[http://www.chem.uky.edu/research/grossman/text/ans1sted/ Answer Keys for Problems from Grossman's Book]

[http://www.chem.ucalgary.ca/shmo/ Simple Program for Huckel MOs, easy to use!]

[http://www.chem.wisc.edu/areas/reich/handouts/NameReagents/namedreag-cont.htm A Broad List of Named Reagents that you may come across]

[http://www.chem.qmul.ac.uk/iupac/gtpoc/ IUPAC Glossary of Physical Organic Chemistry]

==K-12 Educational Resources==
[http://www.physicsclassroom.com/ The Physics Classroom - Tutorials, demonstrations and manipulatives]

[http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ Flash Animations for Physics]

[http://www.micro.magnet.fsu.edu/optics/index.html Molecular Expressions- Science Optics and You]

[http://www.teachersdomain.org/ Teacher domain- K12 resource with lots of media]

[http://www.curriki.org Curriki- K-12 Lessons]

[http://undsci.berkeley.edu/index.php How Science Works - UC Berkeley program gives an excellent overview of scientific process(es)]

[http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html#hph Hyperphysics Georgia State University- concept maps and explanations]

[http://www.pathwaystoscience.org/ Pathyways to Science]

=== Hands On Demos and Activity Ideas ===

[http://projectsol.aps.com/inside/inside_pv.asp APS Project Sol- Animation explains silicon solar solar cells]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.informalscience.org/research/resources Informal Science Education - Good resource to see what museums are doing with outreach activities.]

[http://www.astc.org/ Association of Science and Technology Centers- Main clearinghouse for museum exhibit and demo technologies.]

[http://www.exploratorium.edu/snacks/index.html Exloratorium - Snacks are simple demo ideas - this is the premier organization for hands-on demos and learning]

== E-learning ==
===General Info===
[http://www.nsf.gov/pubs/2008/nsf08204/nsf08204.pdf Fostering E-learning in the Networked World- NSF]

[http://www.ecornell.com/about/approach/whitepaperV2_1.pdf Cornell Learning Molecule Concept]

[http://creativecommons.org/about/licenses/ Creative Commons Content Licenses]

[http://commons.carnegiefoundation.org/ The Carnegie Commons - Technology, teaching and learning]

===Digital Libraries===
[http://www.nsdl.org National Science Digital Library - NSDL]

[http://amser.org/ Applied Math and Science Education Respository]

[http://www.chemeddl.org/ Chemical Education Digital Library]

[http://www.merlot.org/merlot/index.htm MERLOT Multimedia Educational Resource for Learning and Online Teaching]

[http://www.chemcollective.org/ The Chem Collective- Online resources for Teaching and Learning Chemistry]

[http://www.smete.org/smete/ SMETE Digital Library Science Mathematics Engineering and Technology Education ]

===Other Wikis===
[http://thzpolymers.pbwiki.com/ Special wiki from the Thz group at UMBC]

[http://en.wikipedia.org/wiki/Main_Page Wikipedia]

[http://en.wikibooks.org/wiki/Wikibooks:Community_Portal Wikibooks]

[http://commons.wikimedia.org Wikimedia]

[http://en.wikiversity.org/wiki/Wikiversity:Main_Page Wikiversity]

===Open Courseware===
[http://ocw.mit.edu/OcwWeb/web/home/home/index.htm MIT Open Courseware]

[http://www.oercommons.org/ Open Educational Commons]

[http://www.cmu.edu/oli/index.shtml Open Learning Initiative]

==Tools==

[http://exelearning.org/ eXe xhtml authoring software for building modules with SCORM output.]

[http://jmol.sourceforge.net/ JMOL molecular 3D manipulation tool and plugin]

[http://www.openscience.org/links/ Open Science Project - software tools for scientists]

[http://www.chemspider.com/Search.aspx Chem Spider Chemical Structures Database]

[http://moodle.org Moodle Course Management System]

[http://www.sakaiproject.org/portal Sakai Collaboration tools for Higher Ed]

[http://freemind.sourceforge.net/wiki/index.php/Main_Page Freemind Concept Mapping Software]

[http://www.wordle.net/ Wordle- create snazzy graphics from vocabulary, or text]

External Education Links

2009-07-20T22:09:27Z

67.183.23.184: /* Hands On Demos and Activity Ideas */

==Photonics Topics==
These external links may be useful for your research

=== Optoelectronics ===

[http://www.succeed.ufl.edu/content/optical/ Optoelectronics module UNC]

[http://plc.case.edu/tutorial/enhanced/main.htm Liquid Crystals at CWRU]

=== Organic Light Emitting Diodes ===

[http://mrsec.wisc.edu/Edetc/nanolab/oLED/index.html Building a simple OLED]

[http://mrsec.wisc.edu/Edetc/nanolab/index.html Nanotechnology and Photonics Lab videos]

[http://www.google.com/url?sa=t&source=web&ct=res&cd=11&url=http%3A%2F%2Fwww.rsc.org%2Fimages%2FRSCelectro_tcm18-87773.pdf&ei=Pss_SqmnMJLIsQOb_63yCg&usg=AFQjCNHYreUEQKtkqQ20uV-euD3wRBbYdA&sig2=b_UxdYbTo5MT-rxTaMqA0A Royal Society of Chemistry OLED lesson plan]

=== Photovoltaics ===

[http://www1.eere.energy.gov/solar/pv_important.html National Renewable Energy Laborartory]

===Engineering===
[http://www.engineeringpathway.com/ep/ Engineering Pathway]

===Nanotechnology===
[http://www.nclt.us/ National Center for Learning and Teaching in Nanoscale Science and Engineering]

[https://nanohub.org/home Nanotechnology education hub]

==Reference Sources==

[http://www.cope.gatech.edu/ COPE: Center for Organic Photonics & Electronics at Georgia Tech]

[http://www.isiwebofknowledge.com/index.html ISI Science Citation Index]

[http://msds.ehs.cornell.edu/msdssrch.asp Material Safety Data Sheets Search from Cornell University]

[http://webbook.nist.gov/chemistry/ NIST Chemistry Webbook]

[http://physics.nist.gov/cuu/index.html NIST Physics Database]

[http://www.colby.edu/chemistry/cmp/cmp.html Organic Compounds Database]

[http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng Spectral Database System for Organic Compounds]

[http://www.bioscience.org/atlases/jourabbr/list.htm Abbreviations for Journal Names]

[http://www.chem.wisc.edu/areas/organic/index-chem.htm Useful Compilation of Information About Organic Chemistry]

[http://www.unl.edu/CMRAcfem/em.htm Electron Microscopy Overview]

[http://www.ux1.eiu.edu/%7Ecfthb/research/handbook/TLCstains.htm TLC Staining]

[http://www.chem.uky.edu/research/grossman/text/ans1sted/ Answer Keys for Problems from Grossman's Book]

[http://www.chem.ucalgary.ca/shmo/ Simple Program for Huckel MOs, easy to use!]

[http://www.chem.wisc.edu/areas/reich/handouts/NameReagents/namedreag-cont.htm A Broad List of Named Reagents that you may come across]

[http://www.chem.qmul.ac.uk/iupac/gtpoc/ IUPAC Glossary of Physical Organic Chemistry]

==K-12 Educational Resources==
[http://www.physicsclassroom.com/ The Physics Classroom - Tutorials, demonstrations and manipulatives]

[http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ Flash Animations for Physics]

[http://www.micro.magnet.fsu.edu/optics/index.html Molecular Expressions- Science Optics and You]

[http://www.teachersdomain.org/ Teacher domain- K12 resource with lots of media]

[http://www.curriki.org Curriki- K-12 Lessons]

[http://undsci.berkeley.edu/index.php How Science Works - UC Berkeley program gives an excellent overview of scientific process(es)]

[http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html#hph Hyperphysics Georgia State University- concept maps and explanations]

[http://www.pathwaystoscience.org/ Pathyways to Science]

=== Hands On Demos and Activity Ideas ===

[http://projectsol.aps.com/inside/inside_pv.asp APS Project Sol- Animation explains silicon solar solar cells]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.informalscience.org/research/resources Informal Science Education - Good resource to see what museums are doing with outreach activities.]

[http://www.astc.org/ Association of Science and Technology Centers- Main clearinghouse for museum exhibit and demo technologies.]

== E-learning ==
===General Info===
[http://www.nsf.gov/pubs/2008/nsf08204/nsf08204.pdf Fostering E-learning in the Networked World- NSF]

[http://www.ecornell.com/about/approach/whitepaperV2_1.pdf Cornell Learning Molecule Concept]

[http://creativecommons.org/about/licenses/ Creative Commons Content Licenses]

[http://commons.carnegiefoundation.org/ The Carnegie Commons - Technology, teaching and learning]

===Digital Libraries===
[http://www.nsdl.org National Science Digital Library - NSDL]

[http://amser.org/ Applied Math and Science Education Respository]

[http://www.chemeddl.org/ Chemical Education Digital Library]

[http://www.merlot.org/merlot/index.htm MERLOT Multimedia Educational Resource for Learning and Online Teaching]

[http://www.chemcollective.org/ The Chem Collective- Online resources for Teaching and Learning Chemistry]

[http://www.smete.org/smete/ SMETE Digital Library Science Mathematics Engineering and Technology Education ]

===Other Wikis===
[http://thzpolymers.pbwiki.com/ Special wiki from the Thz group at UMBC]

[http://en.wikipedia.org/wiki/Main_Page Wikipedia]

[http://en.wikibooks.org/wiki/Wikibooks:Community_Portal Wikibooks]

[http://commons.wikimedia.org Wikimedia]

[http://en.wikiversity.org/wiki/Wikiversity:Main_Page Wikiversity]

===Open Courseware===
[http://ocw.mit.edu/OcwWeb/web/home/home/index.htm MIT Open Courseware]

[http://www.oercommons.org/ Open Educational Commons]

[http://www.cmu.edu/oli/index.shtml Open Learning Initiative]

==Tools==

[http://exelearning.org/ eXe xhtml authoring software for building modules with SCORM output.]

[http://jmol.sourceforge.net/ JMOL molecular 3D manipulation tool and plugin]

[http://www.openscience.org/links/ Open Science Project - software tools for scientists]

[http://www.chemspider.com/Search.aspx Chem Spider Chemical Structures Database]

[http://moodle.org Moodle Course Management System]

[http://www.sakaiproject.org/portal Sakai Collaboration tools for Higher Ed]

[http://freemind.sourceforge.net/wiki/index.php/Main_Page Freemind Concept Mapping Software]

[http://www.wordle.net/ Wordle- create snazzy graphics from vocabulary, or text]

External Education Links

2009-07-20T22:05:27Z

67.183.23.184: /* Hands On Demos and Activity Ideas */

==Photonics Topics==
These external links may be useful for your research

=== Optoelectronics ===

[http://www.succeed.ufl.edu/content/optical/ Optoelectronics module UNC]

[http://plc.case.edu/tutorial/enhanced/main.htm Liquid Crystals at CWRU]

=== Organic Light Emitting Diodes ===

[http://mrsec.wisc.edu/Edetc/nanolab/oLED/index.html Building a simple OLED]

[http://mrsec.wisc.edu/Edetc/nanolab/index.html Nanotechnology and Photonics Lab videos]

[http://www.google.com/url?sa=t&source=web&ct=res&cd=11&url=http%3A%2F%2Fwww.rsc.org%2Fimages%2FRSCelectro_tcm18-87773.pdf&ei=Pss_SqmnMJLIsQOb_63yCg&usg=AFQjCNHYreUEQKtkqQ20uV-euD3wRBbYdA&sig2=b_UxdYbTo5MT-rxTaMqA0A Royal Society of Chemistry OLED lesson plan]

=== Photovoltaics ===

[http://www1.eere.energy.gov/solar/pv_important.html National Renewable Energy Laborartory]

===Engineering===
[http://www.engineeringpathway.com/ep/ Engineering Pathway]

===Nanotechnology===
[http://www.nclt.us/ National Center for Learning and Teaching in Nanoscale Science and Engineering]

[https://nanohub.org/home Nanotechnology education hub]

==Reference Sources==

[http://www.cope.gatech.edu/ COPE: Center for Organic Photonics & Electronics at Georgia Tech]

[http://www.isiwebofknowledge.com/index.html ISI Science Citation Index]

[http://msds.ehs.cornell.edu/msdssrch.asp Material Safety Data Sheets Search from Cornell University]

[http://webbook.nist.gov/chemistry/ NIST Chemistry Webbook]

[http://physics.nist.gov/cuu/index.html NIST Physics Database]

[http://www.colby.edu/chemistry/cmp/cmp.html Organic Compounds Database]

[http://riodb01.ibase.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng Spectral Database System for Organic Compounds]

[http://www.bioscience.org/atlases/jourabbr/list.htm Abbreviations for Journal Names]

[http://www.chem.wisc.edu/areas/organic/index-chem.htm Useful Compilation of Information About Organic Chemistry]

[http://www.unl.edu/CMRAcfem/em.htm Electron Microscopy Overview]

[http://www.ux1.eiu.edu/%7Ecfthb/research/handbook/TLCstains.htm TLC Staining]

[http://www.chem.uky.edu/research/grossman/text/ans1sted/ Answer Keys for Problems from Grossman's Book]

[http://www.chem.ucalgary.ca/shmo/ Simple Program for Huckel MOs, easy to use!]

[http://www.chem.wisc.edu/areas/reich/handouts/NameReagents/namedreag-cont.htm A Broad List of Named Reagents that you may come across]

[http://www.chem.qmul.ac.uk/iupac/gtpoc/ IUPAC Glossary of Physical Organic Chemistry]

==K-12 Educational Resources==
[http://www.physicsclassroom.com/ The Physics Classroom - Tutorials, demonstrations and manipulatives]

[http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ Flash Animations for Physics]

[http://www.micro.magnet.fsu.edu/optics/index.html Molecular Expressions- Science Optics and You]

[http://www.teachersdomain.org/ Teacher domain- K12 resource with lots of media]

[http://www.curriki.org Curriki- K-12 Lessons]

[http://undsci.berkeley.edu/index.php How Science Works - UC Berkeley program gives an excellent overview of scientific process(es)]

[http://hyperphysics.phy-astr.gsu.edu/Hbase/hph.html#hph Hyperphysics Georgia State University- concept maps and explanations]

[http://www.pathwaystoscience.org/ Pathyways to Science]

=== Hands On Demos and Activity Ideas ===

[http://projectsol.aps.com/inside/inside_pv.asp APS Project Sol- Animation explains silicon solar solar cells]

[http://www.solideas.com/solrcell/cellkit.html Solar Cell Kit-How to build your own solar cell]

[http://spie.org/etop/2007/etop07k12V.pdf Innovative Methods to Teach Optics in the Grade 5- (including jello optics)]

[http://www.informalscience.org/research/resources Informal Science Education - Good resource to see what museums are doing with outreach activities.]

== E-learning ==
===General Info===
[http://www.nsf.gov/pubs/2008/nsf08204/nsf08204.pdf Fostering E-learning in the Networked World- NSF]

[http://www.ecornell.com/about/approach/whitepaperV2_1.pdf Cornell Learning Molecule Concept]

[http://creativecommons.org/about/licenses/ Creative Commons Content Licenses]

[http://commons.carnegiefoundation.org/ The Carnegie Commons - Technology, teaching and learning]

===Digital Libraries===
[http://www.nsdl.org National Science Digital Library - NSDL]

[http://amser.org/ Applied Math and Science Education Respository]

[http://www.chemeddl.org/ Chemical Education Digital Library]

[http://www.merlot.org/merlot/index.htm MERLOT Multimedia Educational Resource for Learning and Online Teaching]

[http://www.chemcollective.org/ The Chem Collective- Online resources for Teaching and Learning Chemistry]

[http://www.smete.org/smete/ SMETE Digital Library Science Mathematics Engineering and Technology Education ]

===Other Wikis===
[http://thzpolymers.pbwiki.com/ Special wiki from the Thz group at UMBC]

[http://en.wikipedia.org/wiki/Main_Page Wikipedia]

[http://en.wikibooks.org/wiki/Wikibooks:Community_Portal Wikibooks]

[http://commons.wikimedia.org Wikimedia]

[http://en.wikiversity.org/wiki/Wikiversity:Main_Page Wikiversity]

===Open Courseware===
[http://ocw.mit.edu/OcwWeb/web/home/home/index.htm MIT Open Courseware]

[http://www.oercommons.org/ Open Educational Commons]

[http://www.cmu.edu/oli/index.shtml Open Learning Initiative]

==Tools==

[http://exelearning.org/ eXe xhtml authoring software for building modules with SCORM output.]

[http://jmol.sourceforge.net/ JMOL molecular 3D manipulation tool and plugin]

[http://www.openscience.org/links/ Open Science Project - software tools for scientists]

[http://www.chemspider.com/Search.aspx Chem Spider Chemical Structures Database]

[http://moodle.org Moodle Course Management System]

[http://www.sakaiproject.org/portal Sakai Collaboration tools for Higher Ed]

[http://freemind.sourceforge.net/wiki/index.php/Main_Page Freemind Concept Mapping Software]

[http://www.wordle.net/ Wordle- create snazzy graphics from vocabulary, or text]

Total Internal Reflection

2009-02-15T01:21:43Z

67.183.23.184:

Total Internal Reflection

2009-02-15T01:19:17Z

67.183.23.184: New page: [[Image:reflexion totale interne.png|thumb|right|250px|The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when '''total internal reflecti...

[[Image:reflexion totale interne.png|thumb|right|250px|The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when '''total internal reflection''' occurs. (The color of the rays is to help distinguish the rays, and is not meant to indicate any color dependence.)]]
'''Total internal reflection''' is an [[optical phenomenon]] that occurs when a ray of light strikes a medium boundary at an angle larger than the '''critical angle''' with respect to the normal to the surface. If the [[refractive index]] is lower on the other side of the boundary no light can pass through, so effectively all of the light is [[Reflection (physics)|reflected]]. The critical angle is the [[angle of incidence]] above which the total internal reflection occurs.

When [[light]] crosses a boundary between materials with different [[refractive index|refractive indices]], the light beam will be partially [[refraction|refracted]] at the boundary surface, and partially reflected. However, if the [[angle of incidence]] is greater (i.e. the ray is closer to being parallel to the boundary) than the critical angle — the angle of incidence at which light is refracted such that it travels along the boundary — then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higher [[refractive index]] to one with a lower refractive index. For example, it will occur when passing from [[glass]] to [[Earth's atmosphere|air]], but not when passing from air to glass.

==Optical description==
[[Image:Total internal reflection.jpg|thumb|250px|Total internal reflection]]
[[Image:TIR in PMMA.jpg|thumb|250px|Total internal reflection in a block of [[PMMA]]]]
Total internal reflections can be demonstrated using a semi-circular glass block. A "ray box" shines a narrow beam of light (a "[[Ray (optics)|ray]]") onto the glass. The semi-circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface.
At the glass/air boundary of the flat surface, what happens will depend on the angle.
Where θ<sub>c</sub> is the critical angle (measured normal to the surface):
*If θ < θ<sub>c</sub>, as with the red ray in the above figure, the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through.
*If θ > θ<sub>c</sub>, as with the blue ray, the entire ray reflects from the boundary. None passes through. This is called total internal reflection.

This physical property makes [[optical fiber]]s useful, and [[rainbow]]s and prismatic [[binoculars]] possible. It is also what gives [[diamond]]s their distinctive sparkle, as diamond has an extremely high refractive index.

==The Critical angle==
''The critical angle'' is the angle of incidence ''above'' which total internal reflection occurs. The angle of incidence is measured with respect to the [[Surface normal|normal]] at the refractive boundary. The critical angle <math>\theta_c</math> is given by:

:<math>\theta_c = \arcsin \left( \frac{n_2}{n_1} \right), </math>

where <math>n_2</math> is the [[refractive index]] of the less dense [[Medium (optics)|medium]], and <math>n_1</math> is the refractive index of the denser medium.

If the incident ray is precisely at the critical angle, the refracted ray is [[tangent]] to the boundary at the point of incidence. If for example, visible light were traveling from a glass (i.e. Lucite with an index of refraction of 1.50) into air (with an index of refraction of 1.00). The calculation would give the critical angle for light from Lucite into air, which is
:<math>\theta _{c}=\arcsin \left( 1.00/1.50 \right)=41.8{}^\circ </math>.
Light incident on the border with an angle less than 41.8° would be partially transmitted, while light incident on the border at larger angles with respect to normal would be totally internally reflected.

The critical angle for [[diamond]] in air is about 24.4°, which means that light is much more likely to be internally reflected within a diamond. Diamonds for jewelry are [[Diamond cut|cut]] to take advantage of this; in particular the [[brilliant cut]] is designed to achieve high total reflection of light entering the diamond, and high [[dispersion (optics)|dispersion]] of the reflected light (known to jewelers as ''fire'').

If the fraction: <math>\frac{n_2}{n_1}</math> is greater than 1, then arcsine is not defined--meaning that total internal reflection does not occur even at very shallow or grazing incident angles.

So the critical angle is only defined for <math>\frac{n_2}{n_1}\leq1</math>.

==Evanescent wave==
An important side effect of total internal reflection is the propagation of an [[evanescent wave]] across the boundary surface. Essentially, even though the entire incident wave is reflected back into the originating medium, there is some penetration into the second medium at the boundary. This wave can lead to a phenomenon known as frustrated total internal reflection. Additionally, the evanescent wave appears to travel along the boundary between the two materials, leading to the [[Goos-Hänchen shift]].

== Frustrated total internal reflection ==
Under "ordinary conditions" it is true that the creation of an [[evanescent wave]] does not affect the conservation of energy, i.e. the evanescent wave transmits zero net energy. However, if a third medium with a higher [[refractive index]] than the second medium is placed within less than several wavelengths distance from the interface between the first medium and the second medium, the evanescent wave will be different from the one under "ordinary conditions" and it will pass energy across the second into the third medium. (See [[evanescent wave coupling]].)

A transparent, low refractive index material is sandwiched between two prisms of another material. This allows the beam to "tunnel" through from one prism to the next in a process very similar to [[quantum tunneling]] while at the same time altering the direction of the incoming ray.

==Applications==
* [[Optical fiber]]s, which are used in [[endoscope]]s and [[telecommunications]].
* [[Rain sensor#Automotive Sensors|Rain sensors]] to control automatic [[Windscreen wiper#History|windscreen/windshield wiper]]s.
* Another interesting application of total internal reflection is the spatial filtering of light.<ref>{{cite journal |url=http://planck.reduaz.mx/~imoreno/Publicaciones/OptLett2005.pdf |format=PDF |title=Thin-film spatial filters |first=Ivan |last=Moreno |authorlink=Ivan Moreno |coauthors=J. Jesus Araiza, Maximino Avendano-Alejo |journal=Optics Letters |volume=30 |number=8 |pages=pp. 914–916 |doi=10.1364/OL.30.000914 |year=2005}}</ref>
* [[Multi-touch]] screens [http://www.multitouch.nl/] use frustrated total internal reflection in combination with a camera and appropriate software to pick up multiple targets.
* [[Gonioscopy]] to view the anatomical angle formed between the eye's [[cornea]] and [[Iris (anatomy)|iris]].
* [[Gait analysis]] instrument, CatWalk [http://www.noldus.com/catwalk], use frustrated total internal reflection in combination with a high speed camera to capture and analyze footprints of laboratory rodents.

==Examples in everyday life==
[[Image:Total internal reflection of Chelonia mydas .jpg|Total internal reflection of the turtle can be seen at the air-water boundary.|thumb]]
Total internal reflection can be observed while swimming, if one opens one's eyes just under the water's surface. If the water is calm, its surface appears mirror-like.

One can demonstrate total internal reflection by filling a sink or bath with water, taking a glass tumbler, and placing it upside-down over the plug hole (with the tumbler completely filled with water). While water remains both in the upturned tumbler and in the sink surrounding it, the plug hole and plug are visible since the angle of refraction between glass and water is not greater than the critical angle. If the drain is opened and the tumbler is kept in position over the hole, the water in the tumbler drains out leaving the glass filled with air, and this then acts as the plug. Viewing this from above, the tumbler now appears mirrored because light reflects off the air/glass interface.

Another very common example of Total Internal Reflection is a critically cut [[diamond]]. This is what gives it maximum sparkle.

==See also==
*[[Evanescent wave]]
*[[Perfect mirror]]
*[[Refraction]]
*[[Refractive index]]
*[[Fresnel equations]]
*[[Snell's window]]
*[[Goos-Hänchen effect]]

==References==
{{reflist}}
*[[Federal Standard 1037C]] and [[MIL-STD-188]]

==External links==
* [http://cs.nyu.edu/~jhan/ftirsense/index.html FTIR Touch Sensing]
* [http://cs.nyu.edu/~jhan/ftirtouch/index.html Multi-Touch Interaction Research]
* [http://www.i-bar.ch/index.php?id=88&L=1 iBar Intelligent Surface System]
* http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/totint.html
* [http://demonstrations.wolfram.com/TotalInternalReflection/ Total Internal Reflection] by Michael Schreiber, [[Wolfram Demonstrations Project]]
* [http://www.noldus.com/catwalk CatWalk] by [http://www.noldus.com/ Noldus Information Technology]

{{Commons|Total internal reflection}}