Second-order NLO Materials - Revision history

Cmditradmin at 17:22, 8 November 2011

2011-11-08T17:22:30Z

Cmditradmin at 16:45, 3 November 2011

2011-11-03T16:45:16Z

Cmditradmin: /* Coarse and fine models */

2011-11-03T16:35:04Z

Coarse and fine models

← Older revision		Revision as of 09:35, 3 November 2011
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	[[Image:r33_Numberdens.JPG\|thumb\|400px\|Improvements in EO activity with dendrimer design.]]		[[Image:r33_Numberdens.JPG\|thumb\|400px\|Improvements in EO activity with dendrimer design.]]
	The beauty of this is ~~that it gives you~~ that it gives you a quantitative prediction of EO activity. This led to the to the design of branched dendrimers which cause steric interactions that helps keep isolated chromophores from interacting each other so they don't line up.		The beauty of this is that it gives you a quantitative prediction of EO activity. This led to the to the design of branched dendrimers which cause steric interactions that helps keep isolated chromophores from interacting each other so they don't line up.

	Once there is a structure in mind an organic synthesis pathway can be devised.		Once there is a structure in mind an organic synthesis pathway can be devised.

Cmditradmin: /* Poling of Chromophores in Polymers */

2011-11-03T16:31:31Z

Poling of Chromophores in Polymers

← Older revision		Revision as of 09:31, 3 November 2011
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	=== Poling of Chromophores in Polymers ===		=== Poling of Chromophores in Polymers ===
	[[Image:NLOmaterial.png\|thumb\|300px\|A NLO material has a bulk material with a suspension of chromophores]]		[[Image:NLOmaterial.png\|thumb\|300px\|A NLO material has a bulk material with a suspension of chromophores]]
	The general approach that has been employed to create a second-order nonlinear optical material has been to assemble		The general approach that has been employed to create a second-order nonlinear optical material has been to assemble a bulk material using an inert “Host” material loaded with active “Chromophores”, molecules that have a high first hyperpolarizability (beta), and then get those molecules oriented in the same direction. For now we will examine orientation for high EO coefficient and will ignore the orientation required for second harmonic generation which require a different orientation.
	a bulk material using an inert “Host” material loaded with active “Chromophores”, molecules that have a high first hyperpolarizability (beta)~~. Then~~ get those molecules oriented in the same direction. (For now we will examine orientation for high EO coefficient and will ignore the orientation required for second harmonic generation which require a different orientation)

	Orientation can be achieved with crystalline materials. The Marder group was able to develop crystals of DAST. (They were working with a Japanese group at the same time who succeeded in making a crystal of the hydrate of the material due to their high local humidity. Marder’s group in California was able to make the DAST crystal due to the low local humidity. One crystal was centro symmetric and one was non-centrosymmetric.) Growing crystals is very difficult. Another group spent 10 years developing the method to grow one crystal. (Rainbow Photonics)		Orientation can be achieved with crystalline materials. The Marder group was able to develop crystals of DAST. (They were working with a Japanese group at the same time who succeeded in making a crystal of the hydrate of the material due to their high local humidity. Marder’s group in California was able to make the DAST crystal due to the low local humidity. One crystal was centro symmetric and one was non-centrosymmetric.) Growing crystals is very difficult. Another group spent 10 years developing the method to grow one crystal. (Rainbow Photonics)
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	[[Image:Poling.png\|thumb\|200px\|Sequence of a poling a chromophore in a glassy polymer]]		[[Image:Poling.png\|thumb\|200px\|Sequence of a poling a chromophore in a glassy polymer]]
	*Assume you ~~are~~ start with molecules that have high nonlinearities but they are arranged in a random orientation. An NLO chromophore with a dipole moment (such as paranitroaniline) and a glassy polymer are dissolved in an organic solvent and spin-coated onto a substrate. The film is then heated above or around its glass transition temperature (T<sub>g</sub>). The glass transition temperature at which there is free motion of the main chain of the polymer.		*Assume you start with molecules that have high nonlinearities but they are arranged in a random orientation. An NLO chromophore with a dipole moment (such as paranitroaniline) and a glassy polymer are dissolved in an organic solvent and spin-coated onto a substrate. The film is then heated above or around its glass transition temperature (T<sub>g</sub>). The glass transition temperature at which there is free motion of the main chain of the polymer.

	*At this temperature, the molecules can rotate in the rubbery matrix. An intense DC electric field as high as 10<sup>6</sup> V/cm is applied and this field creates a force on the dipole moments of the chromophores, aligning them.		*At this temperature, the molecules can rotate in the rubbery matrix. An intense DC electric field as high as 10<sup>6</sup> V/cm is applied and this field creates a force on the dipole moments of the chromophores, aligning them.
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	The goal of "poling" is to get all the chromophores to orient the same direction in a macroscopic sample. There are several ways to do this. We can place the chomophore in a host matrix like a commercial polymer, heat it up to the glass transition temperature, and apply an electric field. The dielectric moment of the chromophore interacting with the field will cause some ordering.		The goal of "poling" is to get all the chromophores to orient the same direction in a macroscopic sample. There are several ways to do this. We can place the chomophore in a host matrix like a commercial polymer, heat it up to the glass transition temperature, and apply an electric field. The dielectric moment of the chromophore interacting with the field will cause some ordering.

	The order parameter will be the dipole moment interaction divided by the 5 times the thermal energy.		The order parameter will be the dipole moment interaction divided by the 5 times the thermal energy. Unfortunately chromophores have strong intermolecular electrostatic interactions such as dipole-dipole interactions. So this going to influence what we see.

	[[Image:poling_centric.JPG\|thumb\|400px\|~~Unfortunately chromophores have strong intermolecular electrostatic interactions such as dipole-dipole interactions. So this going to influence what we see.~~]]		[[Image:poling_centric.JPG\|thumb\|400px\|]]
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Cmditradmin: /* Statistical mechanical calculations */

2010-07-20T15:53:26Z

Statistical mechanical calculations

← Older revision		Revision as of 08:53, 20 July 2010
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	Statistical mechanics has helped explain experimental data. Notice that if we go from a prolate ellipsoid shape to a spherical structure the EO activity can be improved. This has been experimentally observed. This can be used to produce an analytical expression to tell where the maximum EO activity will occur. More importantly it has given us methods such as shape engineering.		Statistical mechanics has helped explain experimental data. Notice that if we go from a prolate ellipsoid shape to a spherical structure the EO activity can be improved. This has been experimentally observed. This can be used to produce an analytical expression to tell where the maximum EO activity will occur. More importantly it has given us methods such as shape engineering.

	:<math>N_{max} = \left ( \frac {kT}{mu^2}\right ) \sqrt{ 0.48 + 0.28 \sqrt{4.8 + f^2}} \approx \left ( \frac {kT}{mu^2}\right )\,\!</math>		:<math>N_{max} = \left ( \frac {kT}{\mu^2}\right ) \sqrt{ 0.48 + 0.28 \sqrt{4.8 + f^2}} \approx \left ( \frac {kT}{\mu^2}\right )\,\!</math>

	<br clear='all'>		<br clear='all'>

Cmditradmin: /* Statistical mechanical calculations */

2010-07-20T15:50:22Z

Statistical mechanical calculations

← Older revision		Revision as of 08:50, 20 July 2010
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	Statistical mechanics has helped explain experimental data. Notice that if we go from a prolate ellipsoid shape to a spherical structure the EO activity can be improved. This has been experimentally observed. This can be used to produce an analytical expression to tell where the maximum EO activity will occur. More importantly it has given us methods such as shape engineering.		Statistical mechanics has helped explain experimental data. Notice that if we go from a prolate ellipsoid shape to a spherical structure the EO activity can be improved. This has been experimentally observed. This can be used to produce an analytical expression to tell where the maximum EO activity will occur. More importantly it has given us methods such as shape engineering.

	:<math>~~N_max~~ = \left ( \frac {kT}{mu^2}\right ) \sqrt{ 0.48 + 0.28 \sqrt{4.8 + f^2}} \approx \left ( \frac {kT}{mu^2}\right )\,\!</math>		:<math>N_{max} = \left ( \frac {kT}{mu^2}\right ) \sqrt{ 0.48 + 0.28 \sqrt{4.8 + f^2}} \approx \left ( \frac {kT}{mu^2}\right )\,\!</math>

	<br clear='all'>		<br clear='all'>

Cmditradmin: /* Statistical mechanical calculations */

2010-07-20T15:50:02Z

Statistical mechanical calculations

← Older revision		Revision as of 08:50, 20 July 2010
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	[[Image:Loading shape.png\|thumb\|300px\|Theoretical prediction of shape effect on EO activity]]		[[Image:Loading shape.png\|thumb\|300px\|Theoretical prediction of shape effect on EO activity]]
	Statistical mechanics has helped explain experimental data. Notice that if we go from a prolate ellipsoid shape to a spherical structure the EO activity can be improved. This has been experimentally observed. This can be used to produce an analytical expression to tell where the maximum EO activity will occur. More importantly it has given us methods such as shape engineering.		Statistical mechanics has helped explain experimental data. Notice that if we go from a prolate ellipsoid shape to a spherical structure the EO activity can be improved. This has been experimentally observed. This can be used to produce an analytical expression to tell where the maximum EO activity will occur. More importantly it has given us methods such as shape engineering.

			:<math>N_max = \left ( \frac {kT}{mu^2}\right ) \sqrt{ 0.48 + 0.28 \sqrt{4.8 + f^2}} \approx \left ( \frac {kT}{mu^2}\right )\,\!</math>

	<br clear='all'>		<br clear='all'>

Cmditradmin at 23:04, 4 January 2010

2010-01-04T23:04:38Z

Cmditradmin at 20:21, 29 December 2009

2009-12-29T20:21:09Z

← Older revision		Revision as of 13:21, 29 December 2009
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	[[category:second order ~~processes~~]]		[[category:second order NLO]]
	<table id="toc" style="width: 100%">		<table id="toc" style="width: 100%">
	<tr>		<tr>

Cmditradmin at 20:20, 29 December 2009

2009-12-29T20:20:31Z

← Older revision		Revision as of 13:20, 29 December 2009
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			[[category:second order processes]]
	<table id="toc" style="width: 100%">		<table id="toc" style="width: 100%">
	<tr>		<tr>

← Older revision		Revision as of 10:22, 8 November 2011
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	Notice that the second term χ<sup>(2)</sup> is field dependent.		Notice that the second term χ<sup>(2)</sup> is field dependent.

	Thus, when an electric field is applied to such a poled polymer, the index of refraction of the material will change. This sensitivity of the material to having its index of refraction changed by application of an external electric field is characterized by its so-called ~~electrooptic~~ coefficient, coefficient (r<sub>33</sub>).		Thus, when an electric field is applied to such a poled polymer, the index of refraction of the material will change. This sensitivity of the material to having its index of refraction changed by application of an external electric field is characterized by its so-called electro-optic coefficient, coefficient (r<sub>33</sub>).

	For many years it had been suggested that ~~electrooptic~~ polymers could exhibit large r<sub>33</sub> greatly surpassing that of a technologically important crystal, lithium niobate (LiNb0<sub>3</sub>). It is transparent, it is inexpensive, it can be grown in large sheets, and it has an r<sub>33</sub> of 30.5 pm/V in the "telecommunications" wavelengths of 1.3 μm. This is a reasonable r<sub>33</sub> that allows you to build devices. When we build organics we have synthesize new compounds, worry about stability, worry about orientation, and how to keep them poled. But there are significant advantages in using organics.		For many years it had been suggested that electro-optic polymers could exhibit large r<sub>33</sub> greatly surpassing that of a technologically important crystal, lithium niobate (LiNb0<sub>3</sub>). It is transparent, it is inexpensive, it can be grown in large sheets, and it has an r<sub>33</sub> of 30.5 pm/V in the "telecommunications" wavelengths of 1.3 μm. This is a reasonable r<sub>33</sub> that allows you to build devices. When we build organics we have synthesize new compounds, worry about stability, worry about orientation, and how to keep them poled. But there are significant advantages in using organics.

	While there are both electronic and vibrational components to the non-linearity in lithium niobate, a large component is vibrational. This puts an upper limit on the frequency with which that LiNbO<sub>3</sub> can be modulated. If a driving field approaches the vibrational frequency then the molecules cannot respond quickly to the applied field. The response trails off and there is only the electronic contribution for the non-linearity.		While there are both electronic and vibrational components to the non-linearity in lithium niobate, a large component is vibrational. This puts an upper limit on the frequency with which that LiNbO<sub>3</sub> can be modulated. If a driving field approaches the vibrational frequency then the molecules cannot respond quickly to the applied field. The response trails off and there is only the electronic contribution for the non-linearity.
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	Another problem is that the high concentrations of chromophores in these systems results in chromophore-chromophore interactions, inhomogeneities of the chromophore concentrations, and chromophore polymer interactions. Each of these factors leads to a variation of the refractive index which can lead to the scattering of light at some level. If the interaction length of the light in the Mach Zehnder devices needs to be long then it is important to keep the scattering in the organic component to a minimum.		Another problem is that the high concentrations of chromophores in these systems results in chromophore-chromophore interactions, inhomogeneities of the chromophore concentrations, and chromophore polymer interactions. Each of these factors leads to a variation of the refractive index which can lead to the scattering of light at some level. If the interaction length of the light in the Mach Zehnder devices needs to be long then it is important to keep the scattering in the organic component to a minimum.

	It is important to have a high index of refraction and high ~~electrooptic~~ coefficient. Index of refraction relates to dielectric constant which relates to susceptibility, which relates to polarizability (α), which relates to the transition dipole moment within the context of a two level model. Change of dipole of moment is the state dipole moment for the excited state minus the state dipole moment for the ground state. Transition dipole moment is an integral of the complex conjugate of the excited state wave function, the transition dipole moment operator (which scales like R) and the ground state wave function Dτ. The transition dipole moment relates to the oscillator strength (the area under the absorption curve) which is related to the extinction coefficient. Organic dyes that are used in second order NLO systems are materials that have a high refractive index and strong low energy absorptions.		It is important to have a high index of refraction and high electro-optic coefficient. Index of refraction relates to dielectric constant which relates to susceptibility, which relates to polarizability (α), which relates to the transition dipole moment within the context of a two level model. Change of dipole of moment is the state dipole moment for the excited state minus the state dipole moment for the ground state. Transition dipole moment is an integral of the complex conjugate of the excited state wave function, the transition dipole moment operator (which scales like R) and the ground state wave function Dτ. The transition dipole moment relates to the oscillator strength (the area under the absorption curve) which is related to the extinction coefficient. Organic dyes that are used in second order NLO systems are materials that have a high refractive index and strong low energy absorptions.

	=== Poling of Chromophores in Polymers ===		=== Poling of Chromophores in Polymers ===
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	where		where
	:<math>r_{33}\,\!</math> is the ~~electrooptic~~ coefficient		:<math>r_{33}\,\!</math> is the electro-optic coefficient
	:<math>\beta(\epsilon,\omega)\,\!</math> is the molecular first hyperpolarizability		:<math>\beta(\epsilon,\omega)\,\!</math> is the molecular first hyperpolarizability
	:<math>N\,\!</math> is the number density of chromophores in the polymer		:<math>N\,\!</math> is the number density of chromophores in the polymer
	:<math><cos^3\theta>\,\!</math> is the order parameter		:<math><cos^3\theta>\,\!</math> is the order parameter

	The [[~~electrooptic~~ cofficient]] r<sub>33</sub> is determined by the molecular property first hyperpolarizability <math>\beta(\epsilon,\omega)\,\!</math> and a number density. So for the maximum effect all the molecules must be lined up in the same direction. You can use quantum mechanics to optimize the first part (hyperpolarizability), and statistical mechanics to optimize the second part (number density), and have a feedback loop between the two approaches.		The [[electro-optic cofficient]] r<sub>33</sub> is determined by the molecular property first hyperpolarizability <math>\beta(\epsilon,\omega)\,\!</math> and a number density. So for the maximum effect all the molecules must be lined up in the same direction. You can use quantum mechanics to optimize the first part (hyperpolarizability), and statistical mechanics to optimize the second part (number density), and have a feedback loop between the two approaches.

	<br clear='all'>		<br clear='all'>
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	=== Statistical mechanical calculations ===		=== Statistical mechanical calculations ===
	[[Image:EOC_loading.png\|thumb\|300px\|Number density affect ~~electrooptic~~ activity]]		[[Image:EOC_loading.png\|thumb\|300px\|Number density affect electro-optic activity]]
	As chromophore number density increases they begin to interact because of their polarity. At extreme close range this forces molecules to flip and this reduces the EO activity of the material. A balance must be struck between number density and beta of molecules to enhance macroscopic EO activity.		As chromophore number density increases they begin to interact because of their polarity. At extreme close range this forces molecules to flip and this reduces the EO activity of the material. A balance must be struck between number density and beta of molecules to enhance macroscopic EO activity.

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	=== Conclusion ===		=== Conclusion ===

	The combination of new QM and SM methods permits quantitative prediction of macroscopic ~~electrooptic~~ activity--Yes, we really do need “Numbers”!		The combination of new QM and SM methods permits quantitative prediction of macroscopic electro-optic activity--Yes, we really do need “Numbers”!

	*Previous analysis has tended neglect dielectric effects, to over estimate acentric order and underestimate molecular first hyperpolarizability.		*Previous analysis has tended neglect dielectric effects, to over estimate acentric order and underestimate molecular first hyperpolarizability.
	*Laser-assisted electric field poling can be used to improve acentric order.		*Laser-assisted electric field poling can be used to improve acentric order.
	*Binary chromophore organic glasses permit significant improvement in both ~~electrooptic~~ activity and optical transparency.		*Binary chromophore organic glasses permit significant improvement in both electro-optic activity and optical transparency.
	*Electro-optic activity of 1000 pm/V (2 orders of magnitude improvement) with optical loss of 2 dB/cm is possible by theoretically-inspired design. This is starting to approach the value of liquid crystals but with a factor of 10<sup>11</sup> improvement in processing speed.		*Electro-optic activity of 1000 pm/V (2 orders of magnitude improvement) with optical loss of 2 dB/cm is possible by theoretically-inspired design. This is starting to approach the value of liquid crystals but with a factor of 10<sup>11</sup> improvement in processing speed.

← Older revision		Revision as of 09:45, 3 November 2011
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	</table>		</table>

	Amorphous polymers are desirable materials for several reasons however in order to take full advantage of the EO potential of the polymer embedded ~~chomophores~~ these molecules must be well organized in the bulk material. Poling is the process of bringing chromophores into a desired alignment in a material.		Amorphous polymers are desirable materials for several reasons however in order to take full advantage of the EO potential of the polymer embedded chromophores these molecules must be well organized in the bulk material. Poling is the process of bringing chromophores into a desired alignment in a material.

	=== Linear and Non Linear Electro-optic Effect ===		=== Linear and Non Linear Electro-optic Effect ===
	'''Linear'''		'''Linear'''
	In linear optics an applied field results in a linear polarization response where the refractive index n and therefore the susceptibility Χ<sup>(1)</sup> is not dependent on ~~the~~ the electric field. When the field is low higher order terms are insignificant and can be ignored.		In linear optics an applied field results in a linear polarization response where the refractive index n and therefore the susceptibility Χ<sup>(1)</sup> is not dependent on the electric field. When the field is low higher order terms are insignificant and can be ignored.

	:<math>P_i= \Chi^{(1)}_{ij}E_j\,\!</math>		:<math>P_i= \Chi^{(1)}_{ij}E_j\,\!</math>
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	:<math>P = ( \chi^{(1)} + 1/2\chi^{(2)} E_2 ) E_1 [cos \omega t]\,\!</math>		:<math>P = ( \chi^{(1)} + 1/2\chi^{(2)} E_2 ) E_1 [cos \omega t]\,\!</math>

	Notice that ~~the~~ the second term χ<sup>(2)</sup> is field dependent.		Notice that the second term χ<sup>(2)</sup> is field dependent.

	Thus, when an electric field is applied to such a poled polymer, the index of refraction of the material will change. This sensitivity of the material to having its index of refraction changed by application of an external electric field is characterized by its so-called electrooptic coefficient, coefficient (r<sub>33</sub>).		Thus, when an electric field is applied to such a poled polymer, the index of refraction of the material will change. This sensitivity of the material to having its index of refraction changed by application of an external electric field is characterized by its so-called electrooptic coefficient, coefficient (r<sub>33</sub>).

	For many years it had been suggested that electrooptic polymers could exhibit large r<sub>33</sub> greatly surpassing that of a technologically important crystal, lithium niobate (LiNb0<sub>3</sub>). It is transparent, it is inexpensive, it can be grown in large sheets, and it has an r<sub>33</sub> of 30.5 pm/V in the "telecommunications" wavelengths of 1.3 μm. This is a reasonable r<sub>33</sub> that allows you to build devices. When we build organics we have synthesize new compounds, worry about stability, worry about orientation, and how to keep them poled. But there are a significant ~~advantage to~~ organics.		For many years it had been suggested that electrooptic polymers could exhibit large r<sub>33</sub> greatly surpassing that of a technologically important crystal, lithium niobate (LiNb0<sub>3</sub>). It is transparent, it is inexpensive, it can be grown in large sheets, and it has an r<sub>33</sub> of 30.5 pm/V in the "telecommunications" wavelengths of 1.3 μm. This is a reasonable r<sub>33</sub> that allows you to build devices. When we build organics we have synthesize new compounds, worry about stability, worry about orientation, and how to keep them poled. But there are significant advantages in using organics.

	While there are both electronic and vibrational components to the non-linearity in lithium niobate, a large component is vibrational. This puts an upper limit on the frequency with which that LiNbO<sub>3</sub> can be modulated. If a driving field approaches the vibrational frequency then the molecules ~~can not~~ respond quickly to the applied field. The response trails off and there is only the electronic contribution for the non-linearity.		While there are both electronic and vibrational components to the non-linearity in lithium niobate, a large component is vibrational. This puts an upper limit on the frequency with which that LiNbO<sub>3</sub> can be modulated. If a driving field approaches the vibrational frequency then the molecules cannot respond quickly to the applied field. The response trails off and there is only the electronic contribution for the non-linearity.

	Organic materials are completely dominated by the electronic contributions and therefore can be modulated at very high frequencies.		Organic materials are completely dominated by the electronic contributions and therefore can be modulated at very high frequencies.
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	It is also possible to get organics with an r<sub>33</sub> that is much higher (for example 55 pm/V) than LiNbO<sub>3</sub>. This means that the V<sub>π</sub> (the voltage required for a π phase shift) can be less to get the same change in optical property.		It is also possible to get organics with an r<sub>33</sub> that is much higher (for example 55 pm/V) than LiNbO<sub>3</sub>. This means that the V<sub>π</sub> (the voltage required for a π phase shift) can be less to get the same change in optical property.

	Finally it possible to integrate electronic with optical parts right on a chip. Polymer technology is going to make it much easier to combine these materials on a chip.		Finally it is possible to integrate electronic with optical parts right on a chip. Polymer technology is going to make it much easier to combine these materials on a chip.

	In the field of silicon photonics there are waveguides built with ebeam lithography on which the polymer can be spin coated and fill the channels. Organics are amorphous whereas LiNbO<sub>3</sub> is a single crystal material which makes it very challenging to apply to chip-scale device.		In the field of silicon photonics there are waveguides built with ebeam lithography on which the polymer can be spin coated and fill the channels. Organics are amorphous whereas LiNbO<sub>3</sub> is a single crystal material which makes it very challenging to apply to chip-scale device.
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	=== Poling of Chromophores in Polymers ===		=== Poling of Chromophores in Polymers ===
	[[Image:NLOmaterial.png\|thumb\|300px\|A NLO material has a bulk material with a suspension of chromophores]]		[[Image:NLOmaterial.png\|thumb\|300px\|A NLO material has a bulk material with a suspension of chromophores]]
	The general approach that has been employed to create a second-order nonlinear optical material has been to assemble a bulk material using an inert “Host” material loaded with active “Chromophores”, molecules that have a high first hyperpolarizability (beta), and then get those molecules oriented in the same direction. For now we will examine orientation for high EO coefficient and will ignore the orientation required for second harmonic generation which ~~require~~ a different orientation.		The general approach that has been employed to create a second-order nonlinear optical material has been to assemble a bulk material using an inert “Host” material loaded with active “Chromophores”, molecules that have a high first hyperpolarizability (beta), and then get those molecules oriented in the same direction. For now we will examine orientation for high EO coefficient and will ignore the orientation required for second harmonic generation which requires a different orientation.

	Orientation can be achieved with crystalline materials. The Marder group was able to develop crystals of DAST. (They were working with a Japanese group at the same time who succeeded in making a crystal of the hydrate of the material due to their high local humidity. Marder’s group in California was able to make the DAST crystal due to the low local humidity. One crystal was ~~centro symmetric~~ and one was non-centrosymmetric.) Growing crystals is very difficult. Another group spent 10 years developing the method to grow one crystal. (Rainbow Photonics)		Orientation can be achieved with crystalline materials. The Marder group was able to develop crystals of DAST. They were working with a Japanese group at the same time who succeeded in making a crystal of the hydrate of the material due to their high local humidity. Marder’s group in California was able to make the DAST crystal due to the low local humidity. One crystal was centrosymmetric and one was non-centrosymmetric.) Growing crystals is very difficult. Another group spent 10 years developing the method to grow one crystal. (Rainbow Photonics)

	The most widely used method for aligning molecules is the poled polymer method. Recall that dipole moment is a vector, and first hyperpolarizability beta is a tensor. Assume that the molecule has one axis (the long axis) along which the hyperpolarizability beta dominates. If the dipole moment is aligned along the long axis then an applied electric field will cause a torque to reorient the molecules. (Boltzman will be working against this attempting to randomize the orientation) There will be a distribution of orientations but if you sum over all the vectors there will be a net orientation. This in turn aligns the hyperpolarizability tensor. In the limiting case in which the hyperpolarizability is perpendicular to the dipole moment there will be an alignment of the hyperpolarizability tensor in a plane but within that plane the tensors will be oriented at all angles. This results in a zero overall second order optical activity. Therefore we need molecules with large dipole moments that are oriented along the same axis as the hyperpolarizability tensor.		The most widely used method for aligning molecules is the poled polymer method. Recall that dipole moment is a vector, and first hyperpolarizability beta is a tensor. Assume that the molecule has one axis (the long axis) along which the hyperpolarizability beta dominates. If the dipole moment is aligned along the long axis then an applied electric field will cause a torque to reorient the molecules. (Boltzman will be working against this attempting to randomize the orientation) There will be a distribution of orientations but if you sum over all the vectors there will be a net orientation. This in turn aligns the hyperpolarizability tensor. In the limiting case in which the hyperpolarizability is perpendicular to the dipole moment there will be an alignment of the hyperpolarizability tensor in a plane but within that plane the tensors will be oriented at all angles. This results in a zero overall second order optical activity. Therefore we need molecules with large dipole moments that are oriented along the same axis as the hyperpolarizability tensor.
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	In this manner you can produce a material that has a second order nonlinear optical effect using molecules that have a second order nonlinear optical effect.		In this manner you can produce a material that has a second order nonlinear optical effect using molecules that have a second order nonlinear optical effect.

	The resulting ~~noncentrosymmetric~~ structure contains the molecular units oriented on the average normal to the film (C∞v symmetry). In this state, the electric field of an optical beam propagating through the film can be maximally modified when the field is parallel to the orientated molecular units.		The resulting non-centrosymmetric structure contains the molecular units oriented on the average normal to the film (C∞v symmetry). In this state, the electric field of an optical beam propagating through the film can be maximally modified when the field is parallel to the orientated molecular units.
	<br clear='all'>		<br clear='all'>
	[[Image:poling_electrode.png\|thumb\|400px\|A DC electric field is a applied to a polymer as it passes through its glass stage.]]		[[Image:poling_electrode.png\|thumb\|400px\|A DC electric field is a applied to a polymer as it passes through its glass stage.]]
	The goal of "poling" is to get all the chromophores to orient the same direction in a macroscopic sample. There are several ways to do this. We can place the ~~chomophore~~ in a host matrix like a commercial polymer, heat it up to the glass transition temperature, and apply an electric field. The dielectric moment of the chromophore interacting with the field will cause some ordering.		The goal of "poling" is to get all the chromophores to orient the same direction in a macroscopic sample. There are several ways to do this. We can place the chromophore in a host matrix like a commercial polymer, heat it up to the glass transition temperature, and apply an electric field. The dielectric moment of the chromophore interacting with the field will cause some ordering.

	The order parameter will be the dipole moment interaction divided by the 5 times the thermal energy. Unfortunately chromophores have strong intermolecular electrostatic interactions such as dipole-dipole interactions. So this going to influence what we see.		The order parameter will be the dipole moment interaction divided by the 5 times the thermal energy. Unfortunately chromophores have strong intermolecular electrostatic interactions such as dipole-dipole interactions. So this going to influence what we see.

← Older revision		Revision as of 16:04, 4 January 2010
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	Notice that the the second term χ<sup>(2)</sup> is field dependent.		Notice that the the second term χ<sup>(2)</sup> is field dependent.

	Thus, when an electric field is applied to such a poled polymer, the index of refraction of the material will change. This sensitivity of the material to having its index of refraction changed by application of an external electric field is characterized by its so-called ~~electro-optic~~ coefficient, coefficient (r<sub>33</sub>).		Thus, when an electric field is applied to such a poled polymer, the index of refraction of the material will change. This sensitivity of the material to having its index of refraction changed by application of an external electric field is characterized by its so-called electrooptic coefficient, coefficient (r<sub>33</sub>).

	For many years it had been suggested that ~~electro-optic~~ polymers could exhibit large r<sub>33</sub> greatly surpassing that of a technologically important crystal, lithium niobate (LiNb0<sub>3</sub>). It is transparent, it is inexpensive, it can be grown in large sheets, and it has an r<sub>33</sub> of 30.5 pm/V in the "telecommunications" wavelengths of 1.3 μm. This is a reasonable r<sub>33</sub> that allows you to build devices. When we build organics we have synthesize new compounds, worry about stability, worry about orientation, and how to keep them poled. But there are a significant advantage to organics.		For many years it had been suggested that electrooptic polymers could exhibit large r<sub>33</sub> greatly surpassing that of a technologically important crystal, lithium niobate (LiNb0<sub>3</sub>). It is transparent, it is inexpensive, it can be grown in large sheets, and it has an r<sub>33</sub> of 30.5 pm/V in the "telecommunications" wavelengths of 1.3 μm. This is a reasonable r<sub>33</sub> that allows you to build devices. When we build organics we have synthesize new compounds, worry about stability, worry about orientation, and how to keep them poled. But there are a significant advantage to organics.

	While there are both electronic and vibrational components to the non-linearity in lithium niobate, a large component is vibrational. This puts an upper limit on the frequency with which that LiNbO<sub>3</sub> can be modulated. If a driving field approaches the vibrational frequency then the molecules can not respond quickly to the applied field. The response trails off and there is only the electronic contribution for the non-linearity.		While there are both electronic and vibrational components to the non-linearity in lithium niobate, a large component is vibrational. This puts an upper limit on the frequency with which that LiNbO<sub>3</sub> can be modulated. If a driving field approaches the vibrational frequency then the molecules can not respond quickly to the applied field. The response trails off and there is only the electronic contribution for the non-linearity.
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	Another problem is that the high concentrations of chromophores in these systems results in chromophore-chromophore interactions, inhomogeneities of the chromophore concentrations, and chromophore polymer interactions. Each of these factors leads to a variation of the refractive index which can lead to the scattering of light at some level. If the interaction length of the light in the Mach Zehnder devices needs to be long then it is important to keep the scattering in the organic component to a minimum.		Another problem is that the high concentrations of chromophores in these systems results in chromophore-chromophore interactions, inhomogeneities of the chromophore concentrations, and chromophore polymer interactions. Each of these factors leads to a variation of the refractive index which can lead to the scattering of light at some level. If the interaction length of the light in the Mach Zehnder devices needs to be long then it is important to keep the scattering in the organic component to a minimum.

	It is important to have a high index of refraction and high ~~electro-optic~~ coefficient. Index of refraction relates to dielectric constant which relates to susceptibility, which relates to polarizability (α), which relates to the transition dipole moment within the context of a two level model. Change of dipole of moment is the state dipole moment for the excited state minus the state dipole moment for the ground state. Transition dipole moment is an integral of the complex conjugate of the excited state wave function, the transition dipole moment operator (which scales like R) and the ground state wave function Dτ. The transition dipole moment relates to the oscillator strength (the area under the absorption curve) which is related to the extinction coefficient. Organic dyes that are used in second order NLO systems are materials that have a high refractive index and strong low energy absorptions.		It is important to have a high index of refraction and high electrooptic coefficient. Index of refraction relates to dielectric constant which relates to susceptibility, which relates to polarizability (α), which relates to the transition dipole moment within the context of a two level model. Change of dipole of moment is the state dipole moment for the excited state minus the state dipole moment for the ground state. Transition dipole moment is an integral of the complex conjugate of the excited state wave function, the transition dipole moment operator (which scales like R) and the ground state wave function Dτ. The transition dipole moment relates to the oscillator strength (the area under the absorption curve) which is related to the extinction coefficient. Organic dyes that are used in second order NLO systems are materials that have a high refractive index and strong low energy absorptions.

	=== Poling of Chromophores in Polymers ===		=== Poling of Chromophores in Polymers ===
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	where		where
	:<math>r_{33}\,\!</math> is the ~~electro-optic~~ coefficient		:<math>r_{33}\,\!</math> is the electrooptic coefficient
	:<math>\beta(\epsilon,\omega)\,\!</math> is the molecular first hyperpolarizability		:<math>\beta(\epsilon,\omega)\,\!</math> is the molecular first hyperpolarizability
	:<math>N\,\!</math> is the number density of chromophores in the polymer		:<math>N\,\!</math> is the number density of chromophores in the polymer
	:<math><cos^3\theta>\,\!</math> is the order parameter		:<math><cos^3\theta>\,\!</math> is the order parameter

	The [[~~electro-optic~~ cofficient]] r<sub>33</sub> is determined by the molecular property first hyperpolarizability <math>\beta(\epsilon,\omega)\,\!</math> and a number density. So for the maximum effect all the molecules must be lined up in the same direction. You can use quantum mechanics to optimize the first part (hyperpolarizability), and statistical mechanics to optimize the second part (number density), and have a feedback loop between the two approaches.		The [[electrooptic cofficient]] r<sub>33</sub> is determined by the molecular property first hyperpolarizability <math>\beta(\epsilon,\omega)\,\!</math> and a number density. So for the maximum effect all the molecules must be lined up in the same direction. You can use quantum mechanics to optimize the first part (hyperpolarizability), and statistical mechanics to optimize the second part (number density), and have a feedback loop between the two approaches.

	<br clear='all'>		<br clear='all'>
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	=== Statistical mechanical calculations ===		=== Statistical mechanical calculations ===
	[[Image:EOC_loading.png\|thumb\|300px\|Number density affect ~~electro-optic~~ activity]]		[[Image:EOC_loading.png\|thumb\|300px\|Number density affect electrooptic activity]]
	As chromophore number density increases they begin to interact because of their polarity. At extreme close range this forces molecules to flip and this reduces the EO activity of the material. A balance must be struck between number density and beta of molecules to enhance macroscopic EO activity.		As chromophore number density increases they begin to interact because of their polarity. At extreme close range this forces molecules to flip and this reduces the EO activity of the material. A balance must be struck between number density and beta of molecules to enhance macroscopic EO activity.

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	=== Conclusion ===		=== Conclusion ===

	The combination of new QM and SM methods permits quantitative prediction of macroscopic ~~electro-optic~~ activity--Yes, we really do need “Numbers”!		The combination of new QM and SM methods permits quantitative prediction of macroscopic electrooptic activity--Yes, we really do need “Numbers”!

	*Previous analysis has tended neglect dielectric effects, to over estimate acentric order and underestimate molecular first hyperpolarizability.		*Previous analysis has tended neglect dielectric effects, to over estimate acentric order and underestimate molecular first hyperpolarizability.
	*Laser-assisted electric field poling can be used to improve acentric order.		*Laser-assisted electric field poling can be used to improve acentric order.
	*Binary chromophore organic glasses permit significant improvement in both ~~electro-optic~~ activity and optical transparency.		*Binary chromophore organic glasses permit significant improvement in both electrooptic activity and optical transparency.
	*Electro-optic activity of 1000 pm/V (2 orders of magnitude improvement) with optical loss of 2 dB/cm is possible by theoretically-inspired design. This is starting to approach the value of liquid crystals but with a factor of 10<sup>11</sup> improvement in processing speed.		*Electro-optic activity of 1000 pm/V (2 orders of magnitude improvement) with optical loss of 2 dB/cm is possible by theoretically-inspired design. This is starting to approach the value of liquid crystals but with a factor of 10<sup>11</sup> improvement in processing speed.