Planar Dielectric Waveguides - Revision history

Cmditradmin at 19:55, 29 December 2009

2009-12-29T19:55:32Z

← Older revision		Revision as of 12:55, 29 December 2009
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	:<math>V < 2.06 \mu m\,\!</math>		:<math>V < 2.06 \mu m\,\!</math>
	[[category:Photonics ~~Applications~~]]		[[category:Photonics applications]]
	<table id="toc" style="width: 100%">		<table id="toc" style="width: 100%">
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Cmditradmin at 19:17, 29 December 2009

2009-12-29T19:17:27Z

← Older revision		Revision as of 12:17, 29 December 2009
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	:<math>V < 2.06 \mu m\,\!</math>		:<math>V < 2.06 \mu m\,\!</math>
			[[category:Photonics Applications]]
	<table id="toc" style="width: 100%">		<table id="toc" style="width: 100%">
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Cmditradmin: /* Planar dielectric waveguides */

2009-08-25T22:49:09Z

Planar dielectric waveguides

← Older revision		Revision as of 15:49, 25 August 2009
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	Where		Where
	:<math>\theta_i\,\!</math> is the internal ray angle (from now on written as theta)		:<math>\theta_i\,\!</math> is the internal ray angle (from now on written as θ)
	[[Image:Internalreflection_2cases.png\|thumb\|300px\|]]		[[Image:Internalreflection_2cases.png\|thumb\|300px\|]]

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	[[Image:Internalreflection_wavefront.png\|thumb\|300px\|]]		[[Image:Internalreflection_wavefront.png\|thumb\|300px\|]]

	The wavefront FC intersects tow the upwardly ~~travelling~~ portions of the same ray at points A and C. Therefore the phase at C and A must be the same or differ by a multiple of 2π.		The wavefront FC intersects tow the upwardly traveling portions of the same ray at points A and C. Therefore the phase at C and A must be the same or differ by a multiple of 2π.

	Otherwise there would be destructive interference between out-of-phase waves and the light will not propagate. It also requires very specific angles theta above the critical angle.		Otherwise there would be destructive interference between out-of-phase waves and the light will not propagate. It also requires very specific angles θ above the critical angle.

	Consider the phase difference between A and C		Consider the phase difference between A and C
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	Where		Where

	:<math>~~Lambda_0~~\,\!</math> is the wavelength of light in the medium		:<math>\lambda_0\,\!</math> is the wavelength of light in the medium

	To determine the path of the light from a to b to c using trigonometry:		To determine the path of the light from a to b to c using trigonometry:
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	m is an integer		m is an integer

	So for each value of m there will be an angle ~~theta_m~~ that satisfies the equation		So for each value of m there will be an angle θ<sub>m</sub> that satisfies the equation

	Each value of θ<sub> m</sub> (those >θ <sub>c</sub>) has a distinct distribution of electric field across the guide. This distribution is known as a mode. Depending on the mode there may a distribution that is centered in the core or may have 2 spots, 4 spots etc when view in cross section.		Each value of θ<sub>m</sub> (those >θ <sub>c</sub>) has a distinct distribution of electric field across the guide. This distribution is known as a mode. Depending on the mode there may a distribution that is centered in the core or may have 2 spots, 4 spots etc when view in cross section.

	When:<math> \theta_m is = \theta_c\,\!</math> : the mode is at cut-off		When:<math> \theta_m is = \theta_c\,\!</math> : the mode is at cut-off

Cmditradmin at 21:16, 20 August 2009

2009-08-20T21:16:32Z

← Older revision		Revision as of 14:16, 20 August 2009
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	:<math>V < 2.06 \mu m\,\!</math>		:<math>V < 2.06 \mu m\,\!</math>

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Cmditradmin: /* Mode Cut-off */

2009-08-10T18:59:53Z

Mode Cut-off

← Older revision		Revision as of 11:59, 10 August 2009
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	Thus the mode shift depends on the relative index of refraction of the materials and the thickness of the waveguide. If you decrease the thickness you decrease the number of modes that can propagate.		Thus the mode shift depends on the relative index of refraction of the materials and the thickness of the waveguide. If you decrease the thickness you decrease the number of modes that can propagate.

	The number of guided modes in a guide (N) is given by		The number of guided modes in a step-index guide (N) is given by

	:<math>N= 1 + int (2V/\pi)\,\!</math>		:<math>N= 1 + int (2V/\pi)\,\!</math>

Cmditradmin: /* Mode Cut-off */

2009-08-06T23:46:52Z

Mode Cut-off

← Older revision		Revision as of 16:46, 6 August 2009
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	Where		Where
	V is the normalized film thickness, normalized frequency, or V parameter
			V is the normalized film thickness, normalized frequency, or V parameter

	D is the thickness of the waveguide		D is the thickness of the waveguide

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	:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>		:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>

	Example		'''Example'''

	Find the maximum waveguide core thickness d for a device with n1 =1.48 and n2 = 1.46 and a wavelength of 1 mu m to achieve single mode propagation.		Find the maximum waveguide core thickness d for a device with n<sub>1</sub> =1.48 and n<sub>2</sub> = 1.46 and a wavelength of 1 μ m to achieve single mode propagation.

	:<math>d< \frac {1}{2( 1.48^2 – 1.46^2)^{1/2}} \mu m \,\!</math>		:<math>d< \frac {1}{2( 1.48^2 – 1.46^2)^{1/2}} \mu m \,\!</math>

	:<math>V < 2.06 \mu m\,\!</math>		:<math>V < 2.06 \mu m\,\!</math>

Cmditradmin: /* Mode Cut-off */

2009-08-06T23:45:13Z

Mode Cut-off

← Older revision		Revision as of 16:45, 6 August 2009
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	:<math>N= 1 + int (2V/\pi)\,\!</math>		:<math>N= 1 + int (2V/\pi)\,\!</math>

	Only one mode propagates if <math> V < \pi \ 2 \,\!</math>, in this case it is called a single mode guide.		Only one mode propagates if <math> V < \frac {\pi} {2} \,\!</math>, in this case it is called a single mode guide.

	:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>		:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>

Cmditradmin: /* Mode Cut-off */

2009-08-06T23:44:40Z

Mode Cut-off

← Older revision		Revision as of 16:44, 6 August 2009
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	:<math>N= 1 + int (2V/\pi)\,\!</math>		:<math>N= 1 + int (2V/\pi)\,\!</math>

	Only one mode propagates if <math> V < \pi \2 \,\!</math>, in this case it is called a single mode guide.		Only one mode propagates if <math> V < \pi \ 2 \,\!</math>, in this case it is called a single mode guide.

	:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>		:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>

Cmditradmin: /* Mode Cut-off */

2009-08-06T23:44:24Z

Mode Cut-off

← Older revision		Revision as of 16:44, 6 August 2009
Line 132:		Line 132:
	:<math>N= 1 + int (2V/\pi)\,\!</math>		:<math>N= 1 + int (2V/\pi)\,\!</math>

	Only one mode propagates if :<math>V < \pi \2 \,\!</math>, in this case it is called a single mode guide.		Only one mode propagates if <math> V < \pi \2 \,\!</math>, in this case it is called a single mode guide.

	:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>		:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>
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	Find the maximum waveguide core thickness d for a device with n1 =1.48 and n2 = 1.46 and a wavelength of 1 mu m to achieve single mode propagation.		Find the maximum waveguide core thickness d for a device with n1 =1.48 and n2 = 1.46 and a wavelength of 1 mu m to achieve single mode propagation.

	:<math>d< \frac {1}{2( 1.48^2 – 1.46^2)^{1/2} \mu m \,\!</math>		:<math>d< \frac {1}{2( 1.48^2 – 1.46^2)^{1/2}} \mu m \,\!</math>

	:<math>V < 2.06 \mu m\,\!</math>		:<math>V < 2.06 \mu m\,\!</math>

Cmditradmin: /* Mode Cut-off */

2009-08-06T23:42:17Z

Mode Cut-off

← Older revision		Revision as of 16:42, 6 August 2009
Line 134:		Line 134:
	Only one mode propagates if :<math>V < \pi \2 \,\!</math>, in this case it is called a single mode guide.		Only one mode propagates if :<math>V < \pi \2 \,\!</math>, in this case it is called a single mode guide.

	:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}\,\!</math>		:<math>\frac {d} {\lambda_0} < \frac {1} {2(n^{2}_{1} – n^{2}_{2})^{1/2}}\,\!</math>

	Example		Example