Planar Waveguides

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Planar Waveguides

• Michael Moewe
• EE290F, Professor Kaminow
• March 2nd, 2004

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Contents

• Planar Waveguides
• Overview
• Uses
• Infinitely wide planar waveguide theory
• Maxwells Equations in Slab Waveguide
• Simplifcation of Maxwells Equations
• TE and TM Mode
• Wavenumbers Boundary Conditions
• Dispersion Curves
• Power Carried in Waveguide
• Rectangular Waveguides
• Marcatilis method of solving E-field
  distribution
• Kumars method

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Planar Waveguides Overview

• Similar function as optical fibers
• Easily fabricated on substrates with a mask

Image from NTT-AT (http//www.keytech.ntt-at.co.jp
/optic2/prd_e0015.html)
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Uses for planar waveguides

• Routing Light
• Devices
• Modulators
• Erbium Doped Planar Waveguide Amplifiers (EDWA)
  (with curved guides)
• Resonators

http//www.ee.ic.ac.uk/optical/Optics.html
http//www.netzartfedorov.com/clients/nanonics/new
nanon/text-industry.html
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Maxwells Equations in Slab Waveguide

• Maxwells Equations
• Simplifications

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Simplifcation of Maxwells Equations

• Substituting into
• Maxwells Equations

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TE and TM Mode

• TE/TM Mode, No y-axis dependency
• (and )

TM Mode
TE Mode
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Wavenumbers

• Fields are confined to core, so
• With wavenumbers

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Boundary Conditions

• Hz components continuous at boundaries, so based
  on previous eq
• Continuity of these boundaries gives

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Substitutions

• Substitution
• Gives the relations

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Dispersion Curves for TE and TM modes

• Dispersion Curves

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Power Carried in Waveguide

• Power Equation
• Simplifies to (for TE mode)

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Rectangular Waveguides (Marcatilis method)

• (Assumed no field in corner areas)

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Electric Field Distributions in Rectangular
Waveguides

• Marcatilis Method (assumes no field in
  corners of waveguide)

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Kumars method for Rectangular Waveguides

• Finite Field in
• Corners

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References

• Okamoto K. 2000 Fundamentals of Optical
  Waveguides (San Diego, CA Academic)
• Prototype trial manufacture of polymer optical
  waveguide. 2 Mar. 2004. NTT-AT.
  http//www.keytech.ntt-at.co.jp/optic2/prd_e0015.h
  tml
• Nanonics Industry Applications. 2 Mar. 2004.
  Nanonics. http//www.netzartfedorov.com/clients/na
  nonics/newnanon/text-industry.html
• Syms R., Tate T., Syahriar A. Waveguide Devices
  by Electron Beam Irradiation of Silica. 2 Mar
  2004. Imperial College of Science, Technology
  Medicine. http//www.ee.ic.ac.uk/optical/Optics.ht
  ml