Planar Waveguides
Michael MoeweEE290F, Professor Kaminow
March 2nd, 2004
Contents Planar Waveguides
Overview Uses
Infinitely wide planar waveguide theory Maxwells Equations in Slab Waveguide Simplifcation of Maxwell’s Equations TE and TM Mode Wavenumbers & Boundary Conditions Dispersion Curves Power Carried in Waveguide
Rectangular Waveguides Marcatili’s method of solving & E-field distribution Kumar’s method
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)
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.htmlhttp://www.netzartfedorov.com/clients/nanonics/newnanon/text-industry.html
Maxwells Equations in Slab Waveguide
Maxwell’s Equations
Simplifications
Simplifcation of Maxwell’s Equations
Substituting into Maxwell’s Equations
TE and TM Mode
TE/TM Mode, No y-axis dependency
(and )TE Mode TM Mode
Wavenumbers
Fields are confined to core, so:
With wavenumbers:
Boundary Conditions
Hz components continuous at boundaries, so based on previous eq:
Continuity of these boundaries gives:
Substitutions
Substitution:
Gives the relations:
Dispersion Curves for TE and TM modes
Dispersion Curves
Power Carried in Waveguide
Power Equation
Simplifies to (for TE mode):
Rectangular Waveguides (Marcatili’s method)
(Assumed no field in corner areas)
Electric Field Distributions in Rectangular Waveguides
Marcatili’s Method: (assumes no field in corners of waveguide)
Kumar’s method for Rectangular Waveguides
Finite Field inCorners
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.html
Nanonics – Industry Applications. 2 Mar. 2004. Nanonics. http://www.netzartfedorov.com/clients/nanonics/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.html
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