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