Planar Waveguides Michael Moewe EE290F, Professor Kaminow March 2 nd, 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 ( )

Uses for planar waveguides Routing Light Devices Modulators Erbium Doped Planar Waveguide Amplifiers (EDWA) (with curved guides) Resonators

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 H z 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 in Corners

References Okamoto K Fundamentals of Optical Waveguides (San Diego, CA: Academic) Prototype trial manufacture of polymer optical waveguide. 2 Mar NTT-AT. at.co.jp/optic2/prd_e0015.htmlhttp:// at.co.jp/optic2/prd_e0015.html Nanonics – Industry Applications. 2 Mar Nanonics. -industry.html -industry.html Syms R., Tate T., Syahriar A. Waveguide Devices by Electron Beam Irradiation of Silica. 2 Mar Imperial College of Science, Technology & Medicine.