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Planar Waveguides

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

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Planar Waveguides

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  1. Planar Waveguides Michael Moewe EE290F, Professor Kaminow March 2nd, 2004

  2. 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

  3. 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)

  4. Uses for planar waveguides • Routing Light • Devices • Modulators • Erbium Doped Planar Waveguide Amplifiers (EDWA) (with curved guides) • Resonators http://www.netzartfedorov.com/clients/nanonics/newnanon/text-industry.html http://www.ee.ic.ac.uk/optical/Optics.html

  5. Maxwells Equations in Slab Waveguide • Maxwell’s Equations • Simplifications

  6. Simplifcation of Maxwell’s Equations • Substituting into Maxwell’s Equations

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

  8. Wavenumbers • Fields are confined to core, so: • With wavenumbers:

  9. Boundary Conditions • Hz components continuous at boundaries, so based on previous eq: • Continuity of these boundaries gives:

  10. Substitutions • Substitution: • Gives the relations:

  11. Dispersion Curves for TE and TM modes • Dispersion Curves

  12. Power Carried in Waveguide • Power Equation • Simplifies to (for TE mode):

  13. Rectangular Waveguides (Marcatili’s method) (Assumed no field in corner areas)

  14. Electric Field Distributions in Rectangular Waveguides • Marcatili’s Method: (assumes no field in corners of waveguide)

  15. Kumar’s method for Rectangular Waveguides • Finite Field in Corners

  16. 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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