1. Planar Waveguides Michael Moewe EE290F, Professor Kaminow March 2 nd, 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.ee.ic.ac.uk/optical/Optics.htmlhttp://www.netzartfedorov.com/clients/nanonics/newnanon/text-industry.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 ) TE Mode TM Mode

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

9. Boundary Conditions H z 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.htmlhttp://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 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 http://www.ee.ic.ac.uk/optical/Optics.html