Rectangular Waveguides: Effective Index Method

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SUMMARY

The discussion focuses on the effective index method for rectangular waveguides, particularly when the width significantly exceeds the thickness. The user seeks clarification on obtaining a y-dependent effective index, starting with the planar waveguide solution. The recommended approach involves solving the planar problem in the x-direction to derive neff(y) and subsequently addressing the y-direction problem. The user contemplates simplifying the process by using the core index from the planar waveguide solution, indicating a need for further understanding of the effective index calculation.

PREREQUISITES
  • Understanding of rectangular waveguides and their geometrical parameters
  • Familiarity with the effective index method in waveguide theory
  • Knowledge of planar waveguide solutions and their mathematical formulations
  • Basic principles of wave propagation and refractive index variations
NEXT STEPS
  • Research the derivation of the effective index for rectangular waveguides
  • Study the mathematical techniques for solving planar waveguide problems
  • Explore numerical methods for calculating refractive indices in waveguide structures
  • Examine case studies or examples of y-dependent effective index calculations
USEFUL FOR

Students and researchers in optics and photonics, particularly those working with waveguide design and analysis, will benefit from this discussion. It is also relevant for engineers involved in the development of optical communication systems.

Phyisab****
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Homework Statement


Is anyone familiar with the effective index method for rectangular waveguides? I have a waveguide for which the width is much greater than the thickness. I think I need to start by treating it as a planar waveguide. But I am supposed to get an effective index which depends on the y coordinate. I know how to solve the planar waveguide, but what do I do differently that gives me a y dependent effective index for the planar waveguide solution?
 
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Is nobody familiar with this method? I only need a brief explanation of how it works.

The explanation I have in my text says "solve the planar problem in the x direction to obtain neff(y). Then solve the planar problem in the y direction"

I just don't understand how to get n effective as a function of y. Right now I'm thinking that it's only a function of y in the sense that it changes outside the core of the waveguide. So I'm leaning towards just solving the planar waveguide, and using the numerical value as the core index for the second planar waveguide problem. If I do this, it's pretty simple. But I have no idea if I'm on the right track at all.
 

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