How Do You Calculate Beta in an Asymmetric Planar Waveguide Using MATLAB?

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SUMMARY

The discussion focuses on calculating the propagation constant (beta) for TE modes in an asymmetric planar waveguide using MATLAB. The parameters specified include refractive indices nf=1.5, ns=1.47, and nc=1.0, with a waveguide thickness of 7 micrometers and an excitation wavelength of 1 micrometer. The equation provided for beta is Beta = (Ko^2 * nf^2 - Kf^2)^(1/2), where Ko is defined as (2π/λ)n. Participants clarified the use of the "fzero" function in MATLAB to find the zeros of the function, which correspond to the allowed values for beta.

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  • Understanding of waveguide theory and TE modes
  • Familiarity with MATLAB programming, specifically the "fzero" function
  • Knowledge of refractive indices and their application in optical physics
  • Basic calculus for solving equations and plotting functions
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This discussion is beneficial for optical engineers, physics students, and MATLAB users interested in waveguide design and analysis, particularly those working with asymmetric planar waveguides.

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Consider an asymmetric planar waveguide with nf=1.5, ns=1.47, nc=1.0. Determine the allowed values of beta for the TE modes in a waveguide with thickness h=7 micrometers. Assume the excitation wavelength is 1 micrometer.

Our prof gave us this equation;
Beta = (Ko2nf2-Kf2)1/2

Ko =(2pi/lambda)n

But which n do we use in this case and similarly for Kf.
 
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Hi,

So I figured out what I'm supposed to do. Using the given equation, plus 2 other equations we that we were given, and then using another equation and plotting them on a graph we can see that where the 2 functions cross is the allowed values for beta.

We have use MATLAB for this question and I'm not to familiar with matlab. So can someone please tell how you use the "fzero" function. This will allow you find the zeros of the function and thus the allowed values for beta.


But how do you type this in matlab?
 

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