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

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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?