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

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In summary, the conversation discusses determining the allowed values of beta for the TE modes in an asymmetric planar waveguide with given parameters, using various equations and the "fzero" function in MATLAB to find the zeros of a function on a graph. The excitation wavelength and thickness of the waveguide are also given.
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Gogsey
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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?
 

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

What is an asymmetric planar waveguide?

An asymmetric planar waveguide is a type of optical waveguide that consists of a thin layer of high refractive index material on top of a low refractive index substrate. This creates a difference in refractive index between the two layers, allowing for the propagation of light along the interface.

How does an asymmetric planar waveguide work?

An asymmetric planar waveguide works by using the principle of total internal reflection. When light enters the high refractive index layer at a certain angle, it is reflected back and forth between the two layers, propagating along the interface. This allows for efficient light transmission through the waveguide.

What are the applications of asymmetric planar waveguides?

Asymmetric planar waveguides have a wide range of applications in optics and photonics. They are commonly used in integrated optical circuits, optical sensors, and telecommunications devices. They can also be used for sensing, imaging, and light manipulation in biomedical and environmental applications.

What are the advantages of using asymmetric planar waveguides?

Asymmetric planar waveguides offer several advantages over other types of waveguides. They have low propagation losses, high confinement of light, and can support a wide range of wavelengths. They are also compatible with standard semiconductor fabrication techniques, making them easy to integrate into devices.

What are the limitations of asymmetric planar waveguides?

One of the main limitations of asymmetric planar waveguides is their sensitivity to fabrication imperfections. Any variations in the layer thickness or refractive index can affect the performance of the waveguide. They also have a limited mode field size, which can result in higher losses for certain applications.

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