# Complex Transmittance of a Multi-Layered Plate

• esradw
In summary, the speaker is asking for help in finding the complex transmittance of a thin plate with multiple layers of different thicknesses and refractive indices. They are unsure how to find the matrix for each layer and how to combine them to reach the answer. They also question the use of the word "complex" and its potential meaning in this context.
esradw
Hello, I really need help on this question,

the wave travels normal to a thin plate made of N thin parallel layers of thickness d1,d2...dN and refractive indices n1,n2...nN, Ignore all the reflactions ,what is the complex ( which I thought transmittane is always real )transmittance of the plate ?

Each of layers having different d and n confuces me, I don't know how to find the matrix for each? M1.M2.M3...MN=M so that I can reach the answer.

Any help ?

thanks

esradw said:
Hello, I really need help on this question,

the wave travels normal to a thin plate made of N thin parallel layers of thickness d1,d2...dN and refractive indices n1,n2...nN, Ignore all the reflactions ,what is the complex ( which I thought transmittane is always real )transmittance of the plate ?

Each of layers having different d and n confuces me, I don't know how to find the matrix for each? M1.M2.M3...MN=M so that I can reach the answer.

Any help ?

thanks
I'm not really familiar with matrix represntations for energy losses. Would you know how to do this for a single layer? I suspect that the word complex might only be referring to the multiple layers of film rather than comlex numbers. Optical systems with multiple elements are often referred to as complex systems. Using this language, M would be the "complex" matrix that combines the effect of all the other Ms.

## What is the concept of complex transmittance?

The complex transmittance of a multi-layered plate is a measure of the amount of light that passes through the plate and the resulting phase shift of the transmitted light. It takes into account both the amplitude and phase of the transmitted light, which is important for understanding the behavior of light as it passes through a multi-layered structure.

## How is the complex transmittance calculated?

The complex transmittance is calculated by taking the ratio of the transmitted electric field amplitude to the incident electric field amplitude, and then taking the complex phase difference between the two. This can be expressed as T = |T|e, where T is the complex transmittance, |T| is the amplitude, and φ is the phase difference.

## What factors affect the complex transmittance of a multi-layered plate?

The complex transmittance of a multi-layered plate is affected by several factors, including the thickness and refractive index of each layer, the angle of incidence of the light, and the polarization of the light. The number of layers and the order of the layers can also have an impact on the complex transmittance.

## Why is the complex transmittance important in studying multi-layered plates?

The complex transmittance is important in studying multi-layered plates because it provides a more complete understanding of how light behaves as it passes through the plate. It takes into account both the amplitude and phase of the transmitted light, which can affect the overall transmission and reflection properties of the plate. This information is crucial in designing and optimizing multi-layered structures for various applications.

## How is the complex transmittance experimentally measured?

The complex transmittance can be experimentally measured using techniques such as ellipsometry or interferometry. These techniques involve measuring the changes in the polarization or phase of the light as it passes through the multi-layered plate. The resulting data can then be used to calculate the complex transmittance of the plate.

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