Understanding Ellipsometry: Intensity Relation for Polarized Light Reflection"

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In summary, the expression for the intensity of light from the analyzer, given by I=k_{0}+k_{1}cos2A+k_{2}sin2A, is a result of the Malus' law and the Fresnel equations. Malus' law states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incident light and the axis of the polarizer. The reflection coefficients for the s and p components of light from the sample are related by the Fresnel equations, and the angle of incidence and reflection are related by these equations as well. Substituting these expressions into the Malus' law, we get the final expression for the
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McLaren Rulez
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This is from a paper that can be found at http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-26-24-5221 (needs a university proxy/payment to view)

The setup is essentially light passing through a polarizer, a thin film sample and then an analyzer followed by a detector. The analyzer is a second polarizer that can be rotated. The paper starts with an expression for the intensity of the light from the analyzer.

[itex]I=k_{0}+k_{1}cos2A+k_{2}sin2A[/itex]

where [itex]k_{0}=n(cos^{2}P+tan^{2}\psi sin^{2}P)[/itex]
[itex]k_{1}=n(cos^{2}P-tan^{2}\psi sin^{2}P)[/itex]
[itex]k_{2}=n*tan\psi*sin2P*cos\Delta[/itex]

where n is an arbitrary factor that relates to the intensity of the light, P and A are the angle of the polarizer and analyzer respectively from the with respect to the plane of incidence and the reflection coefficients of the s and p components of the light from the sample are related by

[itex]\frac{r_{p}}{r_{s}}=tan\psi * e^{i\Delta}[/itex]

Can anyone help me see how this intensity relation is obtained? It is just polarizers and reflections but I'm having trouble seeing how it is derived. Thank you.
 
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Hello,

I can definitely help you understand how this intensity relation is obtained. The expression for the intensity of light from the analyzer, given by I=k_{0}+k_{1}cos2A+k_{2}sin2A, is a result of the Malus' law and the Fresnel equations.

Malus' law states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incident light and the axis of the polarizer. In this case, the incident light is polarized by the first polarizer and then passes through the sample before reaching the analyzer. Therefore, the intensity of light transmitted through the analyzer is given by the Malus' law expression, which is k_{0}+k_{1}cos2A, where k_{0} is the intensity of the unpolarized light passing through the polarizer and k_{1} is the intensity of the polarized light transmitted through the polarizer.

Now, the reflection coefficients for the s and p components of light from the sample are related by the Fresnel equations, given by \frac{r_{p}}{r_{s}}=tan\psi * e^{i\Delta}. Here, r_{p} and r_{s} are the reflection coefficients for the p and s polarized light, respectively. The angle of incidence, P, and the angle of reflection, A, are related by the Fresnel equations as well, and the angle of incidence is equal to the angle of the polarizer, P. Therefore, the angle of reflection, A, can be expressed in terms of P as well.

Substituting these expressions into the Malus' law, we get the final expression for the intensity of light from the analyzer as I=k_{0}+k_{1}cos2P+k_{2}sin2Pcos\Delta, where k_{2} is the intensity of the polarized light transmitted through the analyzer.

I hope this helps you understand how the intensity relation is obtained. If you have any further questions, please don't hesitate to ask. Good luck with your research!
 

What is Ellipsometry?

Ellipsometry is a non-destructive optical technique used to measure the thickness and refractive index of thin films and surfaces.

How does Ellipsometry work?

Ellipsometry works by measuring the change in polarization of light as it is reflected off a sample. This change in polarization is then used to calculate the thickness and refractive index of the sample.

What are the applications of Ellipsometry?

Ellipsometry has many applications in various fields such as materials science, semiconductor industry, biology, and medicine. It is used for characterizing thin films, determining surface roughness, detecting changes in molecular layers, and more.

What are the advantages of using Ellipsometry?

Ellipsometry is a non-destructive technique, meaning the sample does not need to be altered or damaged in any way. It is also highly sensitive, providing precise measurements of surface properties. Additionally, it is a fast and accurate method with a wide range of applications.

What are the limitations of Ellipsometry?

Ellipsometry is limited to transparent or semi-transparent samples, and it cannot be used on opaque materials. It also requires a high level of expertise and specialized equipment to perform. Additionally, environmental factors such as temperature and humidity can affect the accuracy of measurements.

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