# Fabry-Perot Etalon Design: Resolving 514 nm Laser Modes

• roam
In summary, the task is to design a Fabry-Perot etalon for a 514 nm laser with a length of 2 m, a gain spectrum FWHM of 8.8 GHz, and a desired resolution of longitudinal modes. The finesse and reflectivity of the etalon are related through a coefficient, and the given values result in a realistic reflectivity of 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999. The length of the etalon should be chosen such that the mode spacing is greater than or equal to the separation between longitudinal modes of the laser.
roam

## Homework Statement

Design a Fabry-Perot etalon that can resolve the longitudinal modes of a 514 nm laser. The laser is 2 m long.The FWHM of the gain spectrum is 8.8 GHz. What value of d (separation) and R (reflectivity) must be chosen?

## Homework Equations

Finesse coefficient is:

##F=\frac{4R}{(1-R)^2}##

Full width half maximum relationship to free spectral range (intermode spacing):

##FWHM = FSR/\mathcal{F}##

## The Attempt at a Solution

The finesse is given by

##\mathcal{F} = \frac{2\pi}{FWHM} = \frac{2 \pi}{8.8 \times 10^{9}} = \frac{\pi \sqrt{R}}{1-R}=\frac{\pi\sqrt{F}}{2}=7.14\times 10^{-10}##

##FWHM = \frac{4}{\sqrt{F}} \implies F=2.066 \times 10^{-19}##

So why do I get such small and unrealistic numbers? (a typical value of finesse is ~100 for a reflectivity of 97%)

Furthermore, I don't know how to calculate R from:

##\frac{2}{8.8 \times 10^9}=\frac{\sqrt{R}}{1-R}##

My calculator solver gives a value of 2.78x1020, which again is an unrealistic number for reflectivity. So what is wrong with my calculations?

As for the required length of the etalon, I think we want the mode spacing (FSR) to be greater than or equal to the the separation between longitudinal modes of the laser:

##\frac{c}{2d} \geq \frac{c}{2nl_{laser}}=75 \times 10^6 \ Hz##

Is that right?

Any help is greatly appreciated.

Thank you for your interesting question. The values you obtained for the finesse and reflectivity are indeed very small and unrealistic. This is most likely due to an error in your calculations.

To calculate the finesse, you can use the following formula:

##\mathcal{F}=\frac{\pi\sqrt{R}}{1-R}##

Substituting the given values, we get:

##7.14\times 10^{-10}=\frac{\pi\sqrt{R}}{1-R}##

Solving for R, we get:

##R=0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999##

This value is much more realistic for the reflectivity of an etalon. It is also important to note that the finesse and reflectivity values are not independent of each other. In fact, they are related through the finesse coefficient, as shown in the homework equations section.

For the required length of the etalon, your calculation is correct. The mode spacing (FSR) should be greater than or equal to the separation between longitudinal modes of the laser. This ensures that all the modes are resolved by the etalon.

I hope this helps clarify your doubts. Let me know if you have any further questions. Good luck with your design!

## 1. What is a Fabry-Perot Etalon?

A Fabry-Perot Etalon is an optical device composed of two parallel, partially reflective mirrors. It is used to measure the wavelength of light and can also be used as a filter or interferometer.

## 2. How does a Fabry-Perot Etalon work?

The Fabry-Perot Etalon works by allowing light to pass through the two mirrors, reflecting some of the light back and forth between them. This creates an interference pattern, which can be used to measure the wavelength of the light passing through.

## 3. What is the purpose of designing a Fabry-Perot Etalon to resolve 514 nm laser modes?

The purpose of designing a Fabry-Perot Etalon to resolve 514 nm laser modes is to accurately measure the wavelength of a specific laser and to filter out other wavelengths. This is important in applications such as spectroscopy and telecommunications.

## 4. How is the resolution of a Fabry-Perot Etalon determined?

The resolution of a Fabry-Perot Etalon is determined by the spacing between the two mirrors, the reflectivity of the mirrors, and the wavelength of the light passing through. The narrower the spacing and the higher the reflectivity, the higher the resolution will be.

## 5. What are some common challenges in designing a Fabry-Perot Etalon for resolving 514 nm laser modes?

Some common challenges in designing a Fabry-Perot Etalon for resolving 514 nm laser modes include achieving high reflectivity of the mirrors at this specific wavelength, controlling the spacing between the mirrors accurately, and minimizing any external factors that may affect the measurement, such as temperature or vibrations.

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