# Gaussian beam in a Fabry-Perot interferometer

• I
• Malamala
In summary: The transmission of a Gaussian beam through a Fabry-Perot interferometer (FPI) has been investigated. The equation for the electric field of the transmitted beam was derived and then the transmitted irradiance was numerically calculated for different selected parameters of both the FPI and the beam. The results show that the energy profile of the transmitted beam has been distorted to different degrees depending on the various parameters of the Gaussian beam and the FPI. Moreover the results show that the positions of the peaks of the transmitted beam are shifted, especially for intermediate waists for which the arctan term is nonlinear. The results also show that for nonnormal incidence successive transmitted beams are spatially separated and are not interfering appreciably with
Malamala
Hello I am reading some introductory laser cavity stuff and I am a bit confused about the existence of gaussian beams in the Fabry-Perot interferometer. If you solve the stability condition for a cavity (i.e. asking for the q parameter to reproduce itself after one round trip) you get that in order to obtain a stable cavity you need that the radius of curvature of the gaussian beam at each of the 2 mirrors should be the same as the radius of the mirrors. In general this is easily achievable (for stable cavities) by placing the beam waist at the right place. However in the case of Fabry-Perot interferometer, the radius would be infinity, while the gaussian beam has radius infinity just at the waist, and it is not possible to make it has infinite radius at 2 points. Does this mean that Fabry-Perot interferometer is not stable for gaussian beams? Yet it appears on the list of stable resonators. Can someone explain this to me? (I am sorry if the question is dumb, it is my first encounter with the topic). Thank you!

I suppose that the stable FP cavity mentioned in the list refers to the one using curved coupling mirrors, whose radius is finite.

wcghha said:
I suppose that the stable FP cavity mentioned in the list refers to the one using curved coupling mirrors, whose radius is finite.
Yes, I understand that case. But FP cavities with flat mirrors (i.e. almost infinite radius) exist in practice. I am not sure I understand how does the field looks inside the cavity, as a Gaussian beam doesn't make sense.

Malamala said:
Hello I am reading some introductory laser cavity stuff and I am a bit confused about the existence of gaussian beams in the Fabry-Perot interferometer.

Interesting point. If you have seen a 'resonator stability diagram', you will find that planar resonators are "conditionally stable", but it's unclear if there are Gaussian modes for a planar resonator. Here's a link to the worked-out problem:

(Abstract):
The transmission of a Gaussian beam through a Fabry–Perot interferometer (FPI) has been investigated. The equation for the electric field of the transmitted beam was derived and then the transmitted irradiance was numerically calculated for different selected parameters of both the FPI and the beam. The results show that the energy profile of the transmitted beam has been distorted to different degrees depending on the various parameters of the Gaussian beam and the FPI. Moreover the results show that the positions of the peaks of the transmitted beam are shifted, especially for intermediate waists for which the arctan term is nonlinear. The results also show that for nonnormal incidence successive transmitted beams are spatially separated and are not interfering appreciably with each other.

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-33-18-3805

## What is a Gaussian beam?

A Gaussian beam is a type of laser beam that has a bell-shaped intensity profile. It is characterized by a central peak intensity and a gradual decrease in intensity towards the edges.

## What is a Fabry-Perot interferometer?

A Fabry-Perot interferometer is a device that uses multiple reflections between two parallel mirrors to enhance the interference of light waves. It is commonly used in optical systems for measuring the wavelength of light and for spectral analysis.

## How does a Gaussian beam behave in a Fabry-Perot interferometer?

A Gaussian beam in a Fabry-Perot interferometer will experience multiple reflections between the mirrors, resulting in an interference pattern with a central peak and fringes on either side. The intensity of the beam will also be modified depending on the reflectivity of the mirrors and the spacing between them.

## What factors affect the behavior of a Gaussian beam in a Fabry-Perot interferometer?

The behavior of a Gaussian beam in a Fabry-Perot interferometer is affected by several factors, including the reflectivity of the mirrors, the spacing between the mirrors, the wavelength of the beam, and the beam's angle of incidence.

## What are some applications of Gaussian beams in Fabry-Perot interferometers?

Gaussian beams in Fabry-Perot interferometers are commonly used in laser spectroscopy, optical communications, and laser-based measurement systems. They are also used in scientific research for studying the properties of light and for precision measurements.

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