Fabry-Perot Interferometer is a high-resolution interferometer that works based on the principle of multiple beam interference. Multiple beam interference is a phenomenon that occurs when multiple coherent beams of light interact with each other, resulting in the formation of an interference pattern. It is used for measuring precise wavelengths, analyzing two very close wavelengths, determining refractive indices of gases, and calibration of standard meter scale in terms of wavelengths, etc. 

Construction of Fabry-Perot Interferometer

Figure 1: Setup of Fabry-Perot Interferometer

The interferometer is made up of two glass plates that are very flat and parallel to each other. They create a flat gap of air between them. The inside surfaces of the glass plates have a shiny metal coating that reflects 80% of light. The interferometer operates due to the multiple reflections that take place between these plates.

The glass plates used in the interferometer are not the same thickness all over, and the outside of the plates are inclined at a small angle (~0.1º) with respect to the inner surfaces. This is done to eliminate any interference fringes that might arise from glass plates themselves if they are parallel and equally inclined. One of the plates is fixed while the other can be moved using a precision micrometer screw. This changes the thickness of the gap of air between the plates. Sometimes both plates are stationary, and in that case, the instrument is called a Fabry-Perot etalon. The setup of Fabry-Perot interferometer is shown in figure 1.

Working of Fabry-Perot Interferometer

Figure 2: Working of Fabry-Perot Interferometer

The system of glass plates is kept perpendicular to the optical axis. Figure 2 illustrates the working of fabry-perot interferometer. Suppose a narrow light beam from a light source S focused using a collimating lens is incident at an angle θ on the system. Due to multiple reflections between the glass plates, a set of parallel transmitted beams emerge on the other side. These are then focused at a point P at the focal plane of the converging lens L. Similarly, all the incident beams from the other points of the source, inclined at same angle θ, are also focused at P. This creates circular fringes on the screen with lines that are equally spaced apart as shown in figure 3.

Figure 3: Interference fringes from Fabry-Perot Interferometer

The conditions for maxima or minima at P are given by,

Where t is the thickness of air plate, θ is the incident angle, λ is the wavelength of light, and m is an integer.

The highest order maxima is formed when cos θ = 1, θ = 0. That is, central spot is maxima of highest order; outer rings are of lower order.

The spacing between the plates, t, is a critical parameter in the Fabry-Perot interferometer. By adjusting the spacing, the interferometer can select specific wavelengths of light for transmission or reflection.

The free spectral range (FSR) is the range of wavelengths between two successive transmission maxima and is given by:

where c is the speed of light in vacuum and n is the refractive index of the medium between the plates.

Free spectral range varies inversely with the spacing between the plates t.

The finesse (F) of the Fabry-Perot interferometer is a measure of its ability to resolve spectral lines and is given by:

where √R is the half-width at half-maximum of the Airy function, which represents the intensity of the transmitted light as a function of the wavelength and the spacing between the mirrors.

Higher the value of finesse, the better the visibility.

Applications of Fabry Perot Interferometer

Fabry-Perot interferometer is used in astronomy to study the properties of celestial objects such as stars and galaxies. By measuring the wavelengths of light emitted by these objects, astronomers can determine their composition, temperature, and motion relative to Earth. It is also used in spectroscopy to measure the properties of materials, such as their absorption and emission spectra.

It is used in telecommunications to filter and demultiplex optical signals in fiber-optic communication systems. The interferometer can separate multiple signals sent over a single fiber by selecting specific wavelengths of light, allowing for higher data transmission rates and more efficient use of optical bandwidth.