Plane Fabry-Perot Interferometer

The widely used plane Fabry-Perot interferometer (F.P.I.) is applied to absolute wavelength measurements and high-resolution studies of spectral line profiles. Since its spectral resolving power may exceed 10, spectral profiles of Doppler-broadened or pressure-broadened lines can be studied with this instrument. 

When the interference pattern is imaged by a lens with focal length f into the plane of the photoplate, we obtain for the ring diameters the relations 

Provided the distance d is accurately known (n = 1 if the F.P.I. is evacuated), the wavelength X can be obtained from the ring diameters. However, the wavelength is determined by (4.83) only modulo a free spectral range 2nd. This 

Equation (4.84) shows that the angular dispersion becomes infinite for e - 0. The linear dispersion of the ring system on the photoplate is 

A practical realization of the multiple beam-interference discussed in this section may use either a solid plane-parallel glass or fused quartz plate with two coated reflecting surfaces (Fabry-Perot etalon. Fig. 4.41a) or two separate plates, where one 

Both devices can be used for parallel as well as for divergent incident light. We now discuss them in more detail, first considering their illumination with parallel light. 

In laser spectroscopy, etalons are mainly used as wavelength-selective transmission filters within the laser resonator to narrow the laser bandwidth (Sect. 5.4). The wavelength Xm or frequency Vm for the transmission maximum of mth order, where the optical path between successive beams is As = mX, can be deduced from (4.48a) and Fig. 4.37 to be 

For all wavelengths X = Xm im = 1,2.) in the incident light, the phase difference between the transmitted partial waves becomes 8 = 2mjt and the transmitted intensity is, according to (4.61a)-(4.61d), 

X = Xrn find the reflected intensity becomes zero for = 0 while the transmitted intensity is /t = /q- 

however, that this is only true for A 1 and infinitely extended plane waves, where the different reflected partial waves completely overlap. If the incident wave is a laser beam with the finite diameter D, the different reflected partial beams do not completely overlap because they are laterally shifted by b —2d tan P cos a (Fig. 4.40). For a rectangular intensity profile of the laser beam, the fraction b/D of the reflected partial amplitudes does not 

For a Gaussian beam profile the calculation is more difficult, and the solution can only be obtained numerically. The result for a Gaussian beam with the radius w (Sect. 5.3) is [4.34] 

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Fig. 5. Polarized Rayleigh-Brillouin spectrum of amorphous PnHMA taken with a Burleigh plane Fabry-Perot interferometer using a free spectral range of 12.4 GHz at 295 K. The two Brillouin peaks are shifted from the incident frequency by the product of the wave vector q and the sound velocity u. The line width of the Brillouin peaks is related to the attenuation of the sound waves. PnHMA.

A simple model that makes it possible to describe optical bistability in a variety of systems is a plane nonlinear Fabry-Perot interferometer, filled with a medium whose refractive index is intensity dependent [106]. The slow kinetics of a... 

The instrument most commonly used to resolve the Brillouin spectrum is the Fabry-Perot interferometer. This device consists of a pair of highly reflective, optically polished mirrors. The transmission function for a plane parallel Fabry-Perot interferometer is ... 

Fig. 4.39a,b. Two realizations of a Fabry-Perot interferometer (a) solid etalon (b) air-spaced plane-parallel reflecting surfaces... 

More detailed information on the history, theory, practice, and application of plane and spherical Fabry-Perot interferometers may be found in [4.42-4.44]. 

Fig. 5.42a,b. Fabry-Perot interferometer tuned by a piezocylinder (a) two plane-parallel plates with inner reflecting surfaces (b) two Brewster prisms with the outer coated surfaces forming the FPI reflecting planes... 

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