Interferometer free spectral range

We have undertaken an experiment to try to improve the performance of pulse amplifier experiments. The system is shown schematically in figure 2. It consisted of a continuous-wave C102 dye laser amplified in three stages by a frequency tripled Q-switched NdtYAG laser. The output energy was approximately 2.0 mJ in a 150 MHz linewidth and was up-shifted from the continuous-wave laser by 60 MHz caused by the frequency chirp. This light was then spectrally filtered in a confocal interferometer with a finesse of 40 and a free spectral range of 300 MHz. The linewidth of the filtered radiation was approximately 16 MHz. 

There are two important parameters that characterize Fabry-Perot interferometers, the free spectral range (FSR) and the finesse. The FSR is essentially the frequency spacing between adjacent cavity modes. For a flat-plate interferometer, it is given by... 

If a small fraction of the laser output is sent through a long Fabry-Perot interferometer with a separation d of the mirrors (Fig. 1.1b), the photodetector PD3 receives intensity peaks each time the laser frequency is tuned to a transmission maximum at v = mcjd (Vol. 1, Sects. 4.2-4.4). These peaks serve as accurate wavelength markers, which allow one to calibrate the separation of adjacent absorption lines. With a = 1 m the frequency separation Avp between successive transmission peaks is Avp = cjld = 150 MHz, corresponding to a wavelength separation of 10 nm at A. = 550 nm. With a semiconfocal FPI the free spectral range is cfM, which gives Av = 75 MHz for d = 0.5 m. 

Free spectral range (FSR) Frequency spacing between adjacent transmission peaks of a parallel-plate interferometer and, by extension, between orders of other multiply ordered frequency Alters. 

Wave number The number 1 /A of wavelengths in a centimeter (units of cm ), a convenient spectroscopic unit of frequency because the free spectral range of an interferometer of plate spaeing t (cm) is just 1/2/ (cm ). To convert the wave number of a photon to its energy in joules, multiply by he = 1.99 x 10 (h is Planck s constant, c the speed of light). 

It is important to realize that from one interferometric measurement alone one can only determine X modulo m SX because all wavelengths A = Aq H-m X are equivalent with respect to the transmission of the interferometer. One therefore has at first to measure A within one free spectral range using other... 

The frequency range 8v between two maxima is ih free spectral range of the interferometer. With 0 = In s/X and X = c/y, we obtain from (4.46a)... 

The ratio 8v/Av of free spectral range 8v to the halfwidth Av of the transmission maxima is called ht finesse F of the interferometer. From (4.51b) and (4.52c) we obtain for the finesse... 

The spectral resolution, v/Av or A./AA., of an interferometer is determined by the free spectral range 8v and by the finesse F. Two incident waves with frequencies v and V2 = v - - Av can still be resolved if their frequency separation Av is larger than <5i /F, which means that their peak separation should be larger than their full halfwidth. 

Since the laser resonator is a Fabry-Perot interferometer, the spectral distribution of the transmitted intensity follows the Airy formula (4.57). According to (4.53b), the halfwidth Avr of the resonances, expressed in terms of the free spectral range 5y, is Avr = Sy/F. If diffraction losses can be neglected, the finesse F is mainly determined by the reflectivity R of the mirrors, therefore the halfwidth of the resonance becomes... 

Often a Michelson interferometer coupled by a beam splitter BS to the laser resonator is used for mode selection (Fig. 5.37). The free spectral range... 

A single-mode laser is frequency stabilized onto the slope of the transmission maximum of an external reference Fabry-Perot interferometer made of invar with a free spectral range of 8 GHz. Estimate the frequency stability of the laser... 

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.

The different types of wavemeters for very accurate measurements of laser wavelengths are based on modifications of the Michelson interferometer [184], the Fizeau interferometer [185], or on a combination of several Fabry-Perot interferometers with different free spectral ranges [186-188]. The wavelength is measured either by monitoring the spatial distribution of the interference pattern with photodiode arrays, or by nsing traveling devices with electronic counting of the interference... 

Often a Michelson interferometer coupled by a beam splitter BS to the laser resonator is used for mode selection (Fig. 5.39). The free spectral range 8v = c/(L2 + Li) of this Fox-Smith cavity [341] again has to be broader than the width of the gain profile. With a piezoelement PE, the mirror M3 can be translated by a few microns to achieve resonance between the two coupled resonators. For the resonance condition... 

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