Confocal 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. 

Frequency stabilisation and scanning is accomplished by use of a confocal cavity of free spectral range matched to the dye laser repetition rate. Phase modulated sidebands are put on to the mode spectrum of the mode-locked pulse train and used to lock the laser to the reference cavity. The frequency modulation technique is also used to lock the ultra-violet enhancement cavity to the mode-locked pulse train. 

The total finesse of a confocal FPI is therefore mainly determined by the reflectivity R of the mirrors. For R = 0.99, a finesse F = n R/( — R) 300 can be achieved, which is much higher than that obtainable with a plane FPI, where other factors decrease F. With the mirror separation r = d = 3 cm, the free spectral range is 3 = 2.5 GHz and the spectral resolution is Au = 7.5 MHz at the finesse F = 300. This is sufficient to measure the natural linewidth of many optical transitions. With modem high-reflection coatings, values of F = 0.9995 can be obtained and confocal FPI with a finesse F > 10" have been realized [4.41]. 

A confocal FPI shall be used as optical spectrum analyzer, with a free spectral range of 3 GHz. Calculate the mirror separation d and the finesse that is necessary to resolve spectral features in the laser output within 10 MHz. What is the minimum reflectivity R of the mirrors, if the surface finesse is 500 ... 

Equation (5.49) reveals that the frequency spectrum of the confocal resonator is degenerate because the transverse modes with q = q and m- -n = 2p have the same frequency as the axial mode with m = n = 0 and q = q - -p. Between two axial modes there is always another transverse mode with m- -n -f 1 = odd. The free spectral range of a confocal resonator is therefore... 

The free spectral range 8v, i.e., the frequency separation between successive interference maxima, is for the near-confocal FPI with p d... 

Since this corresponds to a planar interferometer with double the mirror separation the free spectral range for a confocal interferometer is given by... 

The external confocal F.P.I. (free spectral range 6v = 2 GHz, finesse 200) serves as an ultranarrow passband filter with a linewidth of about Avp = 10 MHz. The pulse duration of the transmitted laser intensity is of course lengthened to T = l/(2irAvp). The F.P.I. acts like a resonator with the transient time Tp. If the linewidth Av of the laser output incident onto the F.P.I. is much larger than Avp, only the small fraction Avp/Av is being transmitted through the filter. The intensity loss can be compensated... 

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