Confocal finesse

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. 

The novel aspect of this experiment was that the confocal cavity was locked to continuous-wave radiation which was frequency shifted by an acousto-optic modulator such as to centre the filtering cavity onto the chirped amplified radiation. This reduced the residual amplifier shift to -2(1 MHz. The dominant contribution to this shift resulted from the cw light being injected off-axis into the cavity. Because the filter cavity had a high finesse we used a phase modulation scheme for locking. Indeed, we normally locked the dye laser to the filtering cavity and scanned the spectrum by scanning the filter cavity. 

The total finesse of the confocal FPI is, in general, higher than that of a plane FPI for the following reasons ... 

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]. 

For a given finesse F, the etendue of the confocal FPI increases with the mirror separation d — r. The spectral resolving power... 

In Sect. 4.2.10 we saw that for a given resolving power the spherical FPI has a larger etendue for mirror separations r > /Ad. For Example 4.19 with D — 5 cm, d = 1 cm, the confocal FPI therefore gives the largest product RU of all interferometers for r > 6 cm. Because of the higher total finesse, however, the confocal FPI may be superior to all other instruments even for smaller mirror separations. 

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 ... 

A confocal FPI with r = d = 5 cm has for A = 500 nm the etendue U = (2.47 X 10 /F ) cm /sr. This is the same etendue as that of a plane FPI with d = 5cm. and D = 10cm. However, the diameter of the spherical mirrors can be much smaller (less than 5 mm). With a hnesse F = 100, the dtendue is, U = 2.5x10 [cm sr] and the spectral resolving power is v/Av = 4 X 10. With this dtendue the resolving power of the plane FPI is 6x10 , provided the whole plane mirror surface has a surface quality to allow a surface finesse of F > 100. In practice, this is difficult to achieve for a flat plane with D = 10 cm diameter, while for the small spherical mirrors even F > lO is feasible. 

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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