Flatness finesse

The absolute frequency position of the two-photon transition is measured by comparing the infrared dye laser wavelength with an I - stabilized He-Ne reference laser at 633 nm (see Fig.2). The hey of the wavelength comparison is a nonconfocal etalon Fabry-Perot cavity (indicated as FPE in Fig.2) kept under a vacuum better than 10-6 mbar. This optical cavity is built with two silver-coated mirrors, one flat and the other spherical (R = 60 cm), in optical adhesion to a zerodur rod. Its finesse is 60 at 633 nm and 100 at 778 nm. An auxiliary He-Ne laser as well as the dye laser are mode-matched and locked to this Fabry-Perot cavity. Simultaneously the beat frequency between the auxiliary and etalon He-Ne lasers is measured by a frequency counter. 

Here, Dy is an empirical, radial dispersion coefficient and e is the void fraction. The units of diffusivity Dy are square meters per second. The major differences between this model and the convective diffusion equation used in Chapter 8 is that the velocity profile is now assumed to be flat and Dy is an empirically determined parameter instead of a molecular diffusivity. The value of Dy depends on factors such as the ratio of tube to packing diameters, the Reynolds number, and (at least at low Reynolds numbers) the physical properties of the fluid. Ordinarily, the same value for Dy is used for all reactants, finessing the problems of multicomponent diffusion and allowing the use of stoichiometry to eliminate Equation 9.1 for some of the components. Note that Us in Equation 9.1 is the superficial velocity, this being the average velocity that would exist if the tube had no packing. 

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... 

A plane, nearly parallel plate has a diameter D = 5 cm, a thickness d = 1 cm, and a wedge angle of 0.2". The two reflecting surfaces have the reflectivity R = 95%. The surfaces are flat to within A./50, which means that no point of the surface deviates from an ideal plane by more than A./50. The different contributions to the finesse are ... 

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 dielectric coatings of each plate of a Fabry-Perot interferometer have the following specifications R = 0.98, A = 0.3 %. The flatness of the surfaces is A/lOO at A = 500nm. Estimate the finesse, the maximum transmission, and the spectral resolution of the FPI for a plate separation of 5 mm. 

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