Numerical solution of cavity mode

Substituting equation (12.3) into equation (12.2) we obtain an integral equation for the spatial distribution and propagation constant y of the eigenmode eP(Uj, Vj)  

Fox and Li (1961) showed by repeated numerical integration of equation (12.4) for the case of a plane mirror cavity that an initial arbitrary field distribution eventually settled down to a steady-state solution after some 200-300 transits through the resonator. This demonstrates that eigenraodes do exist in open-sided resonators having finite rectangular or circular apertures. The eigenmodes of rectangular symmetry can be classified as where m,n, and 

For a plane-parallel Fabry-Perot type cavity for which F 10, resonance occurs when the cavity length, L, is equal to an integral number of half wavelengths, 

The fractional power loss per transit, 1 - Yq, obtained by Fox and Li (1961) for the lowest-order transverse modes of a plane mirror cavity having circular apertures, is shown in Fig.12.3 as a function of the Fresnel number 

The effects of non-parallelism of the mirrors in a nominally plane-parallel cavity have been studied by Fox and Li (1963). The diffraction loss is found to increase rapidly for only slight deviations from perfect alignment or from perfect optical quality of the windows and mirrors. 

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