By Piergiorgio Uslenghi (Eds.)
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Since a Gaussian beam has a far zone pattern as in (6), insertion of that pattern function into (39) determines the coupling from an incident beam in a layered medium to the guided modes. These considerations 3 are relevant to integrated optical systems. C. Application to Unstable Optical Resonators The injection of quasi-optic waveguide considerations into the analysis of open optical resonators for laser oscillators has provided another timely application. Here, the region containing the active lasing material (usually encased in a large tubular configuration) is terminated at both ends by reflecting mirrors, ^Alternatively the Gaussian beam problem can be tackled by complex displacement of the coordinate location of an isotropic point radiator; see Sec.
Math. Anal. & Appl. 57(1), 170-202 (1977). Krai, J. , The Fredholm Method in Potential Theory, Trans. Am. Math. Soc. 125, 511-547 (1966). , Amsterdam-London (1970). Minnis, C M . and Y. ), "Review of Radio Science 1969-72," International Union of Radio Science (URSI), Brussels, Belgium (1972). M. and H. Feshbach, "Methods of Theoretical Physics," McGraw-Hill, New York (1953). , "Foundations of the Mathematical Theory of Electromagnetic Waves," Springer-Verlag, Berlin (1969). , Integral Equation Perturbation Methods in Low Frequency Diffraction, in "Electromagnetic Waves" (R.
Since it can be shown that the local parallel plane formulation and the single diffraction formulation in (40) have overlapping regions of applicability, the modal coupling coefficients are available ( 4 J High-Frequency Propagation and Scattering 55 for arbitrary mirror curvatures . , the complex eigenvalues) as a function of mirror size and shape are calculated by inser tion of the caustic and edge reflection coefficients into the transverse resonance relation, one obtains remarkably good agree ment with data from numerical solution of the integral equation for the currents induced on the mirror surfaces .