Linking the Quasi-Normal and Natural Modes of an open cavity - Physics > OpticsReport as inadecuate

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Abstract: The present paper proposes a comparison between the extinction theorem andthe Sturm-Liouville theory approaches for calculating the e.m. field inside anoptical cavity. We discuss for the first time to the best of our knowledge, inthe framework of classical electrodynamics, a simple link between the QuasiNormal Modes QNMs and the Natural Modes NMs for one-dimensional 1D,two-sided, open cavities. The QNM eigenfrequencies and eigenfunctions arecalculated for a linear Fabry-Perot FP cavity. The first-order Bornapproximation is applied to the same cavity in order to compare the first-orderBorn approximated and the actual QNM eigenfunctions of the cavity. Wedemonstrate that the first-order Born approximation for an FP cavity introducessymmetry breaking: in fact, each Born approximated QNM eigenfunction producesvalues below or above the actual QNM eigenfunction value on the terminalsurfaces of the same cavity. Consequently, the two error-functions for anapproximated QNM are not equal in proximity to the two terminal surfaces of thecavity.

Author: A. Settimi, S. Severini


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