Complex order fractional Fourier transforms and their use in diffraction theory. Application to optical resonators |
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Authors: | Pierre Pellat-Finet,É ric Fogret |
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Affiliation: | a Laboratoire de mathématiques et applications des mathématiques, Université de Bretagne Sud, B.P. 92116, 56321 Lorient Cedex, France b Département d’optique, École nationale supérieure des télécommunications de Bretagne, UMR CNRS 6082, France |
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Abstract: | The electromagnetic field transfer by diffraction from a spherical emitter to a spherical receiver is expressed by a fractional Fourier transform whose order depends on the distance between the emitter and the receiver and their curvature radii. Special attention is paid to complex order transforms: scaled variables and scaled field amplitudes are defined by complying with mathematical consistency. For a given distance of observation, a simple geometrical condition is set up to determine whether the corresponding transform order is a real or a complex number. The result is applied to check the stability of optical resonators. |
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Keywords: | 42.30.Kq |
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