Approximate analytical expression for the spectrum of polychromatic Gaussian beams passing through a multi-apertured ABCD optical system

Abstract

Abstract: The calculation for the spectrum of beams passing through a multi-apertured ABCD optical system has not been finished in any personal computer when the aperture number is more than a certain value. By means of the expansion of the window function of the hard-edge aperture into a finite sum of complex Gaussian functions, an approximate analytical expression for the spectrum of polychromatic Gaussian beams passing through a multi-apertured ABCD optical system is derived and illustrated with numerical examples. The numerical results find an agreement with those by straightforward integral of the cross-spectral density function, but the computing time is strongly reduced. Key words: Laser optics; fast algorithm; multi-apertured ABCD optical system ; spectrum 1.Introduction In the past twenty years, much interest was focused on the spectral behavior of spatially fully and partially coherent polychromatic beams during propagatione and extensive theoretical and experimental studies of the spectral changes includi ng spectral shifts and spect ral switches have been made