Simple formula for a Gaussian beam with general astigmatism in a homogeneous medium
A simple analytical formula that describes the evolution of a Gaussian beam with general astigmatism in a homogeneous medium is obtained. The quadratic form matrix, which determines the transverse distribution of the field in the beam for an arbitrary value of the longitudinal coordinate, is represe...
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Veröffentlicht in: | Optics and spectroscopy 2009-06, Vol.106 (6), p.910-912 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | A simple analytical formula that describes the evolution of a Gaussian beam with general astigmatism in a homogeneous medium is obtained. The quadratic form matrix, which determines the transverse distribution of the field in the beam for an arbitrary value of the longitudinal coordinate, is represented in the form of a linear combination of such matrix in a certain initial cross section and a unit matrix. The coefficients of the linear combination are complex-valued and are expressed via the longitudinal coordinate of the considered cross section, the refractive index of the medium, and the determinant and the trace of the initial matrix. |
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ISSN: | 0030-400X 1562-6911 |
DOI: | 10.1134/S0030400X09060204 |