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Propagation properties of Hermite-cosine-Gaussian beams

Xi Wang

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Abstract

Based on the generalized HuygensFresnel diffraction integral, the closedform propagation expressions for HermitecosineGaussian(HCsG) beams through a paraxial optical ABCD system are derived. The propagation expressions for HermitecoshGaussian(HChG), cosineGaussian(CsG) and HermiteGaussian(HG) beams are obtained readily as special cases of HCsG beams. As application examples, numerical calculations are performed for HCsG beams propagating in free space and focused by a thin lens. The calculated results are shown that HCsG beams can not preserve their shape, while propagating in free space and through a thin lens.

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What this paper is about

Based on the generalized HuygensFresnel diffraction integral, the closedform propagation expressions for HermitecosineGaussian(HCsG) beams through a paraxial optical ABCD system are derived. The propagation expressions for HermitecoshGaussian(HChG), cosineGaussian(CsG) and HermiteGaussian(HG) beams are obtained readily as special cases of HCsG beams. As application examples, numerical calculations are performed for HCsG beams propagating in free space and focused by a thin lens. The calculated results are shown that HCsG beams can not preserve their shape, while propagating in free space and through a thin lens.

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Available abstract

Based on the generalized HuygensFresnel diffraction integral, the closedform propagation expressions for HermitecosineGaussian(HCsG) beams through a paraxial optical ABCD system are derived. The propagation expressions for HermitecoshGaussian(HChG), cosineGaussian(CsG) and HermiteGaussian(HG) beams are obtained readily as special cases of HCsG beams. As application examples, numerical calculations are performed for HCsG beams propagating in free space and focused by a thin lens. The calculated results are shown that HCsG beams can not preserve their shape, while propagating in free space and through a thin lens.

Key concepts: Paraxial approximation, Hermite polynomials, Gaussian, Diffraction, Thin lens, Trigonometric functions, Optics, Physics

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