27 November 2012 Hermite Gaussian approximation for TE1 mode of dielectric planar waveguide
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Abstract
Based on the definition of beam propagation factor, the relation between beam propagation factor and normalized frequency of TE1 mode of planar waveguide is presented. As the value of beam propagation factor of TE1 mode is close to three for a certain range of normalized frequency, it is rational that the field distribution of TE1 mode of dielectric planar waveguide is expressed by the first order Hermite-Gaussian approximation. When the equivalent mode field half width expressed by the geometric mean of the two kinds of mode field half widths based on the differential operator definition and the second moment definition is employed as the waist size of Hermite-Gaussian approximation, the matching efficiency between the TE1 mode field of planar waveguide and its first order Hermite-Gaussian approximation is near to unit for a certain range of normalized frequency. For giving the characteristics of the beam propagation factor and equivalent mode field half width obviously, the fitting expressions for beam propagation factor of TE1 mode field of planar waveguide as function of normalized frequency and the equivalent mode field half width of the first order Hermite-Gaussian approximation as function of normalized frequency are suggested respectively.
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Ziyun Wang, Ziyun Wang, Lianhuang Li, Lianhuang Li, Fuyuan Guo, Fuyuan Guo, } "Hermite Gaussian approximation for TE1 mode of dielectric planar waveguide", Proc. SPIE 8555, Optoelectronic Devices and Integration IV, 855516 (27 November 2012); doi: 10.1117/12.999773; https://doi.org/10.1117/12.999773
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