Gaussian Waist
The Gaussian Waist beam is an optionally truncated and decentered Hermite-Gaussian of arbitrary order defined by:
where
And Hi (u) is the Hermite polynomial function of order i. Note the order may be specified in the x and y directions independently. The x order is defined by the integer l, and the y order is defined by the integer m. If both l and m are zero, the simple "Gaussian" TEM(0,0) beam is generated. Higher order modes may be generated by modifying the order values; for example, to generate TEM(1,2) set l = 1 and m = 2. For a discussion of Hermite- Gaussian beams see Saleh, B. E. A., and Teich, M. C., Fundamentals of Photonics, John Wiley & Sons, New York (1991). If the order number is set higher than 30, the order zero will be used to prevent excessively long computation time.
The dx and dy values are used to decenter the beam. The transmittance function T (x, y ) is used to (optionally) truncate the beam to a finite aperture. The transmittance function is defined as
otherwise.
Ax and Ay are the truncating aperture values. If Ax or Ay are zero, no truncating aperture is used. A smoothing function is used near the edge of the truncating aperture to reduce pixel related errors. The smoothing function weights the pixel amplitude by the area of the pixel inside the truncating aperture. The truncating aperture is useful for modeling receiver fiber modes, where the truncating aperture is typically 15% greater than the core size.
The value for E0 is chosen to yield the peak irradiance in power per unit area or the total beam power as defined in the settings box.
The beam is defined at the waist and will generally diverge to a larger beam size as it propagates away from the waist. See Gaussian Angle and Gaussian Size+Angle below.
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