Geometrical Optics Beam Shaping

Geometrical Optics Beam Shaping Useful approach for solving certain beam shaping problems.

In this method, a smooth coordinate transform – essentially a controlled distortion– is derived from the Input/Output specification of the optical system. This transformation redistributes the input energy to form the desired output. As a result, if the input intensity distribution is continuous, the output intensity distribution should also be continuous.

In addition, the input field, desired output field, and the resulting transmission should satisfy either Cartesian Separability or Rotational Symmetry.

Cartesian separability means that for the transmission $T (x, y)$ , two independent 1D functions, $T_{x} (x)$ and $T_{y} (y)$ , exist such that:

$T (x, y) = T_{x} (x) T_{y} (y)$

Rotational symmetry means that $T (x, y)$ depends only on the radial coordinate $r$ , and can be written as:

$T (x, y) = T_{r} (r)$ , where $r = \sqrt{x^{2} + y^{2}}$ .

If the input field is continuous but the desired output field is discontinuous, applying geometrical beam shaping alone may introduce significant errors. However, in cases involving discontinuities, non-separability, or rotational asymmetry, Geometrical Optics Beam Shaping can still serve as a good initial design for the Iterative Fourier Transform Algorithm Approach.

If the input field is continuous but the desired output field is discontinuous, applying geometrical beam shaping alone may introduce significant errors. However, in cases involving discontinuities, non-separability, or rotationally asymmetry, Geometrical Optics Beam Shaping can still serve as a good initial design for the Iterative Fourier Transform Algorithm Approach.

Geometrical Optics Beam Shaping as Initial Design for IFTA

The Iterative Fourier Transform Algorithm (IFTA) is a general method for designing beam shapers. It is highly recommended to use the result of Geometrical Optics Beam Shaping as the initial transmission to prevent the solution from getting trapped in local extrema.

Steps to implement this approach:

Perform a design using Geometrical Optics Beam Shaping.
Select the Iterative Fourier Transform Algorithm Approach.
Uncheck Generate Initial Transmission, allowing the geometrical optics beam shaping result to be used as the initial transmission, configure other necessary parameters and click Start Design.