Algorithms

Propagation algorithms is a fundamental key in Diffractio package. The algorithms implemented for scalar propagation are:

  • Fast Fourier Transform (FFT).

  • Rayleigh Sommerfeld (RS).

  • Plane Wave Descomposition (PWD).

  • Beam Propagation Method (BPM).

  • Wave Propagation Method (WPM).

  • Chirp z-transform (CZT).

Fast Fourier Transform (FFT)

It allows, in a single step to determine the field at the far field. The fields and the masks must be defined in a plane.

Rayleigh-Sommerfeld (RS) - Shen, F., and Wang, A. (2006). Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula. Applied Optics, 45(6), 1102–1110. https://doi.org/10.1364/AO.45.001102

Single step to propagate to a near or far observation plane, which allows fast computations.

Plane Wave Descomposition (PWD) - It is implemented as it is required for some other algorithms, although it is recommended to use the WPM algorithm.

Beam propagation method (BPM)

  • Feit, M. D., and Fleck, J. A. (1978). Light propagation in graded-index optical fibers.

Propation of light in volumetric elements, provided that the spatial variations in the refractive index are small. It allows graded index structures. It presents a complexity of O(n) in the two-dimensional and O(n2) in the three-dimensional case. Computed according to split-step propagation scheme.

Wave Propagation Method (WPM)

  • Brenner, K.-H. H., and Singer, W. (1993). Light propagation through microlenses: a new simulation method. Applied Optics, 32(26), 4984–4988. https://doi.org/10.1364/ao.32.004984

  • Brenner, K. H. (2017). A high-speed version of the wave propagation method applied to micro-optics. 2017 16th Workshop on Information Optics, WIO 2017, 1, 2–4. https://doi.org/10.1109/WIO.2017.8038108

  • Schmidt, S., Thiele, S., Herkommer, A., Tünnermann, A., and Gross, H. (2017). Rotationally symmetric formulation of the wave propagation method-application to the straylight analysis of diffractive lenses. Optics Letters, 42(8), 1612. https://doi.org/10.1364/ol.42.001612

Solves the major limitations of the beam propagation method (BPM). The wave propagation scheme provides valid results for propagation angles up to 85° and that it is not limited to small index variations in the axis of propagation. Very fast with a discrete number of refractive indexes.

Chirped z Transform (CZT)

  • Leutenegger, M., Rao, R., Leitgeb, R. A., and Lasser, T. (2006). Fast focus field calculations. Optics Express, 14(23), 11277–11291. http://lob.epfl.ch/

  • Hu, Y., Wang, Z., Wang, X., Ji, S., Zhang, C., Li, J., Zhu, W., Wu, D., and Chu, J. (2020). Efficient full-path optical calculation of scalar and vector diffraction using the Bluestein method. Light: Science and Applications, 9(1). https://doi.org/10.1038/s41377-020-00362-z