Free space propagation without free space

Christian Schulze; Daniel Flamm; Michael Duparré; Andrew Forbes

doi:10.1117/12.2004212

22 February 2013 Free space propagation without free space

Christian Schulze, Daniel Flamm, Michael Duparré, Andrew Forbes

Proceedings Volume 8600, Laser Resonators, Microresonators, and Beam Control XV; 86000X (2013) https://doi.org/10.1117/12.2004212
Event: SPIE LASE, 2013, San Francisco, California, United States

Abstract

We present a novel, fast and easy measurement technique to measure the beam propagation factor M² of laser beams using a spatial light modulator (SLM). Two different measurement procedures are outlined, that are both based on digitally simulating the free space propagation of the beam. Hence, the traditional scan in propagation direction can be avoided and no moving components are required. In the first approach the SLM is employed as variable focus lens, yielding differently focused beams in a fixed plane, in which the beam diameter is determined with a static CCD camera. Using standard Gaussian optics the measured data can be fitted with the theoretical curve yielding the M² value as a fit parameter. The second approach is based on the principles of the angular spectrum method, after which the propagated (near) field is obtained after multiplication with a transfer function of free space in the far field and back transformation to the near field. In the experiment the angular spectrum method is easily implemented by transforming the field under test with a simple lens onto the SLM, displaying the mentioned transfer function on the SLM, and transforming back to a fixed plane, in which the changing beam diameter is recorded with a CCD camera. To prove both techniques, reference beams of Laguerre-Gaussian type with known M² value were generated and the beam propagation ratio measured. The comparison with the theoretical predictions reveals excellent agreement and emphasizes the fidelity of the M² measurement.

Citation Download Citation

Christian Schulze, Daniel Flamm, Michael Duparré, and Andrew Forbes "Free space propagation without free space", Proc. SPIE 8600, Laser Resonators, Microresonators, and Beam Control XV, 86000X (22 February 2013); https://doi.org/10.1117/12.2004212

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KEYWORDS

Spatial light modulators

Beam propagation method

Optical testing

Free space

Electroluminescent displays

CCD cameras

Digital holography

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