9 September 2015 The fast Fresnel diffraction algorithm: from the ray matrix approach to experimental virtual propagation systems
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In this paper the fast Fresnel diffraction algorithm is reviewed and applied to some novel applications. The algorithm (also named the convolution or angular spectrum method) is a very powerful numerical technique that has been employed in the calculation of diffraction patterns. It utilizes two Fourier transform operations, thus becoming computationally much faster than the conventional approach. We analyze the practical implementation with spatial light modulators (SLM). First, the ray matrix approach is applied to derive and reexamine this computational technique. This approach easily allows us to find explicit expressions for the maximum and minimum distances over which the algorithm is accurate. Then, we describe the practical implementation of this algorithm to encode Fresnel propagated masks onto a SLM. We discuss the limitations caused by the Nyquist limit. Finally, we apply the technique to create an experimental virtual optical beam propagator system. This system uses one SLM and allows the experimental study of the beam propagation without physically moving any element. This laboratory propagator system can be extremely useful to build compact optical architectures or to emulate beam propagation without misalignments caused by moving elements in the experimental system. As examples, we design holograms capable of producing different patterns at different distances, and we can change the effective plane of observation by changing the encoded propagation. The technique can find applications in many different contexts, including the analysis of propagation dynamics of nondiffracting beams, and Airy beams.
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Jeffrey A. Davis, Jeffrey A. Davis, Don M. Cottrell, Don M. Cottrell, Cassidy A. Berg, Cassidy A. Berg, Christopher Li Freeman, Christopher Li Freeman, Adriana Carmona, Adriana Carmona, William Debenham, William Debenham, Ignacio Moreno, Ignacio Moreno, } "The fast Fresnel diffraction algorithm: from the ray matrix approach to experimental virtual propagation systems", Proc. SPIE 9598, Optics and Photonics for Information Processing IX, 959803 (9 September 2015); doi: 10.1117/12.2197692; https://doi.org/10.1117/12.2197692

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