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Register a new userAliasing-reduced Fresnel diffraction with scale and shift operations
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Added by
Tomoyoshi Shimobaba Dr.
Publication date
2013
fields
Physics
and research's language is
English
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Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT) is widely used in optics, especially computer holography. Fresnel diffraction with FFT cannot set different sampling rates between source and destination planes, while shifted-Fresnel diffraction can set different rates. However, an aliasing error may be incurred in shifted-Fresnel diffraction in a short propagation distance, and the aliasing conditions have not been investigated. In this paper, we investigate the aliasing conditions of shifted-Fresnel diffraction and improve its properties based on the conditions.
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We demonstrate that beams originating from Fresnel diffraction patterns are self-accelerating in free space. In addition to accelerating and self-healing, they also exhibit parabolic deceleration property, which is in stark contrast to other accelerating beams. We find that the trajectory of Fresnel paraxial accelerating beams is similar to that of nonparaxial Weber beams. Decelerating and accelerating regions are separated by a critical propagation distance, at which no acceleration is present. During deceleration, the Fresnel diffraction beams undergo self-smoothing, in which oscillations of the diffracted waves gradually focus and smooth out at the critical distance.
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It is known that the Fresnel wave surfaces of transparent biaxial media have 4 singular points, located on two special directions. We show that, in more general media, the number of singularities can exceed 4. In fact, a highly symmetric linear material is proposed whose Fresnel surface exhibits 16 singular points. Because, for every linear material, the dispersion equation is quartic, we conclude that 16 is the maximum number of isolated singularities. The identity of Fresnel and Kummer surfaces, which holds true for media with a certain symmetry (zero skewon piece), provides an elegant interpretation of the results. We describe a metamaterial realization for our linear medium with 16 singular points. It is found that an appropriate combination of metal bars, split-ring resonators, and magnetized particles can generate the correct permittivity, permeability, and magnetoelectric moduli. Lastly, we discuss the arrangement of the singularities in terms of Kummers (16,6)-configuration of points and planes. An investigation parallel to ours, but in linear elasticity, is suggested for future research.
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