Geodesic
A new method of obtaining optical super-oscillations based on threewave interference
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 4, pp. 59-65

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Optical super-oscillation is one of the methods to overcome diffraction limit. The phenomenon of super oscillations has been known for more than half a century, but there is still a limited set of shapes of the resulting light distribution patterns. The use of interference of Bessel and Gauss beams is currently the most studied theoretically and in fact the only method of obtaining optical super oscillations in practice. The paper presents a new method of obtaining optical super-oscillations based on three wave interference. We have studied the theoretical basis for obtaining optical super-oscillations considering distribution of the field amplitude in the interference of three coherent collimated sources. The dependence of the contrast of optical super-oscillations on the ratio of wave amplitudes, which has an exponential form, is studied. The correlation of the size of optical super-oscillations depending on the contrast which is proved to be of a power form is analyzed. We have modeled two-dimensional interference patterns of optical super-oscillations obtained by three coplanar waves. In this case optical super oscillations have a constant size along interference fringes. In case of noncoplanar waves when moving along interference fringes periodic extinction and appearance of optical super-oscillations are observed.
Keywords: optical super-oscillations, interference, subwave effects. 
@article{VYURM_2017_9_4_a7,
     author = {M. A. Dryazgov and I. V. Sviridova and D. S. Isakov and Yu. V. Miklyaev},
     title = {A new method of obtaining optical super-oscillations based on threewave interference},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {59--65},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2017_9_4_a7/}
}
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M. A. Dryazgov; I. V. Sviridova; D. S. Isakov; Yu. V. Miklyaev. A new method of obtaining optical super-oscillations based on threewave interference. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 4, pp. 59-65. http://geodesic.mathdoc.fr/item/VYURM_2017_9_4_a7/