Three-Airy beams and their autofocusing plane

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Abstract

The position of the autofocusing plane of three-Airy beams is studied theoretically and experimentally depending on the shift parameter. It is shown that for different values of this parameter, the three-Airy beam may or may not have an autofocusing plane. If the beam has an autofocusing plane, then with increasing absolute value of the shift parameter, the autofocusing plane monotonically moves away from the initial plane.

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About the authors

D. V. Prokopova

Lebedev Physical Institute of the Samara Branch of the Russian Academy of Sciences

Author for correspondence.
Email: prokopovadv@lebedev.ru
Russian Federation, Samara

E. G. Abramochkin

Lebedev Physical Institute of the Samara Branch of the Russian Academy of Sciences

Email: prokopovadv@lebedev.ru
Russian Federation, Samara

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Supplementary files

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2. Fig. 1. Left: intervals in θ for which there exists a solution φ(θ) of equation (15), right: caustics that are obtained from formulae (13) at Z = 2. The enlarged fragment of the centre section shows the presence of a caustic point, which is present only in the autofocus plane

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3. Fig. 2. Plot of the beam intensity dependence Ai3(x, y, a) on the z axis (i.e., at x = y = 0) during propagation in the Fresnel zone for the case when the bias parameter is a = 3-2/3a'100 = -28 966. The asymptotic formula (14) gives the value zs = 14.35; from the numerical experiment we obtain zs = 15.012

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4. Fig. 3. Schematic diagram of the experimental setup

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5. Fig. 4. Experimentally obtained intensity distributions of tri-Eiri beams with different values of the bias parameter at different distances expressed in units of focal length F = 500 mm. The frame side size is 1 mm for a‘1 × 3-2/3 = -0.489 and a1 × 3-2/3 = -1.124, and is 2 mm for a’3 × 3-2/3 = -2.317, a3 × 3-2/3 = -2.654, a'5 × 3-2/3 = -3.545, and a5 × 3-2/3 = -3.819

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