Guoquan Zhou

Properties of Airy-Gauss Beams in the Fractional Fourier Transform Plane

An analytical expression of an Airy-Gauss beam passing through a fractional Fourier transform (FRFT) system is derived. The normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are demonstrated in FRFT plane, respectively. The influence of the fractional order p on the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are examined in FRFT plane. The fractional order p controls the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, the linear momentum, and kurtosis parameter. The period of the normalized intensity, phase, and centre of gravity versus the fractional order p is 4. The period of effective beam size, linear momentum, and kurtosis parameter versus the fractional order p is 2. The periodic behaviors of the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter can bring novel applications such as optical switch, optical micromanipulation, and optical image processing.

Orbital angular momentum density of a general Lorentz–Gauss vortex beam

Based on the vectorial Rayleigh–Sommerfeld integral formulae, the analytical expression of a general Lorentz–Gauss vortex beam with an arbitrary topological charge is derived in free space. By using the analytical expressions of the electromagnetic field beyond the paraxial approximation, the orbital angular momentum density of a general Lorentz–Gauss vortex beam can be calculated. The effects of the linearly polarized angle and the topological charge on the three components of the orbital angular momentum density are investigated in the reference plane. The two transversal components of the orbital angular momentum are composed of two lobes with the same areas and opposite signs. The longitudinal component of the orbital angular momentum density is composed of four lobes with the same areas. The sign of the orbital angular momentum density in a pair of lobes is positive, and that of the orbital angular momentum density in the other pair of lobes is negative. Moreover, the negative magnitude of the orbital angular momentum density is larger than the positive magnitude of the orbital angular momentum density. The linearly polarized angle affects not only the shape and the location of the lobes, but also the magnitude of the three components of the orbital angular momentum density. With increasing the topological charge, the distribution of the orbital angular momentum density expands, the magnitude of the orbital angular momentum density increases, and the shape of the lobe also slightly changes.

The Wigner distribution function of a Lorentz–Gauss vortex beam passing through a paraxial ABCD optical system

Based on the Collins integral formula and the Hermite–Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function (WDF) of a Lorentz–Gauss vortex beam passing through a paraxial ABCD optical system is derived. The WDF properties of a Lorentz–Gauss vortex beam propagating in free space are also demonstrated. During propagation, the WDF pattern shrinks in the direction of the spatial frequency variables and elongates in the direction of the transverse spatial coordinates. With given the transverse spatial coordinates or the spatial frequency variables, the evolvement of the WDF of a Lorentz–Gauss vortex beam during propagation is examined in detail. To show the WDF application, the second-order moments of the WDF for a Lorentz–Gauss vortex beam in free space are also presented. This research exhibits the propagation properties of a Lorentz–Gauss vortex beam from the phase space.

Optical image-hiding method with false information disclosure based on the interference principle and partial-phase-truncation in the fractional Fourier domain

An image-hiding method based on the optical interference principle and partial-phase-truncation in the fractional Fourier domain is proposed. The primary image is converted into three phase-only masks (POMs) using an analytical algorithm involved partial-phase-truncation and a fast random pixel exchange process. A procedure of a fake silhouette for a decryption key is suggested to reinforce the encryption and give a hint of the position of the key. The fractional orders of FrFT effectively enhance the security of the system. In the decryption process, the POM with false information and the other two POMs are, respectively, placed in the input and fractional Fourier planes to recover the primary image. There are no unintended information disclosures and iterative computations involved in the proposed method. Simulation results are presented to verify the validity of the proposed approach.

Exotic localized structures of the (2+1)-dimensional Nizhnik-Novikov-Veselov system obtained via the extended homogeneous balance method

In this paper, we successfully apply the extended homogeneous balance method (EHBM) to derive a new type of variable separation solutions for the (2+1)-dimensional Nizhnik-Novikov-Veselov system. Novel localized coherent structures about multi-valued functions, i.e., special dromion, special peakon and foldon, and the interactions among them are discussed. Moreover, the explicit phase shifts for all the local excitations offered by the quantity U are given and applied to novel interactions among special dromion, special peakon and foldon in detail. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.03Ik

Propagation Properties of Partially Coherent Lorentz-Gauss Beams in Uniaxial Crystals Orthogonal to the X-Axis

Analytical expressions of the elements of a cross spectral density matrix are derived to describe the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis. The intensity and degree of polarization for the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis are also presented. The evolution properties of the partially coherent Lorentz-Gauss beam are numerically demonstrated. The influences of the uniaxial crystal and coherence length on the propagation properties of the partially coherent Lorentz-Gauss beam in uniaxial crystals orthogonal to the x-axis are examined. The uniaxial crystal considered here has the property of the extraordinary refractive index being larger than the ordinary refractive index. The partially coherent Lorentz-Gauss beam in the direction along the x-axis spreads more rapidly than that in the direction along the y-axis. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the spreading of the partially coherent Lorentz-Gauss beam increases in the direction along the x-axis, but decreases in the direction along the y-axis. Meanwhile, the degree of polarization in the edges of the long and short axes of the beam spot increases. With increasing the coherence length, the beam spot of the partially coherent Lorentz-Gauss beam uniformly becomes less, and the maximum degree of polarization in the edge of the beam spot decreases.

OPTICAL SOLITARY WAVES FOR THE GENERALIZED HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

In this paper, four kinds of optical solitary wave solutions, including bright, dark optical solitary waves and new types of solitary waves (W-shaped and M-shaped), for the generalized higher-order nonlinear Schrodinger equation (GHONLSE) with variable coefficients are considered under certain parametric conditions. Among these solutions, the W-shaped and M-shaped solitary waves, which cannot exist in the variable-coefficient nonlinear Schrodinger equation (vNLSE), are first given for the GHONLSE with variable coefficients. As examples, we analyze the properties of these solitary wave solutions in some periodic distributed amplification systems. When α1(z)=0, these bright and dark optical solitary wave solutions agree with the corresponding solutions in Refs. 25, 26 and 27, and the W-shaped solitary wave is in agreement with the corresponding result in Ref. 29. When α3(z)–α7(z) are constants and α1(z)=α2(z)=0, the W-shaped and M-shaped solitary waves in Refs. 14 and 15 can be recovered, respectively. Under the absence of the higher-order terms (α4(z), α6(z), α7(z)) and α1(z)=0, we provide the same results as reported in Refs. 22 and 23. This means that our results have more general forms than the earlier reports.