Alternative formulation for invariant optical fields: Mathieu beams

Instituto Nacional de Astrofisica, Optica y Electrónica, Apartado Postal 51/216, Puebla, Puebla Mexico 72000.
Optics Letters (Impact Factor: 3.29). 11/2000; 25(20):1493-5. DOI: 10.1364/OL.25.001493
Source: PubMed


Based on the separability of the Helmholtz equation into elliptical cylindrical coordinates, we present another class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. These fields are described by the radial and angular Mathieu functions. We identify the corresponding function in the McCutchen sphere that produces this kind of beam and propose an experimental setup for the realization of an invariant optical field.

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Available from: Marcelo David Iturbe-Castillo
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    • "2(d)–2(f) show the transverse profiles at Z = 6, 18 and 30, respectively. An intensity spot of elliptic shape is surrounded by a series of elliptic rings, a typical pattern of the lowest-order Mathieu beam [21]. These patterns remain approximately invariant during propagation. "
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    ABSTRACT: We present a set of beams which combine the properties of accelerating beams and (conventional) diffraction-free beams. These beams can travel along a desired trajectory while keeping an approximately invariant transverse profile, which may be (higher-order) Bessel-, Mathieu- or parabolic-nondiffracting-like beams, depending on the initial complex amplitude distribution. A possible application of these beams presented here may be found in optical trapping field. For example, a higher-order Bessel-like beam, which has a hollow (transverse) pattern, is suitable for guiding low-refractive-index or metal particles along a curve.
    Full-text · Article · Jun 2015 · Physics Letters A
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    • "A big part of the effort in the field has been targeted at the so-called non-diffracting waves, namely waves that resist diffraction (in their realistic finite-energy versions) and thus maintain their transverse intensity profile over large distances.[2] Bessel beams [3] are perhaps the most familiar example with diverse applications in optical manipulation, atom and nonlinear optics. [4] Other examples are Mathieu [5] and parabolic beams [6] which follow as separable solutions of the wave equation in elliptic or parabolic coordinates, respectively. Self-imaging beams that reproduce their profile periodically with distance and beams that rotate their profile around the axis of propagation also qualify as non-diffracting or, more generally, as propagation-invariant waves.[7] "
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    ABSTRACT: Chirped Bessel waves are introduced as stable (non-diffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the propagation of apodized (finite-energy) versions of such waves, with or without vorticity, in antiguides with practical parameters. The new waves exhibit a remarkable resistance against the defocusing effect of the unstable index potentials, outperforming standard Gaussians with the same full width at half maximum. The chirped profile persists even under conditions of eccentric launching or antiguide bending and is also capable of self-healing like standard diffraction-free beams in free space.
    Full-text · Article · Feb 2015 · Journal of the Optical Society of America A
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    • "In the past decades, dark hollow beam (DHB) has been investigated extensively and it has found wide applications in free-space optical communications, laser optics, particles trapping, medical sciences, atomic and binary optics [1–40]. Several theoretical models have been proposed to describe various DHBs [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]. The conventional DHBs such as Bessel Gaussian beam [9] and TEM n 01 beam (also known as doughnut beam) [10] usually have a spiral phase, and their dark hollow beam profiles remain invariant on propagation although their beam spots spread. "
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    ABSTRACT: Hollow Gaussian beam (HGB) was introduced in [Cai et al., Optics Letters 2003;28:1084-1086 [12]] and the fractional Fourier transform (FRT) for a HGB was studied theoretically in [Zheng, Physics Letters A 2006;355:156-161 [53]] . In this paper, we derive the analytical formula for the truncated FRT for a HGB, and we report experimental observation of the FRT and the truncated FRT for a HGB. The influences of the fractional order and the truncation parameter on the intensity distribution of the HGB in the FRT plane have been studied in detail both theoretically and experimentally. It is found that the FRT optical system provides an efficient way for modulating the beam profile of a HGB. Our experimental results agree well with the theoretical predictions.
    Full-text · Article · Mar 2014 · Optics & Laser Technology
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