arXiv physics/97110041997-11-06physics.opticsquant-ph

Fractional Talbot effect in phase space: A compact summation formula

Konrad Banaszek, Krzysztof Wodkiewicz, Wolfgang P. Schleich

备注：: 4 pages, LaTeX. Submitted to Optics Express
发表信息：: Optics Express 2, 169-172 (1998)
DOI：: 10.1364/OE.2.000169

英文摘要：

A phase space description of the fractional Talbot effect, occurring in a one-dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at rational multiples of the Talbot distance is derived. The summation formula shows that the fractional Talbot image in the phase space is generated by a finite sum of spatially displaced Wigner functions of the source field.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Subwavelength fractional Talbot effect in layered heterostructures of composite metamaterials

We demonstrate that under certain conditions, fractional Talbot revivals can occur in heterostructures of composite metamaterials, such as multilayer positive and negative index media, metallodielectric stacks, and one-dimensional dielectric photonic crystals. Most importantly, without using the paraxial approximation we obtain Talbot images for the feature sizes of transverse patterns smaller than the illumination wavelength. A general expression for the Talbot distance in such structures is derived, and the conditions favorable for observing Talbot effects in layered heterostructures is disc…

2006-07-31physics.optics

Generating Lieb and super-honeycomb lattices by employing the fractional Talbot effect

We demonstrate a novel method for producing optically-induced Lieb and super-honeycomb lattices, by employing the fractional Talbot effect of specific periodic beam structures. Our numerical and analytical results display the generation of Lieb and super-honeycomb lattices at fractional Talbot lengths effectively and with high beam quality. By adjusting the initial phase shifts of the interfering beams, the incident periodic beam structures, as well as the lattices with broken inversion symmetry, can be constructed in situ. This research suggests not only a possible practical utilization of th…

2019-02-21physics.optics

Nonparaxial accelerating Talbot effect

We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as the Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A sing…

2016-05-31physics.optics

The structure of quadratic Gauss sums in Talbot effect

The field diffracted from a one-dimensional, coherently illuminated periodic structure at fractional Talbot distances can be described as a coherent sum of shifted units cells weighted by a set of phases given by quadratic Gauss sums. We report on the computation of these sums by use of the properties of a recently introduced integer $s$, which is constructed here directly from the two coprime numbers $p$ that $q$ that define the fractional Talbot plane. Using integer $s$, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In …

2016-12-11math-phmath.MPphysics.optics

Two-dimensional linear and nonlinear Talbot effect from rogue waves

We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a πphase shift; no other recurrences are observed. Different from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the …

2015-10-20nlin.PSphysics.optics

Talbot effect in nonparaxial self-accelerating beams with electromagnetically induced transparency

In this study, we report on the fractional Talbot effect of nonparaxial self-accelerating beams in a multilevel electromagnetically induced transparency (EIT) atomic configuration, which, to the best of our knowledge, is the first study on this subject. The Talbot effect originates from superposed eigenmodes of the Helmholtz equation and forms in the EIT window in the presence of both linear and cubic susceptibilities. The Talbot effect can be realized by appropriately selecting the coefficients of the beam components. Our results indicate that the larger the radial ifference between beam comp…

2020-08-25physics.optics

更多相关论文收起更多论文

Observation of electromagnetically induced Talbot effect in an atomic system

We experimentally demonstrate the Talbot effect resulting from the repeated self-reconstruction of a spatially intensity-modulated probe field under the Fresnel near-field regime. By launching the probe beam into an optically induced atomic lattice (established by interfering two coupling fields) inside a rubidium vapor cell, we can obtain an diffracted probe beam pattern from an formed electromagnetically induced grating (EIG) in a three-level $Λ$-type Doppler-free atomic configuration with the assistance of electromagnetically induced transparency (EIT). The EIG-based diffraction pattern rep…

2016-11-29physics.optics

Diffraction of Bessel beams on 2D amplitude gratings -- a new branch in the Talbot effect study

In this paper, an analytical theory for the diffraction of a Bessel beam of arbitrary order $J_l(κr)$ on a 2D amplitude grating is presented. The diffraction pattern in the main and fractional Talbot planes under certain conditions is a lattice of annular microbeams, the diameters of which depend on the grating period, the illuminating beam diameter, the number of the Talbot plane, and the topological charge $l$. For the rings near the optical axis, the latter reproduces $l$ of the illuminating beam. Experiments carried out on the Novosibirsk free electron laser at a wavelength $λ= 141$$μ$m us…

2019-08-28physics.optics

回音壁模式的Talbot干涉

Talbot interference of whispering gallery modes

本研究利用阶跃折射率多模光纤的回音壁模式，理论与实验结合研究横向角域光波的Talbot效应，实现了基于高阶分数Talbot效应的紧凑多端口分束器，拓展了角向Talbot效应的应用场景。

2024-07-16physics.optics

The Nonlinear Talbot Effect of Rogue Waves

Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lob…

2014-02-13nlin.PSphysics.optics

多缝时间反向杨氏干涉：源空间光栅定律、二次相位效应和Talbot-like复兴

Multi-slit time-reversed Young interference: source-space grating laws, quadratic-phase effects, and Talbot-like revivals

Binghamton University（宾汉姆顿大学）

本文研究了多缝时间反向杨氏干涉，揭示了源空间光栅定律、二次相位效应及Talbot-like复兴的物理机制，展示了多缝系统在源空间分辨与相位结构敏感性方面的独特性质。

2026-04-21physics.app-phphysics.class-phphysics.optics

Space-time analogy and its application to design schemes borrowed from Fourier optics for processing ultrafast optical signals

Square-wave pulse generation with a variable duty ratio can be realized with the help of ideas of Talbot array illuminators formulated for binary phase gratings. A binary temporal phase modulation of CW laser field propagating through a group-delay-dispersion circuit of the fractional Talbot length $P/Q$ results in a well defined sequence of square-wave-form pulses. When $P=1$ a duty ratio of the pulses $D$ is $1/2$ for $Q=4$ and $1/3$ for $Q=3$ and 6. Maximum intensity of the pulses doubles and triples compared to the CW intensity for $D=1/2$ and $1/3$, respectively. These pulses can be used …

2022-07-26physics.optics