Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams

Two forms of the transverse energy circulation within plane-polarized paraxial light beams are specified: one inherent in wave-front singularities (optical vortices) and the other peculiar to astigmatism and asymmetry of beams with a smooth wave front. As quantitative measures of these energy flow components, the concepts of vortex and asymmetry parts of a beam's orbital angular momentum are introduced and their definitions are proposed on the basis of beam intensity moments. The properties and physical meaning of these concepts are analyzed, and their use for the study of transformations of optical vortices is demonstrated.     

The birth, annihilation, and evolution of nonparaxial optical vortices: 2. Topological dipole

The events of the birth and annihilation of optical vortices in topologically neutral nonparaxial combined mode beams (topological dipoles) were studied. It is shown that there exists an extended domain of parameters of the elementary beams, for which the optical vortices of the dipole annihilate near the focal plane, thus restoring a wave field free of the wavefront dislocations.     

Topological activity in Bragg elliptical twisted fibers

We have theoretically shown that Bragg twisted elliptical fibers manifest, in certain spectral regions, the property of topological activity--the ability to change in the reflected field the topological charge of incoming optical vortices and fundamental modes by two units. This property could be used for narrowband generation of optical vortices from Gaussian beams and for changing the topological charge of incoming optical vortices.     

Non-diffracting beams with controlled spatial coherence

We investigate the propagation properties of partially coherent non-diffracting beams. They are obtained as a superposition of plane waves possessing a single radial frequency and interfering with controlled angular correlation. The theoretical model is adapted to the experiments based on the use of the Fourier spatial filter illuminated by the Gaussian shell-model source. As an example, the influence of the partial coherence on the intensity distribution and phase properties of optical vortices is examined.     

Optical vortices produced with a nonspiral phase plate

We present simple methods to produce optical vortices on the axis of beam propagation with nonspiral phase plates. We show that a phase plate that provides linear phase retardation on one half of a laser beam produces optical vortices, which is demonstrated experimentally by use of a thickness-varying glass platelet. We also demonstrate and explain that mixed dislocations of a bent edge dislocation transform into a pair of vortices with opposing topological charges.     

Quadrefringence of optical vortices in a uniaxial crystal

The splitting of a single optical vortex into four separate ones in a singular beam is theoretically and experimentally described for the propagation of obliquely incident light in a uniaxial crystal. We also find the condition under which the generated vortices in each of the four individual beams propagate independently without changing their structure and have different locations in all beams for any crystal lengths.     

3D-vortex labyrinths in the near field of solid-state microchip laser

The usage of vortex-labyrinth fields and Talbot lattices as optical dipole traps for neutral atoms is considered for the wavelength of trapping radiation in the range 0.98–2.79 µm. The square vortex lattices generated in high Fresnel number solid-state microchip lasers are studied as a possible realization. The distribution of light field is obtained via a nonstationary computational model based on Maxwell–Bloch equations for a class-B laser, discrete Fox–Lee map with relaxation of inversion and a static model based on superposition of copropagating Gaussian beams. The spatial patterns obtained numerically and observed experimentally previously are interpreted as nonlinear superposition of vortices with helicoidal phase dislocations. The distribution of light field is approximated analytically by a sum of array of vortex lines and an additional parabolic subtrap. The separable optical trapping potential is proposed with similar intensity distribution. The factorization of the macroscopic wavefunction has led to the solution of the Gross–Pitaevsky equation for an ensemble of quantum particles trapped in a vortex labyrinth formed by a spatially periodic array of Laguerre–Gaussian beams.     

Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane

An analytical and concise formula is derived for the fractional Fourier transform (FRT) of partially coherent beams that is based on the tensorial propagation formula of the cross-spectral density of partially coherent twisted anisotropic Gaussian-Schell-model (GSM) beams. The corresponding tensor ABCD law performing the FRT is obtained. The connections between the FRT formula and the generalized diffraction integral formulas for partially coherent beams passing through aligned optical systems and misaligned optical systems are discussed. With use of the derived formula, the transformation and spectrum properties of partially coherent GSM beams in the FRT plane are studied in detail. The results show that the fractional order of the FRT has strong effects on the transformation properties and the spectrum properties of partially coherent GSM beams. Our method provides a simple and convenient way to study the FRT of twisted anisotropic GSM beams.     

Generation and conversion of optical vortices in long-period twisted elliptical fibers

We theoretically demonstrate that long-period twisted elliptical fibers have the ability to change in a certain wavelength range the topological charge of the incoming field by two units. We also show that such fibers can generate charge-2 optical vortices from the incoming Gaussian beams.     

Method for exploring the orbital angular momentum of an optical vortex beam with a triangular multipoint plate

An efficient method for exploring the orbital angular momentum of an optical vortex beam is provided. The method, based on a triangular multipoint plate, can easily determine both the sign and the magnitude of the topological charge of the optical vortices. We demonstrate its feasibility by measuring the orbital angular momentum of Laguerre-Gaussian laser beams.     

A class of partially coherent beams carrying optical vortices

A new class of partially coherent beams with a separable phase, which carry optical vortices, is introduced. It is shown that any member of the class can be represented as an incoherent superposition of fully coherent Laguerre-Gauss modes of arbitrary order, with the same azimuthal mode index. The free-space propagation properties of such partially coherent beams are studied analytically, and their M2 quality factor is investigated numerically.     

Experimental study of holographic generation of fractional Bessel beams

We demonstrate the experimental generation of a fractional Bessel beam by holographic means. Such fractional modes of Bessel beams possess an intrinsic opening gap across concentric intensity rings on propagation. We also show that the opening gaps within the fractional modes are diffraction free for a working distance while a fractional helical wave front is maintained.     

Fractional Fourier transform for beams generated by Gaussian mirror resonator

Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of beams generated by Gaussian mirror resonator passing through FRFT optical systems have been studied in detail, and some typical numerical examples are given to compare the results obtained by the approximate analytical method with those by the numerical integral method, and it is shown that our method can significantly improve the numerical calculation efficiency. Further, the results indicate that the normalized intensity distributions in the FRFT plane are closely related to the fractional order, truncation parameter and initial beam parameters. The variation period of normalized intensity distributions with p is 2 whatever the value of the truncation parameter δ is.     

Topological defects in moiré fringes with spiral zone plates

We present a study of spatial structures created by superposition of spiral zone plates used for generating optical beams with phase singularities. Moiré fringes are observed that show topological defects similar to those appearing in interference patterns of optical vortices. A brief theoretical discussion is included that supports the similarities between the two phenomena. Our results may lead to interesting applications to digital information processing by optical means.     

Ultrashort intense-field optical vortices produced with laser-etched mirrors

We introduce a simple and practical method to create ultrashort intense optical vortices for applications involving high-intensity lasers. Our method utilizes femtosecond laser pulses to laser etch grating lines into laser-quality gold mirrors. These grating lines holographically encode an optical vortex. We derive mathematical equations for each individual grating line to be etched, for any desired (integer) topological charge. We investigate the smoothness of the etched grooves. We show that they are smooth enough to produce optical vortices with an intensity that is only a few percent lower than in the ideal case. We demonstrate that the etched gratings can be used in a folded version of our 2f-2f setup [Opt. Express 19, 7599 (2005)] to compensate angular dispersion. Finally, we show that the etched gratings withstand intensities of up to 10(12) W/cm(2).     

Interferometry based technique for intensity profile measurements of far IR beams

We present a novel, to the best of our knowledge, method for measuring the intensity profile of far-IR beams. The method is based on the measurements of nonstationary variation in optical thickness of a fused-silica plate heated by the studied radiation. The optical thickness is observed by means of a reflecting interferometer. Purpose-made experimental setup allows one to measure beams with an aperture of up to 60 mm with a spatial resolution of 1 mm. The accessibility of the utilized technologies and the possibility to easily increase the aperture are the major advantages of this approach. The probable area of application for the method is measurements of beams produced by powerful industrial far-IR lasers.     

High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate

We propose using a solitary kinoform-type spiral phase plate structure to generate an array of vortices located in a single beam. Kinoform-type spiral surfaces allow each wavelength component of the phase modulation value to be wrapped back to its 2 pi equivalent for optical vortices of high charge. This allows the surface-relief profiles of high-charge vortices to be microfabricated with the same physical height as spiral phase plates of unity-charged optical vortices. The m-charged optical vortex obtained interacts with the inherent coherent background, which changes the propagation dynamics of the optical vortex and splits the initial m charge into /m/ unity-charged optical vortices within the same beam. Compared to a hologram, a multistart spiral phase plate is more efficient in the use of available spatial frequencies and beam energy and also is computationally less demanding. Furthermore, using microfabrication techniques will allow for greater achievable tolerances in terms of smaller feature sizes.     

Recognition of the interference spiral image in a fiber optical sensor employing optical vortices

Three methods of processing the image of an interference spiral formed in a fiber optical sensor employing optical vortices have been considered. It is established that a method based on recognition of the spiral image is most stable with respect to noises. Using this technique, it is possible to determine the angle of spiral rotation even when the visibility of the interference pattern decreases to 0.2. The passage from intensity measurements to determination of the geometric parameters of the image significantly increases the range of linearity of interferometric devices employing optical vortices.     

基于4π聚焦系统的电磁矢量光学斯格明子的产生

光学斯格明子为实现结构光场以及时空光场的拓扑属性提供了新的研究方法与研究思路。本文在4π聚焦系统中,通过对两对入射柱矢量光束进行偏振与相位调控,实现了聚焦光场纵向分量与横向分量的独立控制,在焦平面上得到了Néel型与Bloch型的电磁矢量光学斯格明子。在4π聚焦系统内调控两对反向传播的径向偏振光时,焦平面处将产生Néel型的电场矢量斯格明子。将其中一对替换为角向偏振光时,焦平面处将同时产生Bloch型的电场矢量斯格明子与相位超前π/2的磁场矢量斯格明子。本工作为进一步研究自由空间中微纳尺度电磁矢量光学斯格明子与物质的相互作用提供了理论基础。