涡旋光束轨道角动量在大气湍流传输下的特性分析

从拉盖尔-高斯涡旋光束表达式出发,基于瑞利衍射理论,通过研究涡旋光束在大气湍流中传输时的旋转相干函数的变化规律,总结了涡旋光束在大气湍流中传输时各轨道角动量之间的串扰情况,使用了拓扑荷数探测概率描述串扰规律,并推导了拓扑荷数探测概率的解析表达式。研究了涡旋光束通过湍流后的拓扑荷数的分布情况,并将结果与涡旋光束通过大气随机相位屏的数值仿真结果进行了对比,给出了理论与仿真的拓扑荷数的探测概率随湍流强度以及初始涡旋光束拓扑荷数大小的关系图对比,验证了推导的拓扑荷数探测概率解析表达式的正确性。通过该表达式可进一步研究大气湍流与涡旋光束相互作用从而影响涡旋光束轨道角动量散射的本质,为涡旋光束的空间光通信中选择合适的拓扑荷数间隔,以及在不同湍流强度下选择合适束腰大小以减少串扰带来的误码率提供了理论依据。     

Determining small angles of beam splitter rotation in optical vortex shearing interferometer

It is suggested to use a singular beam of unit topological charge in a scheme of vortex shearing interferometer intended for the observation of isoclinic fringes. In the interference pattern, the regions of fringe splitting determine the localization of wavefront dislocations and exhibit a shift that depends on the beam splitter rotation angel. Using the proposed method, it is possible to evaluate small angles of beam splitter rotation with an accuracy determined by the interference fringe width.     

Three-dimensional Dammann vortex array with tunable topological charge

We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.     

A dynamic plasmonic manipulation technique assisted by phase modulation of an incident optical vortex beam

A novel phase modulation method for dynamic manipulation of surface plasmon polaritons?(SPPs) with a phase engineered optical vortex?(OV) beam illuminating on nanoslits is experimentally demonstrated. Because of the unique helical phase carried by an OV beam, dynamic control of SPP multiple focusing and standing wave generation is realized by changing the OV beam's topological charge constituent with the help of a liquid-crystal spatial light modulator. Measurement of SPP distributions with near-field scanning optical microscopy showed an excellent agreement with numerical predictions. The proposed phase modulation technique for manipulating SPPs features has seemingly dynamic and reconfigurable advantages, with profound potential for development of SPP coupling, routing, multiplexing and high-resolution imaging devices on plasmonic chips.     

Reducing the peak-to-average power ratio using unitary matrix transformation

A theoretical analysis is presented to show that in orthogonal frequency division multiplexing systems, the peak-to-average power ratio (PAPR) can be reduced by performing a unitary matrix transformation on the input vector of N symbols. The authors also prove that this transformation does not degrade the bit error rate (BER) or power spectral density (PSD) performance. Based on this, the inverse discrete Fourier transform matrix is proposed as the unitary matrix to reduce the PAPR. The simulation results show that the proposed scheme can obtain significant PAPR reduction while maintaining good performance in the BER and the PSD. To further evaluate the performance of the proposed scheme, the authors compare it with some well known PAPR reduction techniques by simulations. It is demonstrated that the proposed scheme can offer better system performance and achieve a better compromise with regard to the PAPR reduction, BER, spectral efficiency and computational complexity.     

Spiral spectrum of anomalous vortex beams propagating in a weakly turbulent atmosphere

ABSTRACT

We study the spiral spectrum of anomalous vortex beams propagating through a turbulent atmosphere. Based on the Huygens–Fresnel integral and the Rytov approximation, the integral expression and then the analytical expression for the spiral spectrum of anomalous vortex beams in the weakly turbulent atmosphere are derived. The capacity of wireless optical links using the anomalous vortex beam is obtained. It is found that the spiral spectrum of the anomalous vortex beam is less affected by turbulence than that of the Laguerre-Gaussian beam. And thus, the information capacity of wireless optical links using the anomalous vortex beam is larger than that using the Laguerre-Gaussian beam. The influence of beam order, wavelength, topological charge, propagation distance, refractive index structure constant and the radius of receiver aperture on spiral spectrum is investigated. These results contribute to reduce the disturbing effects of atmospheric turbulence on the orbital angular momentum of the vortex beam.     

Study of the properties of non-integer order vortex beams at Fraunhofer zone

The intensity and phase distributions of an optical vortex beam with non-integer values of the topological charge are analyzed in Fraunhofer region. There are two annular rings with different size and shape in the intensity patterns. The petal-like bright spots appear on the larger annular rings with higher intensity, and the small rings with lower-intensity. There are ellipse-like dark spots in the middle of the annular rings. The intensity patterns for positive and negative topological charges of vortex beams are mirrored in the x axis, and the number of bright spots and dark spots is related to the topological charge of vortex beam. In phase patters, the new born phase vortex moves gradually to the origin along the y axis, and the positions of phase vortices within the central region move regularly with the increase of the non-integer topological charge of vortex beam.     

Spectral changes of polychromatic stochastic electromagnetic vortex beams propagating through turbulent atmosphere

The unified theory of coherence and polarization and the propagation law of 2 × 2 cross-spectral density are employed to investigate spectral changes of the polychromatic stochastic electromagnetic vortex beam propagating in turbulent atmosphere. It is shown that the spectral changes of a polychromatic stochastic electromagnetic vortex beam in turbulent atmosphere differ from those of the beam without vortex. Specially, the on-axis relative spectral shifts exhibit not only blue-shift, but also red-shift. It is also shown that the topological charge, the correlation length and the refractive index structure constant influence the spectral changes of polychromatic stochastic electromagnetic vortex beams in a turbulent atmosphere.     

Peak-to-average power ratio reduction in space-time block coded multi-input multi-output orthogonal frequency division multiplexing systems using a small overhead selective mapping scheme

The selective mapping (SLM) scheme is one of the most popular peak-to-average power ratio (PAPR) reduction techniques proposed for multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. One of the major disadvantages of this scheme is the need for the transmission of side information (SI) bits to enable the receiver to recover the transmitted data. The authors present a small overhead SLM (s-SLM) scheme for space-time block coded (STBC) MIMO-OFDM systems. This proposed scheme improves the system bandwidth efficiency and achieves a significantly lower bit error rate (BER) than the individual SLM (i-SLM) and direct SLM (d-SLM) schemes. In addition, approximate expressions for the complementary cumulative distribution function (CCDF) of the PAPR and the average BER of the proposed s-SLM scheme are derived. The simulation results show that the proposed s-SLM scheme improves the detection probability of the SI bits and hence gives a better performance than the i-SLM and the d-SLM schemes.     

Focusing of radially polarized Lorentz–Gauss beams with the power–exponent–phase vortex

Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.     

Hollow Gaussian beams with the power-exponent-phase vortex

A kind of hollow Gaussian beams with the power-exponent-phase vortex is introduced. Based on the Collins integral, an analytical expression of a hollow Gaussian beam with the power-exponent-phase vortex passing through a paraxial optical system described by the ABCD matrix approach is derived. The analytical expressions for the beam propagation factors and the orbital angular momentum density of such hollow vortex Gaussian beam passing through a paraxial optical system described by the ABCD matrix approach are also derived, respectively. As a numerical example, the propagation properties of a hollow Gaussian beam with the power-exponent-phase vortex are demonstrated in free space. The evolutions of the normalized intensity, the phase and the orbital angular momentum density distributions are investigated, respectively. The influences of the power order and the topological charge on the beam propagation factors in the x- and y-directions are analysed. The introduced hollow Gaussian beam has potential applications in the atom manipulation and the optical trapping.     

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.     

Statistical properties of an anomalous hollow beam with orbital angular momentum

Due to the wide application of the vortex beam, a new theoretical model is introduced to describe the anomalous hollow beam (AHB) with optical angular momentum (OAM). The analytical propagation expression for the AHB with OAM passing through an ABCD optical system is derived. The effect of topological charge (TC) on the propagation properties of the AHB with OAM is studied numerically. The dependence of the normalized intensity distribution, the phase distribution and the optical angular momentum density (OAMD) distribution of the proposed beam on its TC is illustrated numerically. Furthermore, it is found that the intensity distribution, phase distribution, and the OAMD distribution are shaped through varying the TC and propagation distance. Our results will be useful for optical communication and optical trapping.     

Beam spreading of vortex beams propagating in turbulent atmosphere

We present some results obtained by numerical modeling of the propagation of vortex beams LG(0l) through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre-Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (LG(0l)) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge l is, the smaller the beam broadening is.     

Scintillation behaviour of vortex beams in strong turbulence region

Abstract

We study the scintillation behaviour of vectorial vortex beams in strong turbulence region. For this purpose, a list of vortex source beams is prepared. Then their scintillation performances are analysed one by one using the random phase screen approach. The results indicate that there will always be scintillation reductions with increasing values of topological charge, although its effect will diminish as we go towards higher values of the topological charge. The increases in the other specific beam parameters seem to have opposite effect. For the vectorial Hermite Gaussian beam, the use of higher orders will also aid scintillation reductions. It is foreseen that the outcome of this study will be useful for long haul optical communication links.     

Fingerprint-Based Millimeter-Wave Beam Selection for Interference Mitigation in Beamspace Multi-User MIMO Communications

Millimeter-wave communications are suitable for application to massive multiple-input multiple-output systems in order to satisfy the ever-growing data traffic demands of the next-generation wireless communication. However, their practical deployment is hindered by the high cost of complex hardware, such as radio frequency (RF) chains. To this end, operation in the beamspace domain, through beam selection, is a viable solution. Generally, the conventional beam selection schemes focus on the feedback and exhaustive search techniques. In addition, since the same beam in the beamspace may be assigned to a different user, conventional beam selection schemes suffer serious multi-user interference. In addition, some RF chains may be wasted, since they do not contribute to the sum-rate performance. Thus, a fingerprint-based beam selection scheme is proposed to solve these problems. The proposed scheme conducts offline group-based fingerprint database construction and online beam selection to mitigate multi-user interference. In the offline phase, the contributing users with the same best beam are grouped. After grouping, a fingerprint database is created for each group. In the online phase, beam selection is performed for purposes of interference mitigation using the information contained in the group-based fingerprint database. The simulation results confirm that the proposed beam selection scheme can achieve a signal-to-interference-plus-noise ratio and sum-rate performance which is close to those of a fully digital system, and having much higher energy efficiency.     

Two-dimensional encoding scheme for digital spatial domainmultiplexed large-scale optical fiber sensor arrays

This paper studies a novel two-dimensional (2-D) encoding scheme to increase the multiplexing capacity of the newly developed digital spatial domain multiplexing technique used for integration of large-scale interferometric fiber-sensor arrays. The feasibility of the scheme is assessed via computer simulation and a preliminary experiment which involved strain measurement at multipositions on a cantilever beam     

Generation of optical vortices with an adaptive helical mirror

Generation of optical vortices using a new design of adaptive helical mirror (AHM) is reported. The new AHM is a reflective device that can generate an optical vortex of any desired topological charge, both positive and negative, within its breakdown limits. The most fascinating feature of the AHM is that the topological charge of the optical vortex generated with it can be changed in real time by varying the excitation voltage. Generation of optical vortices up to topological charge 4 has been demonstrated. The presence of a vortex in the optical field generated with the AHM is confirmed by producing both fork and spiral fringes in an interferometric setup. Various design improvements to further enhance the performance of the reported AHM are discussed. Some of the important applications of AHM are also listed.     

Vortex beam propagation through atmospheric turbulence and topological charge conservation

The propagation of vortex beams through weak-to-strong atmospheric turbulence is simulated and analyzed. It is demonstrated that the topological charge of such a beam is a robust quantity that could be used as an information carrier in optical communications. The advantages and limitations of such an approach are discussed.     

Construction and performance analysis of 2-D codes for M-ary OFFH?CDMA systems

A new family of two-dimensional (2-D) codes constructed by combining frequency-hop and time-spreading codes is presented. The proposed codes are designed to overcome the limitation imposed on the maximum permissible number of simultaneous users in optical code-division multiple-access (OCDMA) systems. To increase the data transmission rate, the 2-D codes employ a M-ary signalling scheme. The proposed family of codes has the favourable characteristics of a zero autocorrelation constraint and a cross-correlation constraint of one. The performance of the 2-D code is analysed in terms of the bit error rate (BER) and is compared with that of a conventional OCDMA system using optical orthogonal code (OOC). The numerical and simulation results reveal that the proposed system outperforms conventional OCDMA systems both in terms of the BER and the data transmission rate. In addition, the system capacity is sufficient to ensure reliable communication (BERles10^-9) in local area networks