Distribution of intensity and M2 factor for a partially coherent flat-topped beam in bidirectional turbulent atmosphere and plasma connection.

This study investigates the bidirectional transmission of a partially coherent flat-topped beam in a turbulent atmosphere and plasma. Analytical formulas for the intensity distribution and M2 factor are derived based on the optical transmission matrix, Collins formula, and second moment theory with Wigner distribution function. Numerical results show that the beam order and transverse spatial coherence width can be selected appropriately to mitigate turbulence and plasma induced evolution properties. The partially coherent flat-topped beam propagation through a turbulent atmosphere and plasma of the forward transmission effect on the intensity distribution and M2 factor are smaller than that of the reverse transmission. Under the same conditions, the M2 factor of a partially coherent flat-topped beam is smaller than the Gaussian beam in bidirectional transmission. Our results can be used in long-distance free-space optical communications.

Scintillation mitigation via the cross phase of the Gaussian Schell-model beam in a turbulent atmosphere.

Scintillation is an important problem for laser beams in free space optical (FSO) communications. We derived the analytical expressions for the scintillation index of a Gaussian Schell-model beam with cross phase propagation in a turbulent atmosphere. The numerical results show that the quadratic phase can be used to mitigate turbulence-induced scintillation, and the effects of the turbulent strength and beam parameters at the source plane on the scintillation index are analyzed. The variation trend of the experimentally measured scintillation index is consistent with the numerical results. Our results are expected to be useful for FSO communications.

High-precision clock date recovery for optical wireless communications using orbital-angular-momentum-based mode division multiplexing.

In this Letter, we explore the potential of the application of clock data recovery for the implementation of real-time optical wireless communications (OWCs) employing orbital angular momentum (OAM)-based mode division multiplexing (MDM). We experimentally demonstrate a 3-mode multiplexed optical wireless link with a sum rate of 60 Gbps, in which the time synchronization of different channels is realized by the proposed modified digital feedback clock recovery based on the Gardner algorithm. The experimental results show that high-precision channel synchronization with a low timing error can be achieved, and the bit-error rate of all channels can drop below 7% of the hard-decision forward error correction (HD-FEC) limit of 3.8 × 10-3, which indicates that clock data recovery can potentially provide the implementation of real-time OWCs using OAM-based MDM.

Field recovery via simplified carrier-assisted differential detection with interleaved subcarrier loading scheme at low CSPR condition.

In this Letter, we propose a simplified carrier-assisted differential detection (CADD) receiver with interleaved subcarrier loading scheme to further reduce the system hardware complexity while preserving the capability of field recovery of double sideband (DSB) complex-valued signals at the low carrier to signal power ratio (CSPR) condition. The numerical results show that the simplified CADD receiver requires less gap subcarriers to achieve a bit-error-rate (BER) below the 7% hard-decision forward error correction (HD-FEC) limit of 3.8 × 10-3 as compared with a conventional CADD receiver. Despite the robustness to the time delay fluctuation decreases, which can be avoided using time-independent components in place of time delay line, more than a 3.2-dB optical signal-to-noise ratio (OSNR) gain can be obtained regardless of CSPR.

Evolution properties of twisted Hermite Gaussian Schell-model beams in non-Kolmogorov turbulence.

A general form of twisted Hermite Gaussian Schell-model (THGSM) beams is introduced; analytical expressionsare obtained for cross-spectral density and M2-factor using the extended Huygens-Fresnel principle and Wigner function. The evolution of THGSM beams during propagation in non-Kolmogorov turbulence is shown numerically; the beams exhibit self-splitting and twist into two lobes. The intensity distribution evolves into a Gaussian shape and beam quality worsens with increasing distance; the intensity distribution and M2-factor are determined by the twist factor, beam orders, and other beam parameters. THGSM beams provide more degrees of freedom to regulate beam parameters, thereby enriching the types of partially coherent beams.

Twisted Gaussian Schell-model breathers and solitons in strongly nonlocal nonlinear media.

Based on the Snyder-Mitchell linear model and the cross-spectral density (CSD) function, the analytical propagation formula of twisted Gaussian Schell-model (TGSM) beams in strongly nonlocal nonlinear medium (SNNM) is derived. Then the propagation characteristics of TGSM beam are studied. It is found that the soliton radius is jointly determined by the initial power, coherence length, and twist factor; the degree of spatial coherence is adjusted by changing the twist factor without affecting the soliton intensity. In the case of non-soliton properties, there is a threshold of coherence length which makes partially coherent beams have the same evolution law as completely coherent beams. Furthermore, increasing the twist factor, decreasing the coherence length and initial power can improve the beam quality of the beam propagating in SNNM.

Enhanced fiber-coupling efficiency via high-order partially coherent flat-topped beams for free-space optical communications.

The fiber-coupling efficiency of signal beams is crucial in free space optical (FSO) communications. Herein, we derived an analytical expression for the fiber-coupling efficiency of partially coherent flat-topped beams propagating through atmospheric turbulence based on the cross-spectral density function. Our numerical calculation results showed that the fiber-coupling efficiency of partially coherent flat-topped beams in a turbulent atmosphere could be enhanced by increasing the beam order. Under the same conditions, the fiber-coupling efficiency of the high-order partially coherent flat-topped beams was larger than those connected to the Gaussian and Gaussian Schell-model (GSM) beams. Our results will improve the quality of partially coherent beams used in FSO communications.

Superimposed Hermite-Gaussian-correlated Schell-model beam with multiple off-axis vortices.

We first introduce a class of a superimposed Hermite-Gaussian-correlated Schell model with a multiple off-axis vortices beam, with the side lobe of the beam carrying one to four vortex singularities at the source plane. Subsequently, the variation laws of this beam after being focused by a thin lens are studied theoretically to obtain the optimal beam parameters. The numerical simulation results show that the beam possesses a unique multiple vortex structure, phase structure, and orbital angular momentum. Its intensity resembles a spiral staircase rotating around the axes. The rotational symmetry property of the transverse energy flow along the z axis was broken by the vortices. The hot spot position can be adjusted flexibly by changing the off-axis distance of vortices. This study is of great significance for nondestructive capture and manipulation of multiple particles or cells.

Simultaneous measurement of orbital angular momentum spectra in a turbulent atmosphere without probe beam compensation.

In free-space optical (FSO) communications, the orbital angular momentum (OAM) multiplexing/demultiplexing of Bessel beams perturbed by atmospheric turbulence is of great significance. We used the Gerchberg-Saxton algorithm without a beacon beam to compensate for the aberrant helical phase of the Bessel beam distorted by the turbulent atmosphere. The optical vortex Dammann axicon grating was applied for the simultaneous measurement of the intensities of the demodulated spectra of the OAM modes of the Bessel beams disturbed by atmospheric turbulence. The experimental results demonstrate that the distorted phase of the Bessel beam can be compensated and the mode purity of the target OAM mode is enhanced from 0.85 to 0.92 in case of weak turbulence. Our results will improve the quality of the OAM modes of Bessel beam (de)multiplexing in FSO communication systems.

Optimization of the probability of orbital angular momentum for Laguerre-Gaussian beam in Kolmogorov and non-Kolmogorov turbulence.

We derive the probabilities of the signal OAM state and crosstalk OAM state for a Laguerre-Gaussian (LG) beam propagating through Kolmogorov and Non-Kolmogorov turbulence, and derive the accurate analytical function of the probability for the received OAM state modulated by an arbitrary receiver aperture. The probability of the detected OAM state with a receiver aperture for different values of the radius is demonstrated numerically. Our numerical results show that the probability of the signal OAM state remains almost invariant when the radius of the receiver aperture varies. The probability of the crosstalk OAM state decreases with the decrease of the radius of the receiver aperture, thus it can be optimized by choosing a suitable value of the radius of the receiver aperture. Our results will be useful in free-space optical communications.

Propagation properties of Laguerre-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence.

Analytical formulas are derived for the average intensity, the root-mean-square (rms) angular width, and the M2-factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in non-Kolmogorov turbulence. The influence of the beam and turbulence parameters on the LGCSM beam is numerically calculated. It is shown that the quality of the LGCSM beam can be improved by choosing appropriate beam or turbulence parameter values. It is also found that the LGCSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation. Our results will have some theoretical reference value for optical communications.

OAM-labeled free-space optical flow routing.

Space-division multiplexing allows unprecedented scaling of bandwidth density for optical communication. Routing spatial channels among transmission ports is critical for future scalable optical network, however, there is still no characteristic parameter to label the overlapped optical carriers. Here we propose a free-space optical flow routing (OFR) scheme by using optical orbital angular moment (OAM) states to label optical flows and simultaneously steer each flow according to their OAM states. With an OAM multiplexer and a reconfigurable OAM demultiplexer, massive individual optical flows can be routed to the demanded optical ports. In the routing process, the OAM beams act as data carriers at the same time their topological charges act as each carrier's labels. Using this scheme, we experimentally demonstrate switching, multicasting and filtering network functions by simultaneously steer 10 input optical flows on demand to 10 output ports. The demonstration of data-carrying OFR with nonreturn-to-zero signals shows that this process enables synchronous processing of massive spatial channels and flexible optical network.

Generation and detection of broadband multi-channel orbital angular momentum by micrometer-scale meta-reflectarray.

We theoretically demonstrate the generation and detection of broadband multi-channel Orbital Angular Momentum(OAM) by a micrometer-scale meta-reflectarray. The meta-reflectarray composed of patterned silicon bars on a silver ground plane can be designed to realize phase modulation and work as chip-level OAM devices. Compared to traditional methods of OAM generation and detection, our approach shows superiorities of very compact structure size, broadband working wavelength (1250-1750 nm), high diffraction efficiency (~70%), simultaneously handling multiplex OAMs, and tunable reflection angle (0-45°). These fascinating advantages provides great potential applications in photonic integrated devices and systems for high-capacity and multi-channel OAM communication.

Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment.

A new kind of partially coherent beam with non-conventional correlation function named generalized multi-Gaussian correlated Schell-model (GMGCSM) beam is proposed. The GMGCSM beam of the first or second kind is capable of producing dark hollow or flat-topped beam profile in the focal plane (or in the far field). Furthermore, we carry out experimental generation of a GMGCSM beam of the first or second kind, and measure its focused intensity. Our experimental results verify theoretical predictions. The GMGCSM beam will be useful for free-space optical communications, material thermal processing, particle or atom trapping.

Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal.

We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.

Experimental generation of partially coherent beams with different complex degrees of coherence.

We established an experimental setup for generating partially coherent beams with different complex degrees of coherence, and we report experimental generation of an elliptical Gaussian Schell-model (GSM) beam and a Laguerre-GSM beam for the first time. It has been demonstrated experimentally that an elliptical GSM beam and a Laguerre-GSM beam produce an elliptical beam spot and a dark hollow beam spot in the focal plane (or in the far field), respectively, which agrees with theoretical predictions. Our results are useful for beam shaping and particle trapping.

Nonparaxial propagation properties of a vector partially coherent dark hollow beam.

Based on the generalized Raleigh-Sommerfeld diffraction integrals, analytical nonparaxial propagation formulas for the elements of the cross-spectral density matrix of a vector partially coherent dark hollow beam (DHB) in free space are derived. The effect of spatial coherence and beam waist sizes on the statistical properties of a nonparaxial vector DHB is studied numerically. It is found that one can modulate the statistical properties of a nonparaxial vector DHB by varying its initial spatial coherence, which will be useful in some applications where nonparaxial beams are commonly encountered.

M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere.

Analytical formula is derived for the M(2)-factor of coherent and partially coherent dark hollow beams (DHB) in turbulent atmosphere based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Our numerical results show that the M(2)- factor of a DHB in turbulent atmosphere increases on propagation, which is much different from its invariant properties in free-space, and is mainly determined by the parameters of the beam and the atmosphere. The relative M(2)-factor of a DHB increases slower than that of Gaussian and flat-topped beams on propagation, which means a DHB is less affected by the atmospheric turbulence than Gaussian and flat-topped beams. Furthermore, the relative M(2)-factor of a DHB with lower coherence, longer wavelength and larger dark size is less affected by the atmospheric turbulence. Our results will be useful in long-distance free-space optical communications.

Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere.

The propagation of an elegant Hermite-Gaussian beam (EHGB) in turbulent atmosphere is investigated. Analytical propagation formulae for the average intensity and effective beam size of an EHGB in turbulent atmosphere are derived based on the extended Huygens-Fresnel integral. The corresponding results of a standard Hermite-Gaussian beam (SHGB) in turbulent atmosphere are also derived for the convenience of comparison. The intensity and spreading properties of EHGBs and SHGBs in turbulent atmosphere are studied numerically and comparatively. It is found that the propagation properties of EHGBs and SHGBs are much different from their properties in free space, and the EHGB and SHGB with higher orders are less affected by the turbulence. What's more, the SHGB spreads more rapidly than the EHGB in turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications.

Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams.

Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere. We also demonstrate the Bessel beams based orbital angular momentum (OAM) multiplexing/demultiplexing in FSO communication with atmospheric turbulence. Under the same atmospheric turbulence condition, the bit error rates of transmitted signals carried by high order Bessel beams show smaller values and fluctuations, which indicates that the high order Bessel beams have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.