400-Gbit/s QPSK free-space optical communicationlink based on four-fold multiplexing of Hermite-Gaussian or Laguerre-Gaussian modes by varying both modal indices

Reflection and refraction of higher-order Hermite-Gaussian beams: a vector wave analysis

Hermite-Gaussian beams, as a typical kind of higher-order mode laser beams, have attracted intensive attention because of their interesting properties and potential applications. In this paper, a full vector wave analysis of the higher-order Hermite-Gaussian beams upon reflection and refraction is reported. The explicit analytical expressions for the electric and magnetic field components of the reflected and refracted Hermite-Gaussian beams are derived with the aid of angular spectrum representation and vector potential in the Lorenz gauge. Based on the derived analytical expressions, local field distributions of higher-order Hermite-Gaussian beams reflection and refraction at a plane interface between air and BK7 glass are displayed and analyzed.

Turbulence-resistant high-capacity free-space optical communications using OAM mode group multiplexing

Twisted light carrying orbital angular momentum (OAM), which features a helical phase front, has shown its potential applications in diverse areas, especially in free-space optical (FSO) communications. Multiple orthogonal OAM beams can be utilized to enable high-capacity FSO communication systems. However, for practical OAM-based FSO communication links, atmospheric turbulence will cause serious power fluctuations and inter-model crosstalk between the multiplexed OAM channels, impairing link performance. In this paper, we propose and experimentally demonstrate a novel OAM mode-group multiplexing (OAM-MGM) scheme with transmitter mode diversity to increase system reliability under turbulence. Without adding extra system complexity, an FSO system transmitting two OAM groups with a total of 144 Gbit/s discrete multi-tone (DMT) signal is demonstrated under turbulence strength D/r0 of 1, 2, and 4. In our experiments, the proposed OAM-MGM scheme helps to achieve bit-error-rate (BER) mostly less than 3.8 × 10^-3 under turbulence strength D/r0 of 1 and 2 with a total transmitted power of 10 dBm. Compared with the conventional OAM mode multiplexed system, the system interruption probability decreases from 28% to 4% under moderate turbulence strength D/r0 of 2.

Shaping the transmission trajectory of vortex beam by controlling its radial phase

Vortex beam carrying orbital angular momentum (OAM), which features a helical phase front, has shown its potential applications in diverse areas, especially in free-space optical (FSO) communications. However, when generating vortex beams, the radial phase distribution is usually disregarded in previous reports. In this paper, by controlling the radial phase distribution, we propose a method for the generation of vortex beams with arbitrary convex trajectories. By using this method, we successfully generate vortex beams with different predesigned trajectories with high accuracy. Moreover, we also demonstrate the transmission of the radial phase-controlled vortex beams in FSO links for different scenarios in simulation. Firstly, we generate vortex beams with different OAM states (l=+1, + 3, and +6), which have the same ring diameter at the receiver side. Secondly, we generate three vortex beams (l=+3) with the same ring diameter at different transmission distances (z = 100 m, 200 m, and 300 m). Finally, by carefully controlling the radial phase of the vortex beam, we generate vortex beams that can almost keep the same ring diameter for a long distance. The proposed method for shaping the transmission trajectory of vortex beams may pave the way for more applications in OAM-based FSO communications.

Experimental realization of modulated Hermite-Gaussian laser modes: a maximum number of highly intense lobes

Here, we present an experimental method that redistributes the optical energy among the lobes of high-order standard Hermite-Gaussian (SHG) laser modes in a controlled manner. We numerically designed diffractive optical elements, displayed over a spatial light modulator for redistribution of optical energy that converts low and moderate intense lobes into all highly intense lobes and vice versa at the Fourier plane. Such precise generation of modulated HG (MHG) laser modes offers a maximum number of highly intense lobes compared to SHG modes. Hence, we envisage that MHG beams may surpass SHG beams in many applications, such as particle manipulation and optical lithography, where highly intense lobes play a significant role.

Changes in orbital angular momentum distribution of a twisted partially coherent array beam in anisotropic turbulence

Based on the generalized Huygens Fresnel integral, we derive the analytical formula of the cross-spectral density of a twisted partially coherent array beam propagating in non-Kolmogorov anisotropic turbulence, and investigate the changes in orbital angular momentum (OAM). The results show that the anisotropy of the turbulence causes different effects in horizontal and vertical directions. The spectral density distribution of twisted partially coherent array beam in turbulence presents self-splitting and rotation, which combines the interesting effects of the twist phase and coherent structure. Although OAM is conserved, the spatial distribution of OAM flux density can be changed by changing the propagation distance, power and anisotropy of turbulence, and the modulation of the twist phase affects not only the magnitude of OAM but also its distribution. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications and optical field modulation.

Single-wavelength transmission at 1.1-Tbit/s net data rate over a multi-modal free-space optical link using commercial devices

We employ commercial mode-selective photonic lanterns to implement mode multiplexing and demultiplexing for high-capacity free-space optical communications. Moreover, we design a time-division-multiplexed frame structure to efficiently emulate multiple independent transmitters with channelized precoding using only one transmitter. To maximize the throughput of the system, we optimize the modes selected for carrying data, and apply adaptive loading to different channels. By leveraging mode- and polarization-division multiplexing, the free-space optical data link comprising multiple independent channels provides an aggregate net data rate of 1.1 Tbit/s and net spectral efficiency of 28.35 bit/s/Hz. Different from many previous demonstrations based on delayed or partially delayed copies of identical data streams, to the best of our knowledge, ours is a record-high net data rate and net spectral efficiency achieved by a single-wavelength mode-division multiplexed free-space optical communication system with fully independent channels. Moreover, all key devices used in this work, including optical transponder, multiplexer, and demultiplexer are commercially available.

Propagation Characteristics of Hermite–Gaussian Beam under Pointing Error in Free Space

Hermite–Gaussian (HG) beams have significant potential to improve the capacity of free-space optical communication (FSOC). The influence of pointing error on the propagation characteristics of an HG beam cannot be ignored in the FSOC system. Although the average irradiance of the HG beam under a small pointing error from the FSOC tracking mechanism has been investigated through Taylor series approximation, here, we propose that the average irradiance of the HG beam under an arbitrary magnitude pointing error can be deduced through a statistical averaging method. We firstly found that the average irradiance profile of an HG beam finally changes into an approximately Gaussian shape with the increase in pointing error and propagation distance and a larger beam waist at the transmitter could mitigate the profile change. The correlation coefficient between deduced theoretical expression and Monte Carlo simulation reaches 0.999. Additionally, the effective spot size, location of the local extreme value, average received power and signal-to-noise ratio (SNR) loss for an HG beam under pointing error were theoretically deduced and analyzed for the first time. We found that the effective spot size of the higher-order HG beam experiences less broadening under the pointing error than that of the lower-order HG beam. The fundamental theoretical expressions of average irradiance for an HG beam under pointing error have provided effective guidance for analyzing the propagation characteristics and link performance.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

Divergence-degenerate spatial multiplexing towards future ultrahigh capacity, low error-rate optical communications

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers for free-space optical communication, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and data transmission by the conjugated modulation method, demonstrating lower error rates caused by center offset and coherent background noise, compared with OAM basis. Our work provides a potentially useful basis for the next generation of large-scale dense data communication.

Free-space optical communication with quasi-ring Airy vortex beam under limited-size receiving aperture and atmospheric turbulence

Vortex beams carrying orbital angular momentum (OAM), which feature helical wavefronts, have been regarded as an alternative degree of freedom for free-space optical (FSO) communication systems. However, in practical applications, atmospheric turbulence and limited-size receiving aperture effects will cause OAM modal degradation and seriously reduce the received power. In this paper, by controlling the radial phase distribution of conventional OAM beams, quasi-ring Airy vortex beams (QRAVBs) are successfully generated in the experiments to increase the received power under the limited-size receiving aperture conditions. By employing 72-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) discrete multi-tone (DMT) signals, we successfully demonstrate free-space data transmission with QRAVBs in the experiments. Moreover, the transmission performance of QRAVBs under atmospheric turbulence is also evaluated. Comparing with conventional OAM beam and Bessel beam, the obtained results show that QRAVBs can achieve higher received power and better BER performance under limited-size receiving aperture and atmospheric turbulence conditions.

768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks

Beyond orbital angular momentum of Laguerre-Gaussian (LG) modes, the radial index can also be exploited as information channel in free-space optical (FSO) communication to extend the communication capacity, resulting in the LG- shift keying (LG-SK) FSO communications. However, the recognition of radial index is critical and tough when the superposed high-order LG modes are disturbed by the atmospheric turbulences (ATs). In this paper, the convolutional neural network (CNN) is utilized to recognize both the azimuthal and radial index of superposed LG modes. We experimentally demonstrate the application of CNN model in a 10-meter 768-ary LG-SK FSO communication system at the AT of Cn2 = 1e-14 m^-2/3. Based on the high recognition accuracy of the CNN model (>95%) in the scheme, a colorful image can be transmitted and the peak signal-to-noise ratio of the received image can exceed 35 dB. We anticipate that our results can stimulate further researches on the utilization of the potential applications of LG modes with non-zero radial index based on the artificial-intelligence-enhanced optoelectronic systems.

Experimental mitigation of the effects of the limited size aperture or misalignment by singular-value-decomposition-based beam orthogonalization in a free-space optical link using Laguerre-Gaussian modes

Limited-size receiver (Rx) apertures and transmitter-Rx (Tx-Rx) misalignments could induce power loss and modal crosstalk in a mode-multiplexed free-space link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s four-data-channel free-space optical link. To mitigate the above degradations, our approach of singular-value-decomposition-based (SVD-based) beam orthogonalization includes (1) measuring the transmission matrix H for the link given a limited-size aperture or misalignment; (2) performing SVD on the transmission matrix to find the U, Σ, and V complex matrices; (3) transmitting each data channel on a beam that is a combination of Laguerre-Gaussian modes with complex weights according to the V matrix; and (4) applying the U matrix to the channel demultiplexer at the Rx. Compared with the case of transmitting each channel on a beam using a single mode, our experimental results when transmitting multi-mode beams show that (a) with a limited-size aperture, the power loss and crosstalk could be reduced by ∼8 and ∼23dB, respectively; and (b) with misalignment, the power loss and crosstalk could be reduced by ∼15 and ∼40dB, respectively.

Experimental demonstration of structural robustness of spatially partially coherent fields in turbulence

Structured fields that are spatially completely coherent have been extensively studied in the context of long-distance optical communication, as the structure in the intensity profile of such fields is used for encoding information. This method of doing optical communication works very well in the absence of turbulence. However, in the presence of turbulence, the intensity structures of such fields start to degrade because of the complete spatial coherence of the field, and this structural degradation increases with the increase in turbulence strength. On the other hand, several theoretical studies have now shown that the structured fields that are spatially only partially coherent are less affected by turbulence. However, to the best of our knowledge, no such experimental demonstration has been reported until now. In this Letter, we experimentally demonstrate the structural robustness of partially coherent fields in the presence of turbulence, and we show that for a given turbulence strength, the structural robustness of a partially coherent field increases as the spatial coherence length of the field is decreased.

Coherent optical wireless communication link employing orbital angular momentum multiplexing in a ballistic and diffusive scattering medium

We experimentally investigate the scattering effect on an 80 Gbit/s orbital angular momentum (OAM) multiplexed optical wireless communication link. The power loss, mode purity, cross talk, and bit error rate performance are measured and analyzed for different OAM modes under scattering levels from ballistic to diffusive regions. Results show that (i) power loss is the main impairment in the ballistic scattering, while the mode purities of different OAM modes are not significantly affected; (ii) in the diffusive scattering, however, the performance of an OAM-multiplexed link further suffers from the increased cross talk between the different OAM modes.

Demonstration of a 10 Mbit/s quantum communication link by encoding data on two Laguerre-Gaussian modes with different radial indices

We experimentally demonstrate a 10 Mbit/s free-space quantum communication link using data encoding on orthogonal Laguerre-Gaussian (LG) modes with the same azimuthal index but different radial indices. Data encoding on two LG_ℓp modes (i.e., for ℓ=0, we encode ["0", "1"] as [p=0, p=1], and for ℓ=1, we encode ["0", "1"] as [p=0, p=1]) is demonstrated by employing directly modulated laser diodes and helical phase holograms. The quantum symbol error rate (QSER) of <5% is achieved at an encoding rate of 10 Mbit/s. Moreover, the influence of the circle radius (R) of the receiver phase pattern on registered photon rates and QSERs is investigated. Our results show that a receiver phase pattern whose R does not match the beam size of the LG modes would induce higher cross talk between the two encoded quantum branches.