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Performing pattern recognition via correlation in the optical domain has potential advantages, including: (i) high-speed operation at the line rate and (ii) tunability and scalability by operating on the optical wave properties. Such pattern recognition might be performed on quadrature-phase-shift-keying (QPSK) data transmitted over an optical network, which generally requires using coherent detection to distinguish the phase levels of the correlator output. To enable simpler detection, we combine optical correlation with optical biasing to experimentally demonstrate tunable and scalable QPSK pattern recognition using direct detection. The pattern is applied by adjusting the relative phases of the local pumps. Delayed QPSK signals, a coherent bias tone, and local pumps undergo nonlinear wave-mixing in a periodically poled lithium niobate (PPLN) waveguide to perform optical correlation and biasing. The biased correlator output is captured using direct detection, where the highest power level corresponds only to the pattern. Multiple QPSK pattern recognitions are achieved error-free over 3072 symbols using power thresholding values of (i) 0.78 at a 5-Gbaud rate and 0.73 at a 10-Gbaud rate for 2-symbol pattern recognition and (ii) 0.81 at a 5-Gbaud rate and 0.79 at a 10-Gbaud rate for 3-symbol pattern recognition.

We experimentally demonstrate a 10-Gbit/s free-space communication link using a single Laguerre-Gaussian (LG) beam with tunable radial and azimuthal modal indices generated by a photonic integrated circuit comprising two concentric uniform circular antenna arrays (UCAs). To tune the azimuthal modal indices ℓ of the generated beam, the azimuthal phase gradient inside each UCA is tuned. To tune the radial mode p of the generated beam, the amplitude ratio and phase difference between the two concentric UCA are tuned. To implement the above functions, the integrated device is composed of (a) two concentric UCAs where the inner (outer) UCA has 4 (8) optical antennas, (b) one Mach-Zehnder interferometer to control the amplitude ratio between the two UCAs, (c) one phase shifter to control the phase distribution between the two UCAs, and (d) phase shifters to control the azimuthal phase gradient of the inner and outer UCA. In our experiment, (a) the two modal indices of the generated beam are independently tuned (ℓ ={0,+1},p={0,1}), (b) the measured mode purity of the generated beam ranges from 23% to 38% among different target LG modes, and (c) a 10-Gbit/s chip-to-free-space optical link carried by the generated tunable LG beam is demonstrated.

Compared to its electronic counterpart, optically performed matrix convolution can accommodate phase-encoded data at high rates while avoiding optical-to-electronic-to-optical (OEO) conversions. We experimentally demonstrate a reconfigurable matrix convolution of quadrature phase-shift keying (QPSK)-encoded input data. The two-dimensional (2-D) input data is serialized, and its time-shifted replicas are generated. This 2-D data is convolved with a 1-D kernel with coefficients, which are applied by adjusting the relative phase and amplitude of the kernel pumps. Time-shifted data replicas (TSDRs) and kernel pumps are coherently mixed using nonlinear wave mixing in a periodically poled lithium niobate (PPLN) waveguide. To show the tunability and reconfigurability of this approach, we vary the kernel coefficients, kernel sizes (e.g., 2 × 1 or 3 × 1), and input data rates (e.g., 6-20 Gbit/s). The convolution results are verified to be error-free under an applied: (a) 2 × 1 kernel, resulting in a 16-quadrature amplitude modulation (QAM) output with an error vector magnitude (EVM) of ∼5.1-8.5%; and (b) 3 × 1 kernel, resulting in a 64-QAM output with an EVM of ∼4.9-5.5%.

In this paper, we experimentally demonstrate an 8-Gbit/s quadrature-phase-shift-keying (QPSK) coherent underwater wireless optical communication (UWOC) link under scattering conditions at 532 nm. At the transmitter, we generate the 532-nm QPSK signal using second-harmonic generation (SHG), where the 1064-nm signal modulated with four phase levels of an 8-phase-shift-keying (8-PSK) format is phase doubled to produce the 532-nm QPSK signal. To enhance the receiver sensitivity, we utilize a local oscillator (LO) at the receiver from an independent laser source. The received QPSK data beam is mixed with the independent LO for coherent heterodyne detection. Results show that the bit error rates (BERs) of the received QPSK signal can reach below the 7% forward error correction (FEC) limit under turbid water with attenuation lengths (γL) up to 7.4 and 6.1 for 2- and 8-Gbit/s QPSK, respectively. The corresponding receiver sensitivities are -34.0 and -28.4 dBm for 2- and 8-Gbit/s QPSK, respectively.

In general, space-time wave packets with correlations between transverse spatial fields and temporal frequency spectra can lead to unique spatiotemporal dynamics, thus enabling control of the instantaneous light properties. However, spatiotemporal dynamics generated in previous approaches manifest themselves at a given propagation distance yet are not arbitrarily tailored longitudinally. Here, we propose and demonstrate a new versatile class of judiciously synthesized wave packets whose spatiotemporal evolution can be arbitrarily engineered to take place at various predesigned distances along the longitudinal propagation path. Spatiotemporal synthesis is achieved by introducing a 2-dimensional spectrum comprising both temporal and longitudinal wavenumbers associated with specific transverse Bessel-Gaussian fields. The resulting spectra are then employed to produce wave packets evolving in both time and axial distance - in full accord with the theoretical analysis. In this respect, various light degrees of freedom can be independently manipulated, such as intensity, polarization, and transverse spatial distribution (e.g., orbital angular momentum). Through a temporal-longitudinal frequency comb spectrum, we simulate the synthesis of the aforementioned wave packet properties, indicating a decrease in relative error compared to the desired phenomena as more spectral components are incorporated. Additionally, we experimentally demonstrate tailorable spatiotemporal fields carrying time- and longitudinal-varying orbital angular momentum, such that the local topological charge evolves every ∼1 ps in the time domain and 10 cm axially. We believe our space-time wave packets can significantly expand the exploration of spatiotemporal dynamics in the longitudinal dimension. Such wave packets might potentially enable novel applications in light-matter interactions and nonlinear optics.

In this Letter, we demonstrate turbulence mitigation of four mode-division-multiplexing (MDM) quadrature-phase-shift-keying (QPSK) channels in a pilot-assisted self-coherent free-space optical (FSO) link using a photodetector (PD) array and digital signal processing (DSP)-based channel demultiplexing. A Gaussian pilot beam is co-transmitted with four 1-Gbaud QPSK channels carried by four orbital angular momentum (OAM) modes. The pilot beam experiences similar turbulence-induced wavefront distortion to the data beams. At the receiver, the turbulence distortion is mitigated by its conjugate during the pilot-data mixing in a PD array. Subsequently, we demultiplex the four channels by applying in DSP a fixed matrix on the signals. Results show that our approach has <3-dB turbulence-induced power penalty at a 7% forward error correction (FEC) limit under a turbulence strength of 2w 0 /r 0  = ∼4.4. The same turbulence can cause >18-dB penalties for a local oscillator (LO)-based coherent MDM system.

This publisher's note contains a correction to Opt. Lett.48, 6452 (2023)10.1364/OL.506270.

In general, atmospheric turbulence can degrade the performance of free-space optical (FSO) communication systems by coupling light from one spatial mode to other modes. In this Letter, we experimentally demonstrate a 400 Gbit/s quadrature-phase-shift-keyed (QPSK) FSO mode-division-multiplexing (MDM) coherent communication link through emulated turbulence using four Laguerre Gaussian (LG) modes with different radial and azimuthal indices ( L G 10 , L G 11 , L G -10 , and L G -11 ). To mitigate turbulence-induced channel cross talk and power loss, we implement an adaptive optics (AO) system at the receiver end. A Gaussian beam at a slightly different wavelength is co-propagated with the data beams as the probe beam. We use a wavefront sensor (WFS) to measure the wavefront distortion of this probe beam, and this information is used to tune a spatial light modulator (SLM) to adaptively correct the four distorted data-beam wavefronts. Using this adaptive-optics approach, the power loss and cross talk are reduced by ∼10 and ∼18 dB, respectively., (© 2023 Optical Society of America.)

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

Networks can play a key role in high-speed and reconfigurable arithmetic computing. However, two performance bottlenecks may arise when: (i) relying solely on electronics to handle computation for multiple data channels at high data rates, and (ii) the data streams input to a processing node (PN) are transmitted as phase-encoded signals over an optical network. We experimentally demonstrate the operation of optically-assisted reconfigurable average of two 4-phase-encoded data channels at 10- and 20-Gbaud rates. Our input signals are two streams of 2-bit numbers representing a binary floating-point format, and the operation results in 7-phase-encoded output signals represented by 3-bit numbers. The average operation is achieved in three stages: (1) phase encoding and division-using an optical modulator to encode the data streams; (2) summation-using a highly nonlinear fiber (HNLF); and (3) multicast-using a periodically poled lithium niobate (PPLN) waveguide to multicast back the result into the original signal wavelengths. The experimental results validate the concept, and the measured penalties indicate that: (i) the error vector magnitudes (EVMs) of optical signals increase at each stage and reach ∼18-21% for the final multicast results, and (ii) compared to the inputs, the optical signal-to-noise ratio (OSNR) penalty of output is ∼6.7 dB for the 10-Gbaud rate and ∼6.9 dB for the 20-Gbaud rate at a bit error rate (BER) of 3.8e-3.

Atmospheric turbulence can cause critical problems in many applications. To effectively avoid or mitigate turbulence, knowledge of turbulence strength at various distances could be of immense value. Due to light-matter interaction, optical beams can probe longitudinal turbulence changes. Unfortunately, previous approaches tended to be limited to relatively short distances or large transceivers. Here, we explore turbulence probing utilizing multiple sequentially transmitted longitudinally structured beams. Each beam is composed of Bessel-Gaussian ([Formula: see text]) modes with different [Formula: see text] values such that a distance-varying beam width is produced, which results in a distance- and turbulence-dependent modal coupling to [Formula: see text] orders. Our simulation shows that this approach has relatively uniform and low errors (<0.3 dB) over a 10-km path with up to 30-dB turbulence-structure-constant variation. We experimentally demonstrate this approach for two emulated turbulence regions (~15-dB variation) with <0.8-dB errors. Compared to previous techniques, our approach can potentially probe longer distances or require smaller transceivers., (© 2023. Springer Nature Limited.)

We experimentally demonstrate an optics-based half-adder of two 4-phase-shift-keying (4-PSK) data channels using nonlinear wave mixing. The optics-based half-adder has two 4-ary phase-encoded inputs (i.e., S A and S B ) and two phase-encoded outputs (i.e., Sum and Carry). The input quaternary base numbers {0,1,2,3} are represented by 4-PSK signals A and B with four phase levels. Along with the original signals A and B, the phase-conjugate signal copies A* and B*and phase-doubled signal copies A 2 and B 2 are also generated to form two signal groups S A (A, A*, A 2 ) and S B (B, B*, B 2 ). All of the above signals in the same signal group are (a) prepared in the electrical domain with a frequency spacing of Δf and (b) generated optically in the same IQ modulator. When combined with a pump laser, group S A mixes with group S B in a periodically poled lithium niobate nonlinear (PPLN) device. At the output of the PPLN device, both the Sum (A 2 B 2 ) and the Carry (AB + A*B*) are simultaneously generated with four phase levels and two phase levels, respectively. In our experiment, the symbol rates can be varied between 5 Gbaud and 10 Gbaud. The experimental results show that (i) the measured conversion efficiency of two 5-Gbaud outputs is approximately -24 dB for Sum and approximately -20 dB for Carry, and (ii) the measured optical signal-to-noise ratio (OSNR) penalty of the 10-Gbaud Sum and Carry channels is <10 dB and <5 dB, compared with that of the 5-Gbaud channels at the BER of 3.8 × 10 -3 .

There are various performance advantages when using temporal phase-based data encoding and coherent detection with a local oscillator (LO) in free-space optical (FSO) links. However, atmospheric turbulence can cause power coupling from the Gaussian mode of the data beam to higher-order modes, resulting in significantly degraded mixing efficiency between the data beam and a Gaussian LO. Photorefractive crystal-based self-pumped phase conjugation has been previously demonstrated to "automatically" mitigate turbulence with limited-rate free-space-coupled data modulation (e.g., <1 Mbit/s). Here, we demonstrate automatic turbulence mitigation in a 2-Gbit/s quadrature-phase-shift-keying (QPSK) coherent FSO link using degenerate four-wave-mixing (DFWM)-based phase conjugation and fiber-coupled data modulation. Specifically, we counter-propagate a Gaussian probe from the receiver (Rx) to the transmitter (Tx) through turbulence. At the Tx, we generate a Gaussian beam carrying QPSK data by a fiber-coupled phase modulator. Subsequently, we create a phase conjugate data beam through a photorefractive crystal-based DFWM involving the Gaussian data beam, the turbulence-distorted probe, and a spatially filtered Gaussian copy of the probe beam. Finally, the phase conjugate beam is transmitted back to the Rx for turbulence mitigation. Compared to a coherent FSO link without mitigation, our approach shows up to ∼14-dB higher LO-data mixing efficiency and achieves error vector magnitude (EVM) performance of <16% under various turbulence realizations.

There is growing interest in using multiple multiplexed orthogonal orbital angular momentum (OAM) beams to increase the data capacity of communication systems in different frequency ranges. To help enable future deployment of OAM-based communications, an ecosystem of compact and cost-effective OAM generators and detectors is likely to play an important role. Desired features of such integrated circuits include generating and detecting multiple coaxial OAM beams, tunability of OAM orders, and operation over a wide bandwidth. In this article, we discuss the use of pixel-array-based metasurfaces as OAM transmitters and receivers for mode division multiplexing (MDM) communications in near-infrared (NIR) and terahertz (THz) regimes., (© 2023 the author(s), published by De Gruyter, Berlin/Boston.)

The integration of high-speed optical communication and distributed sensing could bring intelligent functionalities to ubiquitous optical fibre networks, such as urban structure imaging, ocean seismic detection, and safety monitoring of underground embedded pipelines. This work demonstrates a scheme of integrated sensing and communication in an optical fibre (ISAC-OF) using the same wavelength channel for simultaneous data transmission and distributed vibration sensing. The scheme not only extends the intelligent functionality for optical fibre communication system, but also improves its transmission performance. A periodic linear frequency modulation (LFM) light is generated to act as the optical carrier and sensing probe in PAM4 signal transmission and phase-sensitive optical time-domain reflectometry (Φ-OTDR), respectively. After a 24.5 km fibre transmission, the forward PAM4 signal and the carrier-correspondence Rayleigh backscattering signal are detected and demodulated. Experimental results show that the integrated solution achieves better transmission performance (~1.3 dB improvement) and a larger launching power (7 dB enhancement) at a 56 Gbit/s bit rate compared to a conventional PAM4 signal transmission. Meanwhile, a 4 m spatial resolution, 4.32-nε/[Formula: see text] strain resolution, and over 21 kHz frequency response for the vibration sensing are obtained. The proposed solution offers a new path to further explore the potential of existing or future fibre-optic networks by the convergence of data transmission and status sensing. In addition, such a scheme of using shared spectrum in communication and distributed optical fibre sensing may be used to measure non-linear parameters in coherent optical communications, offering possible benefits for data transmission., (© 2023. The Author(s).)

The use of optical interconnects has burgeoned as a promising technology that can address the limits of data transfer for future high-performance silicon chips. Recent pushes to enhance optical communication have focused on developing wavelength-division multiplexing technology, and new dimensions of data transfer will be paramount to fulfill the ever-growing need for speed. Here we demonstrate an integrated multi-dimensional communication scheme that combines wavelength- and mode- multiplexing on a silicon photonic circuit. Using foundry-compatible photonic inverse design and spectrally flattened microcombs, we demonstrate a 1.12-Tb/s natively error-free data transmission throughout a silicon nanophotonic waveguide. Furthermore, we implement inverse-designed surface-normal couplers to enable multimode optical transmission between separate silicon chips throughout a multimode-matched fibre. All the inverse-designed devices comply with the process design rules for standard silicon photonic foundries. Our approach is inherently scalable to a multiplicative enhancement over the state of the art silicon photonic transmitters., (© 2022. The Author(s).)

Due to its absorption properties in atmosphere, the mid-infrared (mid-IR) region has gained interest for its potential to provide high data capacity in free-space optical (FSO) communications. Here, we experimentally demonstrate wavelength-division-multiplexing (WDM) and mode-division-multiplexing (MDM) in a ~0.5 m mid-IR FSO link. We multiplex three ~3.4 μm wavelengths (3.396 μm, 3.397 μm, and 3.398 μm) on a single polarization, with each wavelength carrying two orbital-angular-momentum (OAM) beams. As each beam carries 50-Gbit/s quadrature-phase-shift-keying data, a total capacity of 300 Gbit/s is achieved. The WDM channels are generated and detected in the near-IR (C-band). They are converted to mid-IR and converted back to C-band through the difference frequency generation nonlinear processes. We estimate that the system penalties at a bit error rate near the forward error correction threshold include the following: (i) the wavelength conversions induce ~2 dB optical signal-to-noise ratio (OSNR) penalty, (ii) WDM induces ~1 dB OSNR penalty, and (iii) MDM induces ~0.5 dB OSNR penalty. These results show the potential of using multiplexing to achieve a ~30X increase in data capacity for a mid-IR FSO link., (© 2022. The Author(s).)

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LG ℓ,p ) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

We experimentally demonstrate a 4-Gbit/s 16-QAM pilot-assisted, self-coherent, and turbulence-resilient free-space optical link using a photodetector (PD) array. The turbulence resilience is enabled by the efficient optoelectronic mixing of the data and pilot beams in a free-space-coupled receiver, which can automatically compensate for turbulence-induced modal coupling to recover the data's amplitude and phase. For this approach, a sufficient PD area might be needed to collect the beams while the bandwidth of a single larger PD could be limited. In this work, we use an array of smaller PDs instead of a single larger PD to overcome the beam collection and bandwidth response trade-off. In the PD-array-based receiver, the data and pilot beams are efficiently mixed in the aggregated PD area formed by four PDs, and the four mixing outputs are electrically combined for data recovery. The results show that: (i) either with or without turbulence effects (D/r 0  = ∼8.4), the 1-Gbaud 16-QAM signal recovered by the PD array has a lower error vector magnitude than that of a single larger PD; (ii) for 100 turbulence realizations, the pilot-assisted PD-array receiver recovers 1-Gbaud 16-QAM data with a bit-error rate below 7% of the forward error correction limit; and (iii) for 1000 turbulence realizations, the average electrical mixing power loss of a single smaller PD, a single larger PD, and a PD array is ∼5.5 dB, ∼1.2 dB, and ∼1.6 dB, respectively.

Space-time (ST) wave packets have gained much interest due to their dynamic optical properties. Such wave packets can be generated by synthesizing frequency comb lines, each having multiple complex-weighted spatial modes, to carry dynamically changing orbital angular momentum (OAM) values. Here, we investigate the tunability of such ST wave packets by varying the number of frequency comb lines and the combinations of spatial modes on each frequency. We experimentally generate and measure the wave packets with tunable OAM values from +1 to +6 or from +1 to +4 during a ∼5.2-ps period. We also investigate, in simulation, the temporal pulse width of the ST wave packet and the nonlinear variation of the OAM values. The simulation results show that: (i) a pulse width can be narrower for the ST wave packet carrying dynamically changing OAM values using more frequency lines; and (ii) the nonlinearly varying OAM value can result in different frequency chirps along the azimuthal direction at different time instants.

The channel capacity of terahertz (THz) wireless communications can be increased by multiplexing multiple orthogonal data-carrying orbital-angular-momentum (OAM) beams. In THz links using OAM multiplexing (e.g., Laguerre-Gaussian [Formula: see text] beams with p = 0), the system performance might degrade due to limited receiver aperture size and multipath effects. A limited-size aperture can truncate the received beam profile along the radial direction. In addition, due to beam divergence, part of the beam might interact with reflectors in the environment, causing the signal to reflect and interfere at the receiver with the directly propagating part of the beam; this is known as the multipath effect. In this paper, we simulate and analyze the impact of both effects on the equality of the THz OAM link by considering a full two-dimensional (2-D) LG modal set. The simulation results show (i) a limited-size receiver aperture can induce power loss and modal power coupling mainly to LG modes with the same ℓ but p > 0 for directly propagated OAM beams; (ii) the multipath effect can induce modal power coupling across multiple 2-D LG modes, which leads to inter-channel coupling among the different channels in an OAM multiplexed link; (iii) the interference between the reflected and direct beams can induce intra-channel coupling between the received signals from the reflected and direct beams; and (iv) beams with a higher OAM order (e.g., from ± 1 to ± 5) or a lower carrier frequency (e.g., from 0.1 to 1 THz) experience larger intra- and inter-channel coupling. The intra- and inter-channel coupling in an OAM-multiplexed THz link can degrade the signal-to-noise ratio (SNR) and induce SNR penalty when compared to a single-channel system., (© 2022. The Author(s).)

Integrated photonic circuits are created as a stable and small form factor analogue of fiber-based optical systems, from wavelength-division multiplication transceivers to more recent mode-division multiplexing components. Silicon nanowire waveguides guide the light in a way that single and few mode fibers define the direction of signal flow. Beyond communication tasks, on-chip cascaded interferometers and photonic meshes are also sought for optical computing and advanced signal processing technology. Here we review an alternative way of defining the light flow in the integrated photonic platform, using arrays of subwavelength meta-atoms or metalines for guiding the diffraction and interference of light. The integrated metasurface system mimics free-space optics, where on-chip analogues of basic optical components are developed with foundry compatible geometry, such as low-loss lens, spatial-light modulator, and other wavefront shapers. We discuss the role of metasurface in integrated photonic signal processing systems, introduce the design principles of such metasurface systems for low loss compact mode conversion, mathematical operation, diffractive optical systems for hyperspectral imaging, and tuning schemes of metasurface systems. Then we perceive reconfigurability schemes for metasurface framework, toward optical neural networks and analog photonic accelerators., (© 2022 the author(s), published by De Gruyter, Berlin/Boston.)

We experimentally demonstrate turbulence mitigation in a 200-Gbit/s quadrature phase-shift keying (QPSK) orbital-angular-momentum (OAM) mode-multiplexed system using simple power measurements for determining the modal coupling matrix. To probe and mitigate turbulence, we perform the following: (i) sequentially transmit multiple probe beams at 1550-nm wavelength each with a different combination of Laguerre-Gaussian (LG) modes; (ii) detect the power coupling of each probe beam to LG 0,0 for determining the complex modal coupling matrix; (iii) calculate the conjugate phase of turbulence-induced spatial phase distortion; (iv) apply this conjugate phase to a spatial light modulator (SLM) at the receiver to mitigate the turbulence distortion for the 1552-nm mode-multiplexed data-carrying beams. The probe wavelength is close enough to the data wavelength such that it experiences similar turbulence, but is far enough away such that the probe beams do not affect the data beams and can all operate simultaneously. Our experimental results show that with our turbulence mitigation approach the following occur: (a) the inter-channel crosstalk is reduced by ∼25 and ∼21 dB for OAM +1 and -2 channels, respectively; (b) the optical signal-to-noise ratio (OSNR) penalty is <1 dB for both OAM channels for a bit error rate (BER) at the 7% forward error correction (FEC) limit, compared with the no turbulence case.

Structured electromagnetic (EM) waves have been explored in various frequency regimes to enhance the capacity of communication systems by multiplexing multiple co-propagating beams with mutually orthogonal spatial modal structures (i.e., mode-division multiplexing). Such structured EM waves include beams carrying orbital angular momentum (OAM). An area of increased recent interest is the use of terahertz (THz) beams for free-space communications, which tends to have: (a) larger bandwidth and lower beam divergence than millimeter-waves, and (b) lower interaction with matter conditions than optical waves. Here, we explore the multiplexing of THz OAM beams for high-capacity communications. Specifically, we experimentally demonstrate communication systems with two multiplexed THz OAM beams at a carrier frequency of 0.3 THz. We achieve a 60-Gbit/s quadrature-phase-shift-keying (QPSK) and a 24-Gbit/s 16 quadrature amplitude modulation (16-QAM) data transmission with bit-error rates below 3.8 × 10 -3 . In addition, to show the compatibility of different multiplexing approaches (e.g., polarization-, frequency-, and mode-division multiplexing), we demonstrate an 80-Gbit/s QPSK THz communication link by multiplexing 8 data channels at 2 polarizations, 2 frequencies, and 2 OAM modes.

Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%). Moreover, the group velocity can be controlled from 0.9933c to 1.0069c (c is the speed of light in vacuum). These ST OAM wave packets might find applications in imaging, nonlinear optics, and optical communications. In addition, our approach might also provide some insights for generating other interesting ST beams.

While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with a nontrivial structure, such as Hermite-Gauss, Laguerre-Gauss, and other modes with a nontrivial structure. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information, defined in this way, is detached from a particular alphabet, i.e., communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space and information being a measure of disorder can contribute into future coherent detection algorithms and remote sensing., Competing Interests: The authors declare that there is no conflict of interest regarding the publication of this article., (Copyright © 2021 Maria Solyanik-Gorgone et al.)

When an orbital-angular-momentum (OAM) beam propagates through the dynamic air-water interface, the aerosol above the water and the water surface curvature could induce various degradations (e.g., wavefront distortion, beam wandering, scattering, and absorption). Such time-varying degradations could affect the received intensity and phase profiles of the OAM beams, resulting in dynamic modal power loss and modal power coupling. We experimentally investigate the degradation for a single OAM beam under dynamic aerosol, dynamic curvature, and their comprehensive effects. Our results show the following: (i) with the increase of the aerosol strength (characterized by the attenuation coefficient) from ∼0 to ∼0.7-1.3 dB/cm over ∼7 cm, the power coupling ratio from OAM -1 to +2 increases by 4 dB, which might be due to the amplitude and phase distortion caused by spatially dependent scattering and absorption. (ii) With the increase of the curvature strength (characterized by the variance of curvature slope over time) from ∼0 to ∼2 × 10 -5  rad 2 , the power coupling ratio from OAM -1 to +2 increases by 11 dB. This could be caused by both the wavefront distortion and the beam wandering. (iii) Under the comprehensive effect of aerosol (∼0.1-0.6 dB/cm) and curvature (∼6 × 10 -7  rad 2 ), there is an up to 2 dB higher modal power loss as compared with the single-effect cases. (iv) The received power on OAM -1 fluctuates in a range of ∼6 dB within a 220 ms measurement time under aerosol (∼0.1-0.6 dB/cm) and curvature (∼6 × 10 -7  rad 2 ) effects due to the dynamic degradations. We also demonstrate an OAM -1 and +2 multiplexed 2-Gbit/s on-off-keying link under dynamic aerosol and curvature effects. The results show a power penalty of ∼3 dB for the bit-error-rate at the 7% forward-error-correction limit under the comprehensive effect of aerosol (∼0.1-0.6 dB/cm) and curvature (∼6 × 10 -7  rad 2 ), compared with the no-effect case., (© 2021 Haoqian Song et al., published by De Gruyter, Berlin/Boston.)

We experimentally generate an orbital-angular-momentum (OAM) beam with a tunable mode order over a range of wavelengths utilizing an integrated broadband pixel-array OAM emitter. The emitter is composed of a 3-to-4 coupler, four phase controllers, and a mode convertor. An optical input is split into four waveguides by the coupler. Subsequently, the four waveguide fields are coherently combined and transformed into a free-space OAM beam by the mode convertor. By tuning the phase delay Δ φ between the four waveguides using the integrated phase controllers, the OAM order of the generated beam could be changed. Our results show that (a) a single OAM beam with a tunable OAM order ( ℓ =-1 or ℓ =+1) is generated with the intermodal power coupling of <-11 d B , and (b) in a wavelength range of 6.4 nm, a free-space link of a single 50 Gbaud quadrature-phase-shift-keying (QPSK) channel carried by the tunable OAM beam is achieved with a bit error rate below the forward-error-correction threshold. As proof of concept, a 400 Gbit/s OAM-multiplexed and WDM QPSK link is demonstrated with a ∼1-dB OSNR penalty compared with a single-beam link.

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l 0 at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l 0 with a spacing equal to N ; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l 0 ; and (3) the OAM components of the generated beam could be tuned either by changing the value of l 0 , corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.

Optical pulses carrying orbital angular momentum (OAM) have recently gained interest. In general, it might be beneficial to simultaneously achieve: (i) minimum diffraction, (ii) minimum dispersion, and (iii) controllable group velocity. Here, we explore via simulation the generation of near-diffraction-free and near-dispersion-free OAM pulses with arbitrary group velocities by coherently combining multiple frequencies. Each frequency carries a specific Bessel mode with the same topological charge ( ℓ ) but different k r (spatial frequency) values based on space-time correlations. Moreover, we also find that (i) both positive and negative group velocities could be achieved and continuously controlled from the subluminal to superluminal values and (ii) when the ℓ is varied from 0 to 10, the simulated value of the group velocity remains the same. However, as the ℓ value increases, the pulse duration becomes longer for a given number of frequency lines.

We experimentally demonstrate remotely powered, controlled, and monitored optical switching. The control signal of the switch is modulated on an optical wave and sent from a transmitter. At the switch location, the control signal is converted from an optical to an electrical signal to drive the switch. In addition, to provide electrical power at the switch location, optical power is sent from a distance and converted to electrical power using a series of photodiodes. We experimentally demonstrate (a) 1 Gb/s on-off keying data channel transmission and switching with a 1 MHz optically delivered control signal, and (b) 40 Gb/s quadrature phase-shift keying data channel transmission and remotely monitoring switch state and bias drift. The switching function is demonstrated without using any local electrical power supply. Moreover, the monitoring tones are transmitted to the remote switch and fed back to the transmitter to realize a switch state and detect the bias drift.

A time-dependent change in the refractive index of a material leads to a change in the frequency of an optical beam passing through that medium. Here, we experimentally demonstrate that this effect-known as adiabatic frequency conversion (AFC)-can be significantly enhanced by a nonlinear epsilon-near-zero-based (ENZ-based) plasmonic metasurface. Specifically, by using a 63-nm-thick metasurface, we demonstrate a large, tunable, and broadband frequency shift of up to ∼11.2 THz with a pump intensity of 4 GW/cm 2 . Our results represent a decrease of ∼10 times in device thickness and 120 times in pump peak intensity compared with the cases of bare, thicker ENZ materials for the similar amount of frequency shift. Our findings might potentially provide insights for designing efficient time-varying metasurfaces for the manipulation of ultrafast pulses.

We experimentally investigate the tunable Doppler shift in an 80 nm thick indium-tin-oxide (ITO) film at its epsilon-near-zero (ENZ) region. Under strong and pulsed excitation, ITO exhibits a time-varying change in the refractive index. A maximum frequency redshift of 1.8 THz is observed in the reflected light when the pump light has a peak intensity of ∼140 G W / c m 2 and a pulse duration of ∼580 f s , at an incident angle of 40°. The frequency shift increases with the increase in pump intensity and saturates at the intensity of ∼140 G W / c m 2 . When the pump pulse duration increases from ∼580 f s to ∼1380 f s , the maximum attainable frequency shift decreases from 1.8 THz to 0.7 THz. In addition, the pump energy required to saturate the frequency shift decreases with the increase in pump pulse duration for ∼ x <1 p s and remains unchanged for ∼ x >1 p s durations. Tunability exists among the pump pulse energy, duration, and incident angle for the Doppler shift of the ITO-ENZ material, which can be employed to design efficient frequency shifters for telecom applications.

The large number of spatial modes supported by standard multimode fibers is a promising platform for boosting the channel capacity of quantum and classical communications by orders of magnitude. However, the practical use of long multimode fibers is severely hampered by modal crosstalk and polarization mixing. To overcome these challenges, we develop and experimentally demonstrate a vectorial time reversal technique, which is accomplished by digitally pre-shaping the wavefront and polarization of the forward-propagating signal beam to be the phase conjugate of an auxiliary, backward-propagating probe beam. Here, we report an average modal fidelity above 80% for 210 Laguerre-Gauss and Hermite-Gauss modes by using vectorial time reversal over an unstabilized 1-km-long fiber. We also propose a practical and scalable spatial-mode-multiplexed quantum communication protocol over long multimode fibers to illustrate potential applications that can be enabled by our technique.

We experimentally demonstrate a tunable optical second-order Volterra filter using wave mixing and delays. Wave mixing is performed in a periodically poled lithium niobate waveguide with the cascaded sum-frequency generation and difference-frequency generation processes. Compared to conventional optical tapped delay line structures, second-order taps are added through the wave mixing of two signal copies. We measure the frequency response of the filter by sending a frequency-swept sinusoidal wave as the input. The tap weights are tuned with a liquid-crystal-on-silicon waveshaper for different filter configurations. With the additional second-order taps, the filter is able to perform a nonlinear function. As an example, we demonstrate the compensation of a nonlinearly distorted 10-20 Gbaud 4-amplitude and phase shift keying signal.

Orbital-angular-momentum (OAM) multiplexing has been utilized to increase the channel capacity in both millimeter-wave and optical domains. Terahertz (THz) wireless communication is attracting increasing attention due to its broadband spectral resources. Thus, it might be valuable to explore the system performance of THz OAM links to further increase the channel capacity. In this paper, we study through simulations the fundamental system-degrading effects when using multiple OAM beams in THz communications links under atmospheric turbulence. We simulate and analyze the effects of divergence, turbulence, limited-size aperture, and misalignment on the signal power and crosstalk of THz OAM links. We find through simulations that the system-degrading effects are different in two scenarios with atmosphere turbulence: (a) when we consider the same strength of phasefront distortion, faster divergence (i.e., lower frequency; smaller beam waist) leads to higher power leakage from the transmitted mode to neighbouring modes; and (b) however, when we consider the same atmospheric turbulence, the divergence effect tends to affect the power leakage much less, and the power leakage increases as the frequency, beam waist, or OAM order increases. Simulation results show that: (i) the crosstalk to the neighbouring mode remains < - 15 dB for a 1-km link under calm weather, when we transmit OAM + 4 at 0.5 THz with a beam waist of 1 m; (ii) for the 3-OAM-multiplexed THz links, the signal-to-interference ratio (SIR) increases by ~ 5-7 dB if the mode spacing increases by 1, and SIR decreases with the multiplexed mode number; and (iii) limited aperture size and misalignment lead to power leakage to other modes under calm weather, while it tends to be unobtrusive under bad weather.

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.

We experimentally demonstrate tunable optical single-sideband (SSB) generation using a tapped-delay-line (TDL) optical filter for 10 and 20 Gbit/s on/off-keying (OOK) signals and a 20 Gbit/s four-level pulse-amplitude-modulated (PAM4) signal. The optical SSB filter is realized by using an optical frequency comb, wavelength-dependent delay, and nonlinear wave-mixing to achieve the TDL function. Moreover, SSB tunability is achieved by adjusting the amplitude, phase, frequency spacing, and number of selected optical frequency comb lines. We show that the one-sideband suppression of a double-sideband (DSB) channel can be enhanced as the number of taps is increased; however, we do measure a ∼1.5 % error-vector-magnitude penalty. Furthermore, we demonstrate that the chromatic-dispersion-induced penalty after 80 km standard-single-mode-fiber transmission of a 10 Gbit/s SSB OOK signal without chromatic dispersion compensation has been reduced by >3 d B when compared to DSB.

We simulate and experimentally demonstrate a feedback-based probabilistic constellation shaping (FB-PCS) of a 10 Gbaud 16-ary quadrature amplitude modulation (16-QAM) signal. Our approach is to adaptively modify the distribution of transmitted symbols based on errors at the receiver, and assumptions about the channel model are not required. Specifically, the error feedback enables solving an optimization problem to find the distribution that maximizes the mutual information between the input and output of the channel without knowledge of the channel itself. A known training sequence with uniform distribution is transmitted, and the errors at each constellation point are counted at the receiver. This information is relayed to the transmitter, which then updates the data constellation with a new probability distribution such that constellation points with more errors are used less frequently. We examine four different system scenarios in simulation and one scenario in experiment. In simulation, we find that FB-PCS (a) reduces the number of errors when compared to uniform shaping for the four scenarios, and (b) reduces symbol error rate (SER) by approximately an order of magnitude or has similar SER compared to conventional Maxwell-Boltzmann (M-B) shaping. Moreover, we demonstrate that FB-PCS can lead to an SER reduction of ∼50 % .

In this paper, we experimentally demonstrate an approach that "hides" a low-intensity 50 Gbit/s quadrature-phase-keying (QPSK) free-space optical beam when it coaxially propagates on the same wavelength with an orthogonal high-intensity 50 Gbit/s QPSK optical beam. Our approach is to coaxially transmit the strong and weak beams carrying different orthogonal spatial modes within a modal basis set, e.g., orbital angular momentum (OAM) modes. Although the weak beam has much lower power than that of the strong beam, and the beams are in the same frequency band and on the same polarization, the two beams can still be effectively demultiplexed with little inherent crosstalk at the intended receiver due to their spatial orthogonality. However, an eavesdropper may not readily identify the weak beam when simply analyzing the spatial intensity profile. The correlation coefficient between the intensity profiles of the strong beam and the combined strong and weak beams is measured to characterize the potential for "hiding" a weak beam when measuring intensity profiles. Such a correlation coefficient is demonstrated to be higher than 0.997 when the power difference between the strong fundamental Gaussian beam and the weak OAM beam is ∼8,∼10, and ∼10 d B for the weak OAM -1,-2, and -3 beams, respectively. Moreover, a 50 Gbit/s QPSK data link having its Q factor above the 7% forward error correction limit is realized when the power of the weak OAM -3 beam is 30 dB lower than that of the strong fundamental Gaussian beam.

We experimentally demonstrate the use of orbital angular momentum (OAM) modes as a degree of freedom to facilitate the networking functions of carrying header information and orthogonal channel coding. First, for carrying channel header information, we transmit a 10 Gb/s on-off keying (OOK) data channel as a Gaussian beam and add to it a 10 Mb/s OOK header carried by an OAM beam with the mode order ℓ =3. We recover the header and use it to drive a switch and select the output port. Secondly, for orthogonal channel coding, we configure transmitters to generate orthogonal spatial codes (orthogonal spatial beam profiles of OAM modes), each carrying an independent data stream. We measure the correlation between the OAM codes and demonstrate their use in a multiple access system carrying two 10 Gb/s OOK data channels. At the end of this Letter, we combine the concepts of using OAM modes for carrying channel header information and orthogonal channel coding in one experiment. We transmit a 10 Gb/s OOK data channel as a Gaussian beam and add to it two 10 Mb/s OOK header waveforms carried by different OAM codes. In the routing node, we recover one of the headers to drive the switch.

Novel forms of beam generation and propagation based on orbital angular momentum (OAM) have recently gained significant interest. In terms of changes in time, OAM can be manifest at a given distance in different forms, including: (1) a Gaussian-like beam dot that revolves around a central axis, and (2) a Laguerre-Gaussian ([Formula: see text]) beam with a helical phasefront rotating around its own beam center. Here we explore the generation of dynamic spatiotemporal beams that combine these two forms of orbital-angular-momenta by coherently adding multiple frequency comb lines. Each line carries a superposition of multiple [Formula: see text] modes such that each line is composed of a different [Formula: see text] value and multiple p values. We simulate the generated beams and find that the following can be achieved: (a) mode purity up to 99%, and (b) control of the helical phasefront from 2π-6π and the revolving speed from 0.2-0.6 THz. This approach might be useful for generating spatiotemporal beams with even more sophisticated dynamic properties.

We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the k th input carrying a phase delay of ( k -1) Δ φ . The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay Δ φ ; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., l ={-1},{-1,+1},{-1,0,+1}, or {-2,-1,+1,+2}); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own Δ φ value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for l =-1), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for l ={-1} to 122 nm for l ={-2,-1,+1,+2}), and (c) increased crosstalk within the C-band (from -23.7 to -13.2 d B when the tunable range increases from 2 to 4).

We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intra-group power coupling among linearly polarized (LP) modes in a graded-index few-mode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the L P 11 group can be represented by a combination of orbital-angular-momentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the L P 11 group. We employ two output OAM modes l =+1 and l =-1 as resultant linear combinations of degenerate L P 11 a and L P 11 b modes inside the L P 11 group of a ∼0.6- k m GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20-, 40-, or 100-Gbit/s quadrature-phase-shift-keying data stream. We measure the transmission matrix (TM) in the OAM basis within L P 11 group, which is a subset of the full LP TM of the FMF-based system. An inverse TM is subsequently implemented before the receiver by a spatial light modulator to mitigate the intra-modal-group power coupling. With AO mitigation, the experimental results for l =+1 and l =-1 modes show, respectively, that (i) intra-modal-group crosstalk is reduced by >5.8 d B and >5.6 d B and (ii) near-error-free bit-error-rate performance is achieved with a penalty of ∼0.6 d B and ∼3.8 d B , respectively.

We utilize aperture diversity combined with multiple-mode receivers and multiple-input-multiple-output (MIMO) digital signal processing (DSP) to demonstrate enhanced tolerance to atmospheric turbulence and spatial misalignment in a 10 Gbit/s quadrature-phase-shift-keyed (QPSK) free-space optical (FSO) link. Turbulence and misalignment could cause power coupling from the fundamental Gaussian mode into higher-order modes. Therefore, we detect power from multiple modes and use MIMO DSP to enhance the recovery of the original data. In our approach, (a) each of multiple transmitter apertures transmits a single fundamental Gaussian beam carrying the same data stream, (b) each of multiple receiver apertures detects the signals that are coupled from the fundamental Gaussian beams to multiple orbital angular momentum (OAM) modes, and (c) MIMO DSP is used to recover the data over multiple modes and receivers. Our simulation shows that the outage probability could be reduced from >0.1 to <0.01. Moreover, we experimentally demonstrate the scheme by transmitting two fundamental Gaussian beams carrying the same data stream and recovering the signals on OAM modes 0 and +1 at each receiver aperture. We measure an up to ∼10 d B power-penalty reduction for a bit error rate (BER) at the 7% forward error correction limit for a 10 Gbit/s QPSK signal.

The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge in OAM QKD systems operating over free-space communication channels. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that even though our AO system provides a limited correction, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel. The crosstalk induced by turbulence and the performance of AO systems is investigated in two configurations: a lab-scale link with controllable turbulence, and a 340 m long cross-campus link with dynamic atmospheric turbulence. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing, and accurate wavefront correction is necessary to adequately correct turbulence-induced error. We also propose and demonstrate different solutions to improve the performance of OAM QKD with turbulence, which could enable the possibility of OAM encoding in strong turbulence.

Space-time duality in paraxial optical wave propagation implies the existence of intriguing effects when light interacts with a material exhibiting two refractive indexes separated by a boundary in time. The direct consequence of such time-refraction effect is a change in the frequency of light while leaving the wavevector unchanged. Here, we experimentally show that the effect of time refraction is significantly enhanced in an epsilon-near-zero (ENZ) medium as a consequence of the optically induced unity-order refractive index change in a sub-picosecond time scale. Specifically, we demonstrate broadband and controllable shift (up to 14.9 THz) in the frequency of a light beam using a time-varying subwavelength-thick indium tin oxide (ITO) film in its ENZ spectral range. Our findings hint at the possibility of designing (3 + 1)D metamaterials by incorporating time-varying bulk ENZ materials, and they present a unique playground to investigate various novel effects in the time domain.

We experimentally demonstrate Kramers-Kronig detection of four 20 Gbaud 16-quadrature-amplitude-modulated (QAM) channels after 50 km fiber transmission using two soliton Kerr combs as signal sources and local oscillators. The estimated carrier phase at the receiver for each of the channels is relatively similar due to the coherence between the frequency comb lines. The standard deviation of the estimated carrier phase difference of the channels is less than 0.08 rad after 50 km single-mode fiber (SMF) transmission. This enables the carrier phase recovery derived from one channel to be shared among multiple channels. In the back-to-back scenario, the bit error rate (BER) performance for shared carrier phase recovery shows an optical signal-to-noise ratio penalty of ${\sim}{0.5}\;{\rm dB}$∼0.5dB compared to the BER performance for carrier phase recovery when derived for each channel independently. BERs below the forward error correction threshold are achieved after 50 km SMF transmission with both independent and shared carrier phase recovery for four 20-Gbaud 16-QAM signals.