Demonstration of optically-assisted reconfigurable average of two 20-Gbaud 4-phase-encoded data channels using nonlinear wave mixing.

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.

Experimental demonstration of an optics-based 4-PSK half-adder using nonlinear wave mixing.

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., SA and SB) 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 A2 and B2 are also generated to form two signal groups SA(A, A*, A2) and SB(B, B*, B2). 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 SA mixes with group SB in a periodically poled lithium niobate nonlinear (PPLN) device. At the output of the PPLN device, both the Sum (A2B2) 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.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

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 (LGℓ,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.

High-capacity free-space optical communications using wavelength- and mode-division-multiplexing in the mid-infrared region.

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.

Utilizing multiplexing of structured THz beams carrying orbital-angular-momentum for high-capacity communications.

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.

Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb.

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.

Receiver aperture and multipath effects on power loss and modal crosstalk in a THz wireless link using orbital-angular-momentum multiplexing.

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.

Turbulence-resilient pilot-assisted self-coherent free-space optical communications using a photodetector array for bandwidth enhancement.

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/r0 = ∼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.

Demonstration of generating a 100 Gbit/s orbital-angular-momentum beam with a tunable mode order over a range of wavelengths using an integrated broadband pixel-array structure.

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 Δφ 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 <-11dB, 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.

Experimental demonstration of remotely powered, controlled, and monitored optical switching based on laser-delivered signals.

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.

Simulation of near-diffraction- and near-dispersion-free OAM pulses with controllable group velocity by combining multiple frequencies, each carrying a Bessel mode.

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 kr (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.

Tunable optical second-order Volterra nonlinear filter using wave mixing and delays to equalize a 10-20 Gbaud 4-APSK channel.

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.

Modal coupling and crosstalk due to turbulence and divergence on free space THz links using multiple orbital angular momentum beams.

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.

16-QAM probabilistic constellation shaping by adaptively modifying the distribution of transmitted symbols based on errors at the receiver.

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%.