Topological charge identification of superimposed orbital angular momentum beams under turbulence using an attention mechanism.

Due to the unique features, orbital angular momentum (OAM) beams have been widely explored for different applications. Accurate determination of the topological charge (TC) of these beams is crucial for their optimal utilization. In this paper, we propose a method that combines adaptive image processing techniques with a simple, parameter-free attention module (SimAM) based convolutional neural network to accurately identify the TC of high-order superimposed OAM beams. Experimental results demonstrate that under the combined influence of non-extreme light intensity and turbulence, it can achieve >95% identification accuracy of TCs ranging from ±1 to ±40. Moreover, even under partial-pattern-missing conditions, our method maintains an accuracy rate of over 80%. Compared with traditional attention mechanisms, SimAM does not require additional network design, significantly reducing the computational costs. Our approach showcases remarkable efficiency, robustness, and cost-effectiveness, making it adaptable to challenging factors such as non-uniform lighting and partially occluded light paths. This research provides a new direction for recognizing OAM modes with valuable implications for the future of communication systems.

Turbulence mitigation of four mode-division-multiplexed QPSK channels in a pilot-assisted self-coherent free-space optical link using a photodetector array and DSP-based channel demultiplexing.

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 2w0/r0 = ∼4.4. The same turbulence can cause >18-dB penalties for a local oscillator (LO)-based coherent MDM system.

Adaptive-optics-based turbulence mitigation in a 400 Gbit/s free-space optical link by multiplexing Laguerre-Gaussian modes varying both radial and azimuthal spatial indices: publisher's note.

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

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation.

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.

Automatic turbulence mitigation for coherent free-space optical links using crystal-based phase conjugation and fiber-coupled data modulation.

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.

Adaptive-optics-based turbulence mitigation in a 400†Git/s free-space optical link by multiplexing Laguerre-Gaussian modes varying both radial and azimuthal spatial indices.

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.

System impact and calibration method of power imbalances for a dual-polarization in-phase/quadrature optical transmitter.

For the latest 400-Gb/s or upcoming 1-Tb/s single-carrier optical fiber communications systems, dual-polarization quadrature amplitude modulation (DP-QAM) based on in-phase (I) and quadrature (Q) optical transmitter is the only possible solution. In a coherent DP-IQ transmitter, the power difference between the I and Q branches or orthogonally polarized (X and Y) channels are known as the IQ or XY power imbalance, respectively. Uncompensated IQ and XY power imbalances are always troublesome and can significantly limit the performance in long-haul transmission. In this work, we first experimentally investigate the impact of IQ and XY power imbalances on various QAM formats and baud rates in high-speed transmission. A DP-16-QAM up to 86 GBd is investigated, aiming for beyond 400 Gb/s applications. Then, a convenient pre-calibration method based on optical interference is proposed and experimentally demonstrated to detect and compensate both the IQ and XY power imbalances. This method can use the existing modulator structure and low-speed photodiode in the DP-IQ transmitter to obtain the optical interference power by injecting a specific coded electrical signal. After adjusting the time skew of each channel, the power imbalance between two channels can be calibrated by minimizing the optical interference power. The results fit well with the given theoretical analysis, and the proposed technique can be adopted to the DP-IQ transmitter with different QAM formats.

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.

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.

Tunability of space-time wave packet carrying tunable and dynamically changing OAM value.

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.

Demonstration of turbulence mitigation in a 200-Gbit/s orbital-angular-momentum multiplexed free-space optical link using simple power measurements for determining the modal crosstalk matrix.

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 LG0,0 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.

Adiabatic Frequency Conversion Using a Time-Varying Epsilon-Near-Zero Metasurface.

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/cm2. 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.

Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters.

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 l0 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 l0 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 l0; and (3) the OAM components of the generated beam could be tuned either by changing the value of l0, 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.

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.

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 Doppler shift using a time-varying epsilon-near-zero thin film near 1550 nm.

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 ∼140GW/cm2 and a pulse duration of ∼580fs, at an incident angle of 40°. The frequency shift increases with the increase in pump intensity and saturates at the intensity of ∼140GW/cm2. When the pump pulse duration increases from ∼580fs to ∼1380fs, 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<1ps and remains unchanged for ∼x>1ps 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.

Demonstrating the use of OAM modes to facilitate the networking functions of carrying channel header information and orthogonal channel coding.

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.

Utilizing phase delays of an integrated pixel-array structure to generate orbital-angular-momentum beams with tunable orders and a broad bandwidth.

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 kth input carrying a phase delay of (k-1)Δφ. The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay Δφ; (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 Δφ 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 -13.2dB when the tunable range increases from 2 to 4).

Demonstration of using two aperture pairs combined with multiple-mode receivers and MIMO signal processing for enhanced tolerance to turbulence and misalignment in a 10 Gbit/s QPSK FSO link.

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 ∼10dB power-penalty reduction for a bit error rate (BER) at the 7% forward error correction limit for a 10 Gbit/s QPSK signal.