Model-based end-to-end learning for a self-homodyne coherent system.

We investigate the statistical properties of the inherent intensity fluctuation in a low-cost and low-complexity self-homodyne coherent system employing an amplified spontaneous emission (ASE) source. The noise distribution model of the considered system is established, which is shown to be highly consistent with the experimental results for a 10 GBd 256-ary quadrature amplitude modulation (QAM) signal transmission over a 10 m duplex fiber. With the help of the proposed noise model, we then design advanced mappers and demappers. The optimized system alleviates the need for ASE bandwidth and is evaluated by applying forward error correction codes. Furthermore, we demonstrate an information rate increase of 6.67% with respect to 64-QAM.

In-fiber duplex optical antenna and its programmable spectral filter application: publisher's note.

This publisher's note contains corrections to Opt. Lett.47, 4937 (2022)10.1364/OL.468940.

In-fiber duplex optical antenna and its programmable spectral filter application.

In this Letter, we have proposed an in-fiber duplex optical antenna based on a 45° radiated titled fiber grating (RTFG), in which the 45° RTFG not only radiates the light from the fiber core to the free space, but also harvests the light from the free space back into the fiber core. Using the finite difference time domain method, we have theoretically analyzed the light recoupling efficiency of the RTFG. The simulated results have shown that the RTFG-based optical antennas have a maximum coupling efficiency of 10%. The recoupling wavelength and efficiency are related to the grating period and horizontal incidence angle. Furthermore, we demonstrate a programmable spectral filtering system based on the 45° RTFG antennas, which could achieve filtering with arbitrary spectral shapes. The spectral resolution is 0.4 nm and the insertion loss is around 20 dB. The proposed programmable spectral filtering system has a compact structure compared with the traditional filter.

Experimental characterization of group and phase delays induced by bending and twisting in multi-core fibers.

The local variations of group and phase propagation delays induced by bending and twisting a coupled core three-core fiber are experimentally characterized, for the first time, to the best of our knowledge, along the fiber length, with millimeter-scale spatial resolution. The measurements are performed by means of spectral correlation analysis on the fiber's Rayleigh backscattered signal, enabling for a distributed measurement of the perturbation effects along the fiber length. A mathematical model validating the experimental results is also reported.

Demonstration of terabit coherent on-chip optical interconnects employing mode-division multiplexing.

We experimentally demonstrate a net capacity per wavelength of 1.23 Tb/s with 30 GBaud 16-ary quadrature amplitude modulation (16-QAM) mode-division multiplexing (MDM) signals over a single silicon-on-insulator (SOI) multimode waveguide for optical interconnects employing $11 \times 11$ multiple-in-multiple-out (MIMO) digital signal processing. In order to simplify the receiver architecture for coherent optical interconnects, we further propose and evaluate an on-chip self-homodyne coherent detection (SHCD) scheme. In the experiment, 30 Gbaud quadrature phase shift keying (QPSK) signals carried by 10 waveguide modes are successfully recovered with bit error rates (BERs) below 7% forward error correction (FEC) threshold using the pilot tone delivered by ${{\rm TE}_0}$ mode as a local oscillator. Around 10% penalty on error vector magnitude (EVM) is observed due to modal cross talk compared to homodyne detection.

Phase retrieval with fast convergence employing parallel alternative projections and phase reset for coherent communications.

Phase-retrieval (PR) receivers can reconstruct complex-valued signals using only direct detection without the use of any optical carriers. We propose and demonstrate two PR receiver solutions with faster and better convergence. First, we demonstrate a PR receiver based on parallel alternative projections that are produced by propagating the signal through an array of dispersive elements of increasing length followed by direct detection. Fast convergence and high retrieved phase accuracy are achieved using a modified Gerchberg-Saxton (GS) algorithm that uses each projection as an intensity constraint. Second, we achieve similar performances employing an enhanced single projection GS algorithm with selective phase reset using symbol-wise GS errors. We experimentally reconstruct a 30 Gbaud QPSK signal after 55 km single-mode fiber transmission using the proposed solutions with a reduced number of iterations.

Carrier-less phase retrieval receiver leveraging digital upsampling.

Phase retrieval (PR) receivers can reconstruct the full electrical field of the signal using only intensity measurements without any optical carrier. In this Letter, we investigate the requirement of digital upsampling and receiver bandwidth of the PR receiver based on alternative projection employing a dispersive element. An iteration scheme averaging the interleaved upsampled symbols to maintain two samples per symbol for the estimated complex-valued signal is proposed and experimentally demonstrated with fast algorithm convergence. The PR uses a modified Gerchberg-Saxton algorithm. Experimentally, we measure Nyquist-shaped 30-GBaud quadrature phase shift keying signals after 55-km single-mode fiber transmission using only 110 and 250 iterations to reach, respectively, the 20% and 7% forward-error correction threshold levels.

Temporal and spectral coding over amplified spontaneous emission for secure optical coherent communications.

We demonstrate secure optical coherent communications employing low-coherence matched detection based on the randomness of amplified spontaneous emission (ASE) noise. Two-level physical-layer optical encryption is achieved through temporal and spectral coding over a broadband ASE source. An ASE-carried signal and unmodulated carrier are polarization multiplexed, transmitted over a same single-mode fiber (SMF), and separated with the aid of polarization tracking before having matched detection at the receiving side. The impact of chromatic dispersion on the low-coherence matched detection system is analyzed and experimentally investigated. We experimentally realize optically coded 20 Gbaud QPSK and 8-PSK signals transmission over a 43 km SMF span with a maximum line rate of 60 Gbits/s.

Multiport swept-wavelength interferometer with laser phase noise mitigation employing a broadband ultra-weak FBG array.

Optical vector network analyzers (OVNAs) based on swept-wavelength interferometry are applied widely in optical metrology and sensing to measure the complex transfer functions of optical components, devices, and fibers. Phase noise from laser sweep nonlinearities degrades the measurement quality as the distance increases and limits the usage of the OVNA in characterizing systems with long impulse responses as required in space-division multiplexing links with a high mode count or in the presence of large modal differential group delay (DGD). In this Letter, we use a densely distributed broadband ultra-weak fiber Bragg grating array to directly measure the distortion due to phase noise at a 5-m increment up to 400 m and use this measured data to directly eliminate the distortion. We experimentally extend the measurement range of the swept-wavelength OVNA over 400 m and successfully characterize a 2-km six-mode multimode fiber link with an accumulated impulse response as wide as 20 ns.

Triple-clad photonic lanterns for mode scaling.

We propose a novel triple-clad photonic lanterns for mode scaling. This novel structure alleviates the adiabatic tapering requirement for the fabrication of large photonic lanterns. A 10-mode photonic lantern with insertion losses ranging from 0.6 to 2.0 dB across all the modes and a record-low pairwise 4-dB mode-dependent loss at C-band was demonstrated.

Broadband and low-loss mode scramblers using CO2-laser inscribed long-period gratings.

We demonstrate broadband and low-loss three-mode and six-mode scramblers employing CO2-laser inscribed long-period gratings (LPGs) for space-division multiplexing. Step-index (SI) few-mode fibers are used to avoid mode coupling to the cladding modes. We characterize the mode scramblers using a swept-wavelength interferometer. Mode-dependent loss (MDL) and modal transfer matrices over the C+L band are presented. Demonstrated LPGs with negligible MDL and low insertion loss contributed to high-performance CO2-laser inscription. The total MDLs induced by the SI fiber with LPGs in three-mode and six-mode scramblers are measured to be 2 and 4 dB, respectively.

All-fiber 6-mode multiplexers based on fiber mode selective couplers.

All-fiber 6-mode multiplexer composed of two consecutive LP11-mode selective couplers (MSC), two LP21-MSCs and an LP02-MSC is fully characterized by wavelength-swept interferometer technique. The MSCs are fabricated by polished-type fiber couplers coupling LP01 mode of a single mode fiber into a higher-order mode of a few mode fiber. A pair of the mode multiplexers has minimum mode dependent loss of 4 dB and high mode group selectivity of over 15 dB. Mode division multiplexed transmission enabled by the all-fiber mode multiplexers is demonstrated over fiber spans of 117 km employing an in-line multi-mode optical amplifier. 6 modes of 120 Gb/s dual polarization quadrature phase shift keying signals combined with 30 wavelength channels are successfully transmitted.

Large-bandwidth, low-loss, efficient mode mixing using long-period mechanical gratings.

We propose a new architecture for using long-period fiber gratings (LPGs) to induce strong mode mixing with low loss for space-division multiplexing. In this architecture, LPGs are installed in step-index (SI) few-mode fibers that support more modes than the transmission fiber. Such a design could significantly reduce losses due to coupling from the highest-order mode group to cladding modes. In our experiment, efficient mixing of three spatial modes over a broad bandwidth was achieved by a mechanical long-period grating on a SI fiber that supports eight spatial modes. The insertion loss, including two splice losses, is less than 0.5 dB, and the coupling matrix and mode-dependent loss (MDL) are characterized experimentally for the first time, to the best of our knowledge. Strong mixing between LP01 and LP11 for a whole C band is demonstrated, and MDL introduced to the system is negligible.

Advanced coding techniques for few mode transmission systems.

We experimentally verify the advantage of employing advanced coding schemes such as space-time coding and 4 dimensional modulation formats to enhance the transmission performance of a 3-mode transmission system. The performance gain of space-time block codes for extending the optical signal-to-noise ratio tolerance in multiple-input multiple-output optical coherent spatial division multiplexing transmission systems with respect to single-mode transmission performance are evaluated. By exploiting the spatial diversity that few-mode-fibers offer, with respect to single mode fiber back-to-back performance, significant OSNR gains of 3.2, 4.1, 4.9, and 6.8 dB at the hard-decision forward error correcting limit are demonstrated for DP-QPSK 8, 16 and 32 QAM, respectively. Furthermore, by employing 4D constellations, 6 × 28Gbaud 128 set partitioned quadrature amplitude modulation is shown to outperform conventional 8 QAM transmission performance, whilst carrying an additional 0.5 bit/symbol.

12-mode OFDM transmission using reduced-complexity maximum likelihood detection.

We report the transmission of 163-Gb/s MDM-QPSK-OFDM and 245-Gb/s MDM-8QAM-OFDM transmission over 74 km of few-mode fiber supporting 12 spatial and polarization modes. A low-complexity maximum likelihood detector is employed to enhance the performance of a system impaired by mode-dependent loss.

Compact spatial multiplexers for mode division multiplexing.

Spatial multiplexer (SMUX) for mode division multiplexing (MDM) has evolved from mode-selective excitation, multiple-spot and photonic-lantern based solutions in order to minimize both mode-dependent loss (MDL) and coupler insertion loss (CIL). This paper discusses the implementation of all the three solutions by compact components in a small footprint. Moreover, the compact SMUX can be manufactured in mass production and packaged to assure high reliability. First, push-pull scheme and center launch based SMUXes are demonstrated on two mostly-popular photonic integration platforms: Silicon-on-insulator (SOI) and Indium Phosphide (InP) for selectively exciting LP01 and LP11 modes. 2-dimensional (2D) top-coupling by using vertical emitters is explored to provide a coupling interface between a few-mode fiber (FMF) and the photonic integrated SMUX. SOI-based grating couplers and InP-based 45° vertical mirrors are proposed and researched as vertical emitters in each platform. Second, a 3-spot SMUX is realized on an InP-based circuit through employing 45° vertical mirrors. Third, as a newly-emerging photonic integration platform, laser-inscribed 3D waveguide (3DW) technology is applied for a fully-packaged dual-channel 6-mode SMUX including two 6-core photonic lantern structures as mode multiplexer and demultiplexer, respectively.

Time domain multiplexed spatial division multiplexing receiver.

A novel time domain multiplexed (TDM) spatial division multiplexing (SDM) receiver which allows for the reception of >1 dual polarization mode with a single coherent receiver, and corresponding 4-port oscilloscope, is experimentally demonstrated. Received by two coherent receivers and respective 4-port oscilloscopes, a 3 mode transmission of 28GBaud QPSK, 8, 16, and 32QAM over 41.7km of few-mode fiber demonstrates the performance of the TDM-SDM receiver with respect to back-to-back. In addition, by using carrier phase estimation employing one digital phase locked loop per output, the frequency offset between the transmitter laser and local oscillator is shown to perform similar to previous work which employs 3 coherent receivers and 4-port oscilloscopes which are dedicated to the reception of each the three modes.

Peta-bit-per-second optical communications system using a standard cladding diameter 15-mode fiber.

Data rates in optical fiber networks have increased exponentially over the past decades and core-networks are expected to operate in the peta-bit-per-second regime by 2030. As current single-mode fiber-based transmission systems are reaching their capacity limits, space-division multiplexing has been investigated as a means to increase the per-fiber capacity. Of all space-division multiplexing fibers proposed to date, multi-mode fibers have the highest spatial channel density, as signals traveling in orthogonal fiber modes share the same fiber-core. By combining a high mode-count multi-mode fiber with wideband wavelength-division multiplexing, we report a peta-bit-per-second class transmission demonstration in multi-mode fibers. This was enabled by combining three key technologies: a wideband optical comb-based transmitter to generate highly spectral efficient 64-quadrature-amplitude modulated signals between 1528 nm and 1610 nm wavelength, a broadband mode-multiplexer, based on multi-plane light conversion, and a 15-mode multi-mode fiber with optimized transmission characteristics for wideband operation.

Time reversed optical waves by arbitrary vector spatiotemporal field generation.

Lossless linear wave propagation is symmetric in time, a principle which can be used to create time reversed waves. Such waves are special "pre-scattered" spatiotemporal fields, which propagate through a complex medium as if observing a scattering process in reverse, entering the medium as a complicated spatiotemporal field and arriving after propagation as a desired target field, such as a spatiotemporal focus. Time reversed waves have previously been demonstrated for relatively low frequency phenomena such as acoustics, water waves and microwaves. Many attempts have been made to extend these techniques into optics. However, the much higher frequencies of optics make for very different requirements. A fully time reversed wave is a volumetric field with arbitrary amplitude, phase and polarisation at every point in space and time. The creation of such fields has not previously been possible in optics. We demonstrate time reversed optical waves with a device capable of independently controlling all of light's classical degrees of freedom simultaneously. Such a class of ultrafast wavefront shaper is capable of generating a sequence of arbitrary 2D spatial/polarisation wavefronts at a bandwidth limited rate of 4.4 THz. This ability to manipulate the full field of an optical beam could be used to control both linear and nonlinear optical phenomena.

Laguerre-Gaussian mode sorter.

Exploiting a particular wave property for a particular application necessitates components capable of discriminating in the basis of that property. While spectral or polarisation decomposition can be straightforward, spatial decomposition is inherently more difficult and few options exist regardless of wave type. Fourier decomposition by a lens is a rare simple example of a spatial decomposition of great practical importance and practical simplicity; a two-dimensional decomposition of a beam into its linear momentum components. Yet this is often not the most appropriate spatial basis. Previously, no device existed capable of a two-dimensional decomposition into orbital angular momentum components, or indeed any discrete basis, despite it being a fundamental property in many wave phenomena. We demonstrate an optical device capable of decomposing a beam into a Cartesian grid of identical Gaussian spots each containing a single Laguerre-Gaussian component, using just a spatial light modulator and mirror.