Modeling extended L-band fiber amplifiers using neural networks trained on experimental data.

Producing high performance amplifiers requires accurate numerical models. As the optimization space is large, computationally efficient models are of great value. Parameter-based models for L-band amplifiers have accuracy limited by difficulty in estimating the Giles-parameter. The use a neural network model can avoid parametrization. We exploit a rich, experimentally captured training set to achieve a high accuracy neural network model. Our approach creates independent models for gain and noise figure. We examine both core and cladding pumping methods, again with independent models for each. The neural networks outperform parameter-based models with higher accuracy (variance of error reduced by 50%) and extremely fast simulation times (400 times faster), greatly facilitating amplifier design. As an example application, we design an amplifier to optimize optical signal-to-noise ratio by exhaustive search with our fast neural network models.

Performance vs. complexity in NN pre-distortion for a nonlinear channel.

Optical communications at high bandwidth and high spectral efficiency rely on the use of a digital-to-analog converter (DAC). We propose the use of a neural network (NN) for digital pre-distortion (DPD) to mitigate the quantization and bandlimited impairments from a DAC in such systems. We experimentally validate our approach with a 64 Gbaud 8-level pulse amplitude modulation (PAM-8) signal. We examine the NN-DPD training with both direct and indirect learning methods. We compare the performance with typical Volterra, look-up table (LUT) and linear DPD solutions. We sweep regimes where nonlinear quantization becomes more prominent to highlight the advantages of NN-DPD. The proposed NN-DPD trained via direct learning outperforms the Volterra, LUT and linear DPDs by almost 0.9 dB, 1.9 dB and 2.9 dB, respectively. We find that an indirect learning recurrent NN offers better performance at the same complexity as Volterra, while a direct learning recursive NN pushes performance to a higher level than a Volterra can achieve.

Optimization criteria and design of few-mode Erbium-doped fibers for cladding-pumped amplifiers.

We propose a novel optimization method that combines two design criteria to reduce the differential modal gain (DMG) in few-mode cladding-pumped erbium-doped fiber amplifiers (FM-EDFAs). In addition to the standard criterion that considers the mode intensity and dopant profile overlap, we introduce a second criterion that ensures that all doped regions have the same saturation behavior. With these two criteria, we define a figure-of-merit (FOM) that allows the design of FM-EDFAs with low DMG without high computational cost. We illustrate this method with the design of six-mode erbium-doped fibers (EDFs) for amplification over the C-Band targeting designs that are compatible with standard fabrication processes. The fibers have either a step-index or a staircase refractive index profile (RIP), with two ring-shaped erbium-doped regions in the core. With a staircase RIP, a fiber length of 29 m and 20 W of pump power injected in the cladding, our best design leads to a minimum gain of 22.6 dB while maintaining a DMGmax under 0.18 dB. We further show that the FOM optimization achieves a robust design with low DMG over a wide range of variations in signal power, pump power and fiber length.

Integrated orbital angular momentum mode sorters on vortex fibers.

We design, fabricate, and characterize integrated mode sorters for multimode fibers that guide well-separated vortex modes. We use 3D direct laser printing to print a collimator and a Cartesian to a log-polar mode transformer on the tip of the fiber. This polarization insensitive device can send different modes into different exit angles and is therefore useful for space division multiplexed optical communication. Two types of fibers with two corresponding sorters are used, enabling the sorting of either four or eight different modes in a compact and robust manner. The integration of the vortex fiber and multiplexer opens the door for widespread exploitation of orbital angular momentum (OAM) for data multiplexing in fiber networks.

Overlaying 5G radio access networks on wavelength division multiplexed optical access networks with carrier distribution.

As 5G communication matures, the requirement for advanced radio access networks (RAN) drives the evolution of optical access networks to support these needs. Basic RAN functions, mobile front-haul to the backbone and interconnected front-end remote radio units, must support and enable data rate surges, low-latency applications, RF coordination, etc. Wavelength division multiplexed optical access networks (WDM-OANs) provide sufficient network capacity to support the addition of RAN services, especially in unused portions of WDM. We propose and demonstrate a method for RAN overlay in WDM-OANs that employ distributed carriers. In such systems, the carrier is modulated at the central office for direct-detected downstream digital data services; later the same carrier is remodulated for the uplink. We propose the use of silicon photonics to intercept the downstream and add 5G signals. We examine the distributed-carrier power budget issues in this overlay scenario. The carrier power must be harvested for direct detection of both digital and RoF services, and yet hold in reserve sufficient power for the uplink remodulation of all services. We concentrate on the silicon photonics subsystem at the remote node to add RoF signals. We demonstrate the overlay with a fabricated chip and study strategic allocations of carrier power at the optical network units housing the radio units to support the overlay. After the successful drop and reception of both conventional WDM-OAN and the newly overlaid RoF signals, we demonstrate sufficient carrier power margin for the upstream remodulation.

Recurrent neural networks achieving MLSE performance for optical channel equalization.

We explore recurrent and feedforward neural networks to mitigate severe inter-symbol interference (ISI) caused by bandlimited channels, such as high speed optical communications systems pushing the frequency response of transmitter components. We propose a novel deep bidirectional long short-term memory (BiLSTM) architecture that strongly emphasizes dependencies in data sequences. For the first time, we demonstrate via simulation that for QPSK transmission the deep BiLSTM achieves the optimal bit error rate performance of a maximum likelihood sequence estimator (MLSE) with perfect channel knowledge. We assess performance for a variety of channels exhibiting ISI, including an optical channel at 100 Gbaud operation using a 35 GHz silicon photonic (SiP) modulator. We show how the neural network performance deteriorates with increasing modulation order and ISI severity. While no longer achieving MLSE performance, the deep BiLSTM greatly outperforms linear equalization in these cases. More importantly, the neural network requires no channel state information, while its performance is comparable to conventional equalizers with perfect channel knowledge.

Silicon photonic subsystem for broadband and RoF detection while enabling carrier reuse.

We experimentally validate a silicon photonic subsystem designed for passive optical networks with carrier reuse. The subsystem is intended for future wavelength division multiplexed (WDM) PONs. It enables radio-over-fiber signals to cohabit an assigned wavelength slot without perturbing the PON signal, while conserving carrier power for the uplink. A microring modulator remodulates the residual carrier for the RoF uplink. We successfully detected the dropped 8 GHz broadband signal and five 125 MHz radio-over-fiber signals. Two 125 MHz radio over fiber signals are remodulated onto the carrier. The uplink signal shows good performance, validating the residual downlink signals have been well rejected by the microring filters. The subsystem conserves a clean carrier for remodulation with good signal-to-carrier ratio.

Highly elliptical core fiber with stress-induced birefringence for mode multiplexing.

We report the polarization-maintaining properties of a highly elliptical core fiber surrounded by a trench that was designed to optimize the modal effective indices and bending loss for a total of five spatial modes (10 channels). In addition to the asymmetric core structure, the birefringence of the fiber is increased by the thermal stress introduced during the fabrication. The results show a modal birefringence larger than 10-4 for all guided spatial modes. The mode stability to bending is evaluated by selectively exciting/detecting each spatial mode while perturbing the fiber. This few-mode polarization-maintaining fiber is of interest for multiple-input multiple-output (MIMO)-free mode division multiplexing transmission systems.

Reduced-size lookup tables enabling higher-order QAM with all-silicon IQ modulators.

We experimentally demonstrate 20 Gbaud 256QAM and 40 Gbaud 128QAM in an all-silicon IQ modulator. We combine a linear equalizer and a nonlinear predistortion implemented in a lookup table (LUT). We achieve bit error rate (BER) below the 20% forward error correction threshold; linear equalization alone cannot achieve this performance. To keep LUT size manageable, we use one dimensional LUTs and prune entries. We achieve good BER even when LUT size is halved. Finally, we verify the generality of the proposed methods on different data sets.

Chip-scale, full-Stokes polarimeter.

The polarization of light conveys unique information that can be exploited by crucial applications. The bulky and costly discrete optical components used in conventional polarimeters limit their broad adoption. A compact, low-cost polarimeter would bring this functionality into a myriad of new scenarios and revolutionize its exploitation. Here we present a high-performance, full-Stokes polarimeter on a silicon chip. A surface polarization splitter and on-chip optical interferometer circuit produce the complete analysis matrix of an optimally conditioned polarimeter. A matrix analysis on measurement errors is also performed. This solid-state polarimeter is a system-on-a-chip with exceptional compactness, stability, and speed that could be used singly or in integrated arrays. Large arrays can increase the speed and resolution of full-Stokes imaging; therefore, our design provides a scalable polarimeter solution.

Single-carrier 72 GBaud 32QAM and 84 GBaud 16QAM transmission using a SiP IQ modulator with joint digital-optical pre-compensation.

We establish experimentally the suitability of an all-silicon optical modulator to support future ultra-high-capacity coherent optical transmission links beyond 400 Gb/s. We present single-carrier data transmission from 400 Gb/s to 600 Gb/s using an all-silicon IQ modulator produced with a generic foundry process. The operating point of the silicon photonic transmitter is carefully optimized to find the best efficiency bandwidth trade-off. We present a methodology to split pre-compensation between digital and optical stages. For the 400 Gb/s transmission, we achieved 60 Gbaud dual-polarization (DP)-16QAM, reaching a distance of 1,520 km. Transmission of 500 Gb/s was further tested using 75 Gbaud 16QAM and 60 Gbaud 32QAM, reaching 1,120 km and 480 km, respectively. We finally demonstrated 72 Gbaud DP-32QAM (720 Gb/s) transmitted over 160 km and 84 Gbaud DP-16QAM (672 Gb/s) transmitted over 720 km, meeting the threshold for 20% forward error correction overhead and achieving net rates of 600 Gb/s and 576 Gb/s, respectively. To the best of our knowledge, these are the highest baud-rate coherent transmission results achieved using an all-silicon IQ modulator. We have demonstrated that we can reap the myriad advantages of SiP integration for transmission at extreme bit rates.

Analysis of modal coupling due to birefringence and ellipticity in strongly guiding ring-core OAM fibers.

After briefly recalling the issue of OAM mode purity in strongly-guiding ring-core fibers, this paper provides a methodology to calculate the coupling strength between OAM mode groups due to fiber perturbations. The cases of stress birefringence and core ellipticity are theoretically and numerically investigated. It is found that both perturbations produce the same coupling pattern among mode groups, although with different intensities. The consequence is that birefringence causes the highest modal crosstalk because it strongly couples groups with a lower propagation-constant mismatch. The power coupling to parasitic TE and TM modes is also quantified for both perturbations and is found to be non-negligible. Approximate modal crosstalk formulas valid for weakly-guiding multi-core fibers, but whose parameters are adapted to the present case of strongly guiding OAM fibers, are found to provide a reasonable fit to numerical results. Finally, the effect that modal coupling has on OAM transmission is assessed in terms of SNR penalty.

Integrated flexible-grid WDM transmitter using an optical frequency comb in microring modulators.

Advanced optical interconnects require high-speed links, which can be achieved by combining high channel rates with wavelength-division multiplexing (WDM). We report a multi-channel transmitter using cascaded microring modulators (MRMs) in silicon photonics. One MRM works as a flexible-grid optical comb generator, while the others work as channel modulators. With a single-wavelength laser input, we achieve flexible channel spacing (up to 25 GHz) with a tone-to-noise ratio above 54 dB at low power consumption of less than 4.6 mW. We examine experimentally multi-channel transmission modulating data onto adjacent comb lines without significant signal crosstalk. This single-laser, flexible-grid WDM transmitter is a scalable solution: more comb lines can be obtained using uncoupled MRMs in a series. To the best of our knowledge, this is the first demonstration of monolithic integration of a comb generator and multi-channel modulators for ultra-compact, power-efficient WDM photonic interconnects.

Linearly polarized vector modes: enabling MIMO-free mode-division multiplexing.

We experimentally investigate mode-division multiplexing in an elliptical ring core fiber (ERCF) that supports linearly polarized vector modes (LPV). Characterization show that the ERCF exhibits good polarization maintaining properties over eight LPV modes with effective index difference larger than 1 × 10-4. The ERCF further displays stable mode power and polarization extinction ratio when subjected to external perturbations. Crosstalk between the LPV modes, after propagating through 0.9 km ERCF, is below -14 dB. By using six LPV modes as independent data channels, we achieved the transmission of 32 Gbaud QPSK over 0.9 km ERCF without any multiple-input-multiple-output (MIMO) or polarization-division multiplexing (PDM) signal processing.

Modeling and compensation of transmitter nonlinearity in coherent optical OFDM.

We present a comprehensive study of nonlinear distortions from an optical OFDM transmitter. Nonlinearities are introduced by the combination of effects from the digital-to-analog converter (DAC), electrical power amplifier (PA) and optical modulator in the presence of high peak-to-average power ratio (PAPR). We introduce parameters to quantify the transmitter nonlinearity. High input backoff avoids OFDM signal compression from the PA, but incurs high penalties in power efficiency. At low input backoff, common PAPR reduction techniques are not effective in suppressing the PA nonlinear distortion. A bit error distribution investigation shows a technique combining nonlinear predistortion with PAPR mitigation could achieve good power efficiency by allowing low input backoff. We use training symbols to extract the transmitter nonlinear function. We show that piecewise linear interpolation (PLI) leads to an accurate transmitter nonlinearity characterization. We derive a semi-analytical solution for bit error rate (BER) that validates the PLI approximation accurately captures transmitter nonlinearity. The inverse of the PLI estimate of the nonlinear function is used as a predistorter to suppress transmitter nonlinearity. We investigate performance of the proposed scheme by Monte Carlo simulations. Our simulations show that when DAC resolution is more than 4 bits, BER below forward error correction limit of 3.8 × 10(-3) can be achieved by using predistortion with very low input power backoff for electrical PA and optical modulator.

Design of a family of ring-core fibers for OAM transmission studies.

We propose a family of ring-core fibers, designed for the transmission of OAM modes, that can be fabricated by drawing five different fibers from a single preform. This novel technique allows us to experimentally sweep design parameters and speed up the fiber design optimization process. Such a family of fibers could be used to examine system performance, but also facilitate understanding of parameter impact in the transition from design to fabrication. We present design parameters characterizing our fiber, and enumerate criteria to be satisfied. We determine targeted fiber dimensions and explain our strategy for examining a design family rather than a single fiber design. We simulate modal properties of the designed fibers, and compare the results with measurements performed on fabricated fibers.

Perfect vortex beam: Fourier transformation of a Bessel beam.

We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber.

Design, fabrication and validation of an OAM fiber supporting 36 states.

We present an optical fiber supporting 36 information bearing orbital angular momentum (OAM) states spanning 9 OAM orders. We introduce design techniques to maximize the number of OAM modes supported in the fiber; while avoiding LP mode excitation. We fabricate such a fiber with an air core and an annular index profile using the MCVD process. We introduce a new technique for shaping OAM beams in free-space to obtain better coupling efficiency with fiber with annular index profiles. We excite 9 orders of OAM in the fiber, using interferometry to verify the OAM state on exiting the fiber. Using polarization multiplexing and both signs for the topological charge, we confirm support of 36 states, exploiting to our knowledge the highest number of OAM modes ever transmitted in optical fiber.

Simple analytical model for low-frequency frequency-modulation noise of monolithic tunable lasers.

We employ simple analytical models to construct the entire frequency-modulation (FM)-noise spectrum of tunable semiconductor lasers. Many contributions to the laser FM noise can be clearly identified from the FM-noise spectrum, such as standard Weiner FM noise incorporating laser relaxation oscillation, excess FM noise due to thermal fluctuations, and carrier-induced refractive index fluctuations from stochastic carrier generation in the passive tuning sections. The contribution of the latter effect is identified by noting a correlation between part of the FM-noise spectrum with the FM-modulation response of the passive sections. We pay particular attention to the case of widely tunable lasers with three independent tuning sections, mainly the sampled-grating distributed Bragg reflector laser, and compare with that of a distributed feedback laser. The theoretical model is confirmed with experimental measurements, with the calculations of the important phase-error variance demonstrating excellent agreement.

Tailoring focal plane component intensities of polarization singular fields in a tight focusing system.

The scientific community studies tight focusing of radially and azimuthally-polarized vector beams as it is a versatile solution for many applications. We offer a new method to produce tight focusing that ensures a more uniform intensity profile in multiple dimensions, providing a more versatile and stable solution. We manipulate the polarization of the radially and azimuthally polarized vector beams to find an optimal operating point. We examine in detail optical fields whose polarization states lie on the equator of the relevant Poincaré spheres namely, the fundamental Poincaré sphere, the hybrid order Poincaré sphere (HyOPS), and the higher order Poincaré sphere. We find via simulation that the fields falling on these equators have focal plane intensity distributions characterized by a single rotation parameter α determining the individual state of polarization. The strengths of the component field distributions vary with α and can be tuned to achieve equal strengths of longitudinal (z) and transverse (x and y) components at the focal plane. Without control of this parameter (e.g., using α = 0 in radially and α = π in azimuthally-polarized vector beams) intensity in x and y components are at 20% of the z component. In our solution with α = π / 2 , all components are at 80% of the maximum possible intensity of z. In examining the impact of α on a tightly focused beam, we also found that a helicity inversion of HyOPS beams causes a rotation of 180 degree in the axial intensity distribution.