Solitons are pulses that propagate without change as they travel through a nonlinear, dispersive medium. They exist throughout nature and play an important role in optical fiber photonics. They were first observed in optical fibers over two decades ago, and they are highly robust. There has been continued interest in using them as bits in a high-data-rate communications system. We have studied solitons both theoretically and experimentally. Our experimental studies used recirculating loop systems. Our recent theoretical studies have been based on the Optical Communications System (OCS) simulator. Much of our work on solitons has focused on the impact of randomly varying birefringence in optical fibers. Solitons also play an important role in fiber lasers, which we have studied in collaboration with groups at the Naval Research Laboratory, the Technion, and elsewhere.
In the last two decades, there has been a rapid increase in the data rates that can be transmitted in optical fiber communications systems. Systems that can transmit terabits of data are now possible. The development of the erbium-doped optical amplifier (EDFA) and wavelength division multiplexing (WDM) in conjunction with dispersion management were key advances. More recently, hybrid amplification that uses Raman amplifiers in conjunction with EDFAs plays an increasingly important role. Our work has focused on understanding the physical effects that limit performance in these systems. Polarization mode dispersion due to randomly varying birefringence, as well as polarization-dependent loss and gain, noise, and nonlinearity are all important. Most current systems use the non-return-to-zero (NRZ) pulse modulation format. Our work has explored alternative modulation formats such as return-to-zero (RZ), dispersion-managed solitons (DMS), and, more recently differential phase-shift keying (DPSK). We are carrying out both recirculating loop experiments and network testbed experiments. Our theoretical modeling is done primarily with the Optical Communications System (OCS) Simulator that we developed. Recently, we have begun studying analog communications in collaboration with scientists at the Naval Research Laboratory.
Optical fiber lasers have become an important source of short, modelocked pulses. We have carried out studies of passively modelocked lasers in which we have pointed out the importance of nonlinear polarization rotation in providing a fast saturable absorber for the laser. Our studies of these lasers have been based on complete ab initio simulations and the use of a reduced approach based on the modified Ginzburg-Landau equation in which we find the pulse equilibria and determine their stability. In collaboration with scientists at the Naval Research Laboratory and the Technion, we have investigated systems that combine both active and passive elements, as these can produce highly stable, short pulse trains. A difficulty in modeling fiber lasers is that there can be as many as 10,000 pulses in the laser cavity at one time. We have developed a super-pulse technique that allows us to accurately model collective effects in these lasers. Recently, we have been focusing on applications to metrology.
In collaboration with scientists at the Gwangju Institute of Science and Technology and the Naval Research Laboratory, we have begun an effort to model photonic crystal fiber. Photonic crystal fibers are fibers with small, regularly spaced air holes that go the entire length of the fiber and are embedded in the glass. Our work to date has focused on mode coupling problems in gratings, tapered fiber, and birefringent fibers.
In standard communication fibers, the length scale over which the optical fiber birefringence varies randomly is 30 -100 m, while the dispersive and nonlinear scale lengths are typically hundreds of kilometers. In the linear regime, this random variation leads to polarization mode dispersion and has a significant impact on all pulse modulation formats, including non-return-to-zero (NRZ), solitons, and alternative modulation formats like return-to-zero (RZ). We have demonstrated that light evolution on the long length scale on which dispersion and nonlinearity vary is described by the Manakov-PMD equation. We have also developed powerful, effective algorithms for solving it. We considered in detail two physical models of randomly varying birefringence. In the first model (fixed modulus model), only the orientation of the birefringence varies randomly. In the second model (random modulus model), the birefringence index distribution is Gaussian-distributed in all orientations. Recent polarization optical time domain reflectrometry (POTDR) experiments, carried out by our collaborators at the University of Padua, show that only the random modulus model is consistent with the data. We have extended the theory to account for fiber that is periodically twisted as it is drawn, and we have shown how the twisting reduces the polarization mode dispersion. We have also begun to study these effects in photonic crystal fiber.
The combination of polarization-dependent loss, polarization-dependent gain, and polarization mode dispersion can lead to signal impairments in high-data-rate communications systems and to pulse distortions in fiber lasers. Polarization mode dispersion can be counteracted by polarization scrambling the signal but polarization-dependent loss can lead to repolarization. We are studying methods to reduce the impact of these polarization-dependent effects in both recirculating loops and straight-line systems. We have developed reduced models that allow us to efficiently study these impairments, and we have validated them using both complete simulations and recirculating loop experiments. These reduced models are integrated into the Optical Communications System (OCS) Simulator. These models must be used in conjunction with accurate receiver models. A key theoretical issue in modeling these effects is that we are interested in failure probabilities that are 1 part in 100,000 or even less. We have developed biasing Monte Carlo simulation techniques that allow us to accurately calculate the probability of these low probability events.
To experimentally study high-data-rate optical communications systems, telecommunications companies typically employ recirculating loops. There are very few universities that have recirculating loops available. At UMBC, we have several recirculating loops that range in length from 100 km to 500 km. We have used them to study solitons, and we carried out some of the earliest experiments on dispersion-managed solitons. We have also studied the non-return-to-zero (NRZ) pulse modulation format, as well as a number of alternative modulation formats, including return-to-zero (RZ), differential phase shift keying (DPSK) and differential polarization shift keying (DPolSK). A major focus of our activities has been polarization effects and determining how recirculating loops differ from straight-line systems. We have also studied cross-phase modulation due to nonlinearity in wavelength-division multiplexed (WDM) systems. We have explored methods for characterizing receivers and have validated the accurate receiver models that we have developed. We have developed methods for separating transmitter from receiver impairments. Some of our experiments are based on erbium-doped fiber amplifiers (EDFAs) and some are based on hybrid amplifiers.
Our research group has access to national network testbeds like ATDnet and BOSSnet, where we have carried out experiments on dispersion management. In collaboration with the Mid-Atlantic Crossroads Consortium (MAX), centered at the University of Maryland, College Park (UMCP), and their DRAGON project, we have established a network that includes UMBC, UMCP, the Laboratory for Physical Sciences, the Laboratory for Telecommunications Sciences, and other government and university laboratories. We will be studying network layer mitigation of physical layer impairments like polarization mode dispersion.
In the past five years, our research group has developed a simulator that contains all the basic software that is used by our group members. It is based on solving the nonlinear Schrödinger equation and the Manakov-PMD equation using split-step solvers, but it also contains a wide variety of transmitter and receiver models and amplifier models. It also contains a complete implementation of the reduced polarization model. We have included in it implementations of the covariance matrix method and implementations of biasing Monte Carlo methods such as importance sampling and the multicanonical Monte Carlo method. It also contains components for fiber laser modeling and for modeling photonic crystal fiber. This simulator consists of a suite of codes that are written in C++. Since multiple users can update it, we use the concurrent version system (CVS) to keep it consistent. In our group, we run it on a cluster of machines that has several tens of processors. We are constantly upgrading the machines on which it runs. Portions of this simulator have been commercially licensed, and we use it as a teaching tool at UMBC.
The invention and deployment of erbium-doped fiber amplifiers (EDFAs) in the 1990s revolutionized high-data-rate optical fiber communications. It allowed the deployment of wavelength division multiplexed (WDM) systems. We have used EDFAs in our recirculating loop experimentsfor many years, and we have developed a series of amplifier models that are integrated into the Optical Communications Systems (OCS) Simulator. In massive WDM systems, it is more efficient to either use Raman amplification or hybrid amplification that uses both EDFAs and Raman amplifiers. Raman amplification has been used with solitons since the 1980s, and we have participated in modeling Raman amplifiers since that time.
The receiver has a large impact on the performance of a high-data-rate optical fiber communications system. Because of the nonlinear square-law detection in the photodetector, even Gaussian input noise will lead to non-Gaussian voltage distributions. Moreover, the receiver typically induces substantial pattern dependences. Accurately characterizing the optical and electronic filters in the receiver, as well as the clock recovery system, is critical when determining performance. We have carried out experimental and theoretical studies in conjunction with our studies of polarization effects and nonlinearity and noise. In these studies, we have shown how to deparate the effects of the transmitter and receiver and how to accurately characterize the entire system. The experimental studies were carried out in our recirculating loop systems, and the theoretical studies were carried out with the Optical Communications System (OCS) simulator.
The source of noise in either high-data-rate optical fiber communications systems or in fiber lasers is the amplifiers. The noise that is produced by an amplifier is close to Gaussian-distributed. However, the fiber nonlinearity implies that the distribution does not remain Gaussian. We have developed techniques that allow us to accurately calculate the noise distribution in the presence of fiber nonlinearity. These include the covariance matrix method that assumes that noise-noise beating in the fiber is negligible once phase jitter and, in some cases, timing jitter have been removed. These also include biasing Monte Carlo methods such as standard importance sampling and the multicanonical Monte Carlo method. More recently, we have been focusing on the pattern dependences due to cross-phase modulation in wavelength division multiplexed (WDM) systems.
It was discovered in the early 1990s that one could not transmit high-data-rate signals with zero dispersion because the combination of nonlinearity and noise led to an unacceptable growth of the noise. This noise growth is a phase-coherent (four-wave mixing) effect, and it was also found that it could be largely eliminated by using sections of fiber with high dispersion. At the same time, the total dispersion must add to zero, or close to zero, so that pulses are as compact as possible at the entry to the receiver. The answer to this dilemma was to use dispersion management in which segments of fiber with high positive dispersion alternate with segments of fiber with high negative dispersion. This strategy proved to be successful with the soliton and return-to-zero (RZ) pulse modulation formats as well as with the non-return-to-zero (NRZ) format. In recent years, it has been successfully applied to the differential phase shift keyed (DPSK) and the differential polarization shift keyed (DPolSK) format as well.
High-data-rate systems for the indefinite future will depend on wavelength division multiplexing (WDM). Systems at a terabit and beyond have been implemented. In this approach, 64 or more channels running at 2.5 up to 40 Gbit/s per second are combined to obtain a large throughput. We have investigated many aspects of wavelength division multiplexing in conjunction with our other projects.
Forward error correction and other signal processing technique are increasingly important in high-data-rate optical fiber communication systems. We have investigated line codes and finite impulse response filters that can be quite effective in reducing the impact of nonlinear effects and polarization mode dispersion. We have also investigated the impact that receiver nonlinearity has on the coding gain. Recently, we have explored the use of biasing Monte Carlo simulations to determine the coding gain for LDPC codes. All this work has been carried out in conjunction with accurate receiver models.
In collaboration with scientists at Northwestern University and elsewhere, we have developed biasing Monte Carlo techniques, such as importance sampling and multicanonical Monte Carlo simulations, so that we can study the tails of the probability distributions problems involving polarization effects and nonlinearity and noise. These methods have been integrated into the Optical Communications System (OCS) Simulator.