Curtis R. Menyuk

Nonlinear pulse propagation in birefringent optical fibers

Equations describing nonlinear pulse propagation in birefringent, single-mode fibers are derived. The physical meaning and technical implications of these equations are then discussed in detail. Finally, the modulational instability is studied.

Optimization of the split-step Fourier method in modeling optical-fiber communications systems

We studied the efficiency of different implementations of the split-step Fourier method for solving the nonlinear Schro/spl uml/dinger equation that employ different step-size selection criteria. We compared the performance of the different implementations for a variety of pulse formats and systems, including higher order solitons, collisions of soliton pulses, a single-channel periodically stationary dispersion-managed soliton system, and chirped return to zero systems with single and multiple channels. We introduce a globally third-order accurate split-step scheme, in which a bound on the local error is used to select the step size. In many cases, this method is the most efficient when compared with commonly used step-size selection criteria, and it is robust for a wide range of systems providing a system-independent rule for choosing the step sizes. We find that a step-size selection method based on limiting the nonlinear phase rotation of each step is not efficient for many optical-fiber transmission systems, although it works well for solitons. We also tested a method that uses a logarithmic step-size distribution to bound the amount of spurious four-wave mixing. This method is as efficient as other second-order schemes in the single-channel dispersion-managed soliton system, while it is not efficient in other cases including multichannel simulations. We find that in most cases, the simple approach in which the step size is held constant is the least efficient of all the methods. Finally, we implemented a method in which the step size is inversely proportional to the largest group velocity difference between channels. This scheme performs best in multichannel optical communications systems for the values of accuracy typically required in most transmission simulations.

Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers.

Nonlinear pulse propagation is investigated in the neighborhood of the zero-dispersion wavelength in monomode fibers. When the amplitude is sufficiently large to generate breathers (N > 1 solitons), it is found that the pulses break apart if lambda - lambda(0) is sufficiently small, owing to the third-order dispersion. Here lambda(0) denotes the zero-dispersion wavelength. By contrast, the solitary-wave (N = 1) solution appears well behaved for arbitrary lambda - lambda(0). Implications for communication systems and pulse compression are discussed.

Pulse propagation in an elliptically birefringent Kerr medium

The coupled nonlinear Schrodinger equation, which describes optical propagation in a birefringent Kerr medium, is derived with particular emphasis on optical fibers. It is shown that, when the ellipticity angle theta approximately=35 degrees , Manakovs equation results. Consequences for switching applications are discussed. In particular, if theta not=35 degrees , shadows form when two pulses of opposite polarization interact, i.e. the emerging pulses no longer have their original polarizations. This problem disappears at theta =35 degrees . >

Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes

The effect of birefringence on soliton propagation in single-mode optical fibers is considered. Emphasis is on solitons with multipicosecond widths that are appropriate for communications applications. It is shown that while linear birefringence will lead to a substantial splitting of the two polarizations over 20 km, this effect can be eliminated by use of the Kerr nonlinearity. Above a certain amplitude threshold, the central frequency of each polarization shifts just enough to lock the two polarizations together.

Stability of solitons in randomly varying birefringent fibers.

The effects of randomly varying birefringence on solitons are studied. It is shown analytically that the evolution equation can be reduced to the nonlinear Schrödinger equation if the variation length is much shorter than the soliton period. The soliton does not split at high values of the average birefringence, but it does undergo spreading and loss of polarization. A soliton with a temporally constant initial state of polarization is still largely polarized after 40z(0) if the normalized birefringence is delta </= 1.3.

Dispersion-managed soliton interactions in optical fibers

We simulated dispersion-managed soliton propagation and interaction in optical fibers. The energy-enhancement factor, together with the time-bandwidth product and the stretching factor, were calculated as a function of the difference in absolute values of accumulated dispersion in the fiber spans. The interaction strength of the dispersion-managed solitons was found to depend on the stretching factor. When this factor is less than 1.5, the interaction is weaker than for ideal solitons. When it is more than 1.5, there is a strong interaction between the pulses, which constrains the energy enhancement for practical applications.

Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators

We demonstrate that frequency (Kerr) comb generation in whispering-gallery-mode resonators can be modeled by a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatiotemporal model allows us to explore pulse formation in which a large number of modes interact cooperatively. Pulse formation is shown to play a critical role in comb generation, and we find conditions under which single pulses (dissipative solitons) and multiple pulses (rolls) form. We show that a broadband comb is the spectral signature of a dissipative soliton, and we also show that these solitons can be obtained by using a weak anomalous dispersion and subcritical pumping.

Solitary waves due to χ (2) :χ (2) cascading

Solitary waves in materials with a cascaded χ(2):χ(2) nonlinearity are investigated, and the implications of the robustness hypothesis for these solitary waves are discussed. Both temporal and spatial solitary waves are studied. First, the basic equations that describe the χ(2):χ(2) nonlinearity in the presence of dispersion or diffraction are derived in the plane-wave approximation, and we show that these equations reduce to the nonlinear Schrodinger equation in the limit of large phase mismatch and can be considered a Hamiltonian deformation of the nonlinear Schrodinger equation. We then proceed to a comprehensive description of all the solitary-wave solutions of the basic equations that can be expressed as a simple sum of a constant term, a term proportional to a power of the hyperbolic secant, and a term proportional to a power of the hyperbolic secant multiplied by the hyperbolic tangent. This formulation includes all the previously known solitary-wave solutions and some exotic new ones as well. Our solutions are derived in the presence of an arbitrary group-velocity difference between the two harmonics, but a transformation that relates our solutions to zero-velocity solutions is derived. We find that all the solitary-wave solutions are zero-parameter and one-parameter families, as opposed to nonlinear-Schrodinger-equation solitons, which are a two-parameter family of solutions. Finally, we discuss the prediction of the robustness hypothesis that there should be a two-parameter family of solutions with solitonlike behavior, and we discuss the experimental requirements for observation of solitonlike behavior.

Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization

We present a novel linearization method to calculate accurate eye diagrams and bit error rates (BERs) for arbitrary optical transmission systems and apply it to a dispersion-managed soliton (DMS) system. In this approach, we calculate the full nonlinear evolution using Monte Carlo methods. However, we analyze the data at the receiver assuming that the nonlinear interaction of the noise with itself in an appropriate basis set is negligible during transmission. Noise-noise beating due to the quadratic nonlinearity in the receiver is kept. We apply this approach to a highly nonlinear DMS system, which is a stringent test of our approach. In this case, we cannot simply use a Fourier basis to linearize, but we must first separate the phase and timing jitters. Once that is done, the remaining Fourier amplitudes of the noise obey a multivariate Gaussian distribution, the timing jitter is Gaussian distributed, and the phase jitter obeys a Jacobi-/spl Theta/ distribution, which is the periodic analogue of a Gaussian distribution. We have carefully validated the linearization assumption through extensive Monte Carlo simulations. Once the effect of timing jitter is restored at the receiver, we calculate complete eye diagrams and the probability density functions for the marks and spaces. This new method is far more accurate than the currently accepted approach of simply fitting Gaussian curves to the distributions of the marks and spaces. In addition, we present a deterministic solution alternative to the Monte Carlo method.