Abstract-We studied the efficiency of different implementations of the split-step Fourier method for solving the nonlinear Schrödinger 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.

Context. Sodium laser guide stars (LGS) are about to enter a new range of laser powers. Previous theoretical and numerical methods are inadequate for accurate computations of the return flux, hence for the design of the next-generation LGS systems. Aims. We numerically optimize the cw (continuous wave) laser format, in particular, the light polarization and spectrum. Methods. Using Bloch equations, we simulate the mesospheric sodium atoms, including Doppler broadening, saturation, collisional relaxation, Larmor precession, and recoil, taking all 24 sodium hyperfine states into account and 100-300 velocity groups. Results.LGS return flux is limited by "three evils": Larmor precession due to the geomagnetic field, atomic recoil due to radiation pressure, and transition saturation. We study their impact and show that the return flux can be boosted by repumping (simultaneous excitation of the sodium D 2 a and D 2 b lines with 10−20% of the laser power in the latter). Conclusions. We strongly recommend the use of circularly polarized lasers and repumping. As a rule of thumb, the bandwidth of laser radiation in MHz (at each line) should approximately equal the launched laser power in Watts divided by six, assuming a diffraction-limited spot size.

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-2 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.

Abstract-We evaluate the error-correcting performance of a low-density parity-check (LDPC) code in an AWGN channel using a novel dual adaptive importance sampling (DAIS) technique based on multicanonical Monte Carlo (MMC) simulations, that allows us to calculate bit error rates as low as 10 −19 for a (96, 50) LDPC code without a priori knowledge of how to bias. Our results agree very well with standard MC simulations, as well as the union bound for the code.

We apply the multicanonical Monte Carlo (MMC) method to compute the probability distribution of the received voltage in a chirped return-to-zero system. When computing the probabilities of very rare events, the MMC technique greatly enhances the efficiency of Monte Carlo simulations by biasing the noise realizations. Our results agree with the covariance matrix method over 20 orders of magnitude. The MMC method can be regarded as iterative importance sampling that automatically converges toward the optimal bias so that it requires less a priori knowledge of the simulated system than importance sampling requires. A second advantage is that the merging of different regions of a probability distribution function to obtain the entire function is not necessary in many cases.