Ruo-Ding Li

Pulse propagation in nonlinear optical fiber lines that employ phase-sensitive parametric amplifiers

Recently we proposed using periodically spaced, phase-sensitive optical parametric amplifiers to balance linear loss in a nonlinear fiber-optic communication line [ Opt. Lett.18, 803 ( 1993)]. We present a detailed analysis of pulse propagation in such a fiber line. Our analysis and numerical simulations show that the length scale over which the pulse evolution occurs is significantly increased beyond a soliton period. This is because of the attenuation of phase variations across the pulse’s profile by the amplifiers. Analytical evidence is presented that indicates that stable pulse evolution occurs on length scales much longer than the soliton period. This is confirmed through extensive numerical simulation, and the region of stable pulse propagation is found. The average evolution of such pulses is governed by a fourth-order nonlinear diffusion equation, which describes the exponential decay of arbitrary initial pulses into stable, steady-state, solitonlike pulses.

Long-distance pulse propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers

We analyze pulse propagation in a nonlinear optical fiber in which linear loss in the fiber is balanced by a chain of periodically spaced, phase-sensitive, degenerate parametric amplifiers. Our analysis shows that no pulse evolution occurs over a soliton period owing to attenuation in the quadrature orthogonal to the amplified quadrature. Evidence is presented that indicates that stable pulse solutions exist on length scales much longer than the soliton period. These pulses are governed by a nonlinear fourth-order evolution equation, which describes the exponential decay of arbitrary initial pulses (within the stability regime) onto stable, steady-state, solitonlike pulses.

Combating dispersion with parametric amplifiers

A novel approach to combating the pulse broadening effect of group-velocity dispersion in a fiber-optic communication link is presented. In the scheme linear loss in the fiber is balanced by a chain of periodically spaced, phase-sensitive, degenerate optical parametric amplifiers. Analysis of pulse propagation in such a fiber line shows that, due to attenuation in the quadrature orthogonal to the amplified quadrature, it is possible for a pulse to propagate without significant broadening over lengths much longer than the usual dispersion length of the fiber.<<ETX>>

Evolution of quantum noise in the traveling-wave second-order [χ (2) ] nonlinear process

We analyze the evolution of quantum noise in both the fundamental and the harmonic fields that are undergoing traveling-wave interaction in a second-order [χ(2)] nonlinear medium. Assuming perfect phase matching between the fundamental and the harmonic fields and arbitrary input boundary conditions, the behavior of quantum noise in the propagating fields is studied by linearization of the nonlinear-operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and the harmonic fields. We then analyze the polarization-nondegenerate case that applies to type-II phase-matching geometries. In the special case, when the two orthogonally polarized fundamental inputs are of equal amplitude, we obtain analytical results and show that the type-II phase-matched second-harmonic-generation process can be configured to generate sub-Poissonian light in both polarization components of the fundamental field. Finally, we numerically solve the linearized quadrature-operator equations along with the nonlinear mean-field equations for the general case of type-II phase matching. For both type-I and type-II processes, we find that whenever the fundamental field experiences deamplification it is associated with amplitude squeezing and phase desqueezing. If, in contrast, the fundamental field experiences amplification, then it is accompanied by amplitude desqueezing, but with squeezing in the phase quadrature. The harmonic field is amplitude squeezed if the input boundary condition leads to harmonic conversion and is phase squeezed if the input boundary condition leads to parametric amplification.

Gaussian-wave theory of sub-Poissonian light generation by means of travelling-wave parametric deamplification

A Gaussian wave theory is developed to analyse the sub-Poissonian light generated by means of a travelling-wave optical parametric deamplification. The Gaussian spatial profile of the pump beam limits the observable Fano factor to -3 dB (0.5). Gain-induced diffraction of the signal beam and classical fluctuations of the pump-signal relative phase cause further degradation. The theory is compared with our recent experimental results, and excellent agreement is found after the effect of non-ideal photoelectron efficiency is taken into account.

Coupled lasers asymptotics

Models of coupled lasers are investigated by exploring new asymptotic limits. The class B limit is based on the fact that the decay rate of the cavity is much larger than that of the inversion. By reformulating the laser equations as a weakly perturbed conservative system of equations, we may apply perturbation techniques appropriate for nonlinear oscillators. We illustrate the method by studying the bifurcation diagram of two coupled solid state lasers and determine conditions for a period doubling bifurcation. Semiconductor lasers are also class B lasers but, in addition, the normalized excess pump current is a small parameter. By taking this feature into account, we propose a new asymptotic analysis of the equations for an arbitrary number of coupled lasers. The leading order solution is then a linear combination of supermodes solutions.

Stable long-distance pulse propagation in nonlinear optical fibers using periodically-spaced parametric amplifiers

Parametric amplifiers have been proposed [1] as an alternative to lumped erbium-doped amplifiers for long-distance optical pulse propagation in fibers. While filtering techniques [2] have been demonstrated to suppress the bit-rate limitation caused by the Gordon-Haus jitter [3] — the random walk of solitons caused by spontaneous emission noise of the erbium amplifiers, or by initial fluctuations in the soliton parameters — a chain of lumped parametric amplifiers should have higher possible bit-rates because no such amplifier noise is present [1].