Haiqing Wei

Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation

Optical phase conjugation is demonstrated to enable simultaneous wide-band compensation of the residual dispersion and the fiber nonlinearities in dispersion-managed fiber transmission lines employing slope-compensating fibers. When the dispersion slope of transmission fibers is equalized by slope-compensating fibers, the residual dispersion and the slope of dispersion slope are compensated by middle-span optical phase conjugation. More importantly, fiber nonlinearity may be largely suppressed by arranging the fibers into conjugate pairs about the phase conjugator, where the two fibers of each pair are in scaled translational symmetry. The translational symmetry is responsible for cancelling optical nonlinearities of the two fibers up to the first-order perturbation, then a mirror-symmetric ordering of the fiber pairs about the conjugator linearizes a long transmission line effectively.

Intra-channel nonlinearity compensation with scaled translational symmetry.

It is proposed and demonstrated that two fiber spans in a scaled translational symmetry could cancel out their intra-channel nonlinear effects to a large extent without using optical phase conjugation. Significant reduction of intra-channel nonlinear effects may be achieved in a long-distance transmission line consisting of multiple pairs of translationally symmetric spans. The results have been derived analytically from the nonlinear Schrödinger equation and verified by numerical simulations using commercial software.

Linearity of nonlinear perturbations in fiber-optic transmission lines and its applications to nonlinear compensations

First-order nonlinear perturbations of several fiber spans may be summed up linearly to yield the total nonlinear response of a group of spans, if nonlinear effects are neglected beyond the first order. Such linear additivity of first-order nonlinear perturbations about the nonlinear coefficients enables nonlinear compensations between one span with stronger nonlinearity and a group of spans with weaker nonlinearity, provided that there is a scaled translation symmetry between the strongly and the weakly nonlinear spans, and the dispersion of each span is properly managed. Excellent nonlinear compensations are achieved both in systems with an optical phase conjugator in the middle and in systems without.

Fundamental Equations of Nonlinear Fiber Optics

A set of nonlinear differential equations are derived from the first principles, namely the Maxwells equations and the material responses to electromagnetic excitations. The derivation retains the mathematical exactitude down to details. Still in compact and convenient forms, the final equations include the effect of group-velocity dispersion down to an arbitrary order, and take into account the frequency variations of the optical loss as well as the transverse modal function. Also established is a new formulation of multi-component nonlinear differential equations, which is especially suitable for the study of wide-band wavelength-division multiplexed systems of optical communications. The formulations are applied to discuss the problem of compensating the optical nonlinearity of fiber transmission lines using optical phase conjugation. Two system configurations are identified suitable for nonlinearity compensation. One setup is mirror-symmetric and the other translationally symmetric about the optical phase conjugator, both being in a scaled sense.

Reversing intrachannel ghost-pulse generation by midspan self-phase modulation

Intrachannel pulse interactions are the dominating nonlinear effects in modern transmission systems with high modulation speeds. Scaled symmetries have proved to be effective in suppressing amplitude and timing jitter of mark pulses due to nonlinearity but not for ghost-pulse generation into the empty slots. A method of using midspan self-phase modulation to reverse the generation of ghost pulses due to intrachannel four-wave mixing is proposed. Computer simulations demonstrate significant improvement of signal quality by a combination of scaled symmetries and midspan self-phase modulation.

Quantum noise in optical communication systems

It is noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, which, as an extra source of noise, could become comparable to the amplified-spontaneous-emission noise of optical amplifiers. The optical noise in random loss/gain has a quantum origin, as a manifestation of the corpuscular nature of electromagnetic radiation. This paper adopts the Schrodinger representation, and uses a density matrix in the basis of photon number states to describe the optical signals and their interaction with the environment of loss/gain media. When the environmental degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism provides an intuitive interpretation of the quantum-optical noise as the result of a classical Markov process in the space of the photon number states. The formulism would be more convenient for practical engineers, and should be sufficient for fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Even better, the model admits analytical solutions to the photon-number distribution of the optical signals.

Dispersion-induced signal distortion in cascaded OADMs

The optical add/drop multiplexer (OADM) is an important device in modern optical networks. Optical filters in OADMs often introduce group-velocity dispersion (GVD) and/or slope of GVD, the accumulation of which could distort the signals significantly. A computer model is built for commercial filters, accounting for the filtering gain and dispersion characteristics. When the model is incorporated into a network simulator, the filter dispersion is found to severely limit the number of OADMs that may be cascaded when transmitting 40Gb/s WDM signals with a channel spacing of 100GHz. As such high spectral efficiency difficult to achieve, the next considerations would be to transmit 40Gb/s over 200GHz channel spacing, or 10Gb/s over 50GHz channel spacing. The dispersion problem is mitigated, but still an un-negligible factor of limitation. For a large OADM network size, low-dispersion filters should be used, or a proper dispersion compensator is needed to offset the filter dispersion.

Optimal packaging of dispersion-compensating fibers for matched nonlinear compensation and reduced optical noise

A method of packaging dispersion-compensating fibers (DCFs) is discussed that achieves optimal nonlinearity compensation and a good signal-to-noise ratio simultaneously. An optimally packaged dispersion-compensating module (DCM) may consist of portions of DCFs with higher and lower loss coefficients. Such optimized DCMs may be paired with transmission fibers to form scaled translation-symmetric lines that could effectively compensate for signal distortions due to dispersion and nonlinearity, with or without optical phase conjugation.

Interchannel cross-talk in FWM-based phase conjugators

When a Kerr medium is pumped by a strong laser beam, the nonlinear process of four-wave mixing (FWM) can mix the pump laser and a weak signal to generate a phase-conjugated version of the signal. Optical phase conjugation (OPC) may be employed to compensate the chromatic dispersion and nonlinearity of transmission fibers. It may even serve as a parametric amplifier when the pump is sufficiently intense. Furthermore, the FWM effect is capable of phase-conjugating or amplifying many wavelength-division multiplexed (WDM) signals simultaneously. However, the same FWM effect results in parasitic processes by generating inter-mixing terms among the WDM signals. The center frequency of such unwanted mixing terms may coincide with some of the original or conjugated WDM signals to cause significant interference. This paper studies such interference effect by means of theoretical calculation and computer simulation. It is shown that the coherent interference effect decreases as the pump-power to signal-power ratio (PSR) increases. Unfortunately, there could still be strong interference even with a PSR of 20dB. Some guard-band in the frequency domain is necessary to avoid such coherent interference: if the total bandwidth of the WDM signals is W, then the nearest signal should be more than W away from the pump frequency.