Cross-phase Modulation Effect Research Articles

Self-and cross-phase modulation accompanying third-harmonic generation in a hollow waveguide

The influence of self-and cross-phase modulation on third-harmonic generation in a hollow waveguide is investigated. Analytic solutions of the coupled equations for the slowly varying amplitudes of the pump pulse and the third harmonic in a gas-filled hollow waveguide are obtained with consideration of self-and cross-phase modulation and first-order dispersion effects. The possibility of controlling the nonlinear phase trajectory of the third harmonic by cross-phase modulation is demonstrated.

Analytical Expression for the Reduction of XPM-Induced Crosstalk by Walk-Off

Wavelength division multiplexing (WDM) is an attractive scheme to increase the capacity of the already installed optical links. However, the effect of cross-phase modulation (XPM) causes nonlinear crosstalk in intensity modulated direct detection WDM systems based on dispersive fibers and thus could limit the total number of channels that such a system can support. On the other hand, the interference among channels decreases due to the so-called walk-off with growing difference in group velocity and channel spacing, respectively. Considering the propagation of Gaussian pulses, a formula which describes analytically this diminution as a function of the differential group delay is derived. Since the data signals transmitted in different channels are statistically independent XPM induces random-like intensity fluctuations. The theoretical results for their variance are verified by means of simulations. For comparison purposes, the variance of intensity fluctuations induced by pulses with edges steeper than those of a Gaussian pulse is calculated numerically.

Frequency Characterization of the Nonlinear Refractive Index in Optical Fiber

The Kerr and the electrostrictive contributions to the intensity-dependent nonlinear refractive index in optical fibers are discussed on both theoretical and experimental bases. Particular attention is devoted to the electrostrictive contribution that under particular conditions is enhanced by resonances. The resonant behavior of the electrostrictive effect is calculated, measured, and discussed for standard single-mode fibers and dispersion shifted fibers. Experimental results are also reported. Measure ments have been carried out with a simple and effective technique based on the cross-phase modulation effect that also allows one to evaluate the nonlinear refractive index at any bit rate. Electrostriction contributes 20 % to the total nonlinear refractive index but in the resonant regime becomes comparable to the Kerr effect.

Intensity-dependent phase-matching effects on four-wave mixing in optical fibers

A new phase-matching factor is derived for four-wave mixing (FWM) that includes the effects of self-phase and cross-phase modulation in optical fibers. Theoretical results predict that the wavelength of peak FWM efficiency shifts away from the fiber zero-dispersion wavelength and indicate that the conventional phase-matching factor may induce significant errors in FWM calculations. Experiments are presented to verify the new phase-matching factor and the related theoretical results. The measured results agree well with those predicted by the new phase-matching factor.

Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators

The cross-phase modulation (XPM) effect in intensity modulation-direct-detection (IM)-(DD) optical fiber links with multiple fiber segments with different characteristics and optical amplifiers is investigated theoretically and numerically. A generalized model of the IM induced by an arbitrary number of channels through XPM is derived, compared to simulation results and its validity range is presented. Results show that the XPM-induced IM can be modeled as an intensity modulator driven by the intensity of copropagating waves. The frequency response of the intensity modulator corresponding to each copropagating wave is mainly affected by the walk-off parameter and fiber dispersion. When the walk-off effect is weak the XPM-induced IM is approximately proportional to the square frequency. In single-segment fiber links when the walk-off effect is strong the XPM-induced IM is approximately linearly proportional to the frequency and inversely proportional to the wavelength separation. Both theory and simulation show that the XPM-induced IM in fiber links with multiple optical amplifiers can be enhanced or reduced by properly arranging the dispersion characteristics in each fiber segment. In a nondispersion compensated amplified link and for weak walk-off effect, the total XPM-induced IM increases approximately with the square of the number of fiber segments and of modulation frequency. However, if the dispersion is compensated for within each fiber segment the total XPM-induced IM increases proportionally to the number of fiber segments and to the square frequency. Furthermore, it is shown that in fiber links with a large number of segments placing a single dispersion compensator in the last segment of the link leads to almost the same performance as for non dispersion compensated fiber link and is significantly worse than placing one dispersion compensator in each fiber segment as far as the XPM-induced IM reduction is concerned.

Impact of modulation frequency on cross-phase modulation effect in intensity modulation-direct detection WDM systems

The impact of modulation frequency on the crossphase modulation (XPM) effect in intensity modulation (IM)-direct detection wavelength-division multiplexing systems is investigated theoretically and numerically. A simple expression for IM is derived, verified by simulation and its validity is presented. The dependence of XPM-induced IM on the fiber length, fiber dispersion, channel separation and pump modulation frequency is assessed. It is shown that at very low frequency the walkoff effect has almost no influence on the XPM-induced IM efficiency which increases with the square of the frequency; at higher frequency the IM efficiency can be reduced significantly by the walkoff and scales linearly with modulation frequency.

Analytical description of cross-phase modulation in dispersive optical fibers

The effect of intensity distortion induced by cross-phase modulation in dispersive optical fibers is studied. It is shown that, in most configurations in which distortions that are due to cross-phase modulation can become significant to optical communications, the effect of cross-phase modulation can be described with excellent accuracy by simple analytical expressions. The presented analysis also suggests that intensity distortions owing to cross-phase modulation can be efficiently reduced by linear dispersion compensation.

Two-wave reflection at a nonlinear interface

An analysis of two-wave reflection at a nonlinear interface is presented. We consider the case of two monochromatic plane waves of different frequencies interacting with self-focusing and self-defocusing nonlinear Kerr media. The influence of the cross-phase modulation effect on states of total and partial reflection of waves is examined. It is shown that those states change bistably or multistably and depend on the parameters of the incident waves and the type of boundary between the linear and the nonlinear media. We show that the intensity of one wave can control the state of reflection of the second wave and vice versa.

The effects of channel separation, input power and cross-phase modulation on nonlinear WDM systems with dispersion compensation

This paper analyzes the effects of channel separation, cross-phase modulation and input power on nonlinear WDM systems with conventional single-mode fiber combined with dispersion-compensating fiber. The conclusions are: (i) The performance of different signal channels depends on the input power and the channel separation. (ii) In general, the shorter the channel separation, the shorter the maximum transmission distance; the larger the input power, the shorter the maximum transmission distance. (iii) Cross-phase modulation plays an important role on the performance of nonlinear WDM with DCF compensation.

Generation of time-aligned picosecond pulses on wavelength-division-multiplexed beams in a nonlinear fiber

A fundamentally different way to generate time-aligned data pulses on wavelength-division-multiplexed (WDM) beams in a single-mode fiber is found. A large-amplitude pulse called a shepherd pulse is launched on one of the copropagating beams (shepherd pulse is defined as a pulse that can affect other copropagating pulses in a WDM format while maintaining its own propagation behavior). Initially at the launching plane no other pulse exists on any of the other copropagating wavelength-division-multiplexed beams. Due to the nonlinear cross-phase modulation effect, time-aligned pulses are generated on all other beams after a given fiber length. Both theoretical and experimental results are presented.

Enhanced pulse compression in a nonlinear fiber by a wavelength division multiplexed optical pulse

A way to compress an optical pulse in a single-mode fiber is presented in this paper. By the use of the cross-phase modulation (CPM) effect caused by the nonlinearity of the optical fiber, a shepherd pulse propagating on a different wavelength beam in a wavelength division multiplexed single-mode fiber system can be used to enhance the pulse compression of a copropagating primary pulse. Although CPM will not cause energy to be exchanged among the beams, the pulse shapes on these beams can be altered significantly. For example, a 1-mW peak power 10-ps primary pulse on a given wavelength beam may be compressed by a factor of as much as 25 when a copropagating 10-ps shepherd pulse of peak power of 49 mW on a different wavelength beam is similarly compressed. Results of a systematic study on this effect are presented in this paper. Furthermore, even when the primary pulse on a given wavelength beam has a peak power of much less than 1 mW, it can still be compressed by the same compression factor as a copropagating shepherd pulse of peak power much larger than 1 mW on a different wavelength beam as it undergoes compression. Through CPM, copropagating pulses on separate beams appear to share the nonlinear effect induced on any one of the pulses on separate beams.

One-dimensional spatial solitons in AlGaAs waveguides

We present experimental results on one-dimensional (1-D) spatial solitons in AlGaAs waveguides. Three distinct types of spatial solitons have been observed: namely the fundamental soliton, the Manakov soliton, and the vector soliton. The fundamental soliton is the simplest form of 1-D soliton which consists of a single polarization. The properties of waveguiding and ‘robustness’ are experimentally studied. Vector solitons which result from the complex interplay between the two orthogonally polarized beams due to self-phase modulation, cross-phase modulation, and four-wave mixing effects are studied. The complex beam dynamics and polarization behaviour of the vector solitons are experimentally studied. Manakov solitons which are a special case of the vector soliton exist when the ratio between the self-to-cross-phase modulation is one and the four-wave mixing effects becomes zero are demonstrated experimentally and the basic properties discussed. Finally, some soliton interactions such as trapping and dragging are reported and possible applications of soliton interactions are discussed.

Combined Spectral Effects of Pulse Walk-Off and Degenerate Cross-Phase Modulation in Birefringent Fibers

When a single ultrashort light pulse propagates through a birefringent optical fiber, degenerate cross-phase modulation occurs between the two orthogonal linearly polarized components of the pulse. The combined effects of pulse walk-off and degenerate-cross-phase modulation are characterized theoretically and experimentally. They cause asymmetry and decrease of the induced spectral broadening in comparison with pure self-phase modulation.

Spectral-linewidth broadening in synchronous Raman fiber amplification caused by cross-phase modulation effects and its suppression

When coherent light is amplified by a synchronous Raman fiber amplifier pumped by output pulses from a high-power erbium-doped fiber amplifier operating in an unsaturated gain regime, the detection efficiency with the heterodyne method is degraded. This degradation is caused mainly by cross-phase modulation effects. It is confirmed that using power-flattened pump pulses can suppress these effects.

Analysis of cross-phase modulation (XPM) effecton WDM transmission performance

The authors analyse the effect of cross-phase modulation (XPM) on wavelength division multiplexing (WDM) transmissions by experiments and numerical simulations, and provide the XPM limitation in a normalised and closed form formula. They also investigate the effect of XPM on dispersion compensated transmissions. It is shown that the location of dispersion compensators and the amount of compensation should be determined by considering the XPM effect.

Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer

We show that the cross-phase modulation effect in a Sagnac fibre loop can be used to measure the nonlinear refractive index ( n 2) of the fibre. The setup is simpler than the counterparts that use the self-phase modulation effect but it gives greater sensitivity. The polarisation effect of the Sagnac loop can also be controlled and the reciprocal nature of the loop is ensured. This removes automatically the uncertainties from the thermal and some other sources.

Cascaded χ (2) nonlinearity in QND measurement

QND measurement schemes often use Kerr nonlinearity to couple the intensity fluctuations of the signal beam to the phase fluctuations of the probe beam by means of the cross-phase modulation effect. Such schemes use materials with intrinsic χ(3)nonlinearity. However, it has already been shown that Kerr-effect-like correlation between two light waves may be achieved through cascaded χ(2): χ(2) processes. The value of the nonlinearity induced by cascading χ(2) can, in many cases, be much higher than fibre χ(3).

Optimization and characterization of phase-controlled all-optical switching with fiber solitons

Using a variational approach based on the Lagrangian formulation, consisting of an adiabatic perturbation of two coupled fiber solitonlike pulses, we present an optimization procedure for phase-controlled all-optical switching. Large phase intervals for both the parallel- and cross-state of the nonlinear coupler are determined. By means of a unified theoretical framework, which takes into account the effect of cross-phase modulation (XPM), both twin-core fiber couplers and birefringent optical fibers are considered. The influence of several errors in the weaker control pulse-such as time delay and pulsewidth fluctuations-on the transmission characteristics of the nonlinear coupler is also investigated.

Influence of the cross-phase modulation effect on the polarization states of waves transmitted through a non-linear Fabry–Pe´rot cavity

An analysis of the influence of the cross-phase modulation effect on the polarization states of waves transmitted through a non-linear Fabry–Pe´rot resonator with a self- focusing and self-defocusing Kerr medium is presented. The case is considered of two plane waves with different wavelengths incident on a non-linear Fabry–Pe´rot cavity. It is shown that the polarization states of the transmitted waves change bistably or multistably and depend on the parameters of incident waves and the resonator.

Unified description of ultrafast stimulated Raman scattering in optical fibers

Coupled nonlinear equations that describe the nonlinear process of stimulated Raman scattering in optical fibers are derived. These equations account in a unified manner for the Raman amplification, the Stokes generation, the induced self-frequency shift, and the interpulse stimulated Raman-scattering-induced cross-frequency shift. The equations reduce to a well-known form for relatively wide picosecond pump pulses. Using these equations, we show theoretically that the effects of cross-phase modulation, self-frequency shift, and cross-frequency shift cause two optical pulses copropagating in the anomalous dispersion regime of the fiber to shed some of their energy and evolve into a narrower soliton, which has a higher frequency shift than a single propagating soliton. It is also shown that the self-frequency shift of femtosecond pulses is detrimental to Raman generation. As the input pulse width is reduced, the spectrum of the pulse shifts by an amount comparable with the Raman shift. The shift increases continuously with propagation at such a rapid rate that the Stokes pulse has no time to build up from noise to significant energy levels.