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Journal of Optical Communications

Crosstalk of Signals in Pump Probe Structure with Self-phase Modulation and Cross-phase Modulation

Xiong Jie, Bin Luo, Wei Pan, Yifeng Li

Published Jan 1, 2006• 0 citations
Publisher

Abstract

The transmission of optical signals under the effects of cross-phase modulation (XPM) and self-phase modulation (SPM) together in pump-probe wave structure is investigated in intensity modulation-direct detection wavelength division multiplexing (IM-DD WDM) systems. A simple expression for frequency domain IM of probe channel is derived. The analytical method to determine the temporal shape of probe wave when arbitrary wave is inputted in pump channel is confirmed. The impact of channel separation and transmission rate to XPM is assessed. We find that the SPM in pump channel increase temporal intensity modulation index reflected XPM to a certain extent. The analytical result agrees well with numerical simulation.

DOI
10.1515/joc.2006.27.6.290

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The transmission of optical signals under the effects of cross-phase modulation (XPM) and self-phase modulation (SPM) together in pump-probe wave structure is investigated in intensity modulation-direct detection wavelength division multiplexing (IM-DD WDM) systems. A simple expression for frequency domain IM of probe channel is derived. The analytical method to determine the temporal shape of probe wave when arbitrary wave is inputted in pump channel is confirmed. The impact of channel separation and transmission rate to XPM is assessed. We find that the SPM in pump channel increase temporal intensity modulation index reflected XPM to a certain extent. The analytical result agrees well with numerical simulation.
The four-wave-mixing-based phase-sensitive amplification of pulsed signals is analytically investigated, taking into account the pump depletion and the self- and cross-phase modulation (SPM and XPM) effects of the pumps and signals. Formulas for output phase and power are derived. It is found that, for a single-pulse signal input, the SPM/XPM of the signal will cause frequency chirping to the output; for a pulse-sequence, the amplitude-fluctuation of the input signal will destroy the phase regeneration through the SPM/XPM. In addition, the amplified signal pulse will initially be compressed and distorted, and then it will get broadened due to pump-depletion.
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.
In this paper, we investigate the novel behavior of induced focusing in nonlinear metamaterials (MMs) through designing probe-pump configuration, where the coupled waves may simultaneously experience negative refractive index or positive refractive index, or one experiences positive refractive index and another experiences negative refractive index both analytically and numerically. It is shown that cross-phase modulation (XPM) in MM not only brings some new features to the behavior of induced focusing, but also makes it possible in the ordinary positive-index materials (OMs), where it is otherwise impossible. First, we reveal that weak probe beam can be focused by strong pump beam even when their centers are completely overlapping each other. Moreover, it is found that the separated distance between coupled waves has an optimal value, which results in the strongest focusing of probe beam. Finally, another most notable property is that a spatial induced focusing is found to occur for different combinations of the signs of refractive index decided by the probe and pump beams, respectively, implying that a spatial XPM in MMs can be used as a more powerful tool for controlling the inducing focusing, when compared with the corresponding case in OMs. Our findings demonstrate that MMs can provide us unique opportunities unattainable in OMs to manipulate the all-optical control of optical focusing behavior through the new physical mechanism of XPM.
We show the Cross Phase Modulation (XPM) effect between CW probe that operates in bistability region and strong Gaussian pump in a Fiber Bragg Grating (FBG) by Implicit 4th Order Runge-Kutta Method. The XPM effect results in three unique nonlinear switching behaviors of the probe transmission depending on the pump peak intensity and its Full Width Half Maximum (FWHM) value. From this observation, we offer the FBG three potential nonlinear switching applications in all-optical signal processing domain as: a step-up all-optical switching, an all-optical inverter, and an all-optical limiter. The bistability threshold that determines the nonlinear switching behaviors of probe transmission after Gaussian pump injection is defined numerically and shown to be equivalent to the unstable state inside hysteresis loop.
In this paper, we propose and demonstrate a scheme to enhance nonlinearities of a probe pulse at both cross-phase modulation (XPM) and self-phase modulation (SPM) in a four-level system. Based on standing wave grating generated by counter-propagating resonant signal fields and an additional off-resonant coupling field, a giant nonlinear refractive index of the resonant probe field is obtained with absorption suppressed. Group velocity of the probe pulse can be controlled by both XPM and SPM nonlinearities.
We observed conditional cross-phase modulation (C-XPM) applicable to quantum phase gate. Combinations of two probe field’s polarizations conditioned XPM of two probe fields in the corresponding nonlinear optical system. With optimized parameters of multi-photon transition, we could increase C-XPM more than 1 rad. with small probe absorption. Group velocity matching ratio between probe pulses was estimated to 1.2 in the optical loop system. Because multi-photon interference depends on the ratio between the Rabi frequencies of the probe fields, not the individual intensity, we expect the same phase shift between few photons level’s probe pulses in our scheme.