Cross-phase Modulation Effect Research Articles

Various Nonlinearity Mitigation Techniques Employing Optical and Electronic Approaches

In this letter, we directly compare digital back-propagation (DBP) with spectral inversion (SI) both with and without symmetry correction via dispersive chirping, and numerically demonstrate that predispersed SI outperforms traditional SI, and approaches the performance of computationally exhaustive ideal DBP. Furthermore, we propose for the first time a novel practical scheme employing predispersed SI to compensate the bulk of channel nonlinearities, and DBP to accommodate the residual penalties due to varying SI location, with predispersed SI ubiquitously employed along the transmission link with <;0.5-dB penalty. Our results also show that predispersed SI enables partial compensation of cross-phase modulation effects, increasing the transmission reach by ×2.

Error-free OTDM demultiplexer using the supercontinuum spectrum-slicing induced clock signal

We experimentally demonstrate an 80-Gb/s optical time-division multiplexing (OTDM) demultiplexing system based on the cross-phase modulation (XPM) effect in high-nonlinearity fibers. The message carried by OTDM signal is loaded onto the probe signal by sampling the OTDM packet with a 10-GHz stable and controllable clock pulse train. The clock signal with ~ 11 ps pulse width is achieved by employing supercontinuum spectrum-slicing technique, which is distinct from that based on mode-locked lasers. The demultiplexed signal is obtained by filtering out the XPM-induced spectral sidebands of the probe signal. The OTDM demultiplexer based on this novel technique shows excellent performances and contributes to a bit error rate of as low as 10 −9.

Degenerate four-wave mixing in triply resonant Kerr cavities

We demonstrate theoretical conditions for highly-efficient degenerate four-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency $\omega_0-\Delta \omega$ can, in the presence of pump light at $\omega_0$, be converted with quantum-limited efficiency into an output shifted signal of frequency $\omega_0 + \Delta \omega$, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10mW assuming very conservative cavity parameters (modal volumes $\sim10$ cubic wavelengths and quality factors $\sim1000$. The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting "quantum" arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.

Formation and propagation of ultraslow three-wave-vector optical solitons in a cold seven-level triple-Λatomic system under Raman excitation

In this article, a theoretical scheme is proposed to investigate the formation and propagation of three-wave coupled vector optical solitons with ultraslow group velocities in a lifetime-broadened seven-state triple-$\ensuremath{\Lambda}$ atomic system under Raman excitation. We show that in the presence of a weak applied magnetic field that removes the degeneracy of the corresponding sublevels of the atomic medium, three continuous-wave control fields with circularly left or right polarized fields induce a quantum interference effect which can largely suppress the absorption of the three low-intensity pulsed fields, that is, the circularly ${\ensuremath{\sigma}}^{\ensuremath{-}}$ (right), the linearly $\ensuremath{\pi}$, and the circularly ${\ensuremath{\sigma}}^{+}$ (left) polarized fields converted from one weak linear-polarized probe field. By means of the standard method of multiple scales, we solve the equations of motion of atomic response and probe-control electromagnetic fields and derive three-coupled nonlinear Schr\"odinger equations that govern the nonlinear evolution of the envelopes of the probe fields in this scheme. We then demonstrate that because of the nonlinear coupling to one another, the three probe fields can evolve into three-wave temporal, group velocity, and amplitude-matched optical solitons under appropriate conditions, which are produced from the delicate balance of the dispersion effects and the self- and cross-phase modulation effects. This scheme may thus pave the way to generate ultraslow vector optical solitons composed of three field components in a highly resonant atomic medium and result in a substantial impact on this field of nonlinear optics.

Polarization Rotation in Silicon Waveguides: Analytical Modeling and Applications

The efficient use of optical nonlinearities in silicon is crucial for the implementation of silicon-based photonic devises. In this paper, we present an approximate analytical study of nonlinear polarization rotation in silicon-on-insulator (SOI) waveguides; the rotation is predominantly caused by the effects of self-phase modulation and cross-phase modulation, stemming from the anisotropic Kerr nonlinearity. In the first part of the paper, we analyze the transmittance of the Kerr shutter in the continuous-wave regime and address the problem of its optimization. It is essential for the generality of our conclusions that both free-carrier effects and two-photon absorption are properly accounted for in this study. We specifically show that the signal transmittance may be optimized by adjusting the waveguide length, the pump power, and the incident linear polarizations of pump and signal beams. In the second part of the paper, we examine the problem of power equalization with SOI waveguides. We validate the derived analytical solutions by comparing their predictions with the data from numerical simulations and illustrate the solutions by the examples of practical interest. The results of our work may prove useful for the design and optimization of SOI-based Kerr shutters, all-optical switches, and power equalizers.

Adaptive-Modulation-Enabled WDM Impairment Reduction in Multichannel Optical OFDM Transmission Systems for Next-Generation PONs

The transmission performance of multichannel adaptively modulated optical orthogonal frequency-division multiplexing (AMOOFDM) signals is investigated numerically, for the first time, in optical-amplification-free and chromatic-dispersion-compensation-free intensity-modulation and direct-detection systems directly incorporating modulated distributed feedback (DFB) lasers (DMLs). It is shown that AMOOFDM not only significantly reduces the nonlinear wavelength-division multiplexing (WDM) impairments induced by the effects of cross-phase modulation and four-wave mixing but also effectively compensates for the DML-induced frequency chirp effect. In comparison with conventional modulated optical orthogonal frequency-division multiplexing (OFDM), which uses an identical signal modulation format across all the subcarriers, AMOOFDM improves the maximum achievable signal transmission capacity of a central WDM channel by a factor of 1.3 and 3.6 for 40- and 80-km standard single-mode fibers, respectively, with the corresponding dynamic input optical power ranges being extended by approximately 5 dB. In addition, AMOOFDM also causes the occurrence of cross-channel complementary modulation format mapping among various WDM channels, leading to considerably improved transmission capacities for all individual WDM channels.

Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet

We consider an active-Raman-gain scheme for realizing giant Kerr nonlinearity and superluminal optical solitons in a four-state atomic system with a gain doublet. We show that this scheme, which is fundamentally different from those based on electromagnetically induced transparency (EIT), is capable of working at room temperature and eliminating nearly all attenuation and distortion.We demonstrate that, due to the appearance of a gain spectrum hole induced by the quantum interference effect induced by a signal field, a significant enhancement of Kerr nonlinearity of probe field can be realized effectively, which can be more than ten times larger than that arrived by the EIT-based scheme with the same energy-level configuration. Based on these important features, we obtain a giant cross-phase modulation effect and hence a stable long-distance propagation of optical solitons, which have superluminal propagating velocity and very low generating power.

Darboux Transformation and Soliton Solutions for Inhomogeneous Coupled Nonlinear Schrödinger Equations with Symbolic Computation

With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrödinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.

Cross-phase modulation response of a DCC-DFB-SOA all-optical flip-flop

Using the coupled-mode and carrier rate equations, we have derived a dynamic model for the distributed feedback semiconductor optical amplifier (DFB-SOA) all-optical flip-flop (AOFF). We have analyzed the effects of the coupling coefficient and the corrugation position on the dynamic response of the device. We have also investigated the effects of cross-phase modulation on the switching speed of the DFB-SOA with the distributed coupling coefficient (DCC), known as the DCC-DFB-SOA AOFF. Furthermore, it is shown that by optimizing the coupling coefficient value and the corrugation position, the AOFF speed limitation is improved significantly. The ON and OFF switching time values, in an optimized condition, are 300 and 100 ps, respectively, while the carrier lifetime is about 780 ps. In comparison with those of a conventional DFB-SOA-AOFF, these values show reductions of more than 2 and 14 times in the ON and the OFF switching times, respectively. Under such conditions, a maximum bit rate of 1.4 GHz is achieved. The finite difference time-domain method is utilized for the numerical simulations.

Slow vector optical solitons in a cold four-level inverted-Y atomic system

The authors show the formation of slow temporal vector optical solitons in a cold lifetime-broadened four-level inverted-Y atomic system. We demonstrate that Maxwell's equations for describing two orthogonally polarised components of a low intensity signal field can evolve into two coupled nonlinear Schrodinger equations, which results in various distortion-free temporal vector optical solitons, such as bright-bright or dark-dark vector solitons. These results are produced from the correct balance between dispersion, self- and cross-phase modulation (SPM and XPM) effects. We also show that the integrable Manakov model can be realised by adjusting the corresponding SPM, XPM and dispersion effects of this inverted-Y atomic system.

All-Optical Signal Processing Based on Nonlinear Effects in Semiconductor Optical Amplifiers

In this paper, we report our recent studies on developing nonlinear techniques based on a single SOA for all-optical signal processing at high-speed, with a focus on simple configurations employing commercial SOAs for several key all-optical network applications. Our researches are based on nonlinear polarization rotation (NPR), four-wave mixing (FWM) and cross-phase modulation (XPM) effects in a single SOA. We propose and demonstrate applications of the nonlinear techniques in all-optical logic gates, multi-function format coversion, tunable Lyot birefringent filter and multi-channel optical time division multiplexed (OTDM) demultiplexing.

Four-Wave-Mixing-Based Phase-Sensitive Amplification of Pulsed Signal in Fibers

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.

Wavelength Converter Using Semiconductor Optical Amplifier Mach-Zehnder Interferometer Based on XPM at 40 Gb/s for Future Transport Networks

We have simulated, for the first time, wavelength converter for future broadcast networks at 40 Gb/s using low-cost semiconductor optical amplifiers. The performance analysis is carried out for an all-optical frequency converter based on cross-phase modulation in two semiconductor optical amplifiers arranged in a Mach-Zehnder interferometer configuration to evaluate the efficiency of conversion. The results, evaluated analytically for input, return to zero signal at a bit rate of 40 Gb/s show that conversion is possible over a wavelength separation of 1 nm between the pump and the input wavelength. Increasing the driving current can decrease the cross-phase modulation effect. The cross gain modulation scheme shows extinction ratio degradation for conversion to longer wavelengths.

Ultraslow temporal vector optical solitons in a cold four-level tripod atomic system

We show the possibility of generating ultraslow temporal vector optical solitons in a cold lifetime-broadened four-level tripod atomic medium under Raman excitation. We demonstrate that the two orthogonally polarized components of the low-intensity signal field can evolve into various distortion-free temporal vector optical solitons, such as bright-bright vector solitons with ultraslow group velocity. These results are produced from the balance of self- and cross-phase modulation effects and dispersion. We also show that Manakov temporal vector solitons may be realized by adjusting the corresponding self- and cross-phase modulation and dispersion effects of our system.

All-optical serial-to-parallel converter for simultaneous multiple-channel OTDM demultiplexing

Proposed is a novel structure of a cascadable photonic serial-to-parallel converter (SPC) based on the cross-phase modulation effect in a semiconductor optical amplifier for simultaneous multiple-channel optical time division multiplexed demultiplexing. The proposed SPC features cascadability, compact structure, high-speed operation, and simultaneous two-channel operation. Error-free 20 Gbit/s simultaneous two-channel demultiplexing is experimentally demonstrated.

自散焦介质中的光开关现象

A spatial optical switch phenomenon caused by the induced focusing of a weak probe beam occurring in self-defocusing nonlinear media is discussed theoretically. A weak beam is induced to focus when it copropagates with an intense pump beam under the conditions that the probe and pump beams peak at different positions and propagate in different directions. Due to the effect of cross-phase modulation, the weak beam can not only be focused but also be deflected. The phenomenon is discussed by numerically solving the coupled amplitude equations.

Optical poling in germanium-doped microstructured optical fiber for visible supercontinuum generation

We report visible supercontinuum generation initiated by the second harmonic generation obtained in a germanium-doped microstructured optical fiber after optical poling processing. The visible spectral broadening is due to a cross-phase modulation effect between the generated IR solitons and the second harmonic (532 nm) of the 1064 nm pump wave. The 400-650 nm white-light emission is obtained on the fundamental propagation mode of the fiber.

UWB Pulse Generation and Distribution Using a NOLM Based Optical Switch

An approach is proposed in this paper to generate ultra-wideband (UWB) pulses based on cross-phase modulation (XPM) effects in nonlinear optical loop mirror (NOLM). The NOLM can be considered as an optical switch which is controlled by pump to generate positive and negative Gaussian pulses, which are then delayed by SMF and combined to generate both Gaussian monocycle and doublet pulses. These two pulse shapes can be switched at a high speed by controlling the on-off of one of the probe. In addition, the SMF acting as a chromatic dispersion media in generating the UWB pulses can also be used to distribute the UWB signals from the central station (CS) to remote access points (AP). Different distance between CS and remote APs has no effects on the generated UWB pulses by adopting a wavelength tunable laser as probe.

All-Optical Processing by Means of Cross-Phase-Modulation-Based PM-NOLM Interconnected Structures

Nonlinear optical loop mirrors (NOLMs) are attractive devices that can be exploited in all-optical signal processing (OSP) techniques because of the ultrashort time response of the Kerr effect in the optical fiber. Although several works have been done to study and experimentally demonstrate the behavior of both single and cascaded NOLM structures, the analytical description of a model suitable for the study of multiple and interleaved NOLM configurations is still missing in literature. In this paper, a model based on basic blocks interconnection is proposed and applied to a particular configuration named Mickey NOLM. The model is based on elementary blocks where the cross-phase modulation effect induced in a polarization maintaining loop by a pump signal is exploited to unbalance the overall NOLM characteristics. Several results are shown and their possible applications to all-OSP are proposed.

Experiments of all-optical switching due to cross-phase modulation in fiber grating coupler by lock-in amp. detection scheme

We report results of experiments examining cross-phase modulation effect on fiber grating coupler (FGC). All-optical switching are observed in both cases of high pump pulses emitted from high-power Nd:YAG laser and mode-locked EDF laser. Based on coherent detection using a lock-in amplifier, the red-shift of the Bragg wavelength for a FGC was estimated to be 0.04–0.06 nm/1.5–1.7 kW peak power of EDF pump light at 1.55 μm. To avoid mixture of pump pulse and signal light at 1.55 μm, we have also performed the experiment using high power Nd:YAG laser as a pump power. For a Nd:YAG laser, the red-shift of Bragg wavelength is estimated to be 0.06 nm at maximum pump power of 2.1 kW. A simple model for the proposed detection scheme is given and the resultant red-shift is analyzed numerically.