Effect of four-wave mixing in WDM optical fibre systems

Wavelength division multiplexing (WDM) can both significantly enhance transmission capacity and provide more flexibility in optical network design. Through the use of erbium-doped fibre amplifiers (EDFAs), it is possible to build long-distance transparent optical transmission links without electrical regenerators. In such systems, fibre nonlinearities are likely to impose a transmission limit due to increased total interaction length. There are a number of optical nonlinear effects in optical fibres, such as stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), carrier-induced phase modulation and four-wave mixing (FWM). Out of these SRS and FWM are the dominant effects. In this paper, an algorithm has been suggested to study the effect of FWM in the total system noise considering the combined effect of SRS and FWM in the presence of amplified spontaneous noise (ASE). It has been found from the study that to maximize the signal-to-noise ratio of the transmitted signal in a WDM system FWM noise needs to be reduced as this is the dominant noise factor.     

Four-wave mixing crosstalk in optical fibre parametric amplifiers with orthogonal pumps

We experimentally investigated the generation of new unwanted frequencies generated by four-wave-mixing in fibre optical parametric amplifiers with two orthogonally polarised pumps and 17 dB of small signal gain. At these gain levels, we simultaneously observe two distinct types of mixing interactions and demonstrate that they vary with changing output power and gain at different rates. We also demonstrate that a combination of high pump power and low nonlinearity fibre results in less power in the unwanted peaks than a combination of low pump power and highly nonlinear fibre. Because these new unwanted four-wave mixing peaks result in crosstalk between wavelength division multiplexed channels, building parametric amplifiers with a combination of high pump power and fibre of low nonlinearity is desirable.     

Experimental verification of the existence of optically induced carrier pulsations in SOAs

Experimental investigation of the role of interband effects in four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) is reported. Carrier density pulsations (CDP) in SOAs, caused by optical wave beating, are measured in the RF domain. This gives strong experimental confirmation of the link between CDP and wave mixing, as usually assumed in theory of FWM in SOAs. The dependence of CDP amplitude on bias current and optical power is also established.     

四波混频在长距离相干光纤传输中的影响

本文研究光纤非线性现象之一的四波混频对长距离相干多路光纤传输系统的影响.通过对一条长度为550km,采用9个掺铒光纤放大器的频分复用系统的实验,清楚地观察到了四波混频这一光纤非线性.实验的结果符合对四波混频的理论分析与计算.结果表明:对信息容量在每秒10~9bit数量级,采用常规的不归零码作信号方式的多路传输,光纤中的四波混频现象将严重地影响其传输性能.     

Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain

We present what is to our knowledge the first complete measurement of the dependence of Raman gain on chromatic dispersion, fully revealing the influence of parametric four-wave mixing on stimulated Raman scattering. In particular, a threefold increase of the Raman gain is observed under phase-matching conditions, in excellent agreement with theoretical predictions. Our experiments, which were performed in a photonic crystal fiber, demonstrate that these unique fibers can be exploited to boost the performances of fiber Raman amplifiers.     

Reduction of fiber-nonlinearity-enhanced amplifier noise by means of phase-sensitive amplifiers

In optical fiber transmission systems near the zero-dispersion wavelength that use in-line erbium-doped fiber amplifiers (EDFA's), the enhancement of optical amplifier noise caused by four-wave mixing (FWM) in transmission fibers degrades signal-to-noise ratio (SNR) excessively. We theoretically show that the enhancement of amplifier noise by the FWM in transmission fibers can be effectively eliminated by implementing in-line phase-sensitive amplifiers (PSA's). Small-signal analysis of the nonlinear Schr?dinger equation shows that the transmission distance limited by the SNR of an in-line PSA system is expanded four times more than that of an in-line EDFA system.     

Evolution of first-order sidebands from multiple FWM processes in HiBi optical fibers

The generation of two idler waves inside a high birefringent (HiBi) optical fiber through three four-wave mixing (FWM) processes is studied theoretically. The coupled-equations for the field amplitudes are derived and analytically solved, in the co-polarized and orthogonal polarization schemes. The obtained solutions take into account the delayed Raman response of the medium. The polarization sensitivity of the generation of the idler waves is analyzed. Results show that the stimulated Raman scattering does not change the efficiency of the idler wave generation in the co-polarized scheme, whereas in the orthogonal polarization scheme that nonlinear process decreases the efficiency of the four-wave mixing processes. Results also show that this set of multiple four-wave mixing processes is physically quite different from the typical single or dual pump four-wave mixing configurations. Findings show that the power transfer from the pumps to the idler fields can lead to a monotonous growth, or a periodic evolution of the sidebands along the fiber. Results show that the process efficiency varies greatly with the angle between the two pump polarizations.     

Gain-flattened fiber Raman amplifiers with nonlinearity-broadened pumps

Gain flattening of an E-band (1360-1460-nm) fiber Raman amplifier was achieved by pump spectral broadening to a 16.3-nm linewidth by use of nonlinearity in a 6.2-km standard fiber. With the broadened pump, the characteristic Raman gain ripple was removed and the 3-dB gain bandwidth was increased by 10.6 nm relative to the nonbroadened pump case. The experimental results agreed well with a gain profile simulation. The use of a 100-m holey fiber for pump broadening was also investigated near 1.56 microm for U-band (1625-1675-nm) Raman amplifiers. Much less broadening was observed, which is believed to be a result of less four-wave mixing.     

Fiber four-wave mixing source for coherent anti-Stokes Raman scattering microscopy

We present a fiber-format picosecond light source for coherent anti-Stokes Raman scattering microscopy. Pulses from a Yb-doped fiber amplifier are frequency converted by four-wave mixing (FWM) in normal-dispersion photonic crystal fiber to produce a synchronized two-color picosecond pulse train. We show that seeding the FWM process overcomes the deleterious effects of group-velocity mismatch and allows efficient conversion into narrow frequency bands. The source generates more than 160 mW of nearly transform-limited pulses tunable from 775 to 815 nm. High-quality coherent Raman images of animal tissues and cells acquired with this source are presented.     

Characteristics of wavelength conversion of short optical pulses in quantum dot semiconductor optical amplifiers

The characteristics of short optical pulse four-wave mixing (FWM) and amplification in quantum dot semiconductor optical amplifiers (QD-SOAs) are investigated taken into account the effect of the multi-discrete QD energy levels. Different saturation and recovery response for the electron and hole states are observed, which is attributed to different energy spacing between the energy states. We found that the 3 dB saturation energy of QD-SOA depends on the pulse width for short input pulses. Also, the optimum time delay between the probe and pump pulses in QD-SOAs, which provides maximum FWM efficiency in QD-SOAs, is smaller than the optimum delay in quantum well SOA.     

Analysis of format conversion from optical 16QAM to QPSK based on cascaded four-wave mixing in semiconductor optical amplifier

A scheme of format conversion from optical 16-ary quadrature amplitude modulation (16QAM) to quadrature phase shift keying (QPSK) signal based on cascaded four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) is proposed. Theoretical analysis and simulations of the format conversion scheme are conducted to validate the feasibility of the proposal. In this proposal, the phase conjugated of 16QAM signal is generated after the first FWM process in an SOA, and then the QPSK signal is converted due to the second non-degenerate FWM (ND-FWM) process in another SOA. The performance and the optimal design of the 10 Gbit/s format conversion system under various key parameters of SOAs are evaluated and discussed. Simulation results present useful to enable interconnection between backbone network and access network.     

基于PolSK调制的四波混频型超快全光译码器

提出了一种新型的基于半导体光放大器（semiconductor optical amplifier, SOA）中四波混频（four-wave mixing, FWM）效应的超快全光译码器方案,方案中采用了偏振移位键控（polarization-shift-keying, PolSK）信号光.考虑SOA的偏振相关性,建立了这种全光译码器完整的偏振相关宽带理论模型.通过数值模拟的方法,从理论上实现了超快全光译码器,并研究了两输入信号光功率、SOA注入电流和SOA的偏振相关性对全光译码器输出特性的影响. 关键词： 全光译码器 偏振移位键控 四波混频 半导体光放大器     

Ultrafast nonlinear processes in quantum-dot optical amplifiers

Ultrafast gain dynamics in quantum-dot optical amplifiers has been studied by using the pump-probe and four-wave mixing (FWM) techniques. It was found that there are at least three nonlinear processes, which are attributed to carrier relaxation to the ground states, phonon scattering, and carrier capture from the wetting layers into the quantum dots (QDs). The relevant time constants were evaluated to be ～90 fs, ～260 fs, and ～2 ps, respectively, under a 50 mA bias condition. The compressed gain recovered to 3% of its initial value in 4 ps, and no recovery component slower than 2 ps could be seen in the temporal range tested. This is quite different from the feature in quantum wells, where a very slow component (> 50 ps) exists. This suggests a possibility of enhancing the operation speed of semiconductor optical amplifiers by using QDs as an active layer. The third-order optical susceptibility (χ⁽³⁾) has been evaluated by means of both nonlinear transmission and FWM experiments. The results show that the nonlinearity expressed by χ⁽³⁾/g ₀ is quite similar to that of bulk and quantum wells, which can be explained by the similar relaxation times.     

Narrowband switchable dual-passband atomic filter with four-wave mixing optical amplification

By using Faraday optical filter combined with four-wave mixing (FWM) amplifier, a narrow bandwidth optical amplifying atomic filter with switchable dual-passband is demonstrated experimentally. The two transmission peaks of the filter correspond to the Stokes and anti-Stokes frequencies, exhibiting a Raman gain in 13- and 17-fold, respectively, with bandwidth of ～120 MHz. By properly setting pump laser detuning, switching between filter passbands is realized. We also investigate the dependence of peak transmission on both pump laser intensity and Rb cell temperature. This atomic filter can find practical applications in long-distance laser communications and laser remote-sensing systems.     

Use of multimode optical fibers for fiber-based coherent anti-Stokes Raman scattering microendoscopy imaging

A multimode fiber (MMF) was used for both delivery of excitation lasers and collection of returned coherent anti-Stokes Raman scattering (CARS) signals in a CARS microendoscopy prototype imaging system. We demonstrated a polarization-based scheme for suppression of four-wave mixing (FWM) signals in delivery fibers. Our experimental results showed that this polarization-based FWM-suppressing scheme can dramatically reduce FWM signals generated in MMFs, and MMFs can be used to produce CARS images in this microendoscopy system. The proposed MMF-based CARS microendoscopy imaging system with the polarization-based FWM-suppressing scheme offers a potential platform for building fiber-based CARS microendoscopes that can effectively suppress FWM background noises.     

Low threshold Raman effect in high power narrowband fiber amplifier

A low-threshold Raman effect in a kilowatt ytterbium-doped narrowband fiber amplifier system is reported. The Raman Stokes light at 1120 nm is achieved with the total output power of only ~400 W, indicating that the Raman threshold of this kilowatt codirectional pumped continuous wave fiber amplifier is much lower than the predicted value estimated by the classic formula. To figure out the mechanism of this phenomenon, simulations based on the general stimulated Raman scattering(SRS) model are analyzed indicating that the key factor is the coupling between four-wave mixing(FWM) and SRS. The simulation results are in good agreement with our experiments.     

Numerical analysis of four-wave mixing between picosecond mode-locked laser pulses in a tensile-strained bulk SOA

A numerical model of four-wave mixing between picosecond pulses in a tensile-strained bulk semiconductor optical amplifier is presented. The model utilizes a modified Schrödinger equation to model pulse propagation. The Schrödinger equation parameters such as the material gain first and second order dispersion, linewidth enhancement factors and optical loss coefficient were obtained using a previously developed steady-state model. The predicted four-wave mixing pulse characteristics show reasonably good agreement with experimental pulse characteristics obtained using Frequency Resolved Optical Gating. In particular simulations predict a large increase in the pulse pedestals of the FWM converted pulse, which is verified by experiment.     

Transmission performance of 10-Gb/s DPSK WDM signals due to phase-error and four-wave mixing in SOAs

We present a complete dynamic model of semiconductor optical amplifiers (SOAs) including the inter-channel four-wave mixing (FWM). The model has been implemented using the time-dependent transfer matrix method (TMM) and applying the discretization scheme in both the spatial and spectral domains. In SOA-based wavelength division multiplexing transmission systems using 10-Gb/s differential phase shift keyed (DPSK) signals, the system performance due to the SOA-induced phase-error and the FWM effect has been analyzed. By the injection of a reservoir channel into SOAs, the transmission performance of non-return-to-zero (NRZ) DPSK signals can be improved through the phase-error reduction. Both the NRZ-DPSK and return-to-zero (RZ) DPSK signals are found to be suffered from the FWM-induced crosstalk. The overall nonlinear tolerance of RZ-DPSK is shown to be better than that of NRZ-DPSK.     

Interactions of Three Dual-Dressing Effects of Four-Wave Mixing in a Five-Level Atomic System

We study the four-wave mixing （FWM） in an opening five-level system with two dressing fields. There axe three kinds of doubly dressing mechanisms （parallel cascade, sequential cascade, and nested cascade） in the system for doubly dressed four-wave mixing. These mechanisms reflect different correlations between two dressing fields and different effects of two dressing fields to the FWM. Investigation of these mechanisms is helpful to understand the generated high-order nonlinear optical signal dressed by multi-fields.     

Detection of weak optical signals with a laser amplifier

Detection of weak and extremely weak light signals amplified by linear and four-wave mixing laser amplifiers is analyzed. Photoelectron distributions are found for different input photon statistics over a wide range of gain. Signal-to-noise ratios are calculated and analyzed for preamplification schemes using linear and four-wave mixing amplifiers. Calculations show that the high signal-to-noise ratio (much higher than unity), ensuring reliable detection of weak input signals, can be attained only with a four-wave mixing preamplification scheme. Qualitative dependence of the signal-to-noise ratio on the quantum statistical properties of both signal and idler waves is demonstrated.