Four-wave Mixing Characteristics Research Articles

Measurements of the dispersion, the dispersion slope and nonlinear coefficients of photonic crystal fibers based on degenerate four-wave mixing (FWM)

Abstract A simple and accurate method based on degenerate four-wave mixing (FWM) to evaluate optical fiber dispersion and nonlinearity is presented. We investigated the continuous wave degenerate FWM characteristics of two photonic crystal fibers (PCFs) and a SMF28 fiber. Simply by measuring and analyzing the continuous wave degenerate FWM conversion efficiency as a function of the wavelength difference between pump and signal waves, fitting between experimental data and analytical FWM conversion efficiency expression is carried out to determine the dispersion, dispersion slope and nonlinear coefficient of the fiber. The fiber parameters simultaneously obtained from a single set of FWM measurement for Single Mode Fiber 28 (SMF28) are found to be agreement with the manufacturer specifications for this fiber, thus validating the PCF results and, more generally, the acceptable accuracy of the simple method proposed here.

Four-wave mixing properties in bilayer graphene nanosystem

Graphene thin films are often used to manufacture various optoelectronic nanodevices owing to their advantages such as light weight, small size, high quality factor, and good conductivity. So far, there have been few studies of the four-wave mixing characteristics in a bilayer graphene nanosystem, especially theoretical research. In this work, we study theoretically the four-wave mixing properties in a bilayer graphene nanosystem. Firstly, the analytical formula of the four-wave mixing signal is derived by quantum mechanical method, which is divided into three steps. 1) Total Hamiltonian of the system is written in the rotating wave approximation. 2) By using the Heisenberg equation of motion and the commutation relations between different operators, the corresponding density matrix equations are obtained. 3) To solve these density matrix equations, we make an ansatz and obtain the analytical formula of the four-wave mixing signal. Secondly, we explore the dependence of the four-wave mixing signal on the phonon-exciton coupling strength, pumping intensity and the detuning between the exciton and the pump field. The calculated results show that the lineshape of four-wave mixing spectrum can be switched among two-peaked, three-peaked, four-peaked, five-peaked and six-peaked by adjusting the phonon-exciton coupling strength, the pumping intensity, and the detuning between the exciton and the pump field. In a weak phonon-exciton coupling regime (i.e. phonon-exciton coupling strength <i>g</i> < dephasing rate of exciton <i>Γ</i><sub>2</sub>), the intensity of the left peak and right peak of four-wave mixing signal first increase and then decrease with the increase of the pumping intensity <inline-formula><tex-math id="M1">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M1.png"/></alternatives></inline-formula>. In the intermediate and strong phonon-exciton coupling regime (i.e. <i>g</i> = <i>Γ</i><sub>2</sub> and <i>g</i> > <i>Γ</i><sub>2</sub>), the four-wave mixing spectrum exhibits a two-peaked structure. The maximum values of these two peaks increase as <inline-formula><tex-math id="M2">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M2.png"/></alternatives></inline-formula> increases, and their spacing is equal to 2<i>g</i>. Especially, for a given pumping intensity <inline-formula><tex-math id="M3">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M3.png"/></alternatives></inline-formula> (= 10 THz<sup>2</sup>), the maximum value of the peak for <i>g</i> = 4 THz becomes 0.4% of that for <i>g</i> = 1 THz, indicating that the phonon-exciton coupling inhibits the enhancement of the four-wave mixing signal to a certain extent. Our findings can not only offer an efficient way to measure the phonon-exciton coupling strength in the bilayer graphene system, but also help one to further explore the underlying physical mechanism in such a nanosystem.

Optimization of four-wave mixing wavelength conversion in a quantum-dot semiconductor optical amplifier based on the genetic algorithm

A novel approach based on the artificial neural network (ANN) and the genetic algorithm (GA) is presented for optimization of four-wave mixing (FWM) wavelength conversion in a quantum dot semiconductor optical amplifier (QD-SOA). First of all, we propose a simple, accurate, and fast model based on the feedforward ANN for the characteristics of FWM in a QD-SOA. To train the ANN, we collect the required data from a numerical model. In this model, the efficiency of FWM is obtained numerically taken into account the effect of pump/probe and the occupation probability of energy levels by using the slice technique. Then, the optimal design of QD-SOA as the FWM wavelength converter is performed using the GA.

OSNR and dispersion tolerance of FWM based optical carrier recovery scheme

In this paper we demonstrate the Optical signal-to-noise ratio (OSNR) and Dispersion characteristics of Four-Wave Mixing (FWM) based optical carrier recovery scheme for a 10-Gb/s nonreturn-to-zero binary phase-shift-keyed input. The performance was evaluated by measuring the linewidth of the recovered carrier against different OSNR and accumulated dispersion values and recording the eye diagrams. The system characterization will enable new avenues of using the FWM based carrier recovery system in phase-sensitive amplification and heterodyne detection.

Temporal coherence study of four-wave mixing products with and without the laser cavity effect.

In this work, we have studied the temporal coherence property of a four-wave mixing (FWM)-assisted continuous-wave erbium-doped fiber ring laser source. To understand the temporal coherence characteristics of FWM, we have analyzed the visibility of their interference pattern with the help of a Mach-Zehnder-based fiber interferometer. The visibility of FWM sidebands is compared with respect to the input pumps, with and without the cavity effect. The stand-alone FWM without any cavity effect has a visibility comparable to its input coherent pumps, while the FWM in the presence of the cavity effect has a poorer visibility due to the intra-cavity noise arising from the amplified spontaneous emission, which is not entirely annulled in broadband lasers. The study also confirms that the visibility/temporal coherence property of FWM sidebands does not depend on the efficiency of their generation.

Theory of pulsed four-wave mixing in one-dimensional silicon photonic crystal slab waveguides

We present a comprehensive theoretical analysis and computational study of four-wave mixing (FWM) of optical pulses co-propagating in one-dimensional silicon photonic crystal waveguides (Si-PhCWGs). Our theoretical analysis describes a very general set-up of the interacting optical pulses, namely we consider nondegenerate FWM in a configuration in which at each frequency there exists a superposition of guiding modes. We incorporate in our theoretical model all relevant linear optical effects, including waveguide loss, free-carrier (FC) dispersion and FC absorption, nonlinear optical effects such as self- and cross-phase modulation (SPM, XPM), two-photon absorption (TPA), and cross-absorption modulation (XAM), as well as the coupled dynamics of FCs and optical field. In particular, our theoretical analysis based on the coupled-mode theory provides rigorously derived formulae for linear dispersion coefficients of the guiding modes, linear coupling coefficients between these modes, as well as the nonlinear waveguide coefficients describing SPM, XPM, TPA, XAM, and FWM. In addition, our theoretical analysis and numerical simulations reveal key differences between the characteristics of FWM in the slow- and fast-light regimes, which could potentially have important implications to the design of ultra-compact active photonic devices.

Enhanced four-wave mixing in quantum cascade semiconductor optical amplifier

We designed a quantum cascade semiconductor optical amplifier (QCSOA) structure for enhanced four-wave mixing (FWM) of short optical pulses in midinfrared. To analyze FWM characteristics in a QCSOA, the evolution in the time and spectral domains of two input optical pulses with different frequencies during propagation is calculated using the finite-difference beam propagation method. Calculated third-order susceptibility responsible for FWM resonance nonlinearity of the modified structure is enhanced by two orders of magnitude. Simulation results reveal that quantum cascade structure parameters and injected pump and probe powers are extremely important in determining the amplified FWM optical pulse characteristics in both the time and frequency domains.

Efficiency of four-wave mixing of doped closely spaced energy states quantum dash semiconductor optical amplifiers

A detailed analysis of the efficiency of four-wave mixing (FWM) is performed for a closely spaced energy state quantum dash semiconductor optical amplifier (SOA). The analysis takes into account the effect of all discrete energy states, the gain dispersion of the quantum dash, and the effect of doping on the FWM characteristics. Our analysis reveals that large FWM efficiency can be obtained when the energy of the pump signal is equal to the first excited state. We find that at low-applied current doping the dashes by p -type concentration enhances the FWM efficiency. While at high applied current, we find that doping the SOA with p -type concentration slightly enhances the FWM efficiency of the ground state and the first excited state and lowers the FWM efficiency of the higher excited states. Also we find that doping the dashes by n -type concentration slightly modifies the FWM efficiency spectrum.

Analysis of ultrafast nonlinear phenomena’s influences on output optical pulses and four-wave mixing characteristics in semiconductor optical amplifiers

We have analysed the output pulse characteristics of semiconductor optical amplifier (SOA). It is shown that they can be modified due to the variation of input parameters, such as, gain, input pulsewidth, input pulse energy and effects imposed by the medium. Therefore, the influence of these parameters are analysed on the output pulse shape, spectrum, chirp and pulsewidth. We have used the nonlinear propagation equation taking into account the gain spectrum dynamics, gain saturation which depends on carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. We have used the finite-difference beam propagation method to simulate the wave evolution both in time and spectral domain in the SOA. We have also simulated the four-wave mixing characteristics between pulses for various input pulses. An accurate output pulse shape can be achieved by controlling the mentioned parameters. To the authors knowledge, pulse shaping in co-propagation regime due to medium effect and input pulse shapes in presence of all nonlinear effects relevant to picosecond regime have been studied comprehensively, for the first time in this work.

Experimental demonstration of optical switching and routing via four-wave mixing spatial shift

We demonstrate the shift characteristics of four-wave mixing (FWM) beam spots which are controlled by the strong laser fields via the large cross-Kerr nonlinearity. The shift distances and directions are determined by the nonlinear dispersions. Based on such spatial displacements of the FWM beams, as well as the probe beam, we experimentally demonstrate spatial optical switching for one beam or multiple optical beams, which can be used for all-optical switching, switching arrays and routers.

Detailed Theoretical Investigation on Enhanced Nondegenerate Four-Wave Mixing in Passive Mode-Locked Semiconductor Lasers

The passive mode-locked semiconductor laser (PMLL) can realize terahertz (THz) four-wave mixing (FWM) with high conversion efficiency and no need for pump input. Theoretical investigation on its FWM characteristics has been carried out by using the traveling wave and carrier rate equations combined with nonlinear dynamics of carrier density pulsation (CDP), carrier heating (CH), and spectral-hole burning (SHB). The stable mode-locked conjugate pulse with short-duration high-repetition frequency can be obtained by the PMLL. The pedestal-free conjugate pulse has narrower width and larger amplitude jitter compared with the pump wave. Smaller absorption recovery time is helpful to extend the stable conjugate output regime. There exists a down-limit for absorption recovery time to avoid self-pulsation (SP) instability. The larger injection current is required for smaller absorption recovery time to reach the given conversion efficiency. The larger conversion efficiency and narrower conjugate pulse can be obtained by proper design of distributed Bragg reflector (DBR) coupling strength. The DBR bandwidth must be designed to be within signal-pump detuning to avoid resonance-induced conjugate pulse distortion. The FWM in PMLL has considerable potential such as demultiplexing in optical time-division multiplexing systems.

Simple model for quantum-dot semiconductor optical amplifiers using artificial neural networks

A simple, accurate, and fast multilayer feedforward artificial neural network (ANN) model for quantum-dot semiconductor optical amplifiers (QD-SOAs) is developed. The developed ANN model has demonstrated excellent precision and accurately models the physical characteristics of QD-SOAs such as pulse amplification and four-wave mixing characteristics. Furthermore, the developed ANN model requires a very small computational time compared with numerical models, which is very attractive for computer-aided-design applications. The model is used to create very interesting design curves for QD-SOAs. In addition, the model is suitable for physical-parameter extraction from available measured data

Propagation dynamics of a temporally, amplitude- and group-velocity-matched two-mode ultraslow wave in a three-level Λ system

We investigate the propagation dynamics of a two-mode probe field traveling with ultraslow group velocities. We show that a strong cross-beam coupling occurs between the two modes of the probe wave in the presence of a two-mode control laser field that maintains two-photon resonance excitations in a three-level system. In the adiabatic limit and under appropriate conditions, both modes can travel with matched temporal profiles, amplitudes, and greatly reduced group velocities, and one mode can grow and take on features of the other mode. When only one mode of probe field is injected, the generation and growth of the second mode has the characteristics of four-wave mixing, resulting in a tunable, ultraslow four-wave mixing field with nearly 100% photon flux conversion efficiency. We further show a type of induced transparency resulting from an efficient one- and three-photon destructive interference. This is to be contrasted with the conventional one-mode, three-level electromagnetically induced transparency where the interference involves two one-photon pathways.

Characteristics of nondegenerate four-wave mixing in electroabsorption modulator

The characteristics of nondegenerate four-wave mixing (FWM) in an electroabsorption modulator are reported. The input power dependence of FWM intensity agrees well with theoretical results based on third-order nonlinearity over a wide input power range of 16dB. The detuning characteristics of FWM have a −6dB∕octave response based on the carrier-density pulsation effect. The experimental results show that a higher reverse voltage brings about a faster carrier recombination. The asymmetricity of positive and negative detuning is the reverse of that of the semiconductor optical amplifier and is explained through a rate equation simulation.

Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method

We have numerically analyzed nondegenerate four-wave mixing (FWM) among short optical pulses in a semiconductor optical amplifier (SOA) by the finite-difference beam propagation method (FD-BPM). We used the nonlinear propagation equation taking into account gain spectrum dynamic gain saturation which depends on carrier depression, carrier heating, and spectral hole-burning, group velocity dispersion, self-phase modulation, and two-photon absorption. To analyze FWM in an SOA, the evolution in time and spectral domain of two input optical pulses with different frequencies during propagation was calculated. From this simulation, it has become clear that the method me used here is a very useful technique for simulating FWM characteristics in SOA's. We also found that the wavelength dependence of the gain is crucial if the detuning is larger than 1 THz.

Characteristics of four-wave mixing in a Bose-condensed atomic gas

An analysis is made of four-wave mixing of laser radiation interacting with an ultracold degenerate ensemble of boson atoms trapped in a magnetic trap. It is shown that the existence of long-range order in this type of atomic system leads to a new mechanism for the generation of the reversed wave whose experimental manifestation should differ from four-wave mixing in a nondegenerate gas. A similar nonlinear optical effect may be used for diagnostics of an ultracold gas at temperatures not much lower than the phase transition temperature.

Noise characteristics of four-wave mixing between short pulses in semiconductor optical amplifiers

The noise characteristics of four-wave mixing between short optical pulses in semiconductor optical amplifiers are investigated, with the effects of fast gain saturation taken into account. An approximate simplified expression for the power spectral density of the amplified spontaneous emission noise under the injection of a sequence of short optical pulses is derived, in which the spatial dependence of the inversion factor is included. The dependence of the signal-to-noise ratio of the output four-wave mixing signal on the input pump and signal powers is also investigated.

Time-delay characteristics of four-wave mixing among subpicosecond optical pulses in a semiconductor optical amplifier

We have studied four-wave mixing (FWM) characteristics among subpicosecond optical pulses in a semiconductor optical amplifier for different time-delays between pump and probe beams, for the first time. Our experimental results have shown that an optimum time-delay shifted from the perfect pump-probe overlap condition with an increase in input probe beam energy. An optimum intensity of the pump beam has also been obtained to generate the maximum FWM signal.

Four-wave mixing in multispan dispersion-managed transmission links

We report the first experimental measurement of resonances in four-wave mixing (FWM) fields caused by lumped amplification in wavelength-division-multiplexed systems. Our numerical model allows us to predict the FWM characteristics in great detail. We also show that the FWM is reduced by more than 20 dB when two channels are launched with orthogonal polarizations.

Four-wave mixing characteristics in a phase-conjugated fiber system

This paper shows that four-wave mixing generation can be suppressed significantly by using an optical phase-conjugator if the group-velocity dispersion is close to zero. Otherwise the suppression of four-wave mixing generation will hardly occur.