Multiple Four-wave Mixing Processes Research Articles

All-optical complex-valued convolution based on four-wave mixing

Optical complex-valued convolution can extract the feature of complex-valued data by processing both amplitude and phase information, enabling a wide range of future applications in artificial intelligence and high-speed optical computation. However, because optical signals at different wavelengths cannot interfere, optical systems based on wavelength multiplexing usually can only realize real-valued computation. Here, we experimentally demonstrate an all-optical computing scheme using Kerr-based optical four-wave mixing (FWM) that can perform complex-valued convolution of multi-wavelength signals. Specifically, this all-optical complex-valued convolution operation can be implemented based on the coherent superposition of converted light generated by multiple FWM processes. The computational throughput of this scheme can be expanded by increasing the number of optical wavelengths and the signal baud rate. To exemplify the application, we successfully applied this all-optical complex-valued convolution to four different orientations of image edge extraction. Our scheme can provide a basis for wavelength-parallel optical computing systems with the demanded complex-valued computation capability.

Intermodal-vectorial four-wave mixing processes involving LP01, LP11, LP02 and LP21 modes of birefringent fibers

We present the complete (analytical, numerical and experimental) analysis of intermodal-vectorial four-wave mixings proccesses in birefringent fibers. We analyze phase-matching condition and overlap coeffi-cients to indicate possible processes. Then, we demonstrate multiple four-wave mixing processes in LP01 and LP11 modes numerically and experimentally. Finally, we extend theoretical analysis to account higher-order modes: LP02 and LP21.

Multimode quantum squeezing generation via multiple four-wave mixing processes within a single atomic vapor cell

Multimode quantum squeezing plays an essential role in the fields of quantum metrology and quantum information. In this paper, we first construct a three- and four-mode energy-level cascaded four-wave mixing system in a single 85 R b vapor, and then analyze the quantum properties of the produced states, including the covariance matrix and the intensity squeezing with 11 possible Hamiltonians. In addition, the dressing field is applied to modulate the nonlinear susceptibility and the multimode quantum states. Our scheme allows active modulation of the quantum states integrated within the generation step, without the need for any post-operation of the optics. The mode number of the states also can be extended using more pump fields and the dressing effect. Our study provides a promising candidate to generate multimode quantum states and multimode quantum squeezing within a quantum device involved in the construction of practical quantum networks.

All-optical phase-preserving amplitude-regeneration technology based on bidirectional orthogonal-pumped semiconductor optical amplifier configuration

The phase-preserving amplitude regeneration scheme based on the bidirectional orthogonal-pumped semiconductor optical amplifier (SOA) is proposed in this work. Experimental investigation into the multiple four-wave mixing (FWM) process from the pump, the signal and their corresponding reflective fields is carried out in detail. The regeneration performance obtained from the product between co-propagating fields is also discussed, including its dependence on the signal launch power and the signal quality, to quantify the amplitude regeneration and the phase preserving behaviors. The amplitude distortion is suppressed by 2.2 dB experimentally, confirming the regeneration capability of the proposed scheme. Moreover, the regeneration performance is further investigated for multiple phase shift keying (MPSK) signals through the simulation. According to the numerical results, the operational parameters of the regenerator are the same for advanced modulation formats, proving the robust operation of the proposed bidirectional orthogonal-pumped SOA configuration.

Investigation of the noise figure in a degenerate dual-pump phase-sensitive amplifier using a multi-wave model

A semi-classical seven-wave model is developed to investigate the noise performances of a degenerate dual-pump phase-sensitive amplifier. This approach takes into account the transfer to the signal, through multiple four-wave mixing processes, of the vacuum fluctuations injected into high-order waves. This effect leads to a degradation of the noise figure of the amplifier with respect to the 0 dB value predicted by the usual three-wave model. However, it is proved that a careful choice of the fiber dispersion allows us to use high-order waves to enhance the signal gain without degrading the noise figure above 1 dB.

Spatially multiplexed picosecond pulse-train generations through simultaneous intra-modal four wave mixing and inter-modal cross-phase modulation

We report on the experimental generation of spatially multiplexed picosecond 40 GHz pulse trains at telecommunication wavelengths by simultaneous intra-modal multiple four wave mixing and inter-modal cross-phase modulation in km-long bi-modal and 6-LP-mode graded-index few-mode fibers. More precisely, an initial beat-signal injected into the fundamental mode is first nonlinearly compressed into well-separated pulses by means of an intra-modal multiple four-wave mixing process, while several group-velocity matched continuous-wave probe signals are injected into higher-order modes in such a way to develop similar pulsed profile thanks to an inter-modal cross-phase modulation interaction. Specifically, by simultaneously exciting three higher-order modes (LP11, LP02 and LP31) of a 6-LP-mode fiber along group-velocity matched wavelengths with the fundamental mode, four spatially multiplexed 40 GHz picosecond pulse-trains are generated at selective wavelengths with negligible cross-talks between all the modes.

Observation of giant gain and coupled parametric oscillations between four optical channels in cascaded four-wave mixing

In this work, we explore both the internal and external atomic degrees of freedom to demonstrate the observation of giant gain and parametric oscillation in multiple four-wave mixing (FWM) processes in a sample of cold cesium atoms. We employ a standard backward FWM beam configuration to achieve parametric probe-beam gains exceeding 2000. This giant gain is accompanied by the generation of three other beams of equivalent power emitted along the directions satisfying the phase-matching conditions for multiple cascade forward and backward FWM triggered by the incident probe and the counterpropagating pumping beams. Moreover, we have also observed a simultaneous threshold for parametric oscillation of the four coupled optical fields with the pump intensity. These results point to an alternative pathway to generate multipartite correlated optical fields associated with long-lived atomic systems for applications in quantum information.

Influence of multiple four-wave-mixing processes on quantum noise of dual-pump phase-sensitive amplification in a fiber

Phase-sensitive amplification (PSA) based on nonlinear parametric interaction provides low-noise amplification such that the noise figure can be 0 dB in principle. However, when an optical fiber is used as a nonlinear medium for PSA, multiple four-wave-mixing (FWM) processes other than the PSA process are induced, which can degrade the PSA noise performance, especially in dual-pump PSA with a narrow signal-pump wavelength separation. This paper investigates the influence of multiple FWM processes on quantum noise of dual-pump PSA in an optical fiber. The noise figure is calculated using quantum-mechanical operators, considering multiple FWM processes with the PSA process. Calculation examples are also presented, which indicate that the noise figure is degraded by 0.2–0.4 dB from the ideal 0 dB, depending on the signal-pump wavelength separation and fiber parameters.

Multi-wavelength fiber laser generated by Brillouin-comb assisted four-wave mixing

In this work, we demonstrate a wide-spectrum multi-wavelength fiber laser generated by Brillouin-comb assisted four-wave mixing (FWM). The mechanism of the laser is based on the combination of stimulated Brillouin scattering in cavity and multiple FWM process outside cavity. The experiment results demonstrate that Brillouin-comb assisting is an effective method to improve the FWM process and increase the line number. More than 110 lines are achieved in 10 nm spectral range with the wavelength spacing of ∼0.09 nm. The multi-wavelength fiber laser exhibits good stability on both the operating wavelengths and output power. The tunability of this multi-wavelength fiber laser is improved significantly by inserting a tunable filter in the cavity. The total line number is kept more than 110 in the whole tunable range of 30 nm from 1540 to 1570 nm.

Spectral broadening in narrow linewidth, continuous-wave high power fiber amplifiers

We present an investigation on the spectrum broadening in continuous-wave, sub-nanometer linewidth high power fiber amplifiers caused by the multiple four-wave mixing (FWM) process. The spectrum broadening employing two different types of narrow linewidth seeds, including the multi-longitudinal-mode seed and the broadened single frequency seed generated by high speed phase modulation, is studied. It is shown both theoretically and experimentally that the multi-longitudinal-mode seed experiences serious spectrum broadening induced by the FWM among various longitudinal modes, while the modulated seed can maintain the spectrum profile during the amplifying process even with some noise fluctuation. The different broadening results are mainly caused by the random phase distribution of the multiple waves. It is further explained by an exact solution of the degenerate FWM with three waves. The theoretical predictions on the spectrum and power dependence of the output laser linewidth are in quantitative agreement with the experimental results up to kilowatt.

Experimental generation of quadruple quantum-correlated beams from hot rubidium vapor by cascaded four-wave mixing using spatial multiplexing

Multimode quantum states, such as multipartite quantum entanglement or quantum correlations, are important for both fundamental science and the future development of quantum technologies. Here we theoretically propose and experimentally realize a scheme that can fully exploit the multi-spatial-mode nature of the four-wave-mixing (FWM) process, i.e., spatial multiplexing, and thus integrates multiple FWM processes into a single cell at each stage of the cascaded process. The number of generated quantum-correlated beams ${2}^{n}$ is exponentially dependent on the number of vapor cells $n$. In addition, the quantum correlations between the multiple beams also increase as the number of vapor cell increases. For the case of $n=2$, we experimentally show that the degree of intensity-difference squeezing between the four quantum-correlated beams in our scheme is enhanced to $\ensuremath{-}8.2\ifmmode\pm\else\textpm\fi{}0.2$ dB from $\ensuremath{-}5.6\ifmmode\pm\else\textpm\fi{}0.3$ and $\ensuremath{-}6.5\ifmmode\pm\else\textpm\fi{}0.2$ dB of squeezing obtained with a single FWM process. Our system may find applications in quantum information and precision measurement.

Multiple four-wave mixing and Kerr combs in a bichromatically pumped nonlinear fiber ring cavity.

We report numerical and experimental studies of multiple four-wave mixing processes emerging from dual-frequency pumping of a passive nonlinear fiber ring cavity. We observe the formation of a periodic train of nearly background-free soliton pulses associated with Kerr frequency combs. The generation of resonant dispersive waves is also reported.

Characterization of a FM actively mode-locked fiber optical parametric oscillator

The characteristics of a frequency-modulated (FM) actively mode-locked fiber optical parametric oscillator have been demonstrated experimentally. In particular, the effects of pump power and modulation frequency on the features of the generated pulses (e.g., output power, RMS timing jitter, pulse width, and time-bandwidth product) are analyzed. Moreover, a stable pulse train of 37 ps with a RMS timing jitter of around 2.51 ps and a repetition rate of 10 GHz are generated. The results show that pulse trains with narrow pulse width and low RMS timing jitter are achievable when the modulation frequency increases. The corresponding time-bandwidth products at different pump powers are 0.61–0.66. In addition, stable optical pulses at 1567.38, 1551.92, 1544.29, and 1536.73 nm are generated simultaneously based on multiple four-wave mixing processes.

Output characterization of a fiber optic parametric oscillator based on multiple four-wave mixing.

The output characteristics of a fiber optic parametric oscillator (FOPO) based on multiple four-wave mixing (multi-FWM) processes are investigated numerically and demonstrated experimentally. The theoretical model of a FOPO based on multi-FWM processes is presented. It is proved that the output signal starts to saturate when the high-order parametric products are generated in the multi-FWM processes of FOPOs. Moreover, a higher output power of the idler (i.e., the first-order parametric product) is achieved. On the other hand, the pump power is proved to be a key factor that significantly influences the output of the FOPO.

Quantum optical devices based on four-wave mixing in hot rubidium vapor

In this paper, we briefly review the recent experimental progresses in quantum optics based on four-wave mixing (FWM) processes in hot rubidium vapor, particularly our two recent experiments in quantum information. We have experimentally produced strong quantum correlations between three bright beams generated by two cascaded FWM processes. The intensity difference squeezing with the cascaded system is enhanced to (-7.0±0.1)dB from the (-5.5±0.1)dB/(-4.5±0.1)dB with only one FWM process. Also, this system can be easily extended to multiple modes using multiple FWM processes. Besides, we have also successfully realized a cascade all-optical transistor (AOT), which is driven by a very weak light beam about 800 photons in total. The required probe power for achieving a switching efficiency of 50% can be as low as 180 pW, and it can manipulate a light beam with power of 5.0×106 times more, which proves the cascade of the AOT. Both experiments may find wide applications in quantum information and optical communication.

Dynamic characteristics of a multi-wavelength Brillouin–Raman fiber laser assisted by multiple four-wave mixing processes in a ring cavity

Dynamic characteristics of a multi-wavelength Brillouin–Raman fiber laser (MBRFL) assisted by four-wave mixing have been investigated through the development of Stokes and anti-Stokes lines under different combinations of Brillouin and Raman pump power levels and different Raman pumping schemes in a ring cavity. For a Stokes line of order higher than three, the threshold power was less than the saturation power of its last-order Stokes line. By increasing the Brillouin pump power, the nth order anti-Stokes and the (n+4)th order Stokes power levels were unexpectedly increased almost the same before the Stokes line threshold power. It was also found out that the SBS threshold reduction (SBSTR) depended linearly on the gain factor for the 1st and 2nd Stokes lines, as the first set. This relation for the 3rd and 4th Stokes lines as the second set, however, was almost linear with the same slope before SBSTR −6 dB, then, it approached to the linear relation in the first set when the gain factor was increased to 50 dB. Therefore, the threshold power levels of Stokes lines for a given Raman gain can be readily estimated only by knowing the threshold power levels in which there is no Raman amplification.

Implications of Raman scattering and phase noise on multiple four-wave mixing processes in an optical fiber.

Implications of spontaneous and stimulated Raman scattering (SSRS) and phase noise on the spatial evolution of multiple-order sidebands arising from four-wave mixing (FWM) along the length of an optical fiber are investigated. A modified split-step Fourier method is used to solve the governing coupled nonlinear Schrödinger equations. The phase noise overcomes the depletive nature of SSRS and stabilizes the FWM sidebands, in good agreement with experimental results.

Experimental generation of multiple quantum correlated beams from hot rubidium vapor.

Quantum correlations and entanglement shared among multiple quantum modes are important for both fundamental science and the future development of quantum technologies. This development will also require an efficient quantum interface between multimode quantum light sources and atomic ensembles, which makes it necessary to implement multimode quantum light sources that match the atomic transitions. Here, we report on such a source that provides a method for generating quantum correlated beams that can be extended to a large number of modes by using multiple four-wave mixing (FWM) processes in hot rubidium vapor. Experimentally, we show that two cascaded FWM processes produce strong quantum correlations between three bright beams but not between any two of them. In addition, the intensity-difference squeezing is enhanced with the cascaded system to -7.0±0.1 dB from the -5.5±0.1/-4.5±0.1 dB squeezing obtained with only one FWM process. One of the main advantages of our system is that as the number of quantum modes increases, so does the total degree of quantum correlations. The proposed method is also immune to phase instabilities due to its phase insensitive nature, can easily be extended to multiple modes, and has potential applications in the production of multiple quantum correlated images.

Reconfigurable linear combination of phase-and-amplitude coded optical signals

We introduce an all-optical arithmetic unit operating a weighted addition and subtraction between multiple phase-and-amplitude coded signals. The scheme corresponds to calculating the field dot-product of frequency channels with a static vector of coefficients. The system is reconfigurable and format transparent. It is based on Fourier-domain processing and multiple simultaneous four-wave mixing processes inside a single nonlinear element. We demonstrate the device with up to three channels at 40 Gb/s and evaluate its efficiency by measuring the bit-error-rate of a distortion compensation operation between two signals.

All-optical hash code generation and verification for low latency communications

We introduce an all-optical, format transparent hash code generator and a hash comparator for data packets verification with low latency at high baudrate. The device is reconfigurable and able to generate hash codes based on arbitrary functions and perform the comparison directly in the optical domain. Hash codes are calculated with custom interferometric circuits implemented with a Fourier domain optical processor. A novel nonlinear scheme featuring multiple four-wave mixing processes in a single waveguide is implemented for simultaneous phase and amplitude comparison of the hash codes before and after transmission. We demonstrate the technique with single polarisation BPSK and QPSK signals up to a data rate of 80 Gb/s.