Generation and Manipulation of Spin-Orbit Coupling mode via Four-Wave Mixing with Quantum Interference

Recently, the vectorial nonlinear optical processes driven by spin-orbit coupling (SOC) light have come to the fore, leading to striking optical phenomena and important applications both in classical and quantum optics. However, research on the SOC-mediated light-atom interactions is still in its infancy. Here, the generation and manipulation of SOC mode through a vectorial four-wave mixing (FWM) process in ⁸⁵Rb vapor is demonstrated. Under the excitation of two SOC pump beams, multiple FWM paths can be simultaneously established due to the rich atomic Zeeman sublevels coupling with different circularly polarized components of SOC fields. A higher-order cylindrical or more general SOC FWM signal is observed in the vectorial FWM process, which obeys angular momentum conservation and Gouy phase matching. In particular, quantum interference between different FWM paths plays a crucial role in manipulating the SOC mode of the generated FWM signal, revealing that the conversion of SOC mode is intrinsically quantum. This work provides a pathway toward deeper insight into the vectorial nonlinear optical processes and may advance technology for shaping spatially structured light, which is essential in applications such as nonlinear polarization imaging and the optical communication realm.     

Nontransparency and optical phase erasure characteristic of four-wave mixing

Four-wave mixing (FWM) is a well-known nonlinear optical phenomenon and has attracted great interest in nonlinear all-optical signal processing owing to its ultrafast and transparent properties. Here we report the experimental observation via spectra on the nontransparency and optical phase erasure characteristic of FWM. The distinctive feature of “optical phase erasure” is a consequence of square relationship between the converted idler and input signal. It is interesting to find that the optical phase information carried by the input signal is erased in the converted idler by exploiting FWM. Such new attribute of FWM enables optical phase information removal and all-optical format conversion from carrier-suppressed return-to-zero (CSRZ) to return-to-zero (RZ). Moreover, similar phenomena are observed in the higher-order FWM. In addition, the nontransparency phenomenon and optical phase erasure characteristic are also demonstrated by theoretical analyses with optical spectra and phase diagrams.     

Phase sensitive amplifier for PSK signals based on non-degenerate four-wave-mixing in the optical fiber

A phase-sensitive-amplifier (PSA) using only one pump channel based on frequency non-degenerate four-wave-mixing (FWM) process for phase-shift-keying (PSK) signals is proposed and demonstrated. Theoretical analyses are given first. By optimizing power levels of three channels and parameters of the highly nonlinear fiber (HNLF), the PSA is able to restore the signal fidelity (down to a BER of 10^? 9) as the input signal shows an error-floor with the BER of 10^? 6. Moreover, the PSA for the multi-level PSK signals could be achieved by adjusting the phase relationship between two input signals.     

Relative intensity noise induced by four-wave mixing in the case of two-wave transmission in an optical fiber

Four-wave mixing (FWM) is a significant nonlinear effect in wavelength division multiplexing (WDM) fiber-optic systems. For two-wave transmission, it is easily found that the FWM noise power decreases with frequency spacing and increases with signal power. However, the variation of relative intensity noise (RIN) with frequency spacing and signal power is only 2 dB at most. The intensity fluctuations induced by the energy exchange between the FWM generated new waves and the original ones are trivial and the influence of FWM on RIN can be neglected. It is also found that the increase of RIN with signal power is mainly attributed to stimulated Brillouin scattering (SBS) rather than FWM.     

Analysis of a 2R all-optical regenerator utilizing cascaded four-wave mixing in a highly nonlinear fiber

The properties of an all-optical 2R regenerator based on cascaded four-wave mixing (FWM) in a highly nonlinear fiber (HNLF) are investigated. The regeneration is based on the nonlinear cascaded FWM transfer function and a study of the system's static behavior reveals the operating conditions, under which the transfer function approaches most the ideal, step-like discrimination characteristic function. Numerical simulations for the regenerated temporal satellite wave with different signal and pump powers are investigated, and the optimal transfer function based on different fiber lengths and different injected wavelengths are also demonstrated.     

Stimulated Brillouin scattering limited intensity-dependent four-wave mixing between pump and signal in a non-zero dispersion shifted fiber

The intensity-dependent four-wave mixing (FWM) efficiency is derived by the nonlinear Schrodinger equations including the self phase modulation and cross phase modulation between the two Fabry–Perot modes of a pump and a single-wavelength signal. The maximum FWM for mixing the pump with signal in non-zero dispersion shifted fiber is explained as the minimum phase mismatch for FWM due to equal group delay for the pump and signal. It was also found that the experimental measurements for the generated FWM power are limited by the stimulated Brillouin scattering (SBS) threshold. Under the SBS threshold, the experimental results are still coincided well with the theoretical calculations of the FWM generated power ratio to have the difference of 0.12 dB for the input signal power of 12 mW.     

基于光纤四波混频效应的新型组播方法

组播是波长路由光通信网络中的一项重要功能.提出并实验实现了基于高非线性光纤四波混频效应的全光组播方法,将一束载有数据的输入信号光和一束抽运光一起入射到一段高非线性光纤中,通过两个简并四波混频过程产生了两个携带该数据信息的闲频光,从而实现了单一信号的两信道组播,同时抽运光也会受到数据信息的调制.该方法的优点在于组播的实现只需要单一的抽运光源,而不需要再提供其他输入光,结构简单,组播光信号功率均匀、波长可调,并且具有进一步增加组播信道的能力. 关键词： 组播 四波混频 高非线性光纤     

Enhancing and suppressing four‐wave mixing in electromagnetically induced transparency window

We demonstrate the enhancement and suppression of four‐wave mixing (FWM) in an electromagnetically induced transparency (EIT) window in Y‐type ⁸⁵Rb atomic system. The generated two‐photon FWM signal can be selectively enhanced and suppressed via an EIT window. The EIT of probe as well as the enhancement and suppression of FWM signals can be modified by the sequential‐cascade double dressing. The influence of different probe polarization configurations is also studied. Different polarization states of the probe laser can select different transitions among Zeeman sublevels and different dressing strengths. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis of non-linear refractive index influences on four-wave mixing conversion efficiency in semiconductor optical amplifiers

In this paper, we have analyzed the influences of non-linear refractive index on the four-wave mixing (FWM) characteristics in semiconductor optical amplifiers (SOAs). It has been shown that the generated FWM signal characteristics can be modified due to the variation of non-linear refractive index of the SOA's medium. The wave propagation in the SOA has been modeled using the nonlinear propagation equation taking into account 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. Simulation of optical wave evolution in the SOA has been carried out using the finite-difference beam propagation method (FD-BPM) both in time and spectral domains. Our simulation results confirm that higher FWM conversion efficiency and lower time bandwidth product are achieved for higher absolute values of non-linear refractive index. Moreover, non-linear refractive index is more efficacious for high power propagated waves in SOAs. Finally, we have studied the modification of waveguide refractive index due to the propagation of optical pulses. We have also shown that when |n₂|=1 cm²/TW, refractive index variation is in the order of 10^?4 to 10^?7 for high and low power input pulses, respectively.     

Four-wave mixing with large stokes shifts in heavily Ge-doped silica fibers

Four-wave mixing (FWM) in nonlinear germanosilicate fibers with GeO2 concentrations as high as 67 mol.% in the core is studied theoretically and experimentally. Large frequency shifts of 1875-3829 cm(-1) are observed in the mixed-mode pump parametric process. The dependence of FWM phase matching on the GeO2 concentration, core diameter, and index profile is demonstrated. The 2.5% conversion efficiency of an 887 nm signal to a 1.3 microm communication band is obtained at a 2 W cw pump power inside the fiber.     

基于光子晶体光纤中多抽运四波混频效应的新型光层组播技术

光层组播是未来透明光子网络中一项重要的全光信号处理功能,提出并实验证实了一种基于色散平坦高非线性光子晶体光纤中多抽运四波混频效应的光层组播方法,将一束信号光与两束连续抽运光同时输入高非线性光子晶体光纤中,通过多抽运四波混频过程,产生四个携带该数据信息的闲频光,从而实现了单一信号的四信道光层组播功能,组播信道波长在35.2 nm范围可调谐,组播信道最大间距4.4 THz,最大转换效率-22 dB,最优Q因子为5.3,该方法的特点在于基于光纤中的四波混频效应工作,因而具有对调制格式和比特率透明的 关键词： 光层组播 多抽运四波混频 光子晶体光纤     

Mid-infrared efficient generation by resonant four-wave mixing in a three-coupled-quantum-well nanostructure

We present a cascade configuration for the realization of highly efficient four-wave mixing (FWM) process in an asymmetric semiconductor three-coupled-quantum-well (TCQW) structure based on intersubband transitions (ISBTs). In the proposed TCQW scheme, the efficiency of the generated FWM mid-infrared (MIR) signal is significantly enhanced and the obtained maximum efficiency is greater than 50%. The corresponding explicit analytical expressions for the input probe and generated FWM pulsed fields are derived by use of the coupled Schrödinger-Maxwell approach and the FWM efficiency versus several variables is also discussed in details. Such a semiconductor system is much more practical than its atomic counterpart because of its flexible design and the wide adjustable parameters. This nonlinear optical process in the TCQW solid-state material can be used for efficiently generating coherent short-wavelength radiation.     

Measurement of nonlinear coefficient of a highly nonlinear fiber based on peak four-wave mixing signal generation conditions

We introduce a new measurement method of the nonlinear coefficient (NC) of a highly nonlinear fiber based on a four-wave mixing (FWM) technique. The NC along with the fiber's zero-dispersion wavelength (ZDW) was determined from the precise measurement of the pump power dependent optimum pump frequency for peak FWM signal generation conditions. The measurement errors of the NC and ZDW values determined with this method were less than 4.6% and 0.051 nm, respectively.     

The influence of higher order waveguide modes on coherent four-wave mixing in hollow fibers

Coherent four-wave mixing (FWM) of laser pulses in gas-filled hollow fibers is studied. The experimental data and the expressions derived for the amplitude of the FWM signal indicate that the excitation of higher order waveguide modes is an important physical factor having a considerable influence on nonlinear optical processes in hollow fibers.     

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.     

Polarization insensitive wavelength multicasting of DPSK signal using four-wave mixing in a birefringent photonic crystal fiber

We demonstrate polarization-insensitive wavelength multicasting of differential phase-shift keying (DPSK) signal based on four-wave mixing (FWM) in a highly nonlinear, birefringent photonic crystal fiber (PCF). The 10-Gbit/s RZ-DPSK input signal is copied to 8 wavelength channels through FWM with three optical pumps. The pump wavelengths are unequally spaced to avoid undesirable crosstalk from pump-to-pump beatings. The dependence of conversion efficiency on input signal polarization is suppressed by exploiting the PCF birefringence together with control of the pump polarizations. All pump polarizations are aligned at 45 degrees to the principal axes of the PCF. Open eyes and error-free results are obtained in all the 8 multicast channels for polarization-scrambled RZ-DPSK input signal.     

Quantum cascade structure for mid-IR four-wave mixing

The design and modeling of a quantum cascade optical amplifier (QCOA) using intra-cavity non-linear interactions to achieve wavelength conversion is proposed. The model is based on the nonlinear equation coupled with Maxwell wave equations for different emission modes. In the proposed structure, four wave mixing (FWM) output exhibits a peak as a function of pump and probe frequency if they are tuned to the energy levels of the QC structure subbands. Results demonstrate that the FWM output signal power significantly depends on how subbands are engineered and interact with optical pulses which propagate in multi layer medium. In addition, we show that by adjusting pump and probe signal frequencies, FWM output power can be tuned.     

Competition between Dispersion and Absorption of Doubly-Dressed Four-Wave Mixing and Dressed Six-Wave Mixing

We study the competition between dispersion and absorption of doubly-dressed four-wave mixing （DDFWM） and dressed six-wave mixing. In the case of weak coupling fields limit, we find DDFWM signal is affected by destructive interference between four-wave mixing（FWM） and six-wave mixing as wen as constructive interference between FWM and eight-wave mixing. By analysing the difference between two kinds of doubly dressing mechanisms （parallel cascade and nested cascade） in this opening five-level system, we can further understand the generated high-order nonlinear optical signal dressed by multi-fields.     

Coexisting four-wave mixing and six-wave mixing in three-level atomic system

We demonstrate the coexisting four-wave mixing (FWM) signal and six-wave mixing (SWM) signal which can be enhanced both by electromagnetically induced transparency (EIT) and optical pumping effect in a common three-level and open four-level inverted-Y type systems of ⁸⁵Rb. We also analyze the effect of optical pumping in different energy level systems by arranging laser beams and comparing the strength of the increased and reduced absorption caused by optical pumping.     

N5B五能级系统中重复缀饰四波混频研究

从理论上研究了N5B五能级系统中一个激光场重复缀饰四波混频过程.结合能级图分析,从它特殊的Autler-Town分裂峰中可以非常清晰地看出其重复缀饰的作用.还研究了在强Probe场和强耦合场下N5B五能级下缀饰四波混频信号的抑制增强现象.采取独特的处理方法——独立作用法,研究结果表明一个激光场作用于N5B五能级系统时存在两次缀饰,并形成缀饰能级的二重分裂或者三重分裂,不同于多个耦合场对原子的多重缀饰作用.应用于非线性光谱术中对多峰结构的研究. 关键词： 四波混频 电磁感应透明 重复缀饰