Four-wave Mixing Process Research Articles

Roles of fiber birefringence and Raman scattering in the spontaneous four-wave mixing process through birefringent fibers.

We investigate the impact of fiber birefringence and spontaneous Raman scattering on the properties of photon pairs that are generated by the spontaneous four-wave mixing process in birefringent fibers. Starting from the formulation of the theory of four-wave mixing, we show a theoretical model for a generated optical field with the consideration of the Raman scattering and a Gaussian-distributed pump. The theoretical model is then applied for deriving the closed expressions of the photon-pair spectral properties as a function of the fiber birefringence. Also, with the modeled Raman gain, we evaluate the reduction of the pair production rate due to the presence of the Raman effect as well as the contributions of the Raman-scattered photons over a broad wavelength range. The predictions are experimentally verified with a commercial polarization-maintaining fiber.

Fiber source of femtosecond pulses at 910–940 nm based on a Mamyshev pulse oscillator and wavelength conversion in a photonic crystal fiber

In this work, we present a fiber-based setup for femtosecond pulse generation at ∼ 910 − 940 n m wavelength. Pump pulses from a Mamyshev oscillator with center wavelength at 1036 nm 1 ps duration are amplified and coupled into a photonic crystal fiber forming a soliton at 1051 nm. Due to the nonlinear four-wave mixing process, soliton pulses are converted to 910–940 nm with a few hundred femtosecond pulses with energy up to 0.7 nJ. The proposed design utilizes features of the Mamyshev oscillator, enabling a robust way of generating femtosecond pulses at ∼ 910 − 940 n m .

Frequency and polarization emission properties of a photon-pair source based on a photonic crystal fiber

In this work, we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom.

Narrowband and broadband single-photon sources using custom-tapered waveguides

In this paper, we present a thorough investigation for a spontaneous parametric four-wave mixing process in third-order nonlinear waveguides with various continuous tapering patterns. It has been previously shown that these devices can quasi-phase-match the four-wave mixing process and enhance its conversion efficiency by orders of magnitude. By altering the tapering profile curve we found that these devices can enable single-photon sources with either narrow or broadband spectral widths at on-demand frequencies. Using our model, we were also able to identify the waveguide length at which the single-photon spectral purity is maximized.

Optical Frequency Combs Generated in Silica Microspheres in the Telecommunication C-, U-, and E-Bands

Optical frequency combs (OFCs) generated in microresonators with whispering gallery modes are demanded for different applications including telecommunications. Extending operating spectral ranges is an important problem for wavelength-division multiplexing systems based on microresonators. We demonstrate experimentally three spectrally separated OFCs in the C-, U-, and E-bands in silica microspheres which, in principle, can be used for telecommunication applications. For qualitative explanation of the OFC generation in the sidebands, we calculated gain coefficients and gain bandwidths for degenerate four-wave mixing (FWM) processes. We also attained a regime when the pump frequency was in the normal dispersion range and only two OFCs were generated. The first OFC was near the pump frequency and the second Raman-assisted OFC with a soliton-like spectrum was in the U-band. Numerical simulation based on the Lugiato–Lefever equation was performed to support this result and demonstrate that the Raman-assisted OFC may be a soliton.

Collimated ultraviolet light generated by four-wave mixing process in Cs vapor

Collimated ultraviolet (UV) light is generated via four-wave mixing (FWM) in cesium vapor by continuously tuning the wavelength of the pump laser. Terahertz (THz) Stokes light is generated by the stimulated Raman scattering (SRS) effect in the FWM process, and its frequency is adjustable. When exciting the cesium atom to a virtual level using different combinations of pump lasers (P1 and P2), the strength distribution of UV light is asymmetric, which can be explained through a phase-matching mechanism. Furthermore, the SRS effect and phase matching influence the FWM.

Orbital Angular Momentum Multiplexed Quantum Dense Coding.

To beat the channel capacity limit of conventional quantum dense coding (QDC) with fixed quantum resources, we experimentally implement the orbital angular momentum (OAM) multiplexed QDC (MQDC) in a continuous variable system based on a four-wave mixing process. First, we experimentally demonstrate that the Einstein-Podolsky-Rosen entanglement source coded on OAM modes can be used in a single channel to realize the QDC scheme. Then, we implement the OAM MQDC scheme by using the Einstein-Podolsky-Rosen entanglement source coded on OAM superposition modes. In the end, we make an explicit comparison of channel capacities for four different schemes and find that the channel capacity of the OAM MQDC scheme is substantially enhanced compared to the conventional QDC scheme without multiplexing. The channel capacity of our OAM MQDC scheme can be further improved by increasing the squeezing parameter and the number of multiplexed OAM modes in the channel. Our results open an avenue to construct high-capacity quantum communication networks.

Interference between atomic Rb (5d 5/2–5p 3/2) and (5p 3/2–5s 1/2) coherences: observation of an exceptional point by quantum beating at ∼2.1 THz

Coupled oscillators are prevalent in nature and fundamental to fields as disparate as astrophysics, photonics, the mechanical sciences, and geophysics. Theory has identified singularities in the response of coupled oscillators, known as exceptional points (EPs), that are associated with non-Hermitian operators and lie at the transition between weak and strong coupling of the oscillator. Although several EPs have been reported or predicted to exist in nanophotonic resonators and Feshbach resonances, for example, tuning the phase of two interfering atomic or molecular coherences near an EP has not been demonstrated previously. We report the observation of an EP associated with a pair of interfering atomic coherences in Rb, oscillating at 386.3 and 384.2 THz, and confirm the theoretical prediction of an abrupt phase shift of ∼π/4 as the EP is traversed by independently varying two experimental parameters. Pairs (and trios) of coupled coherences in thermal Rb atoms are established among the 7s 1/2, 5d 5/2, 5p 3/2, and 5s 1/2 states in pump–probe experiments with <200 fs laser pulses, and observed directly in the temporal and spectral domains through the ensuing quantum beating in the ∼2–36 THz interval. Interference between the (5d 5/2–5p 3/2) and (5p 3/2–5s 1/2) coherences is mediated by the 5p 3/2 state and detected through quantum beating in the vicinity of the (5d 5/2–5p 3/2)–(5p 3/2–5s 1/2) difference frequency of 2.11 THz which is monitored by a parametric four-wave mixing process. Phase of this composite atomic oscillator is first controlled by varying the mean Rb–Rb nearest neighbor distance (⟨R⟩) in a thermalized vapor. A discontinuous transition of (0.8 ± 0.2) ∼ π/4 radians in the phase of the coupled oscillator occurs when ⟨R⟩ is varied over the ∼80–90 nm interval, a phase shift associated with the transformation of a broadband, dissipative oscillator (characterized by a Fano interference window) into a strongly-coupled system resonant at 2.1 THz.

Robust Optical Frequency Comb Generation by Using a Three-Stage Optical Nonlinear Dynamic

In this article, we propose and investigate a novel scheme to generate optical frequency combs (OFCs) by using a three-stage generator, which is based on optical injection–induced dynamics cascaded by subharmonic electro-optic modulation and the four-wave mixing (FWM) effect. A primary seed OFC is rooted from the nonlinear dynamics in the optically injected semiconductor laser, and its performance is improved using a two-stage booster based on subharmonic electro-optic modulation and the FWM effect. The comb spacing can be easily tuned by adjusting that of the primary seed OFC or through electro-optic modulation by the use of subharmonics with different orders. Moreover, it becomes stabilized because the phase relationship between the comb teeth can be fixed in the process of subharmonic electro-optic modulation. Its optical spectrum continues to be broadened in the following FWM process. Finally, robust OFCs with a comb spacing of 4 GHz and a comb teeth number of 23 and a comb spacing of 5 GHz and a comb teeth number of 21 are experimentally demonstrated.

Optical nonreciprocity using four-wave mixing in hot atoms

Nonreciprocal optical devices are important in wide areas, ranging from optical telecommunications to signal processing. Here, we experimentally realize the magnet-free and cavity-free optical nonreciprocity based on phase-matched four-wave mixing (FWM) in hot atoms. Specifically, the isolation of more than 20 dB and insertion loss less than 1 dB without using any optical cavity can be achieved simultaneously. Our results provide general insights into a broad class of parametrically modulated nonreciprocal behavior, paving the way toward optimal nonreciprocal devices based on the nonlinear FWM process.

Intramolecular Vibration Energy-Transfer-Driven Cascaded Stimulated Raman Scattering and Four-Wave Mixing in Benzene Series.

Cascaded stimulated Raman scattering (SRS) of benzene, bromobenzene, chlorobenzene, ethylbenzene, and toluene was investigated by a pulsed Nd:YAG laser with 532 nm wavelength. The results showed that the third-order Stokes SRS of the ring skeleton vibration (CC at 3006 cm-1) accompanied by another higher-frequency Stokes SRS of the CH stretching vibration (at 3066 cm-1), which arose only when the third-order Stokes SRS of the ring skeleton was produced, can be attributed to the vibration energy transfer between vibration energy levels of CC and CH. The Stokes and anti-Stokes SRS rings, which originated from the intramolecular energy-transfer-enhanced four-wave mixing (FWM) processes, can be observed only in the forward direction along different angles apart from the pump beam direction. The phenomenon also existed in other derivatives of benzene. We propose the intramolecular energy-transfer-enhanced SRS for the first time, which can be used for a broadband Raman laser.

On-chip non-Hermitian optical parametric amplifiers with a large bandwidth

Recently, our groups have introduced the notion of optical parametric amplification based on non-Hermitian phase matching wherein the incorporation of loss can lead to gain in this nonlinear optical process. Previous simulation results using second-order nonlinear optical coupled-mode theory have demonstrated the potential of this technique as an alternative to the stringent phase-matching condition, which is often difficult to achieve in semiconductor platforms. Here we fortify this notion for the case of third-order nonlinearity by considering parametric amplification in silicon nanowires and illustrate the feasibility of these devices by employing rigorous finite-difference time-domain analysis using realistic materials and geometric parameters. Particularly, we demonstrate that by systematic control of the optical loss of the idler in a four-wave mixing process, we can achieve efficient unidirectional energy conversion from the pump to the signal component even when the typical phase-matching condition is violated. Importantly, our simulations show that a signal gain of ∼ 9 d B for a waveguide length of a few millimeters is possible over a large bandwidth of several hundreds of nanometers ( ∼ 600 n m ). This bandwidth is nearly 2 orders of magnitude larger than what can be achieved in the conventional silicon-photonics-based four-wave mixing process.

Experimental realization of wavelength multiplexed nonlinear upconversion in cesium atoms.

Blue-violet wavelength multiplexing offers the capability to enhance the operational capacity and efficiency in optical information processing, underwater communications, biology, and medicine. Here we present a specially designed atomic scheme of cesium for simultaneously generating two blue-violet lasers at 456 and 459 nm via four-wave-mixing (FWM)-based upconversion processes. We experimentally and theoretically show that a double-diamond-type coherent system pumped with 852 and 921 nm lasers is responsible for the efficient generation of the two blue-violet lasers. In this system, the large population inversions lead to self-amplified spontaneous emissions at 15.6 and 12.1µm, which, in turn, serve as the seeds for enhanced double FWM processes with dual-wavelength upconversions.

Interconversion of orbital and spin angular momenta of light beams in the CARS generation process in isotropic gyrotropic medium

We investigate the conversion of spin and orbital angular momentum (AM) of elliptically polarized light beams at frequencies ω 1 and ω 2, helical phase profiles, and arbitrary radial intensity distributions to AM of a signal beam at frequency resulting from four-wave mixing process in isotropic gyrotropic medium with spatial dispersion of cubic nonlinearity. Conservation of the total z-projections of both spin and orbital angular momenta of interacting waves is demonstrated. A simple classical and quantum interpretation of validity of the AM conservation law is given.

Two-dimensional pattern recognition methods for rapidly recording and interpreting high resolution coherent three-dimensional spectra.

High resolution coherent multidimensional spectroscopy has the ability to reduce congestion and automatically sort peaks by species and quantum numbers, even for simple mixtures and molecules that are extensively perturbed. The two-dimensional version is relatively simple to carry out, and the results are easy to interpret, but its ability to deal with severe spectral congestion is limited. Three-dimensional spectroscopy is considerably more complicated and time-consuming than two-dimensional spectroscopy, but it provides the spectral resolution needed for more challenging systems. This paper describes how to design high resolution coherent 3D spectroscopy experiments so that a small number of strategically positioned 2D scans may be used instead of recording all the data required for a 3D plot. This faster and simpler approach uses new pattern recognition methods to interpret the results. Key factors that affect the resulting patterns include the scanning strategy and the four wave mixing process. Optimum four wave mixing (FWM) processes and scanning strategies have been identified, and methods for identifying the FWM process from the observed patterns have been developed. Experiments based on nonparametric FWM processes provide significant pattern recognition and efficiency advantages over those based on parametric processes. Alternative scanning strategies that use synchronous scanning and asynchronous scanning to create new kinds of patterns have also been identified. Rotating the resulting patterns in 3D space leads to an insight into similarities in the patterns produced by different FWM processes.

Two-beam coupling in the production of quantum correlated images by four-wave mixing.

We investigate the effect of 2-beam coupling in different imaging geometries in generating intensity-difference squeezing from four-wave mixing (4WM) in Rb atomic vapors. A recently-introduced dual-seeding technique can cancel out the classical noise in a seeded four-wave mixing process. This dual-seeding technique, however, can introduce new complications that involve 2-beam coupling between different seeded spatial modes in the atomic vapor and can ruin squeezing at frequencies on the order of the atomic linewidth and below. This complicates some forms of quantum imaging using these systems. Here we show that seeding the 4WM process with skew rays can eliminate the excess noise caused by 2-beam coupling. To avoid 2-beam coupling in bright, seeded images, it is important to re-image the object in the gain medium, instead of focussing through it.

Manipulation of the asymmetric Einstein–Podolsky–Rosen steering via coherent population transfer

We investigate the Einstein–Podolsky–Rosen (EPR) steering of two cavity modes generated via four-wave mixing processes. For a three-level V-type configuration, a strong coherent field as a dressing field couples the atoms, and a weak coherent field as a control filed resonantly couples one dressed state to the auxiliary state. By using the approach of dressed states and Bogoliubov modes, we find that only one Bogoliubov mode is mediated into the interaction with the dressed atoms, and the other one is decoupled. Due to the presence of the coherent control filed, the channel for dressed state population transfer is established, which plays a key role in the generation of the asymmetric EPR steering of two cavity fields. It is shown that the one-way EPR steering can be manipulated by the Rabi frequencies of the control field and the cooperativity parameters.

Far-detuned mid-IR wavelength conversion at 4.05 µm in a tellurium oxide rib waveguide pumped at 1550 nm: Design and analysis

We report the design and numerical analysis of a tellurium oxide rib waveguide pumped with femtosecond laser pulses at 1550 nm for near and mid-infrared wavelength conversion at 0.96 and 4.05 µm, respectively. The wavelength conversion principle is based on the degenerate four-wave mixing in the designed tellurium oxide rib waveguide device. The corresponding detuning in the frequencies is as large as ∼120 THz at both sides of the pump frequency. This is the largest detuning of the frequencies obtained using a TeO2 rib waveguide via a four-wave mixing process to the best of our knowledge. Such waveguide-based light sources are required for various potential applications, including chemical sensing, absorption spectroscopy, and generation of quantum correlated photons on future nonlinear photonic integrated circuits.

Distributed static and dynamic detection of an acoustic wave in a Brillouin random fiber laser

The interaction of random laser and gain medium is important to understand the noise origin in random fiber lasers. Here, using the optical time domain reflectometry method, the time-resolved distributed acoustic wave generated by a Brillouin random fiber laser (BRFL) is characterized. The dynamic property of the acoustic wave reflects the gain dynamics of the BRFL. The principle is based on the polarization-decoupled stimulated Brillouin scattering (SBS)-enhanced four-wave mixing process, where the probe light experiences maximum reflection when the phase match condition is satisfied. Static measurements present exponentially depleted Brillouin gain along the gain medium in the BRFL, indicating the localized random SBS frequency change in the maximum local gain region, which varies with time to contribute random laser noise as revealed in the dynamic measurement. The SBS-induced birefringence change in the Brillouin gain fiber is approximately 10 − 7 to 10 − 6 . The phase noise of the BRFL is observed directly inside the random laser gain medium for the first time via time and spatially varied acoustic wave intensity. By counting the temporal intensity statistical distribution, optical rogue waves are detected near the lasing threshold of the BRFL. Different temporal intensity statistical distribution at high and low gain positions is found, which is caused by the SBS nonlinear transfer function and localized gain. The distributed characterization methods in the paper provide a new platform to study the interaction of random lasers and gain medium, giving us a new perspective to understand the fundamental physics of the random lasing process and its noise property.

Coherent near-infrared light generation based on self-seeded parametric four-wave mixing in Rb vapor

We demonstrate 1.37 µm coherent near-infrared light generation via self-seeded parametric four-wave mixing (FWM) process in Rb atomic vapor. Two lasers (780 nm and 776 nm) in the co-propagating configuration, drive the Rb atoms from the 5S1/2 ground state to the 5D5/2 excited state. The parametric FWM around the 5P3/2–5D5/2–6P3/2–6S1/2–5P3/2 transition loop is effectively established under phase matching conditions. The generated coherent light wavelength is confirmed using an optical spectrum analyzer, and the output power is investigated with the input laser frequency, power and atomic density. Consequently, a 1.37 µm coherent light with the power of 27 µW and the beam quality of = 1.22 and = 1.25 is obtained. An additional 795 nm laser is introduced to enhance the output power by 1.5 times through velocity-selective optical hyperfine repumping.