Four-wave Mixing Process Research Articles

Topological protection of dual-polarization biphoton states in photonic crystals

Polarization control is a major issue in topological quantum optics that limits reliable generation and transmission of quantum states. This study presents what we believe to be a novel topological photonic crystal design that provides topological protection for biphoton pairs for both TE and TM polarization. By well-designed cell configurations within the lattice, two topological boundaries emerge that can accommodate TM and TE modes at the same time. By adjusting the dispersion curves, we can further design nonlinear four-wave mixing processes within the topological photonic crystals and provide theoretical explanations for the entanglement of the dual-polarization biphoton states. Numerical results confirm the robust transport of entangled photon pairs, even when subjected to sharp bending. Moreover, combining the dual-polarization topological photonic crystal with a polarization beam splitter enables the preparation of polarization-encoded maximally entangled states. Our work exhibits significant potential for applications in robust optical quantum information processing and quantum secure communication.

Experimental demonstration of complex four-wave mixing processes with pump of orbital-angular-momentum superposition mode

Orbital angular momentum (OAM), characterized by a topological charge ℓ (ℓ integer), serves as a promising vehicle for carrying quantum information. Generating a nonclassical field involving two or more OAM modes can largely enhance the data-carrying capacity of quantum information processing. In this Letter, we present the implementation of a four-wave mixing (FWM) process, featuring a pump beam of a coherent OAM superposition mode and a probe beam of a single OAM mode. We generate twin beams encompassing multiple OAM modes and illustrate their quantum correlation when the pump beam assumes different coherent OAM superposition modes. Furthermore, we analyze the OAM mode components in each output field to deepen our understanding of the nonlinear interaction among different OAM modes. The obtained results show the rich structure of the nonlinear interaction of OAM modes in the FWM process and provide a perspective to study quantum information protocols.

Optical reciprocity-nonreciprocity-amplification conversion based on degenerate four-wave mixing

Optical nonreciprocity plays an important role in optical communication and quantum networks. In this research, we propose and demonstrate a conversion scheme of magnetic-free dual-channel optical reciprocal amplification (RA) and nonreciprocal amplification (NRA) based on the multiple degenerate four-wave mixing (FWM) process in hot atoms. In our experiment, the dual-channel NRA works with the action of a single pump field based on the establishment of FWM in the same direction and breaking in the opposite direction. Based on stable ground-state Zeeman coherence, by introducing a counter-propagating pump field again, NRA can be changed to RA in the opposite direction of the two original amplified conjugate signals. Moreover, the frequencies of RA signals are very dependent on those of co-propagating pump fields. The experimental realization of NRA-RA conversion may have applications for multichannel angular momentum spatial multiplexing and quantum gate manipulation.

Fully integrated and broadband Si-rich silicon nitride wavelength converter based on Bragg scattering intermodal four-wave mixing

Intermodal four-wave mixing (FWM) processes have recently attracted significant interest for all-optical signal processing applications thanks to the possibility to control the propagation properties of waves exciting distinct spatial modes of the same waveguide. This allows, in principle, to place signals in different spectral regions and satisfy the phase matching condition over considerably larger bandwidths compared to intramodal processes. However, the demonstrations reported so far have shown a limited bandwidth and suffered from the lack of on-chip components designed for broadband manipulation of different modes. We demonstrate here a silicon-rich silicon nitride wavelength converter based on Bragg scattering intermodal FWM, which integrates mode conversion, multiplexing and de-multiplexing functionalities on-chip. The system enables wavelength conversion between pump waves and a signal located in different telecommunication bands (separated by 60 nm) with a 3 dB bandwidth exceeding 70 nm, which represents, to our knowledge, the widest bandwidth ever achieved in an intermodal FWM-based system.

Theory of four wave mixing-based parametric amplification of spin-orbit modes.

We study the generation of spin-orbit (SO) modes via four-wave mixing (FWM)-based parametric amplification. SO modes carry quantized total angular momentum (TAM), and we show that FWM processes that generate new signals conserve TAM. This is a generalization of prior research which operated in a regime where FWM processes conserved spin and orbital angular momenta independently. We calculate the growth rates of new modes for both degenerate and nondegenerate pump configurations. Our theory is validated against numerical simulations for the cases where the generated signals are in the same SO mode(s) as the pump(s). We also calculate the growth rates of signals in SO modes other than the pumps.

Polychromatic and collimated lights generated by nondegenerate four-wave mixing in cesium vapor.

We demonstrate the generation of polychromatic and collimated lights at 456 nm, 459 nm, and 761 nm based on cesium (133Cs) 6S1/2 - 6P3/2 - 8S1/2 - 7P3/2, 7P1/2, 6P1/2 - 6S1/2 multi-diamond-type atomic system via two-photon excitation with two IR pump lasers at 852 nm and 795 nm. The 456 nm, 459 nm (7P3/2, 7P1/2 → 6S1/2) collimated blue lights result from the self-seeded four-wave mixing process (FWM), and the 761 nm coherent light (8S1/2 → 6P1/2) is from a seeded FWM process with the injection of a third laser at 895 nm. We measure the dependency of generated polychromatic fields on the temperature of 133Cs vapor cell and the powers of input lasers, clearly demonstrating the competition between the self-seeded FWM and seeded FWM, as they share the same excitation path. This work is helpful to further produce entangled multi-color photons for quantum communication.

Frequency conversion to the telecom O-band using pressurized hydrogen.

Large-scale quantum networks rely on optical fiber networks and photons as so-called flying qubits for information transport. While dispersion and absorption of optical fibers are minimum at the infrared telecom wavelengths, most atomic and solid state platforms operate at visible or near-infrared wavelengths. Quantum frequency conversion is required to bridge these two wavelength regimes, and nonlinear crystals are currently employed for this process. Here, we report a novel approach of frequency conversion to the telecom band. This interaction is based on coherent Stokes Raman scattering (CSRS), a four-wave mixing process resonantly enhanced in a dense molecular hydrogen gas. We show the conversion of photons from 863 nm to the telecom O-band and demonstrate that the input polarization state is preserved. This process is intrinsically broadband and can be adapted to any other wavelength.

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.

Frequency-Modulated Continuous-Wave Laser Source Based on Four-Wave Mixing process in a Silicon Integrated Waveguide Doped with Reverse-Biased P-i-N Junction

Frequency-Modulated Continuous-Wave Laser Source Based on Four-Wave Mixing process in a Silicon Integrated Waveguide Doped with Reverse-Biased P-i-N Junction

Design and Fabrication of a Photonic Integrated Circuit-based Entangled Photon Pair Source using Microring Resonators

Photonic integrated circuits (PICs) based on silicon-on-insulator (SOI) substrates provide a lightweight, compact platform for applications in quantum optics. We show the evaluation and characterization of an SOI-bascd PIC design for an entangled photon pair source, generating photon pairs by means of the nonlinear process of spontaneous four-wave mixing in microring resonators. Experimental results following from the chip fabrication fed back into the simulated parameter tuning effects, culminating in photon pair generation with measured correlations exceeding classically predicted limits.

Progress on Chip-Based Spontaneous Four-Wave Mixing Quantum Light Sources

Quantum light generated through spontaneous four-wave mixing (SFWM) process in nonlinear materials, such as entangled photon pairs and single photons, is an important resource for various emerging quantum applications. Integrated quantum photonics has enabled the generation, manipulation, and detection of quantum states of light with steadily increasing scale and complexity levels. Importantly, the exploration of on-chip integration has accumulated substantial progresses in recent years toward the realization of low-cost, large-scale quantum photonic circuits. Here, we review the underlying mechanism and discuss state-of-the-art SFWM on-chip quantum light sources fabricated with various structures and materials on chip. Furthermore, we enumerate the most appealing applications of on-chip SFWM such as heralding single-photon source, entangled photon source, and system-level integration.

Multipartite entanglement in bright frequency combs out of microresonators

We present a theoretical model of multimode quantum correlations in bright frequency combs generated in continuous-wave regime by microresonators above threshold. Our analysis shows how these correlations emerge from cascading four-wave mixing processes fed by the input pump as well as the generated bright beams. Logarithmic negativity criterion is employed to quantify entanglement between partitions of modes, demonstrating the transition from a bipartite regime just above the oscillation threshold to the multipartite one at higher input pump powers. Due to its generality, our model can be safely used to describe other kinds of non-linear χ(3) cavities.

Phase Conjugated Mode Conversion Enabled by Two-stage Cascaded Four-wave Mixing Processes

Phase Conjugated Mode Conversion Enabled by Two-stage Cascaded Four-wave Mixing Processes

Local measurement of terahertz field-induced second harmonic generation in plasma filaments

The concept of Terahertz Field-Induced Second Harmonic (TFISH) Generation is revisited to introduce a single-shot detection scheme based on third order nonlinearities. Focused specifically on the further development of THz plasma-based sources, we begin our research by reimagining the TFISH system to serve as a direct plasma diagnostic. In this work, an optical probe beam is used to mix directly with the strong ponderomotive current associated with laser-induced ionization. A four-wave mixing (FWM) process then generates a strong second-harmonic optical wave because of the mixing of the probe beam with the nonlinear current components oscillating at THz frequencies. The observed conversion efficiency is high enough that for the first time, the TFISH signal appears visible to the human eye. We perform spectral, spatial, and temporal analysis on the detected second-harmonic frequency and show its direct relationship to the nonlinear current. Further, a method to detect incoherent and coherent THz inside plasma filaments is devised using spatio-temporal couplings. The single-shot detection configurations are theoretically described using a combination of expanded FWM models with Kostenbauder and Gaussian Q-matrices. We show that the retrieved temporal traces for THz radiation from single- and two-color laser-induced air-plasma sources match theoretical descriptions very well. High temporal resolution is shown with a detection bandwidth limited only by the spatial extent of the probe laser beam. Large detection bandwidth and temporal characterization is shown for THz radiation confined to under-dense plasma filaments induced by < 100 fs lasers below the relativistic intensity limit.Graphical

Incoherently pumped event horizons in optical fibers

Optical event horizons in fibers, driven by coherent pumps, have been a prominent subject of study within the field of nonlinear optics. Previously, optical event horizons involving a potent pump and a linear-wave were interpreted as phase-matching processes wherein new spectral components are derived from the linear-wave due to the influence of the strong pump. This nonlinear interaction, coupled with the wave mixing mechanism, has been elaborated upon in the spectral domain. It’s portrayed as a cascaded four-wave mixing process, achieving quasi-phase-matching through intermediate spectral components. Until now, research focused on event horizons or soliton linear-wave interactions has predominantly relied on coherent laser pump sources. However, there has been a recent resurgence in the exploration of incoherently pumped nonlinear optics. While the specific dynamics of incoherent light fields and their subsequent nonlinear processes might be elusive due to their inherent random field fluctuations, their incoherent nature unveils a multitude of statistical dynamics for nonlinear phenomena. In this work, we delve into optical event horizons encountered by linear-waves propelled by an incoherent light field within nonlinear optical fibers. Our numerical analysis scrutinizes the dynamics of linear-waves during optical event horizons under incoherent pumping. We further dissect the temporal statistics of the newly birthed idler-waves emerging from these event horizon processes.

A five-level cold atomic system for the orbital angular momentum exchange based on a four-wave mixing setup

In this paper, we suggest a theoretical model for the exchange of the orbital angular momentum (OAM) state of laser fields in a real cold atomic system for realization in an experimental setup. By using four-wave mixing (FWM) processes, we study the spatial dependence of the new weak generated signal light under electromagnetically induced transparency conditions when one of the laser lights becomes an optical vortex. We discuss the spatial dependence of FWM processes via experimental parameters for different conditions of the OAM of vortex light. We have found that the intensity and phase distributions of the new generated light depends strongly on the OAM number of the optical vortex light. Moreover, we investigate the absorption spectrum of the new generated signal light for different OAM of the optical vortex light. Our obtained results may have potential applications in quantum information science.

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

AbstractRecently, 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.

Interpretable inverse-designed cavity for on-chip nonlinear photon pair generation

Inverse design is a powerful tool in wave physics for compact, high-performance devices. To date, applications in photonics have mostly been limited to linear systems and it has rarely been investigated or demonstrated in the nonlinear regime. In addition, the “black box” nature of inverse design techniques has hindered the understanding of optimized inverse-designed structures. We propose an inverse design method with interpretable results to enhance the efficiency of on-chip photon generation rate through nonlinear processes by controlling the effective phase-matching conditions. We fabricate and characterize a compact, inverse-designed device using a silicon-on-insulator platform that allows a spontaneous four-wave mixing process to generate photon pairs at a rate of 1.1 MHz with a coincidence to accidental ratio of 162. Our design method accounts for fabrication constraints and can be used for scalable quantum light sources in large-scale communication and computing applications.

Shaping the spectral correlation of bi-photon quantum frequency combs by multi-frequency excitation of an SOI integrated nonlinear resonator.

We reveal the generation of a broadband (> 1.9 THz) bi-photon quantum frequency comb (QFC) in a silicon-on-insulator (SOI) Fabry-Pérot micro-cavity and the control of its spectral correlation properties. Correlated photon pairs are generated through three spontaneous four-wave mixing (SFWM) processes by using a co-polarized bi-chromatic coherent input with power P1 and P2 on adjacent resonances of the nonlinear cavity. Adjusting the spectral power ratio r = P1/(P1 + P2) allows control over the influence of each process leading to an enhancement of the overall photon pair generation rate (PGR) μ(r) by a maximal factor of μ(r = 0.5)/μ(r = 0) ≈ 1.5, compared to the overall PGR provided by a single-pump configuration with the same power budget. We demonstrate that the efficiency aND of the non-degenerate excitation SFWM process (NDP) doubles the efficiency a1 ≈ a2 of the degenerate excitation SFWM processes (DP), showing a good agreement with the provided model.

Multiple conical odd harmonics from filament-inscribed nanogratings

We report on the observation of conical third, fifth, seventh, and ninth harmonics that gradually emerge during the supercontinuum generation by filamentation of femtosecond midinfrared pulses in lithium strontium hexafluoroaluminate crystal. We show that the generation of conical odd harmonics is an optical signature of light-driven material reorganization in the form of volume nanogratings at the site irradiated by repetitive femtosecond filaments. The angle-resolved spectral measurements demonstrate remarkably broad spectra of individual odd harmonics, benefiting from a spectrally broadened pump pulse (supercontinuum), and reveal that filament-inscribed nanogratings represent photonic structures that are able to provide ultrabroad phase-matching bandwidths covering the wavelength range from the ultraviolet to the near infrared. We propose a scenario that interprets the generation of conical fifth, seventh, and ninth harmonics as nanograting phase-matched cascaded noncollinear four-wave mixing processes.