Nonlinear 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.

Parametric amplification based on intermodal four-wave mixing between different supermodes in coupled-core fibers.

Parametric amplifiers relying on the nonlinear four-wave mixing process are known for their signature symmetric gain spectrum, where signal and idler sidebands are generated on both sides of a powerful pump wave frequency. In this article we show analytically and numerically that parametric amplification in two identically coupled nonlinear waveguides can be designed in such a way that signals and idlers are naturally separated into two different supermodes, hence providing idler-free amplification for the supermode carrying signals. This phenomenon is based on the coupled-core fibers analogue of intermodal four wave-mixing occurring in a multimode fiber. The control parameter is the pump power asymmetry between the two waveguides, which leverages the frequency dependency of the coupling strength. Our findings pave the way for a novel class of parametric amplifiers and wavelength converters, based on coupled waveguides and dual-core fibers.

Wavefront shaping with nonlinear four-wave mixing

Wavefront manipulations have enabled wide applications across many interdisciplinary fields ranging from optics and microwaves to acoustics. However, the realizations of such functional surfaces heavily rely on micro/nanofabrication to define the structured surfaces, which are fixed and only work within a limited spectrum. To address these issues, previous attempts combining tunable materials like liquid crystal or phase-change ones onto the metasurfaces have permitted extra tunability and working spectra, however, these additional layers bring in inevitable loss and complicate the fabrication. Here we demonstrate a fabrication-free tunable flat slab using a nonlinear four-wave mixing process. By wavefront-shaping the pump onto the flat slab, we can successfully tune the effective nonlinear refraction angle of the emitting FWM beams according to the phase-matching condition. In this manner, a focusing and a defocusing nonlinear of FWM beam through the flat slab have been demonstrated with a converging and a diverging pump wavefronts, respectively. Furthermore, a beam steering scheme over a 20° angle has been realized through a non-degenerate four-wave mixing process by introducing a second pump. These features open up a door to manipulating light propagation in an all-optical manner, paving the way to more functional and tunable flat slab devices in the applications of imaging and all-optical information.

Efficient transfer of spatial intensity and phase information of arbitrary modes via four-wave mixing in an atomic vapor

We propose a scheme to transfer the spatial intensity as well as phase information encoded initially in the spatial profile of a weak probe field onto a newly generated Stokes field in a nonlinear process of four-wave mixing (FWM). The FWM process is explored in a gaseous medium consisting of atoms modeled as a three-level system in the $\mathrm{\ensuremath{\Lambda}}$ configuration. We found that different orders of Hermite-Gaussian and Laguerre-Gaussian modes carried by a probe beam are effectively transferred to a Stokes beam. Interestingly, the transferred intensity of the Stokes beam is a clone of the probe beam, whereas the phase profile is conjugate to the probe. The phase distribution of the transmitted modes at the exit of the medium is explored by superimposing them on a copropagating plane wave. Moreover, the parametric amplification due to the nonlinear process of FWM prevents any information loss due to linear absorption and permits us to work at high optical depths. We found a structural similarity between transferred images of about $99%$, which provides clear evidence for the successful transfer of information in the FWM process.

Topologically protecting squeezed light on a photonic chip

Squeezed light is a critical resource in quantum sensing and information processing. Due to the inherently weak optical nonlinearity and limited interaction volume, considerable pump power is typically needed to obtain efficient interactions to generate squeezed light in bulk crystals. Integrated photonics offers an elegant way to increase the nonlinearity by confining light strictly inside the waveguide. For the construction of large-scale quantum systems performing many-photon operations, it is essential to integrate various functional modules on a chip. However, fabrication imperfections and transmission cross talk may add unwanted diffraction and coupling to other photonic elements, reducing the quality of squeezing. Here, by introducing the topological phase, we experimentally demonstrate the topologically protected nonlinear process of four-wave mixing, enabling the generation of squeezed light on a silica chip. We measure the cross-correlations at different evolution distances for various topological sites and verify the nonclassical features with high fidelity. The squeezing parameters are measured to certify the protection of cavity-free, strongly squeezed states. The demonstration of topological protection for squeezed light on a chip brings new opportunities for quantum integrated photonics, opening novel approaches for the design of advanced multi-photon circuits.

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 .

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.

Spatial vortex four-wave mixing in a five-level atomic system

We propose a scheme for modulating the spatial vortex four-wave mixing (FWM) in a five-level atomic system. During nonlinear FWM process, we find the FWM field can be easily manipulated by adjusting the corresponding parameters. Practically, the vortex phase can be spatially modulated. Thus, our results may be helpful to study nonlinear quantum phenomena based on orbital angular momentum light.

Interferograms of Votex FWM Beam for Nonlinear Spatial Filter in Photonic Band Gap

We analyze the properties and interferograms of vortex four-wave mixing (FWM) beams by varying the incident angle of the probe field. Based on the properties, we propose the model of a new type of nonlinear spatial filter without diffraction using a Bragg grating in the nonlinear FWM process. We show the evolutions of shapes and interferograms of probe transmission signal (PTS) and FWM by scanning the probe detuning, and demonstrate the Kerr nonlinearity can manipulate the shapes and spatial location of vortex PTS and FWM images. Further, we can determine the center position of the new type of nonlinear filter through interference patterns and use the Kerr nonlinearity of related fields to control the nonlinear filter precisely. In addition, the interferograms of the reflected signal from the photonic band gap (PBG) structure are studied both in experiment and theory. We demonstrate that the number of fork-like patterns of reflected signal changes from one to three, revealing that the superposition of first-order and third-order beams in the reflected signal from PBG structure creates an inverted fork-like pattern.

High-Quality-Factor AlGaAs-on-Sapphire Microring Resonators

We realize an AlGaAs-on-sapphire platform through Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -assisted direct wafer bonding and substrate removal processes. The direct wafer bonding process is optimized concerning the intermediate layer deposition and annealing temperature to obtain a high bonding strength between the AlGaAs and sapphire wafers. High quality-factor (Q) microring resonators are fabricated using electron-beam lithography in which the charging effect is mitigated by applying a thin aluminum layer, and a smooth pattern sidewall definition is obtained using a multi-pass (exposure) process. We achieve an intrinsic Q of up to ~460,000 which is the highest Q for AlGaAs microring resonators. Taking advantage of such high Q resonators, we demonstrate an ultra-efficient nonlinear four-wave mixing process in this platform and obtain a conversion efficiency of -19.8 dB with continuous-wave pumping at a power level of 380 μW. We also investigate the thermal resonance shift of microring resonators with different substrate layouts and observe superior temperature stability for devices in the AlGaAs-on-sapphire platform. The realization of the AlGaAson-sapphire platform also opens new prospects for AlGaAs devices in nonlinear applications in the mid-infrared wavelength range.

Generation of quadripartite entanglement from a hybrid scheme with a four-wave mixing process and linear beam splitters

We theoretically propose a hybrid scheme with nonlinear four-wave mixing process and linear beam splitters to generate continuous-variable quadripartite entanglement. To expose the entanglement properties of the generated state, the coupling strength matrix is derived to reveal the interactions of the resulting modes at first. The generated state is verified to be a H-graph state with a non-full rank coupling strength matrix by using graphical calculus for Gaussian pure states. Then based on the eigenmodes for the generated state, we find that the introduction of beam splitters does not alter the deduced eigenmodes of the nonlinear four-wave mixing process, and only contributes to generate quadripartite entanglement. In the end, we quantitatively investigate the internal entanglement structure of this scheme. Our work paves the way to generate quadripartite entanglement from a hybrid scheme with nonlinear four-wave mixing process and linear beam splitters.

Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing.

Efficient optical frequency mixing typically must accumulate over large interaction lengths because nonlinear responses in natural materials are inherently weak. This limits the efficiency of mixing processes owing to the requirement of phase matching. Here, we report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at telecommunications wavelengths on silicon. We used an integrated plasmonic gap waveguide that strongly confines light within a nonlinear organic polymer. The gap waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of nanometers, thus generating a nonlinear response so strong that efficient FWM accumulates over wavelength-scale distances. This technique opens up nonlinear optics to a regime of relaxed phase matching, with the possibility of compact, broadband, and efficient frequency mixing integrated with silicon photonics.

A plasmonic route for mixing waves

Nanophotonics Nonlinear optics typically requires photons to interact over distances spanning hundreds or thousands of wavelengths. Nonlinear optical devices therefore tend to be bulk components. Nielsen et al. used a polymer material with a high nonlinear coefficient that they embedded within a plasmonic cavity to show that the interaction length scale could be reduced dramatically. The plasmonic cavity focused the light down to the nanoscale, providing an intense electromagnetic field that induced the nonlinear process of four-wave mixing in the polymer. The technique provides a versatile platform for compact nonlinear optical devices. Science , this issue p. [1179][1] [1]: /lookup/doi/10.1126/science.aao1467

Mirrorless Optical Parametric Oscillation with Tunable Threshold in Cold Atoms.

We report the demonstration of a mirrorless optical parametric oscillator with a tunable threshold in laser-cooled atoms with four-wave mixing (FWM) using electromagnetically induced transparency. Driven by two classical laser beams, the generated Stokes and anti-Stokes fields counterpropagate and build up efficient intrinsic feedback through the nonlinear FWM process. This feedback does not involve any cavity or spatially distributed microstructures. We observe the transition of photon correlation properties from the biphoton quantum regime (below the threshold) to the oscillation regime (above the threshold). The pump threshold can be tuned by varying the operating parameters. We achieve the oscillation with a threshold as low as 15 μW.

Hybrid interferometer with nonlinear four-wave mixing process and linear beam splitter.

Optical interferometer has played an important role in optics. Up to now, many kinds of interferometers have been realized and found their applications. In this letter, we experimentally construct an interferometer by using parametric amplifier as a wave splitter and beam splitter as a wave combiner. We make measurements of interference fringes and explore the relationships between the interference visibility of the interferometer and various system parameters, such as the gain of the parametric amplifier, the one-photon detuning and the temperature of the Rb-85 vapor cell.

Directional coherent light via intensity-induced sideband emission

We introduce a unique technique for generating directional coherent emissions that could be utilized to create coherent sources in a wide range of frequencies from the extreme ultraviolet (XUV) to the deep infrared. This is accomplished without population inversion by pumping a two-level system with a far-detuned strong optical field that induces the splitting of the two-level system. A nonlinear process of four-wave mixing then occurs across the split system, driving coherent emission at sidebands both red- and blue-detuned from the pump frequency, and propagates both forward and backward along the pump beam path. We observed this phenomenon in dense rubidium vapor along both the D1 and D2 transitions. The sideband emission exhibits a short pulse duration (<1 ns) with threshold-like behavior dependent on both the pump intensity and Rb vapor density. This technique offers a new capability for manipulating the emission frequency simply through intensity-induced atomic modulation that can be scaled to most frequency regimes using various atomic/molecular ensembles and pump energies.

Coupling of four-wave mixing and Raman scattering by ground-state atomic coherence

We demonstrate coupling of light resonant to transition between two excited states of rubidium and long-lived ground-state atomic coherence. In our proof-of-principle experiment a non-linear process of four-wave mixing is used to achieve light emission proportional to independently prepared ground-state atomic coherence. Strong correlations between stimulated Raman scattering light heralding generation of ground-state coherence and the four-wave mixing signal are measured and shown to survive the storage period, which is promising in terms of quantum memory applications. The process is characterized as a function of laser detunings.

Simulation of Optical Microfiber Strain Sensors Based on Four-Wave Mixing

We investigate the performance of a microfiber strain sensor based on the nonlinear four-wave mixing process. This simple sensor of only an elliptical microfiber has considerable advantages, such as sensing directly by microfiber inherent nonlinearity in the telecommunication range and being compatible with the existing fiber network. Dispersion, nonlinearity, and strain effect are analyzed to find optimum sensing performance. The numerical simulations reveal that the strain can cause a marked wavelength shift of the signal wave. The wavelength shift range can be more than 74 nm within a reasonable strain range. To the ultimate strain range of 30 $\text{m}\varepsilon $ , the average strain sensitivity of 2.46 pm/ $\mu \varepsilon $ can be obtained when the pump wavelength is 1550 nm and the peak power is 100 W. In addition to the range of 5 $\text{m}\varepsilon $ , it could achieve 9.86 pm/ $\mu \varepsilon $ by optimizing the fiber size and highly birefringent characteristic. This strain sensor with high sensitivity, simple configuration, light, and portable performance has wide applications in mechanical detection and fault diagnosis and is of intensified interest for a great deal of wavelength selected devices in quantum information process.

Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide

We demonstrate an ultracompact, chip-based, all-optical exclusive-OR (XOR) logic gate via slow-light enhanced four-wave mixing (FWM) in a silicon photonic crystal waveguide (PhCWG). We achieve error-free operation (<10⁻⁹) for 40 Gbit/s differential phase-shift keying (DPSK) signals with a 2.8 dB power penalty. Slowing the light to vg = c/32 enables a FWM conversion efficiency, η, of -30 dB for a 396 μm device. The nonlinear FWM process is enhanced by 20 dB compared to a relatively fast mode of vg = c/5. The XOR operation requires ≈ 41 mW, corresponding to a switching energy of 1 pJ/bit. We compare the slow-light PhCWG device performance with experimentally demonstrated XOR DPSK logic gates in other platforms and discuss scaling the device operation to higher bit-rates. The ultracompact structure suggests the potential for device integration.

Silicon-chip-based ultrafast optical oscilloscope

With the realization of faster telecommunication data rates and an expanding interest in ultrafast chemical and physical phenomena, it has become important to develop techniques that enable simple measurements of optical waveforms with subpicosecond resolution. State-of-the-art oscilloscopes with high-speed photodetectors provide single-shot waveform measurement with 30-ps resolution. Although multiple-shot sampling techniques can achieve few-picosecond resolution, single-shot measurements are necessary to analyse events that are rapidly varying in time, asynchronous, or may occur only once. Further improvements in single-shot resolution are challenging, owing to microelectronic bandwidth limitations. To overcome these limitations, researchers have looked towards all-optical techniques because of the large processing bandwidths that photonics allow. This has generated an explosion of interest in the integration of photonics on standard electronics platforms, which has spawned the field of silicon photonics and promises to enable the next generation of computer processing units and advances in high-bandwidth communications. For the success of silicon photonics in these areas, on-chip optical signal-processing for optical performance monitoring will prove critical. Beyond next-generation communications, silicon-compatible ultrafast metrology would be of great utility to many fundamental research fields, as evident from the scientific impact that ultrafast measurement techniques continue to make. Here, using time-to-frequency conversion via the nonlinear process of four-wave mixing on a silicon chip, we demonstrate a waveform measurement technology within a silicon-photonic platform. We measure optical waveforms with 220-fs resolution over lengths greater than 100 ps, which represent the largest record-length-to-resolution ratio (>450) of any single-shot-capable picosecond waveform measurement technique. Our implementation allows for single-shot measurements and uses only highly developed electronic and optical materials of complementary metal-oxide-semiconductor (CMOS)-compatible silicon-on-insulator technology and single-mode optical fibre. The mature silicon-on-insulator platform and the ability to integrate electronics with these CMOS-compatible photonics offer great promise to extend this technology into commonplace bench-top and chip-scale instruments.