Optical Wave Mixing Research Articles

Enhancing the efficiency of high-order harmonics with two-color non-collinear wave mixing in silica

The emission of high-order harmonics from solids under intense laser-pulse irradiation is revolutionizing our understanding of strong-field solid-light interactions, while simultaneously opening avenues towards novel, all-solid, coherent, short-wavelength table-top sources with tailored emission profiles and nanoscale light-field control. To date, broadband spectra in solids have been generated well into the extreme-ultraviolet (XUV), but the comparatively low conversion efficiency in the XUV range achieved under optimal conditions still lags behind gas-based high-harmonic generation (HHG) sources. Here, we demonstrate that two-color high-order harmonic wave mixing in a fused silica solid is more efficient than solid HHG driven by a single color. This finding has significant implications for compact XUV sources where gas-based HHG is not feasible, as solid XUV wave mixing surpasses solid-HHG in performance. Moreover, our results enable utilizing solid high-order harmonic wave mixing as a probe of structure or material dynamics of the generating solid, which will enable reducing measurement times compared to the less efficient regular solid HHG. The emission intensity scaling that follows perturbative optical wave mixing, combined with the angular separation of the emitted frequencies, makes our approach a decisive step for all-solid coherent XUV sources and for studying light-engineered materials.

Tunable optical matrix convolution of 20-Gbit/s QPSK 2-D data with a kernel using optical wave mixing.

Compared to its electronic counterpart, optically performed matrix convolution can accommodate phase-encoded data at high rates while avoiding optical-to-electronic-to-optical (OEO) conversions. We experimentally demonstrate a reconfigurable matrix convolution of quadrature phase-shift keying (QPSK)-encoded input data. The two-dimensional (2-D) input data is serialized, and its time-shifted replicas are generated. This 2-D data is convolved with a 1-D kernel with coefficients, which are applied by adjusting the relative phase and amplitude of the kernel pumps. Time-shifted data replicas (TSDRs) and kernel pumps are coherently mixed using nonlinear wave mixing in a periodically poled lithium niobate (PPLN) waveguide. To show the tunability and reconfigurability of this approach, we vary the kernel coefficients, kernel sizes (e.g., 2 × 1 or 3 × 1), and input data rates (e.g., 6-20 Gbit/s). The convolution results are verified to be error-free under an applied: (a) 2 × 1 kernel, resulting in a 16-quadrature amplitude modulation (QAM) output with an error vector magnitude (EVM) of ∼5.1-8.5%; and (b) 3 × 1 kernel, resulting in a 64-QAM output with an EVM of ∼4.9-5.5%.

Giant nonlinear optical wave mixing in a van der Waals correlated insulator.

Optical nonlinearities are one of the most fascinating properties of two-dimensional (2D) materials. While tremendous efforts have been made to find and optimize the second-order optical nonlinearity in enormous 2D materials, opportunities to explore higher-order ones are elusive because of the much lower efficiency. Here, we report the giant high odd-order optical nonlinearities in centrosymmetric correlated van der Waals insulator manganese phosphorus triselenide. When illuminated by two near-infrared femtosecond lasers, the sample generates a series of profound four- and six-wave mixing outputs. The near-infrared third-order nonlinear susceptibility reaches near the highest record values of 2D materials. Comparative measurements to other prototypical nonlinear optical materials [lithium niobate, gallium(II) selenide, and tungsten disulfide] reveal its extraordinary wave mixing efficiency. The wave mixing processes are further used for nonlinear optical waveguide with multicolor emission. Our work highlights the promising prospect for future research of the nonlinear light-matter interactions in the correlated 2D system and for potential nonlinear photonic applications.

Silicon‐Rich Nitride Refractive Index as a Degree of Freedom to Maximize Nonlinear Wave Mixing in Nanowaveguides

Silicon nitride is widely used in integrated photonics for optical nonlinear wave mixing due to its low optical losses combined with relatively high nonlinear optical properties and a wide‐range transparency window. It is known that a higher concentration of Si in silicon‐rich nitride (SRN) magnifies both the nonlinear response and optical losses, including nonlinear losses. To address the trade‐off, four‐wave mixing (FWM) is implemented in over a hundred SRN waveguides prepared by plasma‐enhanced chemical vapor deposition in a wide range of SRN refractive indices varying between 2.5 and 3.2 (measured in the C‐band). It is determined that SRN with a refractive index of about 3 maximizes the FWM efficiency for continuous‐wave operation, indicating that the refractive index of SRN is indeed a crucial optimization parameter for nonlinear optics applications. The FWM efficiency is limited by large nonlinear optical losses observed in SRN waveguides with indices larger than 2.7, which are not related to two‐photon absorption. Finally, the third‐order susceptibility and the nonlinear refractive index are estimated for multiple SRN refractive indices, and, specifically, the nonlinearities as large as and are estimated in a waveguide with an SRN refractive index of 3.2.

Parity-time symmetry enabled ultra-efficient nonlinear optical signal processing

Nonlinear optical signal processing (NOSP) has the potential to significantly improve the throughput, flexibility, and cost-efficiency of optical communication networks by exploiting the intrinsically ultrafast optical nonlinear wave mixing. It can support digital signal processing speeds of up to terabits per second, far exceeding the line rate of the electronic counterpart. In NOSP, high-intensity light fields are used to generate nonlinear optical responses, which can be used to process optical signals. Great efforts have been devoted to developing new materials and structures for NOSP. However, one of the challenges in implementing NOSP is the requirement of high-intensity light fields, which is difficult to generate and maintain. This has been a major roadblock to realize practical NOSP systems for high-speed, high-capacity optical communications. Here, we propose using a parity-time (PT) symmetric microresonator system to significantly enhance the light intensity and support high-speed operation by relieving the bandwidth-efficiency limit imposed on conventional single resonator systems. The design concept is the co-existence of a PT symmetry broken regime for a narrow-linewidth pump wave and near-exceptional point operation for broadband signal and idler waves. This enables us to achieve a new NOSP system with two orders of magnitude improvement in efficiency compared to a single resonator. With a highly nonlinear AlGaAs-on-Insulator platform, we demonstrate an NOSP at a data rate approaching 40 gigabits per second with a record low pump power of one milliwatt. These findings pave the way for the development of fully chip-scale NOSP devices with pump light sources integrated together, potentially leading to a wide range of applications in optical communication networks and classical or quantum computation. The combination of PT symmetry and NOSP may also open up opportunities for amplification, detection, and sensing, where response speed and efficiency are equally important.

Excitonic resonances control the temporal dynamics of nonlinear optical wave mixing in monolayer semiconductors

Monolayer semiconductors are an emerging platform for strong nonlinear light–matter interactions that are enhanced by the giant oscillator strength of tightly bound excitons. Little attention has been paid to the impact of excitonic resonances on the temporal dynamics of such nonlinearities, since harmonic generation and optical wave mixing are generally considered instantaneous processes. We find that a significant time difference, ranging from −40 to +120 fs, is necessary between two light pulses for optimal sum-frequency generation (SFG) and four-wave mixing (FWM) to occur from monolayer WSe2 when one of the pulses is in resonance with an excitonic transition. These resonances involve both band-edge A excitons and high-lying excitons that comprise electrons from conduction bands far above the bandgap. Numerical simulations in the density-matrix formalism rationalize the distinct dynamics of SFG and FWM. The interpulse delays for maximal SFG and FWM are governed primarily by the lifetime of the one-photon and two-photon resonant states, respectively. The method therefore offers an unconventional probe of the dynamics of excitonic states accessible with either one-photon or two-photon transitions. Remarkably, the longest delay times occur at the lowest excitation powers, indicating a strong nonlinearity that offers exploration potential for excitonic quantum nonlinear optics. Researchers show that resonant coupling of light pulses with excitonic transitions affects the optimal time difference between pulses for sum-frequency generation and four-wave mixing in monolayer WSe2.

Higher-Order X-ray - Optical Wave Mixing

Higher-Order X-ray - Optical Wave Mixing

Slow and Fast Light in Plasma Using Optical Wave Mixing.

Slow and fast light, or large changes in the group velocity of light, have been observed in a range of optical media, but the fine optical control necessary to induce an observable effect has not been achieved in a plasma. Here, we describe how the ion-acoustic response in a fully ionized plasma can produce large and measurable changes in the group velocity of light. We show the first experimental demonstration of slow and fast light in a plasma, measuring group velocities between 0.12c and -0.34c.

Towards novel probes for valence charges via X-ray optical wave mixing.

We present a combined theoretical and experimental study of X-ray optical wave mixing. This class of nonlinear phenomena combines the strengths of spectroscopic techniques from the optical domain, with the high-resolution capabilities of X-rays. In particular, the spectroscopic sensitivity of these phenomena can be exploited to selectively probe valence dynamics. Specifically, we focus on the effect of X-ray parametric down-conversion. We present a theoretical description of the process, from which we deduce the observable nonlinear response of valence charges. Subsequently, we simulate scattering patterns for realistic conditions and identify characteristic signatures of the nonlinear conversion. For the observation of this signature, we present a dedicated experimental setup and results of a detailed investigation. However, we do not find evidence of the nonlinear effect. This finding stands in strong contradiction to previous claims of proof-of-principle demonstrations. Nevertheless, we are optimistic to employ related X-ray optical wave mixing processes on the basis of the methods presented here for probing valence dynamics in the future.

Quantum plasmon enhanced nonlinear wave mixing in graphene nanoflakes* *Project supported by the National Natural Science Foundation of China (Grant No. 11947007), the Natural Science Foundation of Guangdong Province, China (Grant No. 2019A1515011499), and the Department of Education of Guangdong Province, China (Grant No. 2019KTSCX087).

A distant-neighbor quantum-mechanical method is used to study the nonlinear optical wave mixing in graphene nanoflakes (GNFs), including sum- and difference-frequency generation, as well as four-wave mixing. Our analysis shows that molecular-scale GNFs support quantum plasmons in the visible spectrum region, and significant enhancement of nonlinear optical wave mixing is achieved. Specifically, the second- and third-order wave-mixing polarizabilities of GNFs are dramatically enhanced, provided that one (or more) of the input or output frequencies coincide with a quantum plasmon resonance. Moreover, by embedding a cavity into hexagonal GNFs, we show that one can break the structural inversion symmetry and enable otherwise forbidden second-order wave mixing, which is found to be enhanced by the quantum plasmon resonance too. This study reveals that the molecular-sized graphene could be used in the quantum regime for nanoscale nonlinear optical devices and ultrasensitive molecular sensors.

Efficient, broadband third-harmonic generation in silicon nanophotonic waveguides spectrally shaped by nonlinear propagation.

Optical emission from silicon is most practically accessible through nonlinear optical wave mixing, due to the indirect bandgap of the material. Although silicon is a material that absorbs visible light, third-harmonic generation driven by infrared signals can be used to generate visible light in silicon structures. In this work, we present a comprehensive investigation into third-harmonic generation in silicon-on-insulator waveguides. We demonstrate that few-micrometer length waveguides can be used to up-convert ultrafast 1550nm laser pulses to their third-harmonic with efficiencies up to ηTHG=2.8×10-5, the highest third-harmonic generation conversion efficiency reported to date in a silicon-based structure. Nonlinear propagation through 200μm long waveguides produces self-compressing temporal solitons, which dramatically broaden and blue shift the observed third-harmonic spectrum. Such devices are envisioned to provide a method for generating coherent visible signals within an integrated, CMOS compatible platform.

Recovery of wave-mixing conversion efficiency in weakly scattering nonlinear crystals.

Nonlinear optical wave mixing is a widely used method to produce light with new frequencies that has a significant impact on laser technology and optical imaging. The most important figure of merit in wave-mixing processes, i.e., high conversion efficiency, is always required in laser applications. We demonstrate a method to recover high conversion efficiency of second harmonic generation in a BaMgF4 single crystal with weakly scattering defects via feedback-based wavefront shaping under birefringent phase-matching condition. By optimizing the fundamental wavefront, a typical second harmonic output with an enhancement factor of 1.14 and a corresponding recovery efficiency of 86.3% is displayed. This investigation may modify the wide understanding of scattering in crystals and provide an avenue to recover the nonlinear optical conversion efficiency in crystals with various defects without special fabrications.

Parametric Down-Conversion of X Rays into the Optical Regime.

We report the observation of parametrically down-converted x-ray signal photons at photon energies that correspond to idler photons at optical wavelengths. The count-rate dependence on the angles of the input beam and of the detector and on the slit sizes agrees with theory within the experimental uncertainties. The nonlinear susceptibility, which we calculated from the measured efficiencies, is comparable to the nonlinear susceptibility evaluated from the measurements of x-ray and optical wave mixing. The results of the present Letter advance the development of a spectroscopy method for probing valence-electron charges and the microscopic optical response of crystals with atomic-scale resolution.

Reconfigurable Channel Slicing and Stitching for an Optical Signal to Enable Fragmented Bandwidth Allocation Using Nonlinear Wave Mixing and an Optical Frequency Comb

A scheme for reconfigurable channel slicing and stitching is proposed and experimentally demonstrated. By employing optical nonlinear wave mixing and a coherent frequency comb, a single channel spectrum is sliced and redistributed into fragmented frequency slots, which can be stitched together to recover the original channel at the receiver. This approach is verified through a single channel experiment with the modulation formats of quadrature phase-shift keying and 16 quadrature amplitude modulation. The system exhibits less than 1.5% error-vector-magnitude deterioration and no more than 2-dB optical signal-to-noise ratio penalty, compared to a back-to-back baseline. To demonstrate robustness of the scheme, different parameters of the channel slices are varied, such as relative phase offset, relative amplitude, and the number of slices. A 10-km transmission experiment is also conducted and the additional system penalty is negligible. This scheme is used to experimentally demonstrate fragmented channel bandwidth allocation in a dense 6-channel wavelength-division-multiplexing system. The incoming 20-Gbaud optical channel is successfully reallocated into two fragmented frequency slots and reconstructed at the receiver.

Pilot-tone-based self-homodyne detection using optical nonlinear wave mixing.

An all-optical pilot-tone-based self-homodyne detection scheme using nonlinear wave mixing is experimentally demonstrated. Two scenarios are investigated using (1) multiple wavelength-division-multiplexed channels with sufficient power of the pilot tones and (2) a single channel with a low-power pilot tone. The eye diagram and bit error rate of the system are studied by tuning various parameters such as pump power, relative phase, and pilot-to-signal ratio.

Digital optical processing of optical communications: towards an Optical Turing Machine

AbstractOptical computing is needed to support Tb/s in-network processing in a way that unifies communication and computation using a single data representation that supports in-transit network packet processing, security, and big data filtering. Support for optical computation of this sort requires leveraging the native properties of optical wave mixing to enable computation and switching for programmability. As a consequence, data must be encoded digitally as phase (M-PSK), semantics-preserving regeneration is the key to high-order computation, and data processing at Tb/s rates requires mixing. Experiments have demonstrated viable approaches to phase squeezing and power restoration. This work led our team to develop the first serial, optical Internet hop-count decrement, and to design and simulate optical circuits for calculating the Internet checksum and multiplexing Internet packets. The current exploration focuses on limited-lookback computational models to reduce the need for permanent storage and hybrid nanophotonic circuits that combine phase-aligned comb sources, non-linear mixing, and switching on the same substrate to avoid the macroscopic effects that hamper benchtop prototypes.

Ultra-strong polarization dependence of surface lattice resonances with out-of-plane plasmon oscillations

The interplay between localized surface plasmon (LSP) resonances and their collective responses, known as surface lattice resonances (SLRs), in metal nanoparticle arrays can lead to resonances with high Q-factors (∼100). These responses have in the past usually been studied for LSP resonances in the plane of the array of the nanoparticles (assumed to be nonmagnetic), thus restricting efficient coupling to particles separated along a specific direction. In the present study, we demonstrate that LSPs oscillating perpendicular to the plane of the surface can lead to stronger inter-particle coupling, which enhances the SLRs. This stronger coupling occurs because the out-of-plane oscillations can couple in all directions within the plane of the array. We study the resulting SLRs for square and hexagonal lattices using the discrete-dipole approximation, and we predict much larger Q-factors in the wavelength range near 650 nm. This prediction suggests that SLRs could be very useful in enhancing various optical processes, and in many applications such as sensing and nonlinear optical wave mixing.

Simultaneous all-optical phase noise mitigation and automatically locked homodyne reception of an incoming QPSK data signal.

Simultaneous phase noise mitigation and automatic phase/frequency-locked homodyne reception is demonstrated for a 20-32 Gbaud QPSK signal. A phase quantization function is realized to squeeze the phase noise of the signal by optical wave mixing of the signal, its third-order harmonic, and their corresponding delayed variant conjugates, converting the noisy input into a noise-mitigated signal. In a simultaneous nonlinear process, the noise-mitigated signal is automatically phase- and frequency-locked with a "local" pump laser, avoiding the need for feedback or phase/frequency tracking for homodyne detection. Open eye-diagrams are obtained for in-phase and quadrature-phase components of the signal and ∼2 dB OSNR gain is achieved at BER 10-3.

Dynamics of triple quantum beats retrieved from coupled four-wave mixing signals

A theoretical model of coupled four-wave mixing (FWM) processes comprising five atomic energy levels was proposed to investigate the coherent characteristics of atomic wave packets using perturbation theory. As several states in atoms are coherently excited by a two-photon transition, triple coupled FWM can be produced, and triple quantum beats associated with the atomic energy levels are embedded in the FWM signals. Triple coupled FWM processes were achieved experimentally in Rb vapor by two-photon excitation using broadband optical pulses. A pump–probe scheme was utilized to record the time-varying FWM signals, and Fourier transform was applied to retrieve the quantum beats. Furthermore, short-time Fourier transform was implemented to investigate the dynamics of quantum beats. The results show that the coherent characteristics of atomic wave packets, which are intimately related to the dynamics of quantum beats, can be probed by coupled nonlinear optical wave mixing.

All-optical tunable multilevel amplitude regeneration based on coherent wave mixing using a polarizer.

We describe and demonstrate an all-optical tunable phase- preserving scheme for multilevel amplitude regeneration based on coherent optical wave mixing using a polarizer for optical star 8-quadrature-amplitude modulation (star-8QAM) and star-16QAM signals with a power ratio of 1:5. Amplitude noise can be efficiently suppressed on both amplitude levels. A regeneration factor of nearly 5 for the higher-amplitude level of star-8QAM and 3 for lower-amplitude level are achieved. The system robustness against nonlinear phase noise originating from the Gordon-Mollenauer effect in a 150 km transmission line is investigated using the proposed amplitude regenerator.