Nonlinear Wave Mixing Research Articles

Directly generating vortex beams in the second harmonic by a spirally structured fundamental wave

Based on nonlinear wave mixing, we experimentally propose a scheme for directly generating optical orbital angular momentum (OAM) by a spirally structured fundamental wave interacting with a nonlinear medium, in which the nonlinear susceptibilities are homogenous. In the experiment, the second-harmonic generation of a fundamental wave carrying positive (negative) integers and fractional OAM states was investigated. This study presents a convenient approach for dynamic control of OAM of vortex beams, which may feature their applications in optical manipulation and optical communication.

Tunable optical single-sideband generation for OOK and PAM4 data channels using an optical frequency comb and nonlinear wave-mixing.

We experimentally demonstrate tunable optical single-sideband (SSB) generation using a tapped-delay-line (TDL) optical filter for 10 and 20 Gbit/s on/off-keying (OOK) signals and a 20 Gbit/s four-level pulse-amplitude-modulated (PAM4) signal. The optical SSB filter is realized by using an optical frequency comb, wavelength-dependent delay, and nonlinear wave-mixing to achieve the TDL function. Moreover, SSB tunability is achieved by adjusting the amplitude, phase, frequency spacing, and number of selected optical frequency comb lines. We show that the one-sideband suppression of a double-sideband (DSB) channel can be enhanced as the number of taps is increased; however, we do measure a ∼1.5% error-vector-magnitude penalty. Furthermore, we demonstrate that the chromatic-dispersion-induced penalty after 80 km standard-single-mode-fiber transmission of a 10 Gbit/s SSB OOK signal without chromatic dispersion compensation has been reduced by >3dB when compared to DSB.

Harmonic spin–orbit angular momentum cascade in nonlinear optical crystals

Optical angular momentum-based photonic technologies demonstrate the key role of the optical spin–orbit interaction that usually refers to linear optical processes in spatially engineered optical materials1. Re-examining the basics of nonlinear optics of homogeneous crystals under circularly polarized light2,3, we report experiments on the enrichment of the spin–orbit angular momentum spectrum of paraxial light. The demonstration is made within the framework of second-harmonic generation using a crystal with three-fold rotational symmetry. Four spin–orbit optical states for the second harmonic field are predicted from a single fundamental state owing to the interplay between linear spin–orbit coupling and nonlinear wave mixing; three of these states are experimentally verified. Besides representing a spin-controlled nonlinear route to orbital angular multiplexing4, modal vortex light sources5,6, high-dimensional parametric processes7 and multi-state optical magnetization8, our findings suggest that the fundamentals of nonlinear optics are worth revisiting through the prism of the spin–orbit interaction of light.

All-Optical Aggregation and De-Aggregation of 4×BPSK-16QAM Using Nonlinear Wave Mixing for Flexible Optical Network

A scheme is proposed for all-optical aggregation from four 10 Gbps binary-phase-shift-keying (BPSK) signals into one 40 Gbps 16-ary quadrature amplitude modulation (16QAM) signal by applying the coherent addition of optical vectors, and de-aggregation for the 16QAM signal to recover the data of four original BPSK signals in high nonlinear fiber (HNLF) without information loss or redundancy using self-phase modulation (SPM) and four-wave mixing (FWM). The simulation results show that the error-vector-magnitude (EVM) curves of BPSK signal before aggregation and the 16QAM signal almost coincide with each other, as well as after the de-aggregation it has about 20% degradation at most. The bit error rate (BER) performance of BPSK signals indicates that when the OSNR of BPSK before aggregation is greater than 21.0 dB, then the wrong code of BPSK signal after de-aggregation can be corrected at the receiving end. Additionally, the expanded methods are also proposed for the aggregation of 8PSK signal and 64QAM signal by employing the similar principle. This proposed method provides a new way for realizing the flexible optical transmission and reception of advanced modulation format signals, and suits for the future dynamically reconfigurable optical network at the gateway nodes between different transmission networks.

Nonlinear guided wave mixing in pipes for detection of material nonlinearity

Pipes have multiple applications in daily life and they are subjected to different types of defects. Nonlinear guided wave has attracted significant attention in detecting microstructural change at early stage of material deterioration. Extensive research using wave mixing with different wave modes has focused on plate-like structures. However, limited experimental studies have been conducted on the detection of material nonlinearity in pipes using two interacting guided waves. This study investigates nonlinear features generated due to mixing of torsional guided waves and material nonlinearity in pipes at low frequency range. The nonlinear theory of elasticity is implemented in a three-dimensional (3D) finite element (FE) method to simulate the effect of material nonlinearity on torsional guided wave mixing. The phenomenon of nonlinear features generated due to torsional guided wave mixing is investigated by 3D FE models. There is good agreement between the data obtained in the laboratory and numerical simulation results. This study demonstrates the existence of the combinational harmonic generation experimentally and provides physical insight into the phenomenon of nonlinear wave mixing. The findings of this study can further advance the damage detection techniques based on material nonlinearity in wave mixing.

Higher radial orders of Laguerre–Gaussian beams in nonlinear wave mixing processes

We generalize the study of Laguerre–Gaussian beams in nonlinear wave mixing processes, considering optical beams with both integer azimuthal and non-null radial mode index as input modes combined in the nonlinear crystal. Here, we present a deeper discussion of the generation of higher radial orders through a nonlinear wave mixing process leading to a more complete understanding of the nonlinear process considered.

Pattern formation in a driven Bose–Einstein condensate

Pattern formation is ubiquitous in nature from morphogenesis and cloud formation to galaxy filamentation. More often than not, patterns arise in a medium driven far from equilibrium due to the interplay of dynamical instability and nonlinear wave mixing. We report, based on momentum and real space pattern recognition, formation of density patterns with two- (D$_2$), four- (D$_4$) and six-fold (D$_6$) symmetries in Bose-Einstein condensates (BECs) with atomic interactions driven at two frequencies. The symmetry of the pattern is controlled by the ratio of the frequencies. The D$_6$ density waves, in particular, arise from a resonant wave mixing process that coherently correlates and enhances the excitations that respect the symmetry.

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.

Spin‐Controlled Nonlinear Harmonic Generations from Plasmonic Metasurfaces Coupled to Intersubband Transitions

AbstractMetasurfaces that generate nonlinear optical responses provide new degrees of freedom for applications such as nonlinear holography, wave mixing, and new frequencies generation. To extend the utility of flat nonlinear optics, metasurfaces providing both giant nonlinear response for efficient frequency mixing in subwavelength films and a single‐beam output with a local wavefront control need to be developed. Metasurfaces with giant nonlinear response have recently been realized using the concept of intersubband polaritons. Separately, nonlinear metasurfaces providing a single‐beam nonlinear output with a local wavefront control have been studied. However, a metasurface platform that possesses both of these properties has yet to be demonstrated. Herein, the first such platform is presented and its operation for three‐ and four‐wave mixing processes is demonstrated. This approach is based on using Pancharatnam–Berry phase control of local nonlinear response and on employing meta‐atoms with specific symmetries to enable generation of only a single nonlinear beam. Experimentally, 400 nm‐thick metasurfaces with a wavefront‐controlled single‐beam output are demonstrated for second‐ and third‐harmonic generation at pump wavelength of approximately 10 µm. Power conversion efficiencies of 7.6 × 10−4% and 3.6 × 10−4% are obtained for the two nonlinear processes, respectively, at peak pumping intensity of only 80 kW cm−2.

Numerical Study of Resonant Optical Parametric Amplification via Gain Factor Optimization in Dispersive Microresonators

The achievement of wideband high-gain optical parametric amplification has not been shown in micrometer-scale cavities. In this paper we have computationally investigated the optical parametric amplification process in a few micrometer-long dispersive microresonator. By performing a gain medium resonance frequency dependent analysis of optical parametric amplification, we have found that it is possible to achieve a wideband high-gain optical amplification in a dispersive microresonator. In order to account for the effects of dispersion (modeled by the polarization damping coefficient) and the resonance frequency of the gain medium on optical parametric amplification, we have solved the wave equation in parallel with the nonlinear equation of electron cloud motion, using the finite difference time domain method. Then we have determined the resonance frequency values that yield an enhanced or a resonant case of optical parametric amplification, via gain factor optimization. It was observed that if the microresonator is more dispersive (has a lower polarization damping coefficient), then there are more resonance frequencies that yield an optical gain resonance. At these gain resonances, a very wideband, high-gain optical amplification seems possible in the micron scale, which, to our knowledge, has not been previously reported in the context of nonlinear wave mixing theory.

Demonstration of Tunable Optical Aggregation of QPSK to 16-QAM Over Optically Generated Nyquist Pulse Trains Using Nonlinear Wave Mixing and a Kerr Frequency Comb

A tunable and reconfigurable optical aggregation system is experimentally demonstrated. Optical Nyquist pulses are generated on multiple channels using a microresonator-based Kerr optical frequency comb and insertion of uniform lines by an intensity modulator. Data are modulated on optically generated Nyquist pulses and aggregated through nonlinear wave mixing in a periodically poled lithium niobate (PPLN) waveguide. Two quadrature-phase-shift-keying (QPSK) channels are aggregated to a single 16-quadrature amplitude modulation (16-QAM) channel of Nyquist pulses. To demonstrate the system tunability, we perform aggregation over different baud rates and different modulation formats. The reconfigurability of the system is demonstrated by aggregating two binary-phase-shift-keying (BPSK) channels into a QPSK or a 2-level amplitude-shift keying and a 2-level phase-shift keying (2-ASK/2-PSK) channel by tuning the relative phase and amplitude of the inputs. Furthermore, three BPSK channels are aggregated into one 4-ASK/2-PSK channel. The quality of the aggregated channel is investigated using two different approaches for wave mixing in the PPLN waveguide.

Demonstration of wavelength tunable optical modulation format conversion from 20 and 30 Gbit/s QPSK to PAM4 using nonlinear wave mixing

We experimentally demonstrate tunable modulation format conversion of quadrature phase shift keying (QPSK) to four-level pulse amplitude modulation (PAM4) using nonlinear wave mixing in periodically-poled Lithium-Niobate (PPLN) waveguides. The conversion operation is accomplished by: (a) rotating the data constellation by applying a phase offset, and (b) offsetting the data constellation in the radial direction by adding a constant bias optical power. In this manner, the constellation data points can be tailored to have different amplitude levels, thus realizing the PAM4 format. In a tunable fashion, we convert 20- and 30-Gbit/s QPSK channels to PAM4, and open eye diagrams and low bit-error-rates (BER) are obtained at the receiver. We investigate the impact of phase rotation on the eye diagram of the received signal, and we determine that a phase rotation of ∼71°provides substantially good performance. Wavelength tunability of the output PAM4 is demonstrated by tuning the wavelength of the pump. In addition, open eye is also obtained when a high phase noise laser is used for modulating QPSK signal.

Numerical modeling of collinear mixing of compressional and shear waves in nonlinear elastic media using the iterative nonlinear contrast source method

In nondestructive testing, nonlinear wave mixing could be used to obtain the nonlinearity parameters of an elastic medium and thereby get information about its state, e.g., aging and fatigue. To better understand the mixing mechanisms and optimize the design of measurement setups, a physics-oriented tool for the simulation of nonlinear elastic wave propagation would be valuable. In this presentation, we extend the iterative nonlinear contrast source method (INCS) to study the nonlinear mixing of two plane, collinear bulk waves (one compressional, one shear) in a homogeneous, isotropic, elastic medium with two independent coefficients of nonlinearity (βL and βT). The method successfully captured the resonant wave generated due to the mixing (one-way and two-way) of primary waves of different frequencies. The obtained results for the resonant wave were in good agreement with the results reported in the literature. In addition, the contrast source allowed the propagating and evanescent components of the scattered wave field to be studied in the wavenumber-frequency domain, which provides physical insight into the mixing process and explains the propagation direction of the scattered wave. Thus, the INCS method seems to be a useful tool to investigate and predict wave mixing in nonlinear elastic media.

Experimental demonstration of tunable de-aggregation from 16-QAM to 4-PAM for two wavelength multiplexed channels using wave mixing in a single nonlinear element to map constellation onto axes

We experimentally demonstrate tunable de-aggregation of two data carrying optical channels using nonlinear wave mixing. For each channel, the signal and its conjugate are coherently added and subtracted in order to map the constellation points onto real and imaginary axes, respectively. Each of two 10 and 15 Gbaud optical channels with a format of 16-quadrature amplitude modulation (16-QAM) are de-aggregated into two 4-level pulse amplitude modulation (4-PAM) signals. We use the same technique to de-aggregate quadrature phase shift keying (QPSK) signals into two binary phase shift keying (BPSK) signals at baud rates of 10 and 15 Gbaud for both channels. System performance is evaluated in terms of the optical signal-to-noise ratio (OSNR), and penalty of ∼0.7 dB is observed at bit error rate (BER) of 10−3.

Nonradiating photonics with resonant dielectric nanostructures

AbstractNonradiating sources of energy have traditionally been studied in quantum mechanics and astrophysics but have received very little attention in the photonics community. This situation has changed recently due to a number of pioneering theoretical studies and remarkable experimental demonstrations of the exotic states of light in dielectric resonant photonic structures and metasurfaces, with the possibility to localize efficiently the electromagnetic fields of high intensities within small volumes of matter. These recent advances underpin novel concepts in nanophotonics and provide a promising pathway to overcome the problem of losses usually associated with metals and plasmonic materials for the efficient control of light-matter interaction at the nanoscale. This review paper provides a general background and several snapshots of the recent results in this young yet prominent research field, focusing on two types of nonradiating states of light that both have been recently at the center of many studies in all-dielectric resonant meta-optics and metasurfaces: opticalanapolesand photonicbound states in the continuum. We discuss a brief history of these states in optics, as well as their underlying physics and manifestations, and also emphasize their differences and similarities. We also review some applications of such novel photonic states in both linear and nonlinear optics for the nanoscale field enhancement, a design of novel dielectric structures with high-Qresonances, nonlinear wave mixing, and enhanced harmonic generation, as well as advanced concepts for lasing and optical neural networks.

Integration of cascaded electro-optic and nonlinear processes on a lithium niobate on insulator chip.

Cascading of the electro-optic (EO) effect and nonlinear wave mixing can provide a way to manipulate photonic conversion in an electrically controllable manner. Here we experimentally demonstrate simultaneous transverse EO coupling and second-harmonic generation (SHG) in a periodically poled lithium niobate on insulator ridge waveguide. With tight light confinement, large EO, and nonlinear coefficients in the LNOI waveguide, the integrated device features a low-voltage fast-speed response for EO coupling and efficient conversion for SHG. The proposed scheme holds promise in realizing electrically controllable on-chip nonlinear devices.

Nondestructive evaluation of thermal aging of adhesive joints by using a nonlinear wave mixing technique

This paper describes the use of a wave mixing technique to monitor thermal aging of adhesive joints. This newly developed technique measures the acoustic nonlinearity parameter of the adhesive in the joint. One of the significant features of this technique is that it requires only one-side access to the adhesive joint being measured, which significantly increases the technique's utility in field applications. To demonstrate the effectiveness of the new technique, measurements are conducted on adhesively joined samples that are thermally aged under different heating conditions, i.e., different temperature profiles and aging times. The results show that the measured acoustic nonlinearity parameter of the adhesive is very sensitive to thermal aging. On the other hand, linear reflection from the adhesive layer remains almost a constant among all the aging conditions investigated in this study. It is therefore concluded that the acoustic nonlinearity parameter is a much more sensitive measure of thermal aging of adhesive joints.

Difference frequency generation of ultraviolet from x-ray pulses in opaque materials

We suggest a new approach for observing x-ray nonlinear wave mixing in opaque materials. We focus on difference frequency generation of ultraviolet radiation from two short x-ray pulses by measuring the depletion of the pumping pulses. Like other processes involving nonlinear interactions between x-rays and longer wavelengths, our method can lead to the development of a probe for spectroscopy of valence electrons at the atomic scale resolution. The two main advantages of the method we propose over the direct observation of the generated signal are the ability to probe the properties of materials at wavelengths where they are opaque and the higher predicted efficiency in the ultraviolet regime. We describe a possible experimental setup with realistic specifications optimized with respect to the characteristics of the input pulses. We expect that experimental observations of the effect will be feasible with the new emerging high-repetition-rate x-ray free-electron lasers.

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.

Optical Mitigation of Interchannel Crosstalk for Multiple Spectrally Overlapped 20-GBd QPSK/16-QAM WDM Channels Using Nonlinear Wave Mixing

Optical mitigation of interchannel interference (ICI) for multiple spectrally overlapped data channels is experimentally demonstrated without multichannel detection and channel spacing estimation. The ICI mitigation takes place in three stages of periodically poled lithium niobate (PPLN) waveguides. In the first PPLN stage, the conjugate copies of channels are generated. In the second stage, the overlapped signals are coherently multiplexed with different complex taps. In the third stage, the concurrent nonlinear processes and the coherent multiplexing of the signals with their delayed copies compensate the ICI. The bit error rate and the constellation diagrams of wavelength division multiplexed (WDM) channels carrying quadrature phase-shift keying (QPSK) or 16 quadrature amplitude modulation (16-QAM) formats demonstrate the potential capability of the proposed method to reduce the ICI and its possible modulation format transparency. The effect of channel spacing on the performance of the method is also demonstrated. After optical ICI mitigation, a reduction of almost 4 dB is achieved for the value of optical signal-to-noise ratio at BER of 10–3 for 20-GBd QPSK signals with a channel spacing of 17.5 GHz. The overlapped WDM system of 20-GBd 16-QAM signals with channel spacing of 17.5 GHz is also ICI mitigated and error vector magnitudes are reduced by almost 28%.