Second-order Nonlinear Response Research Articles

Ac Hall Effect and Photon Drag of Superconducting Condensates.

We suggest a theoretical description of the photogalvanic phenomena arising in superconducting condensates in the field of electromagnetic wave. The ac Hall effect and photon drag are shown to originate from the second-order nonlinear response of superconducting carriers caused by the suppression of their concentration due to the combined influence of the electron-hole asymmetry and charge imbalance generated by the incident electromagnetic wave. Starting from the time-dependent Ginzburg-Landau theory with the complex relaxation constant, we develop a phenomenological description of these phenomena and investigate the resulting behavior of the dc supercurrent and second harmonic induced by microwave radiation incident on a superconductor surface.

Enhanced second harmonic generation by an atomically thin MoS2 sheet attached to a resonant metasurface.

Two-dimensional transition metal dichalcogenides have shown large second-order nonlinear responses due to their broken crystal inversion symmetry. However, their nonlinear interaction with light is restricted to an atomically thin layer. Placing a sheet of transition metal dichalcogenides on a resonant metasurface enhances the field interacting with the nonlinear material thus compensating for this shortcoming. But, it remains a challenge to tune resonances such, that they coincide with fundamental and second harmonic frequencies simultaneously. Here we demonstrate two independent methods to achieve that goal and numerically illustrate our findings for a MoS2 layer combined with silicon nitride photonic crystals. We numerically demonstrate 20-fold and 170-fold enhancement of second-harmonic generation compared with a design based on a single resonant structure. Although we focus on that specific configuration our approach can likewise be applied to other dielectrics combined with highly nonlinear 2D materials.

Efficient Second-Harmonic Generation from Dielectric Inter-subband Polaritonic Metasurfaces Coupled to Lattice Resonance.

Nonlinear optical metasurfaces offer a possibility to perform frequency mixing without the phase-matching constraints of bulk nonlinear crystals and with control of the local nonlinear response at a sub-wavelength scale. Nonlinear inter-subband polaritonic metasurfaces created by combining the semiconductor heterostructures with quantum-engineered inter-subband nonlinear response and electromagnetically engineered metal-clad nanoresonators offer by far the largest second-order nonlinear response of all condensed matter systems reported to date. However, the nonlinear optical response of these metasurfaces is limited by optical intensity saturation in the nanoresonator hot spots that prevented the achievement of power conversion efficiencies over 0.2% in three-wave mixing experiments. In this study, we propose and experimentally demonstrate dielectric inter-subband polaritonic metasurfaces for second-harmonic generation that achieve 0.37% power conversion efficiency. Our structure is created by a new design approach that combines dielectric resonators inducing Mie resonant modes with a lattice resonance to achieve a uniform and high field enhancement throughout the meta-atom volume.

Maneuverability indices estimation of nonlinear response model based on full-scale trial data and square root unscented Kalman filter

Research on ship maneuvering performance provides a theoretical reference for autonomous ship navigation control. The gain and time coefficients accurately describe the dynamic performance of the ship. Given the challenge that the unscented Kalman filter cannot ensure the nonnegativity of the state covariance matrix during the filtering process, this study proposed a parameter identification scheme for a second-order nonlinear response model based on the square root unscented Kalman filter. First, the maneuverability indices of the free-running model were identified based on simulation data. Thereafter, the feasibility and convergence performance of the proposed scheme were verified. Based on full-scale trial data with uncertainty interference, the parameters of the second-order nonlinear response model were estimated for the YUKUN ship. The feasibility, effectiveness, and generalizability of the proposed scheme were further verified. The proposed scheme was analyzed based on three perspectives: parameter convergence, estimation results of the maneuverability indices, and yaw angle prediction results. The results obtained using the proposed algorithm were compared with those obtained using the extended Kalman filter. Finally, the proposed scheme can provide a reference for online parameter identification and prior knowledge for course keeping controllers and autonomous navigation control.

Nonlinear Photocurrent Responses in Janus WSSe Monolayer

Janus WSSe monolayer is a novel two-dimensional (2D) material that breaks the out-of-plane mirror symmetry and has a large built-in electric field. These features lead to sizable Rashba spin-orbit coupling and enhanced nonlinear optical properties, making it a promising material platform for various spintronic and optoelectronic device applications. In recent years, nonlinear photocurrent responses such as shift and injection currents were found to be closely related to the quantum geometry and Berry curvature of materials, indicating that these responses can serve as powerful tools for probing the novel quantum properties of materials. In this work, we investigate the second-order nonlinear photocurrent responses in a Janus WSSe monolayer theoretically based on first-principles calculations and the Wannier interpolation method. It is demonstrated that the Janus WSSe monolayer exhibits significant out-of-plane nonlinear photocurrent coefficients, which is distinct from the non-Janus structures. Our results also suggest that the second-order nonlinear photocurrent response in the Janus WSSe monolayer can be effectively tuned by biaxial strain or an external electric field. Thus, the Janus WSSe monolayer offers a unique opportunity for both exploring nonlinear optical phenomena and realizing flexible 2D optoelectronic nanodevices.

Custom Nonlinearity Profile for Integrated Quantum Light Sources

Heralded single-photon sources are a fundamental building block for optical quantum technologies. These sources need to be unfiltered and integrated to have good scalability and avoid unnecessary losses. To attain this goal, it is necessary to control the effective nonlinearity seen by the fields as they mix and propagate in a waveguide source. In this paper, we introduce a method to design nonlinear waveguides with arbitrarily shaped effective nonlinearity profiles. The method takes advantage of the fact that the second-order nonlinear response is a tensor quantity and thus the local effective nonlinearity of a material depends on the propagation direction of the fields participating in the interaction. Thus, by locally changing the propagation direction of the fields we can modulate the wave-mixing process. Our method allows for the waveguide fabrication process to be significantly simplified. The material structure of the waveguide is made by a single crystal, no longer needing oriented patterning or periodic poling. We use our method to design waveguides with a nonlinearity profile that is Gaussian in the propagation length, allowing the generation of perfectly pure heralded single photons.

Symmetry dictionary on charge and spin nonlinear responses for all magnetic point groups with nontrivial topological nature.

Recently, charge or spin nonlinear transport with nontrivial topological properties in crystal materials has attracted much attention. In this paper, we perform a comprehensive symmetry analysis for all 122 magnetic point groups (MPGs) and provide a useful dictionary for charge and spin nonlinear transport from the Berry curvature dipole, Berry connection polarizability and Drude term with nontrivial topological nature. The results are obtained by conducting a full symmetry investigation of the matrix representations of six nonlinear response tensors. We further identify every MPG that can accommodate two or three of the nonlinear tensors. The present work gives a solid theoretical basis for an overall understanding of the second-order nonlinear responses in realistic materials.

Nonlinear optical responses in noncentrosymmetric superconductors

The unique nonreciprocal responses of superconductors, which stem from the Cooper pairs' quantum condensation, have been attracting attention. Recently, theories of the second-order nonlinear response in noncentrosymmetric superconductors were formulated based on the Bogoliubov-de Gennes theory. In this paper, we study the mechanism and condition for second-order optical responses of time-reversal symmetric superconductors. The numerical results show the characteristic photocurrent and second harmonic generation in the superconducting state. However, the superconductivity-induced nonlinear optical responses disappear under some conditions on pair potential. We show that the coexistence of intraband and interband pairing is necessary for the second-order superconducting optical responses. In addition, the superconducting Berry curvature factor, which is related to a component of Berry curvature in the superconducting state, is essential for the nonlinear responses. Thus, we derived the microscopic conditions where the superconducting nonlinear response appears.

Research progress of bulk photovoltaic effect in two-dimensional materials

The bulk photovoltaic effect is a second-order nonlinear photoelectric response, which refers to a phenomenon that non-centrosymmetric structural material generates a steady-state photocurrent under uniform light irradiation. The bulk photovoltaic effect has attracted widespread attention due to its open-circuit voltage is not limited by the semiconductor bandgap and power conversion efficiency breaks through the Shockley-Queisser limit. In addition, the bulk photovoltaic effect is closely related to the quantum geometric properties (such as Berry curvature and quantum metric) of solids, thus making it an effective means to study crystal polarization, orbital magnetization, and quantum Hall effects. Two-dimensional (2D) materials are rich in electrical, optical, magnetic, topological properties and their interactions, which can effectively improve the performances of bulk photovoltaic devices (such as expanding response range of bulk photovoltaic effect) and have important research value for exploring basic physical problems. This paper reviews the development process of bulk photovoltaic effect and its physical mechanism. The research progress of bulk photovoltaic effect in 2D materials is discussed in detail, including single component 2D materials, 2D material stacking engineering (such as 2D material homojunctions and heterojunctions), and other factors (such as magnetic field, strain engineering) to generate or regulate the bulk photovoltaic effect response. Finally, the development prospect of two-dimensional bulk photovoltaic effect is prospected.

Efficient second-order nonlinear response and upconversion emission from a wide-bandgap quasi-1D lead bromide perovskite

In this work, a new quasi-1D lead bromide perovskite with efficient second-harmonic generation and unexpectedly anomalous green PL phenomenon is developed. The second-order NLO coefficient is about 0.1 pm V−1, 1/4 times that of the commercial crystal KH2PO4 (KDP).

An exact and compact formula for the optical intersubband response of finite-barrier quantum wells, wires and dots

The optical response of quantum wells, wires and dots is frequently modelled without including continuum states. This is reasonable in a low-energy regime but fails to capture phenomena such as bound-to-continuum transitions. We show that, in fact, the full optical intersubband response of quantum confined structures can be expressed in an exceedingly simple exact formula for arbitrary barrier height, confinement dimension, and optical frequency. We illustrate the consequences of transitions reaching the continuum for several representative cases, including asymmetric quantum wells. Moreover, we derive a simple modification that may be added to bound-states-only simulation in order to include the continuum. For the asymmetric quantum well, both linear and second-order nonlinear response is obtained. Finally, excellent agreement with measured bound-to-continuum absorption in narrow quantum wells is demonstrated.

Switching of second-order nonlinear response effected by different acceptors: The impacts of environment and frequency dispersion

In this work, the second-order nonlinear optical (NLO) switch features and electron transition properties for a series of donor-acceptor Stenhouse adducts (DASAs) were explored. The systems we studied contain of a given diethylamine donor and different acceptors, which can be photoinduced from open form to closed form. The calculation results show a remarkable difference in the first hyperpolarizability (β) value between two configurations for each of studied systems, revealing a conspicuous NLO switch feature. Interestingly, in the conditions of gas phase, solid phase polarization effects or frequency dispersion effects, the introduction of indandione acceptor demonstrates the most significant NLO switch feature due to the largest βopen/βclose ratio of compound 5. In general, the differences in the degree of π-electron conjugation and electron transition property between two configurations are responsible for the contrast of NLO response. Our work reveals the features of NLO switch on structure and electron transition property, which will provide some guidance for designing high performance NLO materials.

Enhanced second-harmonic generation in monolayer MoS2 on suspended metallic nanostructures by plasmonic resonances

Abstract Monolayer transition metal dichalcogenides (TMDs) possess large second-order nonlinear responses due to the broken inversion symmetry, which can extend their intriguing applications in nonlinear nanophotonics and optoelectronics. However, the atomic thickness of monolayer TMDs severely decreases the interaction length with free light with respect to bulk materials, leading to rather low second-harmonic generation (SHG) conversion efficiency. Here, we demonstrate a hybrid structure consisting of a monolayer MoS2 on a suspended perforated silver film, on which the SHG signal emitted from the monolayer MoS2 is enhanced by more than three orders of magnitude at room temperature. The pronounced SHG enhancement is attributed to the distinct electric field amplification nearby the nanoholes, which is induced by the symmetric surface plasmon polaritons (SPPs) existing in the ultrathin suspended silver grating. Our results reported here may establish the substrate-free engineering of nonlinear optical effects via plasmonic nanostructures on demand.

Circular photogalvanic effect

The spin and valley degree of freedom are a novel way to extend the functionalities of spintronic and valleytronic devices. A traditional, room-temperature way of examining the spin polarization generates the photocurrent whose magnitude and polarity depend on chirality of induced optical excitation. The circularly polarized photovoltaic effect is a kind of second-order nonlinear photoelectric response, which means that the photocurrent generated varies with the polarization angle of circularly polarized light. The generation of photocurrent depends on many factors such as spin, valley polarization, symmetry and Berry curvature, so it can reveal the fundamental physical properties of materials. In this review, we discuss the main mechanisms of circularly polarized photovoltaic effect in different material systems, including circularly polarized optical current caused by symmetry breakdown of Rashba spin-orbit coupling in semiconductor heterojunction, the electron momentum selection caused by Berry curvature and Pauli blocking in topological Weyl semimetals, and the valley polarization current generated by circularly polarized light in TMDC. Additionally, the recent progress of applications of circular photogalvanic effect is also presented.

Impact of van der Waals interactions on the structural and nonlinear optical properties of azobenzene switches.

The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in the meta-position with functional groups of different bulkiness are investigated using various ab initio and density functional approximations. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that London dispersion interactions existing between bulky meta-substituents stabilize the Z conformer. The ωB97X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of the molecules. We show that density functional approximations should include no less than 50% of Hartree-Fock exchange to provide accurate hyperpolarizabilities. A property-structure analysis of the azobenzene derivatives reveals that the main contribution to the first hyperpolarizability comes from the azo bond, but phenyl meso-substituents can enhance it.

High-order nonlinear response correction method for infrared radiation detector

The infrared detector can generate nonlinear response error when the Fourier transform infrared spectrometer is used for implementing the radiometric calibration or observing the high temperature targets. Based on the relationship between the incident radiation intensity and the electron concentration in the optical conduction band, the mechanism of the nonlinear response error caused by the high incident photon flow is analyzed. According to Planck radiation law and interference principle, the effect of nonlinear error on spectrum is studied by simulating blackbody radiation data with nonlinear error. It is found that the nonlinear response with a different order has a different influence region, and the higher-order nonlinear response has a wider influence range and generates a larger nonlinear response error. By the general nonlinear response correction method the nonlinear response coefficient is obtained through constructing the nonlinear response model of the interference data and then the spectral distortion produced by the detector is corrected. According to the convolution iteration method, the polar orbit meteorological satellite CrIS constructs the convolution equation to correct the second-order nonlinear response by taking the low-wave number band of 50－500 cm<sup>–1</sup> as the characteristic region. The European Meteorological Agency’s Airborne Infrared Interferometer Evaluation System (ARIES) selected two feature areas, 50－500 cm<sup>–1</sup> and 2000－2500 cm<sup>–1</sup>, and iteratively corrected the second-order and third-order nonlinear response. The gradient descent method is often used to solve the optimization problems of unconstrained multivariate functions. Based on the gradient descent algorithm, an iterative method suitable for correcting the high-order nonlinear response errors is proposed in this paper. In this method, the information about the iteration point is obtained by constructing the nonlinear response function of the high-order detector and setting the appropriate iteration initialization. According to the initial value of the iteration and the information about the known iteration point, the gradient of the iteration variable is calculated to determine the iteration value of the next unknown variable, thus quickly searching for the global minimum point and determining the nonlinear response coefficient. We use Fourier transform infrared spectrometer to carry out radiometric calibration experiment and compare the effects of three correction methods: convolution, cross iteration and gradient descent method. The results show that the three correction methods can effectively reduce the nonlinear error, and improve the fitting extent by 0.15%, 0.29% and 0.39% respectively. The spectral data corrected by gradient descent method are more accurate.

Salicylideneaniline-Based Covalent Organic Frameworks: A New Family of Multistate Second-Order Nonlinear Optical Switches

This work demonstrates that covalent organic frameworks (COFs) can exhibit large second-order nonlinear (NLO) responses and that these NLO responses can be modulated as a function of successive eno...

Microscopic quantum description of second-order nonlinearities in two-dimensional hexagonal nanostructures beyond the Dirac cone approximation

Single layers of hexagonal two-dimensional nanostructures such as graphene, silicene, and germanene exhibit large carrier Fermi velocities and, consequently, large light-matter coupling strength making these materials promising elements for nano-opto-electronics. Although these materials are centrosymmetric, the spatial dispersion turns out to be quite large allowing the second-order nonlinear response of such materials to be comparable to the non-centrosymmetric 2D ones. The second-order response of massless Dirac fermions has been extensively studied, however a general approach correct over the full Brillouin zone is lacking so far. To complete this gap, in the current paper we develop a general quantum-mechanical theory of the in-plane second-order nonlinear response beyond the Dirac cone approximation and applicable to the full Brillouin zone of the hexagonal tight-binding nanostructures. We present explicit calculation of the nonlinear susceptibility tensor of 2D hexagonal nanostructures applicable to arbitrary three-wave mixing processes.

Large enhancement of second-harmonic generation in MoS2 by one dimensional photonic crystals

Monolayer transition-metal dichalcogenides (TMDCs) with intrinsically broken crystal inversion symmetry have shown large second-order nonlinear responses, providing a new platform for nonlinear light-matter interaction engineering. Integrating two dimensional monolayers with nanoresonators has been demonstrated to enhance the second harmonic generation. Previous designs suffer from the drawbacks of low cavity quality factor and/or small interaction area. In this letter, we demonstrate the enhancement of second harmonic generation by coupling a TMDC monolayer to the guided-mode resonances of a one-dimensional photonic crystal, showing a 170-fold enhancement of the generated signal relative to a bare monolayer. The work shows a way towards silicon chip-integrated nonlinear devices based on two dimensional materials.

Recent advances in graphene and black phosphorus nonlinear plasmonics

Abstract Over the past decade, the plasmonics of graphene and black phosphorus (BP) were widely recognized as promising media for establishing linear and nonlinear light-matter interactions. Compared to the conventional metals, they support significant light-matter interaction of high efficiency and show undispersed optical properties. Furthermore, in contrast to the conventional metals, the plasmonic properties of graphene and BP structure can be tuned by electrical and chemical doping. In this review, a deep attention was paid toward the second- and third-order nonlinear plasmonic modes of graphene and BP. We present a theoretical framework for calculating the lifetime for surface plasmons modes of graphene and BP assisted by the coupled mode theory. The effect of the Fermi energy on the second-order and third-order nonlinear response is studied in detail. We survey the recent advances in nonlinear optics and the applications of graphene and BP-based tunable plasmonic devices such as light modulation devices, switches, biosensors, and other nonlinear photonic devices. Finally, we highlight a few representative current applications of graphene and BP to photonic and optoelectronic devices.