Second-order Nonlinear Effects Research Articles

Enhanced Second-Harmonic Generation in Thin-Film Lithium Niobate Circular Bragg Nanocavity.

Second-order nonlinearity gives rise to many distinctive physical phenomena, e.g., second-harmonic generation, which play an important role in fundamental science and various applications. Lithium niobate, one of the most widely used nonlinear crystals, exhibits strong second-order nonlinear effects and electro-optic properties. However, its moderate refractive index and etching sidewall angle limit its capability in confining light into nanoscales, thereby restricting its application in nanophotonics. Here, we exploit nanocavities formed by second-order circular Bragg gratings, which support resonant anapole modes, to achieve a 42 000-fold enhanced second-harmonic generation in thin-film lithium niobate. The nanocavity exhibits a record-high normalized conversion efficiency of 1.21 × 10-2 cm2/GW under the pump intensity of 1.9 MW/cm2. Besides, we also show s- and p-polarization-independent second-harmonic generation in elliptical Bragg nanocavities. This work could inspire the study of nonlinear optics at the nanoscale on thin-film lithium niobate, as well as other novel photonic platforms.

Ferroelectric nematic fluids as spontaneous polarization field for enhanced orientational-dependent second-harmonic generation

ABSTRACT Second-order nonlinear optical effects have piqued researchers’ interest in fundamental physics and practical perspectives. The ferroelectric nematic liquid crystals (NF LCs) have recently drawn attention to LC nonlinear optical applications due to their relatively high second-harmonic generation output. Further improving the nonlinear optical properties to get closer to the performance of inorganic nonlinear optical materials is challenging. Here, we take a blending strategy to enhance the nonlinear optical response of a prototype NF LC, DIO. We mixed an organic nonlinear optical crystalline material, 3,5,5-trimethyl (cyclohex-2-enylidene) malononitrile (TCM), with DIO and investigated the effects of TCM doping at various concentrations. We quantitatively determined the second-harmonic generation and spontaneous polarization as functions of temperature and concentration. We found that, compared with the pure DIO, the second-harmonic generation performance increased by about 130% at maximum, 93% in maximum for the nonlinear optical coefficient, and 10% in maximum for spontaneous polarization.

Observation of nonlinear thermoelectric effect in MoGe/Y3Fe5O12

Thermoelectric effects refer to the voltage generation from temperature gradients in condensed matter. Although various power generators are made from them, all the known effects, such as Seebeck effect, require macroscopic temperature gradients; since the sign of the generated voltage is reversed by reversing the temperature gradient, the net voltage disappears when the temperature distribution fluctuates temporarily or spatially with a macroscopic temperature gradient of zero. It is impossible to utilize such temperature fluctuations in the conventional thermoelectric effects, a situation which limits their application. Here we report the observation of a second-order nonlinear thermoelectric effect; we develop a method to measure nonlinear thermoelectricity and observe that a superconducting MoGe film on Y3Fe5O12 generates a voltage proportional to the square of the applied temperature gradient. The nonlinear thermoelectric generation demonstrated here provides a way for making power generators that produce electric power from temperature fluctuations.

Second harmonic generation enhancement based on quasi-BICs in centrosymmetric materials

In centrosymmetric optical materials, the second-order nonlinear polarization of the bulk electric dipolar contribution is zero. More effective utilization of the contribution of the surface term is one of the key methods to efficiently obtain second-order nonlinear responses on these materials. Herein, a design of densely packed slotted nanopillar arrays based on quasi-bound states in the continuum (quasi-BICs) is proposed. The quasi-BICs are analyzed by using the finite element method as an example of silicon and the second harmonic generation (SHG) process is simulated. In the structure, normal-incidence linearly polarized light excites magnetic dipole-like quasi-BICs with a high quality factor which effectively promotes light-matter interactions. Increasing the nanopillar radius or decreasing the lattice constant within a certain range can cause the distribution of quality factors in k-space of the ky direction to contract toward the Γ point, which leads to a quasi-BIC with higher quality factors at the Γ point. By conjunctively adjusting the nanopillar radius and lattice constant or changing the slot azimuth, the resonance wavelength can be adjusted over a wide range (about several hundred nanometers) or finely (within about one nanometer) while maintaining high quality factors. When the symmetry perturbation introduced by the slot is small, it is calculated that the SHG conversion efficiency is about 10−6∼10−5 at an incident light power density of 1 MW/m2, and the SHG power is about 107∼108 times enhancement compared with the structure without slots. As the slot width decreases, higher SHG conversion efficiency with more significant SHG enhancement can be achieved at a specific slot length. The results provide new insights into the modulation of the resonant wavelength and quality factor of quasi-BICs, as well as the control of second-order nonlinear effects in centrosymmetric materials.

Enhanced vertical second harmonic generation from layered GaSe coupled to photonic crystal circular Bragg resonators

Abstract Two-dimensional (2D) layered materials without centrosymmetry, such as GaSe, have emerged as promising novel optical materials due to large second-order nonlinear susceptibilities. However, their nonlinear responses are severely limited by the short interaction between the 2D materials and light, which should be improved by coupling them with photonic structures with strong field confinement. Here, we theoretically design photonic crystal circular Bragg gratings (CBG) based on hole gratings with a quality factor as high as Q = 8 × 103, a mode volume as small as V = 1.18 (λ/n)3, and vertical emission of light field in silicon nitride thin film platform. Experimentally, we achieved a Q value up to nearly 4 × 103, resulting in a 1,200-fold enhancement of second harmonic generation from GaSe flakes with a thickness of 50 nm coupling to the CBG structures under continuous-wave excitation. Our work endows silicon-based photonic platforms with significant second-order nonlinear effect, which is potentially applied in on-chip quantum light sources and nonlinear frequency conversion.

Limitations of mean-field approximations in describing shift-current and injection-current in materials

We theoretically and computationally investigate bulk photovoltaic effects, with a specific focus on shift-current and injection-current. Initially, we perform a numerical analysis of the direct current (dc) induced by a laser pulse with a one-dimensional model, utilizing mean-field theories such as time-dependent Hartree–Fock and time-dependent Hartree methods. Our numerical results, obtained with mean-field theories, reveal that the dc component of the current, as a second-order nonlinear effect, exists even after irradiation with linearly polarized light as a second-order nonlinear effect, indicating the generation of injection-current. Conversely, when we employ the independent-particle approximation, no injection-current is generated by linearly polarized light. To develop the microscopic understanding of injection-current within the mean-field approximation, we further analyze the dc component of the current with the perturbation theory, employing the mean-field approximations, the independent-particle approximation, and the exact solution of the many-body Schrödinger equation. The perturbation analysis clarifies that the injection-current induced by linearly polarized light under the mean-field approximations is an artifact caused by population imbalance, created through quantum interference from unphysical self-excitation pathways. Therefore, investigation of many-body effects on the bulk photovoltaic effects have to be carefully conducted in mean-field schemes due to potential contamination by unphysical dc current. Additionally, we perform the first-principles electron dynamics calculation for BaTiO3 based on the time-dependent density functional theory, and we confirm that the above findings from the one-dimensional model calculation and the perturbation analysis apply to realistic systems. Published by the American Physical Society 2024

Kerr-Enhanced Optical Spring.

We propose and experimentally demonstrate the generation of enhanced optical springs using the optical Kerr effect. A nonlinear optical crystal is inserted into a Fabry-Perot cavity with a movable mirror, and a chain of second-order nonlinear optical effects in the phase-mismatched condition induces the Kerr effect. The optical spring constant is enhanced by a factor of 1.6±0.1 over linear theory. To our knowledge, this is the first realization of optomechanical coupling enhancement using a nonlinear optical effect, which has been theoretically investigated to overcome the performance limitations of linear optomechanical systems. The tunable nonlinearity of demonstrated system has a wide range of potential applications, from observing gravitational waves emitted by binary neutron star postmerger remnants to cooling macroscopic oscillators to their quantum ground state.

Plasmonic hotspot arrays boost second harmonic generation in thin-film lithium niobate

Focusing light down to subwavelength scales to enhance the light-matter interaction has been highly sought after, which has promoted significant researches and applications in nanophotonics. Plasmonic nanoantennae are a significant tool to achieve this goal since they can confine light into ultra-small volumes far below the diffraction limit. However, metallic materials have the property of central symmetry, resulting in weak second-order nonlinear effects. Here, we design plasmonic bowtie nanoantennae on thin-film lithium niobate (TFLN) for deep-subwavelength light confinement to boost the second-harmonic generation (SHG) in TFLN via the plasmonic hotspot enhancement. The SHG enhancement factor of about 20 times as compared to unpatterned TFLN is achieved in the experiment when resonantly excited by femtosecond laser. This work proposes a route for subwavelength nonlinear optics on the TFLN platform.

From C4H7N2Ge0.4Sn0.6Br3 to C6H11N2Ge0.4Sn0.6Br3: Effective Modulation of the Second Harmonic Generation Effect and Optical Band Gap by Planar π-Conjugated Organic Cation Size.

In the search for nonlinear optical (NLO) materials with excellent overall performance, we have devoted ourselves to organic-inorganic hybrids consisting of anionic groups containing stereochemically active lone-pair (SCALP) electron cations and organic planar π-conjugated group cations. Accordingly, in this paper, two novel organic-inorganic hybrid metal halides, C4H7N2Ge0.4Sn0.6Br3 (I) and C6H11N2Ge0.4Sn0.6Br3 (II), have been synthesized. The powder second-harmonic technique shows that both C4H7N2Ge0.4Sn0.6Br3 and C6H11N2Ge0.4Sn0.6Br3 have moderately strong second-order nonlinear optical effects, which are about 2.03 (I) and 1.16 (II) times that of KH2PO4 (KDP), respectively. They also have different optical band gaps of 2.75 (I) and 2.88 eV (II) due to the different sizes of the organic cations, and their photoluminescent and thermal properties were also investigated. This work provides new structural insights for the design and modulation of organic-inorganic hybrid halide materials with multiple excellent optical properties.

Giant intrinsic photovoltaic effect in one-dimensional van der Waals grain boundaries

The photovoltaic effect lies at the heart of eco-friendly energy harvesting. However, the conversion efficiency of traditional photovoltaic effect utilizing the built-in electric effect in p-n junctions is restricted by the Shockley-Queisser limit. Alternatively, intrinsic/bulk photovoltaic effect (IPVE/BPVE), a second-order nonlinear optoelectronic effect arising from the broken inversion symmetry of crystalline structure, can overcome this theoretical limit. Here, we uncover giant and robust IPVE in one-dimensional (1D) van der Waals (vdW) grain boundaries (GBs) in a layered semiconductor, ReS2. The IPVE-induced photocurrent densities in vdW GBs are among the highest reported values compared with all kinds of material platforms. Furthermore, the IPVE-induced photocurrent is gate-tunable with a polarization-independent component along the GBs, which is preferred for energy harvesting. The observed IPVE in vdW GBs demonstrates a promising mechanism for emerging optoelectronics applications.

Resonant x-ray difference frequency generation

Resonantly enhanced x-ray difference-frequency generation (re-XDFG) is a second-order nonlinear effect that involves illuminating a molecule with two-color x-ray pulses with photon energies Ω1 and Ω2. The energy difference is tuned to match an x-ray absorption edge of an atom in the molecule. We have numerically studied the re-XDFG effect considering different individual molecules in the gas phase using density functional theory calculations and have verified the non-centrosymmetric character of the target transitions. Two-level molecular systems with permanent dipoles are evaluated for the description of re-XDFG taking into account different two-color input pulse geometries. This innovative nonlinear x-ray methodology offers a means to measure the K-edge NEXAFS spectrum of light elements, such as carbon, nitrogen, or oxygen, in dense media using non-resonant x-rays. It can also be used to investigate chemical material dynamics that are inaccessible by linear spectroscopy. These findings enable the combination of atomic-scale structure with chemical specificity and the selective and local access to x-ray excitations using hard x-ray pulses.

Nonreciprocal Transport and Optical Phenomena in Quantum Materials

In noncentrosymmetric materials, the responses (for example, electrical and optical) generally depend on the direction of the external stimuli, called nonreciprocal phenomena. In quantum materials, these nonreciprocal responses are governed by the quantum geometric properties and symmetries of the electronic states. In particular, spatial inversion ([Formula: see text]) and time-reversal ([Formula: see text]) symmetries play crucial roles, which are also relevant to the geometric Berry phase. Here, we give a comprehensive review of the nonreciprocal transport and optical responses including ( a) the magnetochiral anisotropy, i.e., the nonlinear resistivity with respect to the electric field, in semiconductors and metals, ( b) the nonreciprocal transport in superconductors such as the nonreciprocal paraconductivity and the superconducting diode effect in bulk and Josephson junctions, and ( c) the second-order nonlinear optical effects in the electric field of light, including the geometric shift current in nonmagnetic systems, magnetic systems, and superconductors.

Manipulation of nonlinear optical responses in layered ferroelectric niobium oxide dihalides

Realization of highly tunable second-order nonlinear optical responses, e.g., second-harmonic generation and bulk photovoltaic effect, is critical for developing modern optical and optoelectronic devices. Recently, the van der Waals niobium oxide dihalides are discovered to exhibit unusually large second-harmonic generation. However, the physical origin and possible tunability of nonlinear optical responses in these materials remain to be unclear. In this article, we reveal that the large second-harmonic generation in NbOX2 (X = Cl, Br, and I) may be partially contributed by the large band nesting effect in different Brillouin zone. Interestingly, the NbOCl2 can exhibit dramatically different strain-dependent bulk photovoltaic effect under different polarized light, originating from the light-polarization-dependent orbital transitions. Importantly, we achieve a reversible ferroelectric-to-antiferroelectric phase transition in NbOCl2 and a reversible ferroelectric-to-paraelectric phase transition in NbOI2 under a certain region of external pressure, accompanied by the greatly tunable nonlinear optical responses but with different microscopic mechanisms. Our study establishes the interesting external-field tunability of NbOX2 for nonlinear optical device applications.

Direct generation of a terahertz vector beam from a ZnTe crystal excited by a focused circular polarized pulse.

A vector beam is a type of topological beam in which the polarization direction of light rotates around a singularity on the wavefront. This paper proposes a method to generate a vector beam by tightly focusing a pump beam in the crystalline direction such that the second-order nonlinear optical effect is forbidden. The directional dependence of the effective nonlinearity in zincblende crystals, such as ZnTe, was analytically investigated. Two types of nonlinear polarization singularities were found in [111] and [100] directions. Their polarization topological charge ℓ was +1 and -1, respectively. To experimentally demonstrate the proposed method, a (111) cut ZnTe crystal was selected as the nonlinear crystal. The polarization state of the generated terahertz (THz) beams was measured with a custom-built THz spectroscopic polarization imaging system. Radially polarized distributions were observed within the entire generated spectral region. Such a broadband feature of the generated vector beam is likely due to the topological nature of the focused pump beam, where the wavevectors are winding once about the optical axis. This simple method for generating THz vector beams will accelerate its applications.

Strong bulk photovoltaic effect in engineered edge-embedded van der Waals structures

Bulk photovoltaic effect (BPVE), a second-order nonlinear optical effect governed by the quantum geometric properties of materials, offers a promising approach to overcome the Shockley-Quiesser limit of traditional photovoltaic effect and further improve the efficiency of energy harvesting. Here, we propose an effective platform, the nano edges embedded in assembled van der Waals (vdW) homo- or hetero-structures with strong symmetry breaking, low dimensionality and abundant species, for BPVE investigations. The BPVE-induced photocurrents strongly depend on the orientation of edge-embedded structures and polarization of incident light. Reversed photocurrent polarity can be observed at left and right edge-embedded structures. Our work not only visualizes the unique optoelectronic effect in vdW nano edges, but also provides an effective strategy for achieving BPVE in engineered vdW structures.

Optical rectification and electro-optic sampling in quartz.

We report the electro-optic sampling (EOS) response and the terahertz (THz) optical rectification (OR) of the z-cut α-quartz. Due to its small effective second-order nonlinearity, large transparency window and hardness, freestanding thin quartz plates can faithfully measure the waveform of intense THz pulses with MV/cm electric-field strength. We show that both its OR and EOS responses are broad with extension up to ∼8 THz. Strikingly, the latter responses are independent of the crystal thickness, a plausible indication of dominant surface contribution to the total second-order nonlinear susceptibility of quartz at THz frequencies. Our study introduces the crystalline quartz as a reliable THz electro-optic medium for high field THz detection, and characterize its emission as a common substrate.

Electric-field-induced quasi-phase-matched three-wave mixing in silicon-based superlattice-on-insulator integrated circuits

We present a theoretical investigation, based on the tight-binding Hamiltonian, of efficient electric-field-induced three-waves mixing (EFIM) in an undoped lattice-matched short-period superlattice (SL) that integrates quasi-phase-matched (QPM) SL straight waveguides and SL racetrack resonators on an opto-electronic chip. Periodically reversed DC voltage is applied to electrode segments on each side of the strip waveguide. The spectra of χxxxx(3) and of the linear susceptibility have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces, and by considering all the transitions between valence and conduction bands. The large obtained values ofχxxxx(3) make the (ZnS)3/(Si2)3 short-period SL a good candidate for realizing large effective second-order nonlinearity, enabling future high-performance of the SLOI PICs and OEICs in the 1000-nm and 2000-nm wavelengths ranges. We have made detailed calculations of the efficiency of second-harmonic generation and of the performances of the optical parametric oscillator (OPO). The results indicate that the (ZnS)N/(Si2)M QPM is competitive with present PPLN technologies and is practical for classical and quantum applications.

Anisotropy-enhanced second-harmonic generation from graphene-wrapped nanoparticles

Due to the various applications of second-harmonic generation (SHG), achieving high SHG conversion efficiency is highly appreciated. In this paper, we achieve high SHG conversion efficiency from graphene-wrapped radial anisotropic nanoparticles by combining the strong second-order nonlinear effects of graphene and the field-enhancing effects of anisotropic materials. We find that the nonlinear conversion efficiency of radial anisotropic nanoparticles can be several orders of magnitude higher than that of isotropic counterpart. This is because the radial anisotropic provides the additional enhancement of field intensity near the boundary, and the graphene that provides SHG nonlinear effect is located at the particle boundary where the fundamental frequency field is significantly enhanced. Meanwhile, the highly tunable characteristic of graphene offers additional flexibility for manipulating the SHG spectrum in actual applications. Our results provide a promising method for improving the nonlinear conversion efficiency of photonic devices and the sensitivity of the nonlinear sensor.

Nonlinear Optical Glass-Ceramic From a New Polar Phase-Transition Organic-Inorganic Hybrid Crystal.

Melt-quenched glasses of organic-inorganic hybrid crystals, i.e., hybrid glasses, have attracted increasing attention as an emerging class of hybrid materials with beneficial processability and formability in the past years. Herein, we present a new hybrid crystal, (Ph3 PEt)3 [Ni(NCS)5 ] (1, Ph3 PEt+ =ethyl(triphenyl)phosphonium), crystallizing in a polar space group P1 and exhibiting thermal-induced reversible crystal-liquid-glass-crystal transitions with relatively low melting temperature of 132 °C, glass-transition temperature of 40 °C, and recrystallization on-set temperature of 78 °C, respectively. Taking advantage of such mild conditions, we fabricated an unprecedented hybrid glass-ceramic thin film, i.e., a thin glass uniformly embedding inner polar micro-crystals, which exhibits a much enhanced intrinsic second-order nonlinear optical effect, being ca. 25.6 and 3.1 times those of poly-crystalline 1 and KH2 PO4 , respectively, without any poling treatments.

Achieving enhanced second-harmonic generation in ferroelectric nematics by doping D–π–A chromophores

A fluidic ferroelectric nematic liquid crystal was deployed as a matrix to achieve spontaneous polarization of D–π–A chromophores and realize a dramatic increase in second-harmonic generation.