Ferroelectric topologies in BaTiO3 nanomembranes for light field manipulation

Ferroelectric topological textures in oxides exhibit exotic dipole-moment configurations that would be ideal for nonlinear spatial light field manipulation. However, conventional ferroelectric polar topologies are spatially confined to the nanoscale, resulting in a substantial size mismatch with laser modes. Here we report a dome-shaped ferroelectric topology with micrometre-scale lateral dimensions using nanometre-thick freestanding BaTiO3 membranes and demonstrate its feasibility for spatial light field manipulation. The dome-shaped topology results from a radial flexoelectric field created through anisotropic lattice distortion, which, in turn, generates centre-convergent microdomains. The interaction between the continuous curling of dipoles and light promotes the conversion of circularly polarized waves into vortex light fields through nonlinear spin-to-orbit angular momentum conversion. Further dynamic manipulation of vortex light fields can also be achieved by thermal and electrical switching of the polar topology. Our work highlights the potential for other ferroelectric polar topologies in light field manipulation.

Vortex solitons in quasi-phase-matched photonic crystals with competing quadratic and cubic nonlinearity

We introduce a methodology for investigating vortex solitons (VSs) within quasi-phase-matched (QPM) photonic crystals, featuring competing quadratic and cubic nonlinearities. The photonic crystal is introduced with a checkerboard structure, which is feasible through contemporary technological advancements. The VS family is constructed as quadrupole and 8-pole configurations, with the quadrupole solitons displaying rhombus and square modes depending on different phase-matching conditions. Notably, an intriguing transformation from the quadrupole to the 8-pole configuration can be achieved by modulating the cubic nonlinear coefficient. Additionally, the square-shaped VSs would transfer to rhombus patterns by adjusting the power and size of the checkerboard cell in the framework of cubic nonlinearity. This work presents a versatile and powerful tool for exploring and manipulating vortex solitons in QPM photonic structures, with potential applications in optical signal processing, optical communications, and nonlinear optics research.

A layered Janus metastructure for multi-physical quantity detection based on the second harmonic wave

In the field of nonlinear optics and physical quantity detection, the use of the second harmonic wave (SHW) generated in ferroelectric crystals is proposed to realize multi-physical quantity detection with the Janus property. In view of the single physical quantity detected by the current research and the single application scenario, this paper proposes a multi-functional and novel nonlinear Janus metastructure (NJMS), which exploits the SHW to achieve highly sensitive multi-physical quantity detection in the terahertz frequency range and shows Janus properties in both the forward and backward directions of the system. The NJMS is realized to detect refractive indices, thicknesses, and angles with different modes in the forward and backward directions. The proposed NJMS broadens the application scenario of the SHW and provides a novel idea for the research of multi-physical quantity detection devices with the Janus property.

Nonlinear geometric phase coded ferroelectric nematic fluids for nonlinear soft-matter photonics

Simultaneous manipulation of multiple degrees of freedom of light lies at the heart of photonics. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting incident light into beams of new frequencies with spatially varied phase, amplitude, and angular momenta. Nevertheless, the reconfigurable control over structured light fields for advanced multimode nonlinear photonics remains a grand challenge. Here, we propose the concept of nonlinear geometric phase in an emerging ferroelectric nematic fluid, of which the second-order nonlinear susceptibility carries spin-dependent nonlinearity phase. A case study with photopatterned q-plates demonstrates the generation of second-harmonic optical vortices with spin-locked topological charges by using cascaded linear and nonlinear optical spin-orbit interactions. Furthermore, we present the dynamic tunability of second-harmonic structured light through temperature, electric field, and twisted elastic force. The proposed strategy opens new avenues for reconfigurable nonlinear photonics, with potential applications in optical communications, quantum computing, high-resolution imaging, etc.

Quasicrystal metasurface for optical holography and diffraction

Quasicrystal metasurfaces, a kind of two-dimensional artificial optical materials with subwavelength meta-atoms arranged in quasi-periodic tiling schemes, have attracted extensive attentions due to their novel optical properties. In a recent work, a dual-functional quasicrystal metasurface, which can be used to simultaneously generate the diffraction pattern and holographic image, is experimentally demonstrated. The proposed method expands the manipulation dimensions for multi-functional quasicrystal metasurfaces and may have important applications in microscopy, optical information processing, optical encryption, etc.

K2HgGe3Se8: A Quaternary Hg-Based Selenide with Nonlinear Optical Properties

A new quaternary Hg-based selenide K2HgGe3Se8 was successfully synthesized and characterized as an engaging infrared (IR) nonlinear optical (NLO) material, which crystallizes in the P21 space group of the noncentrosymmetric monoclinic crystal system. The crystal structure of K2HgGe3Se8 is characterized by the stacking of countless [ H g G e 3 S e 8 ] 2 - ∞ 2 layers with K+ cations filling the interlayers. The UV-vis-NIR diffuse reflectance spectrum shows that K2HgGe3Se8 possesses an indirect band gap of 2.13 eV. The second harmonic generation (SHG) response of K2HgGe3Se8 is approximately 1.1 times that of AgGaS2 (AGS) within the particle size of 20-50 μm along with a nonphase-matching (NPM) behavior at 2090 nm, as indicated by the SHG test. K2HgGe3Se8 also has a large powder laser-induced damage threshold (∼ 2.3 × AGS). As revealed by theoretical calculations, the optical properties of K2HgGe3Se8 are predominantly determined by [HgSe4] and [GeSe4] tetrahedra, and K2HgGe3Se8 possesses a calculated optical band gap of 1.44 eV together with a maximum SHG coefficient d22 of -7.70 pm V-1.

Lithium niobate on insulator - fundamental opto-electronic properties and photonic device prospects

Lithium niobate on insulator (LNOI) combines a variety of optoelectronic properties and can meet practical performance requirements that are uncommon in optoelectronic materials. This review introduces the fundamentals and the photonic device concepts that arise from the LNOI materials platform. Firstly, the nonlinear optical response of LNOI is presented, including birefringent phase matching (BPM), modal phase matching (MPM), and quasi-phase matching (QPM). The tunable properties are also introduced, including electro-optical (EO), thermo-optical (TO), and acousto-optical (AO) effects. The structures of nonlinear optical devices, such as ridge waveguides (including periodically polarized inversion waveguides), Mach-Zehnder interferometer (MZI) modulators and micro-resonators (such as disks and rings) are demonstrated. Finally, the future of LNOI devices is discussed. In the already mature and developed optoelectronic material systems, it is rare to find one particular material system supporting so many basic optical components, photonic devices and optoelectronic devices as LNOI does in the field of integrated photonic chips.

Contrast-enhanced phase-resolved second harmonic generation microscopy

The characterization of inverted structures (crystallographic, ferroelectric, or magnetic domains) is crucial in the development and application of novel multi-state devices. However, determining these inverted structures needs a sensitive probe capable of revealing their phase correlation. Here a contrast-enhanced phase-resolved second harmonic generation (SHG) microscopy is presented, which utilizes a phase-tunable Soleil-Babinet compensator and the interference between the SHG fields from the inverted structures and a homogeneous reference. By this means, such inverted structures are correlated through the π-phase difference of SHG, and the phase difference is ultimately converted into the intensity contrast. As a demonstration, we have applied this microscopy in two scenarios to determine the inverted crystallographic domains in two-dimensional van der Waals material MoS2. Our method is particularly suitable for applying in vacuum and cryogenic environments while providing optical diffraction-limited resolution and arbitrarily adjustable contrast. Without loss of generality, this contrast-enhanced phase-resolved SHG microscopy can also be used to resolve other non-centrosymmetric inverted structures, e.g. ferroelectric, magnetic, or multiferroic phases.

Consideration of non-phase-matched nonlinear effects in the design of quasi-phase-matching crystals for optical parametric oscillators

Femtosecond optical parametric oscillators (OPOs) are widely used in ultrafast nonlinear frequency conversion and quantum information. However, conventional OPOs based on quasi-phase-matching (QPM) crystals have many parasitic non-phase-matched processes which decrease the conversion efficiency. Here, we propose nine-wave coupled equations (NWCEs) to simulate all phase-matched and non-phase-matched interactions in QPM crystals to improve conventional three-wave coupled equations (TWCEs), especially for the situation of high intensity ultrashort pulses and complexly structured crystals. We discuss how to design the poling period of QPM crystal to maximize the conversion efficiency of signal light for a given OPO system. The simulation reveals that the OPO based on chirped periodically poled lithium niobate (CPPLN) with a certain chirp rate has higher signal wave conversion efficiency than that of a PPLN, and demonstrates that NWCEs illustrate more details of the pulse evolution in the OPO cavity. Starting from a CPPLN, an aperiodically poled lithium niobate (APPLN) design is available by modifying the domain lengths of the crystal and optimizing the OPO output power via dynamical optimization algorithm. The results show that by using a properly designed APPLN crystal, a 1600 nm OPO, when pumped by a femtosecond laser with 1030 nm central wavelength, 150 femtosecond pulse duration and 5 GW/cm2 power intensity at the focus, can achieve very efficient output with a signal light conversion efficiency of 50.6%, which is higher than that of PPLN (25.2%) and CPPLN (40.2%). The scheme in this paper will provide a reference for the design of nonlinear QPM crystals of OPOs and will help to understand the complex nonlinear dynamical behavior in OPO cavities.

Numerical investigation of effective nonlinear coefficient model for coupled third harmonic generation

In this paper, the optimal solution of effective nonlinear coefficient of quasi-phase-matching (QPM) crystals for coupled third harmonic generation (CTHG) was numerically investigated. The effective nonlinear coefficient of CTHG was converted to an Ising model for optimizing domain distributions of aperiodically poled lithium niobate (APPLN) crystals with lengths as 0.5 mm and 1 mm, and fundamental wavelengths ranging from 1000 nm to 6000 nm. A method for reconstructing crystal domain poling weight curve of coupled nonlinear processes was also proposed, which demonstrated the optimal conversion ratio between two coupled nonlinear processes at each place along the crystal. In addition, by applying the semidefinite programming, the upper bound on the effective nonlinear coefficients deff for different fundamental wavelengths were calculated. The research can be extended to any coupled dual χ(2) process and will help us to understand better the dynamics of coupled nonlinear interactions based on QPM crystals.

Robust temporal adiabatic passage with perfect frequency conversion between detuned acoustic cavities

For classical waves, phase matching is vital for enabling efficient energy transfer in many scenarios, such as waveguide coupling and nonlinear optical frequency conversion. Here, we propose a temporal quasi-phase matching method and realize robust and complete acoustical energy transfer between arbitrarily detuned cavities. In a set of three cavities, A, B, and C, the time-varying coupling is established between adjacent elements. Analogy to the concept of stimulated Raman adiabatic passage, amplitudes of the two couplings are modulated as time-delayed Gaussian functions, and the couplings' signs are periodically flipped to eliminate temporal phase mismatching. As a result, robust and complete acoustic energy transfer from A to C is achieved. The non-reciprocal frequency conversion properties of our design are demonstrated. Our research takes a pivotal step towards expanding wave steering through time-dependent modulations and is promising to extend the frequency conversion based on state evolution in various linear Hermitian systems to nonlinear and non-Hermitian regimes.

Twist Phase Matching in Two-Dimensional Materials

Optical phase matching involves establishing a proper phase relationship between the fundamental excitation and generated waves to enable efficient optical parametric processes. It is typically achieved through birefringence or periodic polarization. Here, we report that the interlayer twist angle in two-dimensional (2D) materials creates a nonlinear geometric phase that can compensate for the phase mismatch, and the vertical assembly of the 2D layers with a proper twist sequence generates a nontrivial "twist-phase-matching" (twist-PM) regime. The twist-PM model provides superior flexibility in the design of optical crystals, which can be applied for twisted layers with either periodic or random thickness distributions. The designed crystal from the twisted rhombohedral boron nitride films within a thickness of only 3.2  μm is capable of producing a second-harmonic generation with conversion efficiency of ∼8% and facile polarization controllability that is absent in conventional crystals. Our methodology establishes a platform for the rational design and atomic manufacturing of nonlinear optical crystals based on abundant 2D materials.

The generation of genuine quadripartite Einstein-Podolsky-Rosen steering in an optical superlattice

Einstein-Podolsky-Rosen (EPR) steering is a quantum effect based on quantum entanglement and it is the key resource for building quantum networks because of its useful properties. Based on the criterion for genuine multipartite EPR steering, the genuine quadripartite EPR steering is confirmed and it can be generated by a spontaneous parametric down-conversion cascaded process with two sum-frequency generations in an optical superlattice. This occurs either below the oscillation threshold and without oscillation threshold. The influence of the parameters of cascaded nonlinear process on the quadripartite EPR steering among signal, idler, and two sum-frequency beams are also discussed. Choosing appropriate nonlinear parameters can achieve good quadripartite quantum steering. This scheme of the generation of genuine quadripartite EPR steering has potential applications in quantum communication and computing.

Semidiscrete optical vortex droplets in quasi-phase-matched photonic crystals

What we believe is a new scheme for producing semidiscrete self-trapped vortices ("swirling photon droplets") in photonic crystals with competing quadratic (χ(2)) and self-defocusing cubic (χ(3)) nonlinearities is proposed. The photonic crystal is designed with a striped structure, in the form of spatially periodic modulation of the χ(2) susceptibility, which is imposed by the quasi-phase-matching technique. Unlike previous realizations of semidiscrete optical modes in composite media, built as combinations of continuous and arrayed discrete waveguides, the semidiscrete vortex "droplets" are produced here in the fully continuous medium. This work reveals that the system supports two types of semidiscrete vortex droplets, viz., onsite- and intersite-centered ones, which feature, respectively, odd and even numbers of stripes, N. Stability areas for the states with different values of N are identified in the system's parameter space. Some stability areas overlap with each other, giving rise to the multistability of states with different N. The coexisting states are mutually degenerate, featuring equal values of the Hamiltonian and propagation constant. An experimental scheme to realize the droplets is outlined, suggesting new possibilities for the long-distance transmission of nontrivial vortex beams in nonlinear media.

Superlattice Surface Lattice Resonances in Plasmonic Nanoparticle Arrays with Patterned Dielectrics

This paper describes how two-dimensional plasmonic nanoparticle lattices covered with microscale arrays of dielectric patches can show superlattice surface lattice resonances (SLRs). These optical resonances originate from multiscale diffractive coupling that can be controlled by the periodicity and size of the patterned dielectrics. The features in the optical dispersion diagram are similar to those of index-matched microscale arrays of metal nanoparticle lattices, having the same lateral dimensions as the dielectric patches. With an increase in nanoparticle size, superlattice SLRs can also support quadrupole excitations with distinct dispersion diagrams. The tunable optical band structure enabled by patterned dielectrics on plasmonic nanoparticle arrays offers prospects for enhanced nonlinear optics, nanoscale lasing, and engineered parity-time symmetries.

Laser nanoprinting of 3D nonlinear holograms beyond 25000 pixels-per-inch for inter-wavelength-band information processing

Nonlinear optics provides a means to bridge between different electromagnetic frequencies, enabling communication between visible, infrared, and terahertz bands through χ(2) and higher-order nonlinear optical processes. However, precisely modulating nonlinear optical waves in 3D space remains a significant challenge, severely limiting the ability to directly manipulate optical information across different wavelength bands. Here, we propose and experimentally demonstrate a three-dimensional (3D) χ(2)-super-pixel hologram with nanometer resolution in lithium niobate crystals, capable of performing advanced processing tasks. In our design, each pixel consists of properly arranged nanodomain structures capable of completely and dynamically manipulating the complex-amplitude of nonlinear waves. Fabricated by femtosecond laser writing, the nonlinear hologram features a pixel diameter of 500 nm and a pixel density of approximately 25000 pixels-per-inch (PPI), reaching far beyond the state of the art. In our experiments, we successfully demonstrate the novel functions of the hologram to process near-infrared (NIR) information at visible wavelengths, including dynamic 3D nonlinear holographic imaging and frequency-up-converted image recognition. Our scheme provides a promising nano-optic platform for high-capacity optical storage and multi-functional information processing across different wavelength ranges.

Intense ultraviolet-visible-infrared full-spectrum laser

A high-brightness ultrabroadband supercontinuum white laser is desirable for various fields of modern science. Here, we present an intense ultraviolet-visible-infrared full-spectrum femtosecond laser source (with 300-5000 nm 25 dB bandwidth) with 0.54 mJ per pulse. The laser is obtained by sending a 3.9 μm, 3.3 mJ mid-infrared pump pulse into a cascaded architecture of gas-filled hollow-core fiber, a bare lithium niobate crystal plate, and a specially designed chirped periodically poled lithium niobate crystal, under the synergic action of second and third order nonlinearities such as high harmonic generation and self-phase modulation. This full-spectrum femtosecond laser source can provide a revolutionary tool for optical spectroscopy and find potential applications in physics, chemistry, biology, material science, industrial processing, and environment monitoring.

Stacking-Controlled Growth of rBN Crystalline Films with High Nonlinear Optical Conversion Efficiency up to 1

Nonlinear optical crystals lie at the core of ultrafast laser science and quantum communication technology. The emergence of 2D materials provides a revolutionary potential for nonlinear optical crystals due to their exceptionally high nonlinear coefficients. However, uncontrolled stacking orders generally induce the destructive nonlinear response due to the optical phase deviation in different 2D layers. Therefore, conversion efficiency of 2D nonlinear crystals is typically limited to less than 0.01% (far below the practical criterion of >1%). Here, crystalline films of rhombohedral boron nitride (rBN) with parallel stacked layers are controllably synthesized. This success is realized by the utilization of vicinal FeNi (111) single crystal, where both the unidirectional arrangement of BN grains into a single-crystal monolayer and the continuous precipitation of (B,N) source for thick layers are guaranteed. The preserved in-plane inversion asymmetry in rBN films keeps the in-phase second-harmonic generation field in every layer and leads to a record-high conversion efficiency of 1% in the whole family of 2D materials within the coherence thickness of only 1.6 µm. The work provides a route for designing ultrathin nonlinear optical crystals from 2D materials, and will promote the on-demand fabrication of integrated photonic and compact quantum optical devices.

Enhanced electron transport and self-similarity in quasiperiodic borophene nanoribbons with line defects

Recent experiments have revealed multiple borophene phases of distinct lattice structures, suggesting that the unit cells of ν_1/6 and ν_1/5 boron sheets, namely α and β chains, serve as building blocks to assemble into novel borophene phases. Motivated by these experiments, we present a theoretical study of electron transport along two-terminal quasiperiodic borophene nanoribbons (BNRs), with the arrangement of the α and β chains following the generalized Fibonacci sequence. Our results indicate that the energy spectrum of these quasiperiodic BNRs is multifractal and characterized by numerous transmission peaks. In contrast to the Fibonacci model that all the electronic states should be critical, both delocalized and critical states appear in the quasiperiodic BNRs, where the averaged resistance saturates at the inverse of one conductance quantum for the delocalized states in the large length limit and contrarily exhibits a power-law dependence on the nanoribbon length for the critical states. Besides, the self-similarity is observed from the transmission spectrum, where the conductance curves overlap at different energy regions of two quasiperiodic BNRs of different Fibonacci indices and the resistance curves are analogous to each other at different energy scales of a single quasiperiodic BNR. These results complement previous studies on quasiperiodic systems where the multifractal energy spectrum and the self-similarity are observed by generating quasiperiodic potential energies, suggesting that borophene may provide an intriguing platform for understanding the structure-property relationships and exploring the physical properties of quasiperiodic systems.

Second-harmonic and cascaded third-harmonic generation in generalized quasiperiodic poled lithium niobate waveguides

Lithium niobate (LN) thin film has recently emerged as an important platform for nonlinear optical investigations for its large χ⁽²⁾ nonlinear coefficients and ability of light localization. In this Letter, we report the first, to the best of our knowledge, fabrication of LN-on-insulator ridge waveguides with generalized quasiperiodic poled superlattices using the electric field polarization technique and microfabrication techniques. Benefiting from the abundant reciprocal vectors, we observed efficient second-harmonic and cascaded third-harmonic signals in the same device, with normalized conversion efficiency of 1735% W^-1 cm^-2 and 0.41% W^-2 cm^-4, respectively. This work opens a new direction for nonlinear integrated photonics based on LN thin film.

Tunable phase-mismatched mid-infrared difference-frequency generation between 6 and 17 µm in CdTe

In parametric conversion, phase-matching techniques such as birefringence and quasi phase-matching (PM) with the designed crystal angle or periodically poled polarities are employed to fulfill the requirement of momentum conservation. However, directly using phase-mismatched interactions in nonlinear media with large quadratic nonlinear coefficient remains unheeded. Here, for the first time to the best of our knowledge, we study the phase-mismatched difference-frequency generation (DFG) in an isotropic cadmium telluride (CdTe) crystal, with the comparison of other DFG processes based on birefringence-PM, quasi-PM, and random-quasi-PM. Long-wavelength mid-infrared (LWMIR) phase-mismatched DFG with an ultra-broadband spectral tuning range of 6-17 µm based on CdTe is demonstrated. Thanks to the giant quadratic nonlinear coefficient (∼109 pm/V) and good figure of merit in the parametric process, the output power up to 100 µW is obtained, which is comparable to or even better than the DFG output from a polycrystalline ZnSe with the same thickness facilitated by random-quasi-PM. A proof-of-concept demonstration in gas sensing of CH₄ and SF₆ is conducted based on the phase-mismatched DFG as a typical application. Our results demonstrate the feasibility of phase-mismatched parametric conversion in producing useful LWMIR power and ultra-broadband tunability in a simple and convenient way without the necessity of controlling the polarization, phase-matching angle, or pole periods, which could find applications in the fields of spectroscopy and metrology.

Ferroelectric domain engineering with femtosecond pulses of different wavelengths

Direct femtosecond laser writing of ferroelectric domain structures has been an indispensable technique for engineering the second-order optical nonlinearity of materials in three dimensions. It utilizes localized thermoelectric field motivated by nonlinear absorption at the position of laser focus to manipulate domains. However, the impact of laser wavelengths, which is pivotal in nonlinear absorption, on the inverted domains is still sketchy. Herein, the light-induced ferroelectric domain inversion is experimentally studied. It is shown that the domain inversions can be achieved over a broad spectral range, but the optical threshold for domain inversion varies dramatically with the laser wavelength, which can be explained by considering the physical mechanism of femtosecond laser poling and nonlinear absorption properties of the crystal. Meanwhile, the effects of other laser processing parameters are also experimentally investigated. Our findings are useful to guide the fabrication of high-performance optical and electronic devices based on ferroelectric domains.

Photo-induced cascaded harmonic and comb generation in silicon nitride microresonators

Silicon nitride (Si3N4) is an ever-maturing integrated platform for nonlinear optics but mostly considered for third-order [χ(3)] nonlinear interactions. Recently, second-order [χ(2)] nonlinearity was introduced into Si3N4 via the photogalvanic effect, resulting in the inscription of quasi-phase-matched χ(2) gratings. However, the full potential of the photogalvanic effect in microresonators remains largely unexplored for cascaded effects. Here, we report combined χ(2) and χ(3) nonlinear effects in a normal dispersion Si3N4 microresonator. We demonstrate that the photo-induced χ(2) grating also provides phase-matching for the sum-frequency generation process, enabling the initiation and successive switching of primary combs. In addition, the doubly resonant pump and second-harmonic fields allow for effective third-harmonic generation, where a secondary optically written χ(2) grating is identified. Last, we reach a broadband microcomb state evolved from the sum-frequency-coupled primary comb. These results expand the scope of cascaded effects in microresonators.

Transfer matrix optimization of a one-dimensional photonic crystal cavity for enhanced absorption of monolayer graphene

The optical absorption enhancement of graphene is of significant interest due to its remarkable applications in optical devices. One of the most useful methods is placing graphene in an asymmetric Fabry-Perot cavity made of one-dimensional dielectric multilayers forming two mirrors. In that regard, using the transfer matrix method, we have explicitly calculated the required periodicity of the front photonic multilayer mirror to maximize the absorption in the graphene for any given combination of material types and number of layers. Then we studied the equivalence between these structural configurations and those with arbitrary periodicity but with defects, where the equivalence holds when ω=ξω₀,ξ∈Z_≥0. These defects are introduced via layer position alterations, based on which we propose an optimization algorithm to maximize absorption in structures having a cavity with an arbitrary periodicity. Numerical calculations are given for dielectric material combinations of TiO₂/SiO₂ and Ta₂O₅/SiO₂, and to understand the behavior of these optimized structures for any general combination of material types, the mapping of their calculated front mirror periodicity for a range of refractive indices of the two material types has been studied.

Femtosecond laser writing of lithium niobate ferroelectric nanodomains

Lithium niobate (LiNbO₃) is viewed as a promising material for optical communications and quantum photonic chips^1,2. Recent breakthroughs in LiNbO₃ nanophotonics have considerably boosted the development of high-speed electro-optic modulators^3-5, frequency combs^6,7 and broadband spectrometers⁸. However, the traditional method of electrical poling for ferroelectric domain engineering in optic^9-13, acoustic^14-17 and electronic applications^18,19 is limited to two-dimensional space and micrometre-scale resolution. Here we demonstrate a non-reciprocal near-infrared laser-writing technique for reconfigurable three-dimensional ferroelectric domain engineering in LiNbO₃ with nanoscale resolution. The proposed method is based on a laser-induced electric field that can either write or erase domain structures in the crystal, depending on the laser-writing direction. This approach offers a pathway for controllable nanoscale domain engineering in LiNbO₃ and other transparent ferroelectric crystals, which has potential applications in high-efficiency frequency mixing^20,21, high-frequency acoustic resonators^14-17 and high-capacity non-volatile ferroelectric memory^19,22.

Ferroelectric Domain Reversal Dynamics in LiNbO3 Optical Superlattice Investigated with a Real-Time Monitoring System

The optical superlattice structure derived from a periodic poling process endows ferroelectric crystals with tunable optical property regulation, which has become one of the most efficient strategies for fabricating high-efficiency optical devices. Achieving a precise superlattice structure has been the main barrier for preparation of specific optical applications due to the unclear dynamics of domain structure regulation. Herein, a real-time monitoring system for the in situ observation of periodic poling of lithium niobate is established to investigate ferroelectric domain reversal dynamics. The formation of reversed domain nuclei, growth, and expansion of the domain are monitored, which is highly related to domain growth dynamics. The nucleation and growth of domain are discussed combined with the monition of domain reversal and the variation of local electric field distribution along with finite element analysis. An electrode configuration with multiholes is proposed to use the local electric field more efficiently and controllably, which could achieve a higher domain nucleus density with high uniformity. Two-mm-thick periodically poled LiNbO3 crystals with high quality are achieved. A nonlinear light conversion from 1064.2 to 3402.4 nm is realized by the single-resonance optical parameter oscillator with a nonlinear optical efficiency up to 26.2%.

Intense Two-Octave Ultraviolet-Visible-Infrared Supercontinuum Laser via High-Efficiency One-Octave Second-Harmonic Generation

Intense ultrabroadband laser source of high pulse energy has attracted more and more attention in physics, chemistry, biology, material science, and other disciplines. We report design and realization of a chirped periodically poled lithium niobate nonlinear crystal that supports ultrabroadband second-harmonic generation covering 350-850 nm by implementing simultaneously up to 12 orders of quasiphase matching against ultrabroadband pump laser covering 700-1700 nm with an average high conversion efficiency of about 25.8%. We obtain a flat supercontinuum spectrum with a 10 dB bandwidth covering more than one octave (about 375-1200 nm) and 20 dB bandwidth covering more than two octaves (about 350-1500 nm) in the ultraviolet-visible-infrared regime and having intense energy as 0.17 mJ per pulse through synergic action of second-order and third-order nonlinearity under pump of 0.48 mJ per pulse Ti:sapphire femtosecond laser. This scheme would provide a promising method for the construction of supercontinuum laser source with extremely broad bandwidth, large pulse energy, and high peak power for a variety of basic science and high technology applications.

Phosphogermanate Crystal: A New Ultraviolet-Infrared Nonlinear Optical Crystal with Excellent Optical Performances

The phase matching ability is a key factor for nonlinear optical crystals to realize coherent output. Herein, a new design strategy combining ultraviolet and infrared functional groups into a ferroelectric was put forward. Thus, a phosphogermanate crystal, KGeOPO₄, was designed and studied. It exhibits a wide transparency window (0.22-9.70 μm), a strong second harmonic generation response (5× KH₂PO₄), a high laser-induced damage threshold (1.61 GW/cm²), and the typical ferroelectricity (coercive field ∼ 9.8 kV/cm and remnant polarization ∼7.6 μC/cm²). In the infrared region, it could realize coherent output by the birefringence phase matching method, while it could generate ultraviolet coherent lights by the quasi-phase matching technique. Therefore, this work designs a promising ultraviolet-infrared nonlinear optical crystal and provides a new perspective for exploring nonlinear optical crystals.

Material research from the viewpoint of functional motifs

As early as 2001, the need for the ‘functional motif theory’ was pointed out to assist the rational design of functional materials. The properties of materials are determined by their functional motifs and by how they are arranged in the materials. Uncovering the functional motifs and their arrangements is crucial in understanding the properties of materials and rationally designing new materials of desired properties. The functional motifs of materials are the critical microstructural units (e.g. constituent components and building blocks) that play a decisive role in generating certain material functions, and could not be replaced with other structural units without losing or significantly suppressing the relevant functions. The role of functional motifs and their arrangements in materials with representative examples was presented. These examples could be classified into six types of material microscopic structures on a length scale smaller than ∼10 nm with maximum subatomic resolution, i.e. the crystal, magnetic, aperiodic, defect, local, and electronic structures. The method of functional motif analysis could be employed in the function-oriented design of materials, as elucidated by taking infrared nonlinear optical materials as an example. Machine learning is more efficient in predicting material properties and screening materials with high efficiency than high-throughput experimentation and high-throughput calculations. In extracting the functional motifs and finding their quantitative relationships, developing sufficiently reliable databases for material structures and properties is imperative.

Angular engineering strategy of an additional periodic phase for widely tunable phase-matched deep-ultraviolet second harmonic generation

Manipulation of the light phase lies at the heart of the investigation of light-matter interactions, especially for efficient nonlinear optical processes. Here, we originally propose the angular engineering strategy of the additional periodic phase (APP) for realization of tunable phase matching and experimentally demonstrate the widely tunable phase-matched second harmonic generation (SHG) which is expected for dozens of years. With an APP quartz crystal, the phase difference between the fundamental and frequency-doubled light is continuously angularly compensated under this strategy, which results the unprecedented and efficient frequency doubling at wavelengths almost covering the deep-UV spectral range from 221 to 332 nm. What's more, all the possible phase-matching types are originally realized simultaneously under the angular engineering phase-matching conditions. This work should not only provide a novel and practical nonlinear photonic device for tunable deep-UV radiation but also be helpful for further study of the light-matter interaction process.

Midinfrared Tunable Laser with Noncritical Frequency Matching in Box Resonator Geometry

Monolithic optical parametric oscillators extend laser frequencies in compact architectures, but normally guide and circulate all pump, signal, and idler beams. Critical frequency matching is raised among these resonances, limiting operation stability and continuous tuning. Here, we develop a box resonator geometry that guides all beams but only resonates for signal. Such noncritical frequency matching enables 227 GHz continuous tuning, with sub-10 kHz linewidth and 0.43 W power at 3310 nm. Our results confirm that monolithic resonator can be effectively used as a tunable laser including midinfrared wavelength, as further harnessed with methane fine spectral measurement at MHz accuracy.

Design approach for photonic quasicrystals to enable multiple nonlinear interactions

Photonic quasicrystals are poised to transform the field of nonlinear light-matter interactions due to their ability to support an unlimited number of combinations of wavevectors in their reciprocal lattices. Such greatly enhanced flexibility enabled by k-space engineering makes photonic quasicrystals a promising platform for novel approaches to multi-wavelength conversion, supercontinuum generation, and development of classical and quantum optical sources. Here, we develop a new design method for nonlinear photonic quasicrystals, consisting of a combination of one nonlinear material and one linear material that can simultaneously fulfill phase-matching conditions for a desired number of nonlinear optical interactions as long as the frequencies of the interacting waves are outside of the bandgaps of the quasicrystal structure. Our approach provides enhanced design flexibility, enabling new pathways to designing compact, integrated nonlinear photonic devices and systems on a chip.

Dynamically tunable third-harmonic generation with all-dielectric metasurfaces incorporating phase-change chalcogenides

Subwavelength nonlinear optical sources with high efficiency have received extensive attention, although strong dynamic controllability of these sources is still elusive. Germanium antimony telluride (GST) as a well-established phase-change chalcogenide is a promising candidate for the reconfiguration of subwavelength nanostructures due to the strong non-volatile change of the index of refraction between its amorphous and crystalline states. Here, we numerically demonstrate an electromagnetically-induced-transparency-based silicon metasurface actively controlled with a quarter-wave asymmetric Fabry-Perot cavity incorporating GST to modulate the relative phase of incident and reflected pump beams. We demonstrate a giant third-harmonic generation (THG) switch with a modulation depth as high as ∼70dB at the resonant band. We also demonstrate the possibility of multi-level THG amplitude modulation for the fundamental C-band by controlling the crystallization fraction of GST at multiple intermediate states. This study shows the high potential of GST-based fast dynamic nonlinear photonic switches for real-world applications ranging from communications to optical computing.

Storing and retrieving multiple images in 3D nonlinear photonic crystals

A nonlinear hologram enables to record the amplitude and phase of a waveform by spatially modulating the second order nonlinear coefficient, so that when a pump laser illuminates it, this waveform is reconstructed at the second harmonic frequency. The concept was now extended to enable the generation of multiple waveforms from a single hologram, with potential applications in high density storage, quantum optics, and optical microscopy.

Quasi-phase-matching-division multiplexing holography in a three-dimensional nonlinear photonic crystal

Nonlinear holography has recently emerged as a novel tool to reconstruct the encoded information at a new wavelength, which has important applications in optical display and optical encryption. However, this scheme still struggles with low conversion efficiency and ineffective multiplexing. In this work, we demonstrate a quasi-phase-matching (QPM) -division multiplexing holography in a three-dimensional (3D) nonlinear photonic crystal (NPC). 3D NPC works as a nonlinear hologram, in which multiple images are distributed into different Ewald spheres in reciprocal space. The reciprocal vectors locating in a given Ewald sphere are capable of fulfilling the complete QPM conditions for the high-efficiency reconstruction of the target image at the second-harmonic (SH) wave. One can easily switch the reconstructed SH images by changing the QPM condition. The multiplexing capacity is scalable with the period number of 3D NPC. Our work provides a promising strategy to achieve highly efficient nonlinear multiplexing holography for high-security and high-density storage of optical information.

White Laser Realized via Synergic Second- and Third-Order Nonlinearities

White laser with balanced performance of broad bandwidth, high average and peak power, large pulse energy, high spatial and temporal coherence, controllable spectrum profile, and overall chroma are highly desirable in various fields of modern science. Here, for the first time, we report an innovative scheme of harnessing the synergic action of both the second-order nonlinearity (2^nd-NL) and the third-order nonlinearity (3^rd-NL) in a single chirped periodically poled lithium niobate (CPPLN) nonlinear photonic crystal driven by a high-peak-power near-infrared (NIR) (central wavelength~1400 nm, energy~100 μJ per pulse) femtosecond pump laser to produce visible to near infrared (vis-NIR, 400-900 nm) supercontinuum white laser. The CPPLN involves a series of reciprocal-lattice bands that can be exploited to support quasiphase matching for simultaneous broadband second- and third-harmonic generations (SHG and THG) with considerable conversion efficiency. Due to the remarkable 3^rd-NL which is due to the high energy density of the pump, SHG and THG laser pulses will induce significant spectral broadening in them and eventually generate bright vis-NIR white laser with high conversion efficiency up to 30%. Moreover, the spectral profile and overall chroma of output white laser can be widely modulated by adjusting the pump laser intensity, wavelength, and polarization. Our work indicates that one can deeply engineer the synergic and collective action of 2^nd-NL and 3^rd-NL in nonlinear crystals to accomplish high peak power, ultrabroadband vis-NIR white laser and hopefully realize the even greater but much more challenging dream of ultraviolet-visible-infrared full-spectrum laser.

Microstructure and domain engineering of lithium niobate crystal films for integrated photonic applications

Recently, integrated photonics has attracted considerable interest owing to its wide application in optical communication and quantum technologies. Among the numerous photonic materials, lithium niobate film on insulator (LNOI) has become a promising photonic platform owing to its electro-optic and nonlinear optical properties along with ultralow-loss and high-confinement nanophotonic lithium niobate waveguides fabricated by the complementary metal-oxide-semiconductor (CMOS)-compatible microstructure engineering of LNOI. Furthermore, ferroelectric domain engineering in combination with nanophotonic waveguides on LNOI is gradually accelerating the development of integrated nonlinear photonics, which will play an important role in quantum technologies because of its ability to be integrated with the generation, processing, and auxiliary detection of the quantum states of light. Herein, we review the recent progress in CMOS-compatible microstructure engineering and domain engineering of LNOI for integrated lithium niobate photonics involving photonic modulation and nonlinear photonics. We believe that the great progress in integrated photonics on LNOI will lead to a new generation of techniques. Thus, there remains an urgent need for efficient methods for the preparation of LNOI that are suitable for large-scale and low-cost manufacturing of integrated photonic devices and systems.

Three-dimensional nonlinear photonic crystal in naturally grown potassium-tantalate-niobate perovskite ferroelectrics

Since quasi-phase-matching of nonlinear optics was proposed in 1962, nonlinear photonic crystals were rapidly developed by ferroelectric domain inversion induced by electric or light poling. The three-dimensional (3D) periodical rotation of ferroelectric domains may add feasible modulation to the nonlinear coefficients and break the rigid requirements for the incident light and polarization direction in traditional quasi-phase-matching media. However, 3D rotating ferroelectric domains are difficult to fabricate by the direct external poling technique. Here, we show a natural potassium-tantalate-niobate (KTN) perovskite nonlinear photonic crystal with spontaneous Rubik's cube-like domain structures near the Curie temperature of 40 °C. The KTN crystal contains 3D ferroelectric polarization distributions corresponding to the reconfigured second-order susceptibilities, which can provide rich reciprocal vectors to compensate for the phase mismatch along an arbitrary direction and polarization of incident light. Bragg diffraction and broadband second-harmonic generation are also presented. This natural nonlinear photonic crystal directly meets the 3D quasi-phase-matching condition without external poling and establishes a promising platform for all-optical nonlinear beam shaping and enables new optoelectronic applications for perovskite ferroelectrics.

High optical damage threshold on-chip lithium tantalate microdisk resonator

Lithium tantalate (LT) is one of the most attractive optical nonlinear materials, as it possesses a high optical damage threshold and great UV transparency (0.28-5.5 µm). Recently, optical grade LT nanoscale film was developed. Here a high-quality-factor (∼10⁵) LT microdisk resonator based on LT-on-insulator (LTOI) film is fabricated by utilizing focused ion beam (FIB) milling. 2 µW output second-harmonic waves are achieved in the LTOI microdisk at about 500 mW input power. Cascaded third-harmonic generation is also observed in the fabricated device. This work may pave the way for LTOI in integrated photonic chips.

Superposed picosecond luminescence kinetics in lithium niobate revealed by means of broadband fs-fluorescence upconversion spectroscopy

Various manifestations of small polarons strongly affect the linear and nonlinear optical properties of the oxide crystal lithium niobate (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {LiNbO}_3$$\end{document}LiNbO3, LN). While related transient absorption phenomena in LN have been extensively studied in recent decades, a sound microscopic picture describing the blue-green (photo)luminescence of lithium niobate single crystals is still missing. In particular, almost nothing is known about: (i) the luminescence build-up and (ii) its room temperature decay. We present here the results of our systematic experimental study using nominally undoped and Mg-doped LN crystals with different Mg concentration. Picosecond luminescence was detected by means of femtosecond fluorescence upconversion spectroscopy (FLUPS) extended to the inspection of oxide crystals in reflection geometry. Two distinct luminescence decay components on the picosecond time scale are revealed. While a short exponential decay is present in each sample, a longer non-exponential decay clearly depends on the crystal composition. Since transient absorption spectroscopy excludes geminate small polaron annihilation as microscopic cause of the luminescence, both decay components are discussed in the context of self-trapped exciton (STE) transport and decay.

Nonlinear Beam Shaping in Domain Engineered Ferroelectric Crystals

Domain engineered ferroelectric crystals are a type of microstructure functional material that is used widely in the area of nonlinear optics. Herein, research processes in the area of nonlinear beam shaping using domain engineered crystals in the past decade are reviewed. The newly developed design methods, such as the nonlinear Huygens-Fresnel principle, nonlinear volume holography, and caustic design, which have analogs in linear optics, are introduced. Using the proposed methods for nonlinear beam shaping, multiple function integration, generation of Airy beams, and arbitrary curved trajectories are realized. As an extra degree of freedom, orbital angular momentum of light beams is generated and manipulated through domain engineering. Discussions and future directions in this field are presented.

Dual-periodically poled lithium niobate microcavities supporting multiple coupled parametric processes

Periodically poled lithium niobate (PPLN) microcavities with additional reciprocal vectors attract attention as a platform for efficient parametric nonlinear optical processes with wavelength and polarization flexibility. Here, we report the simultaneous realization of multiple coupled parametric processes in PPLN microdisk cavities with dual periods as a result of the significantly increased number of reciprocal vectors to fulfill quasi-phase matchings for a series of nonlinear processes. PPLN microdisks with up to 1.43×10⁵ quality factors and unit domain size of 90 nm in width were fabricated using CMOS compatible microfabrication techniques and electrically poled with the help of piezoresponse force microscopy. The conversion efficiency of second-harmonic signal was measured to be 51%W^-1. Our work paves the way towards efficient cascaded parametric effects including third- and fourth-harmonic generations.

Pushing periodic-disorder-induced phase matching into the deep-ultraviolet spectral region: theory and demonstration

Nonlinear frequency conversion is a ubiquitous technique that is used to obtain broad-range lasers and supercontinuum coherent sources. The phase-matching condition (momentum conservation relation) is the key criterion but a challenging bottleneck in highly efficient conversion. Birefringent phase matching (BPM) and quasi-phase matching (QPM) are two feasible routes but are strongly limited in natural anisotropic crystals or ferroelectric crystals. Therefore, it is in urgent demand for a general technique that can compensate for the phase mismatching in universal nonlinear materials and in broad wavelength ranges. Here, an additional periodic phase (APP) from order/disorder alignment is proposed to meet the phase-matching condition in arbitrary nonlinear crystals and demonstrated from the visible region to the deep-ultraviolet region (e.g., LiNbO₃ and quartz). Remarkably, pioneering 177.3-nm coherent output is first obtained in commercial quartz crystal with an unprecedented conversion efficiency above 1‰. This study not only opens a new roadmap to resuscitate those long-neglected nonlinear optical crystals for wavelength extension, but also may revolutionize next-generation nonlinear photonics and their further applications.

Research development on fabrication and optical properties of nonlinear photonic crystals

Since the lasers at fixed wavelengths are unable to meet the requirements of the development of modern science and technology, nonlinear optics is significant for overcoming the obstacle. Investigation on frequency conversion in ferroelectric nonlinear photonic crystals with different superlattices has been being one of the popular research directions in this field. In this paper, some mature fabrication methods of nonlinear photonic crystals are concluded, for example, the electric poling method at room temperature and the femtosecond direct laser writing technique. Then the development of nonlinear photonic crystals with one-dimensional, two-dimensional and three-dimensional superlattices which are used in quasi-phase matching and nonlinear diffraction harmonic generation is introduced. In the meantime, several creative applications of nonlinear photonic crystals are summarized, showing the great value of them in an extensive practical area, such as communication, detection, imaging, and so on.

Topological photonic crystals: a review

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.

Genuine tripartite Einstein-Podolsky-Rosen steering in the cascaded nonlinear processes of third-harmonic generation

Recently, Einstein-Podolski-Rosen (EPR) steering has important application in quantum information processing, and it has been received considerable attention because of its uniqueness. The properties of quantum steering among three output fields generated by cascaded nonlinear processes of quasi-phase-matching third-harmonic generation in an optical cavity are investigated. Based on the criteria for multipartite EPR steering which proposed by He and Reid [PRL, 111, 250403 (2013)], the genuine tripartite EPR steering among pump, second-harmonic, and third-harmonic is demonstrated. The parameters which affect the quantum property are also discussed.

Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice

Phasonic degrees of freedom are unique to quasiperiodic structures and play a central role in poorly understood properties of quasicrystals from excitation spectra to wave function statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly.

Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals

Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs). Direct nonlinear beam shaping has been achieved to convert second-harmonic waves into focusing spots, vortex beams, and diffraction-free beams. However, previous nonlinear beam shaping configurations in one-dimensional and two-dimensional (2D) NPCs generally suffer from low efficiency because of unfulfilled phase-matching condition. Here, we present efficient generations of second-harmonic vortex and Hermite-Gaussian beams in the recently-developed three-dimensional (3D) lithium niobate NPCs fabricated by using a femtosecond-laser-engineering technique. Since 3D χ⁽²⁾ modulations can be designed to simultaneously fulfill the requirements of nonlinear wave-front shaping and quasi-phase-matching, the conversion efficiency is enhanced up to two orders of magnitude in a tens-of-microns-long 3D NPC in comparison to the 2D case. Efficient nonlinear beam shaping paves a way for its applications in optical communication, super-resolution imaging, high-dimensional entangled source, etc.

Generation of light with desirable amplitude and phase profiles with nonlinear wavefront shaping is of great interest for optical technologies. Here, the authors demonstrate efficient nonlinear beam shaping using three-dimensional lithium niobate photonic crystals fabricated using a femtosecond-laser-engineering technique.