Effective Nonlinear Susceptibility Research Articles

Boosting Second Harmonic Generation Efficiency and Nonlinear Susceptibility via Metasurfaces Featuring Split-Ring Resonators and Bowtie Nanoantennas.

This work investigates a metasurface design to achieve remarkable second harmonic generation (SHG) conversion efficiency and enhance effective nonlinear susceptibility using the finite element method. The elements of the designed structure are composed of a rectangular split-ring resonator Ag film, a bowtie-shaped Ag nanoantenna, and a pair of Bi bars that induce nonlinear optical phenomena due to the nonuniform distribution of the electric and magnetic fields within the device surface. The simulation results agree perfectly with the theory and demonstrate outstanding achievements in terms of SHG conversion efficiency (η) and effective nonlinear susceptibility (χeff(2)). Specifically, the metasurface reaches a peak η value of 4.544×10-8 and an effective nonlinear susceptibility of 3.4×104 pm/V. This work presents a novel and versatile design to achieve high η and χeff(2) in an SHG metasurface.

A Universal Strategy for Synthesis of 2D Ternary Transition Metal Phosphorous Chalcogenides.

The 2D ternary transition metal phosphorous chalcogenides (TMPCs) have attracted extensive research interest due to their widely tunable band gap, rich electronic properties, inherent magnetic and ferroelectric properties. However, the synthesis of TMPCs via chemical vapor deposition (CVD) is still challenging since it is difficult to control reactions among multi-precursors. Here, a subtractive element growth mechanism is proposed to controllably synthesize the TMPCs. Based on the growth mechanism, the TMPCs including FePS3 , FePSe3 , MnPS3 , MnPSe3 , CdPS3 , CdPSe3 , In2 P3 S9 , and SnPS3 are achieved successfully and further confirmed by Raman, second-harmonic generation (SHG), and scanning transmission electron microscopy (STEM). The typical TMPCs-SnPS3 shows a strong SHG signal at 1064nm, with an effective nonlinear susceptibility χ(2) of 8.41×10-11 mV-1 , which is about 8 times of that in MoS2 . And the photodetector based on CdPSe3 exhibits superior detection performances with responsivity of 582mAW-1 , high detectivity of 3.19×1011 Jones, and fast rise time of 611µs, which is better than most previously reported TMPCs-based photodetectors. These results demonstrate the high quality of TMPCs and promote the exploration of the optical properties of 2D TMPCs for their applications in optoelectronics.

Sum-frequency generation at interfaces: A Fresnel story. II. Analytical expressions for multilayer systems.

The well-known formalism for Sum-Frequency Generation (SFG) reflected or transmitted by a three-layer system involves three equations defining the emitted SFG intensity, the effective nonlinear susceptibility, and a set of Fresnel factors specific to the three-layer system. We generalize the equations to an N-layer system, where all media have non-vanishing thicknesses, by leaving the first two equations unchanged and modifying only the Fresnel factors. These universal Fresnel factors bear all the complexity of light propagation and interference in the system, in amplitude and phase. They are analytically known anywhere in the N-layer system, either at any interface or in any of the bulks, and share common expressions for the three beams, incoming or emitted, of the SFG process in reflection. Enclosing an ultrathin layer (e.g., a molecular monolayer) in the system does not modify the Fresnel factors except for boundary conditions at this layer, as in the three-layer case. Specific rules are elaborated to simplify systems containing macroscopic layers. Equations for the four- and five-layer systems are explicitly provided. Simulations in the four-layer system allow for the recovery of the results of the transfer matrix formalism at a lower complexity cost for SFG users. Finally, when several interfaces in the system produce SFG signals, we show that it is possible to probe only the most buried one by canceling all the SFG responses except at this last interface, generalizing the results of the three-layer system.

Gapless detection of broadband terahertz pulses using a metal surface in air based on field-induced second-harmonic generation

We investigate second-harmonic generation (SHG) light from a Pt surface in atmosphere under terahertz (THz) pulses. THz pulse-modulated SHG intensity, ΔI2ω, shows a clear time profile of the THz field, which is similar to that of the conventional electro-optic sampling. The result can be explained by interference between THz field-induced second-harmonic light from air molecules in an optical path and a local oscillator from a Pt surface, whereby heterodyne detection of the THz waveform can be achieved. Using numerical calculations of a wave equation, we discuss the contribution of the Gouy phases of all the pulses, including near-infrared, SHG, and THz pulses, and identification of effective nonlinear susceptibility of the Pt surface. Our method, simply using a polished metal surface and air molecules, does not suffer from phonons or phase matching in solid-state optics and does not require any power supply, bias voltage, or fabrication process, but it offers a simple and gapless sampling method for broadband THz pulses. Here, we demonstrate the gapless detection of a broadband THz pulse in the region of 0.2–20 THz using this method.

Optical switching in composite media containing nonlinear plasmonic coated particles with radial anisotropy

We investigate the nonlinear optical properties of the composite with identical radial-anisotropic/ nonlinear-plasmonic core-shell spherical inclusions randomly embedded in the linear medium. In the weakly-nonlinear case, the enhanced effective third-order nonlinear susceptibility is achieved through the exhibited surface plasmon resonance, and the enhanced peak can be tuned by adjusting the anisotropic parameter. In the strong-nonlinear case, the single optical bistability, double optical bistability or optical tristability in small particles will be found. Furthermore, we demonstrate the optical multistability arising from the high-order modes in low-index surrounding environment for the large particles. And the anisotropy is essential to expand the diversity of the optical switching. Our results are envisioned for the opportunities of anisotropic materials and the applications of the optical switching.

The Kurtz-Perry powder technique revisited: A case study on the importance of reference quality and broadband nonlinear optical measurements using LiInSe2

The Kurtz-Perry powder technique (KPPT) is widely utilized for the rapid characterization of newly grown nonlinear optical (NLO) materials available in pristine powder form. It assesses the effective nonlinear susceptibility of randomly oriented powder in comparison with a reference material. This technique becomes especially versatile when equipped with a broad wavelength range and intensity tunability because it provides key NLO properties of the materials under investigation, such as the frequency dispersion of the NLO susceptibility, phase-matching (PM) range, and laser-induced damage threshold (LIDT) as a guideline. In this study, wavelength-dependent NLO experiments (λ= 1100 – 3700 nm) were conducted on polycrystalline LiInSe2, prepared by high-temperature, solid-state synthesis. Our LiInSe2 was found to be phase-matchable for λ> 2500 nm and the effective NLO susceptibility was estimated as 20.0 ± 1.9 pm/V, assessed at the static limit using commercial-grade single crystals of AgGaS2 and AgGaSe2 that were ground to powders. Alternatively, the effective NLO susceptibility was determined to be twice as large, ~40 pm/V, when utilizing a homemade, microcrystalline AgGaSe2 reference at the static limit. This severe overestimation of the NLO susceptibility that can occur while working with a homemade standard underscores the importance of using a commercial-grade reference with the KPPT. Furthermore, this study also discusses the LIDT of LiInSe2 based on intensity-dependent SHG at 1064 nm with picosecond pulses, and compares with those of the commercial-grade AgGaS2 and AgGaSe2, determined under identical conditions. As defect levels can cause widely varying apparent color, thus optical bandgap, in LiInSe2, this study stresses the importance of using a high-quality standard when exploiting the KPPT for NLO materials characterization. The role of defects is discussed in terms of χ2, phase matching onset and LIDT, parameters that predominantly affect the evaluation of new NLO materials.

Thin Films of Nonlinear Metallic Amorphous Composites.

We studied the nonlinear optical response of metallic amorphous composite layers in terms of a self-phase-modulated, third-order Kerr nonlinearity. A nonlinear effective medium theory was used to describe low densities of gold and iridium nanoparticles embedded in an equally nonlinear host material. The fill fraction strongly influences the effective nonlinear susceptibility of the materials, increasing it by orders of magnitude in the case of gold due to localized surface plasmonic resonances. The enhancement of the nonlinear strength in amorphous composites with respect to the bulk material has an upper limit in metallic composites as dominating absorption effects take over at higher fill factors. Both saturated and induced absorption in the thin films of amorphous composites were observed depending on the selected frequency and relative position to the resonant frequency of electron excitation in the metallic inclusions. We demonstrated the depths to which thin films are affected by nonlinear enhancement effects.

Giant second-harmonic generation in ferroelectric NbOI2

Implementing nonlinear optical components in nanoscale photonic devices is challenged by phase-matching conditions requiring thicknesses in the order of hundreds of wavelengths, and is disadvantaged by the short optical interaction depth of nanometre-scale materials and weak photon–photon interactions. Here we report that ferroelectric NbOI2 nanosheets exhibit giant second-harmonic generation with conversion efficiencies that are orders of magnitude higher than commonly reported nonlinear crystals. The nonlinear response scales with layer thickness and is strain- and electrical-tunable; a record >0.2% absolute SHG conversion efficiency and an effective nonlinear susceptibility $$\chi _{\mathrm{eff}}^{(2)}$$ in the order of 10−9 m V−1 are demonstrated at an average pump intensity of 8 kW cm–2. Due to the interplay between anisotropic polarization and excitonic resonance in NbOI2, the spatial profile of the polarized SHG response can be tuned by the excitation wavelength. Our results represent a new paradigm for ultrathin, efficient nonlinear optical components. Strained NbOI2 flakes with a thickness of 20 nm exhibit a record SHG absolute conversion efficiency of >0.2% and an effective bulk-like nonlinear susceptibility of 1.1 × 10−9 m V−1 at the fundamental wavelength of 1,050 nm. The spatial profile of the polarized second-harmonic generation response can be tuned by the fundamental wavelength.

Terahertz wave emission from the trigonal layered PtBi2

SummaryIn this work, broadband terahertz (THz) wave emissions have been detected from the trigonal layered PtBi2 on the excitation of the femtosecond laser pulses. Such THz generation is found to arise from the dominated linear photogalvanic effect, which is further discovered to strongly depend on the unique electronic structures of PtBi2. Furthermore, an effective nonlinear susceptibility of PtBi2 is also obtained and is nearly two orders of magnitude larger than that of the traditional nonlinear crystal for THz generation.

Modeling of second-order nonlinear metasurfaces

We present a frequency-domain modeling technique for second-order nonlinear metasurfaces. The technique is derived from the generalized sheet transition conditions (GSTCs), which have been so far mostly used for modeling linear metasurfaces. In this work, we extend the GSTCs to include effective nonlinear polarizations. This allows retrieving the effective nonlinear susceptibilities of a given metasurface and predict its nonlinear scattering responses under arbitrary illumination conditions. We apply this modeling technique to the case of metasurfaces made of a periodic arrangement of T-shaped gold nanoparticles. For verification, several metasurfaces are fabricated and a fair agreement is found when comparing simulated data and experimental results. The proposed model may thus serve as a design platform to implement complex nonlinear metasurface based applications.

Third-harmonic Mie scattering from semiconductor nanohelices

Chiroptical spectroscopies provide structural analyses of molecules and nanoparticles but they require sample volumes that are incompatible with generating large chemical libraries. New optical tools are needed to characterize chirality for the ultrasmall (<1 µl) volumes required in the high-throughput synthetic and analytical stations for chiral compounds. Here we show experimentally a novel photonic effect that enables such capabilities—third-harmonic Mie scattering optical activity—observed from suspensions of CdTe nanostructured helices in volumes <<1 µl. Third-harmonic Mie scattering was recorded on illuminating CdTe helices with 1,065, 1,095 and 1,125 nm laser beams and the intensity was around ten-times higher in the forward direction than sideways. The third-harmonic ellipticity was as high as 3° and we attribute this effect to the interference of chiral and achiral effective nonlinear susceptibility tensor components. Third-harmonic Mie scattering on semiconductor helices opens a path for rapid high-throughput chiroptical characterization of sample volumes as small as 10−5 µl.

A New Imaginary Term in the Second-Order Nonlinear Susceptibility from Charged Interfaces.

Nonresonant second harmonic generation (SHG) phase and amplitude measurements obtained from the silica-water interface at varying pH values and an ionic strength of 0.5 M point to the existence of a nonlinear susceptibility term, which we call χX(3), that is associated with a 90° phase shift. Including this contribution in a model for the total effective second-order nonlinear susceptibility produces reasonable point estimates for interfacial potentials and second-order nonlinear susceptibilities when χX(3) ≈ 1.5χwater(3). A model without this term and containing only traditional χ(2) and χ(3) terms cannot recapitulate the experimental data. The new model also provides a demonstrated utility for distinguishing apparent differences in the second-order nonlinear susceptibility when the electrolyte is NaCl versus MgSO4, pointing to the possibility of using heterodyne-detected SHG to investigate ion specificity in interfacial processes.

Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics.

Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and a small material footprint. Ideally, the material system should allow for chip integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light–matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear optical conversion efficiency. Here, we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3 × 10–8 m2/V2, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to a third-harmonic signal with an intensity that is 3 orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to ∼1% using a moderate field strength of ∼30 kV/cm. Finally, we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the ninth harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS-compatible, room-temperature, chip-integrated, THz nonlinear conversion applications.

Giant Nonlinear Circular Dichroism from Intersubband Polaritonic Metasurfaces.

Nonlinear metasurfaces are advancing into a new paradigm of "flat nonlinear optics" owing to the ability to engineer local nonlinear responses in subwavelength-thin films. Recently, attempts have been made to expand the design space of nonlinear metasurfaces through nonlinear chiral responses. However, the development of metasurfaces that display both giant nonlinear circular dichroism and significantly large nonlinear optical response is still an unresolved challenge. Herein, we propose a method that induces giant nonlinear responses with near-unity circular dichroism using polaritonic metasurfaces with optical modes in chiral plasmonic nanocavities coupled with intersubband transitions in semiconductor heterostructures designed to have giant second and third order nonlinear responses. A stark contrast between effective nonlinear susceptibility elements for the two spin states of circularly polarized pump beams was seen in the hybrid structure. Experimentally, near-unity nonlinear circular dichroism and conversion efficiencies beyond 10-4% for second- and third-harmonic generation were achieved simultaneously in a single chip.

Effect of Pb Substitution in Sr2-xPbxGeSe4 on Crystal Structures and Nonlinear Optical Properties Predicted by DFT Calculations.

We investigated the Sr2-xPbxGeSe4 series from 0 ≤ x ≤ 2 to study the impact of Pb on structure and properties. While the noncentrosymmetric (NCS) compounds γ-Sr2GeSe4 and α-Pb2GeSe4 have already been reported previously, the substitution variants Sr1.31Pb0.69GeSe4 (space group Ama2, a = 10.31220(1) Å, b = 10.39320(1) Å, c = 7.42140(1) Å) and Sr0.19Pb1.81GeSe4 (I4̅3d, a = 14.6177(3) Å) are introduced here for the first time. The experimentally determined optical band gaps decrease as predicted with increasing Pb content from γ-Sr2GeSe4 to Sr1.31Pb0.69GeSe4, Sr0.25Pb1.75GeSe4, and α-Pb2GeSe4 from 2.00, to 1.65, 1.45 and 1.42 eV, respectively. The nonlinear optical (NLO) properties of the orthorhombic compounds γ-Sr2GeSe4 and Sr1.3Pb0.7GeSe4 (approximated with the supercell "Sr3PbGe2Se8") were studied both theoretically, using first-principle calculations, and experimentally. The calculations found the effective nonlinear susceptibility, deff, of γ-Sr2GeSe4 and "Sr3PbGe2Se8" at the static limit to be 10.8 and 8.8 pm V-1, respectively. The experimental deff values of γ-Sr2GeSe4, Sr1.31Pb0.69GeSe4, Sr0.25Pb1.75GeSe4, and α-Pb2GeSe4 were 2.6, 2.3, 0.68, and 0.79 pm V-1, respectively.

Quasi-BIC Resonant Enhancement of Second-Harmonic Generation in WS2 Monolayers.

Atomically thin monolayers of transition metal dichalcogenides (TMDs) have emerged as a promising class of novel materials for optoelectronics and nonlinear optics. However, the intrinsic nonlinearity of TMD monolayers is weak, limiting their functionalities for nonlinear optical processes such as frequency conversion. Here we boost the effective nonlinear susceptibility of a TMD monolayer by integrating it with a resonant dielectric metasurface that supports pronounced optical resonances with high quality factors: bound states in the continuum (BICs). We demonstrate that a WS2 monolayer combined with a silicon metasurface hosting BICs exhibits enhanced second-harmonic intensity by more than 3 orders of magnitude relative to a WS2 monolayer on top of a flat silicon film of the same thickness. Our work suggests a pathway to employ high-index dielectric metasurfaces as hybrid structures for enhancement of TMD nonlinearities with applications in nonlinear microscopy, optoelectronics, and signal processing.

Comparison Between the Linear and Nonlinear Homogenization of Graphene and Silicon Metasurfaces

In this article, we use a versatile homogenization approach to model the linear and nonlinear optical response of two metasurfaces: a plasmonic metasurface consisting of graphene patches and a dielectric photonic nanostructure consisting of silicon photonic crystal (PhC) cavities. The former metasurface is resonant at wavelengths that are much larger than the graphene elements of the metasurface, whereas the resonance wavelengths of the latter one are comparable to the size of its resonant components. By computing and comparing the effective permittivities and nonlinear susceptibilities of the two metasurfaces, we infer some general principles regarding the conditions under which homogenization methods of metallic and dielectric metasurfaces are valid. In particular, we show that in the case of the graphene metasurface the homogenization method describes very well both its linear and nonlinear optical properties, whereas in the case of the silicon photonic nanostructure the homogenization method is only qualitatively accurate, especially near the optical resonances.

Growth of Au Hollow Stars and Harmonic Excitation Energy Transfer.

Optical excitation, subsequent energy transfer, and emission are fundamental to many physical problems. Optical antennas are ideal candidates for manipulating these processes. We extend energy transfer to second- and third-harmonic (SH and TH) fields through the collaborative susceptibility χ(n) (n = 1, 2, 3) resonances of nonlinear optical antennas. Hollow gold stars, with a broadband response covering the fundamental, SH, and TH frequencies, are synthesized as nonlinear antennas. Harmonic resonance energy transfer through a χ(3) → χ(1) collaboration is revealed. A χ(3) → χ(2) collaboration is uncovered, with largely enhanced SH radiation demonstrated by exciting the three resonances at the fundamental, SH, and TH frequencies. A theoretical model of the effective nonlinear susceptibilities is proposed to calculate the efficiencies of the two nonlinear energy transfer processes.

Hydrogen bond analysis of a third order nonlinear optical crystal, 2-amino-5-bromopyridinium benzilate, using structural and computational characterizations

The molecular structure of a proton transfer organic material, 2-amino-5-bromopyridinium benzilate crystal, grown by slow-evaporation solution growth technique has been determined by single crystal X-ray diffraction. The crystal has monoclinic structure and crystallizes in a centrosymmetric space group P21/c. The molecular network contains variety of hydrogen bonds that led to stabilization of the structure and optical properties of the crystal. The FT-IR studies confirm the functional groups present. The 1H and 13C NMR spectra were recorded to confirm the molecular skeleton. The crystal is transparent in entire visible region as evidenced by UV–vis spectrum. The photoluminescence spectrum of the compound shows good optical emission properties. Thermal stability of the crystal was determined using TG/DTA studies. Theoretically optimized molecular geometry shows good agreement with experimental bond length and bond angle values. Molecular electrostatic potential analysis confirmed the proton migration during the reaction. The charge transfer occurring in the compound was confirmed by both HOMO-LUMO and Mulliken atomic charge analysis, where electrons get promoted from pyridinium moiety to the benzilate through N–H⋯O hydrogen bonds. Natural bond orbital analysis supports the interactions and structural properties of the proton transfer compound. Z-scan technique was used to measure the effective third-order nonlinear optical susceptibility.

Giant Enhancement of Nonlinear Optical Processes With Split-Ring Resonators for THz Applications

Plasmonic resonances have been widely applied in nonlinear optics due to their unprecedented capability of concentrating and manipulating light at the deep subwavelength scale. Doubly resonant cavities can confine light of different wavelengths in the same cavity with large modal overlap and strong field enhancement. However, designing of such cavities is usually difficult when the resonant wavelengths differ by orders of magnitude. Here, by using plasmonics to match the modal sizes, we propose a split-ring resonator that resonates in both the near-infrared and terahertz (THz) bands simultaneously, with their fields colocalized within a deep subwavelength gap to achieve strong nonlinear interactions. THz wave generation through difference-frequency generation can be significantly enhanced in this resonator, yielding a 4-order-of-magnitude enhancement of the effective nonlinear susceptibility from the material’s intrinsic value. Therefore, such structures can serve as an ideal platform for nonlinear optical processes between the near-infrared and THz waves, which can be employed for THz applications such as THz wave generation and detection.