Second-order Susceptibility Research Articles

First-principles study of water adsorption monolayer on Pt(111): Adsorption energy and second-order nonlinear susceptibility

First-principles study of water adsorption monolayer on Pt(111): Adsorption energy and second-order nonlinear susceptibility

Enhancing second harmonic generation of monolayer WS2 with edge plasmon

Transition-metal dichalcogenide (TMD) monolayers possess large second-order nonlinear susceptibility and have shown great potentials in on-chip nonlinear optical devices. However, the thickness of TMD monolayers is less than 1[Formula: see text]nm, resulting in a rather low second harmonic generation (SHG) efficiency. In this paper, we propose a physical scheme of enhancing SHG of TMD monolayers with edge plasmon. As a proof of concept demonstration, we constructed a hexagonal gold nanoplates/monolayer WS2 heterostructure with high interface quality. By performing SHG measurements, we show that SHG was enhanced by a factor of about 60. Our results set a foundation for on-chip nonlinear optical applications with TMD monolayers.

Obtaining extended insight into molecular systems by probing multiple pathways in second-order nonlinear spectroscopy.

Second-order nonlinear spectroscopy is becoming an increasingly important technique in the study of interfacial systems owing to its marked ability to study molecular structures and interactions. The properties of such a system under investigation are contained within their intrinsic second-order susceptibilities which are mapped onto the measured nonlinear signals (e.g. sum-frequency generation) through the applied experimental settings. Despite this yielding a plethora of information, many crucial aspects of molecular systems typically remain elusive, for example the depth distributions, molecular orientation and local dielectric properties of its constituent chromophores. Here, it is shown that this information is contained within the phase of the measured signal and, critically, can be extracted through measurement of multiple nonlinear pathways (both the sum-frequency and difference-frequency output signals). Furthermore, it is shown that this novel information can directly be correlated to the characteristic vibrational spectra, enabling a new type of advanced sample characterization and a profound analysis of interfacial molecular structures. The theory underlying the different contributions to the measured phase of distinct nonlinear pathways is derived, after which the presented phase disentanglement methodology is experimentally demonstrated for model systems of self-assembled monolayers on several metallic substrates. The obtained phases of the local fields are compared to the corresponding phases of the nonlinear Fresnel factors calculated through the commonly used theoretical model, the three-layer model. It is found that, despite its rather crude assumptions, the model yields remarkable similarity to the experimentally obtained values, thus providing validation of the model for many sample classes.

Berry Curvature Dipole Induced Giant Mid-Infrared Second-Harmonic Generation in 2D Weyl Semiconductor.

Due to its inversion-broken triple helix structure and the nature of Weyl semiconductor, 2D Tellurene (2D Te) is promising to possess a strong nonlinear optical response in the infrared region, which is rarely reported in 2D materials. Here, a giant nonlinear infrared response induced by large Berry curvature dipole (BCD) is demonstrated in the Weyl semiconductor 2D Te. Ultrahigh second-harmonic generation response is acquired from 2D Te with a large second-order nonlinear optical susceptibility (χ(2) ), which is up to 23.3 times higher than that of monolayer MoS2 in the range of 700-1500nm. Notably, distinct from other 2D nonlinear semiconductors, χ(2) of 2D Te increases extraordinarily with increasing wavelength and reaches up to 5.58nmV-1 at ≈2300nm, which is the best infrared performance among the reported 2D nonlinear materials. Large χ(2) of 2D Te also enables the high-intensity sum-frequency generation with an ultralow continuous-wave (CW) pump power. Theoretical calculations reveal that the exceptional performance is attributed to the presence of large BCD located at the Weyl points of 2D Te. These results unravel a new linkage between Weyl semiconductor and strong optical nonlinear responses, rendering 2D Te a competitive candidate for highly efficient nonlinear 2D semiconductors in the infrared region.

A potassium lead 2-methylmalonate-iodide nonlinear optical crystal with strong second-harmonic generation response and large birefringence

Nonlinear optical (NLO) crystals play a significant role in optoelectronic industry. Herein, a new NLO crystal, K(H2O)[KI][PbI(C4H4O4)], has been rationally obtained by tuning halide perovskite materials with 2-methylmalonate group. K(H2O)[KI][PbI(C4H4O4)] features that the highly distorted [PbO4I2] polyhedron with large hyperpolarizability and prominent polarizability anisotropy is served as a bifuntional unit. Remarkably, the distorted [PbO4I2] polyhedrons are aligned in an oriented arrangement that leads to the effective superposition of their microscopic second-order nonlinear susceptibilities and the enhancement of optical anisotropy. Notably, K(H2O)[KI][PbI(C4H4O4)] exhibits a strong phase-matching SHG response of 5.6 × KDP and a large birefringence (Δnobv. = 0.24@546 nm). Theoretical calculations elucidate that the strong SHG response and the large birefringence are predominantly attributed to the directional arrangement of the highly distorted [PbO4I2] polyhedrons. Our discovery provides an effective path for the rational exploration of high-performance NLO crystals.

Crystal structure, electronic structure, and optical properties of Cu4ZnGe2S7 and Cu4CdGe2S7: Polar diamond-like semiconductors exhibiting second harmonic generation

The novel I4-II-IV2-VI7 quaternary diamond-like semiconductors (DLSs), Cu4ZnGe2S7 and Cu4CdGe2S7, were prepared from the constituent elemental powders at elevated temperatures. Cu4ZnGe2S7 crystallizes in the polar, chiral space group C2 and adopts the Cu4NiSi2S7 structure-type, which can be considered a derivative of the cubic diamond structure. The cadmium analog takes on the Cu5Si2S7 structure-type, which is related to the hexagonal diamond structure, and displays polar, Cc space group symmetry. Both compounds contain [Ge2S7]6- anions created by corner-sharing GeS4 tetrahedra. The crystal structures were carefully evaluated using: 1) extended connectivity tables, 2) minimum bounding ellipsoid analysis, and 3) bond valence sum (BVS) and global instability index (G) calculations. Both compounds are thermally stable up to temperatures exceeding 950 °C and melt incongruently. As assessed using diffuse reflectance spectroscopy, Cu4ZnGe2S7 and Cu4CdGe2S7 possess optical bandgaps of 1.65 eV and 1.90 eV, respectively, which are narrower than the analogous I2-II-IV-VI4 DLSs. Electronic structure calculations show that both compounds are direct-bandgap semiconductors with significant contributions of Cu-d and S-p orbitals to the states at the top of the valence band. While Cu4CdGe2S7 displays a weak second harmonic generation (SHG) response, the second-order nonlinear optical susceptibility, χ(2), of Cu4ZnGe2S7 is 14.8 ± 1.5 pm V-1, assessed using the Kurtz-Perry powder method and an optical-grade AgGaSe2 (AGSe) reference. Both compounds exhibit laser-induced damage threshold values similar to AGSe, ∼0.1 GW cm-2, for λ = 1.064 µm using picosecond laser pulses. Most importantly, Cu4ZnGe2S7 exhibits a phase-matching behavior at λ = 3.1 µm. These results suggest that Cu4ZnGe2S7 holds potential for use in low-powered laser applications involving efficient wave mixing in the mid-IR region.

Quantification of Stern Layer Water Molecules, Total Potentials, and Energy Densities at Fused Silica:Water Interfaces for Adsorbed Alkali Chlorides, CTAB, PFOA, and PFAS.

We have employed amplitude- and phase-resolved second-harmonic generation spectroscopy to investigate ion-specific effects of monovalent cations at the fused silica:water interface maintained under acidic, neutral, and alkaline conditions. We find a negligible dependence of the total potential (as negative as -400 mV at pH 14), the second-order nonlinear susceptibility (as large as 1.5 × 10-21 m2 V-1 at pH 14), the number of Stern layer water molecules (1 × 1015 cm-2 at pH 5.8), and the energy associated with water alignment upon going from neutral to high pH (ca. -24 kJ mol-1 to -48 kJ mol-1 at pH 13 and 14, close to the cohesive energy of liquid water but smaller than that of ice) on chlorides of the alkali series (M+ = Li+, Na+, K+, Rb+, and Cs+). Attempts are presented to provide estimates for the molecular hyperpolarizability of the cations and anions in the Stern layer at high pH, which arrive at ca. 20-fold larger values for αtotalions(2) = αM+(2) + αOH-(2) + αCl-(2) when compared to water's molecular hyperpolarizability estimate from theory and point to a sizable contribution of deprotonated silanol groups at high pH. In contrast to the alkali series, a pronounced dependence of the total potential and the second-order nonlinear susceptibility on monovalent cationic (cetrimonium bromide, CTAB) and anionic (perfluorooctanoic and perfluorooctanesulfonic acid, PFOA and PFOS) surfactants was quantifiable. Our findings are consistent with a low surface coverage of the alkali cations and a high surface coverage of the surfactants. Moreover, they underscore the important contribution of Stern layer water molecules to the total potential and second-order nonlinear susceptibility. Finally, they demonstrate the applicability of heterodyne-detected second-harmonic generation spectroscopy for identifying perfluorinated acids at mineral:water interfaces.

Calibrated χ(2)-tensor polarization-resolved second harmonic generation microscopy for precise tissue imaging

Polarization-resolved second harmonic generation (P-SHG) microscopy is commonly used to analyze the second-order susceptibility, χ(2), tensor, which enables the calculation of the molecular structure of harmonophores. However, despite extensive research on type I collagen, the measured χ(2) ratios vary considerably among published values, which raises the question of whether P-SHG imaging is universally applicable to all tissues containing harmonophores. In this work, we propose that the deviation of χ(2) ratios is primarily due to ignoring the molecular tilt angle and chirality in image analysis. To confirm our hypothesis, we present an analytical model based on C6 symmetry that takes into account these two factors. We also introduce an imaging scheme that splits SHG into X- and Y-polarized image components for χ(2) tensor analysis. Our approach effectively improves the precision of determining χ(2) ratios, depending on how much the two factors affect the P-SHG signals.

Effect of magnesium and zinc doping of lithium niobate crystals on nonlinear optical characteristics

The theoretical and experimental values of nonlinear optical susceptibilities for lithium niobate crystals double doped with cations (Zn2+:Mg2+) with similar concentrations obtained using the method of direct and homogeneous impurity introduction were analyzed. The length of Li-O bonds in double-doped crystals (LiNbO3:Zn2+:Mg2+) determined the value of the nonlinear optical second harmonic generation (SHG) coefficients. It was found that impurity and intrinsic defects make a positive contribution to the tensor coefficients of the second-order nonlinear optical susceptibility (dij). The results indicated that the LiNbO3:Zn2+:Mg2+ (3.83:0.97 mol%) crystal is the most suitable medium for SHG application among the crystals studied in the paper, as it showed the maximum calculated value of the nonlinear optical coefficient d33 which was equal to −55.26(2) × 10−9 cm/statV. The measured second harmonic conversion efficiency for this crystal was η = 36%.

Generation of a coherent squeezed like state defined with the Lie--Trotter product formula using a nonlinear photonic crystal

Abstract In this paper, we investigate how to generate coherent squeezed like light using a nonlinear photonic crystal. Because the photonic crystal reduces the group velocity of the incident light, if it is composed of a material with a second-order nonlinear optical susceptibility $\chi^{(2)}$, the interaction between the nonlinear material and the light passing through it strengthens and the quantum state of the emitted light is largely squeezed. Thus, we can generate a coherent squeezed like light with a resonating cavity in which the nonlinear photonic crystal is placed. This coherent squeezed like state is defined with the Lie--Trotter product formula and its mathematical expression is different from those of conventional squeezed coherent states. We show that we can obtain this coherent squeezed like state with a squeezing level $15.9$ dB practically by adjusting physical parameters for our proposed method. Feeding the squeezed light whose average number of photons is given by one or two into a beam splitter and splitting the flow of the squeezed light into a pair of entangled light beams, we estimate their entanglement quantitatively.
This paper is a sequel to H.~Azuma, J. Phys. D: Appl. Phys. \textbf{55}, 315106 (2022).

Revealing the Polarizations of Molecular Ferroelectrics via SHG Polarimetry at the Nanoscale.

Multifarious molecular ferroelectrics with multipolar axial characteristics have emerged in recent years, enriching the scenarios for energy harvesting, sensing, and information processing. The increased polar axes have enhanced the urgency of distinguishing different polarization states in material design, mechanism exploration, etc. However, conventional methods hardly meet the requirements of in situ, fast, microscale, contactless, and nondestructive features due to their inherent limitations. Herein, SHG polarimetry is introduced to probe the multioriented polarizations on a nanosized multiaxial molecular ferroelectric, i.e., TMCM-CdCl3 nanoplates, as an example. Combined with the analysis of the second-order susceptibility tensor, SHG polarimetry could serve as an effective method to detect the polarization orders and domain distributions of molecular ferroelectrics. Profiting from the full-optical feature, SHG polarimetry can even be performed on samples covered by transparent mediums, 2D materials, or thin metal electrodes. Our research might spark further fundamental studies and expand the application boundaries of next-generation ferroelectric materials.

Second Harmonic Generation in Janus Transition Metal Chalcogenide Oxide Monolayers: A First-Principles Investigation.

Due to the unique optical responses induced by vertical atomic asymmetry inside a monolayer, two-dimensional Janus structures have been conceived as promising building blocks for nanoscale optical devices. In this paper, second harmonic generation (SHG) in Janus transition metal chalcogenide oxide monolayers is systematically investigated by the first-principles calculations. Second-order nonlinear susceptibilities are theoretically determined for Janus MXO (M = Mo/W, X = S/Se/Te) monolayers. The calculated values are comparable in magnitude with Janus MoSSe monolayer. X-M-O symmetry breaking leads to non-zero components in vertical direction, compared with the non-Janus structure. Focusing on the SHG induced by incident light at 1064 nm, polarization-dependent responses of six Janus MXO monolayers are demonstrated. The symmetry of p-polarization changes from six-fold to three-fold with acute incidence angle. Moreover, the effects of biaxial strain on band structures and SHG are further investigated, taking MoSO as an exemplary case. We expect these results to bring in recipes for designing nonlinear optical devices based on Janus transition metal chalcogenide oxide monolayers.

Self-consistent simulations of intracavity terahertz comb difference frequency generation by mid-infrared quantum cascade lasers

Portable terahertz (THz) frequency comb sources are highly desired for applications in rotational molecular spectroscopy and sensing. To date, direct THz quantum cascade laser (QCL) frequency comb generation is not achievable at room temperature. However, THz comb generation based on intracavity difference frequency generation (DFG) in mid-infrared (mid-IR) QCLs is a promising alternative. Here, we present a numerical study of THz DFG-QCL comb formation in mid-IR QCLs based on a self-consistent multi-domain simulation approach. The dynamical simulations are performed using our open-source software tool mbsolve, which provides a flexible and efficient codebase for solving the generalized full-wave Maxwell–Bloch equations. Here, DFG in the active region of a dual-wavelength mid-IR QCL is considered for the generation of THz radiation. The mixing process and, thus, THz generation require a high second-order intersubband nonlinear susceptibility in the QCL active region and can be obtained by targeted quantum engineering. The associated nonlinear effects are included in the Hamiltonian of our Maxwell–Bloch simulation approach. All necessary input parameters for the description of the quantum system are determined self-consistently using our in-house ensemble Monte Carlo software tool for stationary carrier transport simulations. Notably, such simulations require a full-wave Maxwell–Bloch solver that does not employ the common rotating wave approximation, as a broadband optical field extending from the THz to the mid-IR region is investigated. Our modeling approach and the obtained simulation results for two THz DFG-QCL comb setups are validated against experimental data, showing reasonable agreement. Furthermore, we obtain a locked frequency modulated comb state for mid-IR and THz regimes.

Second order nonlinear optical properties of poled films containing azobenzenes tailored with azulen-1-yl-pyridine

Azo compounds, which are highly versatile molecules, have attracted a considerable attention both for their fundamental properties and for practical applications, especially in photonics. The conjugated azo-aromatic systems containing 4-(R-azulen-1-yl)-2,6-dimethyl-pyridine were investigated for their nonlinear optical properties. These molecules were embedded in polymethyl methacrylate (PMMA) matrix, and the obtained guest-host systems were processed into good optical quality thin film by spin coating technique. The dipolar moments of dissolved in PMMA molecules were oriented by applying a high DC electric field at a temperature close to the polymer glass transition temperature. The second - order nonlinear optical (NLO) properties of poled films were studied by the optical second harmonic generation technique (SHG). The poling kinetics, studied by in situ SHG as well as the measured second-order NLO susceptibilities of poled films are reported and discussed.

Second-Order Nonlinear Optics as an Orientation-Independent Probe of Molecular Environments at Interfaces.

Measurement techniques that probe the second-order susceptibility, such as second-harmonic and sum-frequency generation, are recognized for their ability to study environments with broken centrosymmetry. As a result, they serve as reporters of molecules at surfaces because the second-order susceptibility is often zero in the adjacent bulk media. Although the signals measured in such experiments carry unique information about the interfacial environment, the challenge is to disentangle properties related to the electronic structure as they are wrapped up in the orientation distribution. Over the past 30 years, this challenge has been turned into an opportunity, as many studies have sought to learn about the arrangement of molecules at surfaces. Here we demonstrate that the flipped case is possible, where fundamental properties of the interfacial environment can be extracted in a manner that is completely independent of, and therefore oblivious to, the orientation distribution. Using p-cyanophenol adsorbed at the air-water interface as an example, we illustrate that the cyano group polarizability varies less along the direction of the C-N bond when at the surface than when the same molecules are in the bulk aqueous phase.

Strong second-harmonic generation by sublattice polarization in non-uniformly strained monolayer graphene

Despite the potential of graphene for building a variety of quantum photonic devices, its centrosymmetric nature forbids the observation of second harmonic generation (SHG) for developing second-order nonlinear devices. To activate SHG in graphene, extensive research efforts have been directed towards disrupting graphene’s inversion symmetry using external stimuli like electric fields. However, these methods fail to engineer graphene’s lattice symmetry, which is the root cause of the forbidden SHG. Here, we harness strain engineering to directly manipulate graphene’s lattice arrangement and induce sublattice polarization to activate SHG. Surprisingly, the SHG signal is boosted 50-fold at low temperatures, which can be explained by resonant transitions between strain-induced pseudo-Landau levels. The second-order susceptibility of strained graphene is found to be larger than that of hexagonal boron nitride with intrinsic broken inversion symmetry. Our demonstration of strong SHG in strained graphene offers promising possibilities for developing high-efficiency nonlinear devices for integrated quantum circuits.

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.

Fluctuations near the liquid-gas and chiral phase transitions in hadronic matter

We investigate the fluctuations of the net-baryon number density in dense hadronic matter. Chiral dynamics is modeled via the parity doublet Lagrangian, and the mean-field approximation is employed to account for chiral criticality. We focus on the qualitative properties and systematics of the second-order susceptibility of the net-baryon number density for individual positive- and negative-parity nucleons whose masses become degenerate at the chiral restoration. It is shown that the second-order susceptibility of the positive-parity state can become negative when the chiral symmetry is restored, as a natural consequence of the unique relationship of the mass to the order parameter. Moreover, we find that such negative fluctuations are indicative of approaching the critical point on the chiral phase boundary. Our results may have consequences for the interpretation of the experimental data on net-proton fluctuations in heavy-ion collisions.

Effect of Surface Nonlinearity Distribution on Second Harmonic Generation under Tightly Focused Beams

A thorough integral formulation describing the second harmonic generation under tightly focused linearly and radially polarized beams for an arbitrary distribution of the nonlinear susceptibility over the surface of isotropic media was presented. We numerically simulated effects caused by the straight edge of the nonlinear region. In particular, we demonstrated that the second harmonic radiation in the normal direction, which is forbidden in common cases of highly symmetrical nonlinear surfaces, is allowed in the presence of the edge. This is provided by χ(2)xzx-component of the second-order susceptibility.

Size dependence of second-harmonic scattering from nanoparticles: Disentangling surface and electrostatic contributions.

Polarimetric angle-resolved second-harmonic scattering (AR-SHS) is an all-optical tool enabling the study of unlabeled interfaces of nano-sized particles in an aqueous solution. As the second harmonic signal is modulated by interference between nonlinear contributions originating at the particle's surface and those originating in the bulk electrolyte solution due to the presence of a surface electrostatic field, the AR-SHS patterns give insight into the structure of the electrical double layer. The mathematical framework of AR-SHS has been previously established, in particular regarding changes in probing depth with ionic strength. However, other experimental factors may influence the AR-SHS patterns. Here, we calculate the size dependence of the surface and electrostatic geometric form factors for nonlinear scattering, together with their relative contribution to the AR-SHS patterns. We show that the electrostatic term is stronger in the forward scattering direction for smaller particle sizes, while the ratio of the electrostatic to surface terms decreases with increasing size. Besides this competing effect, the total AR-SHS signal intensity is also weighted by the particle's surface characteristics, given by the surface potential Φ0 and the second-order surface susceptibility χs,2 2. The weighting effect is experimentally demonstrated by comparing SiO2 particles of different sizes in NaCl and NaOH solutions of varying ionic strengths. For NaOH, the larger χs,2 2 values generated by deprotonation of surface silanol groups prevail over the electrostatic screening occurring at high ionic strengths; however, only for larger particle sizes. This study establishes a better connection between the AR-SHS patterns and surface properties and predicts trends for arbitrarily-sized particles.