Second-order Nonlinearity Research Articles

Giant Enhancement of Second-Order Nonlinearity of Epsilon-near- Zero Medium by a Plasmonic Metasurface.

Nonlinear frequency conversion at the nanoscale is important for many applications in free space and integrated photonics. In epsilon-near-zero (ENZ) materials, second-harmonic generation (SHG) is significantly enhanced but the oblique incidence is required to address nonlinearity. To circumvent this constraint, we design a hybrid metasurface consisting of plasmonic nanostructures on an ENZ nanofilm generating strongly enhanced SHG at normal incidence in transmission. We show that the Au meta-atoms on an indium-tin-oxide (ITO) layer provide an approximately 104-fold experimentally measured SHG enhancement at normal incidence at the fundamental wavelength near the ENZ condition of ITO. This giant enhancement stems from reshaping the vectorial properties of the incident light near the Au nanostructures and its increased coupling to the ENZ film. The proposed hybrid ENZ metasurface offers a promising platform for developing ultracompact and efficient nonlinear optical sources at the nanoscale.

Generalization of Second-Order Quasi-Phase Matching in Whispering Gallery Mode Resonators Using Berry Phase

Second-order nonlinearities in whispering gallery mode resonators are highly investigated for their many applications such as wavelength converters, entangled photon sources, and generation of freq...

Frequency Comb Generation via Cascaded Second-Order Nonlinearities in Microresonators.

Optical frequency combs are revolutionizing modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturization through microresonator-based solutions. The combs in such devices are typically generated using the third-order χ^{(3)} nonlinearity of the resonator material. An alternative approach is making use of second-order χ^{(2)} nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or on relatively low-Q waveguide resonators. Here, we present the first such comb that is based on a millimeter-sized microresonator made of lithium niobate, that allows for cascaded second-order nonlinearities. This proof-of-concept device comes already with pump powers as low as 2mW, generating repetition-rate-locked combs around 1064 and 532nm. From the nonlinear dynamics point of view, the observed combs correspond to Turing roll patterns.

Electrically Micro‐Polarized Amorphous Sodo‐Niobate Film Competing with Crystalline Lithium Niobate Second‐Order Optical Response

AbstractThe design of active optical devices integrating second‐order nonlinear (SONL) optical responses typically relies on the use of dielectric crystalline materials such as lithium niobate (LN) or semiconductors such as GaAs. Despite high SONL susceptibilities, these materials present important geometry constrains inherent to their crystalline nature limiting the complexity of the designed photonic systems. Conversely, amorphous materials are versatile optical media compatible with broad platform designs possessing a wide range of optical properties attributable to their composition flexibility. Demonstrated here for the first time in an amorphous inorganic material, a magnitude of SONL optical susceptibility (χ(2) = 29 pm V−1 at 1.06 µm) comparable to that of LN single crystal is reported. By using a thermo‐electrical imprinting process, fine control of the induced uniaxial anisotropy is demonstrated at the micrometer scale. This work paves the way for the future design of integrated nonlinear photonic circuits based on amorphous inorganic materials enabled by the spatially selective and high SONL optical susceptibility of these promising and novel optical materials.

Integrated lithium niobate photonics

Abstract Lithium niobate (LiNbO3) on insulator (LNOI) is a promising material platform for integrated photonics due to single crystal LiNbO3 film’s wide transparent window, high refractive index, and high second-order nonlinearity. Based on LNOI, the fast-developing ridge-waveguide fabrication techniques enabled various structures, devices, systems, and applications. We review the basic structures including waveguides, cavities, periodically poled LiNbO3, and couplers, along with their fabrication methods and optical properties. Treating those basic structures as building blocks, we review several integrated devices including electro-optic modulators, nonlinear optical devices, and optical frequency combs with each device’s operating mechanism, design principle and methodology, and performance metrics. Starting from these integrated devices, we review how integrated LNOI devices boost the performance of LiNbO3’s traditional applications in optical communications and data center, integrated microwave photonics, and quantum optics. Beyond those traditional applications, we also review integrated LNOI devices’ novel applications in metrology including ranging system and frequency comb spectroscopy. Finally, we envision integrated LNOI photonics’ potential in revolutionizing nonlinear and quantum optics, optical computing and signal processing, and devices in ultraviolet, visible, and mid-infrared regimes. Beyond this outlook, we discuss the challenges in integrated LNOI photonics and the potential solutions.

High-efficiency second-order nonlinear processes in an optical microfibre assisted by few-layer GaSe

The centrosymmetric nature of silica fibre precludes the realisation of second-order nonlinear processes in optical fibre systems. Recently, the integration of 2D materials with optical fibres has opened up a great opportunity to develop all-fibre active devices. Here, we demonstrate high-efficiency second-order nonlinear frequency conversions in an optical microfibre assisted with few-layer gallium selenide (GaSe) nanoflakes. Attributed to the strong evanescent field of the microfibre and ultrahigh second-order nonlinearity of the GaSe nanoflakes, second harmonic generation (SHG) and sum-frequency generation (SFG) are effectively achieved with only sub-milliwatt continuous-wave (CW) lasers in the wavelength range of 1500–1620 nm, covering the C and L telecom bands. The SHG intensity from the microfibre is enhanced by more than four orders of magnitude with the assistance of the GaSe nanoflakes on fibre nonlinear processes. Moreover, in the SFG process, the intensity transfer between different frequencies can be effectively manipulated by changing the wavelengths and powers of two pump lasers. The realised strong second-order nonlinearity in the GaSe-integrated microfibre might expand the applications of all-fibre devices in all-optical signal processing and new light source generation at awkward wavelengths.

Highly tunable second-harmonic generation in all-optically poled silicon nitride waveguides.

The availability of nonlinear parametric processes, such as frequency conversion in photonic integrated circuits is essential. In this contribution, we demonstrate a highly tunable second-harmonic generation in a fully complementary metal-oxide-semiconductor (CMOS)-fabrication-compatible silicon nitride integrated photonic platform. We induce the second-order nonlinearity using an all-optical poling technique with the second-harmonic light generated in the fundamental mode, and a narrow quasi-phase matching (QPM) spectrum by avoiding higher-order mode mixing. We are then able to broadly tune the phase-matched pump wavelength over the entire C-band (1540 nm to 1560 nm) by varying the poling conditions. Fine-tuning of QPM is enabled by thermo-optic effect with the tuning slope Δλ/ΔT in our device being 113.8 pm/°C. In addition, we exploit the measurable variation of the 3 dB QPM bandwidth to confirm how the length of the all-optically inscribed grating varies with exposure time.

Single-photon quantum regime of artificial radiation pressure on a surface acoustic wave resonator

Electromagnetic fields carry momentum, which upon reflection on matter gives rise to the radiation pressure of photons. The radiation pressure has recently been utilized in cavity optomechanics for controlling mechanical motions of macroscopic objects at the quantum limit. However, because of the weakness of the interaction, attempts so far had to use a strong coherent drive to reach the quantum limit. Therefore, the single-photon quantum regime, where even the presence of a totally off-resonant single photon alters the quantum state of the mechanical mode significantly, is one of the next milestones in cavity optomechanics. Here we demonstrate an artificial realization of the radiation pressure of microwave photons acting on phonons in a surface acoustic wave resonator. The order-of-magnitude enhancement of the interaction strength originates in the well-tailored, strong, second-order nonlinearity of a superconducting Josephson junction circuit. The synthetic radiation pressure interaction adds a key element to the quantum optomechanical toolbox and can be applied to quantum information interfaces between electromagnetic and mechanical degrees of freedom.

Enhancement of Second-Order Optical Nonlinearity in a Lutetium Selenite by Monodentate Anion Partial Substitution

The systematic modification of the molecular structure of nonlinear optical (NLO)-active materials is a very attractive approach to the improvement of NLO performance. In this study, one lutetium selenite compound Lu(SeO3)(HSeO3)(H2O)·(H2O) (1) was synthesized by hydrothermal means, while a further two lutetium selenites Lu3F(SeO3)4 (2) and Lu(SeO3)(NO3)(H2O) (3) were successfully synthesized by anion partial substitution (APS) of the parent structure 1 under hydrothermal conditions. Specifically, substitution of the [HSeO3]– anions in the noncentrosymmetric 1 by F– or [NO3]− anions with differing denticity leads to the formation of polar 2 and centrosymmetric 3. Our study reveals that the denticity of the secondary functional anions has a significant influence on the coordination environments of the rare-earth-metal cation Lu3+ and consequently the molecular configuration and NLO performance of the resultant multidimensional selenites. In contrast to 1, which displays a weak second-harmonic generation (SHG) response (0.1 × KH2PO4 (KDP)), 2 exhibits a greatly improved NLO performance, including a strong SHG signal (2.5 × KDP, the highest value among rare-earth-metal-based NLO selenites), a wide band gap (3.57 eV) and optical transparency window (0.35–10.3 μm), high thermal stability (∼550 °C), and a large laser damage threshold (36 × AgGaS2). These results suggest that 2, as the first example of a fluorinated lutetium selenite, is a strong NLO candidate crystal spanning a region from the near-ultraviolet to the mid-infrared. These APS studies highlight a new feasible approach toward high-performance NLO crystals.

Evaluation of yield strength by ultrasonic reconstruction of quadratic nonlinear Stress–Strain curve

The ultrasonic nonlinearity parameter β defined by the ratio of the second-order harmonic amplitude to the square of fundamental frequency amplitude, has been considered as a potential index to evaluate material degradation. However, the yield strength obtained from destructive tensile testing is still widely adopted for this purpose since it is a more intuitive concept to the field engineer than the parameter β. Therefore, this study proposes a nondestructive method to evaluate the yield strength directly from the ultrasonic measurements. In this regard, the tensile stress–strain curve is represented in the form of a quadratic nonlinear stress–strain equation within the elastic range, which includes the linear elastic modulus and the second-order nonlinearity parameter βt. The linear elastic modulus is obtained by measuring the propagation velocity of longitudinal and transverse waves using a traditional ultrasonic pulse-echo method, and the second-order nonlinearity parameter is obtained by measuring the Murnaghan constants using acoustoelastic effects. Then, the tensile stress–strain curve is reconstructed to estimate the 0.01% offset yield strength. To demonstrate the application of the proposed algorithm, the experiments were performed for heat-treated SA508 specimens. The results indicate that the 0.01% offset yield strength obtained using the proposed algorithm exhibit a good agreement with that obtained via destructive tensile testing.

Data-driven prediction of diamond-like infrared nonlinear optical crystals with targeting performances

Combining high-throughput screening and machine learning models is a rapidly developed direction for the exploration of novel optoelectronic functional materials. Here, we employ random forests regression (RFR) model to investigate the second harmonic generation (SHG) coefficients of nonlinear optical crystals with distinct diamond-like (DL) structures. 61 DL structures in Inorganic Crystallographic Structure Database (ICSD) are selected, and four distinctive descriptors, including band gap, electronegativity, group volume and bond flexibility, are used to model and predict second-order nonlinearity. It is demonstrated that the RFR model has reached the first-principles calculation accuracy, and gives validated predictions for a variety of representative DL crystals. Additionally, this model shows promising applications to explore new crystal materials of quaternary DL system with superior mid-IR NLO performances. Two new potential NLO crystals, Li2CuPS4 with ultrawide bandgap and Cu2CdSnTe4 with giant SHG response, are identified by this model.

Giant second-order cross nonlinearities via direct perturbation to the dark state in coherent population trapping

We study the nonlinearities due to direct perturbation to the dark state in coherent population trapping (CPT). To extract the susceptibilities of the CPT atoms with respect to probe fields, we treat the CPT dressing fields as control parameters and redefine susceptibilities with respect to the probe fields alone. With such a redefinition, we reveal that a CPT-based system displays an ultralarge, resonantly enhanced second-order cross susceptibility ${\ensuremath{\chi}}^{(2)}$ together with vanishing linear absorption. Physically, this effect is based on the CPT dark-state shift, which is traced to the six-photon parametric processes for all involved fields (including the dressing and probe fields). Because of the lack of the direct perturbation, this effect is absent in the electromagnetically induced transparency (EIT)-based system, in which only resonantly enhanced third-order (Kerr) susceptibility ${\ensuremath{\chi}}^{(3)}$ is obtainable but much weaker than the second-order one. The second-order nonlinearity, because of its stronger effect, can be more sensitive for quantum nonlinear optics at low light levels than the third-order nonlinearity.

Nonlinear analysis of square concrete-filled double steel tubular slender columns incorporating preload effects

Thin-walled square and circular hollow steel tubes are designed to support the permanent and construction loads of several upper composite floors before filling the concrete into the tubes to form concrete-filled double steel tubular (CFDST) columns. The influences of preloads acting on the steel tubes on the structural responses of slender square CFDST columns have not been investigated either experimentally or numerically. This paper presents a fiber-based computational model for the determination of the interaction behavior of local and global buckling in axially and eccentrically loaded CFDST thin-walled square slender columns including preload effects. The computational modeling method accounts for the influences of the deformations induced by preloads, local-global interaction buckling, geometric imperfections, second-order, and geometric and material nonlinearities. The accuracy of the computational algorithms developed is validated by comparing computations with test data on concrete-filled steel tubular (CFST) columns and finite element results of double-skin CFST (DCFST) columns with preload effects. The computer algorithms are employed to quantify the influences of preloads on the local-global interaction buckling responses of CFDST columns with various important parameters. Proposed is a design method for calculating the ultimate loads of concentrically loaded slender square CFDST columns considering preloads. The computational and design models developed are shown to be efficient modeling and design tools for square CFDST slender columns taking into account the construction method of high-rise composite buildings.

Photocarrier-Induced Active Control of Second-Order Optical Nonlinearity in Monolayer MoS2.

Atomically thin transition metal dichalcogenides (TMDs) in their excited states can serve as exceptionally small building blocks for active optical platforms. In this scheme, optical excitation provides a practical approach to control light-TMD interactions via the photocarrier generation, in an ultrafast manner. Here, it is demonstrated that via a controlled generation of photocarriers the second-harmonic generation (SHG) from a monolayer MoS2 crystal can be substantially modulated up to ≈55% within a timeframe of ≈250 fs, a set of performance characteristics that showcases the promise of low-dimensional materials for all-optical nonlinear data processing. The combined experimental and theoretical study suggests that the large SHG modulation stems from the correlation between the second-order dielectric susceptibility χ(2) and the density of photoexcited carriers in MoS2 . Indeed, the depopulation of the conduction band electrons, at the vicinity of the high-symmetry K/K' points of MoS2 , suppresses the contribution of interband electronic transitions in the effective χ(2) of the monolayer crystal, enabling the all-optical modulation of the SHG signal. The strong dependence of the second-order optical response on the density of photocarriers reveals the promise of time-resolved nonlinear characterization as an alternative route to monitoring carrier dynamics in excited states of TMDs.

Improving lower bounds on the second-order nonlinearity of three classes of Boolean functions

Boolean functions used in symmetric-key cryptosystems must have high second-order nonlinearity to withstand several known attacks and some potential attacks which may exist but are not yet efficient and might be improved in the future. The second-order nonlinearity of Boolean functions also plays an important role in coding theory, since the maximal second-order nonlinearity of all Boolean functions in n variables equals the covering radius of the Reed–Muller code with length 2n and order r. It is well-known that providing a tight lower bound on the second-order nonlinearity of a general Boolean function with high algebraic degree is a hard task, excepting a few special classes of Boolean functions. In this paper, we improve the lower bounds on the second-order nonlinearity of three classes of Boolean functions of the form fi(x)=Tr1n(xdi) in n variables for i=1,2 and 3, where Tr1n denotes the absolute trace mapping from F2n to F2 and di’s are of the form (1) d1=2m+1+3 and n=2m, (2) d2=2m+2m+12+1, n=2m with odd m, and (3) d3=22r+2r+1+1 and n=4r with even r.

Controllable scattering of a single photon inside a one-dimensional coupled resonator waveguide with second-order nonlinearity.

We note that most of the studies of the single photon scattering inside a one-dimensional coupled resonator waveguide are based on the waveguide coupling with the atom systems. In this paper, we will study the single photon scattering enabled by another system, i.e., the second-order nonlinearity, which can act as a single photon switch to control the single photon transmission and reflection inside the one-dimensional coupled resonator waveguide. The transmission rate is calculated to analyze the single-photon scattering properties. In addition, a more complicated second-order nonlinear form, i.e., three-wave mixing, is discussed to control single photon transmission inside the one-dimensional coupled resonator waveguide.

Waveguide-integrated three-dimensional quasi-phase-matching structures

Nonlinear photonic structures with a modulated second-order nonlinearity are used widely for quasi-phase-matched parametric processes. Creating three-dimensional (3D) nonlinear photonic structures is promising but still challenging, since standard poling methods are limited to two-dimensional structures. Light-induced quasi-phase matching (QPM) can overcome this issue by a depletion of the second-order nonlinearity with focused femtosecond laser pulses. We report, to the best of our knowledge, the first integration of a 3D QPM structure in the core of a lithium niobate waveguide applying light-induced fabrication. Depressed-cladding waveguides and embedded QPM structures are fabricated by femtosecond laser lithography. The 3D capability is exploited by splitting the QPM gratings in the waveguide core into two or four parts, respectively. These monolithic nonlinear waveguides feature parallel multi-wavelength frequency conversion. Finally, we demonstrate a concept for second-harmonic beam shaping taking advantage of a helically twisted nonlinear structure. Our results open new avenues for creating highly efficient advanced QPM devices.

Transient Second-Order Nonlinear Media: Breaking the Spatial Symmetry in the Time Domain via Hot-Electron Transfer

Second-order optical effects are essential to the active control of light and the generation of new spectral components. The inversion symmetry, however, prevents achieving a bulk χ^{(2)} response, limiting the portfolio of the second-order nonlinear materials. Here, we demonstrate subpicosecond conversion of a statically passive dielectric to a transient second-order nonlinear medium upon the ultrafast transfer of hot electrons. Induced by an optical switching signal, the amorphous dielectric with vanishing intrinsic χ^{(2)} develops dynamically tunable second-order nonlinear responses. By taking the second-harmonic generation as an example, we show that breaking the inversion symmetry through hot-electron dynamics can be leveraged to address the critical need for all-optical control of second-order nonlinearities in nanophotonics. Our approach can be generically adopted in a variety of material and device platforms, offering a new class of complex nonlinear media with promising potentials for all-optical information processing.

Rational structure design of isoxazolone-based crystals with large second-order optical nonlinearity

Two new acentric isoxazolone-based organic crystals of C24H17NO3 (MPFI) and C18H15NO3S (MPMI) were designed and synthesized by a structure fine-tuning strategy.

Study of the hyper-Rayleigh scattering first hyperpolarizability of a chalcone derivative in various solvent media

In this work we investigate the solvent media effects on the nonlinear optical properties of a chalcone derivative, (2E)-3-(3-methylphenyl)-1-(4-nitrophenyl) prop-2-en-1-one (3MPNP), using the polarizable continuum model (PCM) at DFT/B3LYP/6-311+G(d) level. The behavior of the hyper-Rayleigh scattering first hyperpolarizability and the average second hyperpolarizability, are studied as function of the dielectric constant of the solvent medium in both dynamic and static cases. Full Text: PDF ReferencesL. R. Almeida et al., "Synthesis, structural characterization and computational study of a novel amino chalcone: a potential nonlinear optical material", New J. Chem., vol. 41, no. 4, pp. 1744-1754, 2017. CrossRef P. K. Murthy et al., "An analysis of structural and spectroscopic signatures, the reactivity study of synthetized 4,6-dichloro-2-(methylsulfonyl)pyrimidine: A potential third-order nonlinear optical material", J. Mol. Struct., vol. 1186, pp. 263-275, Jun. 2019. CrossRef J. Kongsted, A. Osted, K. V Mikkelsen, and O. Christiansen, "“Second harmonic generation second hyperpolarizability of water calculated using the combined coupled cluster dielectric continuum or different molecular mechanics methods", J. Chem. Phys., vol. 120, no. 8, pp. 3787-98, Feb. 2004. CrossRef T. L. Fonseca, J. R. Sabino, M. A. Castro, and H. C. Georg, "A theoretical investigation of electric properties of L-arginine phosphate monohydrate including environment polarization effects", J. Chem. Phys., vol. 133, no. 14, pp. 1-8, 2010. CrossRef A. KARAKAŞ, Z. E. KOÇ, M. FRIDRICHOVÁ, P. NĚMEC, and J. KROUPA, "THE INVESTIGATION OF SECOND-ORDER NONLINEAR OPTICAL PROPERTIES OF P-NITROPHENYLAZOANILINE: SECOND HARMONIC GENERATION AND AB INITIO COMPUTATIONS", J. Theor. Comput. Chem., vol. 11, no. 01, pp. 209-221, Feb. 2012. CrossRef T. Seidler, K. Stadnicka, and B. Champagne, "Second‐order Nonlinear Optical Susceptibilities and Refractive Indices of Organic Crystals from a Multiscale Numerical Simulation Approach", Adv. Opt. Mater., vol. 2, no. 10, pp. 1000-1006, Oct. 2014. CrossRef L. M. G. Abegão et al., "Second- and third-order nonlinear optical properties of unsubstituted and mono-substituted chalcones", Chem. Phys. Lett., vol. 648, pp. 91-96, Mar. 2016. CrossRef W. F. Vaz et al., "Synthesis, characterization, and third-order nonlinear optical properties of a new neolignane analogue", RSC Adv., vol. 6, no. 82, pp. 79215-79227, 2016. CrossRef C. Valverde et al., "The solid state structure and environmental polarization effect of a novel asymmetric azine", New J. Chem., vol. 41, no. 19, pp. 11361-11371, 2017. CrossRef P. N. Prasad, D. J. Williams, and others, Introduction to nonlinear optical effects in molecules and polymers, vol. 1. Wiley New York etc., 1991. DirectLink P. Günter, Nonlinear Optical Effects and Materials, 4th ed. Berlin: Springer Berlin Heidelberg, 2000. CrossRef H. Inan et al., "Photonic crystals: emerging biosensors and their promise for point-of-care applications", Chem. Soc. Rev., vol. 46, no. 2, pp. 366-388, 2017. CrossRef H. J. Chang et al., "Chiral Nonlinear Optics in Oxides, Polymers and Liquid Crystals", J. Korean Phys. Soc., vol. 43, no. 4, p. 587, 2003. DirectLink R. Bersohn, Y. Pao, and H. L. Frisch, "Double‐Quantum Light Scattering by Molecules", J. Chem. Phys., vol. 45, no. 9, pp. 3184-3198, Nov. 1966. CrossRef K. Clays and A. Persoons, "Hyper-Rayleigh scattering in solution", Phys. Rev. Lett., vol. 66, no. 23, pp. 2980-2983, 1991. CrossRef J. Campo, F. Desmet, W. Wenseleers, and E. Goovaerts, "Highly sensitive setup for tunable wavelength hyper-Rayleigh scattering with parallel detection and calibration data for various solvents", Opt. Express, vol. 17, no. 6, p. 4587, Mar. 2009. CrossRef S. R. Prabhu, A. Jayarama, K. Chandrasekharan, V. Upadhyaya, and S. W. Ng, "Synthesis, growth, structural characterization, Hirshfeld analysis and nonlinear optical studies of a methyl substituted chalcone", J. Mol. Struct., vol. 1136, pp. 244-252, May 2017. CrossRef K. Clays and A. Persoons, "Hyper‐Rayleigh scattering in solution", Rev. Sci. Instrum., vol. 63, no. 6, pp. 3285-3289, Jun. 1992. CrossRef K. Clays et al., "Nonlinear Optical Properties of Proteins Measured by Hyper-Rayleigh Scattering in Solution", Science (80-. )., vol. 262, no. 5138, pp. 1419-1422, Nov. 1993. CrossRef M. Frisch et al., Gaussian, Inc., Wallingford CT, 2009. DirectLink J. M. F. Custodio et al., "Chalcone as Potential Nonlinear Optical Material: A Combined Theoretical, Structural, and Spectroscopic Study", J. Phys. Chem. C, vol. 123, no. 10, pp. 5931-5941, Mar. 2019. CrossRef