Second-order Nonlinearity Research Articles

Nonlinear Optical Activity of a Chiral Organic-Inorganic ([(NH3CH2CH2)3NH])2[MnBr5]Br5 Photoluminescent and Piezoelectric Crystal.

The family of Mn-based organic-inorganic hybrids has greatly expanded due to their advantages in applications. They also show superior bright and size-tunable photoluminescence and can be considered a perfect alternative to toxic lead-based compounds. In this work, we present the detailed structural, optical, and electrical characterization of ([(NH3CH2CH2)3NH])2[MnBr5]Br5. The title compound exhibits a unique type of inorganic arrangement created by the trigonal bipyramids. It crystallizes in noncentrosymmetric space group R32, indicating its optical activity, piezoelectricity, and second-order optical nonlinearity proven by the second harmonic of light measurements. The studied crystals exhibit intense photoluminescence originating from the Mn(II) ion 4T1(G) → 6A1 transition. The measured lifetime of the photoluminescence emission is ≤1.5 ms, while the measured quantum yield for both powder and crystal samples reaches ∼70%.

Observation of Anisotropic Second Harmonic Generation in Two-Dimensional Niobium Diselenide.

The intrinsic anisotropy of NbSe2 provides a favorable prerequisite of second harmonic generation (SHG) and rich possibilities for tailoring its nonlinear optical (NLO) properties. Here we report the highly efficient SHG of mechanically exfoliated NbSe2 flakes. The nonlinear optical response changes with excitation wavelengths, layer thicknesses, and polarizations of the excitation laser. The anisotropic SHG response further exhibits the intrinsic non-centrosymmetric crystal structure and could effectively assign the crystalline orientation of NbSe2 flakes. Interestingly, although NbSe2 flakes with tens of nanometers thickness experience attenuations in SHG performance, more efficient SHG anisotropy ratios were obtained, which are around 4 times higher than that of the 5-layer counterpart. The determined second-order nonlinearities of NbSe2 flakes (monolayer: ∼1.0 × 103 pm/V; 3-layer: ∼73 pm/V) are comparable to those of the commonly reported two-dimensional materials (e.g., MoS2, WSe2, graphene) with the same number of layers and much higher than those of commercial nonlinear optical crystals.

An integrated 3C-silicon carbide-on-insulator photonic platform for nonlinear and quantum light sources

Silicon carbide (SiC) polytypes are emerging for integrated nonlinear and quantum photonics due to their wide-bandgap energies, second-order optic nonlinearity and process compatibility with complementary metal-oxide-semiconductor technologies. Among polytypes, 3C-SiC is the only one epitaxially grown on wafer-scale silicon substrates. However, on-chip nonlinear and quantum light sources leveraging the second-order nonlinearity of 3C-SiC have not been reported to our knowledge. Here, we design and fabricate an elliptical microring on 3C-SiC. We demonstrate a nonlinear light source with a second-harmonic generation efficiency of 17.4±0.2%W−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$17.4\\pm 0.2 \\% {W}^{-1}$$\\end{document} and difference-frequency generation with a signal-idler bandwidth of 97 nm. We demonstrate a spontaneous parametric down-conversion source with a photon-pair generation rate of 4.8 MHz and a coincidence-to-accidental ratio of 3361±84\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3361\\pm 84$$\\end{document}. We measure a low heralded single-photon second-order coherence gH2=0.0007\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${g}_{H}^{\\left(2\\right)}=0.0007$$\\end{document}. We observe time-bin entanglement with a visibility of 86.0±2.4%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$86.0\\pm 2.4 \\%$$\\end{document} using this source. Our work paves a way toward SiC-based on-chip nonlinear and quantum photonic circuits.

Boosted Second Harmonic Generation and Cascaded Sum Frequency Generation from a Surface Crystallized Glass Ceramic Microcavity.

The development of novel materials and structures for efficient second-order nonlinear micro/nano devices remains a significant challenge. In this study, the remarkable enhancement of second-harmonic generation (SHG) and cascaded sum frequency generation in whispering gallery mode microspheres made of surface-crystallized glass with a 6-µm Ba2TiSi2O8 crystal layer are demonstrated. Attributed to the core-shell design, the Ba2TiSi2O8 located on the surface can be efficiently coupled with whispering gallery modes, resulting in a highly efficient micron-scale cavity-enhanced second-order optical nonlinearity. Greatly enhanced SHG of the microcavity is observed, which is up to 80 times stronger than that of a non-resonant sample. Furthermore, owing to the wavelength non-selectivity of random quasi-phase matching, ultra-wideband SHG with a strong response ranging from 860 to 1600nm and high-contrast polarization characteristics is demonstrated. The glass-ceramic-based microsphere cavity also boosts the cascading optical nonlinearity, manifested by a two-magnitude enhancement of cascaded sum frequency generation. This work delineates an efficient strategy for boosting nonlinear optical response in glass ceramics, which will open up new opportunities for applications in photonics and optical communications.

Boosted Second Harmonic Generation of a Chiral Hybrid Lead Halide Resonant to Charge Transfer Exciton from Metal Halide Octahedra to Ligand.

Chiral hybrid organic-inorganic metal halides (HOMHs) offer an ideal platform for the advancement of second-order nonlinear optical (NLO) materials owing to their inherent noncentrosymmetric structures. The enhancement of optical nonlinearity of chiral HOMHs could be achieved by matching the free exciton and/or self-trapped exciton energy levels with desired NLO frequencies. However, the current scarcity of resonance modes and low resonance ratio hamper the further improvements of NLO performance. Herein, we propose a new resonant channel of charge transfer (CT) excited states from metal halide polyhedra to organic ligand to boost the second-order optical nonlinearity of chiral HOMHs. The model lead halide (C7H10N)PbBr3 (C7H10N=1-ethylpyridinium) exhibits a drastically enhanced second harmonic generation in resonance to the deep CT exciton energy, with intensity of up to 111.0 times that of KDP and 10.9 times that of urea. The effective NLO coefficient has been determined to be as high as ~40.2 pm V-1, balanced with a large polarization ratio and high laser damage threshold. This work highlights the contribution of organic ligands in the construction of a resonant channel for enhancing second-order NLO coefficients of metal halides, and thus provides guidelines for designing new chiral HOMHs materials for advanced nonlinear photonic applications.

Synergic action of linear dispersion, second-order nonlinearity, and third-order nonlinearity in shaping the spectral profile of a femtosecond pulse transporting in a lithium niobate crystal

We present a detailed theoretical and numerical analysis on the temporal-spectral-spatial evolution of a high-peak-power femtosecond laser pulse in two sets of systems: a pure lithium niobate (LN) plate and a periodically poled lithium niobate (PPLN) plate. We develop a modified unidimensional pulse propagation model that considers all the prominent linear and nonlinear processes and carried out the simulation process based on an improved split-step Fourier transformation method. We theoretically analyze the synergic action of the linear dispersion effect, the second-order nonlinearity (2nd-NL) second-harmonic generation (SHG) effect, and the third-order nonlinearity (3rd-NL) self-phase modulation (SPM) effect, and clarify the physical mechanism underlying the peculiar and diverse spectral broadening patterns previously reported in LN and PPLN thin plate experiments. Such analysis and discussion provides a deeper insight into the synergetic contribution of these linear and nonlinear effects brought about by the interaction of a femtosecond laser pulse with the LN nonlinear crystal and helps to draw a picture to fully understand these fruitful optical physical processes, phenomena, and laws.

Time-Dependent Ultrafast Quadratic Nonlinearity in an Epsilon-Near-Zero Platform.

Ultrafast nonlinearity, which results in modulation of the linear optical response, is a basis for the development of time-varying media, in particular those operating in the epsilon-near-zero (ENZ) regime. Here, we demonstrate that the intraband excitation of hot electrons in the ENZ film results in a second-harmonic resonance shift of ∼10 THz (40 nm) and second-harmonic generation (SHG) intensity changes of >100% with only minor (<1%) changes in linear transmission. The modulation is 10-fold enhanced by a plasmonic metasurface coupled to a film, allowing for ultrafast modulation of circularly polarized SHG. The effect is described by the plasma frequency renormalization in the ENZ material and the modification of the electron damping, with a possible influence of the hot-electron dynamics on the quadratic susceptibility. The results elucidate the nature of the second-order nonlinearity in ENZ materials and pave the way to the rational engineering of active nonlinear metamaterials and metasurfaces for time-varying applications.

DC Voltage Induces Quadratic Optical Nonlinearity in Ion-Exchanged Glasses at Room Temperature

We demonstrate that applying DC voltage at room temperature to an ion-exchanged glass induces quadratic optical nonlinearity in a subsurface region of the glass. We associate this with the EFISH (Electric-Field-Induced Second Harmonic) effect due to the Maxwell–Wagner charge accumulation in the subsurface region of the glass, in which a conductivity gradient forms as a result of the ion exchange processing. The second harmonic (SH) signal from the soda–lime glass subjected to potassium-for-sodium ion exchange is comparable with one from the same glass after thermal poling. The signal linearly increases with the duration of the ion exchange. The lower mobility of the potassium ions results in a higher SH signal from the potassium-for-sodium exchanged glass than that from the silver-for-sodium ion-exchanged one. This phenomenon is resistant to thermal annealing: only a 500 °C anneal caused noticeable degradation of the SH signal after “charging” the specimen. The phenomenon found is of interest for characterizing graded conductivity regions and providing and controlling second-order optical nonlinearity in transparent isotropic media.

Electro-Optical Comb Envelope Engineering Based on Mode Crossing.

Resonator-enhanced electro-optical (EO) combs could generate a series of comb lines with high coherence and stability. Recently, EO comb based on thin-film lithium niobate (TFLN) has begun to show great potential thanks to the high second-order nonlinearity coefficient of lithium niobate crystal. Here we demonstrate that EO comb envelope engineering based on mode crossing induced a quality factor reduction in the TFLN racetrack microcavity both in the numerical simulation and experiment. Our method paves the way for the generation of EO combs with an arbitrary envelope.

Electric field induced out-of-plane second-order optical nonlinearity in monolayer transition metal dichalcogenides

Electric field induced out-of-plane second-order optical nonlinearity in monolayer transition metal dichalcogenides

Monomial Boolean functions with large high-order nonlinearities

Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bounds on the second-order, third-order, and higher order nonlinearities of some monomial Boolean functions.We prove lower bounds on the second-order nonlinearities of functions trn(x7) and trn(x2r+3) where n=2r. Among all monomial Boolean functions, our bounds match the best second-order nonlinearity lower bounds by Carlet [IEEE Transactions on Information Theory 54(3), 2008] and Yan and Tang [Discrete Mathematics 343(5), 2020] for odd and even n, respectively. We prove a lower bound on the third-order nonlinearity for functions trn(x15), which is the best third-order nonlinearity lower bound. For any r, we prove that the r-th order nonlinearity of trn(x2r+1−1) is at least 2n−1−2(1−2−r)n+r2r−1−1−O(2n2). For r≪log2⁡n, this is the best lower bound among all explicit functions.

On SINDy Approach to Measure-Based Detection of Nonlinear Energy Flows in Power Grids with High Penetration Inverter-Based Renewables

The complexity of modern power grids, caused by integrating renewable energy sources, especially inverter-based resources, presents a significant challenge to grid operation and planning, since linear models are unable to capture the complex nonlinear dynamics of power systems with coupled muti-scale dynamics, and it necessitate an alternative approach utilizing more advanced and data-driven algorithms to improve modeling accuracy and system optimization. This study employs the sparse identification of nonlinear dynamics method by leveraging compressed sensing and sparse modeling principles, offering robustness and the potential for generalization, allowing for identifying key dynamical features with relatively few measurements, and providing deeper theoretical understanding in the field of power system analysis. Taking advantage of the this method in recognizing the active terms (first and high order) in the system’s governing equation, this paper also introduces the novel Volterra-based nonlinearity index to characterize system-level nonlinearity. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise is adopted to clearly show the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to inverter-based resources, revealing system-level (second-order) nonlinearity compared to module-level (first order) nonlinearity in conventional synchronous generators. The proposed index quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the profile of the proposed index.

Influence of Kerr Effect on Second-Order Nonlinearity Induced Transparency

We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system. We show that in the presence of the Kerr effect, as the strength of the Kerr effect increases, the absorption curve exhibits an asymmetric-symmetric-asymmetric transition, and the zero absorption point shifts with the increase of the Kerr effect. Furthermore, by changing the strength of the Kerr effect, we can control the width of the transparent window, and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak. The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak. The simple dependence of the zero-absorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.

Silicon nitride electric-field poled microresonator modulator

Stoichiometric silicon nitride is a highly regarded platform for its favorable attributes, such as low propagation loss and compatibility with complementary metal-oxide-semiconductor technology, making it a prominent choice for various linear and nonlinear applications on a chip. However, due to its amorphous structure, silicon nitride lacks second-order nonlinearity; hence, the platform misses the key functionality of linear electro-optical modulation for photonic integrated circuits. Several approaches have been explored to address this problem, including integration with electro-optic active materials, piezoelectric tuning, and utilization of the thermo-optic effect. In this work, we demonstrate electro-optical modulation in a silicon nitride microring resonator enabled by electric-field poling, eliminating the complexities associated with material integration and providing data modulation speeds up to 75 Mb/s, currently only limited by the electrode design. With an estimated inscribed electric field of 100 V/μm, we achieve an effective second-order susceptibility of 0.45 pm/V. In addition, we derive and confirm the value of the material’s third-order susceptibility, which is responsible for the emergence of second-order nonlinearity. These findings broaden the functionality of silicon nitride as a platform for electro-optic modulation.

Boolean function classes with high nonlinearity

In 2020, Liu (Q. Liu, The lower bounds on the second-order nonlinearity of three classes of Boolean functions, Advances in Mathematics of Communications, AIMS (2021), Doi: 10.3934/amc.2020136) studied the second-order nonlinearity of three classes of Boolean functions, which have high first-order nonlinearity. Liu gave bounds on the first-order nonlinearity of these classes based on some experimental results using Magma. This article provides theoretical proof for computing the lower bounds on the first-order nonlinearity of two classes of Boolean functions out of three. Our bounds are identical to the bounds obtained by Liu experimentally.

Distributed Nash Equilibrium Seeking for Multi-Cluster Game of Second-Order Nonlinear Systems With Partial Information

Distributed Nash Equilibrium Seeking for Multi-Cluster Game of Second-Order Nonlinear Systems With Partial Information

Hybrid III-V/Silicon photonic circuits embedding generation and routing of entangled photon pairs

Hybrid photonic devices, harnessing the advantages of multiple materials while mitigating their respective weaknesses, represent a promising solution to the effective on-chip integration of generation and manipulation of non-classical states of light encoding quantum information. We demonstrate a hybrid III-V/Silicon quantum photonic device combining the strong second-order nonlinearity and compliance with electrical pumping of the III-V semiconductor platform with the high maturity and CMOS compatibility of the silicon photonic platform. Our device embeds the spontaneous parametric down-conversion (SPDC) of photon pairs into an Al-GaAs source and their subsequent routing to a silicon-on-insulator circuitry. This enables the on-chip generation of broadband telecom photon pairs by type 0 and type 2 SPDC from the hybrid device, at room temperature and with strong rejection of the pump beam. Two-photon interference with 92% visibility proves the high energy-time entanglement quality characterizing the produced quantum state, thereby enabling a wide range of quantum information applications.

Analysis of the Frequency-Dependent Vibration Rectification Error in Area-Variation-Based Capacitive MEMS Accelerometers.

The presence of strong ambient vibrations could have a negative impact on applications such as high precision inertial navigation and tilt measurement due to the vibration rectification error (VRE) of the accelerometer. In this paper, we investigate the origins of the VRE using a self-developed MEMS accelerometer equipped with an area-variation-based capacitive displacement transducer. Our findings indicate that the second-order nonlinearity coefficient is dependent on the frequency but the VRE remains constant when the displacement amplitude of the excitation is maintained at a constant level. This frequency dependence of nonlinearity is a result of several factors coupling with each other during signal conversion from acceleration to electrical output signal. These factors include the amplification of the proof mass's amplitude as the excitation frequency approaches resonance, the nonlinearity in capacitance-displacement conversion at larger displacements caused by the fringing effect, and the offset of the mechanical suspension's equilibrium point from the null position of the differential capacitance electrodes. Through displacement transducer and damping optimization, the second-order nonlinearity coefficient is greatly reduced from mg/g2 to μg/g2.

Mid-infrared second-harmonic generation and its red-shift signal induced by cross-phase modulation in an AsSe2 soft glass microstructured optical fiber

In this study, we investigate an AsSe2 soft glass microstructured optical fiber (MOF) featuring a hexagonal arrangement of six holes. The MOF is subjected to femtosecond laser pumping, employing a pump wavelength range spanning from 3950 nm to 4100 nm. Our experimental results reveal an intriguing outcome: a tunable mid-infrared second-harmonic generation (SHG) effect is observed, yielding a wavelength range of ∼ 1980 nm to ∼ 2203 nm. The maximum conversion efficiency is achieved at 4100 nm with a power of 130 mW, which can be up to 9.2E-5. The observed SHG is primarily due to the surface nonlinearity polarization at the core-cladding interface. Additionally, we increase the additional degrees of freedom of the SH signal by strong third-order nonlinearity, and demonstrate that strong self-phase modulation (SPM) of pump and cross-phase modulation (XPM) of SH signal help broaden the SH signal by means of generating new wavelength lobes. To the best of our knowledge, this is the first time that strong XPM-based SH signal is observed in an optical fiber in the mid-infrared wavelength region. The realized strong second-order and third-order nonlinearity might expand the fundamental physical mechanism of SHG in optical fiber especially in mid-infrared region, which would have important applications in telecommunications, laser technology, and quantum photonics.

In Situ Fatigue Damage Monitoring by Means of Nonlinear Ultrasonic Measurements

In the present work, the results of acoustic nonlinear response of ultrasonic wave propagation when monitoring the progress of damage induced by fatigue on notched C45 carbon steel specimens have been reported. Two ultrasound probes were fixed to the specimens during the tests. The input signal was sinusoidal type, while the corresponding ultrasound response signal was acquired and recorded at each stage of the test by means of a digital oscilloscope. A nonlinear frequency study was performed on the acquired data to evaluate the change in the second- and third-order nonlinearity coefficients of β1 and β2, respectively, on the tested specimens. Ultrasonic results were correlated to plastic strain at the notch tip in the initial phases of fatigue and stiffness degradation. The results showed a significant increase in second-order nonlinearity β1 in the early stages of fatigue life. Subsequently, starting from about 30–40% of the fatigue life, the nonlinearity of β1 increases. Before final failure, from 80 to 85% of fatigue life, the second-order nonlinearity further increases in the crack propagation stages. The nonlinear parameter of the third-order β2 was less sensitive to damage than the parameter β1, showing a rapid increase only starting from approximately 80 to 85% of the fatigue life. The proposed method proved to be valid for detective damage induced by fatigue and to predict the lifetime of metal materials.