Nonlinear Optical Processes Research Articles

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing.

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs—particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

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

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

Third-harmonic generation of spatially structured light in a quasi-periodically poled crystal

Nonlinear optical processes of spatially structured light such as optical vortices and vector optical fields have exhibited many interesting physical effects and found a variety of important applications from classical to quantum regimes. However, high-harmonic generation of a vector optical field with a space-varying polarization state is still a challenge. Here we present a solution to realize third-harmonic generation of spatially structured light including vector optical fields in a nonlinear Sagnac interferometer containing only one carefully designed quasi-periodically poled potassium titanyl phosphate, for the first time, to our knowledge. The experimental results well confirm our theoretical predictions. Our results will enable to manipulate spatially structured light or photons carrying higher orbital angular momentum at new wavelengths. Our scheme has potential applications such as in optical skyrmions and may open up new opportunities to produce spatially structured entangled photons for quantum communication and computation.

Mutlilayer Wedge Disks CROW for an Optical Delay Line

Optical delay lines are vital for the development of all optical telecommunications, optical computers and for many nonlinear and quantum optics processes. Periodic structures such as coupled resonator optical waveguides (CROW) achieve high delays in a compact manner and with a large bandwidth. Wedge disk resonators have demonstrated high quality factors compared to rectangular disks and rings while remaining integrable on chip. Vertical coupling is needed since the optical mode is pushed toward the disk center by the wedge. We propose an optical delay line made of wedge disks arranged in two overlapping layers. Disks are made of silicon dioxide on silicon pillars. Numerical calculations of the device performance and an experimental proof of concept are presented. A maximum delay of 85 ps for eleven disks is achieved with a loss per cavity of 3.91 dB. This is a first proof of concept of a CROW structure made of wedge disk coupled vertically.

Optically Induced Nonlinear Cubic Crystal System for 3D Quasi‐Phase Matching

Quasi‐phase matching (QPM) is a technique in nonlinear optics for achieving efficient energy exchange among optical waves at different frequencies, by spatially modulating the quadratic nonlinearity (χ (2)) of the medium. To realize the full potential of QPM, 3D spatial modulation of χ (2) is required. This has become experimentally feasible recently thanks to the invention of femtosecond laser‐based nonlinearity engineering in ferroelectric crystals. Herein, the first experimental demonstration of QPM second harmonic generation (SHG) in a nonlinear cubic crystal system is presented, in which χ (2) modulations form simple cubic, body‐centered cubic, face‐centered cubic, and diamond cubic lattices, respectively. The experimental results indicate that these nonlinear cubic structures share the same primary reciprocal lattice vectors (RLVs), but possess different Fourier coefficients (in conventional cells), leading to SHG with similar angular resonances but various intensity distributions in the far field. This work contributes to a comprehensive understanding of nonlinear optical processes in 3D periodic media, and thus sheds light on the development of high‐performance QPM devices.

Effect of Interlayer Coupling and Symmetry on High-Order Harmonic Generation from Monolayer and Bilayer Hexagonal Boron Nitride

High-order harmonic generation (HHG) is a fundamental process which can be simplified as the production of high energetic photons from a material subjected to a strong driving laser field. This highly nonlinear optical process contains rich information concerning the electron structure and dynamics of matter, for instance, gases, solids and liquids. Moreover, the HHG from solids has recently attracted the attention of both attosecond science and condensed matter physicists, since the HHG spectra can carry information of electron-hole dynamics in bands and inter- and intra-band current dynamics. In this paper, we study the effect of interlayer coupling and symmetry in two-dimensional (2D) material by analyzing high-order harmonic generation from monolayer and two differently stacked bilayer hexagonal boron nitrides (hBNs). These simulations reveal that high-order harmonic emission patterns strongly depend on crystal inversion symmetry (IS), rotation symmetry and interlayer coupling.

Giant Third-Order Nonlinear Response of Mixed Perovskite Nanocrystals

Mixed (FAPbI3)0.92(MAPbBr3)0.08 perovskite thin films exhibit strong nonlinear optical responses, rendering them promising candidates for applications in photonics and optical communications. In this work, we present a systematic study on the ultrafast third-order nonlinear optical processes in mixed perovskite nanocrystals (NCs) by exploring the generation of third harmonic radiation and giant two-photon absorption-based photoluminescence (PL) when excited by femtosecond laser pulses of a 1030 nm central wavelength. A comparative analysis of the coherent third harmonic generation in the thin-film-containing perovskite nanocrystals has shown a 40× enhancement of the third harmonic signal compared to the signal generated in the pure quartz substrate. The cubic dependence of the third-nonlinear optical response of the (FAPbI3)0.92(MAPbBr3)0.08 perovskites on the intensity of the driving radiation was identified using broadband 38 femtosecond driving pulses. The positive nonlinear refractive index (γ = +1.4 × 10−12 cm2·W−1) is found to play an important role in improving the phase-matching conditions of the interacting pulses by generating a strong third order harmonic. The giant two-photon absorption (TPA)-assisted PL peak was monitored and a blue shift of the PL was obtained in the higher intensity range of the laser pulses, with the absorption coefficient β estimated to be~+7.0 cm·MW−1 at a 1030 nm laser wavelength.

Spectrally Resolved Nonlinear Optical Properties of Doped Versus Undoped Quasi-2D Semiconductor Nanocrystals: Copper and Silver Doping Provokes Strong Nonlinearity in Colloidal CdSe Nanoplatelets

Nonlinear optical processes are crucial for emerging applications including multiphoton-excited fluorescence microscopy and optical power limiting. Therefore, searching for materials of high multiphoton absorption cross sections is essential for the development of these techniques. We present synthesis of 4.5 monolayer CdSe nanoplatelets (NPLs) doped with silver and copper ions along with the evaluation of their two-photon absorption (TPA) and three-photon absorption (3PA) cross sections. Doping significantly increases the TPA cross section of each NPL sample, which reaches up to 1.33 × 107 GM for the most absorbing copper-doped ones. We also detected 1–2 orders of magnitude-enhanced 3PA cross sections for the doped NPLs in comparison with their undoped counterparts. As TPA and 3PA peaks appear, in the first and the second biological transmission windows, respectively, doped NPLs are promising candidates for multiphoton fluorescence microscopy as bioimaging agents. Moreover, the strong nonlinear response suggests application as active optoelectronic materials in optical sensors.

Selective excitation of four-wave mixing by helicity in gated graphene.

Gapless Dirac fermions in monolayer graphene give rise to an abundance of peculiar physical properties, including exceptional broadband nonlinear optical responses. By tuning the chemical potential, stacking order, and photonic structures, the effective modulation of nonlinear optical phenomena in graphene has been demonstrated in recent years. Here, we demonstrate that optical helicity can be used as an extra tuning knob for four-wave mixing in gated graphene. Our results reveal the helicity selection rule for four-wave mixing in monolayer graphene, revealing nearly perfect circular polarization. Corresponding theoretical interpretations of the helicity selection rule that are also applicable to other nonlinear optical processes and materials are presented.

Lithium niobate microring with ultra-high Q factor above 108

We demonstrate integrated lithium niobate (LN) microring resonators with Q factors close to the intrinsic material absorption limit of LN. The microrings are fabricated on pristine LN thin-film wafers thinned from LN bulk via chemo-mechanical etching without ion slicing and ion etching. A record-high Q factor up to 108 at the wavelength of 1550 nm is achieved because of the ultra-smooth interface of the microrings and the absence of ion-induced lattice damage, indicating an ultra-low waveguide propagation loss of ∼0.0034 dB/cm. The ultra-high Q microrings will pave the way for integrated quantum light source, frequency comb generation, and nonlinear optical processes.

Angular birefringence phase matching behaviour of Lithium Triborate (LBO) crystal for second harmonic generation in broad wavelength range

Second Harmonic Generation (SHG) is a nonlinear optical process in which the frequency of the incident radiation gets doubled. There are various types of applications of SHG such as ultra-short pulse measurement, high resolution optical microscopy, characterization of the structure of 2D materials and its physical properties like the thickness of interlayer stacking, stacking angle between different layers, the grain boundary etc. It has also been used to determine the structure of Langmuir-Blodgett films of low symmetry. For SHG, various commercial nonlinear optical (NLO) crystals are generally used. Lithium Triborate (LBO) is one of the best NLO material among them due to its wide transparency range (160–2600 nm), high damage threshold (19 GW/cm2 @1064 nm, 1 ns) and high second order nonlinear coefficient. It has also the ability to establish birefringence phase matching condition for efficient SHG for different wavelengths. The crystal can be used for generation for SHG in broad wavelength range through angular phase matching method. For this, in this work detail investigation has been made to find out the optimum wavelength range that can be used for efficient SHG. This has been done by finding the variation of phase matching angle, second order nonlinearity etc. with respect to wavelength using the SNLO software. Both Type I and Type II phase matching has been considered for various planes of the crystal.

Recent advances in low-power-threshold nonlinear photochromic materials.

Incoherent nonlinear photophysical and photochemical processes based on stepwise two-photon absorption (2PA) processes have been recently used in materials science owing to their unique photoresponses beyond one-photon processes and lower power thresholds to induce the processes than those of coherent nonlinear optical processes. Among them, nonlinear photochromic materials have received considerable attention because they exhibit unconventional photoresponses compared with other incoherent nonlinear processes such as low-power-threshold nonlinear photoresponses with unimolecular systems, gated photochemical reactions and oxygen-insensitive nonlinear photoresponses. Nonlinear photochromic materials are important not only for colorimetric materials, but also for emergent materials that can enrich the next-generation society such as dynamic holographic materials, which are promising for three-dimensional displays. In this tutorial review, we introduce low-power-threshold nonlinear photochromic materials using stepwise 2PA processes. First, we explain the fundamental concepts of photochemistry as well as photochromic reactions. We attempt to provide an intuitive understanding of incoherent nonlinear optical processes using these fundamental concepts. Then, we introduce several recent examples and potential applications of nonlinear photochromic materials. This tutorial review is important for understanding the scientific progress related to these fields and provides a simple unified picture of the incoherent nonlinear optical properties of different types of photofunctional materials.

First Order Hyper polarizability and Intramolecular Charge Transfer of N-Ethyl-N-(2-Hydroxyethyl)-4-(4-Nitrophenylazo) Aniline for Photonic Applications

We report a computational methodology for estimating the first order hyperpolarizability ((3) of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo) aniline, a nonlinear optical (NLO) chromophore being used as anazobenzene dye. The planar and non-planar structures of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo) aniline were optimized by B3LYP/6-311++G (D,P) basis set using GAUSSIAN’09W program package. The dipole moment, static polarizability, first order hyperpolarizability were studied using HF/6-31G (D) basis set. The (3 value of the planar and non-planar structure of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo) aniline is 196 and 124 times higher than that of urea standard, respectively, which qualify both of the novel molecular systems as highly efficient for second order NLO applications and adds evidence to the importance of derealization of ^-electrons in a system for effective second order NLO processes. Experiments were also performed using an Nd-YAG laser of pulses in the range of 5-10 nanoseconds with a tunable peak power of 4.7 W.

Enhanced optical nonlinearity in a silicon–organic hybrid slot waveguide for all-optical signal processing

Silicon photonic integrated devices used for nonlinear optical signal processing play a key role in ultrafast switching, computing, and modern optical communications. However, current devices suffer from limited operation speeds and low conversion efficiencies due to the intrinsically low nonlinear index of silicon. In this paper, we experimentally demonstrate enhanced optical nonlinearity in a silicon–organic hybrid slot waveguide consisting of an ultranarrow slot waveguide coated with a highly nonlinear organic material. The fabricated slot area is as narrow as 45 nm, which is, to the best of our knowledge, the narrowest slot width that has been experimentally reported in silicon slot waveguides. The nonlinear coefficient of the proposed device with a length of 3 mm is measured to be up to 1.43 × 10 6 W − 1 km − 1 . Based on the nanostructure design, the conversion efficiencies of degenerate four-wave mixing showed enhancements of more than 12 dB and 5 dB compared to those measured for an identical device without the organic material and a silicon strip waveguide, respectively. As a proof of concept, all-optical canonical logic units based on the prepared device with two inputs at 40 Gb/s are analyzed. The obtained logic results showed clear temporal waveforms and wide-open eye diagrams with error-free performance, illustrating that our device has great potential for use in high-speed all-optical signal processing and high-performance computing in the nodes and terminals of optical networks.

All-optical modulator based on a microfibre coil resonator functionalized with MXene

A novel all-optical modulator based on a microfibre coil resonator (MCR) functionalized using MXene is reported. The MCR was manufactured by winding a tapered fibre on a polycarbonate (PC) resin cylinder with low refractive index to support the microfibre, which also forms a fluidic channel coil. The MXene dispersion was injected into the channel to allow the deposition of an MXene layer using a photodeposition process. The transmission spectra were tuned using a tunable laser with a centre wavelength of 1550 nm and the light-matter interaction resulting from the photo-thermal effect and MXene absorption provide the all-optical modulation in this device. The variation of the resonance wavelength, phase shift and extinction ratio of transmission spectrum versus power were determined as 50 pm/mW, 0.262 π/mW and 0.554 dBm/mW respectively. The all-optical modulation properties were further characterized using a lens coupling method and adding a chopper to provide a controlled light source. The rise and fall response times for waveforms of the light signal were 0.179 and 0.145 ms, respectively. The intensity and width of the light signal waveform was modulated using the chopper-controlled light source, which indicates that MXene, as a new two-dimensional material, has excellent nonlinear optical effects and the MXene-MCR has the potential for use in ultra-fast optical nonlinear optical processing. The MXene-MCR has several superior characteristics compared with other all-optical modulators including excellent modulation properties, all-fibre construction, easy fabrication and fast response. These advantages demonstrate MXene-MCR has excellent potential for use as a tunable optical filter, an optical switch as well as an all-optical modulator.

Diagrammatic theory of linear and nonlinear optics for composite systems

We present a general formalism to model and calculate linear and nonlinear optical processes in composite systems, based on a graphical representation of light-matter interactions by loop diagrams associated with Feynman rules. Through this formalism, we recover the usual second-order response of a simple system by drawing four times fewer loop diagrams than doubled-sided ones. For composite systems, we introduce coupling Hamiltonians between subsystems (for example, a molecule and a substrate), graphically represented by virtual bosons. In this way, we enumerate all the diagrams describing the second-order response of the system and show how to select those relevant for the calculation of the molecular second-order hyperpolarizabilities under the influence of the substrate, including effective second-order contributions from the molecular third-order response. As it applies to all nonlinear processes and an arbitrary number of interacting partners, this representation provides a general frame for the calculation of the nonlinear response of arbitrarily complex systems.

Fano enhancement of unlocalized nonlinear optical processes

Field localization boosts nonlinear optical processes at the hot spots of metal nanostructures. Fano resonances can further enhance these ``local'' processes taking place at the hot spots. However, in conventional nonlinear materials, the frequency conversion takes place along the entire crystal body. That is, the conversion process is ``unlocalized.'' The path interference (Fano resonance) schemes developed for localized processes become useless in such materials. Here, we develop Fano enhancement schemes for unlocalized nonlinear optical processes. We show that three-orders-of-magnitude Fano enhancement multiplies the enhancements achieved via field-trapping techniques, e.g., in epsilon-near-zero materials. We demonstrate the phenomenon both analytically and using numerical solutions of Maxwell's equations. The agreement between the two solutions is impressive. We observe that the interference scheme for unlocalized processes is richer than that for the local processes. The method can be employed for any kind of nonlinear optical conversion. Moreover, Fano enhancement can be continuously controlled by an applied voltage.

Second Harmonic Generation in Lithiated Silicon Nanowires: Derivations and Computational Methods

This research will examine the computational methods to calculate the nonlinear optical process of second harmonic generation (SHG) that will be hypothesized to be present during lithium ion insertion into silicon nanowires. First it will be determined whether the medium in which SHG is conveyed is non-centrosymmetric or whether the medium is inversion symmetric where SHG as a part of the second-order nonlinear optical phenomenon does not exist. It will be demonstrated that the main interaction that determines SHG is multiphoton absorption on lithium ions. The quantum harmonic oscillator (QHO) is used as the background that generates coherent states for electrons and photons that transverse the length of the silicon nanowire. The matrix elements of the Hamiltonian which represents the energy of the system will be used to calculate the probability density of second-order nonlinear optical interactions which includes collectively SHG, sum-frequency generation (SFG) and difference-frequency generation (DFG). As a result, it will be seen that at varies concentrations of lithium ions (Li+) within the crystallized silicon (c-Si) matrix the second-order nonlinear optical process has probabilities substantial enough to create second harmonic generation that could possibly be used for such applications as second harmonic imaging microscopy.

Manifestation of the Gyrotropy of Topological Media in Nonlinear Optical Processes

Manifestation of the Gyrotropy of Topological Media in Nonlinear Optical Processes

Optical amplification by surface-plasmon-resonant Au grating substrates: Monolayer MoS2 with 170-fold second harmonic generation and 3-fold (off-resonance) Raman scattering

Nanoplasmonics is a potential game-changer in the development of next-generation on-chip photonic devices and computers, owing to the geometrically controlled and amplified linear and nonlinear optical processes. For instance, it resolves the limited light-matter interaction of the unique two-dimensional (2D) crystalline materials like semiconducting monolayer molybdenum disulfide (1L-MoS 2 ). Metal grating (MG) substrates excel at this because their surface plasmons (SPs) can lead to stark field confinement near the surface. This work studies optical amplification of 1L-MoS 2 on the gold (Au) MG substrate, which was designed to operate in a glycerol environment with SP resonance (SPR) at 850 nm excitation wavelength. Its design was verified by simulated and experimental reflectances, and topographically inspected by atomic force microscopy (AFM). Two advanced imaging modalities, second harmonic generation (SHG) and confocal Raman microscopy (CRM) were used to evaluate its 170-fold SHG on- and 3-fold CRM off-resonance optical amplifications, respectively. Some MoS 2 -to-grating adhesion issues due to trapped liquid showed as image nonuniformities. Possible improvements to limitations like surface roughness were also discussed. These Au MG substrates can boost conventional linear and nonlinear backscattering microscopies because they are tunable in the visible and near-infrared range by selecting geometry, metal, and environment. • Plasmonic optical amplification study of monolayer MoS 2 on Au/Si-grating substrate. • 170× on- and 3× off-resonance gains in second harmonic generation and Raman signals. • These nanogratings can boost both linear and nonlinear backscattering microscopies. • Tune by geometry, metal, and environment within the visible and near-infrared range. • Improve light-matter interaction (with less power and less light-induced damage).