Nonlinear optics with structured light

The interest in tailoring light in all its degrees of freedom is steadily gaining traction,driven by the tremendous developments in the toolkit for the creation,control and detection of what is now called structured light.Because the complexity of these optical fields is generally understood in terms of interference,the tools have historically been linear optical elements that create the desired superpositions.For this reason,despite the long and impressive history of nonlinear optics,only recently has the spatial structure of light in nonlinear processes come to the fore.In this review we provide a concise theoretical framework for understanding nonlinear optics in the context of structured light,offering an overview and perspective on the progress made,and the challenges that remain.

SYNTHESIS AND CHARACTERIZATI0N OF POLYMETHACRYLATES BEARING HETEROCYCLIC AZO GROUP AND MESOGENIC GROUP FOR NONLINEAR OPTICS

The methacrylate monomers bearing mesogenic group and heterocyclicazo dye have been synthesized. The monomeric dye was copolymerized with the mesogenicmonomer using a free radical initiator to produce polymers useful for nonlinear optics. Themonomers and polymers were characterized by IR,;H-NMR, and UV-Vis spectra. Theaverage molecular weight （M;and M;） of the polymers were determined by gel permeationchromatography. The thermal properties of the polymers such as thermal stability andphase transition behavior were studied by thermogravimetric analysis, differential thermalanalysis, polarizing optical microscope and X-ray diffractometer. The results demonstratethat the synthesized polymers are crystalline polymers at room temperature and no liquidcrystalline phases were observed for all of them.

Nonlinear waves of the Hirota and the Maxwell Bloch equations in nonlinear optics

In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.

Review on the study of Nonlinear Optics of Iridium Metal Organic Complex

Nonlinear optical materials are one of the key research objects in the field of optics, which mainly research the nonlinear effects of the interaction between luminesce and matter. Compared with inorganic nonlinear optical materials, organic nonlinear materials have outstanding advantages: strong adaptability, high flexibility, low cost, easy modification and damage resistance. In this review, the electric field induced second harmonic generation (EFISH) experimental technology is used to measure and research the nonlinearity of iridium metal complexes. And because of its structural diversity, people can design molecules according to their needs to get the best nonlinear optical response. Organic molecules with large nonlinear coefficients should have the following characteristics: asymmetric charge distribution, the delocalized nature of π electrons, and easy polarization by external electric fields, and a large π conjugated system. In recent years, metal organic compounds have become a leader in the field of optics, mainly because of their very good nonlinear optical properties. In the future, people will do more investigation on the nonlinearity of metal organic complexes. Researchers have shown great interest in iridium metal organic complexes due in particular to their attractive stability and nonlinear activity. This review mainly studies the nonlinear principle, performance test and Measurement of nonlinearity of iridium metal complexes. The nonlinear properties of other metal-metal organic complexes will not be discussed.

Synthesis of Imidazole Derivatives for Their Second-order Nonlinear Optics

The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.

AN EPOXY/(METHYL METHACRYLATE)INTERPENETRATING POLYMER NETWORK FOR NONLINEAR OPTICS

An interpenetrating polymer networks (IPN) consisting of an epoxy-based polymer network and a polymethyl methacrylate network were synthesized and characterized. The IPN showed only one T-g, and hence a homogeneous-phase morphology was suggested. The second-order nonlinear optical coefficient (d(33)) of the IPN was measured to be 1.72 X 10(-7) esu. The study of NLO temporal stability at room temperature and elevated temperature (100 degrees C) indicated that the IPN exhibits a high stability in the dipole orientation due to the permanent entanglements of two component networks in the IPN system. Long-term stability of second harmonic coefficients was observed at room temperature for more than 1000 h.

Light correcting light with nonlinear optics

Structured light,where complex optical fields are tailored in all their degrees of freedom,has become highly topical of late,advanced by a sophisticated toolkit comprising both linear and nonlinear optics.Removing undesired structure from light is far less developed,leveraging mostly on inverting the distortion,e.g.,with adaptive optics or the inverse transmission matrix of a complex channel,both requiring that the distortion be fully characterized through appropriate measurement.We show that distortions in spatially structured light can be corrected through difference-frequency generation in a nonlinear crystal without any need for the distortion to be known.We demonstrate the versatility of our approach using a wide range of aberrations and structured light modes,including higher-order orbital angular momentum(OAM)beams,showing excellent recovery of the original undistorted field.To highlight the efficacy of this process,we deploy the system in a prepare-and-measure communications link with OAM,showing minimal cross talk even when the transmission channel is highly aberrated,and outline how the approach could be extended to alternative experimental modalities and nonlinear processes.Our demonstration of light-correcting light without the need for measurement opens an approach to measurement-free error correction for classical and quantum structured light,with direct applications in imaging,sensing,and communication.

Nonlinear optics of two-dimensional heterostructures

Two-dimensional (2D) materials exhibit exceptionally strong nonlinear optical responses, benefiting from their reduced dimensionality, relaxed phase-matching requirements, and enhanced light-matter interaction. With additional degrees of freedom in the modulation of the physical properties by stacking 2D layers together, nonlinear optics of 2D heterostructures becomes increasingly fascinating. In this perspective, we provide a brief overview of recent advances in the field of nonlinear optics of 2D heterostructures, with a particular focus on their remarkable capabilities in characterization and modulation. Given the recent advances and the emergence of novel heterostructures, combined with innovative tuning knobs and advanced nonlinear optical techniques, we anticipate deeper insights into the underlying mechanisms and more associated applications in this rapidly evolving field.

Solvent-stabilized few-layer violet phosphorus and its ultrafast nonlinear optics

Featured with high thermal decomposition temperature and layered structure,violet phosphorus(VP)offers an unparalleled stable allotrope of phosphorus to demonstrate the optoelectronic device and photonics elements with high performance at the nanoscale.Here,we report few-layer and hundreds of nanometer-sized VP with robust stability in different solvents and ambient conditions by ultrasound-assisted liquid phase exfoliation approach.For the first time,the ultrafast carrier dynamics and thirdorder nonlinear optical response of VP were investigated.Sub-picosecond timescale ultrafast carrier dynamic and ultrafast nonlinear saturable absorption of VP were demonstrated.Our findings demonstrated that VP possessed a promising potential for use in ultrafast nonlinear photonic applications such as saturable absorbers and optical switches.

Metal-organic frameworks for nonlinear optics and lasing

Nonlinear optics(NLO)is a crucial branch of photonics that greatly facilitates the transmission,processing,and storage of photonic signals.It meets the needs of the rapidly growing information demands of modern society.Materials with NLO properties and laser capabilities have a wide range of applications in fields such as optical communication,optical information storage,biomedical imaging,laser technology,and quantum information technology.Metal-organic frameworks(MOFs)have emerged as particularly exciting hybrid inorganic-organic porous materials that can be easily self‐assembled from corresponding inorganic metal ions/clusters and organic linkers.The structural diversity and flexibility of MOFs offer ample opportunities for the orderly or-ganization of highly hyperpolarizable chromophore molecules within confined spaces.This makes it ideal for NLO signal and laser emissions.In this review,we provide a comprehensive overview of strategies to construct MOFs with NLO and laser properties,as well as recent research developments for enhancing and adjusting these properties.Through analysis of chromophore arrangement and various interactions within the framework,we aim to gain insight into the correlation between MOF structures and optical properties.This will facilitate the design and synthesis of MOFs with excellent NLO and laser capabilities through the judicious selection of metal ions and organic linkers.Finally,we outline the future challenges and potential research directions for MOFs in NLO and laser fields.

Resonantly enhanced second-and third-harmonic generation in dielectric nonlinear metasurfaces

Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.

Using harmonic beam combining to generate pulse-burst in nonlinear optical laser

The ultrashort lasers working in pulse-burst mode reveal great machining performance in recent years. The number of pulses in bursts effects greatly on the removal rate and roughness. To generate a more equal amplitude of pulses in burst with linear polarization output and time gap adjustable, we propose a new method by the harmonic beam combining(HBC).The beam combining is commonly used in adding pulses into the output beam while maintaining the pulse waveform and beam quality. In the HBC, dichroic mirrors are used to combine laser pulses of fundamental wave(FW) into harmonic wave(HW), and nonlinear crystals are used to convert the FW into HW. Therefore, HBC can add arbitrarily more HW pulses to generate pulse-burst in linear polarization with simple structure. The amplitude of each pulse in bursts can be adjusted the same to increase the stability of the burst, the time gap of each pulse can be adjusted precisely by proper time delay. Because HBC adds pulses sequentially, the peak power density of the burst is the same as each pulse, pulses can be combined without concern of back-conversion which often occurs in high peak power density. In the demonstration, the extendibility of HBC was verified by combining two beams with a third beam. The combined efficiency rates were larger than 99%, and the beam quality of each beam was maintained at M^(2)≈1.4.

Plasmon-induced nonlinear response on gold nanoclusters

The plasmon-induced nonlinear response has attracted great attention in micro-nano optics and optoelectronics applications,yet the underlying microscopic mechanism remains elusive.In this study,the nonlinear response of gold nanoclusters when exposed to a femtosecond laser pulse was investigated using time-dependent density functional theory.It was observed that the third-order tunneling current was augmented in plasmonic dimers,owing to a greater number of electrons in the dimer being excited from occupied to unoccupied states.These findings provide profound theoretical insights and enable the realization of accurate regulation and control of nonlinear effects induced by plasmons at the atomic level.

Wavelength Dependent Nonlinear Spectroscopic Study of Third Harmonic Generation Probed by Rotational Maker Fringes Method

Efficient third-order nonlinearities of the Zinc Oxide and Al-doped Zinc Oxide were studied by Third Harmonic Generation (Third Harmonic Generation) Maker fringes to establish the effect Aluminum of Aluminum doping (Al-doping) on the cubic nonlinearities. Adding the Al-dopant to the Zinc Oxide crystal structure results in changes that affect the optical and nonlinear characteristics. Presented results indicate that the magnitude of X(3) was enhanced at single experimental wavelengths;however, across the broadband experimental spectrum, the effect of Al-doping remained relatively constant. The observed enhancement of third-order nonlinearity was purely from the bound electronic response. The observation is attributed to increased charge carriers and spontaneous polarization in the Zinc Oxide and Al-doped Zinc Oxide crystal structure.

Symmetry transformation of nonlinear optical current of tilted Weyl nodes and application to ferromagnetic MnBi_(2)Te_(4)

A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and-independent parts of optical conductivity transform under the reversal of tilt and chirality.Built on this theory, we propose ferromagnetic Mn Bi2Te4as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chiralitydependent and-independent DC photocurrents.These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.

Structure,electronic,and nonlinear optical properties of superalkaline M_(3)O(M=Li,Na)doped cyclo[18]carbon

Cyclo[18]carbon has received considerable attention thanks to its novel geometric configuration and special electronic structure.Superalkalis have low ionization energy.Doping a superalkali in cyclo[18]carbon is an effective method to improve the optical properties of the system because considerable electron transfer occurs.In this paper,the geometry,bonding properties,electronic structure,absorption spectrum,and nonlinear optical(NLO)properties of superalkaline M_(3)O(M=Li,Na)-doped cyclo[18]carbon were studied by using density functional theory.M_(3)O and the C_(18) rings are not coplanar.The C_(18) ring still exhibits alternating long and short bonds.The charge transfer between M_(3)O and C_(18) forms stable[M_(3)O]+[C_(18)]-ionic complexes.C_(18)M_(3)O(M=Li,Na)shows striking optical nonlinearity,i.e.,their first-and second-order hyperpolarizability(βvec andγ||)increase considerably atλ=1907 nm and 1460 nm.

Broadband third-order optical nonlinearities of layered franckeite towards mid-infrared regime

The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.

Electrical and nonlinear optical properties of TGZO transparent conducting films deposited by magnetron sputtering

Thin transparent oxide conducting films(TCOFs)of titanium and gallium substituted zinc oxide(TGZO)were fabricated via radio frequency(RF)magnetron sputtering technique.The effects of RF power on electrical,linear and nonlinear optical characteristics were investigated by Hall tester,Ultraviolet(UV)-visible spectrophotometer and optical characterization method.The results indicate that RF power significantly influences the electrical and optical properties of the deposited films.As RF power raises,the resistivity and Urbach energy fall initially and then rise,while the figure of merit,mean visible transmittance and optical bandgap show the reverse variation trend.At RF power of 190 W,the TGZO sample exhibits the highest electro-optical properties,with the maximum figure of merit(1.14×10^(4)Ω^(-1)∙cm^(-1)),mean visible transmittance(86.9%)and optical bandgap(3.50 eV),the minimum resistivity(6.26×10^(-4)Ω∙cm)and Urbach energy(174.23 meV).In addition,the optical constants of the deposited films were determined by the optical spectrum fitting method,and the RF power dependence of nonlinear optical properties was studied.It is observed that all the thin films exhibit normal dispersion characteristics in the visible region,and the nonlinear optical parameters are greatly affected by the RF power in the ultraviolet region.

Integrated sources of photon quantum states based on nonlinear optics

The ability to generate complex optical photon states involving entanglement between multiple optical modes is not only critical to advancing our understanding of quantum mechanics but will play a key role in generating many applications in quantum technologies.These include quantum communications,computation,imaging,microscopy and many other novel technologies that are constantly being proposed.However,approaches to generating parallel multiple,customisable bi-and multi-entangled quantum bits(qubits)on a chip are still in the early stages of development.Here,we review recent advances in the realisation of integrated sources of photonic quantum states,focusing on approaches based on nonlinear optics that are compatible with contemporary optical fibre telecommunications and quantum memory platforms as well as with chip-scale semiconductor technology.These new and exciting platforms hold the promise of compact,low-cost,scalable and practical implementations of sources for the generation and manipulation of complex quantum optical states on a chip,which will play a major role in bringing quantum technologies out of the laboratory and into the real world.