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.

PREPARATION AND SECOND-ORDER OPTICAL NONLINEARITY OF NOVEL PHENOXYSILICON NETWORKS BY SOL-GEL PROCESS

Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d(33)) Of 10(-7)similar to 10(-8) esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120 degreesC) indicated that these films exhibit high d(33) stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.

Influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system

The influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system is investigated theoretically and experimentally.In the theoretical work,a new theoretical algorithm is presented for the coherent combining efficiency,which can be used to quantify the spectral coherence decay induced by optical nonlinearity imbalance between the sub-beams.The spectral information of the sub-beam is obtained by numerically solving the nonlinear Schrödinger equation(NLSE)in this algorithm to ensure an accurate prediction.In the experimental work,the coherent combining of two all-fiber picosecond lasers is achieved,and the influence of imbalanced optical nonlinearity on the combining efficiency is studied,which agrees with the theoretical prediction.This paper reveals the physical mechanism for the influence of optical nonlinearity on the combining efficiency,which is valuable for the coherent combining of ultrashort pulse fiber laser beams.

Dispersive Nonlinearity in Er-Doped Optical Fiber

Optical dispersive nonlinearities in Er-doped optical fiber are discussed and measured at the third window wavelength 1.55 μm for optical communications firstly. The experimental method, which is developed by us, is based on dynamic scanning for fixed-point-interference (DSFPI) of two fiber beams. The real part and complex value of the third-order susceptibility at the wavelength are also obtained from the measured Kerr coefficient and nonlinear-absorption coefficient reported elsewhere.

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.

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the ease of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.

Blind Nonlinearity Equalization by Machine-Learning-Based Clustering for QAM-Based Quantum Noise Stream Cipher Transmission

In quantum noise stream cipher(QNSC)systems,it is difficult to compensate fiber nonlinearity by digital signal processing(DSP)due to interactions between chromatic dispersion(CD),amplified spontaneous emission(ASE)noise from erbiumdoped fiber amplifier(EDFA)and Kerr nonlinearity.Nonlinearity equalizer(NLE)based on machine learning(ML)algorithms have been extensively studied.However,most NLE based on supervised ML algorithms have high training overhead and computation complexity.In addition,the performance of these algorithms have a lot of randomness.This paper proposes two clustering algorithms based on Fuzzylogic C-Means Clustering(FLC)to compensate the fiber nonlinearity in quadrature amplitude modulation(QAM)-based QNSC system,including FLC based on subtractive clustering(SC)and annealing evolution(AE)algorithm.The performance of FLC-SC and FLC-AE are evaluated through simulation and experiment.The proposed algorithms can promptly obtain suitable initial centroids and choose optimal initial centroids of the clusters to achieve the global optimal initial centroids especially for high order modulation scheme.In the simulation,different parameter configurations are considered,including fiber length,optical signal-to-noise ratio(OSNR),clipping ratio and resolution of digital to analog converter(DAC).Further-more,we measure the Q-factor of transmission signal with different launched powers,DAC resolution and laser linewidth in the optical back-to-back(BTB)experiment with 80-km single mode fiber.Both simulation and experimental results show that the proposed techniques can greatly mitigate the signal impairments.

Research progress of third-order optical nonlinearity of chalcogenide glasses

Chalcogenide glasses （ChGs） are a promising candidate for applications in nonlinear photonic devices. In this paper, we review the research progress of the third-order optical nonlinearity （TONL） of ChGs from the following three aspects： chemical composition, excitation condition, and post processing. The deficiencies in previous studies and further research of the TONL property of ChGs are also discussed.

Tunable Terahertz Source Based on Optics Pumped Nonlinear Crystals

Recent progresses about optical pumped tunable terahertz （THz） sources are interviewed, including THz parametric oscillation （TPO） and difference frequency generation （DFG）. We develop high efficiency and high power surface-emitted TPO, as well as DFG with nonlinear crystals. A novel scheme for the high efficiency DFG source based on the Cherenkov phase-matching technology is comprehensively investigated in both bulk crystals. The widely tunable optical THz radiation is also researched based on the organic nonlinear 4-N,N-dimethylamino-4＇-N＇- methylstilbazolium 2,4,6-trimethylbenzenesulfonate （DSTMS） crystal.

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.

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.

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.

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.

Ultrafast third-order optical nonlinearity of several sandwich-type phthalocyaninato and porphyrinato europium complexes

The third-order optical nonlinearity of two sandwich-type phthalocyaninato and porphyrinato europium com- plexes, including double- and triple-deckers （Eu[Pc（OC5H11）8]2, Eu2（Pc）（TPP）2, Pc=phthalocyanine, TPP=5, 10, 15, 20- tetraphenylporphyrinate）, was investigated by using the femtosecond time-resolved optical Kerr gate method at 830 nm wavelength. Their second-order hyperpolarizability is estimated to be 0.74× 10^-30esu and 3.0× 10^-3esu respectively. This exhibits an evident enhancement in comparison with 0.47×10^-30esu for one-decker Eu（Pc）（acac） （acac=acetylacetonate）, which is also measured under the same conditions. The enhancement is attributed to the introduction of lanthanide metal to the large π-conjugated system, intermacrocycle interaction and two-photon resonance etc.

Absorptive Nonlinearity in Er-Doped Optical Fiber

Optical absorptive nonlinearity in Er doped optical fiber has been discussed and measured at the window wavelength 1.55 μm for optical communications firstly. It is proposed that the mechanism of this absorptive nonlinearity is the induced absorption. The first order nonlinear absorptive coefficient and the imaginary part and the complex value of the third order susceptibility at that wavelength are obtained from the measured absorptive nonlinearity.

Studies of Optical Nonlinearity Behaviors of Ultrafine PbS Particles in Perfluorocarboxylated Cation-exchanged Films

Ultrafine PbS particles with different sizes have been prepared in perfluorocarboxylated cation-exchanged films. The variation of PbS particle size was clarified by absorption spectra and TEM graphs. Time-resolved optical Kerr effects were measured by femtosecond pump-probe techniques. Optical Kerr effect response time was estimated to be less than 165 fs. A third-order optical nonlinearity of χ(3)10-12 esu for PbS particles was obtained and it was found that it increases with the decrease of particle sizes, showing the influence of quantum confined effect on optical nonlinear behaviour of ultrafine particles.

Optical nonlinearity measurement of 4-(N-methyl,N-hydroxyethl)amino,4'-nitroazobenzene using a transmittance technique with a phase object(T-PO) with top-hat beams at 600-nm wavelength

The transmittance technique with a phase object（T-PO）,for measuring optical nonlinear coefficients is proposed with a top-hat beam.The sensitivity of the T-PO with a top-hat beam is a factor of 4 greater than that with a Gaussian beam.The validity of this method is verified by measuring the nonlinearity of a well-characterized liquid,CS 2 at 532-nm wavelength.The ease of use of this method has been proved by measuring a new compound 4-（N-methyl,N-hydroxyethyl）amino,4＇-nitroazobenzene（ANAB） at 600-nm wavelength,indicating that this method can be extended to the measurement of optical nonlinearities in a wide-band spectrum.

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.

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.

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.