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.

Fluorine-Mediated Benzothiadiazole Derivatives for Second-Order Nonlinear Optics

With increasing research interests in the field of light-matter interactions,various methods have been developed for regulating nonlinear optical(NLO)materials.However,the design and synthesis of organic molecular materials for second-order nonlinear optics remain a great challenge because of the strict requirement of the materials to possess a noncentrosymmetric structure.In this work,two benzothiadiazole(BTD)derivatives referred to as BTD-H and BTD-F were synthesized,and their NLO properties in the crystalline states were studied.It was found that introducing fluorine into the BTD backbone effectively tuned the crystal packing styles of BTD derivatives to a noncentrosymmetric system for effective second-order NLO responses.Such a strategy to induce the noncentrosymmetric structure by introducing the fluorine atoms and halogen interactions may provide guidance for future engineering of organic NLO molecular materials.

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.

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.

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.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

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.

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.

Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.

An 8-Connected Chiral Lanthanide Metal-organic Framework Constructed from Naturally Camphoric Acid:Crystal Structure,Vibrational Circular Dichroism Spectroscopy and Second-order Nonlinear Optical Effect

A chiral lanthanide metal-organic framework based on enantiopure camphoric acid （D-H2cam）, [Nd3（D-cam）8（H2O）4Cl]n （1）, has been synthesized and characterized by single-crystal X-ray structural analysis, elemental analysis, IR, thermal gravimetric, and X-ray powder diffraction. Crystal data for the title compound are as follows： orthorhombic system, space group P212121 with a = 13.8287（7）, b = 14.0715（7）, c = 25.7403（12） A^°, V = 5008.8（4） A^°3, Mr = 1333.08, Z = 4, F（000） = 2644, Dc = 1.768 g/cm^3, μ（MoKα） = 3.189 mm^-1, the final R = 0.0351 and wR = 0.0814 （I 〉 2σ（I））. Compound 1 displays an 8-connected bcu topology 3D framework and hydrogen-bonding interactions stabilize the solid-state structure. The vibrational circular dichroism （VCD） spectrum and second-order nonlinear optical effect of compound 1 have been studied in the solid state.

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.

A Theoretical Study of Nonlinear Second-Order Optical Properties of Substituted Silanes

On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how different substituents on the phenyl ring attached to the atom silicon influence on the nonlinear second order optical properties of substituted silane series of molecules. The properties of (CH 3) 3Si? ?has been studied particularly. The effect of the length of silica chains on the calculated values has been studied too. The regularity summarized from the calculated results has been explained micromechanically.

Theoretical Investigation on the Second-order Nonlinear Optical Properties of Chiral Amino Acid Zinc(Ⅱ) Porphyrins

Static second-order nonlinear optical effects of amino acid zinc(II) porphyrins 1, 2, 3 and 4 were calculated by the TDHF/PM3 method based on the molecular structures optimized at the semiempirical PM3 quantum chemistry level, showing due to the cancellation of symmetric center, these amino acid zinc(II) porphyrins exhibit second order nonlinear optical response. The analysis of β components indicated that these amino acid zinc(II) porphyrins are of multipola- rizabilities, and they may be ascribed as the “mixture” of octupolar and dipoar molecules with ||βJ=3||/||βJ=1|| ≈ 5. It is found that there are no significant differences between the static β values of non-chiral and chiral amino acid zinc(II) porphyrins. However, the βxyz component, which is quite important to quadratic macroscopic χ (2) susceptibility of chiral material, is increased significantly with the increase of side chain group of amino acids.

Synthesis, Structure, and the Second-order Nonlinear Optical Properties of a Borate-carboxylic Acid Compound: KB[L-（-）-C4H4O5]2·H2O

A new organic-inorganic hybrid noncentrosymmetric potassium bis(malic acid)-borates KB(L-(-)-C4H4O5)2·H2O was synthesized by solution method. It was characterized by elemental analysis, FT-IR, TGA and single-crystal X-ray crystallography. It crystallizes in the monoclinic space group P21/c with a = 5.546(6), b = 11.985(13), c = 9.952(11) ?, β = 97.522(17)°, V = 655.8(13) ?3, Z = 2, Dc = 1.682 g/cm3, μ(MoKa) = 0.46 mm–1 and F(000) = 340. 5009 reflections were measured and 2893 independent reflections(Rint = 0.051) were used for further refinement. Single-crystal X-ray diffraction reveals that the complex exhibits a threedimensional pseudo tunnel structure consisting of fundamental building block [B(L-(-)-C4H4O5)2]– anions. The small cavities are occupied by the H2O molecules, which stabilize the whole structure by O–H×××O hydrogen bonds. The complex exhibits nonlinear optical effect as high as 1.5 times that of KDP standard.

Theoretical Investigation on Structures and Second-order Nonlinear Optical Properties of (Thiophene) Manganese Tricarbonyl Cations

The structures of several recently reported organometallic NLO chromophores, (thio-phene) manganese tricarbonyl cations, were fully optimized at the DFT non-local (GGA) level. The calculated results show that the fragments 2-SC4H3CH=CHC6H4-R in these organometallic chromophores are not planar with dihedral angles of 42.2~59.8 between two aromatic rings, which are different from those of uncoordinated counterparts. Based on the DFT geometry opti-mization, the second-order nonlinear optical polarizabilities were calculated by using RPA method. The calculated results indicate that incorporation of +3Mn(CO) unit with thiophene leads to a sub-stantial increase in the second-order polarizability (b).

Synthesis,Structure and Second-order Nonlinear Optical Activities of a New Tungsten(0) Compound with Pyridine-2-thiolato Ligand,[Et_4N][W(pyS)(CO)_4](pys=C_5H_4NS^-)

The reaction of W（CO）6 with pyOSNa （C5H4NOSNa） and Et4NCl in MeCN affords a new tungsten（0）complex [Et4N][W（pyS）（CO）4] 1 （Mr = 536.29）. The crystal and molecular structures have been determined by X-ray single-crystal diffraction. Complex 1 crystallizes in the orthorhombic system, space group P212121 with α= 8.2429（5）, b = 9.1045（4）, c = 26.8851（14） A, β= 90.00°, V=2017.66（18） A3^, Z = 4, Dc = 1.765 g/cm^3, μ= 58.51 cm^-1, F（000） = 1048, the final R = 0.0204 and wR = 0.0400 for 4432 observed reflections with I 〉 2σ（I）. X-ray structure analysis revealed that the molecule is acentric and has large first=order hyperpolarizability （7.2 × 10^-30 esu）, so it could be an IR second=order nonlinear optical candidate material.

ZINDO-SOS Studies on Second-order Nonlinear Optical Properties of Thiophene S,S-Dioxide Chromophores

The second-order nonlinear optical properties of thiophene S,S -dioxides derivatives were studied by using the ZINDO-SOS method. The computed results show that the thiophene S,S -dioxide derivatives exhibit larger second-order polarizabilities than their thiophene precursors. In order to clarify the origin of the different NLO responses among these chromophores, their electron properties and frontier orbital properties were investigated as well. These thiophene S,S -dioxides derivatives are good candidates for their application in electro-optical device due to their high nonlinearities, good thermal and photo stabilities.

Nonlinear optical imaging by detection with optical parametric amplification(invited paper)

Nonlinear optical imaging is a versatile tool that has been proven to be exceptionally useful in various research fields.However,due to the use of photomultiplier tubes(PMTs),the wide application of nonlinear optical imaging is limited by the incapability of imaging under am-bient light.In this paper,we propose and demonstrate a new optical imaging detection method based on optical parametric amplification(OPA).As a nonlinear optical process,OPA in-trinsically rejects ambient light photons by coherence gating.Periodical poled lithium niobate(PPLN)crystals are used in this study as the media for OPA.Compared to bulk nonlinear optical crystals,PPLN crystals support the generation of OPA signal with lower pump power.Therefore,this characteristic of PPLN crystals is particularly beneficial when using high-repetition-rate lasers,which facilitate high-speed optical signal detection,such as in spec-troscopy and imaging.A PPLN-based OPA system was built to amplify the emitted imaging signal from second harmonic generation(SHG)and coherent anti-Stokes Raman scattering(CARS)microscopy imaging,and the amplified optical signal was strong enough to be detected by a biased photodiode under ordinary room light conditions.With OPA detection,ambient-light-on SHG and CARS imaging becomes possible,and achieves a similar result as PMT detection under strictly dark environments.These results demonstrate that OPA can be used as a substitute for PMTs in nonlinear optical imaging to adapt it to various applications with complex.light ing conditions.

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.

Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.