Second-order Nonlinear Polarizability Research Articles

Second harmonic generation enhancement based on quasi-BICs in centrosymmetric materials.

In centrosymmetric optical materials, the second-order nonlinear polarization of the bulk electric dipolar contribution is zero. More effective utilization of the contribution of the surface term is one of the key methods to efficiently obtain second-order nonlinear responses on these materials. Herein, a design of densely packed slotted nanopillar arrays based on quasi-bound states in the continuum (quasi-BICs) is proposed. The quasi-BICs are analyzed by using the finite element method as an example of silicon and the second harmonic generation (SHG) process is simulated. In the structure, normal-incidence linearly polarized light excites magnetic dipole-like quasi-BICs with a high quality factor which effectively promotes light-matter interactions. Increasing the nanopillar radius or decreasing the lattice constant within a certain range can cause the distribution of quality factors in k-space of the ky direction to contract toward the Γ point, which leads to a quasi-BIC with higher quality factors at the Γ point. By conjunctively adjusting the nanopillar radius and lattice constant or changing the slot azimuth, the resonance wavelength can be adjusted over a wide range (about several hundred nanometers) or finely (within about one nanometer) while maintaining high quality factors. When the symmetry perturbation introduced by the slot is small, it is calculated that the SHG conversion efficiency is about 10-6∼10-5 at an incident light power density of 1 MW/m2, and the SHG power is about 107∼108 times enhancement compared with the structure without slots. As the slot width decreases, higher SHG conversion efficiency with more significant SHG enhancement can be achieved at a specific slot length. The results provide new insights into the modulation of the resonant wavelength and quality factor of quasi-BICs, as well as the control of second-order nonlinear effects in centrosymmetric materials.

Interband second-order nonlinear optical susceptibility of asymmetric coupled quantum wells

Asymmetric molecular bonds possess a microscopic second-order nonlinear optical polarizability p(2). Crystals built from them possess a macroscopic second-order nonlinear optical susceptibility, χ(2), if their structure lacks centrosymmetry. χ(2) can be enhanced by introducing additional asymmetry at the meta-structural level. Here, we use a dipole matrix formalism to calculate χ(2) of asymmetric GaAs/AlGaAs coupled quantum well structures at telecommunication frequencies, for which interband (rather than previously considered intersubband) optical transitions govern optical nonlinearities. Using unit cell and envelope wavefunctions and considering all possible transitions between two bound electron and two bound hole states, we predict tenfold enhancement in χ(2) in previously underexplored ranges of quantum well asymmetry and coupling barrier thickness. This work paves the way toward enhanced, tailorable second-order optical nonlinearities for semiconductor digital alloy and superlattice structures.

Nonlinear polarization tensor measurement with a vectorial complex field in second-harmonic-generation microscopy

Polarization-sensitive second-harmonic-generation microscopy (pSHGM) allows one to determine the molecular orientation of harmonophores. Conventional point scanning based pSHGM is time consuming and subject to the assumption of the cylinder symmetry of the sample. Here, we propose a wide-field pSHGM measurement scheme that is able to measure the second-order nonlinear polarization tensor. The measurement scheme is based on first-order Born approximation, from which the relation between incident fundamental wave, second harmonic wave, and nonlinear polarization tensor has been established. It suggests that the polarization tensor can be solved by measuring the vectorial second harmonic complex fields corresponding to three independent polarization states of the incident fundamental wave. An experiment on measuring the supramolecular orientations, in terms of their symmetric axis, of myosin in rat muscle tissue has been carried out to demonstrate the proposed measurement scheme. Benefiting from the ability of recording the second harmonic signal from different positions parallelly, the proposed method possesses a higher imaging frame rate compared to point scanning based pSHGM. With the present configuration, it takes 0.01 s to acquire a 128\ifmmode\times\else\texttimes\fi{}128 pixels image, which is mainly limited by the excitation power density for wide-field illumination. For the same data throughput using pixel-by-pixel scanning, 0.16 s acquisition time is required for a pixel dwell time of 10 \textmu{}s. Having the ability of wide-field imaging and polarization measurement, the present work also lays a foundation for high-resolution SHG microscopy using computed tomography.

铌酸锂微纳波导中的二阶非线性光学效应研究进展

<p indent="0mm">Lithium niobate (LiNbO₃, LN) crystal has a large second-order nonlinear coefficient (<italic>d</italic>₃₃=25.2 pm/V@1064 nm), wide transparent window (0.35–5 μm), and stable periodic microdomain structure preparation, which is a good platform for the study and application of second-order nonlinear optical effects. Lithium niobate thin film (LNTF) is regarded as a promising integrated photonics platform due to its excellent linear and nonlinear optical properties. As the basic unit of an integrated optical system, lithium niobate micro/nano waveguide has been studied as a transmission and control device, and it shows excellent second-order nonlinear optical characteristics. The second-order nonlinearity plays an important role in modern optics, including second-harmonic generation (SHG), sum- and difference-frequency generation, parametric down conversion, and parametric oscillation. Efficient and compact wavelength converters based on second-order nonlinearity are key components for a wide range of applications, including entangled photon sources, optical parametric oscillators, and optical parametric amplifiers. The second-order nonlinear polarization intensity is proportional to the square of the electric field intensity. Micro/nano optical waveguides can improve the light intensity in the device through the local characteristics of the spatial light field, to improve the conversion efficiency of the nonlinear processes. And significantly enhanced electric field strength makes the normalized nonlinear conversion efficiency of LNTF waveguides exceed that of the reverse proton<bold> </bold>exchange lithium niobate waveguides (frequency conversion efficiency 150% W^–1 cm^–2@1550 nm) by one order of magnitude. The nonlinear conversion efficiency of LNTF micro/nano waveguides can be further improved through mode phase matching (MPM) or quasi-phase matching (QPM) to optimize the spatial overlap between the eigenmodes involved in the nonlinear process. The detailed theory, fabrication and application were demonstrated in the manuscript as follows: (1) The theory of second harmonic generation. As an example of second-order nonlinear process, the factors affecting the conversion efficiency of second harmonic generation were analyzed, and can be summarized as nonlinear coefficient, mode special overlap, mode area and phase-matching condition. (2) The fabrication of periodically poled lithium niobate waveguides and periodically poled technics. Based on the micro fabrication processes such as electron beam lithography, dry etching and chemico-mechanical polishing, the propagation loss could be reduced to <sc>0.027 dB/cm.</sc> With the combination of low loss waveguides and the electrode polarization process, periodically poled lithium niobate microstructures and the detailed fabrication processes were discussed in the manuscript. (3) Efficient second harmonic generation based on MPM and QPM. It was reported that the normalized efficiency can reach 1000% W^–1 cm^–2, and we described broadband and tunable SHG in detail. (4) Spontaneous parametric down conversion. With the development of quantum information technology and its application in the fields of secure communication and precision measurement, quantum photon sources with high speed, high brightness and high purity have attracted more and more attention. Due to the strong optical confinement, the micro/nano waveguides reduce the pump power and improve the quality of generated photon pairs, which is helpful to realize the integrated optical path of quantum information processing. In summary, this paper reviews the recent development of second-order nonlinear optical effects in LNTF micro/nano waveguides. Firstly, the theory of second harmonic conversion is introduced, and then the fabrication and periodically poled techniques of LNTF micro/nano waveguides are discussed. As an example, the efficient SHG and parametric down conversion of LNTF waveguides were detailedly demonstrated. The processes of mode phase matching and quasi-phase matching technics, tunable SHG and wideband frequency doubling effect were emphatically investigated.

Insighting the functionally modified C60 fullerenes as an efficient nonlinear optical materials: A quantum chemical study

It is well-known that π-conjugation plays an important role to tune the nonlinear optical (NLO) response of donor-π-conjugated-acceptor compounds. Fullerenes (C60) are one of a few compounds who are abounded with π-conjugation and perhaps are the largest π-conjugation compounds. In the present study, we systematically designed C60 derivatives (2 (fulleropyrrolidine) and 2a-2c (fulleropyrrolidine tetrathiafulvalene derivatives where 2a, 2b and 2c are with n = 0, n = 1 and n = 2) through the use of pyrrolidine and tetrathiafulvalene moieties. We applied density functional theory (DFT) methods to calculate their respective geometrical structures, electronic properties, linear and nonlinear optical response properties along with their respective UV–Visible spectra using CAM-B3LYP functional and 6-31G* basis set. The isotropic polarizability (αiso) and anisotropic polarizability (αaniso) of 2c was found to be 131.52 × 10-24 and 47.01 × 10-24 esu, respectively. Amongst our designed compounds, the maximum second-order nonlinear optical polarizability amplitude (β//) of 2c was found to be 15.69 × 10-30 esu. Interestingly, 2c shows the highest third-order nonlinear polarizability amplitude <γ> of 284.29 × 10-36 esu that is about three times higher than parent compound 1. Additionally, frontier molecular orbitals (FMOs), molecular electrostatic potential maps (MEPs), transition density matrix (TDM) analysis indicate more effective charge redistribution from donor moiety to acceptor fragments. The density of states (DOS) diagrams reveal distinct electronic contributions of various fragments in the formation of HOMO and LUMO orbitals resulting in efficient intramolecular charge transfer (ICT) and robust third-order NLO response properties of functionalized fullerene derivatives. The current study may arouse the attention of the scientific society to utilize the extensive π-conjugation of functionalized fullerenes for designing efficient NLO materials.

Mid-Infrared Frequency Generation via Intermodal Difference Frequency Generation in AlGaAs-On-Insulator Waveguides

We investigate theoretically mid-infrared (MIR) generation via difference frequency generation in multimode AlGaAs-on insulator (AlGaAs-OI) waveguides. The large refractive index difference between the AlGaAs core and the silica cladding shrinks the modes size down to the sub-μm2 scale, and, together with AlGaAs strong second-order nonlinear polarization, empowers strong nonlinear effects. As a result, efficient MIR generation is obtained in few-cm long waveguides with sub-μm2 transverse section, where higher order modes are exploited to achieve the phase-matching condition. These observations suggest that multimode AlGaAs-OI waveguides could represent a novel promising platform for on-chip, compact MIR sources.

Prediction of NLO response of substituted organoimido hexamolybedate: First theoretical framework based on p-anisidine adduct [Mo6O18(p-MeOC6H4N)]2-

The second-order nonlinear optical (NLO) responses and dipole polarizabilities of p-anisidine adduct (imido derivative of hexamolybdates/polyoxometalates/POMs/Cluster) are studied by means of time dependent density functional (TDDFT) calculations. A substantial molecular second-order NLO response has been noticed in these organic-inorganic hybrid compounds, particularly [Mo6O17 cis-(p-MeOC6H4N)2]2− (system 2) and [Mo6O18 p-MeOC6H4N]2- (system 1) having static second-order polarizability (βvec) calculated to be 1949.60 au and 1565.10 au respectively. Both p-anisidine and cis-(p-anisidine) are found to be preferred choice over the trans-(p-anisidine) adduct. There is a fair probability for these systems to be selected as efficient second-order nonlinear optical materials. The movement of charge transfer from p-anisidine to hexamolybdate cluster (D–A) along the y-axis suggests molybdenum cluster acts as an acceptor (A) whereas p-anisidine working as a donor (D) in all the studied systems which is responsible for NLO response in such adducts. An incremental increase in the computed βvec values were evaluated by incorporation of an electron donor (Metalloporphyrin) instead of p-anisidine. Furthermore, substitution of Fe over Zn in Metalloporphyrin cage has enhanced the optical nonlinearity. This research effort offers a significant understanding into metal (Fe/Zn) to metal (Mo) charge transfer through imido-linkage in hexamolybdates, which has been found to be an efficient mode to enhance NLO response as a prime example in modulation of optoelectronics.

Temperature characteristics of a BGO fiber-optic voltage transformer.

The temperature stability of the optical fiber voltage transformer (OVT) has always been the key factor restricting its practical application. There are many factors affecting temperature characteristics, including residual birefringence during Bi4Ge3O12 (BGO) processing, the thermo-optic effect, the thermal expansion effect, and temperature change of the second-order nonlinear polarization coefficient. These complex effects interact with each other and affect the temperature characteristics of the OVT. Therefore, for a long time, the research of various literatures has not been comprehensive enough, and even has certain contradictions. In this paper, the mechanism between the five influencing factors and the OVT temperature characteristics was investigated. The experimental results show that the temperature characteristics of OVT can be divided into two aspects: the starting point and the conversion coefficient. The starting point is affected by the residual birefringence of the BGO crystal, crystal alignment, the thermal expansion of the crystal, and the thermo-optic effect. The conversion coefficient is affected by the starting point, the thermo-optic effect and the second-order nonlinear polarization coefficient.

Exciton effects on the nonlinear optical properties of the endohedral La@C82 complex

Using the Hartree–Fock single-excitation configuration interaction (CI) model, we calculated the second-order and third-order nonlinear polarizability of the La@C82 molecule. Obtained results indicate that the third-order nonlinear polarizability $$ \gamma $$ is much larger than the second-order nonlinear polarizability $$ \beta $$ and linear polarizability. Also, our results show that the $$ \gamma $$ value of the La@C82 molecule is much larger than those of the C60 and C70 molecules. The spectral shapes of the third-order nonlinear polarizability tensor, the second-order nonlinear polarizability tensor and linear polarizability of the C82 molecule turn out to be determined mainly by the geometrical distributions of the pentagons in the fullerene structures.

Terahertz control of air lasing

The coherent emission from ionized nitrogen molecules is of interest for remote sensing and astronomical applications. To initiate the lasing process, we used an intense ultrashort near-infrared (NIR) pulse overlapped with a terahertz (THz) single-cycle pulse. We observed that coherent emission could be seeded and modulated by the amplitude of the THz field, which is the result of a combined effective second-order nonlinear polarization and the nonlinear effects induced by the NIR pump. Our results shed light on the role of intense transient fields in the coherent emission from photoexcited gas molecules.

Density Functional Theory Predictions of the Nonlinear Optical (NLO) Properties in Triphenylamine based α-Cyanocinnamic Acid Compounds: Effect of Fluorine on NLO Response

In this study, the energy gaps, second-order nonlinear optical (NLO) properties and dipole polarizabilities of triphenylamine based α-cyanocinnamic acid acetylene derivatives have been investigated via using time-dependent density functional response theory. These compounds were designed theoretically by fluorine (F) atom substitution at different positions of phenyl ring end of the α-cyanocinnamic acid segment. The results have indicated that the systems substituted by fluorine show remarkable NLO second-order response, especially D4 system with computed static second-order polarizability (βtot) of 70537.95 (a.u). Hence, these materials have the likelihood to be an excellent second-order nonlinear optical (NLO) materials. The βtot value suggests that along the x-axis the charge transfer (CT) from triphenylamine to α-cyanocinnamic acid (D-A) plays a key role in NLO response; whereas α-cyanocinnamic acid acts as an acceptor (A) and triphenylamine acts as a donor (D) in all the studied systems. Incorporation of an electron acceptor (F) at the phenyl ring end of the α-cyanocinnamic acid segment increases the computed βtot values. The present investigation therefore provides an important insight into the remarkably greater NLO properties of α-cyanocinnamic acid and triphenylamine attached via acetylene.

Wide Frequency Tuning of Continuous Terahertz Wave Generated by Difference Frequency Mixing under Exciton-Excitation Conditions in a GaAs / AlAs Multiple Quantum Well

Continuous terahertz wave sources with narrow bandwidth and wide frequency tunability enable high-resolution terahertz spectroscopy and high-speed information communication. In this study, using the optical nonlinearity of excitons as the source of second-order nonlinear polarization, we realize a continuous terahertz electromagnetic wave demonstrating wide frequency tunability from 0.1 to 18 THz without a decrease in intensity due to phonon scattering. Because of excitation of two exciton states in a Ga As / Al As multiple quantum well using two continuous-wave lasers, terahertz waves are emitted as a result of difference-frequency mixing, where the intensity shows a square dependence on the excitation intensity. Using the inhomogeneous width of exciton lines, we achieve wide frequency tunability without phonon effects.

Broadband gate-tunable terahertz plasmons in graphene heterostructures

Graphene, a unique two-dimensional material of carbon in a honeycomb lattice, has brought remarkable breakthroughs across the domains of electronics, mechanics, and thermal transport, driven by the quasiparticle Dirac fermions obeying a linear dispersion. Here we demonstrate a counter-pumped all-optical difference frequency process to coherently generate and control THz plasmons in atomic layer graphene with an octave tunability and high efficiency. We leverage the inherent surface asymmetry of graphene for a strong second-order nonlinear polarizability chi(2), which together with tight plasmon field confinement, enables a robust difference frequency signal at THz frequencies. The counter-pumped resonant process on graphene uniquely achieves both energy and momentum conservation. Consequently we demonstrate a dual-layer graphene heterostructure that achieves the charge- and gate-tunability of the THz plasmons over an octave, from 9.4 THz to 4.7 THz, bounded only by the pump amplifier optical bandwidth. Theoretical modeling supports our single-volt-level gate tuning and optical-bandwidth-bounded 4.7 THz phase-matching measurements, through the random phase approximation with phonon coupling, saturable absorption, and below the Landau damping, to predict and understand the graphene carrier plasmon physics.

Proton Order toward the Surface of Ice Ih Revealed by Heterodyne-Detected Sum Frequency Generation Spectroscopy.

Using heterodyne-detected sum frequency generation (HD-SFG) spectroscopy, we investigated surface proton order at the basal, primary prism, and secondary prism faces of single-crystalline ice Ih at ca. 130 K. The complex phase of the obtained spectra clearly indicates that second-order nonlinear polarization from which the HD-SFG signal arises is generated exclusively at the surfaces. This suggests surface proton ordering along the normal, whereas the bulk remains proton-disordered, as is well known for ice Ih. A strong positive peak observed in the HD-SFG spectra enables us to determine the "direction" of the surface proton order as "H-up", that is, the hydrogen atom of the OH group pointing away from the bulk, irrespective of the ice faces. Reliable HD-SFG measurements carried out in the present study have greatly advanced our understanding of surface structure of ice Ih.

Second-order nonlinear polarizability of ferrocene-BODIPY donor-acceptor adducts. Quantifying charge redistribution in the excited state.

A series of dyads and triads using ferrocene (Fc) as the donor and 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) as the acceptor, linked either directly or through an N-phenylmethanimine or ethynylbenzene linker have been synthesized. While the former (directly linked) dyads were prepared through acid catalyzed condensation of pyrrole with ferrocenecarboxaldehye or 1,1'-ferrocenedicarboxaldehyde followed by oxidation with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ), the latter two sets (imine and alkyne linked) of dyads were obtained through Schiff base condensation or Sonogashira coupling reactions, respectively. The compounds were fully characterized with spectroscopic data and single crystal X-ray analysis in one case. The peaks corresponding to the Fe(ii)/Fe(iii) redox couple at 0.33 to 0.38 V showed a varying degree of positive anodic shift, which reflected the strong electron withdrawing effect of the corresponding BODIPY unit. The first hyperpolarisability, β, was measured in chloroform using the femtosecond hyper-Rayleigh scattering (HRS) method at 1300 nm. Interestingly, from the βHRS values, the dominating role of the Fc donor and the intervening linker could be established, which correlated well with the experimental linear optical data as well as theoretical data calculated using density functional theory (DFT) and time-dependent DFT calculations. This work constitutes the first report where electron accepting power of BODIPY in combination with the Fc donor moiety, is exploited and we demonstrate that the values are comparable to that of push-pull derivatives where BODIPY was used as the conjugated linker.

Multifunctional geometrical isomers of ferrocene-benzo[1,2-b:4,5-b′]difuran-2,6-(3H,7H)-dione adducts: second-order nonlinear optical behaviour and charge transport in thin film OFET devices

New ferrocene based donor–acceptor chromophores depict structure-dependent second-order nonlinear polarizability and charge transport in thin film OFET devices.

Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals

Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles has been predicted in certain crystalline solids in which either inversion or time-reversal symmetry is broken\cite{WanPRB2011,BurkovPRL2011, WengPRX2015,HuangNatComm2015}. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention \cite{XuScience2015, LvPRX2015, YangNatPhys2015}. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons \cite{anderson1965symmetry,shi2013ferroelectric,kim2016polar}. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, $\chi^{(2)}$, leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic $\chi^{(2)}$ in the TMMPs TaAs, TaP, and NbAs. With the fundamental and second harmonic fields oriented parallel to the polar axis, the value of $\chi^{(2)}$ is larger by almost one order of magnitude than its value in the archetypal electro-optic materials GaAs \cite{bergfeld2003second} and ZnTe \cite{wagner1998dispersion}, and in fact larger than reported in any crystal to date.

Concept of annular vector beam generation at terahertz wavelengths via a nonlinear parametric process.

In this paper, we describe our theoretical investigation and calculations for a terahertz (THz)-wave profile generated by difference frequency mixing (DFM) of focused, cylindrically symmetric, and polarized optical vector beams. Using vector diffraction theory, the second-order nonlinear polarization was estimated from the electric field components of the optical pump beams penetrating uniaxial, birefringent nonlinear optics (NLO) crystals, GaSe and CdSe. The approximate beam patterns of the THz waves were simulated using DFM formulation. The intensity patterns of the THz waves for GaSe and CdSe showed sixfold symmetry and cylindrical symmetry, respectively, based on the nonlinear susceptibility tensor of the crystals. As the phase-matching angle θ(PM) was constant with respect to the c axis of the NLO crystals, an annular vector beam with a narrow width was expected.

Investigation of anti-Stokes Raman processes at phonon-polariton resonance: from Raman oscillation, frequency upconversion to Raman amplification.

Raman oscillation, frequency upconversion, and Raman amplification can be achieved in a second-order nonlinear medium at the phonon-polariton resonance. By beating two optical fields, a second-order nonlinear polarization is generated inside the medium. Such a polarization induces a spatially uniform nonpropagating electric field at the beat frequency, which in turn mixes with the input optical field at the lower frequency to generate or amplify the anti-Stokes optical field. Raman oscillation can be efficiently reached for the copropagating configuration. In comparison, efficient frequency upconversion and large amplifications are achievable for the counterpropagating configuration. These Raman processes can be used to effectively remove transverse-optical phonons before decaying to lower-frequency phonons, achieve laser cooling, and significantly enhance coherent anti-Stokes Raman scattering. The counterpropagating configuration offers advantages for amplifying extremely weak signals.

Synthesis, linear and nonlinear optical properties of thermally stable ferrocene-diketopyrrolopyrrole dyads

Thermally stable ferrocene-DPP dyads exhibit non-zero dipole moments as well as negative solvatochromism and show structure dependent second-order nonlinear polarizabilities.