Quadratic Nonlinear Susceptibility Research Articles

Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense

The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities in the Itô sense, which can further help researchers understand the propagation of soliton nonlinear systems. Firstly, a two-dimensional dynamics system and its perturbation system are obtained by using a traveling wave transformation. Secondly, the phase portraits of the two-dimensional dynamics system are plotted. Furthermore, the chaotic behavior, two-dimensional phase portraits, three-dimensional phase portraits and sensitivity of the perturbation system are analyzed via Maple software. Finally, the embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities are obtained. Moreover, three-dimensional and two-dimensional solitons of stochastic quadratic and cubic nonlinear susceptibilities are plotted.

Optical soliton solutions and various breathers lump interaction solutions with periodic wave for nonlinear Schrödinger equation with quadratic nonlinear susceptibility

Optical soliton solutions and various breathers lump interaction solutions with periodic wave for nonlinear Schrödinger equation with quadratic nonlinear susceptibility

Nonlinear light scattering spectra in water: Dependence on the content of dissolved gas and effects of non‐stationarity

AbstractHere, we study stimulated nonlinear scattering in the spectral range near the second optical harmonic of a laser pump in water samples containing gas nanobubbles. It was found that the spectral and spatial characteristics of nonlinear scattering radiation undergo significant changes upon settling of initially degassed water samples in a flask, open to the atmospheric air. It turned out that the contact with the atmospheric air results in the growth of the volume number density of gas nanobubbles. It appeared that the physical mechanism of nonlinear scattering changes upon increasing the nanobubble content. In fact, four‐photon parametric scattering in degassed water, which occurs due to the cubic nonlinear susceptibility χ(3) of medium, transforms upon increasing the content of nanobubbles into stimulated hyper‐Raman scattering controlled by the constant (∂χ(2)/∂q), where χ(2) is the quadratic nonlinear susceptibility and q is coordinate of a nucleus. The physical nature of the observed phenomenon is the generation of a surface plasmon arising due to the optical breakdown inside a gas nanobubble, which leads to an effective buildup of vibrations of molecules/ions localized in the surface layer of nanobubble. The plasmon bandwidth Δω was theoretically estimated. It turned out that Δω ≈ ω0, where ω0 is the resonant plasmon wavenumber, that is, in our case, the quality factor of the plasmon oscillator is very low.

Directly grown crystalline gallium phosphide on sapphire for nonlinear all-dielectric nanophotonics

Efficient second harmonic generation (SHG) in nanophotonic designs based on all-dielectric nanostructures demands materials with large values of the quadratic nonlinear susceptibility, low dissipative losses, and high refractive index. One of the best materials meeting all these parameters is gallium phosphide (GaP). However, second-order nonlinearity requires high crystallinity and morphology quality of the GaP layer grown for further lithographic processing. Here we develop a method to fabricate high-quality crystalline GaP metasurfaces, which demonstrate pronounced linear and nonlinear optical properties. Direct growth of a GaP layer on a sapphire substrate tackles the previous problem of wafer bonding, because of high optical contrast between fabricated resonant nanoparticles and the substrate. As a result, the fabricated GaP metasurface supports bound state in continuum mode with an experimental quality factor around 100 yielding a strong enhancement of SHG in narrow spectral range. We believe that the developed approach will become a versatile platform for nonlinear all-dielectric nanophotonics.

Mid-infrared tunable, narrow-linewidth difference-frequency laser based on orientation-patterned gallium phosphide

We report on the first characterization of orientation-patterned gallium phosphide (OP-GaP) crystals used to generate narrow-linewidth, coherent mid-infrared (MIR) radiation at 5.85 μm by difference frequency generation (DFG) of continuous-wave (cw) Nd:YAG laser at 1064nm and diode-laser at 1301nm. By comparison of the experimental absolute MIR efficiency versus focusing to Gaussian beam DFG theory, we derive an effective nonlinear coefficient for first-order quasi-phase-matched OP-GaP at the generated DFG wavelength. Using d = (2/π)d14 and taking into account Miller’s delta rule, we retrieve an absolute value of the d14 quadratic nonlinear susceptibility coefficient of GaP of d14 = 27.2(3) pm/V at 5.85 μm, in good agreement with the latest absolute measurement of this nonlinear coefficient from non-phase-matched second-harmonic generation (1.32 μm → 0.66 μm) taking into account multiple reflection effects [Shoji et al 1997 J. Opt. Soc. Am. B 14 2268]. The temperature and signal-wave tuning curves are also in qualitative agreement with a recently proposed temperature-dependent Sellmeier equation for OP-GaP when focusing effects are taken into account.

Generation of photons with all-optically-reconfigurable entanglement in integrated nonlinear waveguides

We predict that all-optically-reconfigurable generation of photon pairs with tailored spatial entanglement can be realized via spontaneous parametric down conversion in integrated nonlinear coupled waveguides. The required elements of the output quantum wave function are directly mapped from the amplitudes and phases of the classical laser pump inputs in each waveguide. This is achieved through special nonuniform domain poling, which locally inverts the sign of quadratic nonlinear susceptibility and accordingly shapes the interference of biphoton quantum states generated along the waveguides. We demonstrate a device configuration for the generation of any linear combination of two-photon Bell states.

Absolute measurement of the quadratic nonlinear susceptibility of lithium niobate in waveguides

Efficiency measurements of second-harmonic generation in quasi-phase-matched lithium niobate waveguides yield a value for the nonlinear optical second-order susceptibility tensor element χzzz(2)(2ω;ω,ω)=d33=(−20.6±2.1)pmV in periodically poled, titanium-indiffused waveguides in congruent composition lithium niobate at room temperature for a fundamental wavelength of 1.52 μm. A special fringe structure in the tuning curves was observed and explained as an unique feature in quasi-phase-matched parametric processes.

Experimental determination of the quadratic nonlinear magnetic susceptibility of a varactor-loaded split ring resonator metamaterial

This letter presents a quantitative measurement of the second harmonic generated by a slab of varactor loaded split ring resonator metamaterial and the retrieval of the effective quadratic nonlinear magnetic susceptibility χm(2) using an approach based on transfer matrices. The retrieved value of χm(2) is in excellent agreement with that predicted by an analytical effective medium theory model.

Study of the local inhomogeneities Δχ^(2) of the quadratic nonlinear susceptibility tensor in KTiOPO_4 crystals

The local inhomogeneities Δχ(2) of the quadratic nonlinear susceptibility tensor in the KTiOPO4 (KTP) crystal have been investigated. A method for visualizing the nonlinear-optical inhomogeneities is proposed that makes it possible to observe monodomain regions in the crystal. The method is based on an analysis of the interference pattern of the second harmonic, generated in KTiOPO4 by a strongly divergent laser beam. A connection is established between the nonlinear-optical homogeneity of the growth pyramids of the {201} and (100) faces and their growth mechanisms.

On the effect of structural and symmetrical features of potassium titanyl phosphate crystals with different contents of niobium, antimony, and zirconium on the second-harmonic intensity

A model is proposed, which shows that, at small deviations from the centrosymmetric state of the atomic structure, the quadratic nonlinear susceptibility of a crystal monotonically decreases with approach of the degree of central symmetry \( \eta _{\overline 1 } \)[φ(r)] of the electric potential function of the crystal structure to unity. The quadratic nonlinear susceptibility of K1 − xTi1 − xNbxOPO4 (x = 0, 0.02, 0.04, 0.11), K1 − xTi1 − xSbxOPO4 (x = 0.01, 0.07, 0.17), and KTi1 − xZrxOPO4 (x = 0.03, 0.04) crystals has been measured. The degree of central symmetry \( \eta _{\overline 1 } \)[φ(r)] has been calculated for the structures of K1 − xTi1 − xNbxOPO4 (x = 0, 0.04, 0.11), K1 − xTi1 − xSbxOPO4 (x = 0.01, 0.07, 0.17), and KTi1 − xZrxOPO4 (x = 0.03, 0.04) crystals. It is shown that, at \( \eta _{\overline 1 } \)[φ(r)] > 0.7, the relationship between the quadratic nonlinear susceptibility of the investigated crystals and the degree of their central symmetry \( \eta _{\overline 1 } \)[φ(r)] is in qualitative agreement with the proposed model.

Structural conditionality for the quadratic nonlinear susceptibility of Sr1−x Ba x Nb2O6 crystals

The intensity of the second harmonic generated in powdered samples of the compositions Sr0.75Ba0.25Nb2O6, Sr0.61Ba0.39Nb2O6, and Sr0.50Ba0.50Nb2O6 under irradiation by a pulsed-periodic YAG: Nd laser is measured. The effective values of the quadratic nonlinear susceptibility of these materials with respect to the reference sample of potassium dihydrophosphate crystals are estimated. The results obtained are compared with the precise parameters of the atomic structure of the single crystals with the corresponding compositions. It is established that the dominant contribution to the nonlinear optical susceptibility of the single crystals under investigation comes from the chains aligned parallel to the c axis of the crystal and composed of Nb octahedra with regularly alternating increased and decreased Nb-O interatomic distances. The occurrence of such a sequence in the crystal structure suggests an alternation of stronger and weaker chemical bonds in the chains −O=Nb−O=Nb−O=. These bonds are characterized by different charge electron densities, a phenomenon confirmed by the X-ray diffraction analysis, which indicates not only a difference in the Nb-O bond lengths but also an anharmonicity in the thermal vibrations of the niobium atoms. The revealed anharmonicity is associated with the difference between the chemical bonds of the niobium atoms with the oxygen atoms located in trans positions in the octahedra.

Bright and dark solitons in quadratic nonlinear periodic structures and application to an all-optical logic gate

By studying one-dimensional periodic structures with modulation of both linear and quadratic nonlinear susceptibilities, we obtain the stable propagation of a fundamental soliton pair with both bright and dark shapes and the stable propagation of a fundamental soliton series with bright shapes. Furthermore, we find that optical logic gate functions can be constructed by using these kinds of periodic structures and by setting different parameters. As examples, OR and XOR gates are presented.

Aligned Inclusion of n‐Propionic Acid Tethering Hemicyanine into Silica Zeolite Film for Second Harmonic Generation

Organization of dipolar second-order nonlinear optical (NLO) dyes in uniform orientations is not only an interesting subject by itself but also an essential step towards a successful application of the dyes for second-harmonic generation (SHG). Zeolites have been tested as the hosts for aligned inclusion of dipolar organic NLO dyes. However, the previously tested dyes have been limited to p-nitroaniline and those that have low molecular second-order hyperpolarizability constants (b ∼ 3 × 10 electrostatic units (esu; 1 esu∼ 3.33564 × 10 C)) and the zeolites have mostly been limited to powders. As a result, the potential of NLO dye-including zeolites as practically viable SHG materials has not been fully explored. It is therefore necessary to develop methods to include high-b dipolar NLO dyes with a high degree of uniform orientation (DUO) into transparent zeolite films with uniformly oriented channels. We recently reported that hemicyanine (HC) with an octadecyl tail (HC-18; Scheme 1A; b ≥ 77 × 10 esu) preferentially enters the vertically aligned channels of transparent silicalite (SL) films (thickness 400 nm) supported on glass (SL/Gs) with the octadecyl chain first because of the hydrophobic interaction between the long alkyl chain and the silicalite channel. Interestingly, despite the fact that the average number of incorporated molecules (NC) in each 400 nm long channel was only 3.5, the measured second-harmonic intensity (I2x) was remarkably high, equivalent to 7.9 % of that of 3 mm thick quartz (along the y-axis). Indeed, the measured d33 value (a tensor component of the quadratic nonlinear susceptibility) was 5.3 pm V, which was ca. 18 times larger than the d11 value of quartz (0.3 pm V ), and was even larger than the d33 value of potassium dihydrogen phosphate (KDP; ca. 3 pm V), one of the widely used NLO materials, by roughly a factor of two. Although HC-18-incorporating SL/Gs were still unusable for practical applications because of the very small NC of HC-18 in the channels, the above result clearly demonstrated the potential of NLO-dye-incorporating SL/Gs, as they could be developed into practically useful SHG films by increasing the NC. In the case of HC, it was found that the NC increases substantially upon decreasing the alkyl chain length. Unfortunately, however, the decrease in the alkyl chain length led to a sharp decrease in I2x because of a larger negative effect caused by the decrease in the DUO than the positive effect caused by the increase in the NC. Thus, increasing both the NC and DUO has been a big challenge. We now report that the DUO of HC with a propionic acid tail (commonly designated as either HC-PA or HC-2-CO2H; Scheme 1B) in SL channels increased by a factor of about four when the dye was included in SL/Gs in the presence of tetrabutylammonium hydroxide (TBAOH), leading to a ca. 16-fold increase in I2x. The procedures for preparation of HC-PA and SL/Gs are described in the Experimental Section. The scanning electron microscope (SEM) image of a typical SL/G is shown in Figure S1 in the Supporting Information. HC-PA was introduced into SL/G from the aqueous solutions (20 mL) of HC-PA (0.1 mM) and TBAOH (see Experimental for detail); the concentration of TBAOH ([TBAOH]) varied from 0.0 to 3.0 mM. HC-PA had a maximum absorption (kmax) at 460 nm in the aqueous solution regardless of the [TBAOH] (Supporting Information Fig. S2), indicating that the base did not affect the C O M M U N IC A TI O N

Second harmonic generation of fluorine-doped zinc oxide thin films grown on soda-lime glass substrates by a chemical spray technique

Second harmonic generation (SHG) studies of fluorine-doped zinc oxide (ZnO:F) thin films deposited on soda-lime glass substrates from an aged solution in conjunction with zinc pentanedionate, using the chemical spray deposition technique were carried out. The χ31(2) and χ33(2) independent tensorial components of the quadratic nonlinear optical susceptibility of the ZnO:F thin films were evaluated. Scanning electron microscopy and X-ray diffraction investigations revealed a homogeneous distribution of nanoparticles of similar size and morphology for various samples deposited at different substrate temperatures (ranging from 400 to 525°C). The SHG-technique revealed a clear dependence of the nonlinear optical response with the deposition temperature. Typical optical transmittance and photoluminescence (PL) studies were also performed, from which a bandgap (Eg) of 3.3eV was evaluated in films deposited under optimal conditions of conductivity and transmittance.

Anisotropy of second-order nonlinear optical susceptibilities of arsenic triiodide–sulfur addition complex: AsI 3 · 3S 8

We report the anisotropic linear and second-order nonlinear optical (NLO) properties of arsenic triiodide–octa-sulfur (1:3) adduct, AsI 3 · 3S 8, which spontaneously crystallizes in the trigonal rhombohedral non-centrosymmetric space group R3 m. The trigonal symmetry of the AsI 3 · 3S 8 molecule coincides with the crystal symmetry. The crystals are optically uniaxial with n o/ n e of about 1.2 and show dichroism at the UV-visible wavelengths. Second harmonic generation (SHG) tensor elements were determined from Maker fringes measured with an Nd:YAG laser (∼10 ns pulse, 1064 nm). The coefficient d 222,eff = 32.0 pm/V for the light polarized parallel to the layers of iodine and sulfur atoms in the AsI 3 · 3S 8 crystal ab plane is markedly larger than d 333 = 11.6 pm/V for the polarization of light parallel to the crystal c axis. The anisotropy parameter, defined as the d 222,eff/ d 333 ratio, is about 2.7 for the AsI 3 · 3S 8 crystal, smaller than that for the isomorphous CHI 3 · 3S 8 crystal (7.3) but larger than for the SbI 3 · 3S 8 crystal (0.7). Highly anisotropic components of the first hyperpolarizability tensor of an AsI 3 · 3S 8 molecule, β, were derived from the quadratic nonlinear susceptibility tensor of the crystal.

Study of nonlinear-optical characteristics of AgGa1-xInxSe2 crystals

The nonlinear-optical characteristics of AgGa1-xInxSe2 crystals with x = 0.25–0.34 are studied. The experimental dependence of the wavelength of noncritical phase matching on the indium concentration is obtained upon second-harmonic generation by pumping the crystal by a CO2 laser. The quadratic nonlinear susceptibility is measured by the absolute method. The radiation resistance threshold for pulsed radiation from the CO2 laser is determined.

Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized π electrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules.

Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements

We consider a possibility to create a metamaterial with nonlinear magnetic response in the microwave frequency range. Such a metamaterial is a regular periodic three-dimensional-array of resonant conductive elements with diodes as nonlinear insertions. We calculate the arising quadratic nonlinear susceptibility and show how it is controlled by the properties and arrangement of the structure elements as well as by the type and characteristics of the diode. We discuss the requirements for the diode necessary to optimize the nonlinear response of the proposed metamaterial.

Photosensitivity of germanosilicate fibres and preforms doped with nitrogen inhomogeneously over the cross section

The effect of the inhomogeneous distribution of nitrogen impurity on the photosensitivity of germanosilicate fibres is studied. For this purpose, single-mode fibres with different alternations of the core layers sintered in nitrogen and oxygen atmospheres were specially prepared by the MCVD technique. Photoinduced variations in the quadratic nonlinear susceptibility and refractive index of these fibres were recorded. It is shown that the recording efficiency depends on the radial distribution of germanium oxygen-deficient centres, which can be controlled at the stage of sintering through a nonuniform doping by nitrogen over the cross-section.

Light-induced χ(2) nonlinear susceptibility and its 1/ ω fluctuations in silica glasses

Results of theoretical and experimental studies of light-driven spatial electronic self-organization in silica glasses resulting in fluctuating static dipole polarization and corresponding phase matched χ (2)-grating are presented. The light-induced quadratic nonlinear susceptibility and corresponding intensity of second-harmonic generation fluctuate with the universal 1/ ω spectrum.