Quadratic Susceptibility Tensor Research Articles

Determination of the spatial profiles of all components of the quadratic susceptibility tensor $\hat \chi ^{(2)} $ (z, 2ω; ω, ω) of a one-dimensionally inhomogeneous absorbing medium

For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor \(\hat \chi ^{(2)} \)(z, 2ω; ω, ω responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of the wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.

Determination of the spatial dependence of the complex components of the tensor $$\hat \chi ^{(2)}$$ (z, ω 1 + ω 2; ω 1, ω 2) of a medium with one-dimensional inhomogeneity using a biharmonic wave

It is proven that the spatial profiles of different components of the complex quadratic susceptibility tensor \(\hat \chi ^{(2)}\) (z,ω1+ω2; ω1, ω2), which is responsible for the generation of sum-frequency wave in a plate with one-dimensional inhomogeneity, can be reconstructed unambiguously. A reconstruction technique is proposed. To implement it, one has to direct a plane biharmonic wave with monochromatic components at frequencies ω1 and ω2 onto a plate and measure (in some range of the angles of incidence) the complex amplitude of the sum-frequency wave reflected from the plate. Changing the plane of incidence of the initial wave and (or) the polarization of its monochromatic components, one can determine the coordinate dependences for more than half of the components of \(\hat \chi ^{(2)}\) (z,ω1+ω2; ω1, ω2). This reconstruction can be performed if the symmetry of the plate medium provides a diagonal form for its linear permittivity tensor. The technique proposed implies measurement of the intensities of the sum-frequency waves generated under special conditions using an auxiliary reference plate; this approach allows one to do without complex phase measurements.

Reconstruction of the coordinate dependences of quadratic susceptibility tensor $$\hat \chi ^{(2)}$$ (z, ω1 ± ω2; ω1, ±ω2) components for the one-dimensionally inhomogeneous absorbing medium

A method for the unambiguous reconstruction of the spatial profiles of all components (except for χ zzz ) of the quadratic susceptibility complex tensor {ie165-2} (z, ω1 + ω2; ω1, ω2), which is responsible for the sumfrequency generation in a one-dimensionally inhomogeneous plate is proposed and proven for the first time. Such reconstruction is possible if the symmetry of the medium provides the diagonal character of the linear permittivity tensor {ie165-3} (z, ω). The procedure involves the measurement of the complex amplitude of the new wave with the frequency ω1 + ω2 that is reflected from the plate for a certain interval of the angles of incidence of the wave with the frequency ω2. The reflected wave results from the nonlinear interaction of the wave with frequency ω2 and the wave with frequency ω1 that exhibits the normal incidence. A similar approach can be used to determine the profiles of the components of the quadratic susceptibility tensor {ie165-4}(z, ω1 − ω2; ω1, − ω2), which is responsible for the difference-frequency generation.

Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionallyinhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonaltensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity.Using the example of several components of the tensors X(2)(z,ω1 ± ω2; ω1, ± ω2), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies ω1 and ω2. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

Anisotropy and dispersion of a Pockels tensor: a benchmark for electro-optic organic thin-film assessment

The dominant components of the χ(2)(-ω; ω, 0) nonlinear quadratic susceptibility tensor of a poled polymer-based nonlinear organic thin film are measured independently with a Fabry–Perot interferometric technique. Electro-optic dispersion is obtained from visible wavelengths up to 1.550 μm leading to a wavelength-independent χ333(2)/χ113(2) nonlinear anisotropy ratio close to 5 for the poly(methyl methacrylate) (PMMA) Disperse Red 1 (DR1) copolymer and close to 3 for the PMMA DR1 guest–host blend. Interaction of the chromophores with their environment is pointed out to be at the origin of these anisotropy ratios and is consequently designated as an important feature in electro-optic device design in view of polarization independence or polarization rotation requirements.

Theory of molecular optoelectronics. IX. Calculation of χ(2) from theoretical hyperpolarizabilities for DAN

AbstractComponents of the crystal quadratic susceptibility tensor χ(2) for second‐harmonic generation are calculated for the title compound, 4‐(N, N‐dimethylamino)‐2‐acetamido‐nitrobenzene. Input data are the crystal structure and refractive indices and CNDO hyperpolarizabilities; two different sets of refractive indices give similar results. The calculations yield effective polarizabilities as well as both rigorous and anisotropic Lorentz local electric fields. Susceptibility components are close to 10 pm V−1, rather smaller than those deduced experimentally and showing a weaker dependence on direction; Kleinman symmetry is mostly observed within 10%. Screened dipoledipole interactions using CNDO dipole moments amount to −80 kJ mol−1, implying permanent fields of 2 GV m−1.

Theory of molecular optoelectronics. X: Calculations for MBANP and NMBA

AbstractComponents of the crystal quadratic susceptibility tensor x(2) for second‐harmonic generation are calculated for the title compounds 2‐(α‐methyl benzylamino)‐5‐nitropyridine (MBANP) and 4‐nitro‐4'‐methyl(benzylidene aniline) (NMBA). Input data are the crystal structure and refractive indices and CNDO hyperpolarizabilities. The calculations also yield effective polarisabilities and local electric fields. Susceptibility components reach 66 pm V−1 in MBANP and 27 pm V−1 in NMBA in the crystal axes; agreement with experiment is poor for MBANP but satisfactory for NMBA. These features seem to reflect the better defined charge transfer axis in NMBA. Screened dipole–dipole interactions calculated from CNDO dipole moments stabilise MBANP by 70 kJ mol−1 and NMBA by 20 kJ mol−1 and imply permanent electric fields of a few GV m−1.

Dispersion of the quadratic optical susceptibility of meta-toluylenediamine crystals

An investigation was made of the dispersion (wavelength dependences) of all independent components of the quadratic susceptibility tensor of molecular crystals of meta-toluylenediamine on approach of the sumfrequency wavelength to the edge of the absorption band of these crystals. The nature of the dispersion of the tensor components agreed with the main ideas of the oscillator model and it ensured effective addition of frequencies in the converted-radiation wavelength range 347–532 nm.

Dispersion of the quadratic optical susceptibility and crystal structure of lithium tantalate

An investigation was made of the dispersion of the components of the quadratic susceptibility tensor of lithium tantalate on approach of the sum frequency of nonlinearly interacting light waves to the absorption edge of the crystal. The experimentally observed features of the dispersion of the various components of the susceptibility tensor were related to the structure of lithium tantalate.

Dispersion of nonlinear susceptibility of lithium iodate crystals

The method of spontaneous parametric light scattering was used to determine the dispersion of a component of the quadratic susceptibility tensor and the dispersion of absorption in the frequency range 1000–2000 cm–1. The nature of the unshifted signal observed in the scattering of light by polaritons was explained.

Nonlinear optical properties of molecular crystals of metatolylenediamine

An investigation was made of the absorption spectra of polarized light, dispersion of principal refractive indices, and collinear phase matching in the generation of the second harmonic of λ = 1.06 μ laser radiation in molecular crystals of meta-tolylenediamine. The relative values of all the independent components of the quadratic susceptibility tensor were determined for these crystals and the value of the second-harmonic conversion coefficient was found. It was concluded that meta-tolylenediamine crystals were promising frequency doublers.