Electro-optic Tensor Research Articles

TEMPERATURE DEPENDENCE ON THE GRATING FORMATION IN PHOTOREFRACTIVE POLYMERIC COMPOSITE

We investigated the dependence of the grating formation on temperature in photorefractive polymeric composite, especially the index contrast of the grating. For photorefractive polymeric materials, temperature is one of the most important factors together with the external electric field, because it is closely related with photogeneration efficiency, carrier mobility, electro-optic coefficient tensor, and so on. The diffraction efficiency of the photorefractive polymeric composite decreased with increasing the temperature, and it could be explained with the magnitude of space-charge field and the electro-optic behavior at various temperatures.

Linear electro-optical properties of tetragonal BaTiO3

Linear optical susceptibility and clamped linear electro-optical tensor coefficients of tetragonal BaTiO3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Ti-O bonds constituting distorted TiO6 octahedral groups are found to be major contributors to the electro-optic coefficients making them more sensitive than the BaO12 groups for these properties. Orientations of chemical bonds play an important role in determining these properties.

Photorefractive properties of (1-10) and (111)-cut sillenite crystals when external electric field is applied along the direction of the optimum diffraction efficiency

We study the influence of the application of an external electric field on the grating formed in (1-10) and (111)-cut photorefractive sillenite crystals. Optimum conditions for application of the bias field are examined, taking into account the shift of the grating orientation for maximum diffraction efficiency along the crystal depth. The contribution of the piezoelectric effect is considered both in the electro-optic tensor and space charge field calculations. An analysis on the diffractive properties under these optimum conditions shows an increase of 30% in maximum diffraction efficiency in Bi12GeO20, and experimental verification for this is provided.

Linear electro-optical properties of orthorhombic KNbO 3

Linear optical susceptibility and clamped linear electro-optical tensor coefficients of orthorhombic KNbO 3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Nb–O bonds constituting distorted NbO 6 octahedral groups are found to be the major contributors making these groups more sensitive than KO 12 groups to electro-optic coefficients.

Reflection-type photorefractive gratings in tin hypotiodiphosphate

Reflection photorefractive gratings recorded by nearly counterpropagating light waves in the near infrared are studied in tin hypothiodiphosphate. The ratios are established for certain electrooptic tensor components responsible for reflection grating recording, and the Debye screening length is evaluated. Reflection holograms of binary objects are recorded.

Synthesis of a photo‐crosslinked stable nonlinear optical polymer and application to external electro‐optic measurement

A photo-crosslinked side-chain second-order nonlinear optical polymer was synthesized with bis-phenol-A as the polymer backbone, p-nitroaniline as the chromophore and cinnamyl group as the photo-sensitizer. The characterization of the polymer was made by nuclear magnetic resonance, infrared, ultraviolet-vis, and dynamic mechanical analysis methods. An electro-optic film was obtained by spin coating of the polymer and corona poling then photo-crosslinking reaction. An external electro-optic measurement system was established based on the film and reflective light path configuration, and successfully applied to measure the electrical signals propagating on the under-test circuits. The poled and crosslinked film showed high glass transition temperature (160°C) and improved chromophore orientation stability. The measuring principle was analyzed by electro-optic tensor matrix and index ellipsoid methods. The results showed that the designed polymer film had the linear electro-optic effect, the voltage sensitivity of the system was measured to be 5 mv/ at the condition of 1 kHz input signal. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1506–1512, 2000

Accurate interferometric method for the measurement of electro-optic coefficients: application to a single β-barium borate crystal

A modified interferometric technique is shown to be able to determine even the small values of electro-optic (EO) coefficients with good accuracy. The experimental setup is a Michelson interferometer that includes an EO modulator in one arm and the crystal under study in the other arm. The method is based on the measurement of the reference modulator phase shift to compensate the phase shift induced by a dc field in the crystal under study. An original technique of detection ensures a better sensitivity since a refractive-index change of 10-7 and an optical path-length variation of λ/1000 can be achieved. The relative sign of EO coefficients, the change of the sample dimensions owing to the piezoelectric effect, and the influence of the temperature are successively discussed. The technique was applied to determine some EO coefficients of a standard lithium niobate crystal and all components of the EO tensor in a β-barium borate crystal.

Synthesis of a photo-crosslinked stable nonlinear optical polymer and application to external electro-optic measurement

A photo-crosslinked side-chain second-order nonlinear optical polymer was synthesized with bis-phenol-A as the polymer backbone, p-nitroaniline as the chromophore and cinnamyl group as the photo-sensitizer. The characterization of the polymer was made by nuclear magnetic resonance, infrared, ultraviolet-vis, and dynamic mechanical analysis methods. An electro-optic film was obtained by spin coating of the polymer and corona poling then photo-crosslinking reaction. An external electro-optic measurement system was established based on the film and reflective light path configuration, and successfully applied to measure the electrical signals propagating on the under-test circuits. The poled and crosslinked film showed high glass transition temperature (160°C) and improved chromophore orientation stability. The measuring principle was analyzed by electro-optic tensor matrix and index ellipsoid methods. The results showed that the designed polymer film had the linear electro-optic effect, the voltage sensitivity of the system was measured to be 5 mv/ at the condition of 1 kHz input signal. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1506–1512, 2000

Electro-optical characterization of h-BN thin film waveguides by prism coupling technique

Waveguides were fabricated by deposition of boron nitride thin films onto glass substrates by a microwave plasma enhanced chemical vapor deposition (PECVD) process. We have characterized the optical linear properties of the as-deposited layers by m-lines spectroscopy. We have used a simple method based on the shift of the synchronous angles of the guided modes to investigate the electro-optic tensor r ij using co-planar electrodes. With TM polarized light the value of r eff computed is of the order of 5 pm V −1.

A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate

Using c- and a-cut plates of strontium-barium-niobate doped with 0.66 mol.% cerium all nonzero components of the linear electrooptic tensor r13, r42, r33 including the sign are determined from angular dependence of the two-beam coupling coefficient Γ using transmission and reflection geometry of holographic recording. We found: r13=56 pm/V, r42=38 pm/V, and r33=333 pm/V. In addition we calculated the effective trap density Neff to be 2.2×1017 cm-3. The advantages of this method as well as the values obtained are discussed.

Influence of Nd:MgO dopants on the electrooptical effect in LiNbO3 single crystals

A new method for calculation of electronic structure for LiNbO3-Nd,MgO was proposed. Our approach is based on molecular dynamics simulation and quantum chemical calculations. The crystalline structure is presented as a superposition of ideal translational lattices. Dopants are considered as modulation centers taken with appropriating weighting factors. We have found that the more probable are two types of local dopants. The first one corresponds to the MgNb configuration and the second to the NdLi centers. Other possible structural configurations were also taken into account. From the ab initio norm-conserving pseudopotential (PP) calculations modified by the LCAO quasi-core states we have calculated electronic part of electrooptic tensor component r222 tensor component. Simultaneously we have evaluated phonon and electron-phonon anharmonic contributions to the r222 tensor component. Role of the particular structural fragments effectively contributing to the electrooptic coefficient is clarified. We have compared theoretically calculated values with the experimental data with the different Nd and Mg contents. Essential role of the electron-phonon contributions in the observed dependencies have been revealed.

Domain inversion by pulse poling in polymer films

We report on an original technique for poling polymeric thin films, which allowed us to obtain a second-order nonlinear inverted domain structure, which could be used for frequency-doubling waveguides under quasi-phase-matching condition. Measurements of the local value and orientation of the electro-optic r33 tensor component were performed by a reflection microscopic electro-optic ellipsometer. The measured parameters for the nonlinear structure induced in the polymeric film result to be consistent with the expected values.

Mach-Zehnder Interferometry Measurement of the Elctro-Optic Effect in a Poled Polymer Film

Two different configurations, reflection and transmission, of Mach-Zehnder interferometer(MZI) are introduced for the measurement of the electro-optic coefficients in a poled polymer thin film. The MZI measurement of the electro-optic coefficients has an advantage of permitting the determination of the electro-optic tensor coefficients, r13 and r33, independently, when compared with the single-beam polarization interferometer. In the reflection configuration of two beam interferometric measurement, a proper consideration of the optical path change, due to the reflection angle change, is found to be critical in determining the absolute value of the electro-optic coefficients, while the transmission configuration allows the independent determination of the electro-optic coefficients in the direction of the ordinary and the extraordinary optic axes.

Dependence of Linear Electro-optic Coefficient on Difference in the Atomic Sizes in Zinc Blende Crystals

Covalent radii of the bonding elements have strong effects on the linear electro-optic coefficients of zinc blende crystals; these effects can be quantitatively determined by investigating the relation between the difference in the atomic sizesρand the magnitude of the linear electro-optic tensor coefficientr41. It is interesting to note that for the same cation Zn2+, Ga3+, or In3+the magnitude ofr41increases with increased covalent radius of the bonded anionrβ. Especially with the increasing tendency of the parameterρ, the magnitude ofr41of crystals that have a same cation will increase suddenly when the value ofrβbecomes larger.

Multiple reflection correction in the determination of the complex electro-optic constant using a Mach-Zehnder interferometer

The effect of multiple reflection was corrected in the measurement of the complex electro-optic (EO) tensor of polymer films doped with dye molecues using a Mach-Zehnder interferometer. The oscillations due to multiple reflection were clearly observed for the incidence-angle dependence of the amplitude ratio and the phase difference between the total light intensity and the EO-modulated signal intensity. An analytical expression was derived for the transmitted light intensity including multiple reflection in order to obtain the correct EO constant. Theoretical and experimental results show that the systematic error due to multiple increases with the transmittance.

Bond-Charge Calculation of Electro-Optic Coefficients of Diatomic Crystals

A theoretical method has been set up to calculate the electro-optic tensor coefficientsrijk, based on the Phillips–Van Vechten (PV) dielectric theory and the Levine bond charge model. Starting from the crystal structure data and only introducing the experimentally determined optical permittivity and dielectric constant, the electro-optic tensor coefficientsrijkcan be quantitatively predicted. The theoretical calculations are in good agreement with experiment in the case of zinc blende and wurtzite crystals. For zinc blende crystals, the effects of covalent radii on the linear electro-optic coefficients are discussed.

Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi_4Ge_3O_12)

To assess the suitability of bismuth germanate as an electro-optic material for high precision applications, we have confirmed and extended previous data on its refractive index, electro-optic tensor element r(41), and thermal expansion coefficient. In addition, we have measured the thermo-optic coefficient dn/dT, the temperature dependence of the electro-optic coefficient, and the stress-optic tensor elements. From the stress-optic tensor elements and previously published data, we have computed the strain-optic tensor elements. The index of refraction is given, to a good approximation, by the single-term Sellmeier equation, n(2) - 1 = S(0)λ(0)(2)/[1 - (λ(0)/λ)(2)], with S(0) = 95.608 µm(-2) and λ(0) = 0.1807 µm. The thermo-optic coefficient is 3.9 × 10(-5)/°C at 632.8 nm and 3.5 × 10(-5)/°C at 1152.3 nm. The electro-optic tensor element varies between approximately 1.05 and 1.11 pm/V over the spectral range of 550-1000 nm; its normalized effective change with temperature is approximately 1.54 × 10(-4)/°C. The thermal expansion coefficient is 6.3 × 10(-6)/°C over the range 15-125 °C. Values of the stress-optic tensor elements are q(11) - q(12) = -2.995 × 10(-13) m(2)/N and q(44) = -0.1365 × 10(-12) m(2)/N. The strain-optic tensor elements are p(11) - p(12) = -0.0266 and p(44) = -0.0595.

Control of epitaxial growth of pulsed laser deposited LiNbO3 films and their electro-optic effects

Epitaxial LiNbO3 films with two orientations were grown on sapphire (112̄0) substrates using pulsed laser deposition. The film deposited at a low oxygen pressure (i.e., 10−4 Torr) was epitaxially grown along the a axis, and that at a oxygen pressure of 10−1 Torr was epitaxially grown along the c axis. Electro-optic properties of these films were quite different, demonstrating importance of controlling the epitaxial growth behaviors. The birefringence measurements of the LiNbO3 (112̄0) film showed a quadratic electro-optic behavior with an effective quadratic coefficient of 2.38×10−15 m2/V2. This behavior was analyzed in terms of the quadratic electro-optic tensor for LiNbO3.

Vector photorefractive spatial solitons

We derive vector soliton solutions for photorefractive media in which the refractive-index perturbations must be treated as tensors. The two polarizations of the vector solitons may be coupled through the space-charge field alone and/or through cross terms in the electro-optic tensor, which requires phase matching and specific configurations. We analyze bright planar vector solitons and verify their stability.

Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals

We relate the linear electro-optic coefficients to the quadratic polarization-optic and the elasto-optic tensors by analyzing the dielectric phenomena driven by the spontaneous and induced polarization as well as the mechanical effects given by the deformation of the crystals. We determine the temperature dependence and the wavelength dispersion of the electro-optic tensor in all the ferroelectric phases from a smaller set of data: the quadratic polarization-optic tensor of the cubic phase, the dielectric permittivity, and the spontaneous polarization. Under the assumption that the elasto-optic tensor at constant polarization is constant, the elasto-optic coefficients at constant electric field in the ferroelectric phases are derived. Numerical evaluations of these coefficients for two perovskite crystals KNbO3 and BaTiO3 are presented. Modifications of the electro-optic properties in doped crystals, mainly due to a change of the dielectric permittivity, are discussed as well.