Elasto-optic Coefficients Research Articles

Optical phase contrast measurement of ultrasonic fields.

This report describes an optical phase contrast imaging technique for the measurement of wide bandwidth ultrasound fields in water. In this method, a collimated optical wavefront (lambda(l) = 810 nm) impinges on a wide bandwidth ultrasound pulse. The method requires that refractive index perturbations induced by the ultrasound field be sufficiently small. Specifically, on exit from the acoustic field, the phase of the optical wavefront must be proportional to the ray sum of local density taken in the direction of propagation of the incident optical wave. A similar restriction is placed on the dimensions of the ultrasound pulse. Repeated measurement of this phase as the ultrasound field is rotated through 180 degrees about an axis normal to the direction of propagation of the incident optical wave generates the Radon transform of the ultrasonically induced refractive index perturbation. Standard tomographic reconstruction techniques are used to reconstruct the full three-dimensional refractive index perturbation. A simple two-lens imaging system and an optical signal processing element from phase contrast microscopy provide a method of directly measuring an affine function of the desired optical phase for small optical phase shifts. The piezo- and elasto-optic coefficients (the first partial derivatives of refractive index with respect to density and pressure) relate refractive index to density and pressure via a linear model. The optical measurement method described in this paper provides a direct, quantitative measurement of the piezo- and elasto-optic coefficients (from the density or pressure fields).

Photorefractive light scattering families in (111)-cutBi12TiO20crystals with an external electric ac field

We investigate here both theoretically and experimentally light-induced scattering in (111)-cut Bi12TiO20 crystals with an external ac field. Our simple analytic solution, which is nearly as precise as the numeric one, allows us to recognize the following otherwise hidden general features. Without the elasto-optic contribution, the scattering patterns are identical for the same value of xi=zeta(0)+(2/3)straight phi(p), where straight phi(p) is the initial polarization angle and zeta(0) is the angle of the external field. With the elasto-optic contribution, the scattering patterns for the same xi are still very similar. For xi not equal0, the scattering patterns depend differently on the elasto-optic coefficients p(12) and p(13) so that in principle p(12) and p(13) can be measured by purely holographic experiments. On the experimental side, we present scattering patterns for xi=0 and +/-30 degrees, showing thereby the similarity of the scattering patterns for equal values of xi. In all cases, we obtain good qualitative agreement of our analytic and numeric calculations with the experimental findings.

The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling

The refractive indices of AlxGa1−xAs epitaxial layers (0.176⩽x⩽1) are accurately determined below the band gap to wavelengths, λ<3 μm. The layers are grown on GaAs substrates by molecular beam epitaxy metal organic and chemical vapor deposition with thicknesses ranging from 4 to 10 μm. They form improper waveguide structures with the GaAs substrate. The measurements are based on the excitation of the improper waveguide modes with grating couplers at 23 °C. The refractive indices of the layers are derived from the modal propagation constants in the range of 730 nm<λ<830 nm with an estimated uncertainty of Δn=5×10−4. The temperature coefficient of the refractive index is investigated in the same spectral range. From the effective indices of the TE and TM modes, we derive the strain-induced birefringence and the elasto-optic coefficients. High-resolution x-ray diffraction is used to determine the strain of the layers. The layer compositions are obtained with inductively coupled plasma atomic emission spectroscopy. The measurement range of the refractive index is extended from the direct gap to λ<3 μm by observing the Fabry-Pérot interference fringes of the transmission spectra of isolated layers. The measured values of the refractive index and the elasto-optic coefficient are compared to calculated data based on semiempirical models described in the literature. Published data of the index of refraction on GaAs, AlAs and GaP are analyzed to permit the development of a modified Sellmeier approximation. The experimental data on AlxGa1−xAs can be fitted over the entire composition range 0⩽x⩽1 to provide an accurate analytical description as a function of composition, wavelength, and temperature.

Anisotropy of piezo- and elastooptical effect in β-BaB2O4 crystals

At first using the elaborated software the indicative surfaces of the piezooptical tensor and their stereographic projections were constructed for the β-BaB2O4 crystals. On this basis the spatial distribution of the longitudinal and transverse piezooptical effect was analysed and the extremal values and anisotropy power for each indicative surfaces were determined. The magnitudes and signs of all elastooptical coefficients were calculated and the conclusion about the possibility for use of the β-BaB2O4 crystals as efficient acoustooptical material was done.

High-power, high-fracture-strength, eye-safe Er:glass laser

We develop a high-power Er:strengthened-glass laser emitting at the eye-safe 1.535 mm wavelength. To maximize the output parameters of an Er:glass laser, whose power supply must also be used with Nd:YAG, a two-lamp laser head with parallel power forming networks (PFNs) that could be fired with an internal delay is used. The system operates at a slope efficiency of 0.45%, yielding a maximum pulse energy of 330 mJ. Thermal effects are measured, indicating strong thermal lensing, of 16 diopter/kW and mild birefringence induced depolarization of 5% at 200 W electrical power. From this data we determine the radial-tangential average and birefringence elasto-optical coefficients, Cr ,O=0.075 ± 0.002 and CB=0.0094, respectively. A TEM00 beam is achieved for a hemispherical resonator configuration. Based on the measurements, a design is presented for improved high-power TEM00 performance using principles based on dynamic compensation of thermal focusing and birefringence correction using a reentrant resonator.

Rayleigh–Brillouin scattering in calcium aluminosilicate glasses

Rayleigh–Brillouin scattering of calcium aluminosilicate (CAS) glasses was studied. The Rayleigh–Brillouin intensities and Brillouin wavenumber shifts along with measurements of refractive index and density allowed the calculation of sound velocities, Pockels elasto-optic coefficients, elastic constants and scattering loss of the material. The physical significances of the Pockels coefficients and elastic constants are discussed in the light of existing theories. The derived loss values of CAS glasses are lower than that observed in fused silica. The low intrinsic Rayleigh scattering loss in these glasses is shown to be reconciled by the bond polarizability model developed by Lines. © 1998 John Wiley & Sons, Ltd.

Rayleigh-Brillouin scattering in calcium aluminosilicate glasses

Rayleigh–Brillouin scattering of calcium aluminosilicate (CAS) glasses was studied. The Rayleigh–Brillouin intensities and Brillouin wavenumber shifts along with measurements of refractive index and density allowed the calculation of sound velocities, Pockels elasto-optic coefficients, elastic constants and scattering loss of the material. The physical significances of the Pockels coefficients and elastic constants are discussed in the light of existing theories. The derived loss values of CAS glasses are lower than that observed in fused silica. The low intrinsic Rayleigh scattering loss in these glasses is shown to be reconciled by the bond polarizability model developed by Lines. © 1998 John Wiley & Sons, Ltd.

Analysis and modelling of a silicon micromachined Mach - Zehnder interferometer for pressure sensing

This work presents analysis and modelling of a silicon micromachined Mach - Zehnder interferometer for pressure sensing, which is based on optimized layer thickness of a sandwich structure. Sensitivity to pressure is achieved by placing the sensing arm of the interferometer on a thin silicon diaphragm fabricated by micromachining from the rear side of the wafer. We analyse mechanical properties for pressure sensing and we have determined closed-form expressions that can be used as satisfactory tools for the design and optimization of optomechanical pressure sensors based on simple membranes with small deflections. The finite element software package ANSYS was used to compare the results. The relative change of the refraction index in the waveguide was calculated using the stress elasto-optical coefficients for SiON.

Low-frequency noise in a phonon system of disordered insulators.

The influence of slowly relaxing structural defects on some nonelectric properties of solids is considered. Fluctuations of phonon occupation numbers caused by energy exchange between the phonon system and the slowly relaxing excitations are analyzed. Fluctuations of the structure parameters caused by structural relaxations are studied. A model for the low-frequency flicker noise of Brillouin light-scattering spectrum is suggested, which relates it to spatial and temporal fluctuations of the elasto-optic coefficient. The results are compared with existing experimental data. \textcopyright{} 1996 The American Physical Society.

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.

Concentration dependences of elastooptic coefficients of germanate glasses containing lead and bismuth oxides

Concentration dependences of elastooptic coefficients of lead — bismuth — germanate glasses with compositions from virtually the entire range of glass formation in the system PbO — Bi2O3 — GeO2 are investigated. Partial elastooptic coefficients of the oxide ingredients of the investigated glasses are determined. The results are interpreted with consideration of the nature of the elastooptic interaction in glasses subjected to uniaxial stress. The data can be used for designing compositions of optical media for the light and acoustic lines of acoustooptical devices.

Relationship between electro-optic, vibrational and dielectric properties in BaTiO 3

The paper is concerned by the origin of the large r 42 electro-optic coefficient in BaTiO 3. First we establish the general relationship giving the dependence of the electro-optic coefficient in a large frequency range in terms of the elasto-optic, piezoelectric and second-harmonic coefficients as well as the dipolar ionic contribution. This last contribution is described as a function of the phonon and relaxation characteristics. We show that in BaTiO 3 the relaxation process around several MHz could be responsible for the large value of the r 42 electro-optic coefficient and its strong dependences on the doping and the temperature.

Elastic and elasto-optic properties of thin films of poly(styrene) spin coated onto Si(001)

Brillouin light scattering (BLS) has been used to study a series of three thin films of poly(styrene) spin coated onto Si(001) wafers. Poly(styrene) molecular weights M̄w of 30 000 and 600 000 were used, and the film thicknesses h were in the range 1730 Å<h<3750 Å. It was found that the poly(styrene) films have isotropic elastic symmetry and that all of the films can be described by the same set of two independent elastic constants c11=5.7±0.15 GPa and c44=1.39±0.03 GPa. Both c11 and c44 were determined unambiguously using a least-squares-fitting procedure by observation of the longitudinal guided and Rayleigh modes of the poly(styrene) films. Calculations have been performed of the BLS spectra which include both surface ripple and elasto-optic light scattering mechanisms. From comparisons of the relative mode intensities in the measured and calculated BLS spectra, it is found that the values of the elasto-optic coefficients for poly(styrene) are k11=−1.4±0.4 and k12=−1.6±0.4.

Coupling between linear dichroism and piezobirefringence in CdS at the isotropic point

The eigenelectromagnetic modes characterizing a uniaxial and dichroic crystal exhibiting an isotropic point for refractive indices and submitted to a natural (optical activity) or artificial perturbation are theoretically investigated. It is demonstrated that these modes are two elliptical and linearly independent vibrations whose respective axes are not perpendicular. Expressions of elliptical birefringence and elliptical dichroism are derived, and it is demonstrated that, for low perturbations, the linear dichroism of the unperturbed crystal cannot be neglected. The experimental study is performed at room temperature with a crystal of CdS submitted to a uniaxial pressure parallel to the [110] direction. The radiation transmitted by the crystal in the filter configuration and the transmission spectrum in light polarized parallel and perpendicular to the optical axis are analyzed, with the linear dichroism of the unperturbed sample taken into account. Finally, the value of the elasto-optic coefficient p44 at the isotropic point is reexamined.

Elastic constants of the orientationally disordered phase of C2F6 by Brillouin spectroscopy

The elastic constants and elasto-optic coefficient ratios of the orientationally disordered β phase of C2F6 have been determined using the technique of high resolution Brillouin spectroscopy. Just below the triple point, at 169 K, the values of the elastic constants (in units of kbar) are C11=26.99±0.10, C12=19.32±0.10, and C44=4.44±0.04. The temperature dependence of all three elastic constants was also determined and appears to be linear for the temperature range investigated, with ΔC11/ΔT=−0.335±0.010, ΔC12/ΔT=−0.236±0.010, and ΔC44/ΔT=0.005±0.011 kbar/K. Values of the ratios of acoustic velocities in high symmetry directions in the crystal indicate near perfect elastic isotropy and that moderately strong rotation–translation coupling is present in β-C2F6.

Comparative Brillouin scattering study of .gamma.-oxygen and cyclooctane I: rotation-translation coupling effects

The technique of Brillouin spectroscopy has been used to determine the adiabatic elastic constants and elastooptic coefficients of single crystals of orientationally disordered γ-oxygen and cyclooctane I as functions of temperature. The spectrum of γ-oxygen, close to the triple point temperature, exhibited almost exact elastic isotropy with slow and very intense transverse components. Cyclooctane I, with the same crystal structure, was also very isotropic

Optical study of the ferroelastic phase transition of (N(CH3)4)2ZnBr4

Abstract (N(CH3)4)2ZnBr4 undergoes a ferroelastic phase transition from an orthorhombic mmm structure to a monoclinic 2/m phase. Birefringence and optical indicatrix rotation about the monoclinic axis have been measured in the ferroelastic phase and their temperature dependences have been related to the order parameter of the transition. The spontaneous strain has also been determined by means of X-ray diffraction. It is shown that in the temperature range covered, this quantity is proportional to the optical polarization coefficient B6, which becomes spontaneous at the transition. This fact has allowed us to obtain a numerical estimate of the p66 elastooptic coefficient at the transition point.

Evaluation of Brillouin scattering intensities from rare gas crystals

Corrections to the dipole-induced-dipole theory coming from both electronic overlaps and dispersion-force effects are introduced into the self-consistent equation for the effective atomic polarizability and applied to the case of rare-gas crystals. We show that the one-phonon expansion for Brillouin-scattered intensities can be rigorously solved, with the difference from a pure dipole-induced-dipole theory that Brillouin intensities now contain three microscopic quantities of the system. In the case of krypton crystals these quantities, which are related to the corrections to elasto-optic coefficients, are estimated by using experimental data. A comparison with theoretical predictions and experimental results is discussed. In the case of neon, argon and xenon available experimental data are not sufficient to estimate the three quantities, so just the rates of the elasto-optic coefficients are discussed. A slight discrepancy might be due to an overestimate of the anisotropic short-range contribution coming...

Elastic constants of the metastable orientationally disordered phase Ia of CCl4 by Brillouin spectroscopy

The technique of Brillouin spectroscopy has been used to determine the adiabatic elastic constants, including their temperature dependence, and the elasto-optic coefficient ratios of single crystals of the metastable orientationally disordered phase Ia of CCl4. The values of the elastic constants at 244.1 K are C11=35.7, C12=31.6, and C44=11.1 (in units of kbar) and the elasto-optic coefficient ratios are P12/P11=0.85 and P44/P11=0.22. The elastic constants results suggest that there is strong rotation–translation coupling in the k=0 acoustic wave vector regime and that this coupling is likely responsible for the metastability of the fcc phase Ia with respect to the rhombohedral phase Ib.

Piezobirefringence effect in GaAs disks subjected to diametrical compression

In this communication, the simulated piezobirefringent images for a diametrically compressed GaAs disk are compared with those obtained experimentally. The values of the piezo-optic coefficients used in these simulations are derived from the elasto-optic coefficients and the stiffness constants for GaAs. The behavior of the stress-optic coefficient C for GaAs is also investigated. For (100)-oriented GaAs, the calculated value of C is found to vary with position for a given load and also found to depend on the orientation of the loading axis with respect to the principal crystal direction chosen to be 〈010〉 in this work. The calculated values of C for this case range from 0.8 to 2.6×10−12 cm2 /dyn. However, for (111)-oriented GaAs, no such dependence is observed and C is a constant with a calculated value of 1.94×10−12 cm2 /dyn.