Piezooptic Constants Research Articles

Characterization of photoelastic materials by Mach–Zehnder interferometry: Application to trigonal calcium galogermanate (CGG) crystals

We explore piezooptic and photoelastic properties of Ca3Ga2Ge4O14 (CGG) crystals. A Mach–Zehnder interferometry technique is utilized to determine a complete set of the piezooptic tensor constants πim, with particular attention to the measurement accuracy, reliability, and uncertainty resolution in the piezooptic measurements. For these reasons, independent piezooptic constants or their combinations were determined by performing interferometric measurements for different geometries of piezooptic coupling using samples of both principal (direct) and non-principal (X/45°) crystallographic cuts. Basing on the results of piezooptic measurements, a complete set of photoelastic tensor constants pim and the acousto-optic performance (figure of merit M2) of CGG crystals were evaluated. The obtained piezooptic, photoelastic, and acousto-optic characteristics of CGG crystals are compared with those of other crystals of the langasite group, langasite and CTGS (Ca3TaGa3Si2O14). A comparative analysis reveals a correlation between the values of the piezooptic or photoelastic constants and the lattice parameters for this group of crystals. High optical quality and optical transparency in the UV region of the spectrum up to 260 nm together with extremely high mechanical resistance to uniaxial compression (≤2000 kg/cm2) opens up the possibility for specific application of CGG crystal as an optical material for piezooptic sensors of high uniaxial compression. The presented piezooptic interference technique along with methodological and metrological approaches paves the way for accurate and unambiguous characterization of photoelastic crystal materials of trigonal symmetry.

Characterization of photoelastic materials by combined Mach-Zehnder and conoscopic interferometry: Application to tetragonal lithium tetraborate crystals

Mach-Zehnder and conoscopic interferometry are used to explore photoelastic properties of anisotropic crystal materials. In a number of cases an application of both techniques significantly improves an accuracy of piezooptic and photoelastic measurements. The performance of such combined approach is demonstrated on tetragonal lithium tetraborate (LTB) single crystals, as an example. Special attention is paid to methodological and metrological aspects, such as measurement accuracy and the quantitative error analysis of the resulting measurements. Performing the interferometric measurements for different geometries of piezooptic coupling the full sets of piezooptic and photoelastic tensor constants of LTB crystals have been determined. The acoustooptic efficiency, on the other hand, has been evaluated using the magnitudes of photoelastic constants derived from the piezooptical measurements. For the geometries with strong photoelastic coupling LTB demonstrates quite large acoustooptic performance with figure of merit value, М2, achieving 2.12 × 10–15 s3/kg. It is several times larger than that of strontium borate crystals, nowadays the best acoustooptic material in deep-ultraviolet spectral region.

Piezo-optic tensor of crystals from quantum-mechanical calculations.

An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO4, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π61 constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.

Piezo-optic properties of K2SO4 crystals

The effect of uniaxial stresses applied along the principal crystallographic directions on the dispersion and temperature dependences of birefringence of K2SO4 crystals is studied. The birefringence is found to be sensitive to uniaxial stresses. The spectral and temperature dependences of the combined and absolute piezo-optic coefficients of these crystals are investigated. Their significant anomalies are observed at the ferroelectric phase transition. They are caused by the change in the induced birefringence due to the occurrence of spontaneous deformation. The contributions of the electro-optic and elasto-optic effects to the spontaneous variations in the piezo-optic constants are separated.

The calculation of absolute piezooptic constants of TGS crystals with L-treonine admixture

The calculation of absolute piezooptic constants of TGS crystals with L-treonine admixture

Refractive indices of (NH4)2SO4 crystals under uniaxial pressure

The effect of uniaxial pressure σm ≤ 200 bar on the spectral (300–800 nm) and temperature (300–77 K) dependences of the refractive indices of(NH4)2SO4 crystals has been investigated. The baric dependences of the electronic polarizability, specific refraction, and parameters of the Sellmeier formula have been calculated. It is established that uniaxial pressure increases the refractive indices, mainly because of the narrowing of the band gap, increase in the oscillator density, and redshift of the UV absorption band maximum. The anomalies arising as a result of ferroelectric phase transition are related to the occurrence of spontaneous deformation and polarization (the latter is a superposition of two sublattice polarizations). The spectral and temperature dependences of the piezooptic constants are analyzed and the values of electro-optic coefficients are estimated.

Piezo-optic properties of TGS crystals doped with D-serine

The effect of uniaxial mechanical pressure along the main crystallophysical axes on the principal values of birefringence Δn i in TGS crystals doped with 5% D-serine is investigated. It is ascertained that the values of Δn i are rather sensitive to the action of uniaxial stresses. The temperature shift coefficients ∂T c /∂σm are determined for the phase-transition points. The temperature and spectral dependences of the combined piezo-optic constants π im 0 are calculated. The contribution of the secondary electro-optic effect to the changes in the birefringence and the piezo-optic constants of doped crystals is determined. It is found that the piezooptic constants π 23 0 and π 12 0 have the same values, which indicates a decrease in the anisotropy of the optical indicatrix of doped crystals under the action of uniaxial stress. The optical and deformation contributions to the relaxation effect of piezo-optical birefringence in doped TGS crystals are found.

The Refractive Properties of Uniaxially Stressed Doped TGS Crystals

The effect of uniaxial mechanical stresses applied along the principal crystal-physical axes on the principal values of birefringence Δ n i is studied on TGS crystals with L-threonine, L-valine and D-serine admixtures. It is revealed that Δ n i are quite sensitive to the stresses and have different values and opposite signs. The baric coefficients ∂Tc/∂ σm for the phase transition (PT) temperature appear to be smaller than those for the pure TGS crystals. Temperature and spectral dependences of the combined piezooptic constants are calculated.

Two-fold interferometric measurements of piezo-optic constants: application to β-BaB 2O 4 crystals

We present the interferometric technique which allows to measure piezooptical and photoelastic characteristics of crystal materials of any symmetry. The offered two-fold interferometric method enables to determine all independent non-zero piezooptic and photoelastic constants by measuring pressure induced changes of optical path. As advantage to known acoustooptical techniques this method allows to measure both the absolute magnitude and sign of photoelastic constants. In general case the determination of 36 components of piezooptic tensor needs to carry out 57 measurements on 16 samples. The corresponding relationships are derived. As an example we apply here the interferometric technique to measure the piezooptic and photoelastic constants in trigonal β-BaB 2O 4 crystals.

Evidence of laser-wavelength effect in picosecond ultrasonics: possible connection with interband transitions.

We have studied the effect of wavelength change on picosecond acoustic pulses generated using a femtosecond laser. For the first time, we show that the pulse shape can be strongly influenced by the laser wavelength. The results are in excellent agreement with a calculation based on a thermoelastic model which connects them to significant changes in the piezo-optical constants. There are similarities between the present study and stress modulation spectroscopy, which allows us to ascribe the observations to interband transitions and suggests thus a new potentiality of picosecond ultrasonics.

Absolute piezo-optic constants of Rochelle salt crystals

The effect of uniaxial mechanical pressures applied along the main crystallophysical axes and the corresponding bisector directions on the birefringence of Rochelle salt crystals has been studied. The temperature (77–300 K) and spectral (300–700 nm) curves of the combined, π im 0 and absolute, πim, piezo-optic constants of crystals are calculated. It is found that the disperse πim curves are intersected in the vicinity of the inversion of the birefringence sign, which indicates a higher symmetry of the piezo-optic constant tensor. The temperature dependences of the absolute piezo-optic constants show no clearly pronounced anomalies in the vicinity of the phase transitions in the Rochelle salt crystals.

THE REFRACTOMETRY OF THE UNIAXIALLY STRESSED FERROELECTRICS

The effect of uniaxial mechanical stresses upon the spectral and temperature dependences of birefringences in some ferroelectric crystals with the incommensurate phase are studied. Considerable baric displacements of para-incommensurate-commensurate phases transition points were observed.The calculated temperature and spectral dependences of combined π im and absolute πim piezooptic constants show a considerable dispersion and anomalies at phase transitions.The increase of the principal refractive indices under stress effect was observed.

Photoelasticity and its relaxation in TGS + Cr3+ crystals

In this work the results of temperature researches of piezooptic constants, describing changes of path difference, and relaxation of piezooptic effect for TGS + Cr3 + crystals are presented. The anomalies in the field of phase transition are explained and designed. The features of photoelasticity relaxations are analysed. It is specified that the anomalous of the dependence of relative amplitude β13(T) has such character as well as the dependence of β13 0(T).

Low‐Temperature Anomalies in the CdI2Cd Crystalline System

AbstractFrom the measurements of elastic coefficients, piezooptical constants, and dilatometrical lengthening the existence of an improper ferroelastic phase transition of first order in the CdI2Cd single crystalline system within the temperature range 40 to 60 K is found. Different values of the temperature hysteresis are revealed for the piezooptical and elastic constants. From the data obtained an essential role of electron‐phonon interaction in the appearance of the mentioned phase transitions is concluded. The obtained results clearly show that in the CdI2Cd single crystalline system at lower temperatures long‐range forces appear between the impurity subsystems, which due to the specific electron‐phonon interactions tend to the appearance of the phase transitions. The behaviour of the elastic constants and the lengthening indicate the possible ferroelastic nature of these transitions. Simultaneously the existence of the temperature hysteresis reflects the first‐order nature of the mentioned transitions.

Influence of Defects on Ferroelastic Phase Transition in InI Single Crystals

InI single crystals (space group D172h) are typical layered A 3Β7 compounds with a pronounced anisotropy of the crystalline stucture and the corresponding optical properties [1-5]. At the same time, the recent revelation of the low temperature phase transitions in these crystals [6, 7] can present them as convenient model objects for the creation of phase transitions theory in high anisotropy media including those with the incommensurate phase. In the circumstances, it is very substantial that similar twodimensional systems are most susceptible to the appearance of the translational symmetry perturbations of different kind, above all at the expense of appearance of defects, dislocations and vacancies. The last ones are in particular fashion exhibited in modulated superstructures [8]. The goal of this work is to describe the influence of the defect subsystem on phase transitions in InI single crystals, because the layering of structure allows one to control smoothly the corresponding parameters. The initial samples were synthesized using reaction between the pure metallic indium and iodine in a hermetical quartz ampoule. After the band cleaning and distillation in the vacuum, single crystals have been grown by the Bridgman method [9]. Independently of crystal perfection all the cleaved monocrystalline specimens possessed mirror surfaces of high quality in αc-plane, which did not require additional polishing. The stuctural parameters were checked using the X-ray DROΝ-05 diffractometer. The temperature measurements were performed in the range 4.2-500 K and were stabilized within 0.1-0.2 K•min -1 . The Senarmon method (λ = 0.6328 μm) was used for measuring of the piezooptical constants. Testing of samples quality was performed by the X-ray method. The broadening of X-ray satellite reflexes permits to select crystals of different quality. To obtain smooth change of the specimens quality, they were annealed in non-inertial

Dispersion of the Kerr constants of doped KCl crystals

The dispersion of the quadratic electro-optic (Kerr) constants of KCl crystals containing two substitutional impurities Pb2+ and Cu+ has been determined. The constants (r11,11-R11,22) and R12,12 are reported for the crystals at different concentrations of the impurities in the region 590-290 nm. The observed wavelength dependence is found to be similar to that of the piezo-optical constants of pure alkali halide crystals. The experimental data have been fitted to a simple Sellmeier relation and the dispersion constants are reported.

Optical distortion coefficient of 〈111〉-oriented CaF2 windows at chemical laser wavelengths

Recently, the piezo-optic constants of CaF2 single crystals have been measured in the infrared. These measurements indicate that the critical orientation in the sense of Joiner, Marburger, and Steier is within 1.9°±1.2° from the [111] direction. It follows that 〈111〉-oriented CaF2 laser windows do not exhibit any detectable stress birefringence independently of the polarization of the incident beam. On using the best data currently available on relevant properties of single-crystalline material at 3.39 μm, an evaluation of the optical distortion coefficient χ of 〈111〉-oriented CaF2 yields an exceptionally small value: χ= (1.0±0.6) ×10−6 K−1. On this basis, it is shown that, in principle, a 1-cm-thick AR-coated CaF2 window can handle average energy fluences of at least 300 kJ/cm2 without violating the Maréchal criterion.

A new method to measure stress-induced birefringence in an opaque material: Stress-induced Raman scattering

We describe a new technique to measure the piezo-optical constants of a material in a frequency region where it is opaque. The technique employs Raman scattering. Using this new method we measure the magnitudes of the piezo-optical constants π11 − π12 and π44 in silicon at 1.92 eV. Previous measurements were limited to below and near the fundamental edge at 1.1 eV. Using this technique it should be possible to extend the measurements of the piezo-optical constants in a large number of opaque materials.

Photoelastic constants of potassium chloride at 106 μm

The piezooptic constants of pure KCl and KCl doped with KI have been measured in the visible and at 10.6 microm by interferometric and polarimetric techniques. The dispersion of the elastooptic constants, computed from the piezooptic constants, differs from the dispersion calculated from a theory based on a two-oscillator model of the refractive index.

Piezooptic and quadratic electrooptic effects in cubic potassium cyanide

Abstract The magnitude and signs of the piezooptic constants of KCN differ considerably from those of comparable alkali halides. In accordance with the anomalous thermoelastic behaviour of KCN the piezooptic constant q 44 increases rapidly as the temperature approaches the phase transition at 168 K. The total quadratic electrooptic effect consists of two components with opposite signs resulting in a small measurable effect which exhibits no pronounced variation with temperature.