Elasto-optic Coefficients Research Articles

Low-loss compact chalcogenide microresonators for efficient stimulated Brillouin lasers.

Chalcogenide glasses (ChGs) possess a high elasto-optic coefficient, making them ideal for applications in microwave photonics and narrow-linewidth lasers based on stimulated Brillouin scattering (SBS). However, current As2S3-based integrated devices suffer from poor stability and low laser-induced damage threshold, and planar ChG devices feature limited quality factors. In this Letter, we propose and demonstrate a high-quality integrated GeSbS ChG Brillouin photonic device. By introducing Euler bending structures, we suppress high-order optical modes and reduce propagation losses in a finger-shaped GeSbS microresonator, resulting in a compact footprint of 3.8 mm2 and a high intrinsic quality factor of 5.19 × 106. The combination of GeSbS material's high Brillouin gain and the resonator's high-quality factor enables the generation of stimulated Brillouin lasers with a low threshold of 0.96 mW and a fundamental linewidth of 58 Hz. Moreover, cascaded stimulated Brillouin lasers can be realized up to the seventh order, yielding microwave beat frequencies up to 40 GHz.

Photoelasticity of CNGS crystals.

All piezo-optic coefficients (POCs) and elasto-optic coefficients (ELOCs) of C a 3 N b G a 3 S i 2 O 14 (CNGS) and C a 3 T a G a 3 S i 2 O 14 (CTGS) trigonal crystals of the langasite group are determined from quantum mechanical calculations based on the hybrid density functional theory, as implemented in the CRYSTAL program. The calculation results for CTGS crystals are compared with experimental data. Indicative surfaces of piezo- and elasto-optic effects are constructed based on the POC and ELOC matrices of CNGS crystals and the largest values of these effects are determined. The maximum values of the coefficient of the acousto-optic figure of merit M 2 of the CNGS crystal are determined for the geometries of elasto-optic interaction, which correspond to the maxima of the elasto-optic effect. These results are compared to the corresponding results for CTGS and langasite crystals. The spectral dependence of the POCs and ELOCs of CNGS and CTGS crystals on the light wavelength is investigated in the 600-1500nm range.

High-speed non-contact measurement of elasto-optic coefficient via laser-induced phonons

The elasto-optic coefficient, which describes the interaction of acoustic waves and light in a medium, allows a contrast mechanism in optomechanics. However, the non-contact measurement is a challenge, limiting the study of some materials such as liquids. We present a high-speed non-contact method based on laser-induced phonons. The elasto-optic coefficients of common liquids are measured with only 10 ms and an averaged relative standard deviation of 1.52%, complementing the rare liquid data. By deciphering Brillouin spectra, the elasto-optic coefficient and viscoelastic parameters can be obtained simultaneously, and the introduction of the elasto-optic coefficient makes the characterization more sensitive. Benefiting from spatially resolved measurement, the elasto-optic coefficient is mapped to provide another contrast mechanism for mechanical imaging and may prove useful to characterize biological cells and tissues.

Acousto-optic interaction in LGS and CTGS crystals

Based on the matrices of elastic and elasto-optic coefficients, the extreme surfaces of the spatial distribution of the acousto-optic (AO) figure-of-merit М2 for langasite and calcium-tantalum gallosilicate crystals are constructed and analyzed. The determined maximal achievable values of М2 for these crystals are commensurate and twice the maximal value of М2 for quartz. The most effective AO interaction geometries and geometry of cuts for optimized AO cells are given. The investigated crystals, due to the temperature stability, excellent optical quality, resistance to environmental aggression and high optical damage threshold can be used for AO modulators of the ultraviolet spectral range.

Effect of ellipticity of optical eigenwaves on the enhancement of efficiency of acousto-optic Bragg diffraction. A case of optically active Pb5Ge3O11 crystals

We show that the existence of optical activity in an optical material can lead to essential enhancement of acousto-optic (AO) figure of merit. The reason is that the ellipticity of interacting optical eigenwaves approaches unity near the optical axis and so additional elasto-optic (EO) tensor components become involved in the effective EO coefficient. We demonstrate on lead germanate crystals that the increase in the efficiency of AO diffraction manifests itself for all types of AO interactions whenever the incident optical wave propagates close to the optical axis. In the particular case of diffraction in the interaction plane XZ of Pb5Ge3O11 crystals, the maximal enhancement of the AO figure of merit takes place under conditions of the isotropic diffraction of ordinary and extraordinary optical waves with a pure transverse acoustic wave (AW) polarized parallel to the Y axis (a so-called AW PT2), with the AO figure of merit increasing from zero to 7.5 × 10−17 s3/kg, and the types of anisotropic diffraction on the AWs QT1 and PT2 when the AO figure of merit increases twice (e.g., from 7.6 × 10−17 to 1.5 × 10−16 s3/kg). The maximal AO efficiency in the interaction plane XZ is reached at types I and II of the isotropic AO interactions of ordinary and extraordinary optical waves with a quasi-longitudinal AW; in these cases, the AO figure of merit increases from 6.8 × 10−15 to 12.4 × 10−15 s3/kg and from 5.6 × 10−15 to 12.4 × 10−15 s3/kg, respectively.

Superior elasto-optic tetragonal SrTiO3 films

Cutting-edge acousto-optic devices require optically transparent thin films, which possess a high index of refraction and large elasto-optic coefficients. For the wide near-infrared to ultraviolet spectral region, the mainstream technology employs lithium niobate crystals, which interferes with the vital demands of global sustainability. Here, we demonstrate unprecedented elasto-optic properties in thin films of sustainable and environmentally friendly strontium titanate [SrTiO3 (STO)]. Compared to cubic STO, a nearly twofold increase in elasto-optic coefficients is achieved in epitaxial tetragonal STO films, which concurrently exhibit excellent transparency and a high index of refraction at wavelengths from 400 to 1700 nm. The room-temperature non-polar state is evidenced by the thermo-optical behavior of the films. The obtained enhancement is related to the tetragonal antiferrodistortive phase of STO. It is suggested that such films can form a platform for future sustainable acousto-optic materials.

Photoelastic Properties of Trigonal Crystals

All possible experimental geometries of the piezo-optic effect in crystals of trigonal symmetry are studied in detail through the interferometric technique, and the corresponding expressions for the calculation of piezo-optic coefficients (POCs) πim and some sums of πim based on experimental data obtained from the samples of direct and X/45°-cuts are given. The reliability of the values of POCs is proven by the convergence of πim obtained from different experimental geometries as well as by the convergence of some sums of POCs. Because both the signs and the absolute values of POCs π14 and π41 are defined by the choice of the right crystal-physics coordinate system, we here use the system whereby the condition S14 > 0 is fulfilled (S14 is an elastic compliance coefficient). The absolute value and the sign of S14 are determined by piezo-optic interferometric method from two experimental geometries. The errors of POCs are calculated as mean square values of the errors of the half-wave stresses and the elastic term. All components of the matrix of elasto-optic coefficients pin are calculated based on POCs and elastic stiffness coefficients. The technique is tested on LiTaO3 crystal. The obtained results are compared with the corresponding data for trigonal LiNbO3 and Ca3TaGa3Si2O14 crystals.

Peculiarities of acousto-optic diffraction at circularly polarized acoustic waves. Determination of elasto-optic coefficients coupled with shear waves. Errata

Peculiarities of acousto-optic diffraction at circularly polarized acoustic waves. Determination of elasto-optic coefficients coupled with shear waves. Errata

Full set of piezo-optic and elasto-optic coefficients of Ca3TaGa3Si2O14 crystals at room temperature.

The photoelasticity of the Ca3TaGa3Si2O14 (CTGS) crystal was studied by an interferometric method based on a single-pass Mach-Zehnder interferometer. The maximum number of sample orientations for the piezo-optic experiments was applied to prove accuracy in the determination of the piezo-optic coefficients. Based on the matrices of the piezo-optic coefficients and the elastic stiffness coefficients, all the coefficients pik of the elastic-optic matrix are calculated. For the highest pik coefficient, the acousto-optic efficiency is evaluated. The results obtained for CTGS are compared with the corresponding results for La3Ga5SiO14 (langasite) crystals. The highest acousto-optic figure of merit of CTGS M2=1.66⋅10-15s3/kg is two and three times higher, compared with langasite and strontium borate, respectively, which are often used for acousto-optic modulation of light in the ultraviolet spectral range.

Space charge assisted evaluation method of the elasto-optic coefficients of electrooptic crystals

We developed a novel technique to evaluate the elasto-optic coefficients of electrooptic (EO) single crystals. Notably, this method uses the deformation of the crystal generated by the space charge formed by the electrons injected into the crystal. For the first time, to our knowledge, the coefficient p12 was quantified separately from p11 for KTa1-xNb x O3(KTN) with this method. Both the coefficients exhibit significant temperature dependence caused by polarization fluctuations. Genuine EO coefficients gg11 and gg12 were calculated by excluding photoelastic contributions from the nominal EO coefficients. gg12 was negligibly small compared to the nominal coefficient before the exclusion. This indicates that the conventional nominal coefficient gn12 is actually composed of strain-induced components but does not reflect the pure effect.

Experimental determination of full matrices of the piezo-optic and elasto-optic coefficients for Pb5Ge3O11 crystals.

We determine full matrices of piezo-optic and elasto-optic coefficients for lead germanate crystals, Pb5Ge3O11, using Dixon-Cohen and interferometric methods. Two different types of samples are studied, single- and multi-domain. We show that the correct data for the Pb5Ge3O11 crystals can be obtained only with single-domain samples, since the domain structure induces a number of features that make the final results unreliable. We demonstrate that the acousto-optic figures of merit reach high-enough values at the isotropic acousto-optic interactions with longitudinal acoustic waves propagating along the principal x and z axes (63×10-15 and 37×10-15s3/kg), respectively. At the same time, the efficiency of the acousto-optic interactions with transverse acoustic waves is low. The same is true concerning anisotropic acousto-optic diffraction, since the appropriate elasto-optic coefficients are small enough.

Anisotropy of acousto-optic figure of merit for the case of a Bragg-diffracted wave propagating along an optic axis in optically biaxial crystals: Tl3AsS4 crystals.

In the present work, we analyze acousto-optic (AO) interactions under the condition when a diffracted optical wave propagates along one of the optic axes in optically biaxial crystals. We find that the number of AO interaction types is reduced from nine, which is typical for the most general case, to six, since some of the isotropic and anisotropic diffraction types manifest themselves simultaneously. We reveal that, in the case of the interactions of quasi-ordinary and quasi-extraordinary optical waves, the dependences of effective elasto-optic coefficients and AO figure of merit on the tracing angle of an incident optical beam around the optic axis are symmetric with respect to the plane that is perpendicular to the plane of optic axes and contains the principal axis Z. We determine the geometry of AO interactions at which the highest AO figure of merit can be expected. Finally, we show that, in the case of propagation of diffracted light along one of the optic axes in the biaxial Tl3AsS4 crystals, the highest AO figures of merit, M2=1290×10-15s3/kg and M2=1305×10-15s3/kg, can be reached when the quasi-longitudinal acoustic wave interacts with the quasi-ordinary or quasi-extraordinary optical waves in the plane of optic axes.

Peculiarities of acousto-optic diffraction at circularly polarized acoustic waves. Determination of elasto-optic coefficients coupled with shear waves

Peculiarities of acousto-optic diffraction at circularly polarized acoustic waves. Determination of elasto-optic coefficients coupled with shear waves

Extraction of Elastooptic Coefficient of Thin-Film Arsenic Trisulfide Using a Mach–Zehnder Acoustooptic Modulator on Lithium Niobate

An acousto-Optic Modulator (AOM) formed by an Arsenic Trisulfide (As $_2$ S $_3$ ) Mach–Zehnder interferometer (MZI), operating in a push-pull configuration and placed inside a surface acoustic wave (SAW) cavity on a Y-cut Lithium Niobate (LN) wafer is demonstrated. This is the first demonstration of such acousto-optic (AO) modulator in this As $_2$ S $_3$ -LN hybrid platform. In this approach, the high index contrast of As $_2$ S $_3$ waveguides is exploited to attain a high optical confinement. Additionally, the placement of the photonic MZI inside the SAW cavity enhances the AO interaction due to the high quality factor (Q) of the SAW resonator. An analytical expression that describes such enhancement as a function of the elasto-optic (EO) coefficient of As $_2$ S $_3$ is derived in conjunction with COMSOL finite element methods to describe strain in the SAW cavity. By fitting this expression to experimental data, the EO coefficient ( $p_{11}$ and $p_{12}$ , where $p_{11} \approx p_{12}$ ) for As $_2$ S $_3$ is extracted to be 0.29 at the wavelength of 1550 nm. This is the first time that the EO coefficient of thin film As $_2$ S $_3$ is experimentally derived.

Degree of locality of elasto-optic response in solids

The elasto-optic effect, or photoelasticity, describes the linear change of dielectric tensor with applied strain and is a universal material property of insulators and semiconductors. Though the elasto-optic responses for solids can be computed directly from first principles (e.g., by using density functional perturbation theory) and measured experimentally, these methods do not provide sufficient insight into the governing microscopic physical principles of photoelasticity. In this work, we describe a microscopic first-principles analysis of photoelasticity in real space and apply it to investigate the elasto-optic responses of Si, diamond, NaCl, and MgO. By writing the random phase approximation (RPA) dielectric constant in the basis of maximally localized Wannier functions, we show that the strain-dependent change of dipole transitions between occupied and unoccupied Wannier functions are the main determinants of photoelasticity. By organizing the dipole transitions into spatially localized shells, we develop a ``constrained sum'' method that converges both the dielectric and photoelastic responses systematically and reveals a relatively long-ranged nature to these responses: one needs to sum up contributions of up to third neighbor shells to converge the elasto-optic coefficient with reasonable precision.

Photoelastic Properties of Potassium Sulfate Crystals

The spectral dependences of the absolute piezooptic coefficients of potassium sulfate crystals are studied. It is established that their dispersion dependence is insignificant. The matrix of elastooptic coefficients pin of these crystals is filled using the elastic stiffness coefficients and the absolute piezooptic coefficients. The coefficient of acoustooptical efficiency M2 is calculated. It is shown that, considering the maximum values, it is more than an order of magnitude higher than that of quartz and strontium borate crystals. Potassium sulfate crystals are proposed for use for acoustooptic modulation of ultraviolet radiation, taking into account the short-wavelength limit of their transparent region (~170 nm).

Designing Multifunctionality via Assembling Dissimilar Materials: Epitaxial AlN/ScN Superlattices.

First-principles calculations are performed to investigate the effect of epitaxial strain on energetic, structural, electrical, electronic, and optical properties of 1×1 AlN/ScN superlattices. This system is predicted to adopt four different strain regions exhibiting different properties, including optimization of various physical responses such as piezoelectricity, electro-optic and elasto-optic coefficients, and elasticity. Varying the strain between these four different regions also allows the creation of an electrical polarization in a nominally paraelectric material, as a result of a softening of the lowest optical mode, and even the control of its magnitude up to a giant value. Furthermore, it results in an electronic band gap that cannot only change its nature (direct vs indirect), but also cover a wide range of the electromagnetic spectrum from the blue, through the violet and near ultraviolet, to the middle ultraviolet. These findings thus point out the potential of assembling two different materials inside the same heterostructure to design multifunctionality and striking phenomena.

Acousto-optic interaction between circularly polarized optical eigenwaves: example of AgGaS2 crystals

We analyze acousto-optic (AO) diffraction occurring at the light wavelength of a so-called "isotropic point" in AgGaS2 crystals. It is shown that a natural optical activity, which manifests itself as circular birefringence at the isotropic point, can lead to two different types of AO Bragg diffraction, isotropic and anisotropic. The first type concerns the interaction of circularly polarized optical eigenwaves with the same sign of rotations of their electric-field vectors. In the case of the second diffraction type, the AO interaction takes place between the circularly polarized waves having opposite signs of electric-field rotations. Relations for effective elasto-optic (EO) coefficients are derived for different types of AO diffraction, including a collinear one. The main peculiarities of the latter diffraction type are revealed. The modules of all the EO coefficients are determined experimentally for the AgGaS2 crystals, using a Dixon-Cohen method. Finally, we evaluate AO figures of merit referring to the AO interactions of circularly polarized optical eigenwaves at the optical wavelength of the isotropic point.

Photoelasticity of ammonium sulfate crystals

All the components of πim matrix of the piezo-optic coefficients of ammonium sulfate crystals are defined using the interferometric method based on the one-pass Mach-Zehnder interferometer. All components of the рin matrix of elasto-optic coefficients are calculated on the basis of the πim matrix and elastic stiffness coefficients Сmn. Ammonium sulfate crystal should be attributed to the best photoelastic crystalline materials considering the highest values of πim and рin coefficients. The highest values of the acousto-optic figure of merit M2 are also established. The value of M2 of this crystal is 1–2 orders of magnitude higher than the value of M2 of known materials suitable for acousto-optic modulation of light in the ultraviolet spectrum region.

Фотоупругие свойства кристаллов сульфата калия

The spectral dependences of the absolute piezo-optic coefficients of potassium sulfate crystals are studied and their insignificant dispersion dependence is established. The matrix of elasto-optic coefficients рin of these crystals is filled using the values of elastic stiffness coefficients and absolute piezo-optic coefficients. The coefficient of the acousto-optic efficiency М2 is estimated and it is shown that, considering the highest values, it is more than an order of magnitude higher than that of quartz and strontium borate crystals. Taking into account the short-wavelength boundary of the transparency region of potassium sulfate crystals (~ 170 nm), it is proposed to use them for acousto-optic modulation of ultraviolet radiation.