Linear Electro-optic Coefficients Research Articles

Erratum: “Modeling temperature, frequency, and strain effects on the linear electro-optic coefficients of ferroelectric oxides” [J. Appl. Phys. 131, 163101 (2022)

Erratum: “Modeling temperature, frequency, and strain effects on the linear electro-optic coefficients of ferroelectric oxides” [J. Appl. Phys. 131, 163101 (2022)

Enhancement of the linear electro-optic effect by high pressure

It is challenging to design electro-optic (EO) crystals with both a large bandgap and a high EO coefficient. We propose that some semiconductors synthesized under a high pressure environment can present both a large bandgap and a high linear EO coefficient because of the enhanced strength of the valence bond. The electronic band structures and linear EO coefficients of the $II\mathrm{Si}{\mathrm{N}}_{2}$ ($II=\mathrm{Mg}$, Sr, Ba) compounds are studied using first-principles calculation. Our calculated results predict that both $\mathrm{SrSi}{\mathrm{N}}_{2}$ and $\mathrm{BaSi}{\mathrm{N}}_{2}$, under a high-pressure condition, will crystalize into an orthorhombic structure with the same space group of $\mathrm{MgSi}{\mathrm{N}}_{2}$ under ambient pressure. The calculated bandgaps are 5.48, 4.41, and 3.57 eV, respectively, for $\mathrm{MgSi}{\mathrm{N}}_{2}, \mathrm{SrSi}{\mathrm{N}}_{2}$, and $\mathrm{BaSi}{\mathrm{N}}_{2}$, while the calculated linear EO coefficients are 1.55, 12.09, and 21.60 pm/V at a fiber communication wavelength of 1550 nm. The increasing linear EO coefficients can be interpreted by the enhanced bond strength and a reduced bandgap. This work indicates that it is feasible to enhance the linear EO coefficient with high pressure.

Higher speed, wider angle linear electro-optic deflection via domain engineered KTN crystals

Pulsed-biased higher speed (> 10 MHz @ 30 V, 100 ns pulse width) and DC-biased wider angle (105 mrads @ 410 V/mm) linear electro-optic (EO) deflection is reported in a thermally-controlled domain engineered (DE) ferroelectric (FE) potassium tantalate niobate [KTa1−xNb x O3, KTN] crystal. DE-FE KTN crystals can not only provide a higher transmittance and larger linear EO coefficient, but also enable higher speed (10X) and wider angle (2X) deflection than that of its paraelectric equivalent. The physical mechanism behind the optimization of injected space charge on high deflection angles at high speeds is also addressed. This significantly improves its use in megahertz EO applications.

Оценки диэлектрических и оптических характеристик бинарных 3D- и 2D-соединений IV группы

Using the Harrison’s bond orbital model for the IV group 3D and 2D com-pounds analytical expressions of the high- and low-frequency dielectric suscepti-bilities and dielectric constants, linear electrooptical coefficient, photoelastic con-stants and pressure dependences of the dielectric constants are obtained.

Estimates of the dielectric and optical characteristics for the IV group 3D- and 2D-binary compounds

Using the Harrison's bond orbital model for the IV group 3D- and 2D-compounds analytical expressions of the high- and low-frequency dielectric suscepti-bilities and dielectric constants, linear electrooptical coefficient, photoelastic con-stants and pressure dependences of the dielectric constants are obtained. Keywords:: dielectric susceptibility and permittivitiy, photoelectric coefficient.

Study of SHG and LE-O Susceptibilities of InAs Crystal: Linear Absorption Taken into Account

We applied a model involving two coupled anharmonic oscillators (electronic and ionic) to estimate the Second Harmonic Generation (SHG) and Linear Electro-Optic (LE-O) susceptibilities of InAs crystal. The crystal of InAs belongs to III-V group compounds owing cubic zinc-blende-type structure. Linear absorption is considered for the selected spectral region 1250 nm – 390 nm. So, the contribution of the imaginary part of the involved complex linear ionic susceptibility to the resultant SHG and LE-O susceptibilities is taken into account and hence the absolute value of complex-linear ionic susceptibility is used in place of the complex-linear ionic susceptibility in the computation of SHG and LE-O coefficients. All of the four constants (nonlinear strength factors), appearing in the model, are determined with the help of experimental data of SHG susceptibility measured in the selected region of 1076 nm-535 nm. Application of such calculated nonlinear strength factors in the concerned modelled expressions, SHG and LE-O susceptibility coefficients are computed as a function of frequency to illustrate the dispersion in the region of 1250 nm –390 nm.

Large linear and nonlinear electro-optic coefficients in two-dimensional ferroelectrics

Analytical derivations and first-principles calculations are performed to investigate the electro-optic (EO) response of the two-dimensional ferroelectric SnS in its monolayer form. In addition to derive the formula for EO coefficients for two-dimensional systems, large linear and nonlinear electro-optic coefficients are discovered, along with a strongly nonlinear electro-optic response as a function of electric field. The origin of these electro-optic responses is further found and involves a few specific phonon modes, in general, and the evolution of their frequencies and atomic characteristics under electric fields, in particular. Large linear and nonlinear electro-optic coefficients can be found in other two-dimensional ferroelectrics, paving the way for potential optical device applications.

Enormous electro-optic effect in paraelectric nanodisordered KTa1-xNbxO3 crystal.

Recent experiments have revealed that the order of the electro-optic (EO) effect depends on the frequency of electric field in paraelectric nanodisordered KTa1-xNbxO3 (KTN) crystal. Through the dielectric frequency spectrum under the bias electric field, enormous linear and quadratic EO effects were discovered at the resonance frequencies, which changed the perception that only the quadratic EO effect exists. Applying just a small AC electric field of 6 V/mm, the effective linear EO coefficient reached 478 pm/V at 609 kHz, and the effective quadratic EO coefficient reached 4.39*10-13m2V-2at 302 kHz. The reason why an extremely low electric field results in an enormous EO coefficient is attributed to the resonance between the polar nanoregions (PNRs) and the electric field, induced by the field-driven reorientation of free dipoles on the boundary of the PNRs. In addition, the order of EO effect depending on the frequency of electric field was attributed to the motion modes of the PNR. This finding improves the understanding of how the EO effect is caused by field-driven PNR dynamics, but also provides a basis for the development of EO devices.

Photonic Assemblies of Randomly Oriented Nanocrystals for Engineered Nonlinear and Electro-Optic Effects.

Nonlinear crystals that have a noncentrosymmetric crystalline structure, such as lithium niobate (LiNbO3) and barium titanate (BaTiO3) exhibit nonzero second-order tensor susceptibilities (χ(2)) and linear electro-optic coefficients (r ij ). The constraints associated with top-down nanofabrication methods have led to bottom up approaches to harness the strong nonlinearities and electro-optical properties. Here, we present an overview of photonic assemblies made of randomly oriented noncentrosymmetric nanocrystals via bottom-up fabrication methods. In this configuration, nanocrystals can form objects with tunable dimensions, increased complexity, and a great span of symmetry level, ranging from thin layers to spheres. At the same time, according to their shape, photonic assemblies may support optical modes, that is, Mie or guided, which can tailor linear optical properties and enhance nonlinear and electro-optic responses. As a result, assemblies of noncentrosymmetric nanocrystals can form a disruptive platform to realize photonic integrated devices free of etching process and over large surface areas. Last, we foresee potential applications of noncentrosymmetric nanocrystals in various fields of nano-optics and sensing.

Modeling temperature, frequency, and strain effects on the linear electro-optic coefficients of ferroelectric oxides

An electro-optic modulator offers the function of modulating the propagation of light in a material with an electric field and enables a seamless connection between electronics-based computing and photonics-based communication. The search for materials with large electro-optic coefficients and low optical loss is critical to increase the efficiency and minimize the size of electro-optic devices. We present a semi-empirical method to compute the electro-optic coefficients of ferroelectric materials by combining first-principles density-functional theory calculations with Landau–Devonshire phenomenological modeling. We apply the method to study the electro-optic constants, also called Pockels coefficients, of three paradigmatic ferroelectric oxides: BaTiO3, LiNbO3, and LiTaO3. We present their temperature-, frequency-, and strain-dependent electro-optic tensors calculated using our method. The predicted electro-optic constants agree with the experimental results, where available, and provide benchmarks for experimental verification.

Domain Engineering Enabled Giant Linear Electro‐Optic Effect and High Transparency in Ferroelectric KTa1−xNbxO3 Single Crystals

A giant linear electro‐optic (EO) effect and high transparency in ferroelectric potassium tantalate niobate [(), KTN] crystal is achieved via a thermally controlled domain engineering method. It involves a two‐step thermal annealing process: 1) a rapid cooling process that forms polar nano‐regions (PNRs), i.e., a cooling rate of from to where is the Curie temperature; and 2) a slow cooling process that facilitates abnormal domain growth (AGG) i.e., a cooling rate of from to . Since PNR can have a faceted boundary and high anisotropy, it can promote AGG within single crystals to realize solid‐state domain conversion macroscopically from a multi‐domain to single‐domain crystal within a slow cooling process. The resultant KTN crystal offers high transparency that is equivalent to its paraelectric phase; and a linear EO coefficient () as large as , which is five times the value of conventional KTN crystals with similar composition. This giant linear EO coefficient represents a major technical advance in EO materials and significantly reduces the driving voltage, power, and footprint of many types of EO devices.

Диэлектрические и оптические свойства кубических монокристаллов SiC, GeC и SnC: модельные оценки

Within the scope of the Harrison’s bond orbital model analytical expressions of the high- and low-frequency dielectric susceptibilities and dielectric constants, linear electrooptical coefficient, photoelastic constants and pressure dependences of the dielectric constants are obtained for the cubic carbides of the group IV elements.

Dielectric and optical properties of the cubic SiC, GeC and SnC monocrystals: Model estimations

Within the scope of the Harrison's bond orbital model analytical expressions of the high- and low-frequency dielectric susceptibilities and dielectric constants, linear electrooptical coefficient, photoelastic constants and pressure dependences of the dielectric constants are obtained for the cubic carbides of the group IV elements. Keywords: dielectric susceptibility, dielectric constants, electrooptical coefficient, photoelastic constant.

Semi-Experimental Determination of the Linear Clamped Electro-Optical Coefficients of Polar Crystals from Vibrational Spectroscopic Data

The present work highlights a new general method devoted to computations of the clamped linear electro-optical coefficients from the measured fundamental vibrational frequencies and the nonlinear dielectric susceptibility constants. The calculations are based on the formula analog to that of the Lyddane–Sachs–Teller relation, which is systematically used for the calculations of the clamped linear electro-optical coefficient of oxide ferroelectric crystals such as LiNbO3, LiTaO3, BaTiO3, PbTiO3, and KNbO3. The computed electro-optical coefficients are in good agreement with those obtained from direct measurements and the first-principles calculations or other semi-empirical models. In addition, the famous r51 or r42 coefficients of the tetragonal BaTiO3, PbTiO3, and KNbO3 crystals are finally calculated with high accuracy and discussed in connection with the soft mode behavior.

Experimental verification of electro-optical effect in LBO crystal based on nonlinear optical process

Lithium triborate (LBO) crystal is a widely used nonlinear crystal and a potential electro-optic (EO) crystal, but there was no report on experimental verification of its EO characteristics. We verified the linear EO effect of LBO crystal experimentally by designing a second harmonic generation (SHG) experiment. In the experiment, the direction of applied voltage was determined by the analysis of LBO EO tensor matrix. By measuring the curve of voltage-tuning SHG efficiency with different angle detuning, the linear EO effect was verified, and the linear EO coefficient was calculated by the slope of phase mismatch with respect to voltage.

Coupled InGaAs Quantum Dots for Electro-Optic Modulation

We investigated the growth of vertically coupled In0.75Ga0.25As quantum dots (QDs) by varying the GaAs spacer thickness (d). Vertically-aligned triple-layer QDs of uniform size and highest accumulated strain are formed with d = 5 nm. The electroluminescence (EL) characteristics for In0.75Ga0.25As QDs show an emission spectrum at optical wavelength (λ) of 1100−1300 nm. The EL spectra exhibit the highest optical gain at λ ~ 1200 nm, and the narrowest FWHM = 151 nm of the sample with d = 5 nm at injection current = 20 mA. Fabry–Perot measurements at λ = 1515 nm of TE and TM polarizations were carried out to investigate the electro-optic modulation for a single-mode ridge waveguide consisting of vertically-coupled triple-layer In0.75Ga0.25As QDs (d = 5 nm). The linear (r) and quadratic (s) electro-optic coefficients are r = 2.99 × 10−11 m/V and s = 4.10 × 10−17 m2/V2 for TE polarization, and r = 1.37 × 10−11 m/V and s = 3.2 × 10−17 m2/V2 for TM polarization, respectively. The results highlight the potential of TE/TM lightwave modulation by InGaAs QDs at photon energy below energy band resonance.

Electro-optic coefficient measurement of a K(H1-xDx)2PO4 crystal based on χ(2) nonlinear optical technology.

We present a novel method utilizing the χ(2) nonlinear optical technology, which can realize high precision measurement of linear electro-optic (EO) coefficients of nonlinear materials. By applying the linear EO effect to the nonlinear optical process, the theoretical model of this measurement method was established, and the calculation formula of the linear EO coefficient was given. In the proof-of-principle experiment, by introducing an external electric field into the fourth harmonic generation (FHG) process, we comprehensively obtained the linear EO coefficients of K(H1-xDx)2PO4 crystals and revealed the relationship between deuterium content (x) and EO coefficient (γ63): γ63 = -9.789 - 16.53x. Meanwhile, the stability of FHG was greatly improved, and the angular range of efficiency stability was increased to 4.4 times in maximum. This work not only systematically demonstrates the FHG characteristics of KDP-family crystals, which provides a good reference for the deep ultraviolet laser generation, but also offers a new way to measure the basic parameters of nonlinear optical materials.

Significant second-harmonic generation and bulk photovoltaic effect in trigonal selenium and tellurium chains.

One-dimensional (1D) selenium and tellurium crystalize in helical chainlike structures and thus exhibit fascinating properties. By performing first-principles calculations, we have researched the linear and nonlinear optical (NLO) properties of 1D Se and Te, and find that both systems exhibit pronounced NLO responses. In particular, 1D Se is found to possess a large second-harmonic generation coefficient with the χ value being up to 7 times larger than that of GaN, and is even several times larger than that of the bulk counterpart. On the other hand, 1D Te also produces significant NLO susceptibility χ which exceeds that of bulk GaN by 5 times. Furthermore, 1D Te is shown to possess a prominent linear electro-optic coefficient rxxx(0). In particular, the Te chain exhibits a large shift current response and the maximum is twice as large as the maximal photovoltaic responses obtained from BaTiO3. Therefore, 1D Se and Te may find potential applications in solar energy conversion, electro-optical switches, and so on. Finally, the much stronger NLO effects of 1D Se and Te are attributed to their one-dimensional structures with high anisotropy, strong covalent bonding and lone-pair electrons. These findings will contribute further to experimental studies and the search for excellent materials with large NLO effects.

Large second-harmonic generation and linear electro-optic effect in trigonal selenium and tellurium

Trigonal selenium and tellurium crystalize in helical chain-like structures and thus possess interesting properties such as current-induced spin polarization, gyrotropic effects and nonlinear optical responses. By performing systematic ab initio calculations based on density functional theory in the generalized gradient approximation plus scissors correction, we study their linear and nonlinear optical (NLO) properties. We find that the two materials exhibit significant second-harmonic generation (SHG) and linear electro-optic (LEO) effect. In particular, the SHG coefficients of tellurium are huge in the photon energy range of 0 ~ 3 eV, with the magnitudes of SHG(xxx) being as large as 3640 pm/V, which are about sixteen times larger than that of GaN, a widely used NLO material. On the other hand, trigonal selenium is found to possesses large LEO coefficients r(xxx,0) which are more than six times larger than that of GaN.Therefore, trigonal tellurium and selenium may find valuable applications in NLO and LEO devices such as frequency conversion, electro-optical switch and light signal modulator.The energy positions and shapes of the principal features in the calculated optical dielectric functions of both materials agree rather well with the available experimental ones, and are also analyzed in terms of the calculated band structures especially symmetries of the involved band states and dipole transition selection rules.

Integrated electro-optic platform using ferroelectric crystals with the point symmetry of orthorhombic mm2

We theoretically and numerically investigate the modulation efficiencies of integrated electro-optic (EO) modulators based on ferroelectric crystals with the point symmetry of orthorhombic mm2. An analytical expression describing the index-ellipsoid under the EO effect is derived, where all 5 non-zero linear EO coefficients of mm2-crystals are considered. As practical candidates for integrated EO platform, three mm2-crystals (KNbO3, KTiOPO4, and Ba2NaNb5O15) that are well-established and commercially available are chosen for numerical simulations. The refractive-index (RI) changes caused by an external electric field applied to each crystal with an arbitrary direction are analyzed in detail for the given optical polarization states of input light wave. For each crystal, the modulation efficiency is evaluated in terms of the half-wave voltage required for a π-phase shift of input wave, which is compared with the established counterpart based on LiNbO3. The results indicate that higher modulation efficiencies are achievable in the two schemes using KNbO3 and Ba2NaNb5O15 than those for other cases, meaning that either lower power-consuming or larger beam-window integrated EO devices are feasible.