Linear Electro-optic Coefficients Research Articles

Temporal behaviour of bright solitons in photorefractive crystals having both the linear and quadratic electro-optic effect

Abstract We investigate the characteristics of formation or time evolution of optical spatial solitons in novel photorefractive media having both the linear and quadratic electro-optic effect. We have derived a one dimensional time dependant wave propagation equation in biased photorefractive media having both the linear and quadratic electro-optic effect. The variation of soliton width with time is investigated for different values of peak intensity ratio and it is shown that these bright solitons can exist both in the quasi steady state and steady state regimes for high saturation values. Two distinct regimes of intensity ratio are identified where the soliton formation characteristics are different. Only steady state solitons are formed if the intensity ratio is small. Soliton characteristics like the initial soliton width, steady state soliton width, and quasi steady state soliton width are investigated for both regimes and found to depend on as varying functions of the intensity ratio. We also find that the individual magnitudes of the linear and quadratic electro-optic coefficients affect the temporal characteristics of formation of the solitons. Appropriate example has been taken for an illustration of our results.

Novel temperature operated electrooptical materials based on K2ZnCl4: PVA polymer nanocomposites

We have discovered significant temperature anomalies of the linear electrooptical (EOE) coefficients for the K2ZnCl4 nanocrystallites embedded into the polymer matrices. The EOE efficiency was operated by external dc-electric field and UV polarized laser light. The maximal enhancement of EOE output was achieved within the temperature range 375 K–420 K. This temperature range corresponds to existence of incommensurate structural modulation. The maximally achieved field induced EOE efficiency was equal to about 1.4 pm/V for off-diagonal EOE tensor component. The size and NC content dependences have been explored for the size range (20 nm–1500 nm) and contents varying within the 25%–35%. For the sizes about 1200 nm, the EOE is commensurable with the EOE of the bulk crystals and is equal to about 0.6 pm/V.

Heteroepitaxial growth of ferroelectric films on Si substrates and their applications in waveguides and electro-optics

We introduce a general route to integrate epitaxially ferroelectric Sr1.9Ca0.1NaNb5O15 (SCNN) thin films on Si(001) substrates by pulsed laser deposition. The In:Mg0.8Zn0.2O (In:MZO)/TiN buffer layer is induced to overcome the large lattice mismatch between SCNN films and Si(001) substrates. The In:MZO layer acts as the buffer layer to bridge the Si and ferroelectric, the buffer layer with low refractive index for waveguide structure and the bottom electrode for electro-optic (EO) modulators. Waveguide and EO properties of the epitaxial integrated heterostructure were characterized by a prism coupler technique. The observed sharp and distinguishable TM and TE propagation mode lines revealed that favorable light confinements were achieved within the SCNN waveguide layer. The extraordinary and ordinary refractive indices were measured to be ne = 2.1802 and no = 2.2164 at 633 nm, respectively, implying a birefringence of 0.0362 was obtained. This large birefringence indicates that a large optically anisotropic property existed in the epitaxial SCNN films. An angular shift of guided mode was observed under applied electric field along with c-axis direction. The linear EO coefficient tensor r33 was measured to be about 860 pm/V. All of these results indicate that the integrated SCNN/In:MZO/TiN/Si epitaxial heterostructure has great potential for integrated optical EO and waveguide applications.

Electro-optic Response in Germanium Halide Perovskites.

Electro-optic materials that can be solution-processed and provide high-crystalline quality are sought for the development of compact, efficient optical modulators. Here we present density functional theory investigations of the linear electro-optic coefficients of candidate materials cesium and methylammonium germanium halide perovskites. As with their lead halide counterparts, these compounds can be solution-processed, but in contrast, they possess the noncentrosymmetric crystal structures needed to provide a linear electro-optic effect. We find substantial electro-optic responses from these compounds; in particular, for the r51 tensor element of CsGeI3, we predict an electro-optic coefficient of 47 pm·V-1 at the communications wavelength of 1550 nm, surpassing the strongest coefficient of LiNbO3 at 31 pm·V-1. The strong electro-optic responses of the germanium compounds are driven by high nonlinear susceptibilities and dynamics of the germanium atoms that ultimately arise from the distorted crystal structures. Alongside the electro-optic coefficient calculations, we provide the frequency responses for the linear and nonlinear electronic susceptibilities.

Nonlinearities of organic electro-optic materials in nanoscale slots and implications for the optimum modulator design.

The performance of highly nonlinear organic electro-optic (EO) materials incorporated into nanoscale slots is examined. It is shown that EO coefficients as large as 190pm/V can be obtained in 150 nm wide plasmonic slot waveguides but that the coefficients decrease for narrower slots. Possible mechanism that lead to such a decrease are discussed. Monte-Carlo computer simulations are performed, confirming that chromophore-surface interactions are one important factor influencing the EO coefficient in narrow plasmonic slots. These highly nonlinear materials are of particular interest for applications in optical modulators. However, in modulators the key parameters are the voltage-length product UπL and the insertion loss rather than the linear EO coefficients. We show record-low voltage-length products of 70 Vµm and 50 Vµm for slot widths in the order of 50 nm for the materials JRD1 and DLD164, respectively. This is because the nonlinear interaction is enhanced in narrow slot and thereby compensates for the reduced EO coefficient. Likewise, it is found that lowest insertion losses are observed for slot widths in the range 60 to 100 nm.

Method for in-depth characterization of electro-optic phase modulators.

A flexible method to measure the modulation efficiency and residual amplitude modulation, including non-linearities, of phase modulators is presented. The method is based on demodulation of the modulated optical field in the optical domain by means of a heterodyne interferometer and subsequent analysis of the I&Q quadrature components of the corresponding RF beat note signal. As an example, we determine the phase modulation efficiency and residual amplitude modulation for both the TE and TM modes of a GaAs chip-based phase modulator at the wavelength of 1064 nm. From the results of these measurements, we estimate the linear and quadratic electro-optic coefficients for a P-p-n-N GaAs/AlGaAs double heterostructure.

Second-order nonlinear optical properties of bulk GeC polytypes, g-GeC and corresponding nanotubes: first-principles calculations.

Very recently, researchers have found that low-dimensional materials display more intriguing second-order nonlinear optical (NLO) phenomena and possess larger second-order NLO susceptibilities than the corresponding bulk forms. Here, we perform a systematic first-principles study of the second-order NLO properties and linear electro-optical coefficients of GeC bulk polytypes, g-GeC and corresponding nanotubes. Remarkably, the second-order NLO susceptibility χ(2) of g-GeC and corresponding nanotubes can be comparable with that of the archetypical NLO semiconductor GaAs. Therefore, g-GeC and corresponding nanotubes have potential applications in NLO and electro-optical devices. We also quantitatively calculate the second-order NLO response contributions from the high density of states near the VBM via dividing NLO susceptibilities into contributions from different valence bands, revealing that the high density of states is the origin of the strong NLO responses in g-GeC and corresponding nanotubes. Such a mechanism will help to find excellent NLO materials more effectively. Moreover, the prominent features in the spectra of χ(2)(-2ω, ω, ω) of GeC polytypes are analyzed in terms of single- and double-photon resonances.

Photoluminescence, electro-optic response and piezoelectric properties in pressureless-sintered Er-doped KNN-based transparent ceramics

Er-doped (K0.5Na0.5)1−xLixNb1−xBixO3 (0.05 ≤ x ≤ 0.08) ceramics have been prepared by pressureless sintering. Because of the cubic-like phase as well as the dense and fine-grained structure, the ceramics are optically clear, exhibiting high transmittances in the near-infrared and mid-infrared (MIR) regions (∼50% and ∼75%, respectively). They also possess strong electro-optic (EO) response, giving a large effective linear EO coefficient (128–184 pm/V). Owing to Er3+, the ceramics exhibit green and red up-conversion photoluminescence (PL) emissions, which are sensitive to the crystal symmetry of the ceramic host. The ceramics also exhibit a low absorption coefficient of OH− groups and then distinct and broadband MIR emissions. Together with the relatively large piezoelectric coefficient (70–90 pC/N), high dielectric constant (∼1400) and low dielectric loss (∼0.03), the ceramics open up potential applications in electrical/optical interdisciplinary field, such as visible displays, MIR solid lasers and optical attenuators.

Ab initio study of the linear and nonlinear optical responses in BiAlO3

The linear and non-linear optical properties of BiAlO3 are studied by employing the density functional perturbation theory within the local density and generalized gradient approximations. The computations are based on the electronic structure obtained within density functional theory. The optical properties such as the dielectric function, refractive index, spectral reflectivity, absorption coefficient and electron energy-loss spectrum are obtained in the energy region of up to 30 eV. The calculated value of the birefringence for BiAlO3 shows that it is a uniaxial negative crystal and has a large birefringence. We also report our studies on the second harmonic generation response coefficient over a large frequency range for BiAlO3 crystal. The predicted second-order optical spectra indicate pronounced structures related to of 1ω and 2ω frequency resonances. Furthermore, the non-linear optic and linear electro-optic coefficients are computed by employing 2n + 1 theorem applied to an electric-field dependent energy functional. The results are compared with the available calculations.

Enhancement of optical transparency in Bi2O3-modified (K0.5Na0.5)0.9Sr0.1Nb0.9Ti0.1O3 ceramics for electro-optic applications

Transparent relaxor ferroelectrics, (K0.5Na0.5)0.9Sr0.1Nb0.9Ti0.1O3–x%Bi2O3 (x = 0, 0.5, 1.0, 1.5, and 2, abbreviated as KNSNT-10x), were fabricated using a pressureless sintering method. With the modification of Bi2O3, the crystal phase of KNSNT ceramics transformed from tetragonal to cubic-like symmetry, and dielectric behaviors became more relaxor like. These changes could reduce the light scattering arisen from birefringence and long-range ordering structure, thus enhancing the optical properties. For KNSNT-10 transparent ceramics, fingerprint morphological nanodomains were observed in the transmission electron microscope image, which made the ceramics sensitive to electric field. Therefore, a large effective linear electro-optic coefficient of 26.1 pm/V was obtained for the KNSNT-10 ceramics, and it is higher than the value (19.9 pm/V) for LiNbO3 single crystal.

Optical and electro-optic anisotropy of epitaxial PZT thin films

Strong optical and electro-optic (EO) anisotropy has been investigated in ferroelectric Pb(Zr0.48Ti0.52)O3 thin films epitaxially grown on Nb-SrTiO3 (001), (011), and (111) substrates using magnetron sputtering. The refractive index, electro-optic, and ferroelectric properties of the samples demonstrate the significant dependence on the growth orientation. The linear electro-optic coefficients of the (001), (011), and (111)-oriented PZT thin films were 270.8, 198.8, and 125.7 pm/V, respectively. Such remarkable anisotropic EO behaviors have been explained according to the structure correlation between the orientation dependent distribution, spontaneous polarization, epitaxial strain, and domain pattern.

Nonlinear Optical Properties of Transition-Metal Dichalcogenide MX2 (M = Mo, W; X = S, Se) Monolayers and Trilayers from First-Principles Calculations

Due to the absence of interlayer coupling and inversion symmetry, transition metal dichalcogenide (MX$_2$) semiconductor monolayers exhibit novel properties that are distinctly different from their bulk crystals such as direct optical band gaps, large band spin splittings, spin-valley coupling, piezoelectric and nonlinear optical responses, and thus have promising applications in, e.g., opto-electronic and spintronic devices. Here we have performed a systematic first-principles study of the second-order nonlinear optical properties of MX$_2$ (M = Mo, W; X = S, Se) monolayers and trilayers within the density functional theory with the generalized gradient approximation plus scissors correction. We find that all the four MX$_2$ monolayers possess large second-order optical susceptibility $\chi^{(2)}$ in the optical frequency range and significant linear electro-optical coefficients in low frequency limit, thus indicating their potential applications in non-linear optical devices and electric optical switches. The $\chi^{(2)}$ spectra of the MX$_2$ trilayers are overall similar to the corresponding MX$_2$ monolayers, {\it albeit} with the magnitude reduced by roughly a factor of 3. The prominent features in the $\chi^{(2)}$ spectra of the MX$_2$ multilayers are analyzed in terms of the underlying band structures and optical dielectric function, and also compared with available experiments.

Optimization of electrooptic and pieozoelectric coupling effects in tetragonal relaxor-PT ferroelectric single crystals

The electrooptic and piezoelectric coupling effects in tetragonal relaxor-based ferroelectric 0.62Pb(Mg1/3Nb2/3)O3–0.38PbTiO3 (PMN–0.38PT) and 0.88Pb(Zn1/3Nb2/3)O3–0.12PbTiO3 (PZN–0.12PT) single-domain crystals have been analyzed by the coordinate transformation. The orientation dependence of the electrooptic and half-wave voltage was calculated based on the full sets of refractive indices, electrooptic and piezoelectric coefficients. The optimum orientation cuts for achieving the best electrooptic coefficient and half-wave voltage were found. The lowset half-wave voltage is only 76V for the PMN–0.38PT single-domain crystal. Compared to commonly used electrooptic crystal LiNbO3, tetragonal relaxor-PT ferroelectric single-domain crystals are much superior for optical modulation applications because of their much higher linear electrooptic coefficients and substantially lower half-wave voltages when the piezoelectric strain influence is considered.

Influence of electrically induced refraction and absorption on the measurement of spin current by pockels effect in GaAs

The pockels effect could be utilized to measure spin current in semiconductors for linear electro-optic coefficient can be induced by spin current. When dc electric field is applied, the carriers will shift in k space, which could lead to the change of refraction and absorption coefficients. In this paper, we investigate the influence of the induced change of the refraction and absorption coefficients on the measurement of spin current by pockels effect in GaAs.

Terahertz electro-optic properties of PbZr0.52Ti0.48O3 and BaTiO3 ferroelectric thin films

Electro-optic effects of PbZr0.52Ti0.48O3 (PZT) and BaTiO3 (BTO) ferroelectric thin films in the terahertz frequency range are studied with high-sensitive terahertz time-domain spectroscopy. A linear response of PZT film with the linear electro-optic coefficient rc = 6.73 × 10−l1 m/V and a quadratic response of BTO film with the second-order electro-optic coefficient Rc = 1.42 × 10−l7 m2/V2 are observed at the frequency of 1 terahertz under the applied static electric field less than 80 kV/cm. The calculation of rc and Rc based on the Landau-Devonshire free energy theory explains the different electro-optic effects of PZT and BTO well.

Growth and nonlinear optical properties of K3B6O10Br crystal

Nonlinear optical (NLO) crystal K3B6O10Br with the size of 27×29 ×14mm3 was successfully grown by top seeded solution growth (TSSG) technique. Its second harmonic generation (SHG) coefficients were determined by Maker fringe method as: d22=1.23±0.01pm/V and d33=0.43±0.01pm/V. Its linear electro-optical (EO) coefficient γ22=0.81±0.06pm/V, which is usually employed in transverse modulation, was measured with polarimetric method.

Linear electrooptic coefficient r_51 of tetragonal potassium lithium tantalate niobate K_095Li_005Ta_040Nb_060O_3 single crystal

The linear electrooptic r51 coefficient of tetragonal K0.95Li0.05Ta0.40Nb0.60O3 single crystal was measured and reported. A modified AC modulating method coupled with high precision sample positioner, coherent light source, and phase-locked signal detection, was used to measure the electric field induced rotation of optical axis. The electrooptic r51 coefficient was found to be exceptionally large, r51 = (1.10 ± 0.14) × 104 pm/V at room temperature. Altogether with high ferroelectric phase transition temperature (~440 K), good optical crystal quality, ultrahigh linear electrooptic r51 coefficient and low frequency dependency, the K0.95Li0.05Ta0.40Nb0.60O3 single crystal offers significant application potential for various electrooptic devices.

Anisotropic electro-optic effect on InGaAs quantum dot chain modulators

We investigated the anisotropic electro-optic (EO) effect on InGaAs quantum dot (QD) chain modulators. The linear EO coefficients were determined as 24.3 pm/V (33.8 pm/V) along the [011] direction and 30.6 pm/V (40.3 pm/V) along the [011¯] direction at 1.55 μm (1.32 μm) operational wavelength. The corresponding half-wave voltages (Vπs) were measured to be 5.35 V (4.35 V) and 4.65 V (3.86 V) at 1.55 μm (1.32 μm) wavelength. This is the first report on the anisotropic EO effect on QD chain structures. These modulators have 3 dB bandwidths larger than 10 GHz.

Low drive voltage optical phase modulator with novel InGaAlAs/InAlAs multiple-quantum-barrier based n-i-n heterostructure

An optical phase modulator based on novel n-i-n InGaAlAs/InAlAs multiple-quantum-barrier (MQBs) is proposed to reduce the waveguide loss and enhance the modulation efficiency. Efficient bias loading with low leakage current is realized by taking advantages of the large conduction band discontinuity in InGaAlAs/InAlAs heterostructure and high electron reflection by MQBs. Low optical transmission loss of 2.3 dB/cm and improved modulation performance with a voltage length product of 1.06 V⋅cm are demonstrated for TE mode at 1550 nm. The linear and quadratic electro-optic coefficients of the fabricated device are estimated to be 1.0 pm/V and 1.4 × 10⁻¹⁹ m²/V², respectively.

Linear Electro-Optic Effect in Electroreflectance Spectra of AlGaN/InGaN/GaN Light Emitting Diodes Structures

The linear electro-optic effect in InGaN/AlGaN/GaN pn-heterostructures for light emitting diodes, grown by metal–organic chemical vapor deposition on sapphire substrates and flip-chip mounted, was studied by electroreflectance spectroscopy. Interference fringes, whose parameters depend on the DC voltage applied on the pn-junction, were observed in electroreflectance spectra. Data analysis, based on a calculation of the built-in electric field in the depletion layer and linear electro-optic effect, yielded the linear electro-optic coefficient r13 of 22±6 pm/V for hexagonal In0.12Ga0.88N.