Linear Electro-optic Properties Research Articles

Chirality and magnetic field engineering of linear and quadratic electro-optic properties in Silicene nanotubes for advanced optoelectronic applications

This study provides a comprehensive investigation of the electronic band structure, dipole matrix elements, and optical susceptibility of SiNTs for arbitrary chirality and under the influence of an external magnetic field. Using a tight-binding model including integral hopping up to third-nearest neighbors, the Hamiltonian matrix elements are derived for different SiNT configurations. Results demonstrate that varying the chiral angle of nanotubes effectively tunes the peak positions and intensities of linear optical susceptibility spectra and third-order nonlinear optical susceptibility χ(3)(ω;0,0,ω). This tunability of the optical response, combined with the ability to engineer the peak positions within the visible and near-UV ranges, makes SiNTs potentially useful for a wide range of optoelectronic devices, such as light-emitting diodes (LEDs), photodetectors, and optical modulators.

Symmetry Breaking Induced Pockels Effect in a Tilted Field Switching BPIII Cell

In this study, we propose driving the amorphous blue phase III (BPIII) with a tilted electric field to enhance or magnify its inherent linear electro-optical properties. The electro-optical properties of in-plane-switching (IPS) BPIII and tilted-field-switching (TFS) BPIII cells are compared here. According to the change in the induced birefringence with varying the strength of the electric field in the TFS-BPIII cell, the Kerr effect occurs in the low electric field and the Pockels effect dominates in the high electric field. In addition, the transmittance of the TFS-BPIII cell depends on the polarity of the applied field from 1 Hz to 10 kHz. It also results in the rise time of the TFS-BPIII cell being almost half of that of the IPS-BPIII cell. These experimental results and discussion allowed us to unravel the mystery of the amorphous BPIII step by step and provide the potential application of BPIII in photonic devices.

Linear electrooptic effect of the monoclinic polar bismuth triborate, BiB3O6

For the monoclinic (point group 2) nonlinear optical crystal BiB3O6 the linear electrooptic properties (Pockels effect), i.e. the 8 independent coefficients of the linear electrooptic tensor [] (at constant stress σ) at the wavelength λ = 632.8 nm are determined by a method based on Michelson interferometry. The electrooptic tensor is analysed with respect to the longitudinal and transverse effects and a classification of BiB3O6 as electrooptic material is given.

On the Origins of Large Interaction-Induced First Hyperpolarizabilities in Hydrogen-Bonded π-Electronic Complexes

In this article we elucidate the origins of interaction-induced linear and nonlinear electro-optic properties of model hydrogen-bonded π-electronic complexes. In particular we report on contributions due to various interaction energy terms to excess dipole moments (Δμ), electric dipole polarizabilities (Δα), and first hyperpolarizabilities (Δβ), focusing on the latter. The analysis of intermolecular interaction-induced electric properties is performed for selected model systems including quasi-linear dimers of urea, diformamide, 4-pyridone, 4-nitroaniline, and the complex of hydrogen fluoride with nitroacetylene. The nature of intermolecular interactions as well as of the Δμ and Δα is very similar in all studied complexes. However, partitioning of Δβ into physically well-defined components reveals that the origins of this term, the magnitude of which is often comparable to the hyperpolarizabilities of isolated monomers, are different in each case. Our results indicate that, even though hydrogen bonding usually diminishes the nonlinear response of interacting species, the first hyperpolarizability of complexes with the nitro group acting as a proton acceptor is substantially increased, essentially due to field-induced changes of electrostatic interactions between subsystems. However, in the remaining complexes the origins of Δβ are much more involved. Even though at large intermolecular separations the origins of interaction-induced electric properties are essentially due to the field-induced electrostatic and induction interactions, in the vicinity of van der Waals minimum the overlap effects cannot be neglected since they may substantially alter the predicted excess properties or even determine their magnitude and sign. On the other hand the Δβ contribution due to dispersion interactions is usually negligible. Interestingly, the values of interaction-induced first hyperpolarizability in some cases depend strongly on the intermolecular separation in the vicinity of equilibrium geometry.

Electrical properties and Pockels effect in BaTiO $$_{3}$$ 3 /SrTiO $$_{3}$$ 3 superlattices

The electrical and linear electro-optical properties of BaTiO $$_{3}$$ (BT)/SrTiO $$_{3}$$ (ST) superlattices epitaxially grown on ST substrate are theoretically investigated using a microscopic quantum mechanical model based on the orbital approximation in correlation with the dipole–dipole interaction. Both the first-, second-, and third-order electronic polarizabilities were considered in this calculation in order to obtain accurate results for both the spontaneous local electric field, spontaneous polarization, relative dielectric constant, and linear electro-optic coefficients (Pockels constants) of BT/ST superlattices. The calculations show that the spontaneous local electric field, spontaneous polarization and linear electro-optic coefficients of BT/ST superlattices increase with their content in BT while the relative dielectric constant increases with their content in ST. Moreover, we have shown that significant enhancement of the linear electro-optic coefficients can be achieved in BT/ST superlattices. This enhancement, which concerns the ST as well as the BT layers, arises from the combined effects of strain, induced in the BT layers by the epitaxial growth, and internal polarizing electric field originating in the BT layers and acting on the electronic clouds of the polarizable constituent ions of the system.

Linear electro-optic properties of relaxor-based ferroelectric 0.24Pb(In1/2Nb1/2)O3-(0.76 − x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals

Linear electro-optic properties of 0.24Pb(In1/2Nb1/2)O3-(0.76 - x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals, with compositions in the rhombohedral, morphotropic phase boundary (MPB) and tetragonal phases, have been investigated. Very large effective electro-optic coefficient [Formula: see text] (204 pm/V) was observed in a crystal with the MPB composition when it is poled along [001]. The rhombohedral phase (x = 0.27 and 0.30) single crystals poled along [111] direction and tetragonal phase (x = 0.39) single crystal poled along [001] direction are in single domain, and their electro-optic coefficients ([Formula: see text] = 76, 94, and 43 pm/V for the crystals with x = 0.27, 0.30, and 0.39, respectively) were found to be much higher than that of traditional electro-optic single crystal LiNbO3 ([Formula: see text] = 19.9 pm/V). The electro-optic coefficients of the single crystal in the rhombohedral phase have excellent temperature stability in the experimental temperature range of 10-40 °C. The half-wave voltage [Formula: see text] was calculated to be much lower (less than 1000 V) than that of LiNbO3 single crystal (2800 V). These superior properties make the ternary relaxor-PT single crystals very promising for electro-optic modulation applications.

Low-frequency–dependent electro-optic properties of potassium lithium tantalate niobate single crystals

A series of lead-free ferroelectric potassium lithium tantalate niobate K0.95Li0.05Ta1−xNbxO3 (x = 0.78, 0.69, 0.60, 0.52) single crystals were grown using the top-seeded melt growth method. The low-frequency–dependent linear electro-optic properties of K0.95Li0.05Ta1−xNbxO3 single crystals in the tetragonal state were investigated using the Senarmont method, autoscanning Mach-Zehnder interferometer technique and AC measurement method at room temperature. The electro-optic measurements were taken with continuous low frequency (from 1 kHz to 100 kHz) of a sinusoidal electric field, and large electro-optic responses were observed. For every component, the values of the electro-optic coefficients γ33, γ13 and γc decrease with the increase of frequency. However, the γ51 shows low sensitivity to the change of frequency. γ33, γ13 and γc increase with tantalum content, but γ51 decreases with the increase of tantalum content. The electro-optic properties of high-optical-quality K0.95Li0.05Ta1−xNbxO3 single crystals forecast their outstanding potential in various electro-optic applications.

A strong electro-optically active lead-free ferroelectric integrated on silicon

The development of silicon photonics could greatly benefit from the linear electro-optical properties, absent in bulk silicon, of ferroelectric oxides, as a novel way to seamlessly connect the electrical and optical domain. Of all oxides, barium titanate exhibits one of the largest linear electro-optical coefficients, which has however not yet been explored for thin films on silicon. Here we report on the electro-optical properties of thin barium titanate films epitaxially grown on silicon substrates. We extract a large effective Pockels coefficient of r(eff) = 148 pm V(-1), which is five times larger than in the current standard material for electro-optical devices, lithium niobate. We also reveal the tensor nature of the electro-optical properties, as necessary for properly designing future devices, and furthermore unambiguously demonstrate the presence of ferroelectricity. The integration of electro-optical active films on silicon could pave the way towards power-efficient, ultra-compact integrated devices, such as modulators, tuning elements and bistable switches.

Linear electro-optic properties of orthorhombic PZN-8%PT single crystal

The optical transmittance spectra of relaxor ferroelectric 0.92Pb(Zn(1/3)Nb(2/3))O(3)-0.08PbTiO(3) (PZN-8%PT) single crystals poled along different directions have been systematically studied at room temperature. After being poled along the [011] direction, the transmittance of induced orthorhombic PZN-8%PT single crystal is more than 50% from 0.5 to 5.7 μm, which is much higher than that poled along the [001] and [111] directions. The refractive indices and linear electro-optic properties of the orthorhombic PZN-8%PT single crystal were characterized at a wavelength of 632.8 nm. Large electro-optic responses were observed, (γ33) = 220 pm/V, (γ13) = 62 pm/V, and (γ23) = 23 pm/V. Thus, orthorhombic PZN-8%PT single crystal is a promising material for high-performance electro-optic devices.

Electro-optic properties and modulating application of langasite single crystals

The linear electro-optic properties of langasite (La 3Ga 5SiO 14, LGS) single crystals were investigated by the phase compensation method. An electro-optic KD 2PO 4 (DKDP) reference crystal was placed in the same laser beam path to compensate for the phase difference induced by the LGS crystal. The linear electro-optic coefficient r 11 of LGS was determined to be 1.8 × 10 −12 m/V at room temperature. The linear modulation of an ultrasonic frequency signal was accomplished by the same setup with a λ/4 wave plate replacing the DKDP crystal.

Electro-optic characterization of tetragonal (1− x)Pb(Mg 1/3Nb 2/3)O 3– xPbTiO 3 single crystals by a modified Sénarmont setup

The refractive indices of tetragonal (1− x)Pb(Mg 1/3Nb 2/3)O 3– xPbTiO 3 (PMN– xPT) single crystals were measured with a prism coupler and their linear electro-optic (EO) properties were investigated from 20 to 80 °C by the automated scanning Sénarmont system with an ac field. The composition and temperature effect on the EO coefficients were also discussed. It has been found that their EO coefficients are much larger than that of widely used LiNbO 3 single crystal and the calculated half-wave voltages are also much lower, which enable the operation at lower voltages and the smaller device dimensions. Since the excellent EO properties are very stable and such high quality single crystals with large-size have been obtained, the PMN– xPT single crystals are a very promising candidate for EO modulation applications. By linking to the polarization-related quadratic EO coefficients, we find that the linear EO properties are related with the spontaneous polarization and dielectric constants.

Refractive indices and linear electro-optic properties of (1−x)Pb(Mg1∕3Nb2∕3)O3−xPbTiO3 single crystals

The refractive indices and linear electro-optic (EO) properties of (1−x)Pb(Mg1∕3Nb2∕3)O3−xPbTiO3 single crystals were investigated over a broad composition range. The orientation and temperature effect on the EO coefficients were also examined. Large EO coefficients rc were observed near the morphotropic phase boundary (MPB). More importantly, rc of the single crystals on the tetragonal side of the MPB were nearly invariant in the experimental temperature range of 20–80°C. The calculated half-wave voltage Vπ was much lower than that of widely used EO single crystal LiNbO3. These excellent EO properties as well as being able to produce large-size and high-quality single crystals make this kind of single crystal very promising for EO modulation applications. The observed EO properties were also analyzed with the spontaneous polarization and dielectric constants.

Effect of low dose high energy O3+ implantation on refractive index and linear electro-optic properties in X-cut LiNbO3: Planar optical waveguide formation and characterization

X-cut LiNbO3 crystals were implanted at room temperature by 5.0 MeV O3+ ions with doses ranging from 1.0×1014 to 6.0×1014 O/cm2. Secondary ion mass spectrometry profiles of atomic species migration as well as damage profiles by the Rutherford backscattering channeling technique and refractive index variation were investigated as a function of dose and subsequent annealing conditions. Two different kinds of damage produced by oxygen implantation were seen: near-surface damage correlated to electronic stopping, which causes an increase of the extraordinary refractive index, and end-of-ion range damage generated by collision cascades, which decreases the extraordinary refractive index values. The different nature of the two kinds of damage is also seen by the different temperature conditions needed for recovery. Low loss planar optical waveguides were obtained and characterized by the prism coupling technique.

Linear electro-optical properties of tetragonal BaTiO3

Linear optical susceptibility and clamped linear electro-optical tensor coefficients of tetragonal BaTiO3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Ti-O bonds constituting distorted TiO6 octahedral groups are found to be major contributors to the electro-optic coefficients making them more sensitive than the BaO12 groups for these properties. Orientations of chemical bonds play an important role in determining these properties.

Composition, temperature, and crystal orientation dependence of the linear electro-optic properties of Pb(Zn1/3Nb2/3)O3–PbTiO3 single crystals

The linear electro-optic (EO) coefficients of Pb(Zn1/3Nb2/3)O3–PbTiO3 single crystals over a broad composition range were investigated at temperatures from −20 to 80 °C. The orientation effect on the EO coefficients was also examined. For crystals poled in the 〈001〉 direction, a large r33 was observed near the morphotropic phase boundary (MPB). More importantly, r33 was found to be independent of temperature for the crystals on the tetragonal side of the MPB. In contrast, r13 was nearly zero for all compositions examined at all the temperatures. The large r33 near the MPB and the observed crystal orientation effect of the EO coefficients were also analyzed.

Characterization of electro-optic polymer films by use of decal-deposited reflection Fabry Perot microcavities

We have used resonant reflection mode Fabry–Perot microcavities (RFPM’s) to determine linear optical and electro-optical properties of poled nonlinear optical polymers (NLP’s). Measured reflectances from angular scans of RFPM’s have been analyzed with an electromagnetic plane-wave multilayer analysis that took into account the anisotropic nature of the NLP layer. We have numerically investigated the mutual dependence of refractive indices and layer thickness and the accuracy of the results obtained. As an illustration of this characterization technique, the refractive indices of a 10 mol. % Disperse Red 1/poly(methyl methacrylate) side-chain NLP have been determined to within ±0.005, the NLP layer thicknesses to within 1%, and electro-optic coefficients to within 5%. We optimized RFPM structures for measurements at the wavelength λ=430 nm by changing the electrode metal from gold to aluminum. Using a guest–host NLP, 5 wt. % diphenyl-tricyanovinyl-aniline in poly(methyl methacrylate), we show that the method is capable of measuring electrorefraction and electroabsorption as well as a converse piezoelectric contribution. We show that a NLP decal deposition technique is particularly well suited to fabrication of these RFPM’s.

Polymeric electro-optic phase modulators formed by self-alignment over channels etched into indium phosphide

Waveguides which are single mode at a wavelength of 1.32 μm, and which have linear electro-optic properties, have been fabricated by spin coating polymers onto etched indium phosphide. The side-chain polymer, which comprises the core of the waveguide, develops linear electro-optic properties following an electric field alignment process. A phase modulator has been fabricated by this method and was found to have a switching voltage of 30 V, for a π phase change. The total insertion loss of the device was measured between single-mode lensed fibers to be 9.4 dB. The electro-optic coefficient of the core polymer was calculated from the switching voltage using the geometry of the device and found to range from 6 to 11×10−12 m/V.

Bond susceptibilities and linear electro-optic properties of KTiOPO 4

Linear electro-optic coefficients (r i j) of the nonlinear optical Potassium Titanyl Phosphate crystal (KTP) are calculated. Results indicate a major contribution of the short Ti-O bonds in the TiO 6 octahedra and practically an insignificant role of long Ti-O bond. Thus as far as linear electro-optic effect is concerned, the crystal behaves as if there are five bonds in the TiO 6 octahedron. The order of magnitude of the r 33 coefficient of Potassium Stannyl Phospate (KSP), the tin analogue of KTP, is estimated for which the experimental value is not known so far.

The effect of CrO42- ions on the electro-optic properties of KDP single crystals

Sufficiently large yellowish single crystals of KDP doped with various concentrations of K2CrO4 have been grown for electro-optic device applications, by the slow-evaporation Holden's rotary crystallizer technique. These crystals have been characterized for their ferroelectric and linear electro-optic properties. The doped crystals have low half-wave voltages as compared with that of pure KDP while there are no significant changes in the ferroelectric properties.

Linear and nonlinear optical properties of 3-methyl-4-methoxy-4′-nitrostilbene single crystals

Single crystals of the new nonlinear optical material 3-methyl-4-methoxy-4′-nitrostilbene (MMONS) have been grown by a seeded solution growth technique and the linear and nonlinear optic and electro-optic properties determined. MMONS is highly birefringent with nz−nx =0.75 (0.532 μm), has large nonlinear optical coefficients with d33=184 pm/V and d24=71 pm/V (1.064 μm), has large electro-optic coefficients with r33=39.9 pm/V (0.6328 μm), and can be efficiently type II phase matched for Nd lasers emitting ∼1 μm.