Linear Electro-optic Effect Research Articles

Carrier-Envelope Phase stabilization of a 20 W, grating based, chirped-pulse amplified laser, using Electro-Optic effect in a LiNbO_3 crystal

Using an original CEP stabilization technique based on the linear electro-optical effect in a specific crystal, we achieved long term CEP stabilization of a 20 W, 1 kHz laser with residual noise as low as 440 mrad (rms). At 3 W, the CEP shot to shot noise is kept as low as 320 mrad (rms) over half an hour.

Electro-optic and electro-gyration effects on light propagation in \bf \overline 4 2mpoint-group crystals

Several nonlinear crystals that are used in laser and optical signal processing technologies belong to the {\overline 4}2m point group. This group exhibits as primary effects natural birefringence, optical activity, linear and quadratic electro-optic effects, and linear and quadratic electro-gyration effects, and, as secondary effects, photo-elasticity and piezo-gyrationviathe inverse piezo-electric phenomenon. The combination of these effects makes the study of light propagation a complicated task. In this work, the influence of each of these effects on light propagation is analytically reviewed, and suitable configurations for the light propagation and applied electric field directions are identified, which decouple the contribution of the individual effects. It is found that the complete decoupling of the linear electro-gyration from the linear electro-optic effect is not possible for this symmetry, while the inverse is feasible, and that the separation of the quadratic from the linear electro-optic effect can be achieved. For the linear phenomena, index ellipsoid geometries and eingenpolarizations are calculated, and analytic expressions are derived for the intensity of a light beam propagating through a crystal followed by a polarizer, thus providing valuable information for the design of devices and/or measurements of corresponding coefficients.

Pockels effect based fully integrated, strained silicon electro-optic modulator

We demonstrate for the first time a fully integrated electro-optic modulator based on locally strained silicon rib-waveguides. By depositing a Si3N4 strain layer directly on top of the silicon waveguide the silicon crystal is asymmetrically distorted. Thus its inversion symmetry is broken and a linear electro-optic effect is induced. Electro-optic characterization yields a record high value χ(2)(yyz) = 122 pm/V for the second-order susceptibility of the strained silicon waveguide and a strict linear dependence between the applied modulation voltage V(mod) and the resulting effective index change Δn(eff). Spatially resolved micro-Raman and terahertz (THz) difference frequency generation (DFG) experiments provide in-depth insight into the origin of the electro-optic effect by correlating the local strain distribution with the observed second-order optical activity.

Wave-coupling theory of linear electro-optic effect for ultrashort laser pulses

A wave-coupling theory of linear electro-optic (EO) effect for ultrashort laser pulses has been developed. As one of its applications, the linear EO effect of ultrashort Gaussian pulses propagating in LiNbO3 crystal is demonstrated, with the intensity lower than the damage threshold. It is found that the EO effect is sensitive to both the azimuth angle and the polar angle of wave vector of light. And the larger the applied electric field, the shorter the crystal used for optimization of EO coupling is. The numerical results show that, with the duration of input pulse changing from 150 fs to 5 fs, the durations of output pulses are broadened due to the group-velocity dispersion, as well as the first- and second-order refractive dispersion. In addition, when input pulse duration is larger than 20 fs, in contrast with zero chirp, the output durations can be slightly compressed if a positive chirp input pulse is used. The validities of slowly varying amplitude approximation and continuous wave approximation are also discussed. The influence of self-phase modulation and cross-phase modulation on the EO effect is also discussed briefly.

Conoscopic interferometry for probing electro-optic coefficients of strontium calcium barium niobate crystal

The relation between the linear electro-optic effect and conoscopic interference has been investigated in a biased electro-optic crystal strontium calcium barium niobate (CSBN). Based on the change of interference patterns with applied field, an interferometric method for probing electro-optic coefficients of electro-optic crystals has been proposed. In our case, the linear electro-optic coefficients of CSBN:50 was first probed at γ 33 =(141.0±0.5)×10 −12 m/V and γ 13 =(85.0±0.5)×10 −12 m/V. ► A interferometric method for probing electro-optic coefficients of CSBN has been proposed. ► The linear electro-optic coefficients of CSBN was first calculated to be γ 33 =(141.0±0.5)×10 −12 m/V and γ 13 =(85.0±0.5)×10 −12 m/V. ► Investigation on conoscopic interference in biased CSBN.

Carrier-envelope phase control using linear electro-optic effect

We present a new method to control the Carrier-Envelope Phase of ultra-short laser pulses by using the linear Electro-Optic Effect. Experimental demonstration is carried out on a Chirped Pulse Amplification based laser. Phase shifts greater than π radian can be obtained by applying moderate voltage on a LiNbO3 crystal with practically no changes to all other parameters of the pulse with the exception of its group delay. Time response of the Electro-Optic effect makes possible shaping at a high repetition rate or stabilization of the CEP of ultra short CPA laser systems.

Adsorbate-induced modification of the surface electronic structure at GaAs(001) surfaces

We report on the influence of hydrocarbon ring molecule adsorption on the surface electronic properties of GaAs$(001)$-$(2\ifmmode\times\else\texttimes\fi{}4)$ and $c(4\ifmmode\times\else\texttimes\fi{}4)$ surfaces. The adsorption geometry has been published previously, and it has been shown that there are strong indications that the surface As dimer bond is cleaved upon the chemisorption of the molecules at the $c(4\ifmmode\times\else\texttimes\fi{}4)$ reconstruction whereas the As dimers remain intact at the $(2\ifmmode\times\else\texttimes\fi{}4)$ reconstruction. At these different interfaces we have studied the adsorption-induced modification of the surface electronic properties. The surface band bending was investigated by synchrotron-based x-ray photoelectron spectroscopy, and the surface electric field was determined optically by reflectance anisotropy spectroscopy via the linear electro-optic effect. While the band bending at the GaAs$(001)$-$(2\ifmmode\times\else\texttimes\fi{}4)$ surface remains unaffected upon molecule adsorption, the surface electronic properties of the $c(4\ifmmode\times\else\texttimes\fi{}4)$ reconstructed surface undergo substantial changes. The surface band bending is reduced by 300 meV while the surface electric field increases significantly. These observations are explained within a model for the band bending at GaAs$(001)$ surfaces that was recently suggested by Lastras-Mart\'{\i}nez et al. [Phys. Rev. Lett. 96, 047402 (2006); Phys. Rev. B 75, 235315 (2007)], and the results underline the important role of dimer-induced strain for the surface band structure at the GaAs$(001)$-$c(4\ifmmode\times\else\texttimes\fi{}4)$ surface.

Simultaneous characterization of the electro-optic, converse-piezoelectric, and electroabsorptive effects in epitaxial (Sr,Ba)Nb2O6 thin films

Implementation of the linear electro-optic (EO) effect in thin film waveguides is expected to allow drastic reductions in the drive voltage, power, and dimensions of devices devoted to light modulation. It should also enable the realization of electrically tunable photonic crystal devices. In this paper we introduce a method which eliminates systematically the sources of the unreliability which strongly affects thin film EO characterization. Based on a Fabry–Perot reflective configuration, the method enables characterizing simultaneously the EO, converse-piezoelectric, and electroabsorptive effects in a film. It provides the magnitude and sign of each of the involved coefficients, and allows accounting for the whole of experimental data versus angle of incidence for both transverse-electric and transverse-magnetic polarizations. At λ=633 nm and room temperature, the results obtained with an epitaxial strontium barium niobate (SrxBa1−xNb2O6, x=0.60) ferroelectric thin film, are: r13=+8.5±1.3 pm/V, r33=+38.9±0.5 pm/V, d33=Δe/ΔV=+21±4 pm/V, and Δko/ΔV=(+9.8±0.6)×10−6, where r13 and r33 are two linear EO coefficients, d33 is a converse-piezoelectric coefficient, and e, ko, V represent, respectively, the film thickness, film ordinary extinction coefficient, and applied voltage. Converse-piezoelectric and electroabsorptive effects are found significant in the film response at a frequency below piezoelectric resonance. Diagonal and effective EO coefficients of the (Sr,Ba)Nb2O6 (SBN) film explored in the present work are larger than those of a crystal of lithium niobate (LN) at the same wavelength λ=633 nm. Taking into account the significant difference in dielectric permittivity between the two materials, advances and potential of LN and SBN thin film paths are compared.

Bioinspired peptide nanotubes: deposition technology, basic physics and nanotechnology applications

Synthetic peptide monomers can self-assemble into PNM such as nanotubes, nanospheres, hydrogels, etc. which represent a novel class of nanomaterials. Molecular recognition processes lead to the formation of supramolecular PNM ensembles containing crystalline building blocks. Such low-dimensional highly ordered regions create a new physical situation and provide unique physical properties based on electron-hole QC phenomena. In the case of asymmetrical crystalline structure, basic physical phenomena such as linear electro-optic, piezoelectric, and nonlinear optical effects, described by tensors of the odd rank, should be explored. Some of the PNM crystalline structures permit the existence of spontaneous electrical polarization and observation of ferroelectricity. The PNM crystalline arrangement creates highly porous nanotubes when various residues are packed into structural network with specific wettability and electrochemical properties. We report in this review on a wide research of PNM intrinsic physical properties, their electronic and optical properties related to QC effect, unique SHG, piezoelectricity and ferroelectric spontaneous polarization observed in PNT due to their asymmetric structure. We also describe PNM wettability phenomenon based on their nanoporous structure and its influence on electrochemical properties in PNM. The new bottom-up large scale technology of PNT physical vapor deposition and patterning combined with found physical effects at nanoscale, developed by us, opens the avenue for emerging nanotechnology applications of PNM in novel fields of nanophotonics, nanopiezotronics and energy storage devices.

Optical properties of BaTiO3/ZnO heterostructures under the effect of an applied bias

We report electro-optical measurements of BaTiO3/ZnO heterostructures grown by pulsed laser deposition. The optical properties of the heterostructures were examined with and without an applied bias. A change in the heterostructure optical properties is found and attributed to a linear electro-optical effect causing a change in the band gap. Moreover the formation of an electric polarization in the BaTiO3 layer causes a remanent change in the dielectric function if the bias is removed. The change could be estimated to be around 5meV.

Coupled-cavity surface-emitting lasers: spectral and polarization threshold characteristics and electrooptic switching

We study spectral and polarization threshold characteristics of coupled-cavity Vertical-Surface-Emitting Lasers (CC-VCSEL) on the base of a simple matrix approach. We show that strong wavelength discrimination can be achieved in CC-VCSELs by slightly detuning the cavities. However, polarization discrimination is not provided by the coupled-cavity design. We also consider the case of reverse-biasing one of the cavities, i.e. using it as a modulator via linear and/or quadratic electrooptic effect. Such a CC-VCSEL can act as a voltage-controlled polarization or wavelength switching device that is decoupled from the laser design and can be optimized for high modulation speed. We also show that using QD stack instead of quantum wells in the top cavity would lead to significant reduction of the driving electrical field.

Second-order nonlinear optical response of zigzag BN single-walled nanotubes

A theory based on the two-band tight-binding approximation for $\ensuremath{\pi}$ electrons is developed to describe the second-order nonlinear optical (NLO) properties of arrays of uniformly sized and well-aligned boron-nitride single-walled nanotubes (BN-SWNTs) with a zigzag achiral structure. It is assumed that the coherent light beam at frequency $\ensuremath{\omega}$, incident upon the nanotube sample, is linearly polarized along the symmetry axis of the nanotubes. The long-axis NLO susceptibility ${\ensuremath{\chi}}^{(2)}(\ensuremath{\omega})$ of those nanotubes is calculated within the independent nanotube approximation and in neglecting local-field effects. Using the perturbation-theory formalism in the crystal-momentum representation, we derive an explicit analytic expression for the ${\ensuremath{\chi}}^{(2)}(\ensuremath{\omega})$ and apply it to study three distinct second-order NLO effects possible in the BN-SWNTs due to their noncentrosymmetric structure---namely, second-harmonic generation (SHG), linear electro-optical (LEO) effect, and nonlinear optical rectification (NOR). The theory is illustrated by numerical model calculations of the SHG, LEO, and NOR susceptibility spectra for several representative BN-SWNT ensembles consisting of large-diameter nanotubes. The calculated SHG spectra are found to be dominated by the highly peaked $2\ensuremath{\omega}$ resonance at half the band-gap energy of the BN-SWNTs, where the absorption of light is negligible. Distinct features are also found in the LEO and NOR susceptibility spectra, e.g., a sudden switching of the susceptibility from a positive peak value to a negative peak one in the near vicinity of the fundamental absorption edge. A fairly large magnitude of those susceptibilities, reaching the order of ${10}^{\ensuremath{-}7}\text{ }\text{esu}$ under off-resonant conditions and up to ${10}^{\ensuremath{-}6}\text{ }\text{esu}$ in the resonant case, suggests that BN-SWNTs are a promising material for various electro-optical device applications.

Electro-optic effect and optical rectification in gold nanoparticles immobilized above a gold surface

Second-order nonlinear optical effects, a linear electro-optic (EO) effect and optical rectification (OR), were observed in surface immobilized gold nanospheres (SIGNs) above a gold surface with a gap of about 1.4 nm. The EO and OR measurements were performed in an attenuated total reflection geometry under a surface plasmon resonance condition. While it has been reported that the SIGN structure shows considerable second-harmonic generation activity, there has been no report on a linear EO effect and OR in the SIGN structure. The effective second-order susceptibilities of a single SIGN structure were evaluated to be 13 pm V−1 (EO) and 40 pm V−1 (OR). Although the theory predicts that the susceptibilities of EO and OR will be equal, the observed susceptibilities were different. The reasons for this discrepancy are discussed.

The spatially varying polarization of a focused Gaussian beam in quasi-phase-matched superlattice under electro-optic effect

We present in this paper a wave coupling theory of linear electro-optic (EO) effect for quasi-phase matched (QPM) of focused Gaussian beam in an optical superlattice (OSL). The numerical results indicate that, due to the EO effect of an appropriate applied electric field, the output beam will form spatially inhomogeneous polarization, changing continuously in transverse section of beam; the confocal parameter has a significant impact on the output polarization of Gaussian beam and determines the half-wave voltage.

Study of domain reversal and its field-dependence in epitaxial BaTiO3 thin films

Polarization switching dynamics were investigated in ferroelectric BaTiO3 epitaxial layers. Using the linear electro-optic (EO) effect, the polarization switching was measured under pulse excitation. The switching is given by a simple analytical model where the EO response follows an extended exponential function in time in the form of [1−exp−(t/τ)β], where τ and β are kinetic parameters, which depend on field. The parameter τ has the value of several milliseconds and β ranges from 0.2 to 0.3. The activation field α for domain growth was measured as a function of pulse width and field strength whereby the value of α decreases as the pulse width decreases. The activation field for the application of a pulse is higher than that upon the removal of the pulse. The difference is attributed to the existence of a depolarization field in the film in the direction of the external electric field.

Electro-optical modulators in polymer-dispersed liquid crystal complexes

The influence of bicolor optical treatment on the behaviour of the linear and quadratic electro-optical effects in the LCBO NC incorporated into the liquid crystalline matrix is studied. Simultaneously their dependence on frequency is analyzed. With increasing power density up to 250–270 MW/cm 2 there is a substantial increase of the electro-optical coefficient at 1150 nm up to 1.75 pm/V and 1.53 pm/V for 5% and 3% LCBO nanocrystallites, respectively. Further enhancement of the photo-inducing treatment leads to a saturation of the process. The behaviour of the maximal quadratic electro-optics coefficient R 2233 demonstrates principally different photo-inducing dependences. For both LCBO contents we observe an occurrence of the maximum in the electro-optical coefficients situated at 120 and 180 MW/cm 2 powers for the fundamental laser beams. However, contrary to the Pockels effect the enhanced content of the LCBO NC leads to a decrease of the observed effect.

The effect of an electric field on the nonlinear response of InAs/GaAs quantumdots

The refractive nonlinearities of InAs/GaAs quantum dots under a dc electric field atphoton energies above its band gap energy have been studied using the reflectionZ-scan technique. The effect of the dc electric field on the nonlinear response of InAs/GaAsquantum dots showed similar linear and quadratic electro-optic effects as in the linearresponse regime at low fields. This implies that the electro-optic effect in the nonlinearregime is analogous to the response in the linear regime for semiconductor quantum dots.Our experimental results show the potential for voltage tunability in InAs quantumdot-based nonlinear electro-optic devices.

Determination of second order nonlinear optical entities for l-alanine single crystals using semi-classical anharmonic oscillator model

The second order nonlinear optical properties associated with second harmonic generation and linear electro-optic effect have been computed for l-alanine amino acid single crystals using semi-classical anharmonic oscillator model. The data obtained for l-alanine were compared with the optical parameters of similar amino acid single crystal. The results have been discussed in detail.

Stark effect, polarizability, and electroabsorption in silicon nanocrystals

Demonstrating the quantum-confined Stark effect (QCSE) in silicon nanocrystals (NCs) embedded in oxide has been rather elusive, unlike the other materials. Here, the recent experimental data from ion-implanted Si NCs is unambiguously explained within the context of QCSE using an atomistic pseudopotential theory. This further reveals that the majority of the Stark shift comes from the valence states which undergo a level crossing that leads to a nonmonotonic radiative recombination behavior with respect to the applied field. The polarizability of embedded Si NCs including the excitonic effects is extracted over a diameter range of 2.5--6.5 nm, which displays a cubic scaling, $\alpha=c D^3$, with $c=2.436\times 10^{-11}$ C/(Vm), where $D$ is the NC diameter. Finally, based on intraband electroabsorption analysis, it is predicted that p-doped Si NCs will show substantial voltage tunability, whereas n-doped samples should be almost insensitive. Given the fact that bulk silicon lacks the linear electro-optic effect as being a centrosymmetric crystal, this may offer a viable alternative for electrical modulation using p-doped Si NCs.

Time-domain polarisation scrambler on one bulk LiNbO3 crystal with quadrupole electrodes

As distinct from the classic Billings depolariser, a simple time-domain polarisation scrambler can be made on one crystal possessing a threefold axis among its symmetry elements and displaying a linear electro-optical effect (Pockels effect). We demonstrate a polarisation scrambler on a LiNbO3 uniaxial crystal with two pairs of electrodes to which two harmonic voltages identical in amplitude and differing in phase by 90° are applied. The residual degree of polarisation of the depolarised light, quantified by the polarisation extinction ratio, is less than 0.1 dB. Tolerances on the crystal orientation and the phase difference between the control voltages are estimated. The quality of the crystal is shown to be critical to the performance of the scrambler.