Electro-optic Tensor Research Articles

Microresonator-based electro-optic dual frequency comb

Microresonator based dual frequency combs offer an integrated photonic solution to a wide range of technological challenges, including spectroscopy, range finding, material characterization and hyperspectral imaging. These applications require a high level of mutual coherence between combs, but achieving such stability can be demanding. Here we experimentally demonstrate that comb generation exploiting the rich structure of the nonlinear electro-optic tensor in lithium niobate can generate ultra-stable dual combs, with the two combs naturally having orthogonal polarizations. We theoretically explore the application of our technique to dual frequency comb generation from the far infrared (IR) to the ultraviolet (UV). Our combs have relative linewidths as low as ~400 μHz, and require no stabilization or post-processing methods.

OPTIMAL FOCUSING CONDITIONS FOR TWO-DIMENSIONAL GAUSSIAN LIGHT BEAMS WITH ARBITRARY INPUT POLARIZATION IN A PHOTOREFRACTIVE BARIUM-STRONTIUM NIOBATE CRYSTAL

Calculating nonlinear optical phenomena in a barium-strontium niobate photorefractive crystal we constructed a mathematical model of the two-dimensional linearly polarized Gaussian light beams propagation taking into account all components of the linear electrooptic tensor. We investigated the dependence of the light beam intensity on the polarization azimuth at the entrance of the crystal and on the direction of the external electric field applied to a photorefractive crystal. We determined the conditions under which the focusing of two-dimensional Gaussian light beams at the exit of the crystal is maximal.

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.

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.

Pockels effect in low-temperature rhombohedralBaTiO3

We report a first principles analysis of the linear electro-optic (EO) or Pockels effect in rhombohedral $\mathrm{BaTi}{\mathrm{O}}_{3}$ (BTO), the lowest temperature phase of this ferroelectric perovskite. Si-integrated BTO is a promising material for EO modulators in Si photonics, with applications in optical quantum computing. This requires a fundamental understanding of the Pockels effect in BTO at low temperature. Through density functional perturbation theory, we explore the origins of a strong Pockels response by examination of the components that make up the ionic contribution to the EO tensor. We identify the phonon modes dominating the EO response and establish their relation to the electronic structure and optical properties of the material.

Linear Versus Nonlinear Electro-Optic Effects in Materials.

Two schemes are proposed to compute the nonlinear electro-optic (EO) tensor for the first time. In the first scheme, we compute the linear EO tensor of the structure under a finite electric field, while we compute the refractive index of the structure under a finite electric field in the second scheme. Such schemes are applied to Pb(Zr,Ti)O_{3} and BaTiO_{3} ferroelectric oxides. It is found to reproduce a recently observed feature, namely, why Pb(Zr_{0.52}Ti_{0.48})O_{3} adopts a mostly linear EO response while BaTiO_{3} exhibits a strongly nonlinear conversion between electric and optical properties. Furthermore, the atomistic insight provided by the proposed abinitio scheme reveals the origin of such qualitatively different responses, in terms of the field-induced behavior of the frequencies of some phonon modes and of some force constants.

Study of the linear and nonlinear response properties of the zinc-blende AlP, GaP and their AlxGa1-xP ternary alloys using first principle calculations

The structural, electronic, thermodynamic, vibrational, elastic, linear and nonlinear optical properties of AlxGa1-xP ternary alloys are studied using plane-wave pseudopotential method based on the density functional theory. The alchemical mixing method is used to construct an alloy by mixing the pseudopotentials in an appropriate way. The local density approximation is used for the exchange and correlation potentials calculations using the ABINIT code. The Born effective charges, phonon frequencies, longitudinal-transvers optical splitting and thermal properties are calculated using density functional perturbation theory. By applying the many-body effects within the Bethe-Salpeter approach using the Tam-Dancoff approximation, the frequency-dependent macroscopic dielectric function is calculated. The nonlinear dielectric (electronic) susceptibility, the electro-optic tensor and the Raman tensor are investigated in the framework of density functional perturbation theory using the 2n+1 theorem. Moreover, due to density functional theory band gap problem, the band-gap correction is performed within the one-shot GW approximation of many-body perturbation theory. The calculated results of AlP and GaP compounds are in acceptable agreement with available theoretical and experimental results, so the present study on the AlxGa1-xP alloys would be helpful for future experimental and theoretical investigations.

Electro-optic properties of singly and doubly doped lithium niobate crystal by rare earth elements for optoelectronic and laser applications

Congruent lithium niobate (LN) doped with rare-earth elements is a promising host for integrated optic combining the properties straightforwardly associated to the dopant with the good electro-optic (EO) properties. By direct technique based on interferometric optical arrangement at a wavelength of 633 nm and at room temperature, we have experimentally determined the figure of merit F = n3reff, (n is the refractive index and reff, the effective EO coefficient) and finally calculated the EO coefficients reff of the third-column of the unclamped EO tensor of three series of singly doped LN with Yb3+, Ho3+, Tm3+ and two series of doubly doped Er3+–Yb3+. It is found that in all the studied opto-geometric configurations, the unclamped figure of merit and consequently the corresponding EO coefficients are relatively constant in the considered dopant concentration range. As the figure of merit, F qualifies crystals for EO modulation and laser applications, all reported results confirm that the LN singly or doubly doped with rare-earth elements are very promising versatile candidates for several multifunctional nonlinear devices in optoelectronic and laser applications.

The clamped and unclamped effective electro-optic coefficients of zirconium-doped congruent lithium niobate crystals

All coefficients of the unclamped and clamped electro-optic tensor of zirconium-doped congruent LiNbO3 single crystals are determined as function of the dopant concentration at room temperature. With a distribution coefficient of zirconium closer to one in the considered range, the dopant concentration is in the range up to 2.5 mol% of ZrO2. The electro-optic coefficients are measured by direct techniques based on interferometric and Sénarmont optical arrangements at the wavelength of 633 nm. It is found that all the unclamped and clamped effective electro-optic coefficients are relatively constant, except for the sample grown with 2 mol% of zirconium. The electro-optic behavior of LN:Zr as function of the dopant concentration was confirmed by dielectric characterizations. The concentration equal 2 mol% of ZrO2 can be considered to a threshold concentration for various physical and optical properties.

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.

Periodic domain inversion in x-cut single-crystal lithium niobate thin film

We report the fabrication of periodically poled domain patterns in x-cut lithium niobate thin-film. Here, thin films on insulator have drawn particular attention due to their intrinsic waveguiding properties offering high mode confinement and smaller devices compared to in-diffused waveguides in bulk material. In contrast to z-cut thin film lithium niobate, the x-cut geometry does not require back electrodes for poling. Further, the x-cut geometry grants direct access to the largest nonlinear and electro-optical tensor element, which overall promises smaller devices. The domain inversion was realized via electric field poling utilizing deposited aluminum top electrodes on a stack of LN thin film/SiO2 layer/Bulk LN, which were patterned by optical lithography. The periodic domain inversion was verified by non-invasive confocal second harmonic microscopy. Our results show domain patterns in accordance to the electrode mask layout. The second harmonic signatures can be interpreted in terms of spatially, overlapping domain filaments which start their growth on the +z side.

Performance and Quality Characterization of the Reference MNA Nonlinear Optical Molecular Crystal by Pockels Electrooptic Confocal Microscopy

The recently proposed Pockels linear electrooptical microscopy is being applied to a quality and performance characterization of the 2‐methyl‐4‐nitroaniline quadratic nonlinear optical molecular crystal down to confocal microscope resolution. Samples are grown between electrodes in single‐film format. The dominant electrooptic tensor coefficient is determined and the distribution of the electric field is mapped so as to characterize polycrystalline features. The Pockels polarization response is shown to provide a unique way to the unambiguous assignment of the principal dielectric axis in the case of a low symmetry crystal. Application toward weak electric‐field sensing at a local scale is demonstrated.

Proposed measurement of spin currents in a GaAs crystal using the electro-optical Pockels effect

A new method for measuring spin currents is proposed, based on the linear electro-optic (Pockels) effect caused by the additional second-order nonlinear electric susceptibility (electro-optic tensor) generated by the spin currents. The non-zero elements of electro-optic tensor induced by spin currents in GaAs crystal are calculated, and the wave coupling theory of linear electro-optic effect is used to analyze the polarization change of a probe beam. The numerical results show that, for a linearly polarized probe beam with a frequency close to the band gap of GaAs crystal, its polarization rotation can be as large as 14 μrad under an applied electric field of about 350 V/mm. This effect should offer an alternative detection method for spintronics.

First-principles characterization of the electronic and optical properties of hexagonal [formula omitted

Within the density functional theory framework, we investigate the structural, electronic, vibrational, dielectric, piezoelectric and optical properties of hexagonal lithium iodate, including some nonlinear response properties, like the nonlinear dielectric (electronic) susceptibility, the electro-optic tensor and the Raman tensor. Beyond the comparison with available experimental data and the associated analysis, we predict the values of several properties or characteristics of this material, e.g. the phonon frequencies with B symmetry, that are silent in both IR and Raman experiments, the Born effective charges, for which a detailed analysis is performed, Raman susceptibilities and the decomposition of the clamped electro-optic tensor in terms of the different modes. The agreement with available experimental results is reasonable to excellent, depending on the property. The lattice parameters and macroscopic dielectric constants agree to the experimental ones within 2%. The Kohn–Sham electronic bandstructure is predicted, but suffers from the well-known DFT band gap problem. Reflectivity spectra computed with the density functional perturbation theory are in qualitative and quantitative agreements with experiments for incident light along the two main hexagonal axes. The phonon frequencies at the Brillouin zone center are, in average, 5.74% apart from the experimental one. The previous assignment of Raman features is discussed, on the basis of our computed Raman spectra, including relative peak heights. Finally, this study confirms theoretically the large nonlinear coefficients d31 and d33 of −6.6pm/V and −7.5pm/V as well as its noteworthy piezoelectric and electro-optic properties that make this material remarkable.

Third column electro-optical coefficients of zirconium-doped congruent lithium niobate crystals

All coefficients of the third-column of the unclamped and clamped electro-optic tensor of zirconium-doped congruent LiNbO3 single crystals, in the concentration range up to 2.5mol%, are determined as function of the dopant concentration by direct techniques based on interferometric and Sénarmont optical arrangements at the wavelength of 633nm and at room temperature. It is found that all the unclamped and clamped electro-optic coefficients are relatively constant, except for the sample doped with 2mol% of zirconium. From the obtained experimental values, the acoustic contribution is then deduced and found constant over all the studied samples. Finally, the electro-optic behavior of LN:Zr as function of the dopant concentration was confirmed by dielectric characterizations.

Enhanced electrooptical active materials based on n-hexyl group flexible isolation in NLO chromophores

Two principally novel organic nonlinear optical chromophores (1 and 2) with flexible (n-hexyl group) or rigid isolated (benzyl group) group are designed and successfully synthesized. The prepared chromophores were characterized by MS, 1H-NMR and UV–Vis spectra. Their thermal stability was studied by thermal gravimetric analyzer and differential scanning calorimetry. Poled films of the chromophores doped in amorphous polycarbonate afford the maximum electro-optic tensor coefficient (r33) equal to 39 pm/V, 63 pm/V for chromophore 1 and chromophore 2, respectively at the wavelength 1,064 nm. The reason of so large differences between these two chromophores’ linear electrooptics coefficients were explained within a framework of performed quantum chemical calculations and it is crucially dependent on distances between the chromophore molecules and the polymer chains.

Analysis of reflective Mach-Zehnder interferometry for electro-optic characterization of poled polymer films in multilayer structures

We consider the Mach-Zehnder interferometer (MZI) method that specifically uses a poled organic thin film as one of the reflective mirrors in order to characterize the two independent electro-optic tensor elements r(13) and r(33). We discuss both a simple analysis based on a three-layer structure and a rigorous method including multiple reflection effects in a multilayer structure. In doing so, we find that the simple analysis of the reflective MZI method yields identical results to the reflection ellipsometric method (simple Teng-Man method), first introduced by Teng and Man as well as Shildkraut in 1990, when the ratio of r(13) to r(33) obtained from the MZI method is used in the analysis of the simple Teng-Man method. Error introduced by ignoring the multilayer nature of the sample structures in the MZI method is discussed and corrections are given for previous expressions in the literature for the simple analysis.

Third column electro-optical coefficients of monoclinic Sn_2P_2S_6

All coefficients of the third-column of the unclamped electro-optic tensor of Sn2P2S6 single crystals are determined by direct interferometric techniques. It is found that the largest coefficient r113T for electric field parallel to the z-axis is ≈ 67 pm/V at the wavelength of 633 nm and room temperature.

Measurement of the linear electro-optic tensor of cubic boron nitride single crystals

The transverse electro-optic (EO) modulation system is built based on cubic boron nitride (cBN) single crystals unintentionally doped and synthesized at a high pressure and high temperature. The photoelectric output of the system includes two parts that can be measured respectively and the value of elements in the linear EO tensor of the cBN crystal can be obtained. This method does not need to measure the absolute light intensity. All of the surfaces of the tiny cBN crystals whose hardness is next to the hardest diamonds are {111} planes. The rectangular parallelepiped cBN samples are obtained by cleaving along {110} planes and subsequently grinding and polishing f112g planes of the tiny octahedral cBN flakes. Three identical non-zero elements of the EO tensor of the cBN crystal are measured via two sample configurations, and the measured results are very close, about 3.68 and 3.95 pm/V, respectively, which are larger than the linear EO coefficients of the general III-V compounds.

The nonlinear optical susceptibility and electro-optic tensor of ferroelectrics: first-principle study

Abstract The nonlinear optical properties of some ABO3 materials (BaTiO3, KNbO3, LiTaO3 and LiNbO3) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO3 structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X ijk(2) (−2ω, ω, ω) over a large frequency range for ABO3 crystals. The electronic linear EO susceptibility X ijk(2) (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X ijk(2) (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.