Quadratic Electro-optic Coefficients Research Articles

Electro-optic properties near the absorption edge of GaAs/AlGaAs multiple-quantum-well waveguides

Measurements are reported of the electro-optic properties of multiple-quantum-well p-i-n diodes at wavelengths where the waveguide propagation losses are small, 55–110 meV below the exciton resonance. Electroabsorptive and electrorefractive properties were measured as a function of polarization and crystal propagation direction. The electroabsorption and electrorefraction data show that there is a wavelength bandwidth of ∼25 nm where the quadratic electro-optic coefficient is large (1–7×10−15 cm2/V2) and the magnitude of the electroabsorption is <0.5 dB/mm for applied fields of up to 1×105 V/cm. Compact, high-dynamic-range interferometric modulators can be realized in this wavelength band.

Properties of Electrooptic (Pb, La)(Zr, Ti)O3 Ceramics Fabricated by Partial Coprecipitation Method

Electrooptic ceramics of (Pb, La)(Zr, Ti)O3 were fabricated by a combination of the partial-coprecipitation and doctor-blade methods. The PLZT powder, with particles of submicron size that were excellently dispersed, was prepared by (Zr, Ti)O2 solid-solution powder and PbO and La2O3 oxide powders. The large-scale PLZT ceramics with the dimension of 10×10∼20 cm and thickness of 1.5 mm were molded by the doctor-blade method and then conventionally sintered at 1200∼1250°C for 20∼60 h under the controlled condition of PbO and oxygen atmosphere. The fabricated PLZT ceramics with 0.5 mm thickness showed the transmittance of 65∼67% in the range of wavelength greater than 600 nm, and the quadratic electrooptical coefficient of 4.5×10-16 O2/V2.

Optical Study of Pb1-xLax(ZryTiz)1-(x/4)O3

Optical properties of La-modified lead zirconate titanate (9/65/35) in the intermediate phase were studied by the HAUP (high accuracy universal polarimeter) method. It was found that this material is optically inactive under electric fields. On the other hand, temperature dependence of the quadratic electrooptic coefficient was measured after careful corrections using the HAUP method.

Analytical model for the quadratic electro-optic effect of perovskites.

A semiclassical model of the transverse electro-optic effects including both electronic and ionic contributions is proposed for perovskite materials. It is found that for perovskite structure the linear and the nonlinear susceptibilities are related via a single parameter of the material. Therefore, the model yields a formula that provides a semiquantitative prediction of the quadratic electro-optical coefficient of the materials from their indices of refraction and dielectric constants.

The electro-optic coefficients of GaAs: Measurements at 1.32 and 1.52 μm and study of their dispersion between 0.9 and 10 μm

The linear (r41) and quadratic (R11 and R12) electro-optic coefficients of GaAs have been measured at the wavelengths 1.32 and 1.52 μm using single-mode AlGaAs/GaAs strip-loaded waveguides. The results are r41=−(1.54±0.08)×10−10 cm/V, R11=−(9.3±2.8)×10−17 cm2/V2 and R12=−(5.1±l.9)×10−17 cm2/V2 at 1.32 μm and r41=−(1.50±0.08)×10−10 cm/V, R11=−(3.2±2.3)×10−17 cm2/V2 and R12=−(5.1±2.6)×10−17 cm2/V2 at 1.52 μm. These results, together with those previously measured at different wavelengths, are compared with published theoretical models. The linear electro-optic coefficient r41 is slightly dispersive near the band gap and roughly constant for longer wavelengths, in good agreement with the models. The quadratic electro-optic coefficients drop rapidly with increasing wavelength, in good agreement with a model based on electroabsorption.

Quadratic electro-optic effect and second-order strain derivatives of electronic susceptibility

Electro-optic effects are related to second order strain derivatives of electronic susceptibility. The method is applied to halite-type alkali halides and KDP crystals. Employing the bond polarizability approach, the values of strain and volume derivatives are evaluated from experimental quadratic electro-optic coefficients. In alkali halides the model based on the decomposition of optical susceptibility into contributions of intraionic and interionic excitations is taken into consideration. For alkali halides, results obtained within the Clausius-Mosotti theory and the Penn model are also presented. Since in noncentrosymmetric KDP crystals the influence of the linear electro-optic effect can lead to large apparent quadratic electro-optic effects, the conditions of measurement are discussed. The earlier experimental results are critically analysed, and to estimate in terms of the bond polarizability model, the second order strain derivative of electronic susceptibility of KDP, we employed our experimental values of the quadratic coefficient g 1111- g 1122.

Spectral characterization of the linear and quadratic electro-optic effects in GaAs/AlGaAs multiple quantum well waveguides

The electro-optic effect in GaAs/AlGaAs multiple quantum well stripe waveguides has been studied extensively for both TE and TM polarization in a spectral range close to the excitonic band edge. The effect has been resolved into two components, a linear electro-optic (LEO) effect and a quadratic electro-optic (QEO) effect. The LEO coefficients r63 and r33 have been measured to be -1.75*10-12 m V-1 and zero respectively, similar to that of bulk GaAs, with no significant wavelength dependence. The quadratic effect, however, has been shown to be highly wavelength-dependent and enhanced compared with bulk GaAs. A QEO coefficient as large as 140*10-20 m2 V-2 has been measured at photon energies 28 meV from the lowest energy exciton. The spectral dependence of the quadratic effect has been studied for both TE and TM polarization.

Quadratic Electrooptic Properties of the Ferroelectric Ceramics of the Ternary System Sr(La1/2Nb1/2)O3-PbZrO3-PbTiO3

Optical and electrooptic properties were studied for some compositions of hot-pressed ceramics of the ternary system Sr(La1/2Nb1/2)O3-PbZrO3-PbTiO3. Optical transmittances were measured as a function of wavelength and temperature. Quadratic electrooptic coefficients R and half-wave voltagcs Vπ were determined at various temperatures. Switching characteristics were also examined. The results obtained were compared with those of electrooptic crystals such as KTaO3 and KTa0.65Nb0.35O3.

Direct interferometric measurements of quantum-confined Stark effect in InAs/GaAs short period strained-layer superlattice MQWs

The electrorefraction within and below the band edge of multiple (50) InAs/GaAs short period strained-layer superlattice quantum wells has been measured. An index change of 4×10−3 was measured near the excitonic resonance with an applied electric field of 27 kV/cm, corresponding to a quadratic electro-optic coefficient of −3×10−13 cm2/V2. These results agree with predictions from the Kramers-Kronig relations based on measurements of electroabsorption.

Electro-optic measurements in PbTiO3single crystals

Abstract Electro-optic properties are investigated in tetragonal PbTiO3 single crystals at room temperature with a technique based upon the Senarmont method. The linear and quadratic electro-optic coefficients are determined from the measurements of the birefringence as function of applied DC electric field. The values of the linear rc and quadratic Rc electro-optic coefficients are given for a wavelength λ = 633 nm. Further, a large memory effect is detected when the electric field is switched off.

Electrical and optical properties of relaxor ferroelectrics

Abstract The dielectric and optic/electro-optic properties of hot-pressed ceramics of composition (1−x)(Pb1−y −La y )(Mg⅓Nb2/3)O3 − xPbTiO3 (y = 0.01) have been investigated. The materials exhibit high peak dielectric constants (>20000) with typical relaxor ferroelectric behavior. The ceramics are adequately transparent for optical and electro-optical evaluation with transmission better than 50% at 600 nm. High refractive indices are observed (>2.5 at 632.8 nm) and the dispersion of the refractive index is well described by a single-term Sellmeier equation. The temperature dependence of the refractive index exhibits a linear region above 390°C and a polarization induced decrease of the index via the electro-optic effect below this temperature. The transverse quadratic electro-optic coefficients, (R11–R12) and (g11–g12), were evaluated both as a function of temperature and frequency. Electro-optic switching experiments indicate rapid response of less than 1 μsec, suitable for transverse shutter mode operation.

Dependence of electro-optic properties of PLZT upon the chemical compositions

Abstract The characteristics of the ferroelectric and the electro-optic properties was investigated on the transparent PLZT ceramics, which had a slim D-E loop. The coercive force Ec was 0.24 × 106 V/m and the remnant polarization Pr was 7.9 × 10−2 C/m2 for the typical composition of PLZT (9/65/35), applying AC 2 kV/mm at 50 Hz. Transmittance of a PLZT electro-optic shutter was studied. The shutter was fabricated by PLZT wafer with a pair of slot electrode sandwiched between artificial polarizers under crossed Nicols. In order to evaluate the electro-optic hysteresis, the ratio of the half width to the applied voltage was employed, and was about 20% for PLZT (9/65/35), 13% for PLZT (10/65/35) and 8% for PLZT (9/69/31), in giving the maximum light intensity. The hysteresis of transmittance were decreased with increment of both La and Zr content, although the quadratic electro-optic coefficient was decreased.

Preparation and properties of PLZT films from metallo-organic precursors

Abstract Crack free and dense PLZT (8/65/35) films 0.4 to 2.5 μm thick were prepared by spinning a solution of metallo-organic compounds of lead, lanthanium, zirconium and titanium onto sapphire substrates, and firing and annealing the films in air in the range 600 to 850°C. These firing temperatures resulted in films with grain sizes from 0.2 to 1.2 μm. Films fired at 650°C had a dielectric constant of 1800 and a dissipation factor of 2% at 1 kHz, and a spontaneous polarization of 5 μC/cm2. The linear and quadratic electro-optic coefficients were 30 × 10−12 m/V and 50 × 10−18 (m/V)2, respectively.

Optical properties of hot pressed relaxor ferroelectrics

Abstract The optical properties of hot pressed transparent ceramics based on the relaxor ferroelectric (1-x)Pb (Mg1/3,Nb2/3)O3−xPbTiO3 (known as PMN-PT) solid solution system have been examined in the visible region. We report transmission as a function of wavelength, refractive indices as a function of temperature and wavelength, and quadratic electro-optic coefficient data for the 632.8 nm HeNe laser wavelength. For our particular ceramic compositions, .93(Pb0.99La0.01)(Mg1/3,Nb2/3)O3−.07PbTiO3 and .90 PMN−.10 PT, the refractive index dispersion is well described by a single term Sellmeier equation. The observed temperature dependence of the refractive indices n(T) can be discussed in terms of polar microregions which alter the refractive indices in these ceramics via the quadratic electro-optic effect. Transverse quadratic electro-optic coefficients measured were in accord with those reported for other Pb containing perovskite oxides.

Quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films

Quadratic phase modulation is used to measure the electronic third-order nonlinear optical susceptibility of thin polymer film solid solutions of organic dyes. This simple technique is shown to provide quick measurements of the χ(3)1133 component of the third-order optical susceptibility. The measured quadratic electro-optic coefficient of 7.5 wt. % (2.5 mol %) of a dicyanovinyl azo dye in poly(methyl methacrylate) (PMMA) is 4.4×10−21 m2/V2, which corresponds to a direct current Kerr coefficient of 1.4×10−11 esu. The electronic and orientational mechanisms, whose response times are faster than 30 ps, are discussed.

Electro-optical effects of Cd1−xMnxTe films prepared by ionized-cluster beams

We report the first investigation of electro-optical properties of Cd1−xMnxTe films, prepared by the ionized-cluster beam deposition technique. Measurements of the birefringence Δn of the films were performed under applied electric field in the wavelength region from 800 to 450 nm. Major results obtained are as follows: The value of Δn rises to second power against the applied electric field, and for a film with x=0.77 a large quadratic electro-optical coefficient of 3.5×10−12 cm2/V2 is obtained at 633 nm. The wavelength dispersion of Δn is observed near its band gap, suggesting that the electro-optical properties of these films are caused by the Franz–Keldysh effect.

Preparation of Pb(Zr,Ti)O3 thin films by sol gel processing: Electrical, optical, and electro-optic properties

Crack-free transparent ferroelectric polycrystalline Pb(Zr,Ti)O3 thin films were prepared by spin-coating solutions of complex alkoxides. The preparation of stock solution, firing, and annealing of films was described. The coating of the intermediate layer of Al2O3 increased the adhesion between Pb(Zr,Ti)O3 thin films and glass substrates. The crystalline phases of films with varying Zr/Ti ratios were investigated. The dielectric constants were about 260. The remanent polarization and coercive field were 6.6 μC/cm2 and 26.7 kV/cm, respectively. The refractive index of the perovskite Pb(Zr,Ti)O3 films was 2.6 at 6328 Å, and the absorption edge was at 3400 Å. The quadratic and linear electro-optic effects were measured with respect to the Zr/Ti ratio from 40/60 to 60/40 for films grown on glass substrates. The quadratic and linear electro-optic coefficients were about 1×10−18 m2 /V2 and 2.4×10−11 m/V at 6328 Å, respectively.

Anomalous electrooptic and electrogyrat1on effects in an incommensurate phase of [N(CH3)4]2ZnCl4

A quadratic electrooptic coefficient rE11 and quadratic electrogyration coefficient μE11 in the incommensurate phase of [N(CH3)4]2ZnCl4 manifest a sharp peak at a temperature Tp, which is 1.5°C lower than the incommensurate transition point Ti of 24.0°C. It is noticeable that any appreciable enhancement of dielectric constants cannot be observed around Tp with the application of electric fields. Accordingly rP11 is enormously large compared with those of other dielectrics. This finding may be the first evidence that an incommensurate phase of a ferroelectric crystal can reveal characteristic physical properties. Brief discussion of the origin of these phenomena is made on a basis of the optical activity of this crystal. It is very likely that these phenomena are related to the onset of the nearly commensurate domains in an incommensurate phase.

A bond-charge calculation of the quadratic electro-optic effect in LiF

Calculations of the ionic contribution to the primary quadratic electro-optic coefficients, based on the Phillips-Van Vechten theory (1969) and the bond-charge model, are presented. Three contributions, namely a stretching of the bond, a rotation of the bond direction and a displacement of the bond charge, are shown to give comparable changes in the refractive index. The calculated results agree with the experimental data.

Orientation dependence of the phase modulation in a p-n junction GaAs/AlxGa1−xAs waveguide

Phase modulation has been measured in a reverse-biased P-i-N GaAs/AlxGa1−xAs double heterostructure with heavily doped (N, P∼1018 cm−3) AlxGa1−xAs layers. These measurements were performed at two wavelengths (1.09 and 1.15 μm), for both TE and TM modes and with light propagating in the [110] and [11̄0] directions. We found that the effective quadratic electro-optic coefficients R11 and R12 have approximately the same magnitude and sign. The values are −(40±10)×10−17 cm2/V2 and −(54±10)×10−17 cm2/V2 for λ=1.15 μm and λ=1.09 μm, respectively. The contribution of the plasma effect due to the free carrier is comparable and has the same sign.