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{112}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.     

Optimal crystal geometry and orientation in electric field sensing using electro-optic sensors

For optimal sensitivity in electric field measurements, electro-optic (EO) crystals are typically selected based on their EO coefficients and dielectric constants. However, the conventional figure of merit yields sensitivity predictions regarding EO materials that are inconsistent with experimental data. In this Letter, we demonstrate that depolarization effects, which are often ignored, can dramatically enhance responsivity depending on the shape and orientation of the EO crystal. For optimal sensitivity, these effects are best exploited in longitudinal EO sensors, where they yield an optical modulation depth that increases quadratically with crystal length.     

Benchmarking of electro-optic monitors for femtosecond electron bunches

The longitudinal profiles of ultrashort relativistic electron bunches at the soft x-ray free-electron laser FLASH have been investigated using two single-shot detection schemes: an electro-optic (EO) detector measuring the Coulomb field of the bunch and a radio-frequency structure transforming the charge distribution into a transverse streak. A comparison permits an absolute calibration of the EO technique. EO signals as short as 60 fs (rms) have been observed, which is a new record in the EO detection of single electron bunches and close to the limit given by the EO material properties.     

Integrated electro-optic platform using ferroelectric crystals with the point symmetry of orthorhombic mm2

We theoretically and numerically investigate the modulation efficiencies of integrated electro-optic (EO) modulators based on ferroelectric crystals with the point symmetry of orthorhombic mm2. An analytical expression describing the index-ellipsoid under the EO effect is derived, where all 5 non-zero linear EO coefficients of mm2-crystals are considered. As practical candidates for integrated EO platform, three mm2-crystals (KNbO₃, KTiOPO₄, and Ba₂NaNb₅O₁₅) that are well-established and commercially available are chosen for numerical simulations. The refractive-index (RI) changes caused by an external electric field applied to each crystal with an arbitrary direction are analyzed in detail for the given optical polarization states of input light wave. For each crystal, the modulation efficiency is evaluated in terms of the half-wave voltage required for a π-phase shift of input wave, which is compared with the established counterpart based on LiNbO₃. The results indicate that higher modulation efficiencies are achievable in the two schemes using KNbO₃ and Ba₂NaNb₅O₁₅ than those for other cases, meaning that either lower power-consuming or larger beam-window integrated EO devices are feasible.     

Electro-optic characterization of tetragonal (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 single crystals by a modified Sénarmont setup

The refractive indices of tetragonal (1−x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (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 LiNbO₃ 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.     

Frequency and wavelength dependencies of the electro-optic coefficients in SBN:60 single crystal

We report the dependence of the high and low-frequency values of the linear electro-optic (EO) coefficient r_c=r₃₃-(n_o/n_e)³r₁₃ of Sr_0.6Ba_0.4Nb₂O₆ (SBN:60) single crystal on the laser wavelength. The EO response has been carried out from dc to 150 MHz for four wavelengths ranging from 465 to 1321 nm. The clamped r^S and unclamped r^T coefficients have been determined and their dispersions as a function of wavelength have been established and discussed.     

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

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.     

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.     

Dispersion of electro-optic coefficients in sillenite crystals

The photorefractive crystals of the sillenite family (Bi₁₂SiO₂₀ or BSO, Bi₁₂GeO₂₀ or BGO, and Bi₁₂TiO₂₀ or BTO) that belong to the cubic 23 point group are optically active, and exhibit the piezoelectric, elasto-optic, electro-optic and electrogyration effect. In this paper we measure the dispersion of the electro-optic coefficient for all the crystals of the sillenite family in the visible spectral range (500–800 nm). For this we measure by ellipsometry the polarization properties of a beam transmitted in the transverse configuration under the action of an externally applied field. The experimental data are fitted with an analytical expression of the beam polarization to find the electro-optic coefficient. The results show a normal dispersion of the electro-optic coefficient in all three sillenite crystals, similarly to other electro-optic crystals.     

Design and fabrication of electro-optic waveguides with self-assembled superlattice films

This paper presents a strategy for fabricating low loss waveguide devices based on high electro-optic (EO) coefficient self-assembled superlattice (SAS) films, a new sort of polymeric films grown on SiO₂ film and coated with other polymeric films to form multi-layer EO waveguides structure without electric field poling. Firstly, the optical propagation loss induced by the absorption of electrodes is simulated and optimized to obtain both the low optical loss and the low drive voltage. Then this paper gives the scanned electron microscopic (SEM) images of the fabricated devices, the simulated and experimental images of the single guided mode, and the measured optical propagation loss of the EO waveguide devices of 1.0 dB/cm. Finally, the very great agreement between the simulated and measured results of propagation loss of devices is observed.     

铌酸锂晶体中飞秒激光脉冲线性电光效应及其色散补偿

针对铌酸锂晶体中飞秒激光脉冲线性电光效应, 研究了光学相位共轭 对群速度色散 以及一阶和二阶折射率色散的补偿方案. 结果发现, 在任意初始输入脉宽条件下, 这些色散基本上都能得到补偿, 输出脉冲波形基本上和输入脉冲相同. 在此方案中, 若同时在色散补偿铌酸锂晶体上对输出脉冲进行电光相位调制, 则在一定外加电场作用下, 输出脉冲的脉宽将进一步被压缩, 初始输入脉宽越小, 压缩程度越大.     

铌酸锂晶体中飞秒激光脉冲线性电光效应及其色散补偿

针对铌酸锂晶体中飞秒激光脉冲线性电光效应, 研究了光学相位共轭 对群速度色散 以及一阶和二阶折射率色散的补偿方案. 结果发现, 在任意初始输入脉宽条件下, 这些色散基本上都能得到补偿, 输出脉冲波形基本上和输入脉冲相同. 在此方案中, 若同时在色散补偿铌酸锂晶体上对输出脉冲进行电光相位调制, 则在一定外加电场作用下, 输出脉冲的脉宽将进一步被压缩, 初始输入脉宽越小, 压缩程度越大.     

Comparison of spatial resolution in internal and external electro-optic probing

A new method, based on zero point of longitudinal electric field, was used to determine the spatial resolution of internal and external electro-optic (EO) probing systems. An interdigital structure electrode was fabricated on GaAs substrate to examine the spatial resolution of internal and external EO probing system. Considering the air gap between the electrode under test and the probe tip, the result of EO probing was simulated which is well accorded with experiment. The result indicates that spatial resolution of less than 0.5 and 1 m are obtained in internal and external EO probing system respectively.     

Research of spatial resolution in external electro-optic probing

A new method, based on zero point of longitudinal electric field, was used to determine the spatial resolution of external electro-optic (EO) probing equipment. Considering the diffraction of Gauss beam, the result of external EO probing was simulated which was in accordance with the experiment. A spatial resolution <1 μm was demonstrated initially in our equipment using 650 nm laser diode as probe beam and semi-insulating GaP as probe tip.     

Intersubband electro-optic modulators for near and mid infrared applications

Optical transitions between conduction subbands of asymmetrical quantum-well structures can produce large second-order optical nonlinearities. In particular, it is possible to engineer asymmetrical quantum-well structures to have very large electro-optic (EO) coefficients. In this paper we study three alternative approaches to design and fabricate intersubband EO modulators, i.e. the Stark modulator, the quantum-interference (QI) modulator, and the carrier-density (CD) modulator. We show that near a given resonance the Stark modulator has the largest EO coefficient. However, the linear intersubband absorption limits the usability of this modulator to a very short device length. Far from resonance we found that the CD and the QI modulators are more efficient. Furthermore, we found that these modulators can be utilized for near-infrared modulation in the 1.3–1.5 μm spectral range. These modulators are almost unaffected by the linear intersubband absorption so that their efficiency can be very high. We present preliminary experimental results that demonstrate the operation of the QI modulator.     

A method for compensating multiple-reflection effect in measurement of electro-optic coefficient

An electro-optic (EO) coefficient can be evaluated from a modulated signal by applying an AC voltage to a plane-parallel sample in an interferometer. We proposed a method for compensating multiple-reflection of a light in the sample. The multiple-reflection causes errors in the evaluated EO coefficient. In measurement using a Mach-Zehnder interferometer, we analyzed the multiple-reflection and clarified its unfavorable effect. The effect could be avoided simply by selecting the incidence angle of the light on the sample. We confirmed this by measuring the EO coefficient of a KTiOPO₄ crystal.     

A semiclassical approach for electro-optic effect

In this article, we present a semiclassical approach for modeling of electro-optic (EO) effect. We calculate phase retardation between x and y polarizations of optical electric field when a transverse external electric field is applied. Our results are well agreed with experimental measurements. Moreover, we show when wavelength of optical signal decreases, the phase retardation increases.     

Study of the Hanle effect with the transverse component of the electron spin orientation in III–V semiconductors

The Hanle effect in n-GaAs and p-AlGaAs is studied in the longitudinal and transverse geometries of the experiment, in which the emission is recorded parallel and perpendicular to the spin direction of optically oriented electrons, respectively. The factors responsible for the error in determining the sign of the electron g factor in GaAs studied in the transverse geometry of the experiment are considered. It is shown that the results obtained from measurements of the transverse spin component of the orientation are useful in determining the parameters of semiconductor structures.     

Polarisation-insensitive strip-loaded waveguide for electro-optic modulators and switches

A polarisation-insensitive electro-optic (EO) waveguide consisting of a dye-doped TiO₂/SiO₂ slab and a SU-8 strip-loaded rib is designed and fabricated. By optimizing the refractive index and size of waveguide, a trade-off between polarisation-insensitive condition and large EO efficiency (optical field interaction with the EO material) is obtained. The average transmission loss of the waveguide is less than 2.0 dB/cm. A Mach-Zehnder (M-Z) interferometer intensity modulator based on this waveguide with excellent poling stability is fabricated and measured, exhibiting 7 V half-wave voltage with 1.8 cm EO interaction length and 2.7 cm total length. This strip-loaded structure is proved to be a valuable application in EO modulators and switches.     

Thermo-optic effects in electro-optic crystals used in an intensity-modulation system. – Application in LiTaO3

Linear electro-optic (EO) and thermo-optic (TO) effects are jointly considered on the basis of field-induced and temperature-affected perturbations of the operating point along the optical transmission curve of an EO-modulation system. In this framework, methods of EO measurements based on the frequency doubling appearing at the minimum-transmission point are formulated. Moreover, TO coefficients for various optical quantities, such as the refractive indices, n₀ and n_e, the spontaneous birefringence Δn⁽⁰⁾, the EO coefficient r, the half-wave voltage V_π, the optical phase retardation Γ, and the intensity modulation (IM) depth, m, are introduced and useful relationships between them are extracted. Also, applications of the above in the experimental field, with determinations of EO parameters and TO coefficients, are presented for the case of a congruent LiTaO₃ crystal. A comparison of the so-obtained experimental results with those derived from literature when a LiNbO₃ crystal is used demonstrates a number of advantages for the LiTaO₃-based system. PACS 78.20.Jq; 65.40.De