Quadratic Electro-optic Coefficients Research Articles

Significantly enhanced transmittance and EO property in PMN-PT via optimized two-step pressure-free sintering

It is a great challenge to prepare Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN-PT) ceramics of very high transparency with only oxygen atmosphere pressureless sintering process. To address this issue, this work proposed an optimal low-cost two-step oxygen atmosphere sintering process with a first step at high temperature (T1) for minutes, followed by a second step at lower temperature (T2) for hours without applied pressure. High transmittance of 70 % in the near-infrared wavelength was achieved by our novel two-step process, which far exceeds the performance of PMN–PT ceramics prepared by only oxygen atmosphere sintering process reported in the past and demonstrates comparable performance compared to the costly hot-pressing sintering process. Meanwhile, it shows a high quadratic electro-optic (EO) coefficient of 42.1 × 10−16 m2 V−2, which is meaningful for applications in EO devices. Furthermore, the effect of the temperature difference between the first and second sintering step on the microstructure, transmittance, domain structure, ferroelectric and dielectric property, and polarization switching were discussed. The enhanced transparency is mainly attributed to the higher relative density, and weaker photoluminescence effect with lesser light absorption loss at optimal T1-T2. The improved EO property is due to greater polarization response originating from the interaction of defect dipoles and nanodomains. Such a process should facilitate the cost-effective preparation of other transparent electro-optic materials for practical applications.

La-doped PMN–PT transparent ceramics with ultra-high electro-optic effect and its application in optical devices

Transparent electro-optic (EO) ceramics of La-doped 0.75Pb(Mg_1/3Nb_2/3)O₃–0.25PbTiO₃ (0.75PMN–0.25PT) were prepared successfully. High transparency of 69% in the near-infrared (IR) wavelength (1550 nm) was achieved at 2 mol% La doping, meanwhile it shows an extremely high quadratic EO coefficient of 45.4×10⁻¹⁶ m²·V⁻², which is indispensable for applications in EO devices. The distribution of a polar nanodomain structure of the samples experiences disorder–order–disorder evolution in a La doping range. It is found that a parallelly-stacked polar nanodomain structure with an easier and faster polarization switching in the 2 mol% La-doped sample suggests that an ordering distribution of polar nanoregions would be critical to inducing large EO effect, transparency, and piezoelectric response. A triple-cavity tunable optical filter (TOF) with a single transmission peak and a tuning voltage below 30 V in a tuning range of 190–197 THz was designed based on our ceramics. The work is believed to bridge the relationship among doping-engineering, EO properties, and polarization behavior, which would guide the further optimization of transparent EO ceramics.

Unveiling the coupling effect of strain behavior and electro-optic property in nanodisordered KTN crystal

High-performance electro-optic (EO) crystals play a key role in optical communication and information processing. Potassium tantalate niobate (KTa1−xNbxO3, KTN) crystals advantageously have an ultrahigh quadratic electro-optic (QEO) coefficient and a wide transparency range, and their excellent QEO properties are closely related to polar nanoregion (PNR)-related polar units. Owing to the PNR-related polar units, KTN crystals have excellent strain properties, which makes them a potential multifunctional material. However, the relationship between strain behavior and QEO properties in nanodisordered KTN crystals has rarely been reported. The promotion of EO activity by regulating the PNRs-related polar units still needs to be studied. Here, we study the coupling effect of strain behavior and QEO properties in KTN crystals. The QEO, elastic-optic, electrostrictive, and elastic coefficients of KTN crystals are characterized, and the strain–QEO property coupling relation is established. The results show that the strain-induced QEO response significantly affects the QEO properties. The existence and response of PNRs near ferroelectric–paraelectric phase transition are demonstrated by variable-temperature x-ray diffraction and Raman spectroscopy. Combined with the heating and cooling QEO response time tests, the response of PNRs is shown to be an important reason for the enhancement of the QEO response of KTN crystals through the promotion of the strain-induced QEO response. This study provides guidance for clarifying the origin of the QEO properties of nanodisordered KTN crystals and is beneficial for further improving the EO properties of perovskite crystals by manipulating the strain behavior.

Continuous control of polarization state and tunable dual-channel optical communication based on highly transparent PMN-PT electro-optic ceramics

Transparent ferroelectric materials have excellent electro-optic properties, suitable to be used to develop high-performance optical communication devices. La-doped 88Pb(Mg1/3Nb2/3)O3–12PbTiO3 (88PMN-12PT) transparent ceramics with excellent comprehensive performances, including high transparency of 70.5% at near-infrared wavelength (close to its theoretical value), large quadratic electro-optic coefficient of 23.6 × 10−16 m2 V−2, low half-wave voltage (Vπ) of 146 V, and good extinction ratio of 34 dB, are successfully prepared in this paper. Based on the electro-optic effect of PMN-PT transparent ceramics, laser polarization state is transformed continuously from linear polarization to elliptical polarization, later to circularly polarization by applying electric field. Furthermore, dual-channel optical communication with a tunable laser intensity ratio is first reported here. Results indicate that PMN-PT transparent ceramic is a promising candidate for electro-optic material in polarization controller, optical switch, and information monitor in optical communication.

Effects of Ba2+doping on microstructure and properties of PLMNT electro-optic ceramics fabricated by hot-pressed sintering process

A series of highly transparent electro-optic (EO) ceramics Pb0.975-xBaxLa0.025(Mg1/4Nb1/2Ti1/4)0.99375O3 with the Ba2+ content of 0, 0.005, 0.01, 0.02, 0.04 were fabricated through the vacuum/oxygen hot-press sintering process. The effects of the barium substitution on the material phase transition, transmittance, dielectric, ferroelectric and electro-optic properties have been investigated and analyzed. With the Ba2+ content increasing, the shape of the ferroelectric hysteresis loop changed from rectangular to slim, the values of remnant polarization (Pr) and coercive electric field (Ec) decreased obviously. The maximum reduction of Pr can reach up to ∼89.8%. All the samples present the high transparency of ∼68% in the near infrared wavelength. The quadratic EO coefficients declines slightly while the Ba2+ content increasing. When the x is 0.01, the sample shows a relatively larger quadratic EO coefficient of ∼30.42 × 10−16 (m/V)2 and a lower Pr value of ∼2.08 μC/cm2, which promise the material a hopeful application in EO modulator.

Enormous electro-optic effect in paraelectric nanodisordered KTa1-xNbxO3 crystal.

Recent experiments have revealed that the order of the electro-optic (EO) effect depends on the frequency of electric field in paraelectric nanodisordered KTa1-xNbxO3 (KTN) crystal. Through the dielectric frequency spectrum under the bias electric field, enormous linear and quadratic EO effects were discovered at the resonance frequencies, which changed the perception that only the quadratic EO effect exists. Applying just a small AC electric field of 6 V/mm, the effective linear EO coefficient reached 478 pm/V at 609 kHz, and the effective quadratic EO coefficient reached 4.39*10-13m2V-2at 302 kHz. The reason why an extremely low electric field results in an enormous EO coefficient is attributed to the resonance between the polar nanoregions (PNRs) and the electric field, induced by the field-driven reorientation of free dipoles on the boundary of the PNRs. In addition, the order of EO effect depending on the frequency of electric field was attributed to the motion modes of the PNR. This finding improves the understanding of how the EO effect is caused by field-driven PNR dynamics, but also provides a basis for the development of EO devices.

Giant electro-optic coefficient in a graphene oxide film.

The electro-optic effect is an important mechanism for actively tuning the refractive index of materials. This effect has various important applications in communication, switching, modulation, and nonlinear optics. This research measured the quadratic electro-optic coefficient for a graphene oxide (GO) film with ellipsometry spectroscopy. The results show that this coefficient is about three orders of magnitude greater than that of other materials. The GO film with its giant electro-optic Kerr coefficient can improve devices based on this effect. For example, it can decrease power consumption and the complexity of these devices due to the need for a lower electric field. In addition, birefringence is obtained of about Δn = 0.08 at 730 nm, which can lead to promising improvements in commercial devices, such as the reduction of working voltage below 10 V.

Measurement of the Quadratic Electro-Optic Coefficient of KTN Crystal with an Electro-Optic Modulation System in the Presence of Polar Nano-Regions

An electro-optic modulation system was adopted for measuring the quadratic electro-optic coefficient of KTN crystal. Theoretical analysis and experimental results verified the feasibility of this method. The quadratic electro-optic coefficient of a KTN crystal chip, which has a Curie temperature of 0 °C, was measured using this system in the temperature range of 2 °C to 18 °C (Tc = 0 °C). The influences of temperature, AC voltage and frequency on the quadratic electro-optic coefficient were discussed. It was found that the relaxation effect of PNRs (polar nano-regions) played an important role in the determination of the quadratic electro-optic coefficient of KTN crystal.

Effect of rare earth additives on the properties of the PLMN-13PT:RE transparent ceramics

The transparent relaxor ferroelectric ceramics of the system lanthanum modified lead magnesium niobate (PLMN-13PT) have been investigated for a variety of electro-optic, properties; good electro-optic switching times and modest half-wave voltages. In this work, the dependence of microstructural, structural, dielectrical, optical, and electro-optical properties in function of Rare Earth (RE=Tm3+, Nd3+, Yb3+, Er3+ and Ho3+) has been reported. PLMN-13PT:RE with excellent properties were obtained, highlighting the electrical, optical, and electrooptical properties, suitable for the fabrication of multifunctional devices. The most prominent or important feature is the largest quadratic Electro-optic coefficient achieved ((9.37±0.39)×10−16m2/V2) corresponding to PLMN-13PT:Ho transparent ceramics. This result in addition to the electrical and photoluminescence properties becomes a promising alternative to building multifunctional devices.

Coupled InGaAs Quantum Dots for Electro-Optic Modulation

We investigated the growth of vertically coupled In0.75Ga0.25As quantum dots (QDs) by varying the GaAs spacer thickness (d). Vertically-aligned triple-layer QDs of uniform size and highest accumulated strain are formed with d = 5 nm. The electroluminescence (EL) characteristics for In0.75Ga0.25As QDs show an emission spectrum at optical wavelength (λ) of 1100−1300 nm. The EL spectra exhibit the highest optical gain at λ ~ 1200 nm, and the narrowest FWHM = 151 nm of the sample with d = 5 nm at injection current = 20 mA. Fabry–Perot measurements at λ = 1515 nm of TE and TM polarizations were carried out to investigate the electro-optic modulation for a single-mode ridge waveguide consisting of vertically-coupled triple-layer In0.75Ga0.25As QDs (d = 5 nm). The linear (r) and quadratic (s) electro-optic coefficients are r = 2.99 × 10−11 m/V and s = 4.10 × 10−17 m2/V2 for TE polarization, and r = 1.37 × 10−11 m/V and s = 3.2 × 10−17 m2/V2 for TM polarization, respectively. The results highlight the potential of TE/TM lightwave modulation by InGaAs QDs at photon energy below energy band resonance.

Precise Measurements of the Quadratic Electro-Optic Effect in KH2PO4 Crystals Using a Sénarmont-Type System.

This paper presents precise measurements of the temperature dependencies of the quadratic electro-optic coefficients and in KH2PO4 crystals. In addition to traditional electro-optic coefficients describing changes in the function of an applied electric field, intrinsic coefficients, defined in terms of induced polarization, are also considered. Both intrinsic coefficients decrease with increases in temperature, but the relative temperature changes are of different orders of magnitude: 10−4 and 10−3 K−1. A Sénarmont-type setup was used for the electro-optic measurements. To achieve the best accuracy, a new approach was developed, in which, instead of using only one specific point on the modulator’s transmission characteristic, the operating point is changed during the measurements.

Determining the Quadratic Electro-Optic Coefficients for Polycrystalline Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) Using a Polarization-Independent Electro-Optical Laser Beam Steerer

A polarization-independent electro-optical (EO) laser beam steerer based on a bulk relaxor ferroelectric polycrystalline Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) was developed in this study to steer light ranging from visible to mid-IR wavelengths. A large number of the resolvable spots was achieved with this EO steerer. A Fourier-transform infrared (FTIR) spectroscopy was employed to determine the refractive index of the polycrystalline PMN-PT over a wide range of optical wavelengths. Besides measuring the transmission of this material, the capacitance bridge analysis was used to characterize the effect of temperature on the dielectric constant of PMN-PT. The performance of the steerer over a variety of wavelengths was simulated using COMSOL Multiphysics. The deflection angle for the wavelengths of 532, 632.8, 1550, and 4500 nm was measured in the lab in terms of mrad.mm/kV at two different temperatures and compared to the simulation results. The quadratic Kerr electro-optic coefficient and the halfwave electric field were determined for those four wavelengths at two different temperatures. The results showed polycrystalline PMN-PT has a large quadratic EO coefficient for visible light, almost as large in the near IR, but drops significantly in the mid-IR. No significant temperature dependency for the EO coefficients was observed for any of those four wavelengths.

Potassium tantalate niobate (KTN) crystal-based polarization-modulated 3D ladar with a large field of view.

An innovative 3D ladar that utilizes potassium tantalate niobate (KTN) crystal as a polarization modulator is proposed in this Letter. The optical isotropy of KTN in cubic phase can effectively suppress the range errors induced by the incident angles of collected beams in 3D imaging. The giant quadratic electro-optic coefficient can dramatically lower the voltage that is required to modulate the polarization so that a high voltage amplifier with less noise can be used to improve the ranging performances. By virtue of these two advantages, a range error of 4.8 cm and a range precision of 4.4 cm at 15 m have been achieved under a large field of view of 20° (about 0.35 rad) and a maximum detection range without ambiguity of 60 m.

Electro-optic eigenfrequency tuning of potassium tantalate-niobate microresonators

Eigenfrequency tuning in microresonators is useful for a range of applications including frequency-agile optical filters and tunable optical frequency converters. In most of these applications, eigenfrequency tuning is achieved by thermal or mechanical means, while a few non-centrosymmetric crystals such as lithium niobate allow for such tuning using the linear electro-optic effect. Potassium tantalate-niobate ($\mathrm{KTa}_{1-x}\mathrm{Nb}_{x}\mathrm{O}_{3}$ with $0\leq x \leq1$, KTN) is a particularly attractive material for electro-optic tuning purposes. It has both non-centrosymmetric and centrosymmetric phases offering outstandingly large linear as well as quadratic electro-optic coefficients near the phase transition temperature. We demonstrate whispering-gallery resonators (WGRs) made of KTN with quality factors of $Q>10^{7}$ and electro-optic eigenfrequency tuning of more than 100 GHz at $\lambda=1040\,$nm for moderate field strengths of $E=250\,$V/mm. The tuning behavior near the phase transition temperature is analyzed by introducing a simple theoretical model. These results pave the way for applications such as electro-optically tunable microresonator-based Kerr frequency combs.

Temporal behaviour of bright solitons in photorefractive crystals having both the linear and quadratic electro-optic effect

Abstract We investigate the characteristics of formation or time evolution of optical spatial solitons in novel photorefractive media having both the linear and quadratic electro-optic effect. We have derived a one dimensional time dependant wave propagation equation in biased photorefractive media having both the linear and quadratic electro-optic effect. The variation of soliton width with time is investigated for different values of peak intensity ratio and it is shown that these bright solitons can exist both in the quasi steady state and steady state regimes for high saturation values. Two distinct regimes of intensity ratio are identified where the soliton formation characteristics are different. Only steady state solitons are formed if the intensity ratio is small. Soliton characteristics like the initial soliton width, steady state soliton width, and quasi steady state soliton width are investigated for both regimes and found to depend on as varying functions of the intensity ratio. We also find that the individual magnitudes of the linear and quadratic electro-optic coefficients affect the temporal characteristics of formation of the solitons. Appropriate example has been taken for an illustration of our results.

Optical effects induced by epitaxial tension in lead titanate

Single-crystal-type epitaxial films of perovskite oxide ferroelectrics are attractive for integrated photonic applications because of the remarkable optical properties and effects in ferroelectrics. The properties of the films may be influenced by epitaxial strain arising from the film-substrate mismatch. Here, dramatic strain-induced changes of the absorption and refraction are experimentally detected by spectroscopic ellipsometry in epitaxial films of archetypical ferroelectric PbTiO3. Comparison of the properties of a tensile-strained film with those of reference films and crystals reveals that epitaxial tension produces blueshifts of the primary above-bandgap absorption peaks by 1 eV and a decrease in the refractive index by 0.5 in the transparent spectral range. The obtained quadratic electrooptic and effective elastooptic coefficients exceed the bulk values by orders of magnitude. The experimental observations prove that epitaxy is a powerful tool for engineering unprecedented optical properties that may enable future photonics innovations.

Application of polarimetric technique for determining the sign of quadratic electro-optic coefficients in crystals

So-called polarimetric methods are based on measurements of the intensity of light emerging from a modulator composed of a “sandwich” of investigated crystal placed between polarizer and analyzer. The polarimetric technique is known for its high accuracy in determining absolute values of electro-optic coefficients; however, the method is considered unable to find their signs. In this paper, we propose an examination of changes in the modulated signal phase that result from a controlled shift through the transmission characteristic of the modulator. We show that analysis of the changes allows one to obtain the sign of the coefficients. The sensitivity of the method is examined in measurements of quadratic electro-optic coefficients. It is found that the technique may be easily applied to crystals for which relatively low values of the coefficients, i.e., of the order of magnitude 10−20 m2/V2, are observed. Configurations where the light beam is sent along the optical axis and perpendicularly to the axis in a uniaxial crystal are considered. Examples of measurements of the quadratic electro-optic coefficients g1111−g1122 in KDP and ne3g3333−no3g1133 in DKDP are presented.

Fabrication and electro-optic properties of 0.9Pb[(Mg,Zn)1/3Nb2/3]O3–0.1PbTiO3 transparent ceramics by a conventional sintering technique

0.9Pb[(Mg1−xZnx)1/3Nb2/3]O3–0.1PbTiO3 (x = 0–0.4) ceramics were fabricated by a conventional sintering technique. The ceramics became transparent at x = 0, 0.1, and 0.2, and the transmittances were 47, 43, and 53% at an infrared wavelength of 1310 nm, respectively. Birefringence of the transparent ceramics was quadratically increased as a function of electric field, with some deviations observed beyond certain electric fields at x = 0 and 0.2. An effective quadratic electro-optic (EO) coefficient was calculated with a half-wave electric field, and it was 6.30, 25.5, and 13.8 × 10−16 m2/V2 at x = 0, 0.1, and 0.2, respectively. The large EO effect at x = 0.1 was associated with the composition where a transition from a relaxor state to a ferroelectric state occurred. Microstructure, density, refractive index, and dielectric and ferroelectric properties were also investigated.

Method for in-depth characterization of electro-optic phase modulators.

A flexible method to measure the modulation efficiency and residual amplitude modulation, including non-linearities, of phase modulators is presented. The method is based on demodulation of the modulated optical field in the optical domain by means of a heterodyne interferometer and subsequent analysis of the I&Q quadrature components of the corresponding RF beat note signal. As an example, we determine the phase modulation efficiency and residual amplitude modulation for both the TE and TM modes of a GaAs chip-based phase modulator at the wavelength of 1064 nm. From the results of these measurements, we estimate the linear and quadratic electro-optic coefficients for a P-p-n-N GaAs/AlGaAs double heterostructure.

Electro-optic effect in SrTiO3 and Sr1–x Ca x TiO3 (x = 0.014)

The results of the investigation of the quadratic electro-optic effect in Sr1–xCaxTiO3 with x = 0.014 (SCT) and in nominally pure SrTiO3 (STO) at room temperature in applied direct-current (dc) and alternating-current (ac) electric fields have been presented. It has been shown that the quadratic (in polarization) electro-optic coefficients of STO and SCT crystals coincide within the accuracy of the determination (±5%). It has been found that, in nominally pure STO measured in a dc electric field, there is a relaxation of the electro-optic effect with a relaxation time τ ≈ 30 s due to the formation of a space charge in the sample. No similar effect in SCT has been observed. A possible mechanism for the formation of a space charge in STO and SCT has been discussed.