Linear Electro-optic Effect Research Articles

Electro-optic effect in hexagonal compounds RFeO<sub>3</sub>

The linear electro-optic effect is investigated in films of RFeO3 compounds (R = Y, Lu, Yb) possessing hexagonal symmetry. A general equation for the optical indicatrix of the film at arbitrary orientation of an external electric field is derived. The equation of the indicatrix in the principal axes, as well as the principal refractive indices, are determined for the particular case of an external electric field orientation along the [010] axis. Two novel optical axes are identified in the presence of an electric field. It was determined that two isonormal modes propagate in the film when light propagates along the [100] direction. The refractive indices associated with these modes were also found. The phase shift associated with the propagation of these modes and caused by the presence of an electric field is calculated. The shift is linear along the electric field, thereby demonstrating the Pockels effect.

High-Linearity Dual-Parallel Mach–Zehnder Modulators in Thin-Film Lithium Niobate

Microwave photonic (MWP) systems are inseparable from conversions of microwave electrical signals into optical signals, and their performances highly depend on the linearity of electro-optic modulators. Thin-film lithium niobate (TFLN) is expected to be an ideal platform for future microwave photonic systems due to its compact size, low optical loss, linear electro-optic effect, and high bandwidth. In this paper, we propose a TFLN modulator with a low voltage–length product (VπL) of 1.97 V·cm and an ultra-high-linearity carrier-to-distortion ratio (CDR) of 112.33 dB, using a dual-parallel Mach–Zehnder interferometer configuration. It provides an effective approach to fully suppress the third-order intermodulation distortions (IMD3), leading to 76 dB improvement over a single Mach–Zehnder modulator (MZM) in TFLN. The proposed TFLN modulator would enable a wide variety of applications in integrated MWP systems with large-scale integration, low power consumption, low optical loss, and high bandwidth.

Second-order electrogyration effect in BSO crystal

Using a non-holographic optical setup, we employed a Mueller–Stokes polarimeter to measure both the linear electro-optic and second-order electrogyration effects. The second-order electrogyration effect was observed in a Bi12SiO20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Bi_{12}SiO_{20}$$\\end{document} (BSO) crystal with a (110) cut. This response was found for the electric field applied both parallel and perpendicular to the [001] direction, where the values for the second-order electrogyration are 4.86×107pm2/V2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4.86\ imes 10^{7} \\, \ ext {pm}^{2}/\ ext {V}^{2}$$\\end{document} and 1.87×107pm2/V2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.87\ imes 10^{7} \\, \ ext {pm}^{2}/\ ext {V}^{2}$$\\end{document}, respectively. Additionally, the linear electro-optic coefficient γ41\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma _{41}$$\\end{document} was measured to be 1.17pm/V\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.17 \\, \ ext {pm/V}$$\\end{document} for 660.5nm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$660.5 \\, \ ext {nm}$$\\end{document}.

Determination of optimal directions of the wave vector of the phase holographic grating in cubic photorefractive crystal

The dependence of the change in the components of the inverse permittivity tensor of a cubic photorefractive Bi12SiO20 crystal on the direction of the wave vector of holographic grating in the crystal coordinate system has been studied. It is shown that, when recording a phase hologram, the largest change in the refractive index of Bi12SiO20 crystal is attained when the holographic grating wave vector is oriented along symmetrically equivalent 111 directions. The maximum possible modulation amplitude of the refractive index of a holographic grating with the wave vector oriented along the 110 directions is found to exceed that in the case of orientation along the 100 directions. The components of the inverse permittivity tensor of Bi12SiO20 crystal were calculated taking into account that a phase hologram is recorded under linear electro-optic, photoelastic, and inverse piezoelectric effects.

End-fire optical phased array for passive beam steering on thin-film lithium niobate.

Autonomous driving technology has put forward higher requirements for sensors, including light detection and ranging. An optical phased array (OPA) is a viable solution, and numerous efforts have been made in this area. For its outstanding optical properties such as linear electro-optic effect and low optical loss, lithium niobate exhibits great potential and unique advantages in solid-state light-emitting arrays. Here we propose and experimentally demonstrate an end-fire optical phased array on a thin-film lithium niobate (TFLN) for passive beam steering. Furthermore, based on this work, we propose a three-line optical phased array to achieve a larger beam steering range. Our results provide a solution for the integrated optical phased array that shows potential in sensing and imaging with reduced size and power.

Non-Hermitian linear electro-optic effect in three-dimensional materials

Non-Hermitian linear electro-optic effect in three-dimensional materials

Linear Electro-Optic Effect in 2D Ferroelectric for Electrically Tunable Metalens.

The advent of 2D ferroelectrics, characterized by their spontaneous polarization states in layer-by-layer domains without the limitation of a finite size effect, brings enormous promise for applications in integrated optoelectronic devices. Comparing with semiconductor/insulator devices, ferroelectric devices show natural advantages such as non-volatility, low energy consumption and high response speed. Several 2D ferroelectric materials have been reported, however, the device implementation particularly for optoelectronic application remains largely hypothetical. Here, the linear electro-optic effect in 2D ferroelectrics is discovered and electrically tunable 2D ferroelectric metalens is demonstrated. The linear electric-field modulation of light is verified in 2D ferroelectric CuInP2S6. The in-plane phase retardation can be continuously tuned by a transverse DC electric field, yielding an effective electro-optic coefficient rc of 20.28 pm V-1. The CuInP2S6 crystal exhibits birefringence with the fast axis oriented along its (010) plane. The 2D ferroelectric Fresnel metalens shows efficacious focusing ability with an electrical modulation efficiency of the focusing exceeding 34%. The theoretical analysis uncovers the origin of the birefringence and unveil its ultralow light absorption across a wide wavelength range in this non-excitonic system. The van der Waals ferroelectrics enable room-temperature electrical modulation of light and offer the freedom of heterogeneous integration with silicon and another material system for highly compact and tunable photonics andmetaoptics.

High-Bandwidth Lumped Mach-Zehnder Modulators Based on Thin-Film Lithium Niobate

Recently, lumped Mach-Zehnder Modulators (MZMs) have received renewed attention due to their potential for low power consumption and compact size. However, the practicality of lumped MZMs with conventional lumped electrodes (C−LEs) is limited by their lower electro−optical (EO) bandwidth. The reduction in EO bandwidth results from the inherent trade−off between EO bandwidth and half−wave voltage length product (VπL) within the C−LE architecture. This paper proposes a thin−film lithium niobate (TFLN)−based lumped MZM with capacitively−loaded lumped electrodes (CL−LEs). The purely linear EO effect of the LN eliminates the parasitic capacitance in the doped PN junction and enhances the EO bandwidth. Furthermore, the CL−LE structure can break the limitation between EO bandwidth and VπL inherent in the C−LE design. Simulations show the proposed device achieves a high EO bandwidth of 32.4 GHz and a low VπL of 1.15 V·cm. Due to the reduced capacitance and lower VπL, the power consumption of the device is as low as 0.1 pJ/bit. Simulation results indicate that the open−eye diagrams are achieved at 64 Gb/s for 1.5 mm TFLN lumped MZM, with an ER of 2.97 dB. Consequently, the proposed device architecture substantially enhances the performance of lumped MZMs, showing promise for application in short−reach optical interconnects within data centers.

Linear electro-optic effect in strontium barium niobate: A first principles study

We report a first-principles study of the linear electro-optic or Pockels effect in SrxBa1-xNb2O6 (SBN). SBN is an attractive material for building electro-optic modulators in silicon photonics as it has one of the highest known Pockels coefficients and can be integrated on Si. We investigate the microscopic mechanism behind the giant Pockels effect and find that the optical phonon contribution dominates the electro-optic response. We identify the phonon modes that have a significant contribution to the Pockels response and discuss the microscopic origin of the response. In addition, we analyze the contribution of the converse piezoelectric effect to the Pockels response. We find good agreement when comparing our results to available experiment.

Lithium niobate thin film electro-optic modulator.

The linear electro-optic effect offers a valuable means to control light properties via an external electric field. Lithium niobate (LN), with its high electro-optic coefficients and broad optical transparency ranges, stands out as a prominent material for efficient electro-optic modulators. The recent advent of lithium niobate-on-insulator (LNOI) wafers has sparked renewed interest in LN for compact photonic devices. In this study, we present an electro-optic modulator utilizing a thin LN film sandwiched between top and bottom gold (Au) film electrodes, forming a Fabry-Pérot (F-P) resonator. This resonator exhibits spectral resonance shifts under an applied electric field, enabling efficient modulation of reflected light strength. The modulator achieved a 2.3 % modulation amplitude under ±10 V alternating voltage. Our approach not only presents a simpler fabrication process but also offers larger modulation amplitudes compared to previously reported metasurface based LN electro-optic modulators. Our results open up new opportunities for compact electro-optic modulators with applications in beam steering devices, dynamic holograms, and spatial light modulators, and more.

Arbitrary electro-optic bandwidth and frequency control in lithium niobate optical resonators.

In situ tunable photonic filters and memories are important for emerging quantum and classical optics technologies. However, most photonic devices have fixed resonances and bandwidths determined at the time of fabrication. Here we present an in situ tunable optical resonator on thin-film lithium niobate. By leveraging the linear electro-optic effect, we demonstrate widely tunable control over resonator frequency and bandwidth on two different devices. We observe up to ∼50 × tuning in the bandwidth over ∼50 V with linear frequency control of ∼230 MHz/V. We also develop a closed-form model predicting the tuning behavior of the device. This paves the way for rapid phase and amplitude control over light transmitted through our device.

High-energy single-longitudinal-mode Q-switched double-cladding fiber laser based on the injection seeding technique.

This paper demonstrates a high-energy, single-longitudinal-mode (SLM), actively Q-switched fiber laser based on the injection seeding technique. The large-mode-area double-cladding fiber is used as the gain medium to improve energy storage. Simultaneously, by using the linear electro-optic effect of the negative uniaxial crystal (β-B a B 2 O 4, BBO), a matching frequency-shift-free Q-switch with high damage threshold and high extinction-ratio is designed. Before reaching the stimulated Brillouin scattering threshold, the SLM Q-switched pulses can be achieved with energy higher than 15µJ over a wide range of repetition rates from 10 to 80kHz, and the maximum output power reaches 1.2W at the repetition rate of 80kHz, which may be the highest output pulse energy for such a SLM Q-switched fiber laser so far, to our best knowledge.

One-Dimensional Modulational Instability of Broad Optical Beams In Photorefractive Crystals with Both Linear and Quadratic Electro-Optic Effects

One-Dimensional Modulational Instability of Broad Optical Beams In Photorefractive Crystals with Both Linear and Quadratic Electro-Optic Effects

Why phenomenological theory cannot be used to analyze the dynamics of dark photorefractive solitons

The currently used theory of both bright and dark spatial photorefractive (PR) solitons is a phenomenological theory. In the work we consider the dynamics of dark beams using a microscopic model based on the PR transport equations. It is generally believed that such a theory is more accurate. It has been found that these two approaches can give completely different predictions regarding the formation time of dark beams. The discrepancies can reach up to two orders of magnitude. An approximate analytical solution was presented and a new time constant was introduced taking into account crystals from three classes of PR materials: ferroelectrics, sillenites and semiconductors. Full Text: PDF References A. Katti, R.A. Yadav, Optical Spatial Solitons in Photorefractive Materials (Singapore, Springer, 2021) CrossRef E. DelRe, M. Segev, Ch. 23 in Self-focusing: Past and Present, ed. by R.W. Boyd, S.G. Lukishova, Y.R. Shen (New York, Springer, 2009). CrossRef M. Wichtowski, "On conformity of solutions for one-dimensional photorefractive screening solitons with the Kukhtarev–Vinetskii model", Appl. Phys. B 120, 527 (2015). CrossRef M. Segev, B. Crosignani, P. Di Porto et al., in Photorefractive Spatial Solitons, (Kluwer Academic Publisher, New York, 2002). DirectLink K. Zhan, Ch. Hou, S. Pu, "Temporal behavior of spatial solitons in centrosymmetric photorefractive crystals", Opt. Laser Technol. 43, 1274 (2011). CrossRef J. Maufoy, N. Fressengeas, D.Wolfersberger, G. Kugel, "Simulation of the temporal behavior of soliton propagation in photorefractive media", Phys. Rev. E 59, 6116 (1999). CrossRef A. Katti, M.S. Pande, "Formation characteristics of dark solitons in photorefractive crystals having both linear and quadratic electro-optic effect simultaneously", Opt. Quantum Electron. 55, 1132 (2023). CrossRef

Measurement of the voltage evolution on a load of X-pinch plasma system using the Pockels effect

A diagnostic system using the Pockels effect (linear electro-optic effect) has been developed to measure a voltage on a load of the SNU X-pinch device [Ryu et al., Rev. Sci. Instrum. 92, 053533 (2021)]. The sensor component of the diagnostic system comprises of a lithium niobate (LN) crystal and its mount. When the LN crystal is subjected to an external electric field, the refractive indices of the LN crystal change due to the Pockels effect, leading to a change in the polarization state of the propagating laser beam through the crystal. This concept allows the separation and shielding of electronic devices from the intense electric pulses generated by the X-pinch system. Furthermore, the compact size and high electric field tolerance of the LN crystal enable us to position the sensor in a close proximity to the load of the X-pinch, facilitating the measurement of voltage evolution on the load. In contrast to circuit-based voltage probes, our sensor possesses low inductance, allowing us to measure resistive-dominant voltage even in the presence of rapid current changes within the X-pinch system. In this paper, we outline the configuration of our voltage measurement system using the LN crystal within the X-pinch device and provide measurement results of the load voltage. Additionally, we explore the temporal evolution of the voltage in relation to the phase transition of the load.

Formation characteristics of dark solitons in photorefractive crystals having both linear and quadratic electro-optic effect simultaneously

Formation characteristics of dark solitons in photorefractive crystals having both linear and quadratic electro-optic effect simultaneously

Effect of CF4 additive on dynamic surface charge deposited on dielectric by helium atmospheric pressure plasma jet

Abstract The addition of active trace components to non-thermal plasmas effectively enhances their chemical activity and has attracted considerable academic attention in the plasma community. It is essential to quantitatively estimate the effect of active addition on the properties of the plasma–surface interaction (PSI). In this study, we focus on the fundamental properties of dynamic surface charge deposited by a He-atmospheric pressure plasma jet (APPJ) with 0%–2% CF4 additive. The charge distribution is measured by a reflective optical measurement platform based on linear electro-optic effect, and is calculated with surface charge density inversion algorithm. Results show that a higher CF4 concentration can shrink the region of surface charge accumulation. Polarity effect is observed in aspects of maximum charge density when the CF4 concentration gradually rises. The negative charge deposition is suppressed by the addition of CF4, nearly disappearing at 2% concentration. While the maximum density of positive charge rises to ∼25 nC cm−2 at 0.5% CF4 before it decreases to ∼10 nC cm−2. The dispersions of total surface charge at 0.5% and 1.5% additives indicate the unstable periodic bombardment of ionization waves in He/CF4 APPJ. The double effect of CF4 additive on the surface charges by He-APPJ is also discussed. These results provide fresh and deep insights into the interaction between dielectric surface modification and ionization waves that occurs in other plasmas processing fed with composite gases.

Lead-Free Perovskite Thin Films with Tailored Pockels-Kerr Effects for Photonics.

Pockels and Kerr effects are linear and nonlinear electro-optical effects, respectively, used in many applications. The modulation of the refractive index is employed in different photonic circuits. However, the greatest challenge is in photonic elements for quantum computing at room temperature. For this aim, materials with strong Pockels/Kerr effects and χ(2)/χ(3) nonlinear susceptibilities are necessary. Here, we demonstrate composition-modulated strong electro-optical response in epitaxial films of (Ba,Ca)(Ti,Zr)O3 perovskite titanate. These films are grown by pulsed laser deposition on SrTiO3. Depending on the ratios of Ca/Ba and Ti/Zr, films show high Pockels or Kerr optical nonlinearities. We relate the variable electro-optic response to the occurrence of nanopolar domains with different symmetries in a selected composition range. These findings open the route to easily implement nonlinear optical elements in integrated photonic circuits.

Experimental and Computational studies on Intramolecular charge transfer, Terahertz and Two photon absorption of 3-[(4-Nitrophenyl Azo)]-9H-Carbazole-9-Ethanol (NPACE) from their Vibrational spectra for Optical limiting and NLO applications

Non-linear optical (NLO) features of 3-[(4-Nitrophenyl Azo)]-9H-Carbazole-9-Ethanol (NPACE) chromophore were investigated by FT-IR, FT-Raman, and UV–visible spectra aided by Density Functional Theory (DFT) using the B3LYP/6–311++G(d,p) basis set of Gaussian 16 W package. It is observed from the DFT calculation that the slight increase in the endocyclic angle of C13 -C14 -C15 and the reduction in exocyclic angle of N40 –N39 -C14 and C15 -C14 –N39 ascertained by experimental XRD values indicating the intramolecular charge-transfer interaction between the carbazole and nitrophenyl group through the diazo bridge. The vibrational contribution to the linear electro-optic effect is 15% of the total hyperpolarizability being calculated at B3LYP/6–311++G (d, p) for the NPACE molecule. It is also observed that the 8a, 19a, and 19b modes of the carbazole ring and the 8a, 8b, and 19b modes of the phenyl ring are found to be simultaneously and intensely active in IR and Raman spectra explaining the charge transfer interactions throughout the molecule. The low value of the HOMO- LUMO energy gap (2.5843 eV) and the deviation between the measured absorption wavelength (3.36 eV) from the computed (3.87 eV), both these facts substantiate the intramolecular charge transfer. The polarizability and first-order hyperpolarizability were calculated as 6.48 × 10-24 and 3.8 × 10-29 esu, respectively. The second harmonic generation (SHG) measurement experiment of NPACE was carried out using the powder method. The SHG efficiency is measured in comparison with the urea standard. The calculated torsional mode at 20 cm−1 is in excellent quantitative agreement with the experimentally determined terahertz absorption peak. The two-photon absorption coefficient of NPACE was estimated to be 0.9 × 10-11 mW−1, which is mainly due to the D-π-A type of molecular structure, and the optical limiting threshold for NPACE was estimated to be 1.52 × 1013 Wm−2 enabling this material as a potential candidate for optical limiting applications.

Strain engineering of the electro-optic effect in polycrystalline BiFeO3 films [Invited

Electro-optic thin film materials, which change their refractive index upon the application of an electric field, are crucial for the fabrication of optical modulators in integrated photonic circuits. Therefore, it is key to develop strategies to tune the linear electro-optic effect. Strain engineering has arisen as a powerful tool to optimize the electro-optic coefficients in ferroelectric thin films. In this report, the electro-optical properties of polycrystalline bismuth ferrite (BiFeO3) thin films are studied. The electro-optic coefficients (reff) of low-cost solution-processed BiFeO3 films under different substrate-induced thermal stress are characterized using a modified Teng-Man technique in transmission geometry. The influence of poling state and substrate stress on the electro-optical properties are discussed. The films show a notable piezo-electro-optic effect: the effective electro-optic coefficient increases both under compressive and tensile in-plane stress, with compressive stress having a much more profound impact. Electro-optic coefficients of 2.2 pm/V are obtained in films under a biaxial compressive stress of 0.54 GPa.