Nonlinear Electro-optical Effects Research Articles

Microdisk modulator-assisted optical nonlinear activation functions for photonic neural networks

On-chip implementation of optical nonlinear activation functions (NAFs) is essential for realizing large-scale photonic neural chips. To improve the reconfigurability and enrich the functions of photonic neural network (PNN), an NAF unit with a unique capability of performing multiple types of NAFs is highly preferred. In this work, we propose and experimentally demonstrate a microdisk modulator (MDM)-assisted NAF unit, in which multiple types of electro-optic NAFs with a high response speed and multiple types of all-optical NAFs with a low latency and reduced power consumption are performed in a single device. The fabricated MDM has an add-drop configuration, in which a lateral PN junction is incorporated to achieve high-speed resonance wavelength tuning. With the use of the high-speed nonlinear electro-optic effect, three different kinds of electro-optic NAFs including sigmoid function, radial basis function (RBF), and negative rectified linear unit (ReLU) function are realized by exploiting the free-carrier dispersion effect on silicon. Moreover, thanks to the strong optical confinement in the disk cavity, all-optical NAFs can be performed by exploiting the thermo-optic effect on silicon. In the experiment, four different kinds of all-optical NAFs including softplus function, RBF, clamped ReLU function, and leaky ReLU function are demonstrated. With the use of the realized clamped ReLU function, a convolutional neural network is simulated to perform a handwritten digit classification benchmark task, and an accuracy as high as 98 % is demonstrated. Thanks to its strong electro-optic and thermo-optic effects, the proposed MDM provides a unique capability of performing multiple types of electro-optic and all-optical NAFs, which is potential to be served as a flexible nonlinear unit in large-scale PNN chips.

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.

Power Dither Technique for Measuring the RF Half-Wave Voltage of a Silicon Mach–Zehnder Modulator

A novel method to measure the radio frequency(RF) half-wave voltage of the silicon Mach-Zehnder modulator (SMZM) is presented based on a low-frequency power dither signal. In our method, the power dither is applied to the thermo-optic phase shifter built into the SMZM, and an RF modulation signal applied to the SMZM is produced by a pulse-code generator. Then, a low-frequency monitor photodiode is used to detect the output signal of the SMZM, and a pair of orthogonal trigonometric functions with the same frequency as the power dither signal is constructed. This performs the cross-correlation integral operations with the output signal of the SMZM. The aforementioned integral results versus different amplitude RF modulation signals are plotted as two third-order polynomial functions, and the intersection point of the third-order polynomial functions corresponding to the RF voltage is the half-wave modulation voltage. Compared with the conventional methods, this new method not only removes the electrical absorption effect and nonlinear electro-optic effect of the SMZM-induced measurement error but also improves measurement accuracy and reduces measurement complexity.

Engineering tunability through electro-optic effects to manifest a multifunctional metadevice.

Ultrafast modulation of the refractive index exhibits either linear or nonlinear electro-optic (EO) effect, which is extensively utilized in tunable photonic circuits. Silicon, a mature material for on-chip devices, lacks a strong electro-optic (EO) Pockels effect. Utilization of the Pockels effect alters the intrinsic property (refractive index) of the material that manifests tunability and offers expanded functionalities. Driven by the limited space constraints in data storage, sensing, and imaging applications, we propose an electrically tunable meta-device whose resonance wavelength and focal length can be tuned by varying applied electric fields in the visible range. The fundamental unit of a metalens is the barium titanate (BTO) diffractive optical element placed on indium titanium oxide (which serves as an electrode) with SiO2 as the substrate. The metalens' tunability is characterized by point spread function (PSF), full-width half-maximum (FWHM), and imaging bandwidth that demonstrates the tuning of resonance wavelength and focal length. Moreover, polarization-insensitive meta-holograms are realized at a wavelength of 633 nm without utilizing propagation and Pancharatnam–Berry (PB) phase. The proposed study can find exciting applications in machine vision, broadband microscopy, and spectroscopy.

Characterization of short-range molecular interaction by empirical solvent polarity scale to analyze the Kerr effect of nematic liquid crystals in the isotropic phase

It is well known that a relatively large Kerr effect in the isotropic phase of nematic liquid crystals (NLCs) is related to the existence of short-range ordering (SRO). Thus, the conversion of the long-range ordering (LRO) behavior in the nematic phase to the SRO in the isotropic phase of NLCs can characterize the nonlinear electro-optic Kerr effect. To show conversion from LRO to SRO, we employ an empirical solvent polarity scale (ETN). Interestingly, ETN originates from the solvatochromic polarity (SP) parameters, which demonstrates the quantitative value for describing the molecular interaction in each temperature point, even in the isotropic phase of NLCs. Our results show that the higher ETN value leads to a larger Kerr constant (B) owing to the larger short-range molecular interaction between rigid rod-like NLCs. To demonstrate a linear relationship of the B value with the ETN and SP parameters, a new correlation is introduced for the first time. Our investigations and newly introduced parameters strongly indicate that short-range molecular interactions still exist in the isotropic phase of NLCs, even when the macroscopically observable LRO behaviors disappear.

Study on auto bias control of a silicon optical modulator in a four-level pulse amplitude modulation format.

Recently, the high-speed silicon optical modulator has played a greater and greater role in optic fiber communication. Due to the silicon material nonlinear electro-optic effect, the quadrature (Quad) bias point of the modulator is difficult to be locked precisely. In this paper, a novel automatic bias control (ABC) method for four-level pulse amplitude modulation format silicon modulator is presented. First, a sinusoidal dither signal is applied to the modulator DC bias, and the normalized output optical signal function, which is modulated by the dither signal, is obtained. Then, a pair of orthogonal reference functions is created, whose numerical size is equal to the absolute value of sinusoidal and cosine functions so that the frequency is the same as the dither signal. Through the cross-correlation integral operation between the normalized and reference functions above, we find that the zero point of the above integral operation is the best Quad bias point through numerical simulation and experiment. The phase accuracy error of ABC is lower than 2deg, and it satisfies the business specifications of a high-speed silicon optical modulator.

Non-linear electro-optical effects in the study of the helical smectic liquid crystals

Measurements of the non-linear electro-optical effects for the well-known prototype liquid crystal material (MHPOBC) are presented. The method to identify liquid crystalline phases and to determine temperatures of phase transitions based on the analysis of the second harmonic component of electro-optical response spectra is used. Applying that method, the values of the frequency () at which the second harmonic electro-optic response (EOR) possesses an extremum are determined for each smectic phase. We suggest that this characteristic frequency correspond to the phase-type mode processes. Furthermore, we show that the usually neglected results on heating can be useful in discussions of dynamical behaviour of second harmonic EOR in case of smectic phases.

Two-dimensional function photonic crystal

Photonic crystal is a kind of periodic optical nanostructure consisting of two or more materials with different dielectric constants, which has attracted great deal of attention because of its wide range of potential applications in the field of optics. Photonic crystal can be fabricated into one-, or two-, or three- dimensional one. Among them, the two-dimensional photonic crystal turns into a hot focus due to its fantastic optical and electrical properties and relatively simple fabrication technique. Since the tunable band gaps of two-dimensional photonic crystals are beneficial to designing the novel optical devices, to study their optical and electrical properties for controlling the electromagnetic wave is quite valuable in both theoretical and practical aspects. In this work, we propose a new type of two-dimensional function photonic crystal, which can tune the band gaps of photonic crystals. The two-dimensional function photonic crystal is different from the traditional photonic crystal composed of medium columns with spatially invariant dielectric constants, since the dielectric constants of medium column are the functions of space coordinates. Specifically, the photorefractive nonlinear optical effect or electro-optic effect is utilized to turn the dielectric constant of medium column into the function of space coordinates, which results in the formation of two-dimensional function photonic crystal. We use the plane-wave expansion method to derive the eigen-equations for the TE and TM mode. By the Fourier transform, we obtain the Fourier transform form (G) for the dielectric constant function (r) of two-dimensional function photonic crystal, which is more complicated than the Fourier transform in traditional two-dimensional photonic crystal. The calculation results indicate that when the dielectric constant of medium column is a constant, the Fourier transforms for both of them are the same, which implies that the traditional two-dimensional photonic crystal is a special case for the two-dimensional function photonic crystal. Based on the above theory, we calculate the band gap structure of two-dimensional function photonic crystal, especially investigate in detail the corresponding band gap structures of TE and TM modes. The function of dielectric constant can be described as (r) = kr + b, in which k and b are adjustable parameters. Through comparing the calculation results for both kinds of photonic crystals, we can find that the band structures of TE and TM modes in two-dimensional function photonic crystals are quite different from those in traditional two-dimensional photonic crystal. Adjusting parameter k, we can successfully change the number, locations and widths of band gaps, indicating that the band gap structure of two-dimensional function photonic crystal is tunable. These results provide an important design method and theoretical foundation for designing optical devices based on two-dimensional photonic crystal.

Can molecular ferroelectrics challenge pure inorganic ones?

Molecular materials have attracted much attention due to their advantages of easy modification and fabrication, environmentally friendly and less energy-cost processing, transparent, light weight, mechanical flexibility and possible multi-functionalities, compared to their counter parts of pure inorganic or metallic ones, and many functionalities and properties have been discovered and realized inmolecule-basedmaterials [1–4]. Ferroelectrics, as an important class of multifunctional electroactive materials possessing electrically or mechanically switchable, temperature-dependent polarization and/or tunable dielectric responses and nonlinear electro-optic effects, have many applications in temperature sensing, data storage, mechanical actuation, energy harvesting, electromagnetic wave manipulation, and so on [5–8]. The first ferroelectrics, Rochelle salt, which was discovered in 1920–1, is in fact a molecular material, and later a few other molecular systems, such as the well-known potassium dihydrogen phosphate and tri-glycine sulfate, were discovered and developed. However, the rapid development of ferroelectrics took place only after the discovery of pure inorganic ferroelectrics, perovskite barium titanate (BTO) and lead zirconate titanate, because of their large spontaneous polarization (PS), high Curie temperature (TC), large dielectric constant (e′), and low dielectric loss (e′′ or tanδ), which are usually unavailable for molecular ferroelectrics [5,6]. These shortcomings for molecular ferroelectrics have been gradually overcome [9–13]; for example, an organic ferroelectrics, croconic acid, has been reported to possess aPS of 21μCcm−2 at room temperature, comparable to BTO [9]. Very recently, a research team led by Professor Ren-Gen Xiong in Southeast University, Nanjing, China, has reported [14] that a molecular ferroelectric crystal of diisopropylammonium bromide salt (DIPAB, Figs 1 and 2) showed a PS of 23 μC cm−2, high TC of 426 K, large e′ up to 103, and low tanδ of ∼0.4%, all close to or beyond the pure inorganic BTO, representing a breakthrough in the research of molecular ferroelectrics.

Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators

Methods for measuring and compensating the nonlinear electro-optical effect of transmissive, parallel-aligned liquid crystal (LC)-based spatial light modulators (SLMs) are presented. Particularly, the analysis is focused on the spatial nonuniformity of the voltage versus phase modulation characteristics for an active-matrix-driven, electrically controlled birefringence type LC-SLM. A high-quality reconstruction from phase-only modulating SLMs requires a well-calibrated phase addressing across the entire SLM panel. I discuss how the commonly inherent phase-response inhomogeneity of LC-SLM is characterized by purposeful localized measurement techniques. This phase-response inhomogeneity is efficiently compensated by utilizing a Legendre polynomial representation in combination with a remapping of an 8 bit gray level addressing. The calibration procedure is corroborated by measurement data. The LC-SLM's experimental demonstration finally verifies the resultant improvement in holographic imaging.

Surface plasmon modulation induced by a direct-current electric field into gallium nitride thin film grown on Si(111) substrate

We report here the experimental results on a field effect refractive index change into gallium nitride (GaN) structures. This effect is characterized through the common prism-coupling technique with the application of a vertical direct-current electric field. Surface plasmon propagation was used to increase the sensitivity of the electro-optic measurements. We have obtained a large refractive index variation for GaN epilayer, around 1.4×10−2 at 1.55μm wavelength. In order to understand the origin of the index modulation, we have conducted a scanning transmission electron microscopy analysis and discussed the influence of threading dislocations density acting as traps and thermo-optic effect. According to recent works, we observed experimentally the optical response of a non-linear electro-optic effect on GaN on Si(111) substrate and estimated a Kerr coefficient of about 2.14×10−16m2 V−2.

Non-linear electrooptic effect in antiferroelectric liquid crystal

AbstractElectrooptic phenomena caused by weak electric fields, much lower than those needed for the helix unwinding, in helical smectic liquid crystals were studied in thin planar samples. The investigations were performed in chiral liquid crystal 4-(1-methyl-heptyloxycarbonyl) phenyl 4′-(3-butanoyloxy propyl-1-oxy) biphenyl-4-carboxylate which exhibits antiferro-electric properties. We have found that electric field applied to a helical smectic liquid crystal caused two effects. First, the helix was deformed and the position of effective optic axis changed by an angle proportional to the field strength. The second effect, quadratic in field, causes the change in the shape of the indicatrix. As a consequence, the relative changes in the light intensity caused by external electric field consist of two components. The first component represents the modulation with the fundamental frequency and the second one with the doubled frequency (second harmonic of the electrooptic effect). The ab- solute values of the first- and second-order electrooptic coefficients have been determined and their temperature dependence discussed.

Electrically and optically controlled cross-polarized wave conversion

Light wave propagation in third-order nonlinear media with applied external electric field is investigated. Interplay between the nonlinear electro-optic and all-optical effects is examined theoretically. Energy exchange between the orthogonal light polarizations, the cross polarization conversion, results. The assisting external field acts as either the effect-enhancing or functionality-controlling parameter. Various materials such as silica glass, silicon, other bulk and quantum well semiconductors, organic materials, and particle-doped nanostructures are referred to as possible candidates for device implementations. Numerical estimates of achievable parameters in a selected suitable material are discussed.

Dispersion enhancement of the nonlinear electro-optical effect

It is proposed for the first time how an electrically poled chirped Bragg grating in an optical fiber may be used for creating efficient, electrically controllable optical fiber delay lines. The tunable range for the delay can be chosen by fixing the chirp rate of the Bragg grating. Additionally, strain and temperature may be used to change the centre wavelength of the delay line. Dispersion may also be used to increase phase-modulation in nonlinear optical fibers.

Exciton effects on nonlinear electro-optic effects in semi-parabolic quantum wires

The nonlinear electro-optic effects in quasi-one-dimensional semi-parabolic quantum wires are studied, in which the exciton effects are taken into account. The analytical expression of the electro-optic co-efficient is derived by compact density-matrix approach. Finally, the numerical results are presented for GaAs/AlGaAs semi-parabolic quantum wires. The results show that the electro-optic coefficient is over two times bigger than that obtained by without considering exciton effects. Furthermore, the electro-optic coefficient is related to the relaxation time.

Electro-optic size effects and effects of nonlinear saturation in PLZT ceramics

Results of studying electro-optic size effects and nonlinear electro-optic effects in ferroelectric PLZT ceramics are presented. It is established that the presence of electro-optic size effects makes microvolume samples of PLZT ceramics promising for designing efficient modulating devices.

Electro-optic property of ZnO:X (X=Li,Mg) thin films

We have proposed an application of ZnO:X (X=Li,Mg,Ni,Al etc.) films for monolithic optical integrated circuits (OICs) (Mat. Res. Soc. Symp. Proc. 574 (1999) 317). Although non-doped ZnO has an electro-optic effect, it is only a Pockel’s effect. The electro-optic effect of Pb(Zr,Ti)O 3 (Jpn. J. Appl. Phys. 34 (1995) 5091) is superior to ZnO, because that is caused by a non-linear Kerr effect. Our group demonstrated that Li-doped ZnO (ZnO:Li) films exhibited ferroelectric behavior (Appl. Phys. A, in press). ZnO with ferroelectricity should have a non-linear electro-optic effect against the applied voltage. In this paper, to design the ZnO monolithic slab waveguide for electro-optical switch, the refractive indices of top and bottom electrode layers and core layer were investigated. Then, electro-optical property of ZnO:Li,Mg films was evaluated, and the possibility of applying to an optical switch was also discussed.

Linear and nonlinear dielectric constant tensor for monolayer films in terms of orientational order parameters

We give a general expression of the dielectric constant tensor in orientational orders in the applied static or low-frequency electric field for the semi-two-dimensional monolayer films with C∞v symmetry. The dielectric anisotropic orientational tensor and orientational polarization tensor are derived in orientational order parameters. The nonlinear electro-optical Pockels effect including the local-field influence is also discussed using the orientational orders. A numerical calculation result shows that the first orientational order parameter S1 is a destructive order while the second orientational orientational order parameter S2 is a constructive one to the dielectric constant in the normal direction of monolayer films.

Ensemble averages for Smoluchowski–Debye rotational diffusion in the presence of a two-angle-dependent reorienting force

An approximate method of solving the Smoluchowski–Debye equation for rotational diffusion of molecules subjected to the action of a two-angle-dependent external driving field within the Kasprowicz–Kielich and Kielich method is proposed. This calculation method, introduced in the Kielich papers for the case of `weak molecular reorientation', describes molecular relaxation in various non-linear electro-optical effects for an external reorienting field dependent on the polar angle only. Taking advantage of the properties of spherical harmonic functions, the Kielich method is extended to the case of reorienting fields dependent on the azimuthal and polar angles.

Investigations on electrooptical effects in chiral discotic columnar mesophases

Abstract Investigations on the nature of both linear and nonlinear electrooptic effects in columnar mesophases of chiral discotic dibenzopyrene and triphenylene derivatives and their mixtures are presented. We specially focus on the influence of chirality on the switching process.