Silicon nitride (SiN) is emerging as a competitive platform for CMOS-compatible integrated photonics. However, active devices such as modulators are scarce and still lack in performance. Ideally, such a modulator should have a high bandwidth, good modulation efficiency, low loss, and cover a wide wavelength range. Here, we demonstrate the first electro-optic modulators based on ferroelectric lead zirconate titanate (PZT) films on SiN, in both the O-band and C-band. Bias-free operation, bandwidths beyond 33 GHz and data rates of 40 Gbps are shown, as well as low propagation losses (α ≈ 1 dB cm⁻¹). A half-wave voltage-length product of 3.2 V cm is measured. Simulations indicate that further improvement is possible. This approach offers a much-anticipated route towards high-performance phase modulators on SiN.

Liquid crystals are nowadays widely used in all types of display applications. However their unique electro-optic properties also make them a suitable material for nondisplay applications. We will focus on the use of liquid crystals in different photonic components: optical filters and switches, beam-steering devices, spatial light modulators, integrated devices based on optical waveguiding, lasers, and optical nonlinear components. Both the basic operating principles as well as the recent state-of-the art are discussed.

The Poisson-Nernst-Planck equations describe the dynamics of charge transport in an electric field. Although they are relevant in many applications, a general solution is not known and several aspects are not well understood. In many situations nonlinear effects arise for which no analytical description is available. In this work, we investigate charge transport in a planar device on application of a voltage step. We derive analytical expressions for the dynamical behavior in four extreme cases. In the “geometry limited” regime, applicable at high voltages and low charge contents, we neglect diffusion and the electric field induced by the charges. This leads to a uniform movement of all charges until the bulk is completely depleted. In the “space charge limited” regime, for high voltages and high charge contents, diffusion is still neglected but the electric field is almost completely screened over transient space charge layers. Eventually, however, the bulk becomes depleted of charges and the field becomes homogeneous again. This regime is solved under the assumption of a homogeneous current density, and is characterized by a typical $t^{-3/4}$ behavior. In the “diffusion limited” regime, valid for low voltages and low charge contents, diffusion is the dominant transport mechanism and prevents the charges from separating. This results in only very small deviations from a homogeneous charge distribution throughout the device. In the “double layer limited” regime, for low voltages and high charge contents, the combination of dominant diffusion and screening of the electric field results in large variations occurring only in thin double layers near the electrodes. Numerical simulations confirm the validity of the derived analytical expressions for each of the four regimes, and allow us to investigate the parameter values for which they are applicable. We present transient current measurements on a nonpolar liquid with surfactant and compare them with the external current predicted by the theoretical description. The agreement of the analytical expressions with the experiments allows us to obtain values for a number of properties of the charges in the liquid, which are consistent with results in other works. The confirmation by simulations and measurements of the derived theoretical expressions gives confidence about their usefulness to understand various aspects of the Poisson-Nernst-Planck equations and the effects they represent in the dynamics of charge transport.

Owing to the nonlinear effect of optical field-induced director reorientation, self-focusing of an optical beam can occur in nematic liquid crystals and an almost diffraction-compensated propagation can be observed with milliwatts of light power and propagation lengths of several millimeters. This opens the way for applications in all-optical signal handling and reconfigurable optical interconnections. Self-focusing of an optical beam in nematic liquid-crystal cells has been studied experimentally and by means of numerical simulation. The relationships between bias voltage, cell thickness and required optical power have been examined, thus allowing the determination of the most favorable conditions for soliton-like beam propagation.

We demonstrate a phase shifter using a silicon slot waveguide infiltrated with liquid crystal. For a 1-mm long device we achieve 73π phase shift with a 5 V voltage, with a voltage-length product of 0.0224 V· mm ~1 V. We drive the phase shifter with a digital 1 V, duobinary pulsewidth-modulated signal, or a 1 V frequency-modulated signal. This enables direct digital CMOS control of an analog optical phase shifter.