Perturbation theory for Kerr nonlinear leaky cavities.

In emerging open photonic resonators that support quasinormal eigenmodes, fundamental physical quantities and methods have to be carefully redefined. Here, we develop a perturbation theory framework for nonlinear material perturbations in leaky optical cavities. The ambiguity in specifying the stored energy due to the exponential growth of the quasinormal mode field profile is lifted by implicitly specifying it via the accompanying resistive loss. The capabilities of the framework are demonstrated by considering a third-order nonlinear ring resonator and verified by comparing against full-wave nonlinear finite element simulations. The developed theory allows for efficiently modeling nonlinear phenomena in contemporary photonic resonators with radiation and resistive loss.

On the calculation of the quality factor in contemporary photonic resonant structures.

The correct numerical calculation of the resonance characteristics and, principally, the quality factor Q of contemporary photonic and plasmonic resonant systems is of utmost importance, since Q defines the bandwidth and affects nonlinear and spontaneous emission processes. Here, we comparatively assess the commonly used methods for calculating Q using spectral simulations with commercially available, general-purpose software. We study the applicability range of these methods through judiciously selected examples covering different material systems and frequency regimes from the far-infrared to the visible. We take care in highlighting the underlying physical and numerical reasons limiting the applicability of each one. Our findings demonstrate that in contemporary systems (plasmonics, 2D materials) Q calculation is not trivial, mainly due to the physical complication of strong material dispersion and light leakage. Our work can act as a reference for the mindful and accurate calculation of the quality factor and can serve as a handbook for its evaluation in guided-wave and free-space photonic and plasmonic resonant systems.

Coupled-mode-theory framework for nonlinear resonators comprising graphene.

A general framework combining perturbation theory and coupled-mode theory is developed for analyzing nonlinear resonant structures comprising dispersive bulk and sheet materials. To allow for conductive sheet materials, a nonlinear current term is introduced in the formulation in addition to the more common nonlinear polarization. The framework is applied to model bistability in a graphene-based traveling-wave resonator system exhibiting third-order nonlinearity. We show that the complex conductivity of graphene disturbs the equality of electric and magnetic energies on resonance (a condition typically taken for granted), due to the reactive power associated with the imaginary part of graphene's surface conductivity. Furthermore, we demonstrate that the dispersive nature of conductive materials must always be taken into account, since it significantly impacts the nonlinear response. This is explained in terms of the energy stored in the surface current, which is zeroed-out when linear dispersion is neglected. The results obtained with the proposed framework are compared with full-wave nonlinear finite-element simulations with excellent agreement. Very low characteristic power for bistability is obtained, indicating the potential of graphene for nonlinear applications.

Beam-splitter switches based on zenithal bistable liquid-crystal gratings.

The tunable optical diffractive properties of zenithal bistable nematic liquid-crystal gratings are theoretically investigated. The liquid-crystal orientation is rigorously solved via a tensorial formulation of the Landau-de Gennes theory and the optical transmission properties of the gratings are investigated via full-wave finite-element frequency-domain simulations. It is demonstrated that by proper design the two stable states of the grating can provide nondiffracting and diffracting operation, the latter with equal power splitting among different diffraction orders. An electro-optic switching mechanism, based on dual-frequency nematic materials, and its temporal dynamics are further discussed. Such gratings provide a solution towards tunable beam-steering and beam-splitting components with extremely low power consumption.

Switchable beam steering with zenithal bistable liquid-crystal blazed gratings.

Switchable beam steerers based on zenithal bistable liquid crystal (LC) gratings are designed and theoretically investigated. The nematic orientation profiles and the optical transmittance properties of the gratings are rigorously calculated, respectively, via a tensorial formulation of the Landau-de Gennes theory and the full-wave finite-element-method. By proper design of the grating geometry, beam steering with high diffraction efficiency is demonstrated between the two stable LC states. The tolerance of the device performance with respect to material parameters is assessed, evidencing spectral operation windows of more than 50 nm in the visible for a beam steering efficiency higher than 90%.

Silicon-loaded surface plasmon polariton waveguides for nanosecond thermo-optical switching.

A MHz-bandwidth thermo-optical (TO) plasmonic switch operating at telecommunication wavelengths and based on a hybrid solid-state silicon-loaded surface plasmon polariton waveguide design is demonstrated numerically. The nanosecond (ns) TO response of the switch is due to the high thermal conductivities of the employed materials and we demonstrate specifically a 10 dB extinction ratio in the time-dependent switch transmission which features a pulsed 1 ns rise time followed by a 25 ns fall time when the switch is photo-thermally activated by a ns pulse at 532 nm wavelength.

Dual-band electro-optic polarization switch based on dual-core liquid-crystal photonic crystal fibers.

Compact voltage-controlled all-in-fiber polarization switches are designed and investigated based on dual-core photonic crystal fibers, by selectively infiltrating one of the fiber's cores with a nematic liquid crystal. The electro-optical control of the liquid crystal core's optical properties allows for the splitting of the two orthogonal polarizations, showing crosstalk values lower than -20 dB in a 40 nm window at 1550 nm, for an ultracompact length less than 0.6 mm. With proper selection of the control voltage and the component length, dual-band operation with a crosstalk lower than -20 dB is also demonstrated for the 1300 and 1550 nm telecom bands.

Diffraction grating with suppressed zero order fabricated using dielectric forces.

An electric-field-assisted method to produce diffractive optical devices is demonstrated. A uniform film of liquid UV curable resin was produced as a drying ring from an organic solvent. Dielectrophoresis forces maintained the stability of the thin film and also imprinted a periodic corrugation deformation of pitch 20 µm on the film surface. Continuous in situ voltage-controlled adjustment of the optical diffraction pattern was carried out simultaneously with UV curing. A fully cured solid phase grating was produced with the particular voltage-selected tailored optical property that the zero transmitted order was suppressed for laser light at 633 nm.

Explicit finite-difference vector beam propagation method based on the iterated Crank-Nicolson scheme.

We introduce and develop a new explicit vector beam propagation method, based on the iterated Crank-Nicolson scheme, which is an established numerical method in the area of computational relativity. The proposed approach results in a fast and robust method, characterized by simplicity, efficiency, and versatility. It is free of limitations inherent in implicit beam propagation methods, which are associated with poor convergence or uneconomical use of memory in the solution of large sparse linear systems, and thus it can tackle problems of considerable size and complexity. The advantages offered by this approach are demonstrated by analyzing a multimode interference coupler and a twin-core photonic crystal fiber. A possible wide-angle generalization is also provided.

Theoretical and experimental optical studies of cholesteric liquid crystal films with thermally induced pitch gradients.

The reflection properties of cholesteric films with thermally induced pitch gradients are theoretically and experimentally studied. It is shown that the optical behavior of such films corresponds to the averaged contribution of a number of stochastic pitch variation profiles, due to the transversal and longitudinal nonuniformities that develop in the helical structure of such samples. Depending on the annealing time, both narrow-band and broadband behavior can be selectively achieved. The influence of the pitch profile gradient on the broadband reflection performance of cholesteric samples is theoretically analyzed, and a multi-slab structure for achieving optimum efficiency is proposed.

Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation.

A rigorous method for transforming an electromagnetic near-field distribution to the far field is presented. We start by deriving a set of self-consistent integral equations that can be used to represent the electromagnetic field rigorously everywhere in homogeneous space apart from the closed interior of a volume encompassing all charges and sinks. The representation is derived by imposing a condition analogous to Sommerfeld's radiation condition. We then examine the accuracy of our numerical implementation of the formula, also on a parallel computer cluster, by comparing the results with a case when the analytical solution is also available. Finally, an application example is shown for a nonanalytical case.

Surface-stabilized ferroelectric liquid-crystal diffraction gratings with micrometer-scale pitches.

The first-order diffraction efficiency eta1 of surface-stabilized ferroelectric liquid-crystal (SSFLC) phase gratings is calculated for device thicknesses in the range d = 1 to 5 microm and for pitches p of 5 to 20 microm assuming incident light at 633 nm. The peak value of eta1 as a function of d has negligible dependence on the incoming polarization when p = 20 microm. For smaller pitch values the peak value of eta1 decreases and becomes increasingly dependent on the orientation of the incoming polarization owing to the influence of the domain walls that occur between the SSFLC pixels.

Calculation of the efficiency of polarization-insensitive surface-stabilized ferroelectric liquid-crystal diffraction gratings.

A rigorous analysis is presented of the diffraction efficiency of a polarization-insensitive surface-stabilized ferroelectric liquid-crystal (SSFLC) phase grating, taking full account of the internal structure of the ferroelectric liquid-crystal layer. When no field is applied, the twisted director profile in the relaxed state gives an optimum diffraction efficiency for a device thickness between the half-wave-plate and the full-wave-plate conditions. The influence of the magnitude of the spontaneous polarization and applied ac fields are investigated, and it is shown that the diffraction efficiency of a binary SSFLC phase grating can be strongly enhanced with the technique of ac stabilization.

Three-dimensional simulations of light propagation in periodic liquid-crystal microstructures.

A composite scheme based on the finite-difference time-domain method and a plane-wave expansion method is developed and applied to the optics of periodic liquid-crystal microstructures. This is used to investigate three-dimensional light-wave propagation in grating-induced bistable nematic devices with double periodicity. Detailed models of realistic devices are analyzed with emphasis on two different underlying surface-relief grating structures: a smooth bisinusoidal grating and a square-post array. The influence of the grating feature size is quantified. Device performance is examined in conjunction with an appropriate compensation layer, and the optimum layer thickness is determined for the different grating geometries.