Integrated microcavity optomechanics with a suspended photonic crystal mirror above a distributed Bragg reflector.

Increasing the interaction between light and mechanical resonators is an ongoing endeavor in the field of cavity optomechanics. Optical microcavities allow for boosting the interaction strength through their strong spatial confinement of the optical field. In this work, we follow this approach by realizing a sub-wavelength-long, free-space optomechanical microcavity on-chip fabricated from an (Al,Ga)As heterostructure. A suspended GaAs photonic crystal mirror is acting as a highly reflective mechanical resonator, which together with a distributed Bragg (DBR) reflector forms an optomechanical microcavity. We demonstrate precise control over the microcavity resonance by change of the photonic crystal parameters. We find that the microcavity mode can strongly couple to the transmissive modes of the DBR. The interplay between the microcavity mode and a guided resonance of the photonic crystal modifies the cavity response and results in a stronger dynamical backaction on the mechanical resonator compared to conventional optomechanical dynamics.

A Gaussian reflective metasurface for advanced wavefront manipulation.

Metasurfaces enable us to control the fundamental properties of light with unprecedented flexibility. However, most metasurfaces realized to date aim at modifying plane waves. While the manipulation of nonplanar wavefronts is encountered in a diverse number of applications, their control using metasurfaces is still in its infancy. Here we design a metareflector able to reflect a diverging Gaussian beam back onto itself with efficiency over 90% and focusing at an arbitrary distance. We outline a clear route towards the design of complex metareflectors that can find applications as diverse as optical tweezing, lasing, and quantum optics.

Do Optomechanical Metasurfaces Run Out of Time?

Artificially structured metasurfaces make use of specific configurations of subwavelength resonators to efficiently manipulate electromagnetic waves. Additionally, optomechanical metasurfaces have the desired property that their actual configuration may be tuned by adjusting the power of a pump beam, as resonators move to balance pump-induced electromagnetic forces with forces due to elastic filaments or substrates. Although the reconfiguration time of optomechanical metasurfaces crucially determines their performance, the transient dynamics of unit cells from one equilibrium state to another is not understood. Here, we make use of tools from nonlinear dynamics to analyze the transient dynamics of generic optomechanical metasurfaces based on a damped-resonator model with one configuration parameter. We show that the reconfiguration time of optomechanical metasurfaces is not only limited by the elastic properties of the unit cell but also by the nonlinear dependence of equilibrium states on the pump power. For example, when switching is enabled by hysteresis phenomena, the reconfiguration time is seen to increase by over an order of magnitude. To illustrate these results, we analyze the nonlinear dynamics of a bilayer cross-wire metasurface whose optical activity is tuned by an electromagnetic torque. Moreover, we provide a lower bound for the configuration time of generic optomechanical metasurfaces. This lower bound shows that optomechanical metasurfaces cannot be faster than state-of-the-art switches at reasonable powers, even at optical frequencies.

Optical Force Enhancement Using an Imaginary Vector Potential for Photons.

The enhancement of optical forces has enabled a variety of technological applications that rely on the optical control of small objects and devices. Unfortunately, optical forces are still too small for the convenient actuation of integrated switches and waveguide couplers. Here we show how the optical gradient force can be enhanced by an order of magnitude by making use of gauge materials inside two evanescently coupled waveguides. To this end, the gauge materials inside the cores should emulate imaginary vector potentials for photons pointing perpendicularly to the waveguide plane. Depending on the relative orientation of the vector potentials in neighboring waveguides, i.e., pointing away from or towards each other, the conventional attractive force due to an even mode profile may be enhanced, suppressed, or may even become repulsive. This and other new features indicate that the implementation of complex-valued vector potentials with non-Hermitian waveguide cores may further enhance our control over mode profiles and the associated optical forces.

Broadband, Spectrally Flat, Graphene-based Terahertz Modulators.

Advances in the efficient manipulation of terahertz waves are crucial for the further development of terahertz technology, promising applications in many diverse areas, such as biotechnology and spectroscopy, to name just a few. Due to its exceptional electronic and optical properties, graphene is a good candidate for terahertz electro-absorption modulators. However, graphene-based modulators demonstrated to date are limited in bandwidth due to Fabry-Perot oscillations in the modulators' substrate. Here, a novel method is demonstrated to design electrically controlled graphene-based modulators that can achieve broadband and spectrally flat modulation of terahertz beams. In our design, a graphene layer is sandwiched between a dielectric and a slightly doped substrate on a metal reflector. It is shown that the spectral dependence of the electric field intensity at the graphene layer can be dramatically modified by optimizing the structural parameters of the device. In this way, the electric field intensity can be spectrally flat and even compensate for the dispersion of the graphene conductivity, resulting in almost invariant absorption in a wide frequency range. Modulation depths up to 76% can be achieved within a fractional operational bandwidth of over 55%. It is expected that our modulator designs will enable the use of terahertz technology in applications requiring broadband operation.

Transformation optics beyond the manipulation of light trajectories.

Since its inception in 2006, transformation optics has become an established tool to understand and design electromagnetic systems. It provides a geometrical perspective into the properties of light waves without the need for a ray approximation. Most studies have focused on modifying the trajectories of light rays, e.g. beam benders, lenses, invisibility cloaks, etc. In this contribution, we explore transformation optics beyond the manipulation of light trajectories. With a few well-chosen examples, we demonstrate that transformation optics can be used to manipulate electromagnetic fields up to an unprecedented level. In the first example, we introduce an electromagnetic cavity that allows for deep subwavelength confinement of light. The cavity is designed with transformation optics even though the concept of trajectory ceases to have any meaning in a structure as small as this cavity. In the second example, we show that the properties of Cherenkov light emitted in a transformation-optical material can be understood and modified from simple geometric considerations. Finally, we show that optical forces--a quadratic function of the fields--follow the rules of transformation optics too. By applying a folded coordinate transformation to a pair of waveguides, optical forces can be enhanced just as if the waveguides were closer together. With these examples, we open up an entirely new spectrum of devices that can be conceived using transformation optics.

Numerical investigation of the flat band Bloch modes in a 2D photonic crystal with Dirac cones.

A numerical method combining complex-k band calculations and absorbing boundary conditions for Bloch waves is presented. We use this method to study photonic crystals with Dirac cones. We demonstrate that the photonic crystal behaves as a zero-index medium when excited at normal incidence, but that the zero-index behavior is lost at oblique incidence due to excitation of modes on the flat band. We also investigate the formation of monomodal and multimodal cavity resonances inside the photonic crystals, and the physical origins of their different line-shape features.

Controlling Cherenkov radiation with transformation-optical metamaterials.

In high energy physics, unknown particles are identified by determining their mass from the Cherenkov radiation cone that is emitted as they pass through the detector apparatus. However, at higher particle momentum, the angle of the Cherenkov cone saturates to a value independent of the mass of the generating particle, making it difficult to effectively distinguish between different particles. Here, we show how the geometric formalism of transformation optics can be applied to describe the Cherenkov cone in an arbitrary anisotropic medium. On the basis of these results, we propose a specific anisotropic metamaterial to control Cherenkov radiation, leading to enhanced sensitivity for particle identification at higher momentum.

Large quality factor in sheet metamaterials made from dark dielectric meta-atoms.

Metamaterials--or artificial electromagnetic materials--can create media with properties unattainable in nature, but mitigating dissipation is a key challenge for their further development. Here, we demonstrate a low-loss metamaterial by exploiting dark bound states in dielectric inclusions coupled to the external waves by small nonresonant metallic antennas. We experimentally demonstrate a dispersion-engineered metamaterial based on a meta-atom made from alumina, and we show that its resonance has a much larger quality factor than metal-based meta-atoms. Finally, we show that our dielectric meta-atom can be used to create sheet metamaterials with negative permittivity or permeability.

Enhancing optical gradient forces with metamaterials.

We demonstrate how the optical gradient force between two waveguides can be enhanced using transformation optics. A thin layer of double-negative or single-negative metamaterial can shrink the interwaveguide distance perceived by light, resulting in a more than tenfold enhancement of the optical force. This process is remarkably robust to the dissipative loss normally observed in metamaterials. Our results provide an alternative way to boost optical gradient forces in nanophotonic actuation systems and may be combined with existing resonator-based enhancement methods to produce optical forces with an unprecedented amplitude.

Electromagnetically induced transparency and absorption in metamaterials: the radiating two-oscillator model and its experimental confirmation.

Several classical analogues of electromagnetically induced transparency in metamaterials have been demonstrated. A simple two-resonator model can describe their absorption spectrum qualitatively, but fails to provide information about the scattering properties--e.g., transmission and group delay. Here we develop an alternative model that rigorously includes the coupling of the radiative resonator to the external electromagnetic fields. This radiating two-oscillator model can describe both the absorption spectrum and the scattering parameters quantitatively. The model also predicts metamaterials with a narrow spectral feature in the absorption larger than the background absorption of the radiative element. This classical analogue of electromagnetically induced absorption is shown to occur when both the dissipative loss of the radiative resonator and the coupling strength are small. These predictions are subsequently demonstrated in experiments.

Interaction between graphene and metamaterials: split rings vs. wire pairs.

We have recently shown that graphene is unsuitable to replace metals in the current-carrying elements of metamaterials. At the other hand, experiments have demonstrated that a layer of graphene can modify the optical response of a metal-based metamaterial. Here we study this electromagnetic interaction between metamaterials and graphene. We show that the weak optical response of graphene can be modified dramatically by coupling to the strong resonant fields in metallic structures. A crucial element determining the interaction strength is the orientation of the resonant fields. If the resonant electric field is predominantly parallel to the graphene sheet (e.g., in a complementary split-ring metamaterial), the metamaterial's resonance can be strongly damped. If the resonant field is predominantly perpendicular to the graphene sheet (e.g., in a wire-pair metamaterial), no significant interaction exists.

Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial.

Metamaterials are engineered materials composed of small electrical circuits producing novel interactions with electromagnetic waves. Recently, a new class of metamaterials has been created to mimic the behavior of media displaying electromagnetically induced transparency (EIT). Here we introduce a planar EIT metamaterial that creates a very large loss contrast between the dark and radiative resonators by employing a superconducting Nb film in the dark element and a normal-metal Au film in the radiative element. Below the critical temperature of Nb, the resistance contrast opens up a transparency window along with a large enhancement in group delay, enabling a significant slowdown of waves. We further demonstrate precise control of the EIT response through changes in the superfluid density. Such tunable metamaterials may be useful for telecommunication because of their large delay-bandwidth products.

Optical forces in nanowire pairs and metamaterials.

We study the optical force arising when isolated gold nanowire pairs and metamaterials with a gold nanowire pair in the unit cell are illuminated with laser radiation. Firstly, we show that isolated nanowire pairs are subject to much stronger optical forces than nanospheres due to their stronger electric and magnetic dipole resonances. We also investigate the properties of the optical force as a function of the length of the nanowires and of the distance between the nanowires. Secondly, we study the optical force in a metamaterial that consists of a periodic array of nanowire pairs. We show that the ratio of the size of the unit cell to the length of the nanowires determines whether the electric dipole resonance leads to an attractive or a repulsive force, and we present the underlying physical mechanism for this effect.

Frequency converter implementing an optical analogue of the cosmological redshift.

According to general relativity, the frequency of electromagnetic radiation is altered by the expansion of the universe. This effect-commonly referred to as the cosmological redshift--is of utmost importance for observations in cosmology. Here we show that this redshift can be reproduced on a much smaller scale using an optical analogue inside a dielectric metamaterial with time-dependent material parameters. To this aim, we apply the framework of transformation optics to the Robertson-Walker metric. We demonstrate theoretically how perfect redshifting or blueshifting of an electromagnetic wave can be achieved without the creation of sidebands with a device of finite length.

Pattern formation without diffraction matching in optical parametric oscillators with a metamaterial.

We consider a degenerate optical parametric oscillator containing a left-handed material. We show that the inclusion of a left-handed material layer allows for controlling the strength and sign of the diffraction coefficient at either the pump or the signal frequency. Subsequently, we demonstrate the existence of stable dissipative structures without diffraction matching, i.e., without the usual relationship between the diffraction coefficients of the signal and pump fields. Finally, we investigate the size scaling of these light structures with decreasing diffraction strength.

Planar designs for electromagnetically induced transparency in metamaterials.

We present a planar design of a metamaterial exhibiting electromagnetically induced transparency that is amenable to experimental verification in the microwave frequency band. The design is based on the coupling of a split-ring resonator with a cut-wire in the same plane. We investigate the sensitivity of the parameters of the transmission window on the coupling strength and on the circuit elements of the individual resonators, and we interpret the results in terms of two linearly coupled Lorentzian resonators. Our metamaterial designs combine low losses with the extremely small group velocity associated with the resonant response in the transmission window, rendering them suitable for slow light applications at room temperature.

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material.

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.

Dissipative structures in left-handed material cavity optics.

We study the spatiotemporal dynamics of spatially extended nonlinear cavities containing a left-handed material. Such materials, which have a negative index of refraction, have been experimentally demonstrated recently, and allow for novel electromagnetic behavior. We show that the insertion of a left-handed material in an optical resonator allows for controlling the value and the sign of the diffraction coefficient in dispersive Kerr resonators and degenerate optical parametric oscillators. We give an overview of our analytical and numerical studies on the stability and formation of dissipative structures in systems with negative diffraction.