Alessandro Salandrino

Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern

In this work, we investigate the response of epsilon-near-zero metamaterials and plasmonic materials to electromagnetic source excitation. The use of these media for tailoring the phase of radiation pattern of arbitrary sources is proposed and analyzed numerically and analytically for some canonical geometries. In particular, the possibility of employing planar layers, cylindrical shells, or other more complex shapes made of such materials in order to isolate two regions of space and to tailor the phase pattern in one region, fairly independent of the excitation shape present in the other region, is demonstrated with theoretical arguments and some numerical examples. Physical insights into the phenomenon are also presented and discussed together with potential applications of the phenomenon.

Circuit Elements at Optical Frequencies: Nanoinductors, Nanocapacitors, and Nanoresistors

We present the concept of circuit nanoelements in the optical domain using plasmonic and nonplasmonic nanoparticles. Three basic circuit elements, i.e., nanoinductors, nanocapacitors, and nanoresistors, are discussed in terms of small nanostructures with different material properties. Coupled nanoscale circuits and parallel and series combinations are also envisioned, which may provide road maps for the synthesis of more complex circuits in the IR and visible bands. Ideas for the optical implementation of right-handed and left-handed nanotransmission lines are also forecasted.

Negative effective permeability and left-handed materials at optical frequencies

We present here the design of nano-inclusions made of properly arranged collections of plasmonic metallic nano-particles that may exhibit a resonant magnetic dipole collective response in the visible domain. When such inclusions are embedded in a host medium, they may provide metamaterials with negative effective permeability at optical frequencies. We also show how the same inclusions may provide resonant electric dipole response and, when combining the two effects at the same frequencies, left-handed materials with both negative effective permittivity and permeability may be synthesized in the optical domain with potential applications for imaging and nano-optics applications.

Airy plasmon : a nondiffracting surface wave

We introduce a new class of nondiffracting surface plasmonic wave: the Airy plasmon. The propagation properties of such a field configuration are unique among the family of surface waves and could lead to interesting applications in plasmonic energy routing. The self-bending and self-healing behavior of these solutions is discussed. Schemes for experimental realization and potential applications are proposed.

Phase Mismatch–Free Nonlinear Propagation in Optical Zero-Index Materials

Nonlinear Optics Made Easier Nonlinear optical materials can change their optical properties in the presence of light. The nonlinearity results from the constructive addition of interacting photons, but the amount of nonlinear light produced is crucially dependent on meeting strict phase-matching conditions of the interacting photon fields. Suchowski et al. (p. 1223; see the Perspective by Kauranen) now show that metamaterials can be designed with optical properties that relax the phase-matching requirements. At a specific wavelength where the metamaterial exhibits zero refractive index, the photons are found to interact nonlinearly with the phasematching done automatically. Metamaterials relax the requirement for phase matching in nonlinear optics. Phase matching is a critical requirement for coherent nonlinear optical processes such as frequency conversion and parametric amplification. Phase mismatch prevents microscopic nonlinear sources from combining constructively, resulting in destructive interference and thus very low efficiency. We report the experimental demonstration of phase mismatch–free nonlinear generation in a zero-index optical metamaterial. In contrast to phase mismatch compensation techniques required in conventional nonlinear media, the zero index eliminates the need for phase matching, allowing efficient nonlinear generation in both forward and backward directions. We demonstrate phase mismatch–free nonlinear generation using intrapulse four-wave mixing, where we observed a forward-to-backward nonlinear emission ratio close to unity. The removal of phase matching in nonlinear optical metamaterials may lead to applications such as multidirectional frequency conversion and entangled photon generation.

Predicting nonlinear properties of metamaterials from the linear response

The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Millers Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.

Generation of linear and nonlinear nonparaxial accelerating beams

We study linear and nonlinear self-accelerating beams propagating along circular trajectories beyond the paraxial approximation. Such nonparaxial accelerating beams are exact solutions of the Helmholtz equation, preserving their shapes during propagation even under nonlinearity. We generate experimentally and observe directly these large-angle bending beams in colloidal suspensions of polystyrene nanoparticles.

Parallel, series, and intermediate interconnections of optical nanocircuit elements. 2. Nanocircuit and physical interpretation

Applying the analytical closed-form solutions of the quasi-static potential distribution around two conjoined resonant half-cylinders with different permittivities, reported in the first part of this manuscript, here we interpret these results in terms of our nanocircuit paradigm applicable to nanoparticles at infrared and optical frequencies [Phys. Rev. Lett.95, 095504 (2005)]. We investigate the possibility of connecting in series and parallel configurations plasmonic and/or dielectric nanoparticles acting as nanocircuit elements, with a goal for the design of a more-complex nanocircuit system with the desired response. The present analysis fully validates the heuristic predictions regarding the parallel and series combination of a pair of nanocircuit elements depending on their relative orientation with respect to the field polarization. Moreover, the geometries under analysis present interesting peculiar features in their wave interaction, such as an intermediate stage between the parallel and series configurations, which may be of interest for certain applications. In particular, the resonant nanocircuit configuration analyzed here may dramatically change, in a continuous way, its effective total impedance by simply rotating its orientation with respect to the polarization of the impressed optical electric field, providing a novel optical nanodevice that may alter its function by rotation with respect to the impressed optical local field.

Coupling of optical lumped nanocircuit elements and effects of substrates

We present here an analytical quasi-static circuit model for the coupling among small nanoparticles excited by an optical electric field in the framework of the optical lumped nanocircuit theory [N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 095504 (2005)]. We derive how coupling effects may affect the corresponding nanocircuit model by adding lumped controlled sources that depend on the optical voltages applied on the coupled particles as coupled lumped elements. With the same technique, we may model the presence of a substrate located underneath the nanocircuit elements, relating its presence to the coupling with a properly modeled image nanoparticle. These results are of importance in the understanding and the design of complex optical nanocircuits at infrared and optical frequencies.

Parallel, series, and intermediate interconnections of optical nanocircuit elements. 1. Analytical solution

Following our recent development of a paradigm for extending the classic concepts of circuit elements to the infrared and optical frequencies [Phys. Rev. Lett.95, 095504 (2005)], in this paper we investigate the possibility of connecting nanoparticles in series and in parallel configurations, acting as nanocircuit elements. In particular, here we analyze a pair of conjoined half-cylinders whose relatively simple geometry may be studied and analyzed analytically. In this first part of this work, we derive a novel closed-form quasi-static analytical solution of the boundary-value problem associated with this geometry, which will be applied in Part 2 for a nanocircuit and physical interpretation of these results.