Patrick Grahn

Electromagnetic multipole theory for optical nanomaterials

Optical properties of natural or designed materials are determined by the electromagnetic multipole moments that light can excite in the constituent particles. In this paper, we present an approach to calculating the multipole excitations in arbitrary arrays of nanoscatterers in a dielectric host medium. We introduce a simple and illustrative multipole decomposition of the electric currents excited in the scatterers and connect this decomposition to the classical multipole expansion of the scattered field. In particular, we find that completely different multipoles can produce identical scattered fields. The presented multipole theory can be used as a basis for the design and characterization of optical nanomaterials.

Theoretical description of bifacial optical nanomaterials

We introduce a formalism that describes the interaction of light with bifacial optical nanomaterials. They are artificial noncentrosymmetric materials in which counter-propagating waves behave differently. We derive electromagnetic material parameters for uniaxial crystalline media in terms of the complex transmission and reflection coefficients of a single layer of the constituent nanoscatterers, which makes the numerical evaluation of these parameters very efficient. In addition, we present generalized Fresnel coefficients for such bifacial nanomaterials and investigate the fundamental role of higher-order electromagnetic multipoles on the bifaciality. We find that two counter-propagating waves in the material must experience the same refractive index, but they can have dramatically different wave impedances. The use of our model in practice is demonstrated with a particular example of a bifacial nanomaterial that exhibits a directional impedance matching to the surrounding medium.

Interferometric description of optical metamaterials

We introduce a simple theoretical model that describes the interaction of light with optical metamaterials in terms of interfering optical plane waves. In this model, a metamaterial is considered to consist of planar arrays of densely packed nanoparticles. In the analysis, each such array reduces to an infinitely thin homogeneous sheet. The transmission and reflection coefficients of this sheet are found to be equal to those of an isolated nanoparticle array and, therefore, they are easy to evaluate numerically for arbitrary shapes and arrangements of the particles. The presented theory enables fast calculation of electromagnetic fields interacting with a metamaterial slab of an arbitrary size, which, for example, can be used to retrieve the effective refractive index and wave impedance in the material. The model is also shown to accurately describe optically anisotropic metamaterials that in addition exhibit strong spatial dispersion, such as bifacial metamaterials.

Interaction of metamaterials with optical beams

We develop a general theoretical approach to describing the interaction of metamaterials with optical beams. The metamaterials are allowed to be anisotropic, chiral, noncentrosymmetric, and spatially dispersive. Unlike plane waves, beams can change their field distributions upon interaction with metamaterials, which can reveal new optical effects. Our method is based on a vector form of the angular spectrum representation and a technique to calculate the wave parameters for all required directions of wave propagation. Applying the method to various metamaterial designs, we discover a new optical phenomenon: the conversion of light polarization by spatial dispersion. Because of this phenomenon, the refractive index and impedance cannot be introduced for many metamaterial designs. In such cases, we propose an alternative approach to treating the beam–metamaterial interaction. This work takes a step forward in describing optical metamaterials by moving from unphysical plane waves to realistic optical beams.

Fabrication and characterization of a large-area metal nano-grid wave plate

We introduce a fast and cost-effective technique to fabricate large-area periodically nanopatterned metal samples and apply this technique to create reflective nano-grid wave plates for optical wavelengths. The technique makes use of azo-polymer-based interference lithography and a special imprint method that enables creating large-area metal nanopatterns with high vertical walls. We fabricate and experimentally test a gold nano-grid wave plate that operates as reflective λ/4-plate for λ = 604 nm and λ/2-plate for λ = 997 nm.

Internally twisted spatially dispersive optical metamaterials

Abstract. We introduce and theoretically describe internally twisted optical metamaterials, in which the metamolecules can have an arbitrary, but common, orientation in the unit cells. The molecules, and consequently the material, are not chiral, but they are allowed to be noncentrosymmetric. While such internally twisted crystalline structures are difficult to find in natural materials, metamaterials of this type can be designed and fabricated at will. Here, we present a theoretical method that enables a detailed analysis of such metamaterials. The method establishes a connection between the optical properties of a metamaterial and the plane-wave optical response of a single two-dimensional array of metamolecules. In the theory, the effective wave parameters, such as the refractive index and wave impedance, are retrieved. Using the model, we show that these parameters can dramatically depend on the wave propagation direction and metamolecular orientation, which can be used, along with optical anisotropy, to efficiently adjust and control the plane-wave content of optical beams.

Spatially dispersive functional optical metamaterials

Abstract. Functional optical metamaterials usually consist of absorbing, anisotropic, and often noncentrosymmetric structures of a size that is only a few times smaller than the wavelength of visible light. If the structures were substantially smaller, excitation of higher-order electromagnetic multipoles in them, including magnetic dipoles, would be inefficient. The required non-negligible size of metamolecules, however, makes the material spatially dispersive, so that its optical characteristics depend on the light propagation direction. We consider the possibility to use this usually unwanted effect. We present a theoretical model that allows one to study the interaction of such spatially dispersive metamaterials with optical beams. Applying the model, we show that a strong spatial dispersion, combined with optical anisotropy and absorption, can be used to efficiently control propagational characteristics of optical beams and create new types of optical elements.

Functional optical metamaterials employing spatial dispersion and absorption

Functional optical metamaterials usually consist of absorbing, anisotropic and often non-centrosymmetric structures of a size that is only a few times smaller than the wavelength of visible light. If the structures would be substantially smaller, excitation of higher-order electromagnetic multipoles in them, including magnetic dipoles, would be inefficient. As a result, the material would act as an ordinary electric-dipole material. The required non-negligible size of metamolecules, however, makes the material spatially dispersive, so that its optical characteristics depend on light propagation direction. This phenomenon significantly complicates the description of metamaterials in terms of conventional electric permittivity and magnetic permeability tensors. In this work, we present a simple semianalytical method to describe such spatially dispersive metamaterials, which are also allowed to be optically anisotropic and non-centrosymmetric. Applying the method, we show that a strong spatial dispersion, combined with absorption and optical anisotropy, can be used to efficiently control propagational characteristics of optical beams.

Design and characterization of metamaterial building blocks using electric current multipoles

We have developed an electrodynamic multipole theory that can be used to characterize the interaction of light with arrays of arbitrary nanoparticles forming a metamaterial. In this theory, every nanoscatterer is substituted with an equivalent point particle in which the incident light excites current multipole moments. The electromagnetic fields scattered by the designed nanoparticles inside the metamaterial are exactly the same as those created by the introduced point multipoles. Thus, we are in a position to assign polarizability tensors that completely characterize the nanoparticles. Tuning the polarizabilities of the higher-order multipoles is essential in order to obtain metamaterials with extraordinary properties.