Abstract
The complete understanding of the electromagnetic field characteristics in artificially created bulk or thin media is essential to the efficient harnessing of the multitude of linear and nonlinear effects resulting from it. Due to the fact that recently developed artificial metastructures exhibit controllable electric and magnetic properties that are completely different from natural ones, the spectrum of behavior resulting from subjecting such media to electromagnetic fields has to be revisited. In this paper, we introduce a k-surface framework that offers complete information on the dispersion properties of media with designer electric and magnetic responses with positive and negative values, as well as for the coupling between the two. The extension from the classic k-surface case resides in the consideration of magnetic and bianisotropic materials with positive and negative permittivity and permeability values, as well as the introduction of the chirality coefficient.To illustrate the applicability of our framework, we have investigated the conditions to obtain collinear second harmonic generation in the case of artificial media with positively and negatively valued electric and magnetic responses. As expected, the phase matching tuning curves, defined as the intersections between the k-surfaces at both frequencies, are significantly modified with respect to the classic ones.
Highlights
The control of optical effects including refraction, reflection, state of polarization description, interference, pulse creation and manipulation, energy transfer, harmonics generation and frequency mixing are a direct consequence of the interaction between the electromagnetic field and material media [1]
We have theoretically characterized the set of possible behaviors exhibited by artificial media by means of extending the k-surface framework to negative-valued electromagnetic properties, as well as chiral media
Our framework finds a virtuallyendless set of applications due to the possibility of creating artificial media with designer properties with individual sign and dispersion control of all the e and μ components across each direction, as well as the possibility of artificially-introducing chirality in the desired medium
Summary
The control of optical effects including refraction, reflection, state of polarization description, interference, pulse creation and manipulation, energy transfer, harmonics generation and frequency mixing are a direct consequence of the interaction between the electromagnetic field and material media [1]. The spectral response of such a unit cell differs considerably from that of the composing elements, and can provide a relatively-large amount of customization of the electromagnetic field properties (polarization spatial phase controllers [11,12], frequency-selective surfaces [13,14], giant magnetoresistance-based devices [15,16], high-resolution imaging below the diffraction limit [17,18], second harmonic generators [19,20,21]), including the exotic effects introduced by a negative refractive index (e.g., generalized reflection and refraction [22,23], object cloaking in the radio frequency and optical regimes [24,25], hyperbolic wave front generators [26,27], dispersion sign controllers [28,29,30], Huygens surfaces [31,32,33,34]) Regardless of their nature, metastructures violate the principle of locality, which states that the electric and magnetic properties of a material are the same in all directions and for all positions of that material. The net advantage of our framework is that it offers a clear, graphical solution, in the form of a modified k-surface, which can be evaluated in order to evaluate the optical properties of the artificial media under consideration
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