An analytical description for plane-wave propagation in metamaterials is presented. It follows the usual approach for describing light propagation in homogeneous media on the basis of Maxwell's equations, although applied to a medium composed of metallic nanostructures. Here, as an example, these nanostructures are double (or cut) wires. In the present approach it is assumed that the carriers perform collective oscillations in a single wire. These oscillations are coupled to those in the adjacent wire; thus, the internal carrier dynamics may be described by a coupled-oscillator model. The multipole expansion technique is used to account for the electric and magnetic dipole as well as the electric quadrupole moments of these carrier oscillations within the nanostructure. It turns out that the symmetric normal mode is related to the electric dipole moment whereas the antisymmetric normal mode evokes simultaneously a magnetic dipole and an electric quadrupole moment. It is shown how effective permittivity and permeability can be derived from analytical expressions for the dispersion relation, the magnetization, and the electric displacement field. The results of the analytical model are compared with rigorous simulations of Maxwell's equations yielding the limitations and the domain of applicability of the proposed model
Metasurfaces have recently emerged as a promising technology to realize flat optical components with customized functionalities. In particular, their application to lenses in various imaging systems is of significant interest. However, a systematic and complete study of the focusing and imaging behavior of metalenses has not yet been conducted. In this work we analyze not only the on-axis focusing performance, but also the field-dependent wavefront aberrations via a phase-retrieval optimization method. We find that, particularly for high-NA metalenses, the field-dependent geometrical aberrations like coma are dominant at the design wavelength, while for longer and shorter operation wavelengths, the effective numerical aperture is decreased and mainly spherical aberrations are dominant. Additionally, we investigate the spectral and angular bandwidth of a polarization-insensitive metalens by analyzing the metalens efficiencies as a function of numerical aperture, field angle, and wavelength. We then compare the metalens performance to its refractive and diffractive counterparts and show how the respective metalens properties affect the imaging performance. For this purpose, we perform an imaging simulation for these three cases based on their field- and wavelength-dependent absolute deflection efficiencies and analyze the imaging properties of an extended test object. Our calculations show that metalenses can outperform diffractive lenses in terms of their angle-dependent efficiency for large deflection angles.
We explain the origin of the electric and particular the magnetic polarizabiltiy of metamaterials employing a fully electromagnetic plasmonic picture. As example we study an U-shaped split-ring resonator based metamaterial at optical frequencies. The relevance of the split-ring resonator orientation relative to the illuminating field for obtaining a strong magnetic response is outlined. We reveal higher-order magnetic resonances and explain their origin on the basis of higher-order plasmonic eigenmodes caused by an appropriate current flow in the split-ring resonator. Finally, the conditions required for obtaining a negative index at optical frequencies in a metamaterial consisting of split-ring resonators and wires are investigated.
We demonstrate that a high-numerical-aperture photonic crystal fiber allows lensless focusing at an unparalleled resolution by complex wavefront shaping. This paves the way toward high-resolution imaging exceeding the capabilities of imaging with multi-core single-mode optical fibers. We analyze the beam waist and power in the focal spot on the fiber output using different types of fibers and different wavefront shaping approaches. We show that the complex wavefront shaping technique, together with a properly designed multimode photonic crystal fiber, enables us to create a tightly focused spot on the desired position on the fiber output facet with a subwavelength beam waist.
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