Design of metamaterials with exotic electromagnetic properties
Nanostructured materials are attracting enormous attention since they suggest entirely new ways of controlling the macroscopic properties of the structures made with them.
Besides other properties, their electromagnetic properties can be very strongly modified by manipulating matter on micro- and nanoscale level.
Our goals include invention and engineering of materials with novelty or exotic electromagnetic properties.
Existence of coherent Bloch waves that propagate in ideal periodic structures without scattering strongly suggests that photonic crystals are probably the best candidates for that new generation of materials.
Fig.1. Negative refraction of a Gaussian beam formed by a line source, in the ordinary-dielectric 2D crystal (air holes in silicon).
Here are some examples of discovery and engineering of structures with extreme, exotic and often counter-intuitive features.
Example 1: How to achieve extreme anisotropy and divergent density of states for vanishing wavenumbers in a highly-symmetric crystal?
Anisotropic properties of crystals are known for centuries since the discovery of fluorite and other birefringent optical crystals.
However, it was widely believed that crystals of higher symmetry classes (such as cubic) can not have anisotropy in zeroth order by small wavenumber in the vicinity of a high symmetry point of the Brillouin zone. We predict theoretically and demonstrate in numerical simulations that this actually happens in a structure as simple as a square lattice of air holes buried in crystalline silicon (see Fig. 1).
The clue to theoretical explanation is the denegeracy of the eigenmodes. Degenerate waves have less symmetry than the crystal itself, thus making it possible for them to interact non-isotropically with other eigenstates in the crystal. Anisotropy can be so strong that the effective mass tensor changes its sign upon rotation of the wavevector, right in the vicinity of the Gamma-point. This changes the topology of the isofrequency surface dramatically, leading to logarithmic divergence in the density of states and extreme anisotropy of wave propagation.
Fig.2. Equifrequency contours of the extremely anisotropic propagation band in a square-lattice photonic crystal.
Example 2: How to make a negative index of refraction material?
For physical reasons, the frequencies of magnetic resonances in ordinary atomic and molecular systems are much lower than that of electric dipole resonances, which virtually excludes a possibility to find a naturally occurring molecular/crystalline material with simultaneously negative dielectric permittivity and magnetic permeability. Negative refractive index (NIR) must be invented and made artificially.
The basic principle of electromagnetic meta-material design is a so-called "super-lattice" or a "photonic crystal". A super-lattice is a periodic pattern in usual dielectric or metallic material, such as, periodic alternation of two different materials, with period that is much larger than the typical atomic or crystalline size, and typically comparable to or a few times smaller than the wavelength of light. Under such conditions, each of the alternating materials can be described locally with its bulk dielectric tensor, while the whole structure can be globally be described as an effective medium with certain macroscopic material constants. This description works best when the super-lattice period is significantly smaller than the wavelength. In fact, if the latter is not the case, the effective dielectric constant or effective refractive index can only be introduced phenomenologically, separately in each narrow band of frequencies, in order to match the material's refraction law and/or reflection and transmission coefficients. From the super-lens' point of view, only sub-wavelength photonic crystals can provide sub-wavelength resolution, because of the important limit that the Bragg diffraction imposes on the possible values of wavenumbers: |k|<π/a, where a is the lattice period (considering square lattice for example).
Sub-wavelength photonic crystals (SPCs) made of two positive-dielectric non-magnetic materials, although having very novelty optical properties such as extreme anisotropy [7] in the higher bands, are not very interesting in the low frequency limit, where they have only one "acoustic" propagation band describable with constant positive index of refraction. The most bizarre properties can be found in plasmonic SPC's [2,4], which are binary composites of some positive-dielectric materials (say, silicon or simply air) with materials that have a frequency band in which they exhibit negative dielectric constant. The two most important classes of such materials are metals, which have negative ε due to plasma oscillations in Fermi liquid of conducting electrons, and polaritonic semiconductors (such as silicon carbide), which have negative ε thanks to optical phonons. Unlike ordinary sub-wavelength PC's, plasmonic SPC's show multiple propagation bands, some of which are left-handed and can actually be described with negative refractive index.
We are pursuing theoretical studies of plasmonic SPC's, aimed at engineering
a metamaterial which could have simultaneously negative dielectric and magnetic
permittivities at infrared and/or optical frequencies, and at achieving the
super-lensing effect with such metamaterials.
To learn more about this
project, click here.
Who needs NIR materials?
One of the most exciting applications of the NIR materials is a so-called "super-lens", also known as a "perfect lens".
Super-lens is a near-field electromagnetic phenomenon capable of increasing the resolution of an optical imaging device beyond the diffraction limit.
Super-lensing is based upon the concentration of electromagnetic energy into surface waves, thus confining it onto sub-wavelength scale.
Actually, there are two possible implementations of this technique, both requiring surface waves and negative dielectric constant.
Approach 1: Negative-index super-lens ("Veselago lens").
A slab of material which has negative ε and μ supports both surface waves AND propagation of light.
The light behaves somewhat counter-intuitively because of the left-handed nature of waves propagating in such a material. For example, the group velocity in NIR medium opposes the phase velocity, and refraction bends the rays in the ``abnormal'' direction.
Fig.3. A cartoon of a super-lens ("Veselago lens").
As a proof of principle, we resolved two slits separated by λ/2.5 with a sub-wavelength plasmonic crystal. The operating frequency belongs to the narrow left-handed band associated with a hybridized octupole-monopole resonance of the crystal.
Fig.4. Resolving two slits with a plasmonic photonic crystal via superlensing. Left: field distribution in space. Right: electric field profiles in the object plane (solid blue line) and the image plane (red dashed - no losses, green dashed - realistic losses). Also shown is an "image" when the frequency is detuned by 1% from the right value (black dotted line).
Approach 2: Negative-dielectric superlens ("Poor man's super-lens").
The other possible implementation of the super-lensing phenomenon is a negative-dielectric superlens, which is opaque to propagating radiation and provides focusing by concentrating energy of the incident radiation into surface waves.
A multi-layer planar super-lens can be constructed from two materials: one with a negative dielectric permittivity inserted between two slabs of another material with a positive dielectric permittivity whose absolute value of dielectric constant matches that of the negative-dielectric slab.
Fig.5. Schematic of our negative-dielectric near-field superlens.
A problem of imaging of a light spot (created, for example, by a dipole or by
an illuminated hole in a screen) can be solved analytically. Imaging applications
more complicated than that can be simulated numerically.
Click here to find out more about our theoretical studies
of such a lens.
As a proof of principle, we experimentally implement [1] a super-lens in mid-infrared spectral range (around 11 μm) by creating three-layered structure of sub-micron thickness, SiO2/SiC/SiO2, in which the polaritonic material SiC has a negative dielectric permittivity in the restrahlen band between the frequencies of the transverse and longitudinal optical phonons. A far-field diagnostic of super-lensing based on measuring transmission and reflection coefficients through the metal coated superlens has been implemented using a tunable CO2 laser.
Fig.6. Left (inlay): SEM image of a segment of SiO2/SiC/SiO2 membrane covered with a 60nm thick silver film on both sides. Right: periodic array of slits produced in the silver film using ion milling.
Here you can read more about our experiment
References:
[1] D. Korobkin, Y. Urzhumov, C. Zorman and G. Shvets, "Far Field Detection of the Super-Lensing Effect in Mid-Infrared: Theory and Experiment", submitted to J. Mod. Opt., February 2005.
[2] G. Shvets and Y. Urzhumov, "Electric and magnetic properties of sub-wavelength plasmonic crystals", J. Opt. A: Pure Appl. Opt. 7 (2005) S23-S31.
[3] G. Shvets and Y. Urzhumov, "Polariton-enhanced Near-field Lithography and Imaging with Infrared Light", Mat. Res. Soc. Symp. Proc., Vol. 820 (2004).
[4] G. Shvets and Y. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances", PRL 93, 243902 (2004), e-print cond-mat/0403400
[5] G. Shvets, "Left-Handed Surface Waves in a Photonic Structure", Physica B, 338, 338 (2003), e-print cond-mat/0207626 .
[6] G. Shvets, A. K. Sarychev, and V. M. Shalaev, "Electromagnetic properties of three-dimensional wire arrays: photons, plasmons, and equivalent circuits", SPIE Proceedings, San Diego, CA, Aug.3-8 (2003).
[7] Y. A. Urzhumov and G. Shvets, "Extreme anisotropy of two-dimensional photonic crystals due to mode degeneracy and crystal symmetry", SPIE Conf. Proc., Vol. 5184, 47 (2003), San Diego, CA, Aug.3-8 (2003).
[8] G. Shvets, "Applications of surface plasmon and phonon polaritons to developing left-handed materials and nano-lithography", SPIE Conference Proceedings, v. 5221, 124 (2003), San Diego, CA, Aug.3-8 (2003).
[9] G. Shvets, "Photonic approach to making a material with a negative index of refraction", Phys. Rev. B, 67, 035109 (2003)
[10] A. Pletzer and G. Shvets, "Simulating photons and plasmons in a three-dimensional lattice", Physica B 338, 190 (2003).
