Mark S. Wheeler

The influence of material absorption on the quality factor of photonic crystal cavities

Accounting for material absorption is very important for developing high quality factor (Q) photonic crystal cavities. However, to our knowledge, there have been very few systematic experimental investigations of its role in such cavities. In this paper, we present detailed experiments to reveal the relationship between Q, material absorption coefficient and field pattern. Modes with different field patterns and materials with different absorption coefficients were tested. We have developed a simple formula to describe the relationship, which can be used to replace time-consuming numerical calculations. The experimental and numerical data agree well with this formula.

Highly confined mode above the light line in a two-dimensional photonic crystal slab

We found that certain modes above the light line can satisfy total internal reflection in a two-dimensional photonic crystal slab, resulting in negligible vertical leakage. A heterogeneous cavity utilizing such a mode was designed and constructed for the microwave spectrum. Numerical calculations show the mode has a quality factor (Q) of 6×105 neglecting the material loss and 7600 including it. The measured Q (9000), resonance frequency, and mode pattern agreed well with the calculation. The mode has more than 50% of electric field energy in void space and is promising to have stronger interaction with materials introduced there.

Magnetic response in non-magnetic materials and coupled dipole interactions

Research into the fabrication of negative permeability and negative index metamaterials has focused on intricately-shaped metallic constituent particles. However, a simpler design for a magnetic metamaterial could instead use non-magnetic spheres with a large permittivity [1]. This is possible because each sphere acts as a cavity resonator with a fundamental magnetic dipole resonance, operating in the long wavelength limit due to the large permittivity. Furthermore, coating the spheres with a metal or semiconductor shell would result in a negative index metamaterial [2]. Depending on the choice of materials, this design can be applied at microwave, infrared, or visible frequencies.

Determining the sign of the index in metamaterials composed of split ring resonators and strip wires using dispersion diagrams or the insertion phase

Using full wave simulations the behavior of two structures composed of split ring resonators (SRRs) and strip wires (SWs) is examined. In the region where the real parts of the permittivity and permeability are both expected to be negative both structures exhibit a transmission peak, a property which is generally assumed to imply a negative index of refraction. However, through an analysis of the dispersion characteristics and insertion phase of the two structures it is shown that only the index in the first structure, in which the SRRs and SWs are printed on opposite sides of a dielectric substrate, is negative in the passband. In the second structure, in which SRRs and SWs are printed on the same side of the substrate, the index in the passband is positive. Therefore the emergence of transmission peaks does not provide sufficient evidence of the existence of a negative index of refraction. To determine the correct sign of the index two methods are investigated. The first uses the transmission phase for propagation through various lengths of the structure and the second utilizes its dispersion diagrams. The dependence of the sign of the index on the dimensions of the unit cell size is also examined.

Negative permittivity and permeability in the infrared due to dielectric spheres

In this paper we consider the effective electric and magnetic properties of a three-dimensional collection of non-magnetic spheres. Polaritonic materials are used, so that the Mie resonances of the spheres are excited in the long-wavelength regime of the surrounding medium. We consider a simple cubic lattice based on LiTaO3 and find that it is possible to engineer a fundamental resonant magnetic response. The effective media parameters derived by this approach are isotropic, and closely match those obtained by band structure calculations. Frequency ranges with either negative permittivity or negative permeability are found. Within these ranges a negative group velocity is observed. Coated spheres with a negative index of refraction are also presented.

Left-handed and right-handed metamaterials composed of split ring resonators and strip wires

It was shown that the existence of transmission peaks in the regions where the real parts of the electric permittivity and magnetic permeability are expected to be simultaneously negative is not sufficient evidence of LHM behavior. In order to properly determine the sign of the index, the insertion phase for propagation through several lengths of the structure is necessary. Alternately, the dispersion diagrams can be used to determine the sign of the index, In addition, it was shown that both the OS and SS configurations can produce LHM behavior, but that in the SS case, because of the interference between the SRR and SW, the lattice spacing must be smaller than that of the OS case. In other words, the interference between the SRR and SW in the SS case does not completely destroy the potential for LHM behavior, it weakens it.