Iman Vakili

Optical Theorem and Forward Scattering Sum Rule for Periodic Structures

Based on energy conservation, an optical theorem is constructed for a slab having an arbitrary periodic microstructure in a plane. A sum rule for low pass structures is derived using analytic properties of Herglotz functions based on causality and passivity. The sum rule relates the total cross section to the static polarizability per unit cell, and quantifies the interaction between the slab and electromagnetic fields possible over all wavelengths. The results are illustrated with several numerical and experimental examples.

Time-Domain System for Millimeter-Wave Material Characterization

Time-domain material characterization using a leaky lens antenna and an in-house fabricated millimeter-wave wavelet generator using III-V technology is investigated. The wavelet generator produces short high-frequency pulses and is connected to a wideband and nondispersive leaky lens antenna. A purely time-domain methodology is used to extract the complex permittivity of nondispersive and nonmagnetic materials. The permittivity is found from the phase delay and the amplitude mismatch introduced by the object at the carrier frequency of the pulse. The wide bandwidth of the wavelet is used to investigate frequency-dependent material properties. Measurement results from two dielectric slabs are illustrated. The time-domain methodology is verified by frequency-domain measurements and analysis.

Scattering measurements in a parallel plate waveguide — First results

This paper describes a parallel plate waveguide designed for scattering and material measurements. The experimental setup can for certain scatterers be considered as a two dimensional radar cross section range. Measurements on metallic circular cylinders of finite length are performed, and the forward radar cross section and the extinction cross section are determined. Two different calibration methods are used, and it is found that the method employing a calibration object is the most accurate. It is concluded that the two dimensional radar cross section in the forward direction can be measured with ±1 dB accuracy at the level of 10cm and the accuracy at the level of 1 cm is estimated to ±3 dB.

Sum Rules for Parallel Plate Waveguides: Experimental Results and Theory

An experimental approach to investigate the forward scattering sum rule for periodic structures is presented. This approach allows an upper bound on the total cross section integrated over a bandwidth from a simple static problem to be found. Based on energy conservation, the optical theorem is used to construct a relation between the total cross section and the forward scattering of periodic structures as well as single scatterers inside a parallel-plate waveguide. Dynamic measurements are performed using a parallel-plate waveguide and a parallel-plate capacitor is utilized to find the static polarizability. Convex optimization is introduced to identify the total cross section in the dynamic measurements and estimate an optimal lower bound on the polarizability for objects. The results show that the interactions between the electromagnetic field and an object over all wavelengths are given by the static polarizability of the object.

On the extraordinary transmission through sub-wavelength apertures in perfectly conducting sheets

Extraordinary transmission of electromagnetic power through sub-wavelength apertures is usually observed in a narrow bandwidth range and the transmission outside this range is low. In this paper, it is shown that the transmission through periodic apertures in an otherwise perfectly electric conducting sheet satisfies a sum rule that relates wavelength regions with transmission above a threshold with the polarizability of the complementary structure. The theoretical results are illustrated with a numerical example for split ring apertures.

Time domain material characterizations using leaky lens antennas

A novel time domain methodology to find the permittivity of materials at mm-wave frequencies is investigated. A wide-band, and non-dispersive leaky lens antenna together with an in-house fabricated wavelet generator, transmit high frequency short pulses through a dielectric slab. A non-dispersive dielectric represents an amplitude change due to the losses and the mismatch at the dielectric interface and a delay in the time domain signal that associated with the permittivity. The effects of a plexiglas dielectric slab on the time domain signal is shown and the delay in the signal is used to find the permittivity of the slab.

Sum rules for metamaterials in parallel plate waveguides

An optical theorem and forward scattering approach for a bounded object confined between the plates of a parallel plate waveguide is investigated. A forward scattering sum rule together with the properties of positive real functions is used to show that the total absorption and scattering of an object is bounded by its static polarizability. A parallel plate waveguide and a parallel plate capacitor are used to estimate the dynamic and static properties, respectively. The results verify that the total cross section of an object integrated over the entire spectrum is proportional to the static polarizability.