Microwave Volumetric Probe Measurements of Field localization, Zero and Negative Index within Photonic Bandgap Metamaterial Structures

摘要

Electromagnetic mode localization within photonic bandgap (PBG) crystals has been evidenced by external measurement of enhanced optical emission from quantum dots or photoemissive polymers that are placed within the structure. In this paper wavelength is decreased and photonic crystal dimensions increased to allow insertion of a loop probe in the PBG to directly measure volumetric electromagnetic fields; thereby producing a volumefrequency map of field amplitude and phase within the PBG. The unit cells of the PBG are formed from arrays of Alumina strips which are supported by surrounding acrylic supports. Electromagnetic fields of single, two and three layer PBGs are predicted and these compare well with measurement. Field localization within the PBG and transmission coefficients of the PBG, with and without electrical perturbations, are presented. Predictions assume layered unit cells formed from sections in which translational invariance along the Z-axis is assumed for z_(n-1)≤z≤z_n for the nth section. Periodicity implies that field X dependence can be represented as a sum of Floquet modes and field solutions are found by mode matching techniques in combination with multimode cascade matrix formalism. Transmission coefficient is measured using a focused beam, network analyzer based system and volumetric fields within the PBG are measured using a loop probe antenna inserted between Alumina strips and moved to different positions. Measurements at 1600 frequencies over the 4-18 GHz band at each of 100 positions are made. PBG fields are calibrated to probe measurements at identical positions and frequencies but absent the PBG. Both electromagnetic model and measurement shows field localization and effective negative or zero indexes at multiple frequencies within the 4 to 18 GHz band. Volumetric field magnitudes increase by at least one order of magnitude and local field phase-frequency derivatives are negative or near zero near localization frequencies. Field localizations and transmission are sensitive to small perturbations of electrical properties or geometry. Wideband measurements of PBGs, perturbed by small cylindrical inserts placed at high field locations, allow precision measurements of an insert's electromagnetic properties.