Design and analysis of inhomogeneous photonic media:From mode converters to optical cloaking

After nearly a century from the Lord Rayleigh's demonstration of band-gap characteristic of one dimensional periodically sequenced layers, the requirement of band-gap devices in modern day optics led the researchers to derive two and three dimensional frequency selective devices. Pioneering studies of Yablonovitch and John provided control over the electromagnetic wave propagation by the structures denominated as photonic crystals (PCs). The interaction between these periodical dielectric structures and photon waves are similar to that of semiconductor crystals and electron waves regarding the investigations of dispersion diagrams. The PCs also have inhibited and allowed frequency/energy regimes as for the semiconductor crystals. However, bandwidths of photonic devices are usually greater compared to electronic ones. A great interest is aroused in photonic devices, also in PCs, due to this bandwidth distinction and irreducible response time of modern electronic components. Some optical/photonic designs require spatial inhomogeneity with respect to the refractive index. Except of being the standard band-gap devices, PCs are also useful to generate inhomogeneous photonic media, such as gradient index waveguides. The effective medium theory is utilized to mimic the continuous gradient which explains long wavelength behavior within the unit cells of discrete PCs. Highly efficient and broad band photonic designs are generated implementing numerical methods based on frequency and time domain.