arXiv subjects
Publications and source records attributed to Adriaan Tip.
Photonic band structure of metal-dielectric and semiconductor-dielectric layered structures are studied in the presence of a strong absorption. It is shown that absorption can enlarge some gaps by as much as 50%.
For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $ε_s$ is greater than the dielectric constant $ε_b$ of the background medium, then for any filling fraction $f$ there exists a critical $ε_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $ε_s <ε_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5%$.
The transition operator T for the scattering of a particle from N potentials V_j can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in < k|T(sigma^{2}+ i0)|k' >, |k|=|k'|=σ, then each t_j is also on-shell.