Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials

Abstract

We show theoretically that a one-dimensional photonic crystal containing a negative-index material has an omnidirectional gap, owing to the mechanism of zero (volume) averaged refractive index. In contrast to the Bragg gap, the edge of such a zero-n̄ gap is insensitive to incident angle and polarization. When an impurity is introduced, a defect mode appears inside the zero-n̄ gap with a very weak dependence on incident angle and invariant with scaling.

Physics of the zero- photonic gap: fundamentals and latest developments

“…In contrast to Ref. [36] where only the normal incidence case was considered, Jiang et al [37] studied how a zero-n -gap and a Bragg gap evolve as incident angle and polarization change in a carefully designed 1D PC. The results were reproduced in Figure 3 where the upper band gap was identifi ed as a conventional Bragg gap and the lower one the zero-n -gap.…”

“…By inserting a angle and polarization, calculated for a 1D PC containing alternative stacking of homogeneous positive-n and negative-n slabs with structural and material details recorded in Ref. [37] . Reproduced from Ref.…”

“…Reproduced from Ref. [37] with the permission of American Institute of Physics. defect layer into a PC, defect modes can be induced inside both zero-n -and Bragg gaps.…”

“…It was shown in Ref. [37] that the defect mode inside the zero-n -gap remains invariant with the scaling of non-defect part, while the defect mode inside the Bragg gap shifts greatly in frequency with scaling. On the other hand, when the incident angle increases from 0 ° to 30 ° , the defect mode inside the zero-n -gap remains nearly invariant, while the defect mode inside the Bragg gap changes quickly (see Figure 4 ).…”

“…E z Four different samples were experimentally measured [ Figure 7 A Figure 4 Transmittance through a doped 1D PC containing both positive-n and negative-n slabs (see Ref. [37] for the structural and material parameters), calculated at different incident angles and polarizations. Reproduced from Ref.…”