Band structure for a one-dimensional photonic crystal containing left-handed materials

Abstract

The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some abnormal phenomena such as spurious modes with complex frequencies, discrete modes and photon tunnelling modes are observed in the band structure. The existence of spurious modes with complex frequencies is a common problem in the calculation of the band structure for such a photonic crystal.Physical explanation and significance are given for the discrete modes (with real values of wave number) and photon tunnelling propagation modes (with imaginary wave numbers in a limited region).

Tunable transmission and bistability in left-handed band-gap structures

“…More importantly, a onedimensional stack of layers with alternating RH and LH material with vanishing average refractive index <n> displays a novel bandgap [8,9,10] that differs from a conventional Bragg reflection gap.…”

Photonic Modes in Dispersive and Lossy Superlattices Containing Negative-Index Materials

“…For layered structures containing LHMs and ordinary right-handed materials (RHMs), several results have been reported [7][8][9][10][11][12][13][14]. For example, unusual photon tunneling between two semi-infinite media separated by a RHM-LHM bilayer was found in the microwave regime [10].…”

“…Reference [14] explicitly demonstrates the existence of four types of bulk electromagnetic modes in periodic LHM/RHM arrays: the spurious modes, without physical meaning because they exhibit complex frequency, the discrete modes, real modes that appear at the center or the border of the Brillouin zone, the tunneling modes, characterized by evanescent (decreasing or increasing) fields in subsequent layers, and, the ordinary propagating modes. The same electromagnetic modes are expected even when absorption is not ignored [10,14].…”

Band Structures and Abnormal Behavior of One Dimensional Photonic Crystal Containing Negative Index Materials

“…The dispersion relations, reflection characteristics, group velocities and n eff of the periodic structure contain negative index materials is calculated numerically using transfer matrix method [16,19,26]. The geometry of the structure under study is shown in Fig.…”

“…They have shown that photon is tunneled through a much greater distance when a NIM has same magnitude of refraction index and thickness as those of the positive index material. Wu et al [16] have shown the dispersion relation of onedimensional periodic structure with alternate positive index material (PIM) and negative index material (NIM). The periodic structure has described unusual phenomena such as spurious modes with complex frequencies, discrete modes and photon tunneling modes.…”