Photonic band structure of the photonic crystal made of triangular-arrayed magnetic (solid lines) or dielectric (dashed lines) rods for (a) TM and (b) TE modes. The magnetic rods have (10,1.5) for , whereas dielectric rods have (15, 1). The ratio of the rod diameter to the rod spacing is 0.4.
Frequency-dependent (a) phase index , (b) refractive angle , and (c) resolution for TM modes propagating through the photonic-crystal prisms consisting of triangular-arrayed magnetic (solid lines) or dielectric (dashed lines) rods.
Scheme of the 30°–60°–90° photonic-crystal prism investigated here. Continuous-wave TM modes of various frequencies (a) lower than and (b) higher than are incident normally to the prism through the hypotenuse and propagate effectively in the photonic-crystal prism along the direction. For , TM modes come out of the prism through the long leg at a refractive angle , whereas TM modes having experience total reflections at the long and short legs and transmit through the hypotenuse.
Frequency-dependent (a) phase index , (b) refractive angle , and (c) resolution for TE modes propagating through the photonic-crystal prisms composed of triangular-arrayed magnetic (solid lines) or dielectric (dashed lines) rods. The scheme of the photonic-crystal prism and the propagating direction of a guided TE mode are shown in the inset of Fig. 2(b).
Parameters of a dielectric and a magnetic PC prism/demultiplexer to spread TM/TE modes of 1540 and in wavelength. is the rod spacing and is the rod diameter of a PC prism. The corresponding dimensionless frequency and prisming resolution are denoted with and , respectively. is the difference in the refractive angles of these two modes (1540 and in wavelength) propagating through a PC prism. The transmission denotes the amplitude ratio of the electric fields of the reflected mode to the incident mode at the hypotenuse of the triangular PC prism.
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