By Ibanescu, Mihai
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Extra resources for Cylindrical Photonic Crystals
Eigenvalues were considered converged when the residue was less than 10-6. 1%. 4 Modes of Coaxial Omniguide A In the projected band structure for coaxial omniguide A (Fig. 3-2(c)), the red and yellow bands represent guided modes localized within the region defined by the inner and outer coaxial radii of the waveguide. The dashed lines represent modes with less than 20% localization within the coaxial region. There is close correspondence between the modes within the omnidirectional reflectivity range labeled m = 1 to m = 6 and those of the coaxial cable labeled TE1l1 to TE61 .
These are k, the axial component of the wave vector, and m, the angular momentum (m = 0, 1, 2, ... ). For a given mode, the radial and angular components of the electric and magnetic fields can be calculated from the corresponding z (axial) components . For a given wave vector kz and angular momentum m, the axial field components in a layer of index n have the general form F(z, r, 0) = [AJm(kTr) + BY(kTr)] . (C1iee m + C2e- i m o ) where F stands for either Ez or Hz; Jm and Ym are Bessel functions of the first and second kind, respectively; and kT is a transverse wave vector kT = V/(nw/c) 2 - k 2.
2 (27r/a) in Fig. 3-4. Parts (a) through (c) are the electric field components along the x, y, and z directions, respectively. The color bar indicates that large positive and negative values are shown as dark red and dark blue regions, respectively, whereas white areas represent regions of zero values of the electric field, and light-colored areas represent regions of low values of the electric field. The field distribution clearly reveals a high confinement of the mode in the coaxial waveguiding region, and in this region it is nearly completely transverse to the direction of propagation (less than 10 - 3 of the intensity is along z), as desired.
Cylindrical Photonic Crystals by Ibanescu, Mihai