Figure 1

(a) The real (thick solid line) and imaginary (dashed line) parts of the polaritonic model dielectric function of $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ $({ϵ}_0=41.4,{ϵ}_{\infty }=13.4,\Gamma =0.035{\omega }_T)$. The (real) dielectric function in the absence of absorption $(\Gamma =0)$ is shown by the thin solid line. (b) The change in the density of states $\Delta n$ induced by a nonabsorbing $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ sphere of radius $S=0.5c∕{\omega }_T$ in air. The shaded regions indicate the frequency interval of the polariton gap.Reuse & Permissions

Figure 2

A square array, with lattice constant $a=1.1c∕{\omega }_T$, of nonabsorbing $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ spheres, with radius $S=0.5c∕{\omega }_T$, in air. Change in the density of states of the system with respect to air for ${\mathbf{k}}_{\Vert }=\mathbf{0}$ (a), and transmittance at normal incidence (b). The shaded regions indicate the frequency interval of the polariton gap. The region about the first dipole electric and quadrupole magnetic resonances of the single sphere below the polariton gap are shown with a higher resolution in the right panel.Reuse & Permissions

Figure 3

Transmittance (solid line) and absorbance (dashed line) of a square array, with lattice constant $a=1.1c∕{\omega }_T$, of absorbing $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ spheres, with radius $S=0.5c∕{\omega }_T$, in air, at normal incidence. The shaded region indicates the frequency interval of the polariton gap.Reuse & Permissions

Figure 4

(a) The photonic band structure of a sc photonic crystal of nonabsorbing $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ spheres $(S=0.5c∕{\omega }_T)$ in air, with $f=39.3\%$, along the [001] direction. (b) Transmittance at normal incidence of a slab of $N_L=8$ (001) planes of spheres of the above crystal. The shaded regions indicate the frequency interval of the polariton gap. The region about the first dipole electric and quadrupole magnetic resonances of the single sphere below the polariton gap are shown with a higher resolution in the lower panel. The thick (thin) lines refer to doubly degenerate (nondegenerate) bands.Reuse & Permissions

Figure 5

A detail view of diagrams (a) and (b) of Fig. 4 over a limited frequency region about the first dipole magnetic resonance of the single sphere. In the band-structure diagram (a), over the frequency gap, we show by broken lines the real-frequency lines with the smallest imaginary part. The imaginary part is shown in the shaded region. In the inset of the transmittance diagram (b) we show the transmittance at a given frequency $\omega =0.71{\omega }_T$ within the gap as a function of the thickness of the slab (filled circles). The straight line has a slope equal to $-2a\mathrm{Im}\left[k_z\right]$, where $\mathrm{Im}\left[k_z\right]$ is the smallest imaginary part of $k_z(0.71{\omega }_T,{\mathbf{k}}_{\Vert }=\mathbf{0})$.Reuse & Permissions

Figure 6

The complex photonic band structure of a sc photonic crystal of nonabsorbing $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ spheres $(S=0.5c∕{\omega }_T)$ in air, with $f=39.3\%$, along the [001] direction, over a limited frequency region about the first dipole magnetic resonance of the single sphere. The thick (thin) lines refer to doubly degenerate (nondegenerate) bands. The dotted lines show the projection of the complex bands on the $\omega \text{−}\mathrm{Re}\left[k_z\right]$ plane.Reuse & Permissions

Figure 7

Projection of the photonic band structure of a sc crystal of nonabsorbing $\mathrm{Li}\mathrm{Ta}{\mathrm{O}}_3$ spheres $(S=0.5c∕{\omega }_T)$ in air, with $f=39.3\%$, on the SBZ of the sc (001) surface, along the symmetry lines shown in the inset. The dashed line $\omega =c\mid {\mathbf{k}}_{\Vert }\mid$ shows the light cone in air. Next to this diagram we show the variation of the absolute gap (blank area) of the above crystal with the dielectric constant of the host medium.Reuse & Permissions

Figure 8

Resonance structures in the transmittance of a slab according to Eq. (A7). The sequential diagrams correspond to different values of $\varphi$, from 0° to 300° with a step of 60°.Reuse & Permissions