Mesoscopic Self-Collimation and Slow Light in All-Positive Index Layered Photonic Crystals

We demonstrate a mesoscopic self-collimation effect in photonic crystal superlattices consisting of a periodic set of all-positive index 2D photonic crystal and homogeneous layers. We develop an electromagnetic theory showing that diffraction-free beams are observed when the curvature of the optical dispersion relation is properly compensated for. This approach allows us to combine slow-light regime together with self-collimation in photonic crystal superlattices presenting an extremely low filling ratio in air.

Figure 1

Isofrequency curves of the first band for TE polarization (magnetic field parallel to the air hole axis). The arrows indicate the direction of ${\mathbf{v}}_{\mathbf{g}}$ and the red and blue areas correspond, respectively, to IFCs of positive and negative curvatures.

Figure 2

Curvature function $1/n_c$ computed in the $\Gamma M$ direction versus the reduce frequency. (a) For the infinite 2D PhC described in Fig. 1 and of unit cell depicted in the inset. The intersection points between $1/n_c$ and the straight dashed lines for $\alpha =0$, 1, and 3 correspond, respectively, to the self-collimation frequencies for the unbounded 2D PhC and for PhC superlattices of two filling ratios in PhC layers. (b) Graph of $1/n_c$ computed for the supercell corresponding to a PhC superlattice with $\alpha =1$ and $d_1=3a\sqrt{2}$ shown in the inset. Mesoscopic self-collimation arises for $a/\lambda =0.239$, where $1/n_c$ vanishes.

Figure 3

Map of the magnetic field modulus for a Gaussian beam of waist $W_0=8a$ (a) At the reduce frequency $a/\lambda =0.239$ for a PhC superlattice for $d_1=4a\sqrt{2}$ and $\alpha =1$. (b) At the reduce frequency 0.243 for $d_1=3a\sqrt{2}$ and $\alpha =3$. (c) The same Gaussian beam propagating in a homogeneous medium of optical index $n_2=2.9$ and for $a/\lambda =0.239$.

Figure 4

(a) Band diagram in the $\Gamma M$ direction of the PhC superlattice for $\alpha =1$ and $d_1=4a\sqrt{2}$ depicted in the inset. The red circles indicate the location of the self-collimation frequency 0.239. (b) Group index versus the reduce frequency.