Superscattering of a pseudospin-1 wave in a photonic lattice

We uncover a superscattering behavior of a pseudospin-1 wave from weak scatterers in the subwavelength regime where the scatterer size is much smaller than the wavelength. The phenomenon manifests itself as unusually strong scattering characterized by extraordinarily large values of the cross section even for arbitrarily weak scatterer strength. We establish analytically and numerically that the physical origin of superscattering is revival resonances, for which the conventional Born theory breaks down. The phenomenon can be experimentally tested using synthetic photonic systems.

Figure 1

Pseudospin-1 band structure and the underlying photonic lattice structure. The lattice has a triangular configuration constructed by cylindrical alumina rods in air. (a) The band structure with an accidental-degeneracy-induced Dirac point at the center of the first Brillouin zone, (b) sketch of the physical lattice, and (c) band structures outside and inside of the scatterer. A possible experimental parameter setting is $a_1=17\mathrm{mm}, r_1=0.203a_1,a_2=0.8a_1$, and $r_2=0.203a_2$. The dielectric constant of the alumina rod is 8.8.

Figure 2

Persistent revival resonances of pseudospin-1 particles from a weak circular scatterer at low energies. (a) Contour map of transport cross section in units of $R$ (on a logarithmic scale) versus the scatterer strength $\rho =V_{0}R$ and size $x=kR$ for relativistic quantum scattering of 2D massless pseudospin-1 particles. Revival resonances occur, which can lead to superscattering (see Fig. 3). (b) Similar plot for pseudospin-$1/2$ particles for comparison, where no resonances occur, implying total absence of superscattering. The scatterer is modeled as a circular steplike potential $V\left(r\right)=V_0\mathrm{\Theta }(R-r)$, representing a finite-size scalar impurity or an engineered scalar type of scatterer. The markers correspond to the theoretical prediction, where the black circles and crosses are from $\rho \approx {\rho }_{0,m},{\rho }_{1,n}$ (for $x\ll 1$), and the red stars follow the revival resonant condition given by $\rho =2x$ for $\rho \ll 1$.

Figure 3

Superscattering of pseudospin-1 wave. (a) Transport cross section as a function of $x\equiv kR$ for a weak scatterer of strength $\rho \equiv V_{0}R=0.1$ and (b) dependence of the maximum transport cross section on $V_{0}R$.

Figure 4

Wave-function patterns associated with superscattering. For $V_{0}R=0.5$ and $kR=0.2485$, the distribution of the real part of one component of the spinor wave function $\text{Re}\left({\mathrm{\Psi }}_2\right)$ for (a) pseudospin-$1/2$ and (b) pseudospin-1 waves. (c) and (d) Magnification of part of (a) and (b), respectively. Both axes in (a)–(d) are in units of the incident wavelength $\lambda$. The color code denotes the quantity $\text{Re}\left({\mathrm{\Psi }}_2\right)$.

Figure 5

Total and transport cross sections versus $x\equiv kR$ for a given weak-scattering potential $\rho \equiv V_{0}R=0.1$ in cases of pseudospin-1 and pseudospin-$1/2$.