Designing Spinning Bloch States in 2D Photonic Crystals for Stirring Nanoparticles

Based on an optical analogy of spintronics, the generation of spinning Bloch states is theoretically investigated in two-dimensional photonic crystals without space-inversion symmetry. We address its close relation to the Berry curvature in crystal momentum space, which represents the nontrivial geometric property of a Bloch state. It is shown that the Berry curvature is easily controlled by tuning two types of dielectric rods in a honeycomb photonic crystal. Bloch states with large Berry curvatures appear as optical tornadoes in real space. The radiation force of such a configuration is analyzed, and its possible application for selective optical stirrer is discussed as a complementary proposal in optical tweezers technology.

Figure 1

(a) Photonic band structure of the honeycomb PhC with ${\epsilon }_A=1.44$, ${\epsilon }_B=1$, ${\epsilon }_b=4$, $r_A=r_B=0.2a$. Black solid lines for the TM mode and red dashed lines for the TE mode. (b) BC of the TE first band.

Figure 2

Minkowski momentum density of the Bloch state at the $K$ point $(\frac{4\pi }{3a},0)$ of the TE first band; see Fig. 1. Inset for the state at the point $(\frac{4\pi }{3a}-0.004\times \frac{2\pi }{a},0)$ of the same band. The circles of solid lines and dashed lines stand for $A$-type and $B$-type rods, respectively. The magnitude is normalized by $(\mathrm{\text{average energy density}})/c$. Color contour is the absolute value in the main panel and that multiplied by 4 in the inset.

Figure 3

Radiation force per unit length induced by the tornado at the $K$ point of the TE first band in Fig. 1. The probe is a thin metallic rod with ${ϵ}_p=-4.1$ and $r_p=0.02a$. The magnitude is normalized by $(\mathrm{\text{average energy density}})\times a$. The arrow size is the actual size multiplied by 0.05.