Electromagnetic forces in photonic crystals

We have developed a general methodology for computing electromagnetic (EM) fields and forces in matter, based on solving the macroscopic Maxwell’s equations numerically in real space and adopting the time-averaged Maxwell stress tensor formalism. We can treat both dielectric and metallic systems characterized by a local frequency-dependent dielectric function, and of any size and geometry in principle. In this paper, we are particularly interested in calculating forces on nanostructures, induced by a beam of monochromatic light (such as a laser). The motivation behind this particular direction is the facilitation of self assembly in colloidal systems with the aim of aiding the fabrication of photonic crystals. We first look at two homogeneous systems: a half space and a layer. In passing from a low-$\epsilon$ to a high-$\epsilon$ medium, the light beam always attracts the interface (i.e., the surface force is negative). Thus the surfaces of two liquids separated by a layer of lower $\epsilon$ will generally be attracted towards each other, whereas for solids the total force must also be negative. This condition is not satisfied for the EM field of a traveling wave, but may be fulfilled for an evanescent wave. Thus, by shining evanescent light in the region between two solid bodies an attraction between them may be induced. We then study the EM forces induced by a laser beam on a three-dimensional crystal of dielectric spheres of GaP in air. At wavelengths comparable to the lattice constant, multiple scattering effects tune in: band gaps, Bragg scattering. But in all these cases the incident beam induces positive pressure on (and between) the spheres. Much more interesting is the regime where the radiation couples to the EM eigenmodes supported by isolated spheres (Mie resonances). These modes are analogous to electronic orbitals and, like their electronic counterparts, can form bonding and antibonding interactions between neighboring spheres. By irradiating the system with light at the bonding frequency an attractive interaction is induced between the spheres. For moderate intensities of the incident radiation these forces can overcome all other interactions present (gravitational, thermal, and Van der Waals) and may provide the main mechanism for formation of stable crystal structures in colloidal systems.