Electromagnetic fields and forces in nanostructures

• Main Author: Antonoyiannakis, Emmanuel (Manolis) Ioannou
• Other Authors: Pendry, John
• Published: Imperial College London 1998
• Subjects: 621.384
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.632409

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. Our approach can be applied to both dielectric and metallic systems characterised by a local frequency-dependent dielectric function, and in principle to any size and geometry. In this study we are particularly interested in calculating forces on nanostructures, induced by a beam of monochromatic light (such as a laser) of frequency w. These forces are the direct analogue of Van der Waals interactions at a single frequency: the presence of matter scatters the light and alters the EM field, resulting in an energy-change that manifests itself as a force. 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. In order to understand the main features of light-induced EM forces, as well as to provide a testbed for our numerical methodology, we first solve (analytically and numerically) for two homogeneous systems: a half-space and a slab. We find that in passing from a low-e to a high-e medium, the light beam always attracts the interface {i.e. the surface force is negative). The implication is that light will generally induce an attraction between the surfaces of two liquids separated by a layer of lower e. For attraction between solids there is a tougher requirement: the total force must also be negative. When the EM field is that of a travelling wave the total pressure is positive. In contrast, evanescent waves may cause the total pressure to become attractive (negative). Thus by shining evanescent light in the region between two solid bodies an attraction between them may be induced. We then study numerically the influence of monochromatic light (a travelling wave) on a crystal of dielectric spheres of GaP, concentrating on total forces induced on each sphere and on the crystal as a whole. We identify three regimes in the response of the system to radiation: • At large wavelengths the crystal may be approximated by a homogeneous slab with an effective permittivity eg//. The analytical results for reflectance and forces apply. • At wavelengths comparable to the lattice constant, multiple scattering effects tune in: when lo is inside the photonic band gaps the reflectivity of a thick crystalline slab rises to unity, the beam bounces off the crystal and there is a maximum momentum exchange (and largest forces). Also, a multitude of force orientations results when the Bragg conditions for multiple outgoing waves are met. • Much more interesting is the regime where the radiation couples to the E M eigenmodes supported by isolated spheres (Mie resonances). These modes are analogous to electronic orbitals and, like their electronic counterparts, can form bonding and anti-bonding interactions between neighbouring spheres. By irradiating the system with light at the bonding frequency an attractive interaction is induced between the spheres. The photo-induced attraction is strong; for a moderate I₀ ~ 3 x 10⁸ W/m² it surpasses all other interactions present (gravitational, thermal and Van der Waals) by 1-2 orders of magnitude. These resonant forces are sensitive to absorption, but, for GaP spheres in water (a common liquid medium for colloids), their effect should still be clearly seen, even for a polydispersion of a few percent. Thus we suggest that by judicious selection of bonding states we can drive a system towards a desired structure, rather than rely on the structure dictated by gravitational and Van der Waals forces. Apart from possible applications in the fabrication of 3D photonic crystals, the resonant mechanism leading to the bonding/anti-bonding effect may contribute to our understanding of novel non-linear phenomena arising due to the application of laser light fields in nanostructures.