Michael Berry

Geometry of 3D monochromatic light

Wave geometry beyond the scalar and paraxial approximations can involve the electric field (E) alone, or in combination with the magnetic field (‘electric-magnetic democracy’, EH). The orbital part of the E Poynting vector is proportional to the nonconservative ‘curl force’ exerted on small absorbing polarisable particles; its circuit integral represents the work done transporting a particle. Normalised versions of the E and EH orbital Poynting vectors naturally represent the direction of the wave at each point, generalising the phase gradient for scalar waves; there are associated geometric phases. For isotropic ensembles of random waves, the probability distributions of the different wavevectors are estimated by codimension arguments and calculated exactly for statistically isotropic superpositions of plane waves. Interference detail is weaker for E properties than for scalar, and weaker still for EH.