Lorentz force and radiation pressure on a spherical cloak

Abstract

The mechanical behavior of a transformation based spherical cloak under wave illumination is derived. We show that the equatorial region of the cloak is subject to much higher stress than the polar regions, where the polar axis is defined along the wave propagation direction. These forces do not exist before transformation but stem from the squeezed electromagnetic space. The trajectory of the ray can be interpreted as a result of the recoil force that the cloak exerts upon the ray. The total radiation pressure on an ideal cloak is shown to be exactly zero, effecting a stationary cloak. It is well known that electromagnetic waves carry both momentum and energy 1,2. When light impinges onto a dielectric particle, part of the optical momentum will transfer to it 3‐6, and the radiation pressure will accelerate the particle. That is the reason why we can see the comet’s tail, which results from the radiation pressure of the sunlight pushing particles of the tail away from the comet. The recently proposed invisibility cloak 7‐9, which neither absorbs nor reflects light, will be immune to the light radiation pressure. The idea of cloak has been proposed based on the coordinate transformation method, where a hole is created in the transformed space and an object in the hole can be concealed from detection 7‐9. Compared with the cloak design based on other approaches, such as the scattering cancellation method 10‐12, the anti-object method 13, and the dipole moment cancellation method using anomalous localized resonance 14,15 etc., the transformation based design has advantages that it does not depend on the parameters of the hidden object. The ray tracing method 7,16 and the full wave method 17‐22 have both shown that light can be smoothly guided around the transformation based cloak. Such interesting phenomena have been experimentally demonstrated by a two-dimensional cylindrical cloak with simplified parameters 23, a ground-plane cloak 24,25, and dielectric optical cloaks 26,27. The reason that the rays are guided around the invisibility cloak can be interpreted as a result of the bending of electromagnetic space, which is always associated with some force appearance, such that the gravity is the appearance of the bent time and space. Therefore, a bent electromagnetic space must exhibit certain force properties and affect the mechanical behavior of light in physical space. Such mechanical behavior is a very fundamental physical problem associated with the transformed invisibility cloak but has not been revealed. In this Rapid Communication, the mechanical behavior of a general transformation based spherical cloak under planewave illumination is revealed based on Lorentz force, which links the Maxwell equations to mechanics in the theory of electromagnetics. We show that the equatorial region of the cloak is subject to much higher stress than the polar regions, where the polar axis is defined along the wave propagation direction. These forces do not exist before transformation but stem from the squeezed electromagnetic space and are one of the ways that it appears in physical space. In addition, the force distribution exhibits a symmetric pattern in the cross section perpendicular to the wave propagation direction, therefore the total radiation pressure on an ideal cloak is exactly zero. The trajectory of the ray inside of the cloak can be interpreted vividly as a result of the recoil force that the cloak exerts upon the ray. The three-dimensional spherical cloak we consider here has an inner radius R1 and outer radius R2. The cloak shell within R1rR2 is a radially uniaxial and inhomogeneous