Mass of the photon propagating in an optical medium and mass of its electromagnetic and mechanical components

Abstract

A propagation of a photon or light pulse in an optical medium is accompanied by appearance of the mechanical momentum in a form of a mechanical motion of optical medium located between the leading and trailing edges of the pulse. As a result, a propagation of the pulse is accompanied by the mechanical momentum that is a part of total momentum of the pulse. Since a trajectory, momentum and speed of the pulse in an inhomogeneous optical medium are known, the pulse acceleration and the force applied to the pulse can be calculated. It turns out that directions of the acceleration and the force are different in a general case. Then the mass of the pulse based on the second Newton law cannot be presented by a single real number. It is shown that the total mass of the pulse can be expressed by a single complex number. Modulus of the mass increases by n2 times as compared with the mass of the same pulse in free space where n is the reflective index in the place where the pulse is propagating. Argument of the mass is equal to the double angle between the main normal to the pulse trajectory and the grad(n) in the same place. Electromagnetic component of the mass of the pulse is not changed and is equal to the pulse mass is free space. The mechanical component of the pulse mass is a difference between the total and electromagnetic masses.