Abstract

Seven quantities are found to be invariant for a monochromatic electromagnetic beam (that is, they have the same value everywhere along the length of the beam). These quantities are related to the conservation of energy, momentum and angular momentum. The simplest of them can be interpreted as the momentum content per unit length of the beam, . The energy content per unit length depends on position, in general, and we always have . The angular momentum content per unit length is also not an invariant. The six other invariants are integrals over elements of the Maxwell stress tensor. Examples of the invariants, and of the non-invariant quantities and , are given for TM and 'circularly polarized' beams based on exact solutions of the Maxwell equations.

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