Optically induced band structure of free electrons in an external plane wave field

The motion of a nonrelativistic free charged particle in a classical electromagnetic plane wave field is investigated. By introducing the ansatz of a modulated plane wave for the wave function the problem is reduced to the solution of the general Mathieu equation for circularly polarized field and to the solution of the Hill equation for linearly polarized field. The corresponding eigenvalue equations show that physical values of the energy are separated into bands. The relationship with earlier methods is also discussed. (author)