Laser-particle interactions in shaped beams: Beam power normalization

We present a semi-analytic theory for calculating light-particle interactions in shaped laser beams even when the paraxial beam description is invalid. It requires weighting the expressions for the cross sections with a beam normalization parameter, Ï°, associated with the incident power. An analytical formula for Ï° in terms of the beam shape coefficients [1-3] is derived. We show that approximate expressions for this beam normalization parameter based on either a Parseval or paraxial type approximation are inadequate for optics involving high numerical apertures.

► A formula relating the power of shaped laser beams to their beam shape coefficients is derived. ► Differences between this exact formula and a Parseval type relation are explained. ► Differences between this formula and a paraxial beam approximation are discussed. ► Applications of this formulation in cross section calculations are demonstrated.