Analytical Descriptions of Finite-Energy Bessel Beams in the Generalized Lorenz-Mie Theory

The present work is a first attempt to introduce physical or finite energy axially symmetric fields, under the paraxial approximation, into the theoretical framework of the generalized Lorenz-Mie theory. Based on analytical descriptions in terms of a discrete superposition of Bessel-Gauss beams, we derive the beam shape coefficients of a particular class of axially symmetric beams, viz. truncated zero-order scalar Bessel beams. The analyticity of the present approach is interesting from the perspective that it avoids, from the very outset, extensive computational optimization processes involved in ABCD optical systems or the introduction of non-physical ideal (infinite energy) solutions of Maxwell's equations. As an example of application, optical forces exerted on spherical nano and microparticles are calculated and compared with those forces as evaluated with ideal scalar Bessel beams. Since it can be readily extended so as to encompass other types of axially symmetric truncated beams, we envision the present approach as a fast computational technique for immediate implementation in the analysis of light scattering by nano-and micro-particles.