Basic full complex-argument Laguerre-Gauss wave

Abstract

The paraxial wave equation in the cylindrical coordinate system has a series of higher-order solutions known as the complex-argument Laguerre-Gauss beams [1,2]. This series of eigenfunctions is a complete set. These higher-order Gaussian beams are characterized by the radial mode number n and the azimuthal mode number m. The fundamental Gaussian beam is the lowest-order (n = 0, m = 0) mode in this set. The higher-order hollow Gaussian beams discussed in Chapter 8 correspond to n = 0. In this chapter, a treatment of the complex-argument Laguerre-Gauss beams is presented. As for the fundamental Gaussian beam, for the complex-argument Laguerre-Gauss beams also, the reactive power vanishes. The higher-order point source in the complex space required for the full-wave generalization of the complex-argument Laguerre-Gauss beams is deduced. The basic full complex-argument Laguerre-Gauss wave generated by the complex space source is determined [3,4]. The real and reactive powers of the basic full higher-order wave are evaluated. As expected, the reactive power is infinite, as for the basic full Gaussian wave. The general characteristics of the real power are examined. The real power increases monotonically, approaching the limiting value of the paraxial beam as kw0 is increased. For a fixed kw0, in general, the real power decreases as the mode order increases.