OPTIMAL BEAM FORMING FOR LASER BEAM PROPAGATION ...

YYouXθvXAZZ = 0Z = dFigure 3.1: The scalar diffraction of optical wave from the aperture plane tothe target plane.and c is the propagation speed of the wave in the medium. For monochromaticwaves, the complex wave function f(⃗r, t) can be written in the formf(⃗r, t) = f(⃗r)e j2πνt , (3.3)where f(⃗r) is the complex amplitude and satisfies the Helmholtz equation:(∇ 2 + k 2 )f(⃗r) = 0, (3.4)where k = 2π/λ is the wave number. For homogeneous media, the wavelengthand corresponding wave number is constant. For propagation in inhomogeneousmedium, the wave number can be expressed as a function ofthe position k(⃗r).Consider the wave propagation from aperture plane z = 0 to plane z = das shown in Figure 3.1. By applying the integral theorem of Helmholtz andKirchhoff, the wave diffraction by an aperture A in an infinite opaque screen17