H. Guo et al., GEOMETRICAL STUDY OF PARAXIAL LIGHT-BEAM TRANSMISSION IN FREE-SPACE, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 40(6), 1997, pp. 644-651
By introducing an imaginary space transform curvature rho(s), a comple
x space called Riemannian space is constructed, in which the light pro
pagating in free space has the trajectory of straight line while propa
gating. Moreover, this curvature couples with that of the wave front o
f the paraxial beam rho(w), and therefore a complex curvature rho(c) i
s constructed, which can be employed to investigate the behavior of th
e light transmission and to generalize the ABCD law.