Light propagation in connection with communication by laser light is discussed. As a model of the field, with extension α and radius of curvature of wave surface l, uA= α-1 exp[ - (ρ2/2α2)+jk(ρ2/2l)], is chosen. The field up after propagation to distance Z is up = β-1je-iδ exp[- (r2/2β2)-jk (Z + γr2)].
The position of minimum extension β is not the ordinary focus because of the significant effect of diffraction by the aperture. By use of these results, the condition of α and l is analyzed in order to transfer the light with minimum loss over the distance D through a pipe with the linear dimension Φ, and the proper relay optical system is discussed.
KENRO MIYAMOTO, "Propagation of Laser Light," J. Opt. Soc. Am. 54, 989-990 (1964)