The Statistical Effects of Random Variations in the Components of a Beam Waveguide

A long sequence of spaced lenses is of considerable interest for optical communications. It is known that the diffraction losses in such an optical beam waveguide can be kept very small for moderate size lenses.1,2 This means that if a transmission line is made of identical low-loss lenses, spaced identically along a straight line with each lens centered on this straight line, there is a mode of propagation which is low loss. However, if there are imperfections in the transmission line, the light beam will begin to wander from the axis or the beam size will grow and the beam will eventually strike the edge of the lens and be lost. Since the diffraction loss of the beam in a perfect line can be kept very small, it is the line imperfections, the line axis curvature, and the scattering and absorption at each lens which will primarily determine the 451 452 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , MARCH 1966 optical loss. Gas lenses have been considered for reducing the scattering and absorption losses.3 Rowe4 and Hirano and Fukatsu 5 have shown how the beam position is affected by random lateral lens displacements. Berreman, 6 Marcuse,7 and Unger8 have considered correlated lateral lens displacements in the form of bends. All of these analyses have assumed perfect lenses and perfect spacing and have shown the growth of the beam displacement due to lateral lens displacements only. It is the purpose of this paper to show how the previously obtained results are altered when the lens focal lengths and lens spacings have random variations.