Mode-conversion loss in a sequential confocal lens system

Abstract

A sequence of equally spaced confocal lenses can be used for guiding electromagnetic energy. It has modes in which the field pattern is repeated at successive lenses. Each mode is effectively confined within a cylinder whose axis is the common axis of the system.The cylinder diameter is smaller for the lower modes and for close spacing of the lenses. At visible wavelengths a spacing of as much as a fraction of a mile may yet be small enough to make overspill of the lowest mode negligible and the attenuation virtually zero.For wider spacing or for higher modes the cylinder diameter may become comparable with the lens diameter, with consequent attenuation. For high enough modes, the attenuation may be so great that the mode virtually does not exist.If the lenses are perturbed from their correct positions, coupling between modes occurs. Sideways (off-axis) displacements seem most likely to be troublesome. The low-loss lowest mode tends to degenerate into higher modes with higher loss.If the sideways displacements are random, a distribution of power between a number of modes occurs, and a pattern exists that is repetitive. This power pattern replaces the modal amplitude pattern.The attenuation, which can be reduced in the simple case by close spacing of the lenses, can no longer be so reduced. Calculation for a numerical case at a visible wavelength shows that, if it is assumed that the r.m.s. offset cannot be expected to be less than 0.1–0.15 in, owing to instability of the lens mountings, then it would be necessary to have some form of automatic beam centring to reduce the attenuation below about 1 dB/mile. To this must be added the transmission losses of lenses and beam benders.