Mode Conversion in Lens Guides with Imperfect Lenses

There has been much uncertainty about the optical quality required for the components in an optical transmission link. Particularly for a lens guide with thousands of lenses, this is a major cost factor. It lias been shown that systematic lens aberrations may lead to a severe degeneracy of a transmitted laser beam, 1 but hardly anything is known about random errors. Previous work in this field dealt with antenna or imaging problems, 2,3 - 4 but none of these theories can be applied to iterative structures. The theory presented here was developed in parallel with experiments in a half-mile underground lens guide designed to gain data about the required component quality. 5 This guide employed antireflection-coated quartz lenses separated by about 140 m. A loss of roughly 1 percent per lens was measured, so that a transmission over 100 miles without amplification seems feasible. Systematic aber2467 2408 T H E BELL SYSTEM TECHNICAL JOURNAL, DECEMBER lflf>7 rations are negligible as compared with random surface irregularities. These irregularities are of various nature and origin. There arc minute scratches in the polished surface and tiny holes or craters in the antireflection coatings. Both cause a wide angle scattering and part of the measured overall loss without considerably changing the intensity profile or the phasefront of the transmitted light beam. On the other hand, the polishing process achieves a spherical surface only to a certain degree, so there are always small smooth protuberances and recesses called "polishing errors." They show up in an interferometer check and their magnitude is usually given in fringes or wavelength of the light used in the interferometer.