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The transmission of light waves for communication in a medium sheltered from atmospheric effects requires wave guidance providing frequent changes in direction of propagation. This paper shows that, in any electromagnetic waveguide having transverse planes in which the field is essentially equiphase, the transverse width of the field distribution 2a and wavelength λ determine the order of magnitude of the direction-determining parameters, Rmin, the minimum bending radius, and δmax, the maximum abrupt angular changes, according to the relationsR₌₈₍ = ₂ (₀^₃/ ^{2) ₌₀ₗ = 1 2 (/a) which are valid in the region λmin. The quantity δmaxmay be regarded as the maximum value of the accumulated angular errors (rms sum, for example) in a transmission line including reflecting or refracting elements for directional control. For a light beam at λ = 0. 6328 microns having a diameter of 1. 0 mm, δmax= 0. 036° and Rmin= 600 meters. Small-diameter beams ease the problem of directional control. There is no fundamental reason why small beams should not be achievable with low loss in the straight condition, but many guiding structures do have an inverse relation between beam diameter and straight-condition attenuation coefficient. To explore the direction-controlling properties of specific media and the interaction of Rminand δmaxwith straight attenuation coefficient, the following waveguides and associated criteria for establishing Rminand δmaxwere studied:
Stewart E. Miller (1964) studied this question.