The field configurations and propagation constants of the normal modes are determined for a hollow circular waveguide made of dielectric material or metal for application as an optical waveguide. The increase of attenuation due to curvature of the axis is also determined. The attenuation of each mode is found to be proportional to the square of the free‐space wavelength λ and inversely proportional to the cube of the cylinder radius a. For a hollow dielectric waveguide made of glass with v = 1.50, λ = 1μ, and a = 1 mm, an attenuation of 1.85 db/km is predicted for the minimum‐loss mode, EH11. This loss is doubled for a radius of curvature of the guide axis R ∼ 10 km, Hence, dielectric materials do not seem suitable for use in hollow circular waveguides for long distance optical transmission because of the high loss introduced by even mild curvature of the guide axis. Nevertheless, dielectric materials are shown to be very attractive as guiding media for gaseous amplifiers and oscillators, not only because of the low attenuation but also because the gain per unit length of a dielectric tube containing He‐Ne “masing” mixture at the right pressure can be considerably enhanced by reducing the tube diameter. In this application, a small guide radius is desirable, thereby making the curvature of the guide axis not critical. For λ = 0.6328μ and optimum radius a = 0.058 mm, a maximum theoretical gain of 7.6 db/m is predicted. It is shown that the hollow metallic circular waveguide is far less sensitive to curvature of the guide axis. This is due to the comparatively large complex dielectric constant exhibited by metals at optical frequencies. For a wavelength λ = 1μ and a radius a = 0.25 mm, the attenuation for the minimum loss TE01 mode in an aluminum waveguide is only 1.8 db/km. This loss is doubled for a radius of curvature as short as R ∼ 48 meters. For λ = 3μ and a = 0.6 mm, the attenuation of the TE01 mode is also 1.8 db/km. The radius of curvature which doubles this loss is approximately 75 meters. The straight guide loss for the EH11 mode for λ = 1μ and a = 0.25 mm is 57 db/km and is increased to 320 db/km for λ = 3μ and a = 0.6 mm. In view of the low‐loss characteristic of the TE01 mode in metallic waveguides, the high‐loss discrimination of noncircular electric modes, and the relative insensitivity to axis curvature, the hollow metallic circular waveguide appears to be very attractive as a transmission medium for long distance optical communication.

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Light transmission through a curved dielectric rod of rectangular cross section embedded in different dielectrics

New technologies of fiber manufacture and a demand for unuaucd fiber qtudities in communication systems have intensified the interest in a comprehensive theory of multimode fibers vnth nonuniform index distribu tions. This paper deals with a general class of circular symmetric profiles which comprise the parabolic distribution and the abrupt core-cladding index step as special cases. We obtain general results of useful simplicity for the impulse response, the mode volume, and the near-and far-field power distributions. We suggest a modified parabolic distribution for best eqvalvnation of mode delay differences. The effective width of the resulting impulse is more than four times smaller than that produced by the parabolic profile. Of course, practical manufacturing tolerances are likely to ϊτιfluence this distribution. A relation is derived between the maximum index error and the impulse response.1563

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