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Radiation Characteristics of Circular Dielectric Waveguides

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Abstract

The radiation characteristics of isolated circular optical waveguides capable of supporting only low-order dielectric waveguide modes are studied both theoretically and experimentally for several combinations of modes, wavelength, diameter, and waveguide numerical aperture. Photographic and photoelectric measurements of the far-field intensities are compared with numerical predictions based on the equivalent current method of Schelkunoff. For a cross-sectional intensity distribution in the mode pattern of the approximate form Jn+12(ur/a) the predicted Fraunhofer pattern has the form:

[Jn+1(x)XJn(x)Jn+1(u)uJn(u)(u2x2)(q2+x2)]2,
where Jn is the Bessel function of order n, u(= k1a sinθ1) the mode eigenvalue, and x(= k0a sinθ) the customary diffraction parameter. θ1 is the characteristic angle of the mode in the fiber of core refractive index n1 and coating n2. Generally, the pattern has its strongest maximum at an angle slightly less than the Snell complement of θ1. However, the parameter q2 = (k0a)2(n12n22) − u2 becomes vanishingly small as the modes approach cutoff, giving rise to strong intensities in the forward direction. Photometric data show agreement with numerical predictions within experimental accurate limits.

© 1965 Optical Society of America

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