Far-field Radiation From a Cleaved Cylindrical Dielectric Waveguide

A determination of the angular spread in the far-field radiation pattern of a cleaved dielectric waveguide is made from the modal structure at the surface of the waveguide using the Smythe vector integral formulation. The essential features are the following. First, a mode exists in the fiber that has no wavelength cutoff - the so-called HEn mode. This mode arises when non-azimuthal angular dependence of the incoming radiation is present. Second, the energy flow from this hybrid mode fills the fiber face and is not annularly shaped as opposed to the symmetric TE and TM modes. Third, the HE11 mode is not polarization dependent in contrast to the TE and TM modes. Fourth, for small differences in the indices of refraction between the core and cladding regions only the HE11 mode will be supported until the next modes appear around 3.33λ. At this point, three new modes can propagate and the modal structure of the radiation becomes more complicated. Fifth, the far-field radiation pattern will have negligibly small angular dependence in the phases of the vector fields when only the lowest mode is present; the amplitude has an overall angular dependent form factor. Furthermore, when other modes are present (above 3.33λ), the phase of the vector fields will acquire an angular dependence.