Modal analysis of triangular-cored glass-fibre waveguide

The modal analysis is given of a new optical glass-fibre waveguide configuration having a core with an equilateral triangular-shaped cross-section. Calculations are based on the point-matching method, which is known to be inaccurate if sharp corners exist in the boundary geometry. In view of this, two numerical methods are derived to check and correct the resulting eigenvalues and their fields. These new methods involve, respectively, a varia-tional formula and a harmonic-correction integral. A comparison of computations shows that the lower-order point-matched eigenvalue solutions are sufficiently accurate for the constraints laid down by manufacturing tolerances, and apart from regions near to the dielectric interface, the field plots require only a small correction. Close to the apexes, however, the mathematically exact correction procedure also becomes numerically unstable. Modal charts, field and power-density plots, and estimates of cladding field leakage, are given, and degenerate modes and symmetry properties are discussed. Experimental data available confirm the usefulness of the analysis, and it is concluded that the new triangular-cored guide may be operated in a very similar manner to the circular-cored monomode fibre.