Relation between new `field radius´ w∞ and Petermann II field radius wd in single-mode fibres with arbitrary refractive index profile

The author reports a new simple relation between the `field radius´ w_∞ and the Petermann II field radius w_d. This relation is derived from the scalar wave equation and holds for single mode fibres with arbitrary radial refractive index profiles. With this new relation the spectral behaviour of w_∞ can be predicted from the value of w _∞ at one wavelength (e.g. 1.5 μm) and the spectral behaviour of w_d