Complex-source-point theory of Gaussian beams resonators

This paper presents the generalisation of the complex-source-point method for all the `series A¿¿ and `series B¿¿ Laguerre-Gaussian beams. When complex values are assigned to the source co-ordinates in the field expressions of point multipoles, the resulting fields have paraxially the form of a Laguerre-Gaussian beam. An application of this technique is found in deducing a generalised resonant formula for the spherical open resonator with a `large aperture¿¿. The result is more accurate than the conventional one in order of magnitudes. Moreover, the small difference in resonant frequencies between the `series A¿¿ and the `series B¿¿ modes of the same order when l > 0 confirms the nonexistence of the commonly accepted linearly polarised modes with angular dependence. The theoretical pedictions are substantiated by experimental work.