Complex-Source-Point Theory and the Open Resonator

Abstract

The theory of the open resonator is now established, at least so far as scalar wave functions are adequate to describe the field distribution. In this treatment we shall pay particular attention to the rather subtle modifications to the theory that arise when a complete vector description of the electromagnetic field is undertaken. The complex-source-point method, so powerfully applied to related problems by Felsen (1), is the basis of the present theory. We shall, however, omit the complicating effects of diffraction, and we begin by justifying this apparently serious defect. We then outline briefly the main results of the scalar theory of open resonatiors, and follow this by describing the procedures and results when the vector theory is applied. In particular, we shall show, following Yu and Luk (2), that the linearly-polarised higher-order modes of conventional theory do not exist. The situation is analogous in some ways to the erroneous assumptions that higher-order TE and TM modes exists in lossy rectangular waveguides, though in the present case the curvature of the mirrors rather then ohmic losses is the crucial factor. In a final section, some experimental aspects of the problem are considered. Experimental evidence is given confirming the vector theory of the higher-order modes, and applications of the open resonator to microwave measurements are briefly indicated.