A dispersion formula for analyzing modal interference among guided and free electromagnetic wave modes and other phenomena in a circular optical fiber

Electromagnetic energy within an Optical Fiber is known to propagate in the continuous as well as the Partially and Fully Guided Modes. Through the development of a dispersion formula, it can be shown that these modes can interfere among them selves and one important consequence of such "interference" is that the guidance of a large number of partially guided modes can be destroyed. The simple formula for the effective attenuation distance, -1Imkzn for each complex partially guided mode kzn (where kz is the wave vector along the direction of the optical fiber axis), is no longer valid when there is heavy interference or modal "overlap". A simple criterion will be developed to distinguish those modes which remain observable from those which exist physically only as part of the general background. The dispersion formula can be used to show that a discrete mode should be described by two parameters. One is the usual modal position kzn, while the other is the "weight", which varies with different modes. There is also the possible existence of yet another form of guided mode and which we will call the virtually guided mode and which possesses characteristics quite different from the other guided modes.