Higher-Order Loss Processes and the Loss Penalty of Multimode Operation

Higher-order loss processes have been discussed in a previous paper.1 The idea of loss processes of different orders is based on perturbation theory. Two modes of a dielectric waveguide are coupled if their propagation constants obey the relation1 | -- | = m. (1) > is the mechanical frequency of the Fourier spectrum of the coupling f function; m is a positive integer that specifies the order of the coupling process. If m = 1, mode v is coupled to mode n by a first-order process, m = 2 indicates a second-order process, etc. For small values of a/B, (a is the Fourier amplitude that belongs to the mechanical frequency tf>', A,, is the free space wavelength of the light in the waveguide) the coupling strength is proportional to (a/X0)m so that the coupling decreases with increasing order of the coupling process. If mode v represents a guided mode, mode n may either be a guided or a radiation mode. In the latter 1819 1820 T H E BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1972 case, mode v loses power by radiation. An explanation of the coupling process in terms of diffraction gratings is given in Ref. 1. There is a different loss process that cannot be understood in terms of higher-order grating lobes. Consider two guided modes. Mode 2 is inherently lossless, while mode 1 suffers high loss. If we couple these two modes by means of a first-order process, a large amount of loss will be transferred from the lossy mode to the hitherto lossless neighbor. However, even if we couple these two modes by means of a sinusoidal coupling function the mechanical frequency of which does not satisfy (1) for any integer m, some loss will be imparted from the lossy mode to the inherently lossless mode.