Optics deals with continuous objects: The electromagnetic fields are continuous functions of space and time. There are situations, however, in which the evolution of an optical field can be represented as a discrete problem. This happens when the field can be described as a sum of discrete modes. One such simple and important case is that of a coupled one-dimensional (1D) waveguide array. In a waveguide array, a large number (infinite in principle) of single-mode channel waveguides are laid one near the other such that their individual modes overlap. The evolution of the transversal field distribution is described by an infinite sum of coupled complex amplitudes of the individual modes. The problem of light propagation in a linear array was first treated theoretically by Jones, and later studied by Yariv and co-workers, who fabricated and tested such arrays in gallium arsenide.
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