By adopting appropriate early approximations a weak coupling theory of optical waveguides is developed, which is featured by its particular simplicity in mathematics. Coupling of ideal modes may not be sufficiently weak for the simple theory to apply. Local modes and super-local modes are in some cases used, preferably, for their successively weakening coupling properties. The said three sets of modes are all related by similar matrices in the sense of Lowey. Problems of periodic coupling and of discrete coupling are also discussed, the former imposing a rather severe restriction on the weak coupling criteria.
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