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The fundamental mode of a multiple-fibre coupler, consisting of an arbitrary number of identical parallel fibres, has exactly the same cutoff wavelength as one of the fibres in isolation from the others and is independent of the separation of the fibres. For a single-mode coupler composed of two depressed inner-cladding fibres, both the fundamental and second modes have finite cutoff wavelengths provided the fundamental mode of each fibre is cut off.