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A resonator side coupled to a pair of waveguides can switch an optical signal between two ports by means of absorption. The absorptive mechanism is used to suppress the resonant power transfer, rather than to promote loss. Thus, the input signal only suffers small attenuation, provided that the mode volumes of the resonators can be made small enough. Multiply-coupled resonators lead to improved crosstalk performance for both the ON and OFF switched states. The performance of such devices are analyzed analytically, and universal switching curves are derived.