By reductio ad absurdum, we show that a perfect power combiner of single-mode waveguides is impossible for incoherent input waves of the same frequency and same polarization as it is against the law of conservation of energy. The inevitable 3 dB loss of a three-port power combiner is explained physically. An incoherent power combiner of nearly 100% efficiency can be realized only if the two input fields have different wavelengths, have different polarizations, or are of orthogonal modes.
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