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This paper introduces a new formalism for analyzing two-photon devices (eg, parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes are created or destroyed two at a time. The key property of a two-photon device is that it excites pairs of output modes independently. Thus our new formalism deals with two modes at a time; a continuum multimode description can be built by integrating over independently excited pairs of modes. For a pair of modes at frequencies Ω±ε, we define (i) quadrature-phase amplitudes, which are complex-amplitude operators for modulation at frequency ε of waves ‘‘cos [Ω (tx/c)]’’and ‘‘sin [Ω (tx/c)]’’and (ii) two-mode squeezed states, which are the output states of an ideal two-photon device. The quadrature-phase amplitudes and the two-mode squeezed states serve as the building blocks for our formalism; their properties and their physical interpretation are …