Complete dispersion characteristics are exhibited for electromagnetic waves propagating in a time-space periodically-modulated medium which is all-pass and dispersionless in the absence of the (pump) modulation, A rigorous solution, in¬cluding all of the infinite number of time-space harmonics, is obtained for the lin¬earized model, which also is representative of a traveling wave parametric circuit. In contrast with previous work relating to traveling wave parametric circuits, how¬ever, no assumptions are imposed on the present model regarding mode coupling. The dispersion relation is represented graphically in a form which is a generaliza¬tion of the familiar one-dimensional Brillouin diagram for stationary periodic struc¬tures. From the repeated cell pattern one ascertains that for this medium only two types o£ interaction are possible: (1) stable interactions, of the stop-band type, associated with frequency conversion effects, and (2) potentially unstable interac¬tions, characterized by a stop band in wavenumber rather than in frequency. These types of interaction occur, respectively, when the phase velocity of the pump modu¬lation is less than or greater than that of a signal in the unmodulated medium. Sep¬arating these two types of interaction is a "sonic" region, which appears whenever these two phase velocities are approximately equal. The characteristics of the stable interactions and the sonic region are discussed in the present paper;the un¬stable interactions are considered in Part II. The amplitudes of several of the time-space harmonics have also been, calculated, and are shown to satisfy the Manley-Rowe relations in the stop bands;of particular interest is the role of the minor harmonics and the error introduced by using only two harmonics, as in coupled-mode theory.
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