## Abstract

We introduce a formalism that provides a unified solution for the gain spectrum of fiber optical parametric amplifiers (OPAs) using either linearly or circularly polarized waves. There are 12 basic types, including five that have not been previously investigated to our knowledge. We provide a simple method for calculating the maximum gain and nonlinear phase mismatch for such OPAs. All these OPAs have similar elliptical graphs for parametric gain versus propagation constant mismatch, with a width equal to four times the height. This implies that, when fiber dispersion is taken into account, any two-pump OPA can be used to obtain the same gain spectrum as any other OPA in the same fiber, provided that the pump power is adjusted for equal maximum gain and that real solutions exist for the resulting equation for the required pump spacing. In that sense, all these fiber OPAs form an equivalence class.

© 2003 Optical Society of America

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