A fiber optic parametric amplifier comprising: a pump source for emitting an optical pump pulse; an input port for receiving the optical pump pulse, with a first pump pulse duration, at a pump wavelength; a resonating cavity comprising: a first coupler for coupling the optical pump pulse into the resonating cavity; a linear fiber optic gain medium that increases the intensity of the pump pulse and increases the first pump pulse duration to a second pump pulse duration after exiting the linear fiber optic gain medium; a nonlinear fiber optic gain medium that provides parametric gain to light which exits the linear fiber optic gain medium, wherein the nonlinear fiber optic gain medium transfers energy from the pump pulse after exiting the linear fiber optic gain medium to a signal pulse with a first signal pulse duration after exiting the nonlinear fiber optic gain medium; a power splitter that receives light that exits the nonlinear fiber optic gain medium and provides: a first portion of the light that exits the nonlinear fiber optic gain medium to an output port to exit the resonating cavity; and a second portion of the light that exits the nonlinear fiber optic gain medium is fed back into the resonating cavity so that it passes through the linear fiber optic gain medium, wherein the linear fiber optic gain medium increases the pulse duration of the signal pulse with a first signal pulse duration to a second signal pulse duration after exiting the linear fiber optic gain medium; wherein the signal pulse includes a signal light or an idler light; wherein the linear fiber optic gain medium has negative chromatic dispersion in either one of the wavelengths of the signal light and the idler light; and the nonlinear fiber optic gain medium has positive chromatic dispersion in either one of the wavelengths of the signal light and the idler light. a pump source for emitting an optical pump pulse; an input port for receiving the optical pump pulse, with a first pump pulse duration, at a pump wavelength; a resonating cavity comprising: a first coupler for coupling the optical pump pulse into the resonating cavity; a linear fiber optic gain medium that increases the intensity of the pump pulse and increases the first pump pulse duration to a second pump pulse duration after exiting the linear fiber optic gain medium; a nonlinear fiber optic gain medium that provides parametric gain to light which exits the linear fiber optic gain medium, wherein the nonlinear fiber optic gain medium transfers energy from the pump pulse after exiting the linear fiber optic gain medium to a signal pulse with a first signal pulse duration after exiting the nonlinear fiber optic gain medium; a power splitter that receives light that exits the nonlinear fiber optic gain medium and provides: a first portion of the light that exits the nonlinear fiber optic gain medium to an output port to exit the resonating cavity; and a second portion of the light that exits the nonlinear fiber optic gain medium is fed back into the resonating cavity so that it passes through the linear fiber optic gain medium, a first coupler for coupling the optical pump pulse into the resonating cavity; a linear fiber optic gain medium that increases the intensity of the pump pulse and increases the first pump pulse duration to a second pump pulse duration after exiting the linear fiber optic gain medium; a nonlinear fiber optic gain medium that provides parametric gain to light which exits the linear fiber optic gain medium, wherein the nonlinear fiber optic gain medium transfers energy from the pump pulse after exiting the linear fiber optic gain medium to a signal pulse with a first signal pulse duration after exiting the nonlinear fiber optic gain medium; a power splitter that receives light that exits the nonlinear fiber optic gain medium and provides: a first portion of the light that exits the nonlinear fiber optic gain medium to an output port to exit the resonating cavity; and a second portion of the light that exits the nonlinear fiber optic gain medium is fed back into the resonating cavity so that it passes through the linear fiber optic gain medium, a first portion of the light that exits the nonlinear fiber optic gain medium to an output port to exit the resonating cavity; and a second portion of the light that exits the nonlinear fiber optic gain medium is fed back into the resonating cavity so that it passes through the linear fiber optic gain medium, wherein the linear fiber optic gain medium increases the pulse duration of the signal pulse with a first signal pulse duration to a second signal pulse duration after exiting the linear fiber optic gain medium; wherein the signal pulse includes a signal light or an idler light; wherein the linear fiber optic gain medium has negative chromatic dispersion in either one of the wavelengths of the signal light and the idler light; and the nonlinear fiber optic gain medium has positive chromatic dispersion in either one of the wavelengths of the signal light and the idler light.