In this paper, optical parametric amplification based on the degenerate four-wave mixing principle in a one-dimensional photonic bandgap (PBG) structure has been numerically studied. First, the multiple scale method was introduced to derive a complete set of nonlinear coupled-mode equations for a finite structure with different inhomogeneous nonlinear coefficients than those used in previous works. This finite structure is composed of 680 dielectric layers, which are alternating half-wave/eight-wave films. The wavelengths of the pump, signal, and idler pulses have been determined from the transmission spectrum, which was illustrated by using the transfer matrix method. The parametric interaction of the pump, signal, and idler pulses inside PBG structure has been numerically simulated by using the split-step Fourier transform method. The results of the simulation have shown that the intensities of the signal and idler have exponential growth with respect to the number of layers in the medium. Meanwhile, pump wavevector detuning directly affects the intensities of both pulses due to a band-edge phase-matching condition that might be achieved from only one optimal detuning parameter. Moreover, both the amplification gain and the conversion efficiency of the idler pulse have been shown to be dependent on the bandwidth of the pump pulse spectrum. A very narrow pulse, with a bandwidth much less than the relevant transmission peak, enables the highest amplification and conversion efficiency in this medium because the most efficient phase-matched condition occurs in this situation. Finally, the conversion efficiency grows exponentially with input pump intensity for several input signal intensities. Furthermore, the maximum conversion efficiencies directly vary with input signal intensity.
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