The Coupled Mode Equations are derived in the context of a monochromatic
frequency CW light source for linear propagation. The spectrum of the input pulse can
be obtained by taking a Fourier transform of the input time-dependent waveform. The
response to the input pulse can be calculated by considering each spectral
component separately and adding over the spectrum of the input pulse. The output
pulse spectrum can be obtained by multiplying by the appropriate grating device
frequency response. The corresponding output time waveforms can then be
recovered by taking the inverse Fourier transform.