In this paper, we develop a general first-order perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity, valid for arbitrary pulse shapes. We obtain a general expression of the sampled signal after optical filtering, coherent detection, and optimal sampling. We include intrachannel and as well as interchannel nonlinear effects. We obtain simplified expressions in the case in which the accumulated dispersion is high (equivalent to the far-field limit in paraxial optics). This general theory is applied in detail to the special case of spectral-efficient sinc pulses. This exercise shows that the characteristics of the neighboring wavelength-division multiplexed channels are essential in determining the nonlinear impairments.
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