Optimization Methods of Optical Signals by the Criterion of the Minimum of the Presented Base

Abstract

The article is devoted to the development of methods for improving the spectral efficiency of fiber-optic transmission systems in terms of optimizing signals in a narrowband channel. The channel width is conventionally taken in the range of 50-100 GHz. The following conditions are also considered to be fulfilled: the signal at the input has approximately circular polarization; the instantaneous power of the signal is relatively small, which makes it possible to neglect nonlinear effects such as four-wave mixing or phase self-modulation; the fiber profile in the refractive index is strictly stepped; fiber operates in single mode; the core material is an isotropic medium; the dependence of the attenuation coefficient in the frequency in the considered range can be considered a constant function. Thus, the considered model of signal transformations in a fiber is reduced to its deformation due to material dispersion. The leading optimization criterion is the minimum of the reduced base. This concept was introduced earlier in the works of the authors. This criterion requires minimizing the product of the effective spectral width on the transmission side by the effective signal duration on the receiving side. The solution of the problem in general form is given-in the formulation of the isoperimetric problem of the calculus of variations. It is shown that the solution of the optimization problem by the minimum criterion of the reduced base can be reduced to the problem of optimizing the signal base in the classical sense. A general solution of the isoperimetric problem is given as functions of a parabolic cylinder. Also presented are particular solutions of the optimization problem on parametric families from the Nyquist pulse class. The obtained solutions show that the optimal values of the variable parameters practically do not depend on the carrier frequency and on the length of the regeneration section. This allows the extension of the optimal solutions obtained for a single narrowband channel to the case of multichannel fiber-optic transmission systems using frequency (spectral) multiplexing.