Solitons in nonlinear optics. I. A more accurate description of the 2π pulse in self-induced transparency

A more accurate description of the 2 pi pulse of self-induced transparency is obtained. This is an exact solution of an approximate form of the Maxwell-Bloch equations in which only backscattering is neglected; the equations are valid at densities less than about 10¹⁸ atoms cm^-3. At such densities the 2 pi sech pulse of McCall and Hahn (1967, 1969) remains a good approximate well into the picosecond range. The more accurate solution is chirped by a factor proportional to the square of the ratio of the spectral width of the pulse to its carrier wave frequency. The stability of this pulse solution and other N soliton solutions of the approximate Maxwell-Bloch equations is demonstrated.