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.

[1]  J. C. Eilbeck,et al.  Exact multisoliton solution of the inhomogeneously broadened self-induced transparency equations , 1973 .

[2]  J. C. Eilbeck,et al.  Exact Multisoliton Solutions of the Self-Induced Transparency and Sine-Gordon Equations , 1973 .

[3]  T. W. Barnard.  2 N π Ultrashort Light Pulses , 1973 .

[4]  R. Slusher,et al.  Sharp-Line Self-Induced Transparency , 1972 .

[5]  J. C. Eilbeck,et al.  A possible N soliton solution for a nonlinear optics equation , 1972 .

[6]  J. C. Eilbeck.  Reflection of short pulses in linear optics , 1972 .

[7]  Joseph H. Eberly,et al.  Analytic Study of Pulse Chirping in Self-Induced Transparency , 1972 .

[8]  J. C. Eilbeck,et al.  The method of characteristics in the theory of resonant or nonresonant nonlinear optics , 1972 .

[9]  J. Lamb.  Propagation of coherent optical pulses in an inhomogeneously broadened medium , 1972 .

[10]  T. Benjamin.  The stability of solitary waves , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[11]  R. Bullough,et al.  Exact Solutions of the Self-Induced Transparency Equations , 1971 .

[12]  G. Lamb.  Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium , 1971 .

[13]  L. Narducci,et al.  Coherent absorption in a homogeneously broadened medium , 1970 .

[14]  R. Slusher,et al.  Peak Amplification and Breakup of a Coherent Optical Pulse in a Simple Atomic Absorber , 1970 .

[15]  S. Mccall,et al.  Self-Induced Transparency , 1969 .

[16]  A. Szöke,et al.  On Consequences of the different phase and signal velocities in self-induced transparency☆ , 1968 .

[17]  S. Mccall,et al.  Self-Induced Transparency by Pulsed Coherent Light , 1967 .