Optical precursors with self-induced transparency

Optical Sommerfeld-Brillouin precursors significantly ahead of a main field of comparable amplitude have been recently observed in an opaque medium with an electromagnetically induced transparency window [Wei et al., Phys. Rev. Lett. 103, 093602 (2009)]. We theoretically analyze in this paper the somewhat similar results obtained when the transparency is induced by the propagating field itself and we establish an approximate analytic expression of the time-delay of the main-field arrival, which fits fairly well the result obtained by numerically solving the Maxwell-Bloch equations.