Experimental Observation of Coherent Continuous-Pulsetrain Soliton Solutions to the Maxwell-Bloch Equations

Abstract

Coherent propagation of pulse trains through a two-level absorber has been investigated, from a theoretical view point, by many researchers. These investigations have been based on the self-induced transparency¹ (SIT) equations with^2–5 and without⁶ the assumption of zero relaxation. While these theoretical studies have been very thorough, few if any corresponding experimental studies have been reported. In this paper, we report the experimental observation of pulse-train solutions to the SIT equations. It is shown via experiment that an input pulse train, with a rather arbitrary input envelope shape, evolves through interaction with a two-level absorber to an analytic, shape-preserving, pulse-train solution to the SIT equations. The electric field envelope functions for the predicted analytical solutions are given by

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaacqaH1oqzcqGH9aqpdaqadaqaaiaaikda % caWGRbGaai4laiabloriSnaaBaaaleaacqaHepaDaeqaaaGccaGLOa % GaayzkaaWaamWaaeaacaaIXaGaeyOeI0IaeS4eHW2aaWbaaSqabeaa % caaIYaaaaOGaam4Caiaad6gadaahaaWcbeqaaiaaikdaaaGcdaqada % qaaiaadshacaGGVaGaeqiXdqNaai4oaiaadUgaaiaawIcacaGLPaaa % aiaawUfacaGLDbaadaahaaWcbeqaaiaaigdacaGGVaGaaGOmaaaaaa % a!5A7D!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\varepsilon = \left( {2k/{\ell _\tau }} \right){\left[ {1 - {\ell ^2}s{n^2}\left( {t/\tau ;k} \right)} \right]^{1/2}}$$

where k, ℓ, and τ are constants with k being the modulus of the Jacobi elliptic function. The full range of solutions is obtainable by taking 0≤k²≤ℓ²≤ 1.