Waves, Solitons and Turbulence in Optical Systems - Abstract

Arkhipov, Rostislav

Self-Induced Transparency Coherent Passive Mode-Locking: Qualitative Consideration Based on McCall and Hahn Area Theorem

Passive mode-locking (PML) is a well-known technique to obtain ultrashort pulses from lasers [1]. The generation of ultrashort optical pulses (in femtosecond range) with multigigahertz repetition rates opened up new range of applications. PML can be achieved by incorporating a saturable (nonlinear) absorber with suitable properties into the laser cavity. In all existing passively mode-locked lasers, generation of ultrashort pulses arises due to the absorption/gain saturation. In this case, the ultimate limit on the output pulse duration is set by the inverse bandwidth of the gain medium. To overcome this limit it was proposed to use coherent light-matter interactions and self-induced transparency [2] with formation of a $2pi$ pulse in absorber and a $pi$ pulse in the gain medium [3-6]. This so-called coherent mode-locking (CML) technique (or self-induced transparency CML) allows generating optical pulses with duration much shorter than the medium polarization relaxation time $T_2$. It is easy to estimate and to predict the main features of CML using a graphical representation of the McCall and Hahn Area Theorem for both amplifier and absorber. In this approach, a pulse propagation in a laser is described through an evolution of the pulse area via transition from the branches of solutions given by the area theorem Ref. [7]. In this talk, we demonstrate in details this elegant diagram technique. It allows to elucidate CML qualitatively, in particular, to find stable limit cycles in the system, estimate the possibility of lasing self-starting, changing of the pulse duration and pulse shaping and find attractors of such system. The results of numerical simulations of a CML using the system of Maxwell-Bloch equations are in the agreement with the predictions based on our approach based on McCall and Hahn Area Theorem. References: 1. U. Keller Appl. Phys. B, 100, 15 (2010). 2. S. L. McCall, E. L. Hahn Physical Review, 183(2), 457 (1969). 3.V. V. Kozlov Phys. Rev. A, 56, 1607 (1997). 4.M. A. Talukder, C. R. Menyuk Phys. Rev. A 79, 063841 (2009). 5. V. V. Kozlov, N. N. Rosanov Phys. Rev. A 87, 043836 (2013). 6. R. M. Arkhipov, M. V. Arkhipov, I. Babushkin, JETP Letters 101(3), 149 (2015). 7. R. M. Arkhipov, M. V. Arkhipov, I. Babushkin, in preparation [WIAS Preprint No. 2019 (2014)].