Coherent passive mode-locking in lasers: Qualitative analysis and numerical simulations

In the present work we report the possibility of passive mode-locking based on the coherent interaction of light with the amplifying and absorbing media in lasers with ring and linear cavities. We consider the realistic and practically interesting case when the absorbing and amplifying media are separated in the cavity space but not homogeneously mixed in the volume of the cavity, as was considered earlier in the literature. We perform qualitative consideration of coherent passive mode-locking based on the area theorem of McCall and Hahn and its graphical representation for the first time. We show that other, not soliton scenarios of passive mode-locking exist, and that coherent mode-locking is self-starting (lasing without an injection seeding pulse is possible). We point to the fact that the spectral width of the laser generation can be significantly larger than the spectral bandwidth of the gain medium. Numerical simulations were performed using the system of Maxwell-Bloch equations in the slowly varying envelope approximation. 1 Passive mode-locking in lasers, basic theoretical approaches Investigations of mode-locking in lasers began as soon as the first lasers were developed in the 1960s [1–7]. As we mentioned in the introduction, discovering mode-locking led to a great success in the realization of extremely short laser pulses with high peak power. Below we consider the basic approaches that are used to describe theoretically passive mode-locking regimes in lasers. The primary element allowing periodic pulse generation is the nonlinear absorber. A nonlinear absorber is a material where the absorption decreases with increase of the light intensity. Such materials as dyes, crystals or semiconductors with strong resonant absorption can be used for this purpose. The latter are most actively used nowadays, because of their significant advantages in comparison to dye absorbers and other solid state materials used before (see Refs. [8–12]). As an example of the recent progress in this area, the discovery of so-called semiconductor saturable absorber mirror (SESAM) [8, 13] can be mentioned. In this device, semiconductor absorber material is integrated into the laser mirror which results in dependence of the mirror reflectivity on the light intensity. Such a technique allows for the creation of passively mode-locked solid state lasers generating light pulses with a duration from femtoseconds to nanoseconds [8,13]. Passive mode-locked semiconductor lasers are actively studied today. In such lasers, quantum dot and quantum well materials can be used for both gain and absorbing sections, resulting in short optical pulses with a repetition rate in the range from few to hundreds GHz [9–12,14]. Due to their compact size and high repetition rate they are considered as promising candidates for optical communication systems.