Optical networks as complex lasers

We discuss the main features of a recently introduced system capable of laser action: the complex active optical network, or lasing network (LANER) [Lepri et al., Phys. Rev. Lett. 118, 123901 (2017)]. The system is experimentally realized with optical fibers linked each other with couplers and with one or more coherently amplifying sections. The LANER displays a standard laser behavior: When the gain provided by the active sections is high enough to overcome the losses, a coherent emission is produced, with a complicated intensity spectrum. A linear theoretical description is discussed in detail, showing how the LANER can be considered as a generalization of the laser with the physical network acting as a complicated cavity. Among its main aspects, the system can be represented by directed graphs disclosing the analogies with the problem of quantum chaos on graphs. Moreover, when the links' lengths are all integer multiples of the same value, the LANER framework corresponds to a lattice problem, with the equivalence of the Brillouin zone with the cavity free spectral range. Experiments in simple configurations are also performed, reporting the evidence of lasing action and its characterization. Examples of spectra of the detected emitted intensity are obtained in different cases, in a phenomenological agreement with the numerical findings of the theory.