The mode-locking transition of random lasers

Abstract

The discovery of the spontaneous mode-locking of lasers, i.e., the synchronous oscillation of electromagnetic modes in a cavity, has been a milestone of photonics allowing the realization of oscillators delivering ultra-short pulses. This process is so far known to occur only in standard ordered lasers with meter size length and only in the presence of a specific device (the saturable absorber). Here we demonstrate that mode-locking can spontaneously arise also in random lasers composed by micronsized laser resonances dwelling in intrinsically disordered, self-assembled clusters of nanometer-sized particles. Moreover by engineering a novel mode-selective pumping mechanism we show that it is possible to continuously drive the system from a configuration in which the various excited electromagnetic modes oscillate in the form of several, weakly interacting, resonances to a collective strongly interacting regime. By realizing the smallest mode-locking device ever fabricated, we open the way to novel generation of miniaturized and all-optically controlled light sources.Random lasers[1] (RLs) are made by disordered highly scattering materials able to amplify light when externally pumped. The simultaneous presence of structural disorder and nonlinearity makes these devices a fertile ground to connect photonics with advanced theoretical paradigms[2] like chaos [3], non Gaussian statistics[4], complexity [5] and also the physics of Bose Einstein condensation [6]. Historically there has been a bridge in the RL interpretation. In pioneering experiments a smooth, single-peaked emission was produced by pumping finely ground laser crystals [7], or titania particles dispersed in a dye-doped solution [8,9]. This phenomenon has been dubbed RL with incoherent feedback (IFRL) because it may be explained in the framework of the diffusion approximation [10] that neglects interference and treats light rays as the trajectories of random walking particles. However this theoretical framework does not explain another kind of RL exhibitting subnanometre sharp spectral peaks [11][12][13] associated with high-Q resonances[14-17] and labeled resonant feedback random laser(RFRL).Standard multimode lasers without disorder and characterized by equispaced resonances may be driven to a synchronous regime through the so called mode-locking transition [18,19], which so far has only been shown to occur spontaneously in the presence of a saturable absorber and allows to generate ultra-short light pulses [20,21]. We show that the same transition occurs in RLs and allows to lock modes of a RFRL casting its emission in the typical IFRL spectrum and demonstrating the inherently coherent nature of the random lasing phenomenon.The system we consider is an isolated micrometer sized cluster of titania nanoparticles immersed in a rhodamine dye solution (see supplementary information (SI)). In our novel setup we use the amplified spontaneous emission (ASE) from the surrounding dye to pump the cluster. The the ASE areas are defined by shaping the beam of an e...

Non-locality and collective emission in disordered lasing resonators

“…(H) (the average is taken over the N(N21)/2 possible pairs among the N55 considered points) and demonstrates that the correlation between spectra at different positions increases with H. A key point is that the increment of Q is not due merely to an average smoothing of the envelope of the spectrum but also includes the persistence of 'small features' (some examples are marked with asterisks in Figure 3b) present in all the considered positions that should not be mistaken for noise. These small features have been previously noticed in earlier experiments, both in titanium dioxide 23 and in zinc oxide microclusters 20 and thin layers. 21 This measurement is the first direct experimental connection between the strong nonlinear interaction 13 and the appearance of such spectral features.…”

“…The small frequency differences can be embedded in the time-dependent a j (t), which corresponds to letting a j R a j exp [2i(v 0 2v i )t]. The coupled mode equations 23,34,35 are written as:…”

“…23 Such control is possible for a system composed of an individual micrometer-sized cluster of titanium dioxide nanoparticles lying in a bath of a rhodaminedoped solution. By pumping the area surrounding the cluster, one can generate a flux of directional stimulated emission capable of pumping only modes that are well coupled with the pump shape, and the lasing threshold may be surpassed ( Figure 2).…”

“…By pumping the area surrounding the cluster, one can generate a flux of directional stimulated emission capable of pumping only modes that are well coupled with the pump shape, and the lasing threshold may be surpassed ( Figure 2). The number of activated modes is controlled by selecting, through a spatial light modulator, the angular aperture H of the wedge-shaped pumped area (see Figure 1b and studies [23][24][25] for further details).…”

Dynamics of phase-locking random lasers

“…When the number of modes is relatively low, it is possible to follow experimentally the transition to a collective state, which has been associated with phase locking [20,21]. When the number of modes is huge, mean-field approximations are possible [22] and allow us to predict the existence of various phases including a mode-locked one [23].…”