Résumé:

Three-dimensional solitons are highly sought after objects in nonlinear science. In nonlinear photonics they correspond to light bullets, but their experimental observation as long-term stable structures remains elusive in spite of impressive advances [1]. Broad-area vertical-cavity surface-emitting lasers (VCSELs) combine a large Fresnel number with a high nonlinearity and fast time scales. Stationary spatial solitons in 2D as well as mode-locking and temporal solitons without self-localization in space are known to exist. It is intriguing to explore a combination of these two aspects to achieve self-localization of light in three dimensions [2]. Here we report on the observation of mode-locked states of spatial solitons.The experimental system consists of a VCSEL with a 200 micrometer emission aperture emitting around 980 nm. It is coupled to a self-imaging external cavity closed by a volume Bragg grating (VBG) as a frequency-selective element. The round-trip time in the external cavity is about 0.7 ns. By varying the VCSEL current, the detuning between the VCSEL and the VBG resonances is changed and single-mode operation in the external cavity and multi-mode operation can be realized. The latter may correspond to irregular dynamics or fairly regular self-pulsing which represents mode-locked states (Fig. 1). These data are in a range where the self-pulsing spatial soliton is bistable, i.e. it coexists with the non-lasing state as expected for a self-localized state. We obtain self-pulsing at the fundamental and the harmonic round-trip frequency, as well as occasionally at even higher harmonics. The peaks in the RF-spectrum are extremely narrow (<; 100 kHz, close to the resolution limit) indicating a high phase-correlation between the participating modes. The optical spectrum displays three dominant modes. The pulse width (FWHM) is about 110 ps for the harmonic mode-locking and 270 ps for the fundamental mode-locking, roughly consistent with the expectation from spectral bandwidth. The results clearly establish mode-locking of spatial solitons on 3 modes creating temporal structures shorter than the external cavity. Numerical simulations of the model introduced in [4] are in good agreement with the experimental data [3].