Observation of Mode-Locked Spatial Laser Solitons

Abstract

A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets. DOI: 10.1103/PhysRevLett.118.044102 Wave packets in general, and light wave packets in particular, do not remain confined to small regions in space or time, but have the natural tendency to broaden. In space this is due to diffraction and in time this is due to dispersion, at least in a medium. Although localization can be achieved by confining potentials (e.g., optical fibers and photonic crystals in optics), it was always the vision of researchers to obtain confinement by self-action. This is why the concept of solitary waves, or, more loosely speaking, of solitons, received a lot of attention over the last decades. A soliton is a wave packet in which the tendency to broaden is balanced by nonlinearities. Spatial and temporal solitons in one or two dimensions are known in many fields of science [1][2][3][4][5][6][7]. There was also early interest in three-dimensional (3D) self-localization, not least as a model for elementary particles [8]. However, early results [8] were discouraging as they indicated that stationary 3D localized states are not stable in a broad class of nonlinear wave equations. Significant interest continued in the theoretical and mathematical literature (e.g., Refs. [9][10][11][12][13][14][15]), but to our knowledge there is only evidence for 3D self-organized periodic patterns [16], but not for 3D self-localization.In optics, spatiotemporal localization of light, i.e., a "bullet" of light being confined in all three spatial dimensions (and time, because it is propagating), was considered as early as 1990 in the framework of a 3D nonlinear Schrödinger equation (NLSE) [17], but realized to be unstable due to the well-known blow-up experienced for cubic nonlinearities in more than one dimension [18,19]. There were several proposals of how to stabilize multidimensional solitons [19][20][21][22][23][24][25][26][27][28]. Spatiotemporal compression [29][30][31], metastable 2D spatiotemporal solitons [24,32], and metastable discrete light bullets [33,34] were observed in pioneering experiments, the latter constituting the closest realization of a stable light bullet up until now. However, these quasiconservative bullets are only stable over a few characteristic lengths and are long-term unstable due to losses and Raman shifts.This makes it attractive to look for solitons in dissipative optical systems in which losses are compensated by driving [5]. Indeed solitons can exist in two dimensions with a cubic nonlinearity within ...

Three-Dimensional Spatiotemporal Pulse-Train Solitons

“…The higher-order nonlinear effects, that lead to spectral redshift, upsets the balance between the wavelength-sensitive discrete diffraction and self-focusing effects and eventually results in the disintegration of these LBs. Early this year, mode-locked spatial cavity solitons with pulse duration shorter than the cavity round-trip were observed [28]. This research direction may enable generation of bright 3D cavity solitons.…”

Laser cavity-soliton microcombs

“…Laser cavity-solitons [22,[25][26][27][28] have been largely studied in spatial configurations such as semiconductor lasers [25], where they enabled breakthroughs such as alloptical reconfigurable memories [26]. More recently, they have been observed in both temporal [28] and spatio-temporal [35] contexts. They are fundamentally different to externally driven cavity-solitons, which are sustained by the energy of the pumping background.…”

Mapping the dynamical regimes of a SESAM mode-locked VECSEL with a long cavity using time series analysis

“…5 ps is the sampling period. Figure 4 shows a space-time representation of the single pulse within each round-trip, for 100 round-trips [24,25]. Each pixel in the figure is a representation of the acquired discrete signal amplitude for one sampling period of the oscilloscope and is scaled to the color according to the color-scale located on the right hand side of the figure.…”