Observation of Mode-Locked Spatial Laser Solitons

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.

Figure 1

(a) Scheme of experimental setup. The inset illustrates spatial localization by showing the soliton within the much larger pumped VCSEL aperture indicated by the dotted white line. Lens (L), beam sampler (BS), linear polarizer (LP), volume Bragg grating (VBG), iris (IR), optical isolator (IS), charge-coupled device (CCD) camera, half-wave plate (HWP), polarizing beam splitter (PBS), Fabry-Perot (FP) interferometer [free spectral range (FSR) of 12 GHz and a Finesse of about 40], photodector (PD), fast photodetector (FPD). (b)–(d) Correlation functions and spectra obtained for different currents (scanning down) in the bistable range, (b) Autocorrelation function, (c) Optical spectra obtained from FP (the overall blueshift with decreasing current is due to the reduced thermal load; approximately 1.7 FSR are displayed to show unwrapped spectra in spite of the blueshift) and (d) rf spectra of the intensity signal on the FPD from an electrical spectrum analyzer (ESA) around the fundamental round-trip frequency.

Figure 2

Example of harmonic mode locking, $I=413.7\mathrm{mA}$. Left panel, from top to bottom: Envelope of time series, zoom on pulses (the ac-coupled rf amplifier removes the dc component and hence the signal has positive and negative amplitudes), rf spectra obtained from a numerical fast Fourier transform (FFT) of the recorded time series around the fundamental round-trip frequency, rf spectrum around harmonic. The right panel shows space-time representations of the dynamics, the horizontal axis displays time within a round-trip (spacelike) and the vertical axis the number of round-trips. The inset shows the time averaged intensity profile of the pulsing soliton in a square with a size of $55\mu \mathrm{m}$.

Figure 3

Example of fundamental mode locking, $I=410.6\mathrm{mA}$. Explanation of subpanels as in Fig. 2.

Figure 4

Example of quasiperiodic dynamics in mode locking, $I=410.24\mathrm{mA}$. Explanation of subpanels as in Fig. 2.

Figure 5

Numerical results on mode-locked soliton for a cavity round-trip time of 0.28 ns. (a) Envelope of time series, (b) zoom on pulses, (c) space-time representation. Parameters (see Ref. [68]): $\alpha =9$, $\theta =-0.95$, $\sigma =0.9$, $\gamma =0.01$, $T_1=0.008$, $T_2=0.002$, $\beta =0.6$, $r_g=0.8$, $\delta =0$, ${\tau }_f=28$. The inset shows a snapshot of the intensity profile of the pulsing soliton.