Fig. 1. (a) Experimental setup showing the L-shaped VECSEL. HRM, high reflectivity beam splitter (>99.5% at 1.060 nm). Li are lenses whose focal lengths are f1=f4=8  mm, f2=100  mm, f3=200  mm. While in a cold cavity, the SI condition is reached for telescopic arrangement of optical elements, the presence of a thermal lens [41] due to an optical pump beam (fth≈10  mm  WPp), requires slight correction to telescopic arrangement to achieve a degenerate condition. Accordingly, distances for SI condition are: d1=f1, with d1 the distance between gain section and L1; d2=f1+f2+z0, with d2 the distance between L1 and L2; d3=f2+f3−z0, with d3 the distance between L2 and L3; d4=f3+f4, with d4 the distance between L3 and L4; and d5=f4+x0, with d5 the distance between L4 and the SESAM. The correction terms to the telescopic configuration are given by z0=−fc22fth and x0=−fc42M2f22fth, where M=f3/f2=2. For typical pump power values used in our experiment (Pp≈170  mW) and fth≈60  mm:z0≈−0.53  mm and x0≈−0.8  μm [33]. (b) Microscope pictures of some of the masks deposited onto the gain mirror. Darker zones correspond to the Cr layer that provides losses larger than 90%. The masks shown exhibit arrangements of circular holes where the absorptive material has been removed. Diameters of holes (D) and separations between centers (T) are D=15  μm, T=30  μm in mask 1, D=30  μm, T=32  μm in mask 2, D=15  μm, T=16  μm in mask 3, D=15  μm, T=20  μm in mask 4. (c) Transverse profile of the losses and phase shift experienced by the electromagnetic field when reflected by the gain mirror around the Cr mask borderline. The Cr edge has less than 5 nm rising thickness. The phase shift of the mask is less than 2π/50.

Fig. 2. Spatiotemporal behavior of the light emitted by the VECSEL with two hot-spots in the gain section (A and B). (a), (b) Time-averaged near-field and far-field profiles of the VECSEL emission. (c) Bifurcation diagrams of the mode-locking emission from each hot-spot. These diagrams are obtained according to the following procedure: pump power Pp is increased from zero up to the VECSEL threshold value (Pp,th=192.5  mA), where an off solution becomes unstable at the advantage of mode-locked emission having Nmax pulses per round trip. Then, Pp is decreased until the emission jumps to the emission having Nmax−1 pulses per round trip. At this point, the stability of this solution is tested by increasing again Pp up to Pp,th and by decreasing it down to the point where the emission jumps to the solution with Nmax−2 pulses per round trip. This is repeated for every solution with a number of pulses per round trip different from zero, until the system jumps to the off solution. The difference in the number Nmax of pulses per round trip for the two hot-spots is due to a non-perfectly homogeneous level of pumping of the two regions. (d), (e) Two different emission states obtained for the same parameter values in the multi-stable region (Pp=185  mW). The blue (red) time trace represents the intensity emitted by hot-spot A (B). In panel (d), we show the state (NA=3, NB=4), while in panel (e), we show the state (NA=6, NB=5). Space–time diagrams of these states, picturing the evolution of pulses emitted round trip after round trip, are represented in panels (f) (NA=3, NB=4) and (g) (NA=6, NB=5).

Fig. 3. Space–time diagram of the writing process of TLS in each hot-spot. (a) Writing of one LS in hot-spot A while hot-spot B is emitting three TLSs per round trip (NB=3). The writing pump pulse is applied at round trip #10,000, and spot A emits a TLS that follows the timing of the perturbation pulse that is incidentally different from the round trip of the system. When the writing pulse is removed at round trip #15,000, the solution NA=1 remains stable. (b) Writing of one TLS in the hot-spot B while hot-spot A is emitting NA=2 TLSs per round trip. In the inset, we show the time-averaged near-field emission of the VECSEL during application of the perturbation to hot-spot B. The waist of the perturbation beam can be compared with the interference fringes.

Fig. 4. (a) Evolution of the TLS emitted by hot-spots A (red trace) and B (blue trace) in presence of two continuous wave (CW) 7-μm-waist pump beams targeting hot-spots A and B. Their powers PA and PB can be controlled independently. Here PA=35  mW and PB=45  mW. Both narrow waist pump beams are superimposed to the homogeneous pump beam, which is kept to a power Pp=120  mW. Inset: near-field time-averaged emission of the VECSEL showing the presence of the two 7-μm-waist independent pumps targeting hot-spots A and B. (b) Power spectra of the two outputs from hot-spots A (red trace) and B (blue trace).