June Morten Bache1 The Cavity Soliton Laser M. Bache *, F. Prati, G. Tissoni, I. Protsenko, L. Lugiato Dipartimento di Fisica e Matematica, Università dell’Insubria, Como (Italy) M. Brambilla Dipartimento di Fisica Interateneo, Università e Politecnico di Bari (Italy) *Current address: Research Center COM, Technical University of Denmark CLEO-EQEC Europe (Munich) June VCSEL with saturable absorber Cavity solitons and the cavity soliton laser The model Exciting the solitons Deleting the solitons

June Morten Bache2 Motivation: Cavity soliton laser? What is a cavity soliton laser? Compact tunable laser Spatial solitons are supported  Excitation pulse: turn-on  Deleting pulse: turn-off Bistability required  Saturable absorber included in the model Important: no holding beam needed to keep soliton alive!!!

June Morten Bache3 The model: Broad area VCSEL with saturable absorber We use semiconductor rate equations with adiabatic elimination of the polarization, describing an active region where radiative recombination dominates and a passive region where nonradiative recombination dominates. Major bifurcation parameters: injected currents μ and γ. We fix γ=0.5. The detuning does not play any role except fixing the frequency of the field. N.G. Basov, IEEE J. Quant. Electr. QE-4, 855 (1968); C.H. Henry, J. Appl. Phys. 51, 3051 (1980); S.V. Fedorov et al., PRE 61, 5814 (2000). See also M. Yamada, IEEE J. Quant. Elec. 29, 1330 (1993). Optical field Absorber carrier density Amplifier carrier density linewidth enhancement factors loss rates injected currents, note the sign saturation parameter detuning

June Morten Bache4 Exciting a soliton may be A soliton may be excited in the regime where the stable trivial solution coexists with a modulational instability (gray area). A suitably sized (space/time/duration/phase) Gaussian pulse is injected, and after turn-off the dynamics are followed. possible soliton area The soliton converges to a steady state after roughly 10 4 t.u. (app. 100 ns) current value

June Morten Bache5 Exciting a soliton Exciting a soliton is possible if  Peak field intensity inside certain regime  Beyond regime no soliton is created  Injected profile has proper width  Injected field phase not important!! Soliton excited Soliton not excited Injected field on

June Morten Bache6 Existence of the solitons The solitons exist in a certain range of the injected current of the active material Region 1 the soliton starts oscillating and eventually breaks down Region 2 the solitons oscillate, but are eventually stable Region 3 the soliton becomes modulationally unstable Region 4 does not support solitons because the background is unstable profile for μ=

June Morten Bache7 Deleting the solitons Field frequency ω 0 + Ω depends on the field intensity The field phase is random Impossible to “engineer” an injected field with a given phase and frequency to delete the soliton Soliton can be deleted nonetheless!! Strong field: the soliton is deleted Weaker field: the soliton survives

June Morten Bache8 Deleting the solitons Deleting a soliton  Peak field intensity beyond the regime found before  Thus, if the field is too too weak, soliton is not destroyed Increasing injected field strength Soliton deleted Soliton not deleted

June Morten Bache9 Exciting and deleting more solitons Neighbor solitons may be excited as well as deleted. The existing ones are not affected as long as a certain distance between them is kept.

June Morten Bache10 Model parameters Linewidth enhancement factors  α=2 (active material)  β=0 (passive material)  For larger β solitons appear to become unstable Loss rates  Carrier dynamics (much) slower than field dynamics  If carriers are too slow, solitons become oscillatory and eventually unstable  For faster carrier dynamics solitons can be excited spontaneously The solitons are stable due to a balance between field-matter interaction

June Morten Bache11 Conclusions and outlook Excite and delete a soliton in broad area VCSEL with saturable absorber  existence regime in bistable region  does not depend on phase  excitation and deletion threshold  several solitons excited and deleted individually Cavity Soliton Laser can be realized  No holding beam (no thermal problems)  Soliton has maximum contrast  Beam entirely determined by the radiation-matter interaction and not the boundary conditions M. Bache et al., submitted to Applied Physics B - Lasers and Optics (special issue on saturable absorbers)