Towards a Cavity Soliton Laser Y. Tanguy1, T. Ackemann1 additional input: M. Schulz-Ruhtenberg2, M. Sondermann2, K. F. Jentsch2, X. Hachair3, M. Giudici3, J. R. Tredicce3, R. Jäger4, Andrew Scroggie1, W. J. Firth1 1Department of Physics, University of Strathclyde, Glasgow, Scotland, UK 2Institut für Angewandte Physik, Universität Münster, Münster, Germany 3Institut Non Lineaire de Nice, UMR 6618 CNRS-UNSA, Valbonne, France 4ULM Photonics, Lise-Meitner-Str. 13, 89081 Ulm, Germany FunFACS meeting, Como 28.-29.9.2005

WP1: cw cavity soliton laser VCSEL with frequency-selective feedback f1 + f2 grating 200mm 8 mm self-imaging condition kills diffraction semiconductor lasers with frequency-selective feedback known to be bistable for fundamental-mode operation / plane-wave models

devices: R. Jäger, Ulm Photonics three InGaAs/GaAs quantum wells emission wavelength  980 nm p-side: 30 stacks + metallic mirror, R > 0.9998 n-side: 20.5 stacks, R > 0.992 oxide layer for current and optical confinement; diameter: 80 µm bottom emitter (more homogeneous than top emitter) mounted on TO-can Ref. on early work of University of Ulm: e.g. IEEE Photon. Tech. Lett. 10 (1998) 1061

Solitary laser: LI-curves

Solitary laser: Spatial structures Near-field 60mA Far-field 60mA 28° On axis emission: “broad” features at perimeter of laser Off-axis emission: small-scale standing wave along perimeter Indicates that the maximum gain is blue shifted with respect to the longitudinal cavity resonance

Solitary lasers: Spectra On-axis emission Off-axis emission in qualitative agreement with expectations for tilted waves

Set-up (feedback) Grating VCSEL 1800/mm f= 200 mm f= 8 mm Far-field FPI CCD NDF Power OSA MM Near-field CCD NDF Grating HWP VCSEL 1800/mm f= 200 mm f= 8 mm

Matrix for the grating: 33 matrices = xout out 1 A B E C D F 0 0 1 xin in Usual 2x2 ABCD matrix Angular dispersion Spatial chirp 3x3 matrices to take into account the angular dispersion from the grating. The propagation is calculated for gaussian beams. Matrix for the grating: cos2 cos1 A = ( 1 –(1/n)(F0 sin2)) D = ( 1 –(1/n)(F0 tan2)) A 0 0 0 D F0 0 0 1 F0 = -(2pcn2Dw)/(w2d cos2) Where: Refs: O. Martinez, IEEE JQE, 24, 12, 1988

Deviation from Littrow condition f2 = 200mm f1 = 8mm Grating 1800 g/mm mm Dl = 1nm from ideal Littrow configuration, initial beam radius 10mm. Propagation forward Propagation backward Backwards propagating angle of about 6 degrees.  Grating behaves as “normal” mirror for Littrow wavelength introduces angle-mismatch otherwise.

LI-curve with feedback LI curves

Bistability bistable localized emission spot

Efficiency of feedback commercial small-area VCSEL (8 µm,850 nm proton- implanted) assumption: r2=0.9975 external cavity threshold reduction achievable considerably lower than expected from nominal values for reflection (here coupling efficiency between 0.11 and 0.3) seems to be common observation many uncertainties: reflectivity of output coupler, transparency current high feedback: strong quantitative corrections due to multiple round-trips Naumenko et al., PHYSICAL REVIEW A 68, 033805 (2003)

Feedback rate coupling efficiency feedback strength sum over all round trips Lang-Kobayashi (one round-trip) threshold reduction: corrections due to many round-trips in addition: resonance because narrower (multiple beam interference) Naumenko et al., PHYSICAL REVIEW A 68, 033805 (2003)

Properties of external cavity d1 d2 works only in geometrical optics beam broadening due to diffraction  f1  focus on mirror Gaussian beam optics: beam waist on mirror obvious solution: B=C=0 (telescope d1 = f1 = d2 =L/2 )  broad-area laser but for single Gaussian modes other solutions with d1  f1 exist, in general

Quantitative measurements f = 8 mm „short enough“ cavities: two equivalent optimal solutions experiment: best coupling 0.6 – 0.75  rule of thumb for other set-ups !? Warning: make cavity longer  solutions merge „too long“ cavity: best theoretical coupling < 1 ! K. Jentsch, M. Sondermann, M. Schulz-Ruthenberg, T. Ackemann, unpublished

Summary WP1 Achieved: robust observation of bistable, localised emission spot in several lasers and several external cavity geometries. some indications for feasibility of external control from preliminary experiments To be done: demonstrate that these localised emission states are cavity solitons independent external control of at least two of them broader devices Study parameter dependencies, especially detuning conditions. Check for feedback induced instabilities Develop theoretical description with CNQO group

WP 2 recent experiment (Brown Univeristy, MIT, Novalux) BS 0.2 mm thin forward biased electrically pumped MQW device 980 nm aperture 150 µm reverse biased electrically pumped MQW device (fast saturable absorber) aperture 70 µm f=1.6 mm 1mm thin HR R0.7 R0.35 HR threshold current about 400 mA  mode-locking L= 15 cm ... 1 cm; repetition rate 1 ... 15 GHz pulse length in 10 ps range interpretation/phrasing w/o internal reflector: passive mode-locking with internal reflector(s): tamed feedback Jasim et al., Electron. Lett. 40, 34 (2004); 39, 373 (2003); modelling Mulet + Balle, CLEO-Europe 2005

Transfer to cavity light bullets self-imaging forward biased laser BS reverse biased laser HR HR self-imaging  simultaneous spatial and temporal localization problem 1: devives with reduced reflectivity problem 2: saturation intensity of absorber < saturation intensity of gain demagnification ? (but then resolution problems) quantum dot SA ? approach: a) reproduce mode-locking in fundamental mode (stable cavity) b) achieve solely (?) spatial localization in short cavity needed: high gain devices (RPG), reduced reflectivity

probably related to speed of medium response WP 3: Drift velocity unit velocity typically 5103 µm/ns (k=300109/s, l=1µm, n=3.5) assume diameter of CS of 10 µm transit time 2 ns some 100 Mbit/s but: plenty of room at the top limits ? probably related to speed of medium response strength of gradient Maggipinto et al., PHYSICAL REVIEW E 62, 8726, 2000 (USTRAT and INFM Bari)

Non-instantaneous Kerr cavity instantaneous medium  drift velocity = 2 gradiant D=0.47 D=0 (1D, perturbation analysis) A. Scroggie, USTRAT, unpublished

„Slow“ medium D=0.47 D=0 slope 1 slope 1 velocity determined by response time of medium faster medium will speed up response ! limits for increasing gradients need to be accessed by numerical simulation A. Scroggie, USTRAT, unpublished

Some numbers slow light in the vicinity of resonances: electro-magnetically induced transparency, linear cavities, photonic crystals interplay of useful bandwidth and achievable delay system speed length delay bandwidth EIT in cold vapor1 6 17 m/s 230 µm ~ 10 µs 300 kHz 2.1 EIT in SC QD1 4 (calc) 125000 m/s 1 cm 8 ns 10 GHz 81 SC QW (PO) 5 9600 m/s 0.2 µm 0.02 ns 2 GHz 0.04 SBS in fiber3 70500 km/s 2 m 18.6 ns 30-50 MHz > 1 Raman in fiber2 2 km 0.16 ns > tens of GHz > 8 CS (calc, more ambitious) 10000 m/s 250 µm 25 ns 5 GHz 125 CS (calc, conservative) 5000 m/s 100 µm 20 ns 0.25 GHz 5 1Tucker et al., Electron. Lett. 41, 208 (2005); 2Dahan, OptExp 13, 6234(2005); 3GonsalezHerraez, APL 87 081113 (2005); 4ChangHasnain Proc IEE 91 1884 (2003); 5Ku et al., Opt Lett 29, 2291(2004); 5Hau et al., Nature 397, 594 (1999)