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Control of of bistability in broad-area Realization a cavity-soliton laser using broad-area VCSELs vertical-cavity surface-emitting lasers with with frequency-selective feedback frequency-selective feedback T. Ackemann1, Y. Tanguy1, A. Yao1, A. V. Naumenko2, N. A. Loiko2 , R. Jäger3 1Department of Physics, University of Strathclyde, Glasgow, Scotland, UK Funding: • FP6 STREP 004868 2Institute of Physics, Academy of Sciences of Belarus, Minsk, Belarus FunFACS 3ULM Photonics, Lise-Meitner-Str. 13, 89081 Ulm, Germany • U Strathclyde Faculty starter grant also thanks to: W. J. Firth, L. Columbo 28/06/2006 Laser Optics 2006, workshop „Dissipative Solitons“ WeW5-11 1 Outline motivation for pursuing a cavity soliton laser setup • devices • design of external cavity results interpretation • mechanism of optical bistability • master equation for general cavities summary 2 Motivation for a cavity soliton laser cavity soliton = (spatially) localized, bistable solitary wave in a cavity look for bistable nonlinear optical systems prerequisite: coexistence between different states optical bistability between homogeneous states or bistability between pattern and homogeneous state symmetry-breaking pitchfork bifurcation mirror laser: extracts energy from incoherent source but „normal“ laser: continuous turn-on no cavity solitons output driven cavity: need for light field of high temporal and spatial coherence mirror nonlinear medium bad news pump level 3 Cavity soliton laser II bistable laser schemes laser with injected signal gain laser with frequency-selective feedback gain filter laser with saturable absorber gain SA extract energy solely from incoherent source „better“ cavity soliton laser go for VCSEL with frequency-selective feedback look for incoherent manipulation active device robustness cascadability 4 Devices TiPtAu contact pad 33 stacks + metallic mirror, R > 0.9998 p-Bragg oxide aperture QWs (3 InGaAs/GaAs) emission wavelength 980 nm n-Bragg 20.5 stacks, R > 0.992 GaAs substrate GeNiAu contact • AR coating bottom emitter (more homogeneous than top emitter) output e.g. IEEE Photon. Tech. Lett. 10 (1998) 1061 5 Near field intensity distribution free-running laser (below threshold) with feedback (tuned slightly off-axis) • not lasing cw (thermal roll-over) • defect lines • apart from that “rather homogeneous“ • some more defects apparent 6 Setup: Scheme Detection part Writing beam f1=8mm f2=300mm Grating VCSEL HWP1 HWP2 Littrow self- imaging • self-imaging • high anisotropy of grating maintains high Fresnel number of VCSEL polarization selective 7 33 propagation matrices usual 2x2 ABCD matrix spatial chirp for grating: xout A B E xin out C D F in 0 0 1 1 1 = A 0 0 0 D 0 0 F0 1 angular dispersion w Littrow frequency Dw detuning from Littrow frequency d spacing between grooves 2 and 1 angles of reflection and incidence from the grating c velocity of light n refractive index). A = cos2 ( 1 –(1/n)(F tan )) 0 2 cos1 D = cos1 ( 1 +(1/n)(F tan )) 0 2 cos2 O. Martinez, IEEE J. Quantum Electron. 24, 12, 1988 F0 = -(2pcn2Dw)/(w2d cos2) 8 At Littrow frequency 2.0 Dl = 0, on-axis 1.5 0.8 0.6 0.4 1.0 0.2 0.5 0.0 -0.2 0.0 -0.4 -0.6 -0.5 mm -0.8 -2 0 2 4 6 8 10 12 -1.0 „normal“ mirror -1.5 mm -2.0 -100 0 100 200 300 400 500 600 2.0 700 2.0 Dl = 0, 5 deg. angle 1.5 1.5 1.0 0.5 1.0 0.0 -0.5 0.5 -1.0 0.0 -1.5 -2.0 -2 -0.5 mm 0 2 4 6 8 10 12 -1.0 -1.5 perfect reproduction after one round-trip mm -2.0 -100 0 100 200 300 400 500 all rays/beams return to same position with same angle 600 700 9 Detuned from Littrow frequency Dl = 1nm, on-axis 2.0 2.0 1.5 1.5 1.0 0.5 1.0 0.0 0.5 -0.5 0.0 -1.0 -0.5 -1.5 -1.0 -5 0 mm -2.0 -100 0 100 200 300 400 500 600 5 10 15 mm 20 700 Dl = 1nm, 5 deg. angle 2.0 1.4 1.5 1.2 1.0 1.0 0.5 0.8 0.0 0.6 -0.5 0.4 -1.0 0.2 -1.5 0.0 mm -2.0 -100 0 100 200 300 400 500 600 700 still same location, but angle different no closed path; rejected by VCSEL cavity mm -0.2 -4 -2 0 2 4 6 8 10 12 14 16 angular dispersion 0.15 rad/nm; estimated width of resonance 0.026 rad bandwidth of feedback 55 GHz 10 A loophole Dl = 1nm, 4.21 degrees angle 2.0 1.5 1.4 1.2 1.0 1.0 0.5 0.8 0.6 0.0 0.4 0.2 -0.5 0.0 -1.0 -0.2 -2 0 2 4 6 8 mm 10 12 14 -1.5 mm -2.0 -100 0 100 200 300 400 500 600 700 beam is exactly retroreflected into itself: - this is not a closed path in external cavity after one round-trip! but reflection at boundaries and nonlinearities couple wavevectors k - k within VCSEL spurious feedback 11 Setup: Details tunable laser 1800/mm Main external cavity L 0.603 m 12 Near field: Increasing current feedback tuned close to longitudinal resonance 13 Near field: Decreasing current feedback tuned close to longitudinal resonance 14 Current dependence: Spots Increasing current 370mA 381.5mA bistable localized spots 386mA 391mA decreasing current 15 Hysteresis loop local detection around single spot • clearly bistable • „kinks“ related to jumps between external cavity modes 16 Switch-on of spots • independent switchon of two spots • „independent entities“ • cavity solitons ? • does not depend critically on frequency detuning of WB to emerging spot • robust • need resonance in external cavity (but question of power) 17 Spectra low resolution spectrum (plano-planar SFPI) • frequencies of spots different 0.05 nm 20 GHz • further indication for independence • probably related to inhomogeneities • linewidth (confocal FPI) 10 MHz • These are small lasers! 18 Spectra with writing beam WB injected directly onto the spot, at different frequencies. • red-detuned: injection locking • equal or blue-detuned: red-shift (carrier effect) • blue-detuned: switch-off excitation of background 19 Switch-off by excitation of background • under some conditions for blue-detuning: - switch-off - excitation of background wave • not very well understood but nevertheless: incoherent manipulation 20 Switch-on/off by position • switch-on: hit it head-on (or on some locations in neighbourhood) • switch-off: hit at (other locations in) neighbourhood • complete manipulation CS ! • incoherent, robust 21 „Plasticity“ / „Motility“ CS ought to be self-localized, independent of boundary conditions can easily couple to external perturbation motion (on gradients) trapping (in defects) possibilities: writing beam aperture diffractive ripples comb 22 „Pushing“ by aperture shift by about 5 µm 23 Dragging with comb • spots exist in a broad range with small perturbations 24 Intermediate summary experiment: bistable localized spots can exist at several points, though preferentially at defects independent manipulation indications for motility these guys have the properties of cavity solitons, though defects might play a role in nucleation and trapping some interpretation: why bistability? approach to model details of the external cavity dynamical model: Paulau et al. Talk WeW5-14, 17.30 25 Theoretical model (without space) we start with spin-flip model (though spin not important for idea) feedback noise • delayed feedback terms (Littman) • single round-trip (Lang-Kobayashi approximation) • feedback anisotropic Naumenko et al., Opt. Commun. 259, 823 (2006) 26 Results: Steady-states + simulations feedback favoring weaker pol. mode green: analytic solutions for stationary states / external cavity modes black: simulations (red/blue for other polarization). ~ current thermal shift of solitary laser frequency bistability between lasing states and off-states; abrupt turn-on; small hysteresis 27 Interpretation: Mechanism of OB operating frequency with feedback laser originally blue detuned with respect to grating green/black weaker pol. increase of power, decrease of carriers feedback induced red-shift red/blue stronger pol. laser better in resonance with grating positive feedback frequency of solitary laser ~ current (Joule heating) 28 Conditions for OB OB should exist for: bandwidth of feedback phase-amplitude coupling feedback strength exp. threshold for OB: 45% =3 1.2 =5 2.0 makes sense ! in 80 µm device with intracavity aperture in near field „stabilization“ of small-area laser 29 Master equation offset Gaussian aperture thin lens thin lens nonlinear medium idea: derive a closed equation for dynamics of nonlinear non-plano-planar resonators by using ABCD matrix to decribe intra-cavity elements master equation benefits / aims: ability to model complex real-world cavities (e.g. VECSELs) address effects of small deviations from self-imaging condition in external cavity describe misaligned cavity describe properly action of grating in VEGSEL Dunlop et al., Opt. Lett. 21, 770 (1996); Firth and Yao, J. Mod. Opt., in press 30 Examples ~ E i TR T 2 sin ~ E ( B 2 E~ k 1 S 2 2 B k x ) x 2 ~ E k (1 S ) ~ i 2 ~ (1 iD )E E Ei 2 ~ 2 kB(1 S ) 1 D E S ( A D) 2 ; (BG (1 A)H ) 2 ik l related to misalignment, proportional to aperture offset fundamental mode of linear cavity: off-axis initial conditions on-axis t pattern formation people involved: A. Yao, W. J. Firth, L. Columbo (Bari) 31 Summary experiment: bistable localized spots can exist at several points, though preferentially at defects independent manipulation (switch-on/off) indications for motility these guys are cavity solitons though defects might play a role in nucleation and trapping some interpretation: why bistability approach to model details of the external cavity Email: [email protected] 32 Control of spots aa b c d e f g h i b) And d): Switch-on of two independent spots, they remain after the WB is blocked. f) And h): Switch-off, by injecting the WB beside the spot locations. phase insentivbe 33 Current dependence: Spots II Increasing current bistable localized spots 395.4mA 397.7mA 400mA decreasing current 34 Rays in external cavity telescope with 1 lens (unfolded) f f on-axis soliton ok, but off-axis inversion telescope with 2 lenses f1 + f 2 35 Spurious feedback 4.0 not relevant, too large angles wave number (1/µm) 3.5 3.0 2.5 2.0 but possibly here, if resonances have finite width 1.5 1.0 experiments free-running fit free-running line with spurious feedback 0.5 0.0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 detuning (nm) 36