Realization of a cavity-soliton laser Control of bistability in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback Realization of a cavity-soliton laser using broad-area VCSELs with 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 2Institute of Physics, Academy of Sciences of Belarus, Minsk, Belarus 3ULM Photonics, Lise-Meitner-Str. 13, 89081 Ulm, Germany Funding: FP6 STREP 004868 FunFACS U Strathclyde Faculty starter grant happy to be here also thanks to: W. J. Firth, L. Columbo 28/06/2006 Laser Optics 2006, workshop „Dissipative Solitons“ WeW5-11

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

Motivation for a cavity soliton laser cavity soliton = (spatially) localized, bistable solitary wave in a cavity prerequisite: coexistence between different states optical bistability between homogeneous states or bistability between pattern and homogeneous state symmetry-breaking pitchfork bifurcation  look for bistable nonlinear optical systems driven cavity: need for light field of high temporal and spatial coherence nonlinear medium mirror laser: extracts energy from incoherent source but „normal“ laser: continuous turn-on no cavity solitons pump level  output  bad news

Cavity soliton laser II bistable laser schemes laser with injected signal laser with frequency-selective feedback gain filter laser with saturable absorber gain SA gain extract energy solely from incoherent source  „better“ cavity soliton laser go for VCSEL with frequency-selective feedback look for incoherent manipulation  robustness active device  cascadability

Devices TiPtAu contact pad p-Bragg oxide aperture 33 stacks + metallic mirror, R > 0.9998 20.5 stacks, R > 0.992 p-Bragg oxide aperture QWs (3  InGaAs/GaAs) emission wavelength  980 nm n-Bragg GaAs substrate GeNiAu contact AR coating bottom emitter (more homogeneous than top emitter) output e.g. IEEE Photon. Tech. Lett. 10 (1998) 1061

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

Setup: Scheme Detection part Writing beam self- imaging Littrow f1=8mm f2=300mm Grating VCSEL HWP1 HWP2 Littrow self- imaging self-imaging  maintains high Fresnel number of VCSEL high anisotropy of grating  polarization selective

33 propagation matrices usual 2x2 ABCD matrix spatial chirp for grating: = xout out 1 A B E C D F 0 0 1 xin in A 0 0 0 D F0 0 0 1 angular dispersion cos2 cos1 A = ( 1 –(1/n)(F0 tan2))  Littrow frequency  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). cos1 cos2 D = ( 1 +(1/n)(F0 tan2)) F0 = -(2pcn2Dw)/(w2d cos2) O. Martinez, IEEE J. Quantum Electron. 24, 12, 1988

At Littrow frequency Dl = 0, on-axis „normal“ mirror Dl = 0, 5 deg. angle perfect reproduction after one round-trip all rays/beams return to same position with same angle

Detuned from Littrow frequency Dl = 1nm, on-axis still same location, but angle different  no closed path; rejected by VCSEL cavity Dl = 1nm, 5 deg. angle angular dispersion  0.15 rad/nm; estimated width of resonance 0.026 rad  bandwidth of feedback  55 GHz

A loophole Dl = 1nm, 4.21 degrees angle this is not a closed path in external cavity after one round-trip! beam is exactly retroreflected into itself:   -  but reflection at boundaries and nonlinearities couple wavevectors k - k within VCSEL  spurious feedback

Setup: Details tunable laser 1800/mm Main external cavity L  0.603 m

Near field: Increasing current Movie_nf_currentUp.wmv feedback tuned close to longitudinal resonance

Near field: Decreasing current Movie_nf_currentDown.wmv feedback tuned close to longitudinal resonance

Current dependence: Spots Increasing current bistable localized spots 370mA 381.5mA 386mA 391mA decreasing current

Hysteresis loop local detection around single spot clearly bistable „kinks“ related to jumps between external cavity modes LI_spot3_17deg_all.png

Switch-on of spots independent switch- on 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)

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!

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

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

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

„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

„Pushing“ by aperture shift by about 5 µm

Dragging with comb spots exist in a broad range with small perturbations

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

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)

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

Interpretation: Mechanism of OB laser originally blue detuned with respect to grating increase of power, decrease of carriers  feedback induced red-shift positive feedback green/black weaker pol. red/blue stronger pol.  laser better in resonance with grating operating frequency with feedback frequency of solitary laser ~ current (Joule heating)

Conditions for OB in 80 µm device „stabilization“ of small-area laser with intra-cavity aperture in near field OB should exist for: phase-amplitude coupling bandwidth of feedback feedback strength exp. threshold for OB: 45% = 3  1.2 = 5  2.0 makes sense !

Master equation offset Gaussian aperture idea: derive a closed equation for dynamics of nonlinear non-plano-planar resonators by using ABCD matrix to decribe intra-cavity elements master equation thin lens thin lens nonlinear medium 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

Examples fundamental mode of linear cavity: off-axis t  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)

though defects might play a role in nucleation and trapping 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: thorsten.ackemann@strath.ac.uk

Control of spots a a 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

Current dependence: Spots II Increasing current bistable localized spots 395.4mA 397.7mA 400mA decreasing current

Rays in external cavity telescope with 1 lens (unfolded) f f on-axis soliton ok, but off-axis  inversion telescope with 2 lenses f1 + f2

Spurious feedback not relevant, too large angles but possibly here, if resonances have finite width