1. 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, Ulm, Germany
FunFACS meeting, Como

2. 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

3. devices: R. Jäger, Ulm Photonics
three InGaAs/GaAs quantum wells
emission wavelength  980 nm
p-side: 30 stacks + metallic mirror, R >
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

4. Solitary laser: LI-curves

5. 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

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

7. 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

8. Matrix for the grating:
33 matrices =
xout
out 1
A B E
C D F
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
D F0
F0 = -(2pcn2Dw)/(w2d cos2)
Where:
Refs: O. Martinez, IEEE JQE, 24, 12, 1988

9. 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.

10. LI-curve with feedback
LI curves

11. Bistability
bistable localized emission spot

12. 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, (2003)

13. 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, (2003)

14. Properties of external cavityd1 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

15. 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

16. 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

17. 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 cm; repetition rate 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

18. 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

19. 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)

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A. Scroggie, USTRAT, unpublished

21. „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

22. 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)
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 (2005); 4ChangHasnain Proc IEE
(2003); 5Ku et al., Opt Lett 29, 2291(2004); 5Hau et al., Nature 397, 594 (1999)