Transcript Towards a cavity soliton laser

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
28.-29.9.2005
FunFACS meeting, Como
1
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
2
Devices
TiPtAu contact pad
Bragg reflector (p-type)
oxide aperture
QWs (active zone)
devices: R. Jäger, Ulm Photonics
GaAs substrate
Bragg reflector (n-type)
AR coating
GeNiAu contact
output
•
•
•
•
•
•
•
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
3
Solitary laser: LI-curves
40
35
Power (mW)
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90 100 110 120
current (mA)
4
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
5
Solitary lasers: Spectra
Spectrum 60mA
2000
Power (linear, a.u.)
1800
1600
On-axis emission
1400
1200
1000
800
600
400
Off-axis emission
200
0
Spectrum 80mA
974 975 976 977 978 979 980 981 982 983 984 985 986
Wavelength (nm)
7000
Power (linear, a.u.)
6000
5000
4000
in qualitative agreement with
expectations for tilted waves
3000
2000
1000
0
974 975 976 977 978 979 980 981 982 983 984 985 986
wavelength (nm)
6
Set-up (feedback)
Far-field
FPI
CCD
NDF
Power
OSA
MM
Near-field
NDF
CCD
Grating
HWP
VCSEL
f= 8 mm
f= 200 mm
1800/mm
7
33 matrices
3x3 Propagation
Matrices
Usual 2x2
ABCD
Usual
2x2 matrix
ABCD matrix Spatial Spatial
chirp chirp
xout x
out
out =
out
1
1
A
C
=
0
BA
D
C
E
B
F
D
E xin
F in
0
0
1
0
1
1
xin
in
1
3x3 matrices
to take
the the
3x3 matrices
tointo
takeaccount
into account
angular
dispersion
from the
grating.
angular
dispersion
from
the grating.
The propagation
is calculated
for for
The propagation
is calculated
gaussian
beams.
gaussian
beams.
See O. Martinez, IEEE JQE, 24, 12, 1988
AngularAngular
dispersion
dispersion
MatrixMatrix
for the
forgrating:
the grating:
A
0
0
A0
0D
00
00
DF0
01
0
F0
1
cos2 cos
2
0 sin2)) sin ))
A = ( 1 –(1/n)(F
( 1 –(1/n)(F
0
2
cos1 cos
1
cos1 cos
1
D=
0 tan2)) tan ))
D = ( 1 –(1/n)(F
( 1 –(1/n)(F
0
2
cos2 cos
2
A=
Where:
Where:
2Dw)/(w2d cos )
F0 = -(2pcn
2Dw)/(w2d
2 cos )
F0 = -(2pcn
2
(c = velocity of light, n refractive index, wfrequency, d spacing between grooves in grating,
2 and 1 angles of reflection and incidence from the grating).
Refs: O. Martinez, IEEE JQE, 24, 12, 1988
8
Deviation from Littrow condition
Dl = 1nm from ideal Littrow configuration, initial beam radius 10mm.
8
6
4
f2 = 200mm
f1 = 8mm
Grating 1800 g/mm
mm
2
0
-2
Propagation forward
2.0
-4
1.5
Propagation backward
1.0
mm
-6
-100
0
100
200
300
400
500
0.5
mm
Backwards propagating angle of about 6 degrees.
 Grating behaves as “normal” mirror for Littrow wavelength
introduces angle-mismatch otherwise.
0.0
-0.5
mm
-1.0
-2
0
2
4
6
8
10
12
9
LI-curve with feedback
LI curves
40
35
Power (mW)
30
25
20
solitary laser
15
With selective feedback
10
5
0
0
10 20 30 40 50 60 70 80 90 100 110 120
current (mA)
10
Bistability
bistable localized emission spot
0.25
Local power (a.u.)
0.21
0.17
0.13
0.09
0.05
28
29
30
31
32
33
34
35
36
37
38
39
Current (mA)
11
Efficiency of feedback
commercial
external cavity
small-area
VCSEL
(8 µm,850 nm
protonimplanted)
assumption: r2=0.9975
• 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)
12
Feedback rate
coupling efficiency
feedback strength
sum over all round trips
threshold reduction:
Lang-Kobayashi
(one round-trip)
corrections due to many round-trips
in addition: resonance because narrower (multiple beam interference)
Naumenko et al., PHYSICAL REVIEW A 68, 033805 (2003)
13
Properties of external cavity
d1
L
d2
works only in geometrical optics
beam broadening due to diffraction
 focus on mirror
 f1
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
14
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
15
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
16
WP 2
recent experiment (Brown Univeristy, MIT, Novalux)
BS
forward biased
0.2 mm thin
electrically pumped
MQW device
f=1.6 mm
980 nm
1mm thin
aperture 150 µm
HR R0.7
R0.35
reverse biased
electrically pumped
MQW device
(fast saturable absorber)
•aperture 70 µm
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
17
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
HR
reverse biased
laser
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
18
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)
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Non-instantaneous Kerr cavity
instantaneous
medium

D=0.47
drift velocity =
2 gradiant
D=0
(1D, perturbation analysis)
A. Scroggie, USTRAT, unpublished
20
„Slow“ medium
D=0.47
slope 1
D=0
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
21
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
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
2m
18.6 ns
30-50 MHz
>1
2 km
0.16 ns
> tens of GHz
>8
Raman in fiber2
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
et al., Electron. Lett. 41, 208 (2005); 2Dahan, OptExp 13, 6234(2005); 3GonsalezHerraez, APL 87 081113 (2005); 4ChangHasnain Proc
22 IEE
5
5
91 1884 (2003); Ku et al., Opt Lett 29, 2291(2004); Hau et al., Nature 397, 594 (1999)
1Tucker