. Random Lasers Gregor Hackenbroich, Carlos Viviescas, F. H.
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Transcript of . Random Lasers Gregor Hackenbroich, Carlos Viviescas, F. H.
![Page 1: . Random Lasers Gregor Hackenbroich, Carlos Viviescas, F. H.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649dd15503460f94ac745b/html5/thumbnails/1.jpg)
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Random Lasers
Gregor Hackenbroich, Carlos Viviescas, F. H.
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Random Lasers
wavelength (nm)
Inte
nsity
(a.
u.)
Inte
nsity
(a.
u.)
Inte
nsity
(a.
u.)
376 384 392 400
pum
ping
Disordered ZnO-clusters and films
1 m
pumping
H. Cao et al., 1999:
feedback by chaotic scattering of light
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Theoretical Ideas
Lethokov: 1967– photon diffusion + linear gain
John, Wiersma & Lagendijk: 1995--– photon & atomic diffusion– non-linear coupling
Beenakker & coworkers: 1998--– random scattering approach– focus on linear regime below laser threshold– rate equations for strongly confined chaotic resonator
Soukoulis & coworkers: 2000--– numerical simulation of time-dependent Maxwell-equations coupled to
active medium
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issues to be discussed here:
- quantization for bad chaotic /disordered resonators
- statistics for # of laser peaks
- increase of laser linewidth for bad resonators
- statistics for # of emitted photons
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Why modifications to laser theory?
• spectrally overlapping
• modes have simple spatial form • approximation: eigenmodes of
closed resonator
• modes have complex spatial distribution
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field quantization for open resonators
PRL 89, 083902 (2002),PRA 67, 013805 (2003)J. Opt. B 6, 211 (2004)
†[ , ]a a †[ ( ), ( )]
( )m m
mm
b b
( ), ( ):m mV W Integrals of mode functions along the openings
system bath dropantiresonantterms!
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Dynamics: Heisenberg picture
a i a a F
†WW
damping noise
standard laser:
open laser:
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master equation
†
† †
,
, ,
[
[ ] [ ]
]
{ }
ia a
a a a a
Schrödinger picture, low temperature: Bk T
generalization of single-mode master equation to many overlapping modes
G. Hackenbroich et al., PRA 013805 (2003):
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open laser
pumpingemission
...a
...pS
...zpS
field modes
polarization of p-th atom
inversion of p-th atom
non-linear coupled Heisenberg equations
field-atom coupling (spatially randomfor chaotic modes)
modes couplednot only via atomsbut also throughdamping
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increase of laser linewidth
regime of a singlelaser oscillation
STK
2
| |1
| | |
L L R RK
L R
laser linewidth
Petermann factor
wavelength
Inte
nsity
ST
PRL 89, 083902 (2002):
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multimode lasing and mode competition
modes of passive system overlap, fast atomic medium
' ''
k k kk k k kk
k kI I I I I A B
loss linear gain
saturation
mode competition for atomic gain
*
cav( ) ( )k k kdV L RA r r
* *' 'cav
cav * *' 'ca
'
v cav
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
k k k k
k k k k
kk
dV L R R RV
dV L R dV R R
Br r r r
r r r r
wavelength
Inte
nsity
kI 1kI ...
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mean number of lasing modes
0.1 1 10 50
0.1
1
10
100
0.1 1 10 50
0.1
1
10
100
N
pumping strength
neglecting mode competition
including mode competition
1 linear gain = 0
• universal exponent: 1/3
• non-linear mode competition relevant
3las
1/N
ohne We1
tt/ 2N no-comp
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summary
- theory of (weakly confined) random lasers
- generalization of standard laser theory
- characteristics:
• increase of laser linewidth
• universal increase of # of lasing modes
thanks to: D. Savin, H. Cao
• mode coupling through damping
• increased intensity fluctuations in output (not discussed here)
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Random matrix-model
ensemble of non-Hermitian random matrices
†GOEH i WW H
internal coupling
chaoticdynamics
M: # channelsT: channel trans-
mission coefficient
statistics of eigenfunctions: ' '1 2kk kk B
Fyodorov & Sommers: 1997
( )P / 2 1
0,M 2
01/ ,
eigenvalues of :H i
{
0 4
TM
frequency-separation