random laser - physics &...
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2583-14
Workshop on Coherent Phenomena in Disordered Optical Systems
Hui CAO
26 - 30 May 2014
Depts. of Applied Physics and Physics Yale University
New Haven U.S.A.
Random Laser - Physics & Application
Random Laser -Physics & Application
H i CHui CaoDepts. of Applied Physics & Physics, Yale University
Group members
Jonathan Andreasen
Northwestern Univ.
Robert P. H. ChangJonathan AndreasenBo LiuHeeso NohBrandon Redding
Robert P. H. ChangEric SeeligXiang Liu
gXiaohua WuJunying XuAlexey Yamilov
Yale Univ.
Michael ChomaJin-Kyu YangYong Ling
Doug StoneMichael Rooks
Laser
Essential components for a laser
Gain medium Light amplification
Cavity Coherent feedback
Gain mediumMirror Mirror
R1 R212 ggLeRRThreshold
mLk c 22
121geRRThreshold
Resonance
Laser with Scattering Reflector
Scattering MirrorRubyScattering medium
MirrorRuby crystals
Nicolay Basov
Non-Resonant Feedback
1221
ggLeRRLasing Threshold
Ambartsumyan, Basov, Kryukov, and Letokhov, IEEE J. Quantum Electron. 2 442 (1966)
VladilenLetokhov
Photonic BombPhotonic Bomb
Instability for Amplification of Spontaneous Emission (ASE)
Average path length of photon exceeds amplification lengthexceeds amplification length
Photon multiplication
Letokhov, Sov. Phys. JETP 26, 1109 (1968)
Laser Paint
Dramatic narrowingDye molecules and Dramatic narrowing of emission spectra
Dye molecules and scattering particles
Lawandy, Balachandran, Gomes & Sauvain, Nature 368, 436 (1994)
Light Diffusion, Absorption, Emission, and Amplification
Pump light and probe light in 4-level atomic media
Wiersma & Lagendijk, Phys. Rev. E 54, 4256 (1997)
Discrete Lasing Peaks
ZnO powder DDO-PPV film
HC et al, Phys. Rev. Lett. 82, 2278 (1999) Frolov et al, Phys. Rev. B 59, 5284 (1999)
Electromagnetic Mode
Maxwell’s equations
),(1),(
0
trEt
trH
),()(
1),(2
0
trHrnt
trE
t
)(
Complex refractive index ir innn
Boundary condition: only outgoing waves
HC et al, Phys. Rev. E, 61, 1985 (2000)Jiang & Soukoulis, Phys. Rev. Lett. 85, 70 (2000)
Localized Modes
Mode Pattern
Spectrum
Vanneste & Sebbah, Phys. Rev. Lett. 87,183903 (2001)
ZnO Powder
')'()'()( * dxxxExExCEAverage particle
0.5
0.6
Exponential decay l h d 2 3
diameter ~ 100 nm
0.3
0.4
E(x
)|
length d = 2.3 m
0.1
0.2
|CE
0 5 10 150.0
x ( m)x ( m)
HC et al, Phys. Rev. E 66, R25601 (2002)
Porous GaP
6tlk
van der Molen et al, Phys. Rev. Lett. 98, 143901 (2007)
Weak Scattering System
Dye solution withDye solution with scattering particles
1tlk
Amplification of spatially extended p ymodes in random laser
Mujumdar et al, Phys. Rev. Lett. 93, 053903 (2004)
Overlapping Resonancesg
1TNThouless number 1TNThouless number
Excitation spectrum
1020
u.)
pof a passive system
R t l
1015
al In
tens
ity (a
.uResonances are strongly overlapped spatially and spectrally. 430 440 450 460
1010
Spec
tra
y 430 440 450 460Wavelength (nm)
Coherent Lasing Mode
Lasing Lasing Mode
Max
gspectrum
gPattern
1030
ensi
ty (a
.u.)
1025
Spec
tral I
nt
440 450 460 470 48010
20
Wavelength (nm)
Laser Field AmplitudeMin
Vanneste, Sebbah & HC, Phys. Rev. Lett. 98,143902 (2007).
Non-Uniform Gain and Absorption
Absorption outside gain region effectively reduces the size of random structure byreduces the size of random structure by suppressing feedback from the unpumped region, and creates localized lasing modes.
Yamilov et al., Opt. Lett. 30, 2430 (2005)Andreasen & HC, Opt. Lett. 30 2430 (2009)
Directional Laser Emission
Local pumping of weakly scattering samples
Cone shaped l
Angular distribution f t t i t itpump volume of output intensity
10000
n
Laser emission
4000
6000
8000
ted
Em
issi
on
nsi
ty (
a. u
.)
100 m Spontaneous emission-6 -4 -2 0 2 4 6
0
2000
Inte
gra
In
ten
Wu & HC, Phys. Rev. A 74,053812 (2006)
Detection Angle (degree)
Mode Interaction
Mode competition for gainMode competition for gain
Gain saturation, spatial hole burning
Localized modes, spatially non-overlapping, , p y pp g,weak interaction
Extended modes spatial overlappingExtended modes, spatial overlapping, strong interaction
Composite Lasing Modes
Nonlinear Dynamics
Conti et al, Phys. Rev. Lett. 96, 065702 (2006); Leonetti, Conti & Lopez, Nat. Photon. 5, 615 (2011)
QuestionQuestion
What is the statistical properties of random lasing modes?of random lasing modes?
Single-Shot Emission SpectraDye solution with
scattering particlesDye solution without scattering particles
Peak Spacing Statistics
Dye solution with Dye solution without scattering particles scattering particles
Wu & HC, Opt. Lett. 32, 3089 (2007)
Peak Height Statistics
Dye solution with scattering particles
Dye solution without scattering particles
2 7 2 2IIIIP IIIIP 5 6= -2.7, -2.2IIIIP IIeIIP = 5.6
Wu & HC, Phys. Rev. A 77,013832 (2008)
QuestionQuestion
How coherent is random laser emission?emission?
Temporal Coherence
z
Temporal coherence length is determined by spectral bandwidth of laser emission
22ln 2cz ct
Noginov et al, Opt. Mater. 12, 127 (1999); Papadakis et al, J. Opt. Soc. Am. B 24, 31 (2010)
Spatial Coherence
Young’s double slit experiment
Tailoring Spatial Coherence by Varying Pump Region
= 0.61MFP=500 m d=215 m
600 610 620Wavelength (nm)
100 m
= 0.19MFP=500 m d=290 m
600 610 620Wavelength (nm)
100 m
MFP=500 m d=390 m = .036
600 610 620Wavelength (nm)
100 m
Tailoring Spatial Coherence by Changing Scattering Strengthby C a g g Scatte g St e gt
Weaker scattering
= 0.61MFP=500 m d=215 m
600 610 620Wavelength (nm)
100 m
= .057MFP=50 m d=215 m
Stronger scattering
600 610 620Wavelength (nm)
100 m
B. Redding, M. Choma, & HC, Opt. Lett. 36, 3404 (2011).
Second-Order Coherence
Emission intensity or photon number fluctuations
2
2
2
IIG 22
I
12GSingle-mode coherent light:
22GSingle-mode chaotic light:
Emission Intensity Statistics of Nonresonant Feedback Laser
Fluctuation of total emission intensity is d b i t tisuppressed by gain saturation.
Intensity fluctuation of individual moderemains large due to mode interaction.
22G
Ambartsumyan et al. Sov. Phys. JETP 26, 1109 (1968)
Photon Statistics of Random Laser with Resonant Feedback
2391
1.6
1.8
G2389
390
ngth
(nm
)
1.2
1.4
386
387
388
Wav
ele
10 2 4 6 8 10
P/Pth
0 50 100 150 200Time (ps)
HC et al, Phys. Rev. Lett. 86, 4524 (2001)
Nonlinear Effect in Random Laser
Strong third-order nonlinearity Innn 20Strong third order nonlinearity Innn 20
Liu et al, Phys. Rev. Lett. 91, 063903 (2003); Appl. Phys. Lett. 83,1092 (2003).
Partially-Ordered Random Laser
??
1 2
1.6
2.0
Mo
de
(ps)
Optimal degree of disorder
0.4
0.8
1.2
me
of
Las
ing
Strongest light confinement0.0 0.2 0.4 0.6 0.8 1.0
0.0Lif
eti
Degree of disorder
Strongest light confinement
Yamilov & HC, Phys. Rev. A, 69, 031803 (2004)
Short-Range Order
GaAs membraneSpatial pFourier spectra
Coupled modeLocalized mode
Noh et al., Phys. Rev. Lett. 106, 183901 (2011)
Deterministic Aperiodic Structure
The Rudin-Shapiro structure creates localized modes with well-defined frequencies and positionsmodes with well-defined frequencies and positions
Yang et al., Appl. Phys. Lett. 97, 223101 (2010)
Light Transport in Amplifying Random Media
In a diffusive system below lasing threshold
Effect of coherent amplification on transport:
• Enhances long-range correlation
• Increases fluctuation of transmission & reflection
• Pushes a diffusive system towards localization
Yamilov, HC et al, Phys. Rev. E 70, 037603 (2004); Phys. Rev. B 71, 092201 (2005); Phys. Rev. E 74, 056609 (2006); Physica B 405, 3012 (2010).
Amplification Enhances I t f Eff tInterference Effect
L1 In the absence of gain
E = E1 + E2 + �…Returning field
|E1| > |E2|
In the absence of gain
L1 < L2
L2Weak interference
In the presence of gain
Longer path, more amplification
In the presence of gain
|E1| ~ |E2| Stronger interference
Light Localization Induced byRandom Imaginary Permittivity
Basiri, Bromberg, Yamilov, Cao, Kottos, arXiv 1403.2120
PhysicsPhysics
Random lasers are complex, open, nonlinear chaotic systems.
Mesoscopic transport, laser physics, nonlinear optics, quantum optics, statistical physics, quantum chaos, nonlinear dynamics, atomic physics …p y
Applicationpp
Microlaser
X-ray laser, -ray laser
Galaxy maser stellar laserGalaxy maser, stellar laser
Optics & Photonics News, 16, 24 (2005)
Speckle-free Laser Imaging
AF IPS IrisLens
CCDSource Obj Obj
RandomLaser
He:NeLaserLaser Laser
Redding, Choma & HC, Nature Photonics 6, 355 (2012)
Spatial cross talkObject
Came-ra
j
Coherent illumination
Came-ra )cos(222
221
2
EEEE
EEEI
Co e e t u at o
)cos(2 2121 EEEE
Came- III
Incoherent illumination
ra 21 III
On-chip Electrically-Pumped Semiconductor Random laserSemiconductor Random laser
Development of a New Light Source for Massive Parallel Confocal Microscopy and Optical Coherence Tomography
Ideal Illumination Source
Lasers
acy/
n
ce Hig
h
Random LasersLasers
Superluminescent
Deg
ener
al R
adia
n Diodes
Th l hit li ht
Ph
oto
n D
Sp
ectr
a
Lo
w
Pinhole filtered white light
Light emitting diodes
Thermal white light
Low High
Light emitting diodes
Spatial Coherence
Low High