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