Nonlinear Optics: Past Successes and Future Challenges

Presented at the Conference on Lasers and Electro-Optics and Quantum Electronics andLaser Science Conference (CLEO: 2012), 6-11 May 2012 in San Jose, California.

Making Ottawa the world’s photonics center

OTTAWA, Ontario, Canada –

A $55 million photonics center that was expected to break ground on the

make Ottawa the global hub of photonics.

From Photonics Spectra Magazine

Our research interests include Nanophotonics Plasmonics Photonic crystals Photonic device Applications of slow and fast light Quantum nonlinear optics Optical methods for quantum information

Why Study Nonlinear Optics?

It is good fundamental physics.

It leads to important applications.

It is a lot of fun.

Demonstrate these features with examples in remainder of talk.

Nonlinear Optics and Light-by-Light Scattering

The elementary process of light-by-light scattering has never been observed in vacuum, but is readily observed using the nonlinear response of material systems.

Nonlinear material is fluorescein-doped boric acid glass (FBAG)

M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A, 34, 2026, 1986.W. R. Tompkin, M. S. Malcuit, and R. W. Boyd, Applied Optics 29, 3921, 1990.

n2�)%$*��Ⱦ���14 n2(silica) [But very slow response!]

Brief Introduction to Nonlinear Optics

Timeline – The Early Days of Nonlinear Optics

1958 - Schawlow and Townes; optical maser (laser) proposed

1960 - Maiman, ruby laser demonstrated

1961 - Franken, Hill, Peters, and Weinreich, second-harmonic generation (SHG) observed

1962 - Armstrong, Bloembergen, Ducing, and Pershan; systematic formulation of NLO

1962 - McClung, Hellwarth, Woodbury, and Ng, stimulated Raman scattering (SRS)

1964 - Chiao, Garmire, and Townes, self-trapping of light

$1 online

Some Fundamental Nonlinear Optical Processes: II

Sum-Frequency Generation

r (2)

t1

t 2

t1

t 2

t3

t3 = t1 +t2

rt

tt = t < t

Optical Parametric Amplification

Optical Parametric Oscillator (very broadly tunable)

tt

t

Difference-Frequency Generation and Optical Parametric Amplification

Nonlinearcrystal | (2)

IdlerSignal

PumpAmpli!ed

signalSignal

bandwidth

a k P

k I" ,k S" ,

Optical Parametric Amplication Can Amplify Extremely Broadband Pulses

tt

t

Work of Jake Bromage and others at U. Rochester LLE.See also Lozhkarev et al. Laser Phys. Lett. 4, 421 (2007) and Y. Tang et al. Opt. Lett. 33, 2386 (2008).

Goal: Design laser source capable of reaching focused intensities as large as 1024 W/cm2.

Can amplify extremely short laser pulses or broadband chirped pulses.

Parametric Downconversion: A Source of Entangled Photons

The signal and idler photons are entangled in:

(a) polarization

(b) time and enegy

(c) position and transverse momentum

(d) angular position and orbital angular momentum

tp

ts

ti

kp

ks ki

Entanglement is important for:

(a) Fundamental tests of QM (e.g., nonlocality)

(a) Quantum technologies (e.g., secure communications)

Nonlinear Optics Leads to Creation of Entangled Photons

Quantum Correlations in Optical Angle-Orbital Angular Momentum Variables, Leach et al., Science 329, 662 (2010).

Optical Phase Conjugation: A Nonlinear Optics Success Story

Zakharenkov, Clatterbuck, Shkunov, Betin, Filgas, Ostby, Strohkendl, Rockwell, and Baltimore, IEEE JSTQE (2007).

distortingmedium

phase-conjugate mirror

���$�SKDVH�FRQMXJDWH�PLUURU��D�QRQOLQHDU�RSWLFDO�GHYLFH��FDQ�UHPRYH�WKH�LQIOXHQFH�RI� aberrations in double pass.

���3KDVH�FRQMXJDWLRQ�LV�H[WUHPHO\�XVHIXO�LQ�KLJK�SRZHU�ODVHU�V\VWHPV��N:�DYHUDJH�SRZHU�SKDVH�FRQMXJDWH�PDVWHU�RVFLOODWRU�SRZHU�DPSOLILHU

QHDU�GLIIUDFWLRQ�OLPLWHG�RXWSXW

(Zeldovich, Pilipetsky, Shkunov, Yariv, Hellwarth, Fisher, 1980s).

Intense Field and Attosecond Physics

Attosecond pulses to sample a visible E-field

atomic core

High-harmonic generation Measuring the molecular nitrogen wavefunction

Theory of nonlinear optics

Local Field E!ects in Nonlinear Optics

Bloembergen (1962, 1965) showed that E PEloc

!(3)(" = " + " ! ") = N#(3)|L(")|2[L(")]2.

where #(3) is the second hyperpolarizability and where

L(") =$(") + 2

3

For the typical value n = 2, L = 2, and L4 = 16. Local field e!ectscan be very large in nonlinear optics! But can we tailor them for ourbenefit?

We have been developing new photonic materials with enhanced NLOresponse by using composite structures that exploit local field e!ects.

Alternating layers of TiO2 and the conjugated polymer PBZT.

Fischer, Boyd, Gehr, Jenekhe, Osaheni, Sipe, and Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995).

Measure NL phase shift as a function of angle of incidence.

A composite material can display a larger NL response than its constituents!

Enhanced NLO Response from Layered Composite Materials

3.2 times enhancement!35% enhancement in r(3)

Diode Laser(1.37 um)

polarizer

photodiode

gold electrode

ITO

BaTiO3

1 kHz

lockin amplifier

signal generator

dc voltmeter

glass substrate

AF-30 inpolycarbonate

Quadratic EO effect

Nelson and Boyd, APL 74 2417 (1999)

Metamaterials and Nanocomposite Materials for Nonlinear Optics

��0D[ZHOO�*DUQHWW ��%UXJJHPDQ���LQWHUGLVSHUVHd)

� Fractal StrXFWXUe ��Layeredh

2a

b

¡i

¡h

¡a¡b

¡a

¡b

- In each case, scale size of inhomoJeneity << optical ZaveleQJWK

-�7KXs all optical properties, VXch as n and Ƶ���, can be described by effective �YROXPH�DYHrDJHG)�YDOXHs

5HFHQW�UHYLHZ��'ROJDOHYD�DQG�%R\G��$GYDQFHV�LQ�2SWLFV�DQG�3KRWRQLFV�����²�����������

Slow Light, Fast Light, and their Applications

Controlling the Velocity of Light

– Light can be made to go: slow: vg << c (as much as 106 times slower!) fast: vg > c backwards: vg negative Here vg is the group velocity: vg = c/ng ng = n + Ʒ (dn/dƷ)

Review article: Boyd and Gautier, Science 326, 1074 (2009).

“Slow,” “Fast” and “Backwards” Light

– Velocity controlled by structural or material resonancesabsorption

profile

n

ng

t

t

t

t 0

absorptionresonance

slow light

fast light

_

n

ng

t

t

t

t 0

gainresonance

g

fast light

slow light

Slow and Fast Light Using Isolated Gain or Absorption Resonances

ng = n + Ʒ (dn/dƷ)

Light speed reductionto 17 metres per secondin an ultracold atomic gasLene Vestergaard Hau*!, S. E. Harris", Zachary Dutton*!& Cyrus H. Behroozi*§

NATURE | VOL 397 | 18 FEBRUARY 1999 |www.nature.com

1.8 GHz

60 MHz

D line

λ = 589 nm

ω ωc p

|2 = |F =2, M = –2〉 〉F

|1 = |F =1, M = –1〉 〉F

|4 = |F =3, M = –2〉 〉F

|3 = |F =2, M = –2〉 〉F

2

–30 –20 –10 0 10 20 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tra

nsm

issio

n

a

–30 –20 –10 0 10 20 30

Probe detuning (MHz)

0.994

0.996

0.998

1.000

1.002

1.004

1.006

Refr

active index

b

–2 0 2 4 6 8 10 12

Time (μs)

0

5

10

15

20

25

30

PM

T s

ign

al (m

V)

T = 450 nK

τDelay

= 7.05 ± 0.05 μs

L = 229 ± 3 μm

vg = 32.5 ± 0.5 m s

–1

* Rowland Institute for Science, 100 Edwin H. Land Boulevard, Cambridge,Massachusetts 02142, USA! Department of Physics, § Division of Engineering and Applied Sciences,Harvard University, Cambridge, Massachusetts 02138, USA" Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

Note also related work by Chu, Wong, Welch, Scully, Budker, Ketterle, and many others

Crucial for many real-world applications

We have identified two preferred methods for producing slow light

(1) Slow light via coherent population oscillations (CPO)

(2) Slow light via stimulated Brillouin scattering (SBS)

Goal: Slow Light in a Room-Temperature

Solid-State Material

Slow Light by Stimulated Brillouin Scattering (SBS)

1t

L

tS

dI Sdz

= ïgILIS

g = Ƣ2eƷ2

nv c3Ư0ƊB.

z

We often think of SBS as a pure gain process, but it also leads to a change in refractive index

t�� t - 1S L

SBS

gain

refra

ctiv

e in

dex

monochromatic pump laser

Stokes gain

anti-Stokes loss

slow light fast light

Ʒ

Ʒ

TdG

BThe induced time delay is where G= g Ip L and is the Brillouin linewidth B

=

Okawachi, Bigelow, Sharping, Zhu, Schweinsberg, Gauthier, Boyd, and Gaeta Phys. Rev. Lett. 94, 153902 (2005). Related results reported by Song, González Herráez and Thévenaz, Optics Express 13, 83 (2005).

Slow Light via Coherent Population Oscillations

PRL 90,113903(2003); Science, 301, 200 (2003)

� Ground state population oscillates at beat frequency b (for b < 1/T1).

Kba=

1T

12a

ba=

2T

2

a

bsaturablemedium

t

t + b t + b

E1,

E3,

measureabsorption

� Population oscillations lead to decreased probe absorption (by explicit calculation), even though broadening is homogeneous. � Ultra-slow light (ng > 106) observed in ruby and ultra-fast light (ng = –4 x 105) observed in alexandrite.

� Slow and fast light effects occur at room temperature!

absorptionprofile

Want a narrow feature in absorption profile to give a large dn/dt�

ng = n + t�dn/dt��� 1/T1

1/T2

T2 << T1

Relation of CPO to the Basov Mechanism

time delay

propagation distance

leading edge sees far moreabsorption than trailing edge

referencepulse

Assume that Tpulse << T1 = time scale for saturation changes

Then absorption decreases with time during pulse due to saturation

T(response)

CPO slow light: a strong pump beam createsa narrow transparency window, and strong spectral variation of the refractive index leads to a large group index.

Basov mechanism: an isolated intense pulse passing through a saturable material experiences a time delay.

�

�

Slow and Fast Light in an Erbium Doped Fiber Amplifier

6 ms

outin

• Fiber geometry allows long propagation length• Saturable gain or loss possible depending on pump intensity

-0.1

-0.05

0

0.05

0.1

0.15

Frac

tiona

l Adv

ance

men

t

10 100Modulation Frequency (Hz)

10 3 10 4 10 5

- 97.5 mW- 49.0 mW- 24.5 mW- 9.0 mW- 6.0 mW- 0 mW

Advance = 0.32 ms

InputOutput

Time

FWHM = 1.8 ms

Schweinsberg, Lepeshkin, Bigelow, Boyd, and Jarabo, Europhysics Letters, 73, 218 (2006).

Topic 1: Photon Drag Effects with Slow Light

For L = 25 mm, v = 2000 cm/s, displacement = 6 nm.

Transverse Photon Drag

Measured by R.V. Jones, 1972.

L

Observation of Rotary Photon Drag

Franke-Arnold, Gibson, Boyd and Padget, Science, 2011

Effect clearly visible by eye!!

Experimental setup

rotating, 10-cm-long ruby rod

The world as seen through a spinning window.

(Laser-excited ruby has a group index of 106.)

(See also the earlier work of Leach et al., 2008.)

Topic 2: “Backwards” Propagation and Negative Group Velocities

Observation of Backward Pulse Propagation in an Erbium-Doped-Fiber Optical Amplifier

0 2 4 6

0

1

2

3

time (ms)

norm

aliz

ed in

tens

ity

in

out

We time-resolve the propagation of the pulse as a function of position along the erbium-doped fiber.Procedure • cutback method • couplers embedded in fiber

1550 nm laser ISO80/20

coupler

980 nm laserWDM

WDM1550980

EDF

Ref

Signal

or

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, R. W. Boyd, Science 312, 985 2006.

pulse is placed on a cw background to minimizepulse distortion

Observation of Superluminal and

“Backwards” Pulse Propagation

rcoun erin v

B n rc en

y

Normalized length |ng|Z (m)0 0.5-0.5 1x10-1 5

6t = 0

6t = 3

6t = 6

6t = 9

6t = 12

6t = 15

or or rconc r c

G ring,

c ,

propagation distance

ng negative

time

puls

e am

plitu

de

road spectral content at points of discontinuityce moves at vacuum speed of light

see, for instance, R. Y. Chiao

Causality?

g g

Applications of Slow and Fast Light (where the action is now!)

Slow/fast light for interferometeryPhased- and synchronized-array laser radar

Buffers and regenerators for telecom

Construction of quantum memories

Beam Splitter

Beam Splitter

Slow Light Medium

LTunable Laser

Detector

d ¨ƴGƷ

=dGƷ

ƷnLc

=Lc

(n + ƷdnGƷ

) =Lng

c

���The spectral sensitivity of an interferometer is increased by a factor as large as the group index of a material placed within the interferometer.

Slow-light interferometer:

���+Hre is why it works:

Shi, Boyd, Gauthier, and Dudley, Opt. Lett. 32, 915 (2007)6KL��%R\G��&DPDFKR��9XG\DVHWX��DQG��+RZHOO��35/�������������������6KL�DQG�%R\G��-��2SW��6RF��$P��%�����&�������������

���:H�ZDQW�WR�H[SORLW�WKLV�HIIHFW�WR�EXLOG�FKLS�VFDOH�VSHFWURPHWHUV�ZLWK�WKH�VDPH� resoluation as large laboratory spectromters

See also the group of Shahriar on fast-light and interferometry

Simple analysis

Interferometry and Slow Light

���:H�XVH�OLQH�GHIHFW�ZDYHJXLGHV�LQ�SKRWRQLF�FU\VWDOV�DV�RXU�VORZ�OLJKW�PHFKDQLVP

Slow-down factors of greater than 100 have been observed in such structures.

Regeneration of Pulse Timing

time window

Need to recenter each pulse in its time window

Removes timing jitter caused by NL and

environment effects in fiber

Most conveniently done by access to both slow

and fast light

Need only approximately ±1 pulse width of delay!

Z. Shi, A. Schweinsberg, J. E. Vornehm Jr., A. Martinez Gamez, and R. W. Boyd, Physics Letters A 374 4071–4074 (2010).

Recent implementation using SBS with EO-contolled gain spectrum

Phased-Array Laser Radar Based on Slow Light

Schweinsberg et al., Optics Express 19, 15760 (2011)Schweinsberg et al., Optics Letters, 37 329 (2012).

Nonlinear Optics and Quantum Information Science

���:H�use nonlinear optics to create quantum states of light

���6RPH�TXHVWLRQV�XQGHU�LQYHVWLJDWLRQ

How many bits of information can one photon carry?

Can we perform quantum communications with more thanone bit of classical information per photon?

BucketDetector

HologramBBO Crystal Obj. b

entangled photons

cba d

A

B

C

D

Basis 1 (LGs) Basis 2 (Angular)Basis 1 (LGs)Theory Experiment Experiment Theory

Quantum Key Distribution with Many Bits Per PhotonOffers absolutely secure communicationsEncode in a large alphabet (the Laguerre-Gauss modes)

Thank you for your attention!

NLO is as exciting today as it was 51 years ago NLO has spun off many new research fields, such as ultrafast phenomena, photonics, optical solitons, . . . One exciting future direction is that of quantum nonlinear optics

Closing Remarks