“Everything Photonic”

or

Slow Light, Enhanced Optical Nonlinearities, andPhotonic Biosensors based on Quantum Coherence

and on Artificial Optical Materials

Robert W. BoydThe Institute of Optics and

Department of Physics and AstronomyUniversity of Rochester, Rochester, NY 14627

http://www.optics.rochester.edu

Presented at the 33rd Winter Colloquium on the Physics of QuantumElectronics, Snowbird Utah, January 9, 2003.

Prospectus

Introduction to Slow Light and to Nonlinear Optics

Slow Light in Ruby

Slow Light in Artificial Materials

Slow-Light and Enhanced Optical Nonlinearities

Devices Based on Slow Light Concepts

Photonic Biosensors

NONLINEAROPTICS

SECOND EDITION

Robert W. Boyd

NO

NL

INE

AR

OPT

ICS

SECONDEDITION

Boyd

ISBN 0-12-121682-9ACADEMIC

PRESS

Boyd_final_layout 11/19/02 12:21 PM Page 1

Interest in Slow Light

Fundamentals of optical physics

Intrigue: Can (group) refractive index really be 106?

Optical delay lines, optical storage, optical memories

Implications for quantum information

Slow Light

group velocity ≠≠≠≠ phase velocity

Challenge/Goal

Slow light in room-temperature solid-state material.

• Slow light in room temperature ruby

(facilitated by a novel quantum coherence effect)

• Slow light in a structured waveguide

Slow Light in RubyNeed a large dn/dω. (How?)

Kramers-Kronig relations: Want a very narrow absorption line.

Well-known (to the few people how know itwell) how to do so:

Make use of “spectral holes” due topopulation oscillations.

Hole-burning in a homogeneouslybroadened line; requires T2 << T1.

1/T2 1/T1

inhomogeneously broadened medium

homogeneously broadened medium(or inhomogeneously broadened)

Γba

=1

T1

2γba

=2

T2

a

b b

a

cω

Γca

Γbc

atomicmedium

ω

ω + δω + δ

E1,

E3,

measure absorption

Spectral Holes Due to Population Oscillations

ρ ρbb aa w−( ) = δ δ δ δi t i tw t w w e w e≈ + +− −( ) ( ) ( ) ( )0

Population inversion:

δ T≤ / 11population oscillation terms important only for

ρ ω δ µω ω

δba

ba

ba i TE w E w+ =

− ++[ ]( )

/( ) ( )

23

01

1

Probe-beam response:

α ω δδ β

β

wT

T+ ∝ −

+

=

( )

( /

( )02

2

12 2

1

1

Ω

TT T T12

1 21) ( )+ Ω

Probe-beam absorption:

linewidth

h

Argon Ion LaserRuby

f = 40 cm

Function Generator

EO modulator

Digital

Oscilloscope

f = 7.5 cm

Diffuser

Reference Detector

Experimental Setup Used to Observe Slow Light in Ruby

7.25 cm ruby laser rod (pink ruby)

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4D

elay

(m

s)

2000 400 600 800 1000Modulation Frequency (Hz)

P = 0.25 W

P = 0.1 W

Measurement of Delay Time for Harmonic Modulation

solid lines are theoretical predictions

For 1.2 ms delay, v = 60 m/s and ng = 5 x 106

512 µs

Time (ms)

0

0.2

0.4

0.6

0.8

1.0

1.2

No

rma

lize

d I

nte

nsity

Input Pulse

Output Pulse

0 10 20-10-20 30

Gaussian Pulse Propagation Through Ruby

No pulse distortion!

v = 140 m/s

ng = 2 x 106

Artificial Materials for Nonlinear OpticsArtifical materials can produce Large nonlinear optical response Large dispersive effects

ExamplesFiber/waveguide Bragg gratingsPBG materialsCROW devices (Yariv et al.)SCISSOR devices

MotivationTo exploit the ability of microresonators to enhancenonlinearities and induce strong dispersive effects for creatingstructured waveguides with exotic properties.

A cascade of resonators side-coupled to an ordinarywaveguide can exhibit:

slow light propagationinduced dispersionenhanced nonlinearities

Ultrafast All-Optical Switch Based On Arsenic Triselenide Chalcogenide Glass

We excite a whispering gallery mode of a chalcogenide glass disk.

The nonlinear phase shift scales as the square of the finesse F of the resonator. (F ≈ 10 2 in our design)

Goal is 1 pJ switching energy at 1 Tb/sec.

r5050

RingResonator

Input-2

Output-1

J. E. Heebner and R. W. Boyd, Opt. Lett. 24, 847, 1999. (implementation with Dick Slusher, Lucent)

Input-1

Output-2

Pulses spread when only dispersion is present

050

100150

0 20 40 60 80 100 120 t (ps)z (resonator #)

inte

nsity

050

100150

0 20 40 60 80 100 120 t (ps)z (resonator #)

inte

nsity

But form solitons through balance of dispersion and nonlinearity.

Displays slow-light, tailored dispersion, and optical solitons.

NLO of SCISSOR Devices(Side-Coupled Integrated Spaced Sequence of Resonators)

Description by NL Schrodinger eqn. in continuum limit.

(J.E. Heebner, Q-Han Park and RWB)

Fn

Slow Light and SCISSOR Structures

frequency, ω

FnR

c c

FnR

cnR

grou

p in

dex

buil

d-u

pk

eff −k

0

Fncslope =

F

n

2π

F2π n

0

FnR

c

2πL

FnR

c

cslope =

E3

E4

E1

E2 L

R

What is the relation between slow light andenhanced optical nonlinearity?

Comment: We know that there is a connection from the work of Hau,Harris, Lukin, Soljacic, Scully, Imamoglu, Bennink and many others.

Note: For n(phase) ª 1, there is no enhancement of the electric fieldwithin the material. Thus the enhancement must be of c(3), not of E.

Possible explanation: In a slow light situation, the light spends more timeinteracting with the medium. Can this be the explanation for enhancednonlinearity? (Ans: Yes and no.)

If this were the whole story, we would expect c(3), to scale in proportionto the group index n(group), which it does in some but not all situations.

What is the relation between slow light andenhanced optical nonlinearity?

The scaling laws seem to be very different for EIT media than forstructured artificial materials (PBG, CROWs, SCISSORSs, etc), becausein the latter case the E field is enhanced.

To first approximation:

For EIT: c(3) scales as n(group)For artificial materials: c(3) scales as the square of n(group)

Detailed analyses of the relation between slowlight and enhanced optical nonlinearity

• Heebner and Boyd show that the nonlinear phase shift scales as thesquare of the finesse of a ring resonator. Since n(group) scales as thefinesse, it follows that scales as the square of n(group).

• Lukin points out that the nonlinear phase shiftcan be expressed as f dwNL = T , whereT L c ng= / ( / ) is the interaction time and where

dw m= 2 2 2E / (h/2p) Dis the Stark shift of the optical transition. Thismodel predicts that scales as n(group). a

w1 w2

c

b

fNL

fNL

Unwanted Complication in Two-Level-Atom EIT

wc-2 -1 0 1 2

-0.5

0

0.5

Re c (1)

Im c(1)

-2 -1 0 1 2-2

-1

0

1

Ds

Re c (3)

Im c (3)

-5 0 5-0.1

0

0.1

-5 0 5-0.04

0

0.04

-10 0 10

-0.1

0

0.1

0.2

-0.05

0

Ds

Re c (1)

Re c (1)

Im c(1)

Im c(1)

DsDs

DsDs

Im c (3)Re c (3)

-10 0 10

0.05 Re c (3)

Im c (3)

-2 0 2-2

0

2

b1 -10

0

10b2

Ds

-5 0 5-0.1

0

0.1

-0.5

0

0.5b2

b1

-20 0 20-0.2

0

0.2

-0.2

0

0.2

Ds

Ds

b2b1

Response in absence of control field (Wc = 0, g = 0.5)

Response with a moderate, centrally tuned control field (Wc = 2, Dc= 0, g = 0.5)

Response with a stronger, detuned control field (Wc = 9, Dc= 3, g = 0.5)

Im c is proportional to ng, but Re c(3) is not.

(3)

Bennink et al., Phys.Rev. A, 2001.

What is the relation between slow light andenhanced optical nonlinearity?

Summary: This remains a somewhat open question.

Nanofabrication

• Materials (artificial materials)

• Devices

(distinction?)

Disk Resonator and Optical Waveguide in PMMA Resist

AFM

Photonic Devices in GaAs/AlGaAs

time (ps)po

wer

(m

W)

00

6

0

6

50 100

0

6

Input(duty factor = 1/3)

0

6

Output --delayed one time slot by six resonators in linear limit

Output --delayed four time slots by 26 resonators in linear limit

pow

er (

mW

)po

wer

(m

W)

pow

er (

mW

)

Output --delayed four time slots by 26 resonators in nonlinear limit

Performance of SCISSOR as Optical Delay Line

"Fast" (Superluminal) Light in SCISSOR Structures

pow

er (

arb.

uni

ts) 1.0

overcoupledcoupledcritically

undercoupled

overcoupled

0.5

0

k eff

-k 0

frequency detuning, w-wR

2pL

400delay (ps)

propagationthroughvacuum

(time-advanced)propagation

throughundercoupled

SCISSOR

-40-80-120

0 8 dw- 8 dw

Requires loss in resonator structure

Frequency Dependence of GVD and SPM Coefficients

-4p 0

-0.5

0.0

0.5

1.0

F -2pF

4pF

2pF

normalized detuning, f0

geffk''eff

(2FT/p)2/L g (2F/p)2 (2pR/L)

p3F

soliton condition

(GVD) (SPM)

Fundamental Soliton

Weak Pulsepulse

disperses

pulsepreserved

Soliton Propagation

050

100150

200250

0 20 40 60 80 100

050

100150

200250

0 20 40 60 80 100

0

0.1

0.2

0.3

t (ps)

z (resonator #)

pow

er (

µW)

0

0.1

0.2

0.3

t (ps)

z (resonator #)

pow

er (

W)

simulation assumes a chalcogenide/GaAs-

like nonlinearity

5 µm diameter resonators with a

finesse of 30

SCISSOR may be constructed from 100 resonators spaced by

10 µm for a total length of 1 mm

soliton may be excited via a 10 ps, 125mW

pulse

Dark Solitons

0100300

20

60

100

0

20

t (ps)z (resonator #)

po

wer

(m

W)

SCISSOR system also supports the propagation of dark solitons.

0 2 4 6 8 100

0.5

1.0

1.5

2.0

input power (watts)

input output

outp

utpo

wer

(wat

ts)

Optical Power Limiting in a Nonlinear Mach-Zenhder Interferometer

Objective:Obtain highsensitivity, highspecificity detectionof pathogens throughoptical resonance

Approach:Utilize high-finessewhispering-gallery-mode disk resonator.

Presence of pathogenon surface leads todramatic decrease infinesse.

Simulation of device operation:

Intensity distribution in absense of absorber.

Intensity distribution in presence of absorber.

Alliance for Nanomedical Technologies

Photonic Devices for Biosensing

FDTD

GaAs or AlGaAsGaAs or AlGaAsSiO2

Deposition of Surface Binding Layer

GaAs or AlGaAsSiO2

GaAs or AlGaAsSiO2

~1.2 nm

~300 nm

~12 nm

~1-5microns

GaAs or AlGaAsSiO2

1) Bare device surface

targetpathogen

2) SiO2 layer deposited by PECVD

3) Silane coupling agent deposited on surface

(C6H16O3SSi)

3-MercaptopropylTrimethoxysilane (MPT)

4) Antibodies washed over surface / adhere to MPT

5) Pathogen captured by antibody layer

streptavidin over biotin on GaAs

streptavidin over biotin on silica-coated GaAs

biotin on silica-coated GaAs

Notes: 1. false-color images of fluorescent intensity are shown 2. streptavidin is tagged with the dye Cy3

Demonstration of Selective Binding onto GaAs

University of Rochester/Corning Collaboration

biotin on GaAs

biotin on microscope slide

streptavidin over biotin on microscope slide

Summary

Artificial materials hold great promise for applications in photonics because of

• large controllable nonlinear response

• large dispersion controllable in magnitude and sign

Demonstration of slow light propagation in ruby

Thank you for your attention.

L 2L2L

SCISSOR Dispersion Relations

20 0

1.498

1.522

1.546

1.571

1.597p p- p

Bloch vector (keff)intensity build-up

Single-Guide SCISSOR

wav

elen

gth

(mm

)

Bragg gap

resonator gap

Bragg + resonator gap

No bandgap

Lp

Large intensity buildup

-

Double-Guide SCISSORBandgaps occur Reduced intensity buildup

L 2L2L20 0 p p- p0

Bloch vector (keff)intensity build-up

Lp-

separation = 1.5 p R

Alliance for Nanomedical Technologies

Optical Logic On A ChipOptical Logic On A Chip

A(1)

A(2)

Out(1)

Out(2)

In

Pathogen Out(1) Out(2)

none 1 0P(1) 1 1P(2) 1 1P(1) and P(2) 0 0

Is This a Good Idea?

Vollmer et al., Appl. Phys. Lett. 80, 4057 (2002).

Protein detection by optical shift of a resonant microcavity

The Promise ofNonlinear Optics

Nonlinear optical techniques hold great

promise for applications including:

• Photonic Devices

• Quantum Imaging

• Quantum Computing/Communications

• Optical Switching

• Optical Power Limiters

• All-Optical Image Processing

But the lack of high-quality photonicmaterials is often the chief limitation inimplementing these ideas.

Approaches to the Development ofImproved NLO Materials

• New chemical compounds

• Quantum coherence (EIT, etc.)

• Composite Materials:(a) Microstructured Materials, e.g.

Photonic Bandgap Materials,Quasi-Phasematched Materials, etc

(b) Nanocomposite Materials

These approaches are not incompatible and in fact can beexploited synergistically!

Nanocomposite Materials for Nonlinear Optics

• Maxwell Garnett • Bruggeman (interdispersed)

• Fractal Structure • Layered

λ

2a

b

εi

εh

εaεb

εa

εb

scale size of inhomogeneity << optical wavelength

Gold-Doped Glass

A Maxwell-Garnett Composite

gold volume fraction approximately 10-6

gold particles approximately 10 nm diameter

• Composite materials can possess propertiesvery different from their constituents.

• Red color is because the material absorbsvery strongly at the surface plasmonfrequency (in the blue) -- a consequence oflocal field effects.

Demonstration of Enhanced NLO Response

• Alternating layers of TiO2 and the conjugated polymer PBZT.

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

Fischer, Boyd, Gehr, Jenekhe, Osaheni, Sipe, and Weller-Brophy, Phys. Rev. Lett. 74, 1871, 1995.Gehr, Fischer, Boyd, and Sipe, Phys. Rev. A 53, 2792 1996.

— =^

DE

0( )e is continuous.

implies that

Thus field is concentrated in lower index material.

.

Enhanced EO Response of LayeredComposite Materials

Diode Laser(1.37 um)

Polarizer

Photodiode Detector

Gold Electrode

ITO

BaTiO3

Ω =1kHz

Lockin Amplifier

Signal Generator

dc Voltmeter

Glass Substrate

AF-30/Polycarbonate

χ ω ωε ωε ω

ε ωε ω

εε

εε

χ ω ωijkleff

aeff

a

eff

a

eff

a

eff

aijklaf( ) ( )( ; , , )

( )

( )

( )

( )

( )

( )

( )

( )( ; , , )′ =

′′

′Ω Ω

ΩΩ

ΩΩ

Ω Ω1 21

1

2

21 2

• AF-30 (10%) in polycarbonate (spin coated)n=1.58 ε(dc) = 2.9

• barium titante (rf sputtered)n=1.98 ε(dc) = 15

χ

χzzzz

zzzz

i m V( )

( )

( . . ) ( / ) %

. ( )

3 21 2

3

3 2 0 2 10 25

3 2

= + × ±

≈

−

AF-30 / polycarbonate

3.2 times enhancement in agreement with theory

R. L. Nelson, R. W. Boyd, Appl. Phys. Lett. 74, 2417, 1999.

E

z

SiO2 Cu

L0

E

z

Cu

R.S. Bennink, Y.K. Yoon, R.W. Boyd, and J. E. Sipe Opt. Lett. 24, 1416, 1999.

• Metals have very large optical nonlinearities but low transmission.

• Solution: construct metal-dielectric PBG structure. (linear properties studied earlier by Bloemer and Scalora)

pure metal80 nm of copperT= 0.3%

PBG structure80 nm of Cu (total)T= 10%

• Low transmission is because metals are highly reflecting (not because they are absorbing!).

Accessing the Optical Nonlinearity of Metals with Metal-Dielectric PBG Structures

40 times enhancment of NLO response is predicted!

Z-Scan Comparison of M/D PBG and Bulk Sample

35 @¢¢

¢¢

Cu

PBG

fdfd

0.50

0.75

1.00

0 50 100 150 200 250

z,mm

Tnorm

Cu

PBG

l = 640 nm

I = 500 MW/cm2Open-aperture Z-scan

(measures Im c(3))

Spectral Dependence of the Nonlinear Response

0

0.5

1.0

1.5

2.0

500 550 600 650 700

PBG

Bulk

wavelength, nm

Im f

NL

OPG:

Q = 2 to 5 mJ

I @ 100 MW/cm2

t = 25 ps

Nonlinear Schrödinger Equation (NLSE)

Fundamental Soliton Solution

Propagation Equation for a SCISSOR

L

∂∂z A = −i 12 β2 ∂2

∂t2A + iγ |A|2A

A(z,t) = A0 sech tTp

ei12

γ|A0 |2z

By arranging a spaced sequence of resonators, side-coupled to an ordinary waveguide, one can create an effective, structured waveguide that supports pulse propagation in the NLSE regime.

Propagation is unidirectional, and there is NO photonic bandgap to produce the enhancement. Feedback is intra-resonator and not inter-resonator.

ω R

γ eff

β2

Balancing Dispersion & Nonlinearity

A0 = |β2 |

γ Tp2= T2

3 γ2πRTp2

Resonator-induced dispersion can be 5-7 orders of magnitude greater than the material dispersion of silica!

Resonator enhancement of nonlinearity can be 3-4 orders of magnitude!

An enhanced nonlinearity may be balanced by an induced anomalous dispersion at some detuning from resonance to form solitons

A characteristic length, the soliton period may as small as the distance between resonator units!

soliton amplitude

adjustable by controlling ratio of transit time to pulse width

GaAs

AlxGa1-xAs(x = 0.4)

Microdisk Resonator Design

(Not drawn to scale)All dimensions in microns

0.5

2.0

10 10

0.450.25

s1 = 0.08s2 = 0.10s3 = 0.12s4 = 0.20

25

2.0

trench

gap

lineartaper

20

trench

d = 10.5

25lineartaper

J. E. Heebner and R. W. Boyd

Pulse Distortion on Propagation through SCISSOR Structure

strong pulse, at GVD extremum

weak pulse, on resonance

pow

er (

mW)

weak pulse, at GVD extremum

6

4

2

0

0 1 2 3 4time (ns)

8

input output

input

input

output

output (soliton)

pow

er (

mW)

6

4

2

0

8

pow

er (

mW)

6

4

2

0

Maximum delay, but pulse distorted by higher-orderdispersion.

Slightly reduced delay, no distortion, but spreading due to GVD.

Slightly reduced delay, no distortion, SPM com-pensates for spreading

Photonic Device Fabrication Procedure

RWB - 10/4/01

PMMA

AlGaAs-GaAs

structure

Oxide (SiO2)

AlGaAs-GaAs

structure

Oxide (SiO2)

PMMA

AlGaAs-GaAs

structure

PMMA

Oxide (SiO2)

(2) Deposit oxide

AlGaAs-GaAs

structure

(1) MBE growth

(3) Spin-coat e-beam resist

(4) Pattern inverse with

e-beam & develop(6) Remove PMMA

(7) CAIBE etch AlGaAs-GaAs

(8) Strip oxide

AlGaAs-GaAs

structure

Oxide (SiO2)

AlGaAs-GaAs

structure

AlGaAs-GaAs

structure

Oxide (SiO2)

(5) RIE etch oxide

AlGaAs-GaAs

structure

Oxide (SiO2)

Intensity Enhancement ( |E3 / E1|2 )

Modified Dispersion Relation ( β vs. ω )

Properties of a Single Microresonator

frequency (ω)

effe

ctiv

e pr

opag

atio

nco

nsta

nt (

β)B

uild

-up

Fac

tor

|E3

/ E

1|2

ωR

r2 = 0.90

r2 = 0.75

r2 = 0.25

r2 = 0.00

r2 = 0.00 r2 = 0.25

r2 = 0.75 r2 = 0.90

ωR − 2πT

ωR + 2πT

E

R

3E

4

E1

E2

Assuming negligible attenuation, this resonator is, unlike a Fabry-Perot, of the "all-pass" device -

there is no reflected or drop port.

Definitions

Finesse

Transit Time

E4E2

= r it

rit

E3E1

F = π1−r

T = n2πRc