control of light -matter coupling in silicon photonic...

Control of lightControl of light--matter coupling matter coupling

in silicon photonic crystal nanocavitiesin silicon photonic crystal nanocavities

M. Galli, S.L. Portalupi, M. Belotti, L.C. Andreani

Department of Physics “Alessandro Volta,”

University of Pavia, Italy

L. O’Faolain (W. Whelan-Curtin), T.F. Krauss

School of Physics and Astronomy,

University of St. Andrews, United Kingdom

Work sponsored by: Fondazione CARIPLO, MIUR FIRB, EU FP6 ePIXnet

OUTLINE

1. Introduction to PhC slab nanocavities

2. Resonant light scattering and Fano lineshapes

3. Geometry optimization and effects of disorder

4. Conclusions

“Resonant light scattering in Silicon photonic crystal cavities”

Nanocavities in photonic crystal slabs

L3 cavity Heterostructure cavity

T. Akahane, T. Asano, B.S. Song, and S. Noda, Nature 425, 944 (2003); B.S. Song, S. Noda, T. Asano, and T. Akahane, Nature Mat. 4, 207 (2005).

Photonic crystal slab nanocavities: strong light-matter interaction, QED effects

Purcell effect:

Chang et al., PRL 96, 117401 (2006)

Strong-coupling regime:

Hennessy et al., Nature 445, 896 (2007)

T. Akahane, T. Asano, B.S. Song, and S. Noda, Nature 425, 944 (2003)

Measurement of Q-factor:waveguide coupling (channel-drop filter)

• Needs coupling waveguide• Loading effect has to be taken into account

probe

emissiontransmission

Measurement of Q-factor: fiber (evanescent) coupling

• Needs accurate control of probe distance• Loading effect has to be taken into account

K. Srinivasan, P. Barkley, M. Borselli, O. Painter, Phys. Rev. B 70, 081306R (2004)




4. Conclusions

M. Galli et al., Appl. Phys. Lett. 94, 071101 (2009)

CW tunable laser

Detector

BS

SampleX

Z

Y

P

A

P

A

X

Y

1 µm

Resonant Scattering of light: reflectance with crossed polarizations first introduced by M.W. McCutcheon et al., APL 87, 221110 (2005);

see also P.G. Deotare, M.W. McCutcheon et al., APL 94, 121006 (2009)

PhC cavity axis is tilted by 45°� no mirror symmetry w.r.t. plane of incidence.

In resonance with the cavity mode: strong enhancement of polarization mixing.

Sample and resonant scattering spectra

1526.1 1526.2 1526.3 1526.4

2

4

6

8

10

12

14 Expt.

Sca

tte

red

In

ten

sity (

a.u

.)

Wavelength (nm)1.5 µm

Asymmetric lineshape (even below background level) � evidence for Fano interference effect

L3 cavity on Si membrane with d=220 nm, a = 420 nm, r/a = 0.3

Fano resonances in photonic crystals slabs: scattering by quasi-guided modes

0.6 0.7 0.8 0.9 1.0 1.10.0

0.2

0.4

0.6

0.8

1.0

Experiment

Fano best-fit

Reflecta

nce

Energy (eV)

Theoretical description: S. Fan, J.D. Joannopolulos, PRB 65, 235112 (2002);

A.R. Cowan, JOSA A 18, 1160 (2001); …

Experiment: V. Pacradouni et al., Opt. Quantum Electron. 34, 161 (2002);

M.Galli et al., IEEE J. Sel. Areas Commun. 23, 1402 (2005); …

The Fano interference effect

Interference between a discrete and a continuum scattering channel � asymmetric lineshape, depending on coupling parameter u

U. Fano, Phys. Rev. 124, 1866 (1961)

In the case of L3 PhC cavities:

Scattering by 2D photonic crystal � continuum of extended states

Scattering by cavity mode �discrete, localized state

( )( )

( )( )20

20

00/21

/2)(

Γ−+

Γ−++=

ωω

ωωω

uFAF u=resonant / non-resonant

( )( )

( )( )20

20

00/21

/2)(

Γ−+

Γ−++=

ωω

ωωω

uFAF

u = resonant / nonresonant

• |u| » 1 → weakly asymmetric • |u| ~ 1 → strongly asymmetric• |u| = 0 → reversed Lorentzian

Possible Fit with parameters |u| < 1 and F < 0 or |u| > 1 and F > 0

Fit with Fano lineshape

1540 1550 15600.0

0.2

0.4

0.6

0.8

1.0

1.2

u = 3

u = 1

u = 0

Sig

nal (a

.u.)

Wavelength (a.u.)

1526.1 1526.2 1526.3 1526.4

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Exp.

Fano fit

Scattere

d Inte

nsity (

a.u

.)

Wavelength (nm)

d1=2 µm

Tailoring the Fano lineshape by the spot size

Condition 1: d1=2 µm

d2=10 µm

1526.1 1526.2 1526.3 1526.4

0.1

0.2

0.3

0.4

0.5

0.6

Exp.

Fano fit

Scatt

ere

d I

nte

nsity (

a.u

.)

Wavelength (nm)

Q = 81700 ± 900 Q = 82400 ± 900

25)/( 2

12 ≅= dd12/areaarea2221 ≅uu

u = resonant / nonresonantu1 = 0.348 u2 = 0.016

relative difference ~ 0.85 %

Condition 2: d2=10 µm




4. Conclusions

Q-factor and geometry optimization

L3L3

L2L2

L1L1

Calculations by guided-mode expansion (GME): LCA, D. Gerace and M. Agio,

Photon. Nanostruc. 2, 103 (2004); LCA & DG, PRB 73, 235114 (2006)

See also C. Sauvan, Ph. Lalanne and J.P. Hugonin, Phys. Rev. B 71, 165118 (2005)

*Expt: T. Akahane, S. Noda et al, Nature 425, 944 (2003).

0.0 0.1 0.2 0.3 0.410

2

103

104

105

L3 defect

L2 defect

L1 defect

expt.(*)

Q-f

acto

r

Displacement ∆x/a

A model of disorder: size variations

Random distribution of hole radii within a large supercell:

Dielectric perturbation couples guided modes to leaky PhC slab modes � out of plane losses can be calculated by electromagnetic perturbation theory

−−=

2

2

2

)(exp)(

σ

rrrP

)()()( dis rrr εεε −=∆

σ≡ r.m.s. deviation of radius

losses of linear (W1) waveguides Q-factors of nanocavities

Effect of size disorder on L3-cavity Q-factors

0.0 0.1 0.210

3

104

105

0.0 0.1 0.2 0.310

3

104

105

σ/a=0.020σ/a=0.015

σ/a=0.010

σ/a=0

σ/a=0.005

Shrinkage ∆r/a

σ/a=0.020σ/a=0.015

σ/a=0.010

σ/a=0

σ/a=0.005

Q-f

acto

r

Displacement ∆x/a

D. Gerace and L.C. Andreani, Photon. Nanostruc. 3, 120 (2005)

Experimental results on optimized L3 cavities

0.12 0.14 0.16 0.18 0.20 0.2220

40

60

80

100120140160

Theory (no disorder)

Experiment

Q f

acto

r (x

10

3)

∆x/a

a = 420 nm; r/a = 0.3; ∆r/r = – 0.06;

∆x/a = 0.14 to 0.20

Local geometry optimization

-100 -50 0 50 100

0

1

2

3

4

5

6

7

Experiment

Fano fit

Inte

nsity (

a.u

.)

Wavelength detuning (pm)

Maximum Q = 110 x 103

∆x/a = 0.19

M. Galli et al., Appl. Phys. Lett. 94, 071101 (2009)

Disorder parameter σ = r.m.s. deviation of holes radii

2

intrinsicexp

11

+=

aA

QQ

σ

Theoretical value: A = 0.62

0.14 0.16 0.18 0.200.7

0.8

0.9

1.0

1.1

((1

/Qe

xp-1

/Q0 )/A

)1/2

a (

nm

)

∆x/a

115 120 125 130 1350

50

100

150

200

250

300

350

400

Fre

qu

ency

Radius (nm)

σSEM=0.9 nmHoles radius distribution by SEM image

Experimental determination of disorder parameter

mean value: σRS=0.89 nm

20

40

60

80

100

120

140160

Theory (no disorder)

ExperimentQ fa

cto

r (x

103

)

80 100 120 140 1600

10

20

30

40

50

60

Holes radius (nm)

100 120 140 1600

20

40

60

80

100

Holes radius (nm)

Nominal σ = 0 nm

SEM σ = 0.91 nm

Nominal σ = 5 nm

SEM σ = 5.41 nm

Nominal σ = 10 nm

SEM σ = 10.65 nm

Effects of intentional disorder

100 120 1400

50

100

150

200

250

300

350

400

450

500

Fre

que

ncy

Holes radius (nm)

1523.8

1524.0

1524.2

1524.4

1.0

1.5

2.0

2.5

3.0

3.5

1518.4

1518.6

1518.8

1509.6

1509.8

1510.0

1510.2

RS

Sig

na

l (a

.u.)

Wavelength (nm)

∆λ = 22.5 pm

Q=67700

0 nm disorder 5 nm disorder

Wavelength (nm)

∆λ = 61.4 pm

Q=24760

9 nm disorder

Wavelength (nm)

∆λ=109.5 pm

Q=13852

a=420 nm, r/a=0.3, hole shift ∆x/a=0.16, hole shrink ∆r/r= - 0.06

Reduction of Q-factor

Quality factors Q decreases rapidly as a function of disorder parameter σ. Trends for cavities with different nearby holes shift ∆x/a are reproduced.

Dependence of Q-factor on disorder parameterQ

fa

cto

r (x

10

3)

0 2 4 6 8 100

20

40

60

80

100

120

0 2 4 6 8 100

20

40

60

80

100

120

Disorder parameter σ (nm)

∆x/a 0.14

0.16

0.17

0.18

0.19

0.2

expt.

Disorder parameter σ (nm)

∆x/a 0.14

0.16

0.17

0.18

0.19

0.2

theory

d=220 nm, a=420 nm, r/a=0.3, hole shrink ∆r/a=−0.06Theoretical calculation is non-perturbative (large σ)

1518.8 1519.0 1519.2

0.001

0.002

0.003

0.004

0.005

0.006

45 degrees

Sig

nal (a

.u.)

Wavelength (nm)

1518.8 1519.0 1519.2

0.001

0.002

0.003

0.004

0.005

0.006 90 degrees

Sig

nal (a

.u.)

Wavelength (nm)

1518.8 1519.0 1519.2

0.001

0.002

0.003

0.004

0.005

0.006

0 degrees

Sig

nal (a

.u.)

Wavelength (nm)

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r Polarizer X

Y

Effect of disorder on mode symmetry

and polarization mixing: σσσσ=0

45°

90°

0°

σ = 0 nm

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r Polarizer X

Y

1519.8 1520.0 1520.2 1520.4 1520.6

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

45 degrees

90 degrees

0 degrees

Sig

nal (a

.u.)

Wavelength (nm)

45°

90°

0°

σ = 4 nm


and polarization mixing: σσσσ=4 nm

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r Polarizer X

Y

1515.2 1515.4 1515.6

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035 45 degrees

90 degrees

0 degrees

Sig

na

l (a

.u.)

Wavelength (nm)

45°

90°

0°

σ = 6 nm



An

aly

ze

r

Polarizer X

Y

An

aly

ze

r

Polarizer X

Y

An

aly

ze

r Polarizer X

Y

1510.8 1511.2 1511.6 1512.0

0.000

0.005

0.010

0.015

0.020

0.025

0.030

45 degrees

90 degrees

0 degrees

Sig

nal (a

.u.)

Wavelength (nm)

45°

90°

0°

σ = 10 nm



CONCLUSIONS

• Resonant Scattering of light with crossed polarizations yields an accurate and loadless measurement of Q-factors in PhC

nanocavities.

• Resonant scattering spectra display Fano-type lineshapes

that can be tailored by changing the excitation spot size (but

fitted Q is unchanged).

• Behaviour of Q-factor as a function of local geometry

optimization as well as of intentional disorder is well reproduced

by theory.

• Resonant scattering has both an intrinsic origin (when the

plane of incidence is not a mirror plane of the cavity: 45°) and a

disorder-induced origin (when the plane of incidence is a mirror plane of the cavity: 0°or 90°).

control of light -matter coupling in silicon photonic...

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