Surface-waves generated by nanoslits Philippe Lalanne Jean Paul Hugonin Jean Claude Rodier INSTITUT d'OPTIQUE, Palaiseau - France Acknowledgements : Lionel

Surface-waves generated Surface-waves generated by nanoslitsby nanoslits

Philippe Lalanne

Jean Paul Hugonin

Jean Claude Rodier

INSTITUT d'OPTIQUE, Palaiseau - France

Acknowledgements : Lionel Aigouy , 40 100 Béziers

Basic diffraction problemBasic diffraction problem

Basic diffraction problemBasic diffraction problem

Motivation : providing a Motivation : providing a microscopic description microscopic description

of the interaction of the interaction between nanoslits between nanoslits

= 750 nm

320-nm-thick Ag film

Ebbesen et al., Nature 391, 667 (1998)

=/3

Motivation : ETMotivation : ET

Motivation : beaming Motivation : beaming effecteffect

H. Lezec et al., Science 297, 820 (2002)

Garcia-Vidal et al., APL 83, 4500 (2003)

Gay et al., Appl. Phys. B 81, 871-874 (2005)

20 µm

calculation

measurements

OutlineOutline

Nature of the surface wavesNature of the surface waves SPP?

Try to answer basic questionsTry to answer basic questions

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Nature of the surface wavesNature of the surface waves SPP? – other waves?


OutlineOutline


Influence of the geometrical parameter


slitwidth

w

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Influence of the metal dielectric property


visible or IR illumination

silveror

gold

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Experimental validation


slit groove experiment

d

Young’s experiment

d

SPP generationSPP generation

n2

n1

+(x) -(x)

r0


n2

n1

n2

n1

+(x) -(x)

t0


S = + [t0 exp(2ik0neffh)] / [1-r0 exp(2ik0neffh)]

Easy generalizationEasy generalization

S S

(a) (b)

General theoretical formalismGeneral theoretical formalism

1) Calculate the transverse (Ez,Hy) near-field

2) make use of the completeness theorem for the normal modes of waveguides

Hy=

Ez=

3) Use orthogonality of normal modes

(z)(x)Ha(z)H(x)α(x)α (rad)σσ σSP

(z)(x)Ea(z)E(x)α(x)α (rad)σσ σSP

(x)α(x)α2(z)Ez)(x,Hdz SPy

(x)α(x)α2(z)Hz)(x,Edz SPz

P. Lalanne, J.P. Hugonin and J.C. Rodier, PRL 95, 263902 (2005)

Analytical modelAnalytical model

-The SP excitation probability ||2 scales as ||-1/2

-Immersing the sample in a dielectric enhances the SP excitation ( n2/n1)

n2

n1

+(x) -(x)

1) assumption : the near-field distribution in the immediate vicinity of the slit is weakly dependent on the dielectric properties

2) Calculate this field for the PC case


012

1

1/2

221

2

Iw'nn1

Iw

nεε

nn

π4αα

describe material properties

P. Lalanne, J.P. Hugonin and J.C. Rodier, JOSAA 23, 1608 (2006)

n2

n1

+(x) -(x)

1) assumption : the near-field distribution in the immediate vicinity of the slit is weakly dependent on the dielectric properties

2) Calculate this field for the PC case


012

1

1/2

221

2

Iw'nn1

Iw

nεε

nn

π4αα

describe material propertiesdescribe geometrical properties-A universal dependence of the SPP excitation that peaks at a value w=0.23.

-For w=0.23 and for visible frequency, ||2 can reach 0.5, which means that of the power coupled out of the slit half goes into heat

Analytical modelAnalytical model

tota

l SP

exc

itat

ion

pro

bab

ility

Results obtained for gold

Tot

al S

P e

xcit

atio

n e

ffic

ien

cy

model : solid curves

vectorial theory : marks

SPP? - other waves?

z

H(x,x’,z=0)

x’=0

Green function (1D)Green function (1D)

x

,kHkzH1

zxH1

x20

20

H = HSP + Hc

)xikexp(k

kSP

dm

md20

2SP

HSP =

Hc = Integral over a single real variable

zGreen function (1D)Green function (1D)

10-1

10-2

100

10-3

101 102100 101 102100

=0.633 µm =1 µm

=9 µm=3 µm

x/ x/

|H| (

a.u.

)|H

| (a.

u.)

|H| (

a.u.

)|H

| (a.

u.)

x/ x/

10-1

10-2

100

10-3

(result for silver)

HSP

Hc

(x/)-1/2

P. Lalanne and J.P. Hugonin, Nature Phys. 2, 556 (2006)

w=100 nm

-0.5

0

0.5w=352 nm

-1

0

1

=0.

852

µm

=3

µm

plane waveillumination

()

x/

x/P. Lalanne and J.P. Hugonin, Nature Phys. 2, 556 (2006)

dS

= 852 nm

S0

= 852 nm

d/

|S/S

0|2

m

m

m

m

m

PC

….. SPP only computational results

(d/


OutlineOutline




Experimental validation


slit groove experiment

d

Young’s experiment

d

Validation : Young’s slit experiment

H.F. Schouten et al., PRL. 94, 053901 (2005).

d

gold

glass

TM incident light

d=4.9 µm

d=9.9 µm

d=14.8 µm

d=19.8 µm

P. Lalanne, J.P. Hugonin and J.C. Rodier, PRL 95, 263902 (2005)

S = |t0 + - + exp[ikSPd)]|2 S

+ -

d

gold

*** semi-analytical modelo o o Schouten’s experiment numerical results

d=4.9µm

d=9.9µm

S

S

Validation : Young’s slit experiment

d

|S|2

|S0|2

|S/S

0|2

d (µm)

Slit-Groove experiment

G. Gay et al. Nature Phys. 2, 262 (2006) promote an other model than SPP

d Fall off for d < 5

frequency = 1.05 k0

kSP=k0 [1-1/(2Ag)] 1.01k0

silver

=852 nm

|S/S

0|2

d (µm)

dS

= 852 nm

S0

= 852 nm

computational resultso o o experiment….. SPP theory

SPP theory and computational results are in perfect agreementSPP theory and computational results are in perfect agreement


Lionel Aigouy, Laboratoire ‘Spectroscopieen Lumière Polarisée’ ESPCI, Paris

2 µm

2 µm

Gwénaelle Julié,Véronique MathetInstitut d’ElectroniqueFondamentale, Orsay, France

Near field validation

gold

TM incident light

slit slit

Real part Imaginary part

Real part Imaginary part

distance distance

----- extracted from fit computational results

total field

creeping wave ONLY

Field at a single aperture

Conclusion

•The surface wave is a combination of SPP [exp(ikSPx)] and a creeping wave with a free space character [exp(ik0x)]/x1/2 •SPP is predominant at optical frequency for noble metal•The creeping wave is dominant for >1.5 µm and for noble metals•The SPP generation probability can be surprisingly high for subwavelength slits (50%) at optical wavelengths•The probability scales as ||-1/2

•The probability is enhanced when immersing the sample•Experimental validation is difficult but on a good track

Documents

Surface-waves generated by nanoslits Philippe Lalanne Jean Paul Hugonin Jean Claude Rodier INSTITUT d'OPTIQUE, Palaiseau - France Acknowledgements : Lionel