surface-waves generated by nanoslits philippe lalanne jean paul hugonin jean claude rodier institut...

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

OutlineOutline

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

Try to answer basic questionsTry to answer basic questions

OutlineOutline

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

Influence of the geometrical parameter

Try to answer basic questionsTry to answer basic questions

slitwidth

w

OutlineOutline

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

Influence of the geometrical parameter

Influence of the metal dielectric property

Try to answer basic questionsTry to answer basic questions

visible or IR illumination

silveror

gold

OutlineOutline

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

Influence of the geometrical parameter

Influence of the metal dielectric property

Experimental validation

Try to answer basic questionsTry to answer basic questions

slit groove experiment

d

Young’s experiment

d

SPP generationSPP generation

n2

n1

+(x) -(x)

r0

SPP generationSPP generation

n2

n1

n2

n1

+(x) -(x)

t0

SPP generationSPP generation

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

3) Use orthogonality of normal modes

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

3) Use orthogonality of normal modes

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/

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

OutlineOutline

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

Influence of the geometrical parameter

Influence of the metal dielectric property

Experimental validation

Try to answer basic questionsTry to answer basic questions

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

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

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