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Experimental investigation of lateral wave contribution to the shift of a reflected beam at surface plasmon resonance
Optics Communications 96 (1993) 221-224 North-Holland
OPTICS COMMUNICATIONS
Experimental investigation of lateral wave contribution to the shift of a reflected beam at surface plasmon resonance P. Maddalena a G. Abbate a, p. Mormile b, G. Pierattini b and E. Santamato a a Dipartimento di Scienze Fisiche, Universit& di Napoli, Pad. 20, Mostra d'Oltremare, 80125 Napoli, Italy b Istituto di Cibernetica del C.N.R., Via Toiano n. 6, 80072Arco Felice (NA), Italy
Received 25 September 1992
Reflected field intensity distributions are reported for surface plasmon wave excitation in an attenuated total internal reflection configuration for different metal film thicknesses. The measured lateral shift is compared with theoretical predictions.
1. Introduction A light beam, when totally reflected at a dielectric interface, undergoes a lateral shift which is usually of the order of a few wavelengths [ 1 ]. Amplification of this shift can be achieved when the beam is reflected by multilayered media [ 2 ]. In particular, when thin metal films are present in layered structures, the beam can undergo even larger displacements if the reflection occurs near a surface plasmon (SP) resonance. In this case observation of an enhanced lateral shift o f several ~tm in the visible region was reported [3]. The SP was excited in a Kretschmann attenuated total reflection (ATR) configuration (e.g. glass p r i s m - m e t a l - a i r ) . The experimental results were in good agreement with a simple theoretical model, due to Renard, based on energy-flux conservation for bounded light beams [4]. At resonance, indeed, there is an energy flow associated to the SP wave in the dielectric, which is parallel to the metal dielectric interface. Consequently, a lateral shift o f the beam must occur if energy has to be conserved. In that case, however, the transmitted and reflected field distributions were calculated by means of a leaky-wave theory in which the reflection coefficient o f the layer structure was expanded near the pole of the leaky SP mode. It must be noted that the series expansion of the reflection coefficient around the pole cannot be assumed in general since contributions from other singularities,
such as branch points, can be important [ 5 ]. This is true especially if Kretschmann configurations are studied in which the metallic film is very small with respect to the light wavelength. It is, then, necessary to proceed to a direct numerical integration of the equations for the fields in order to have the reflected intensity distribution of the beam. In this work the contribution of lateral waves (due to the presence of a branch point) to the beam displacement near a SP resonance is experimentally investigated for different film thicknesses and the observed results are compared with theory.
2. Experimental results and discussion In our experiment, an aluminum film was grown on the base of a glass prism. The film had a stepgraded thickness ranging from 40 ~, to 520 A in steps of 40 A. A linearly polarized HeNe laser was focused to a spot size of 8 g m by a cylindrical lens at the SP resonance angle on the prism base. The reflected beam was enlarged by a microscope and sent to a photodiode via a rotating mirror driven by a stepping motor. The electrical output signal was recorded by a personal computer for display and data analysis. A translation of the rotating base supporting the prism coupler allowed signal recording for each film thickness. The experimental layout is shown in fig. 1 to-
0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
221
Volume 96, number 4,5,6
OPTICS COMMUNICATIONS •
glass
Z
laser
with
prism
+oo
~ Hl(fl) = ~
beam AI f
i
l
m
~
~
15 February 1993
\"
~ X
I
H,(x) exp(-ikoflx) dx,
(3)
the reflected field is given by +oo
I
~
H~(x)=(koW/2x/~) I R(B)
MS
HE-NE
-oo
M
dB,
×exp[-kgw2(l?-B~)2/4+ikoBx]
I Fig. 1. Experimental lay-out. P: polarizer; 2/2: halfwave plate; CA: coupling assembly; MS: microscopy; RM: rotating mirror; PM: photomultiplier; PC: personal computer. The insert shows the coupling assembly in greater detail. gether with an enlarged view of the coupling assembly. The half-wave plate behind the laser allowed polarization switching between the s- and p- state. Since SP waves are excited only by p-polarized light, the s-polarized reflected beam provided the zero reference in the shift measurements. Proper calibration of the recorded signal in absolute spatial units along the prism base was achieved by means of a reticle scale attached to the prism ~1 Let us refer to a theoretical model based on planewave expansion and consider a p-polarized gaussian beam incident at an angle 0~ whose amplitude (at the prism base) is
where R (fl) is the reflection coefficient of the whole layered medium. If a direct numerical integration in eq. (4) is performed, one obtains the curves of fig. 2 which show the reflected field intensity at the prism
!
I
I
• 520 a 480 440 - - - 400 ....... 360 ....... 320° ....
~F-~, r,:' ~'~ ~
0.6 o*
0.2
(A)
-lO
o
10
30
20
x (~m) !
I
( 1)
where x is taken along the propagation direction o f the SPW (see insert of fig. 1 ). In the preceding equation, w is the beam waist, ko= 2n/2 is the wavenumber (2 is the laser wavelength in v a c u u m ) and fl~= ~ sin 0~, ~ being the dielectric constant o f the glass prism. Using the plane wave spectrum of the incident field,
I
• --
I
HI(x) = e x p ( - x 2 / w 2 +ikofli x) ,
(4)
I
• -- • -
-
-
........ 0 . 6 -
/-\ I
~'
280 ?, 240 ~, 200,~ 160,~ 120° 80,~ 40,~
."" ".."
_.
~
"
// • ,~\ ",.. ,/., J/'. x., ",,.. //., ../- ~,~a "\ /}," .;<'~ '.\~"- ' 0.2
#, ///
\ \*~ ....."<', %,
//,)~7
[B]
+oo /I
Hi(x) =
j H i ( r ) exp(ik0flx) d r ,
(2)
-10
0
10
20
30
× O,m)
--oo
~ A more detailed description of the experimental apparatus and of the calibration procedure can be found in ref, [ 3 ]. 222
Fig. 2. Reflected field intensity distribution p(x) at the prism base for different values of the metallic film thickness d computed by exact theory.
Volume 96, number 4,5,6
OPTICS COMMUNICATIONS
base for an incident field of unit amplitude at various film thicknesses. In the computation a refractive index n o = x / ~ t = 1.515 for the glass prism and a dielectric constant eA~= ( - - 2 9 . 8 + i 1 1 . 6 ) for the aluminum film are used. Moreover, according to the experimental configuration, the incident beam wavelength is 2 = 0 . 6 3 2 8 pm and w = 8 p,m is the waist. For 40 A film thickness, the lateral shift is of the order of 2 pm. A m a x i m u m value o f the shift of about 4 p m is reached at 120 ~,. For thicker films, the shift rapidly decreases to zero as shown by the solid curve of fig. 3. This is to be expected since the coupling between the incident radiation and the surface plasmon field, which is localized at the metalair interface, is low for a large film thickness. Consequently, there is no amplification of the lateral shift due to surface plasmon resonance. In this limit, the reflected field distribution is mainly due to the reflection at the prism-metal interface which, as is well known, shows no lateral shift. In fig. 3 we have also reported the experimental values of the shift. They were obtained by measuring the spatial distance between the maxima o f the reflected intensity distributions at the prism base for the s- and p-polarized light. The agreement between the experiment and the theoretical prediction is good. Moreover, the shape of the observed distributions closely resembles the theoretical one. In order to point out the lateral wave contribution to the shift, we have also reported in fig. 4 the in-
I
I
|
I
I
¢2
o 0
0
0
O,
o
o
o
0
I
I
I
I
• -- -- •-
_
L,{f/'-). "'~
......... - --
....... "~,}. ~,........,:{
0.6
520 4 8 0 ,~ 440~, 400,: 360,~ 3 2 0 ~,
x
l: 0.2 -
:::,}
!
(A)
I
0
-10
I
10
x (.m /
I
l
I -
---
-
-.... ---....
--
..........
0.6 x
3O
20
I
280
2 4 0 ,~ 200 160~ 120,~ 8 0 ,~
40
I' \~..
B
/
. ~ \~ i'1.1 '\ II .-...
0.2 -
2~.'"
-10
",~
'
",
0
10
(B)
20
30
x( m)
Fig. 4. Reflected field intensity distribution p(x) at the prism base for different values of the metallic film thickness d computed by the approximate leaky-wavetheory. tensity profiles referring to a simplified model in which only contributions to the reflected beam distribution from the SP mode are considered. The curves refer, indeed, to a leaky-wave theory in which the reflection coefficient o f the layered structure is expanded near the pole of the leaky SP mode [6]. In that case, it can be shown that the reflected field is expressed by
E 4
¢n
15 February 1993
n
HR(X) = r12 [HI (x) - ( 2/lr)Hw(x) ] ,
(5)
0
1
100
I
I
I
300 thickness
I
500
(A)
Fig. 3. Lateral shift of the reflected beam versus the aluminum film thickness. The solid curve refers to the theory; circles to measured values•
where H i ( x ) is the incident field amplitude given by eq. (1) and
HT(X) = ~ ] 2 w
exp [w2/ ( 4l 2) --x/lc + i k o k x ]
X {l +erf[x/w-w/
(2lc) ]}
(6) 223
Volume 96, number 4,5,6
OPTICS COMMUNICATIONS
is the transmitted field amplitude at the prism base. In the above formulas lc and lr are the coupling and radiative lengths respectively and depend on the coupling system constants. The former is the length at which the SP wave decays to the fraction 1/e and the latter describes the energy leakage out of the prism, r12 is the Fresnel reflection factor of the interface p r i s m - a l u m i n u m film. It can be seen from eq. (5), that the reflected field intensity is due to the contribution of the c o n t r i b u t i o n of two terms: direct reflection of the incident beam at the prism base and the field leaked out of the SP wave back into the prism. Referring to fig. 4, interference of these terms accounts for the characteristic double peak structure shown in figure when a thickness in the range 80280 g m is considered. For sake of comparison, in fig. 5 we reported both the theoretical curves and the experimental one giving the reflected field distribution at 240 A film thickness. The curves are normalized to the maxim u m amplitude of the corresponding ones obtained for 520 A thick film, in order to account for energy loss at the prism input face. The agreement between the experimental curve and the theoretical one given by direct numerical inte-
I
I
I
gration is good. Their shape is similar while the maxi m u m amplitude and the lateral shift are of the same order of magnitude. Differences can be ascribed to slight variations between the thickness values considered in the experiment and in theoretical calculations. The curve obtained from approximate leakywave theory shows a complex structure which was not observed in the experiment. Moreover the lateral shift is overestimated. We think that these discrepancies come out since lateral wave effects are not taken into account by the approximate leaky-wave theory: for very thin metallic films, indeed, part of the energy from the incident beam is coupled to the lateral wave and is subtracted to the surface-plasmon mode. This effect results in a reduced SP wave propagation length, that is in a reduction of the lateral shift according to what is observed experimentally. At higher film thicknesses ( > / 4 0 0 / k ) , where the lateral wave contribution is negligible, either the approximate theory or the direct numerical calculations give the same predictions.
Acknowledgements
This work was supported by the Ministero dell'Universit/: e della Ricerca Scientifica e Tecnologica and by Consiglio Nazionale delle Ricerche.
I d = 240 /~
<
15 February 1993
~6 z klJ
I---
References
z _.1 t.i.. 1.1.1
.- ~ 1 " ' . ~ " -10
0
10 x (,am)
~=':":" :; :~~ ' ' ~ ' ~ ' ~
........
20
30
Fig. 5. Reflected field intensity distribution at the prism base for a metallic film thickness d=240 A. Solid line refers to the experimental curve, dotted to approximate leaky-wavetheory, dashed to direct numerical integration.
224
[ 1] F. Goos and H. H~inchen,Ann. Physik 1 ( 1947 ) 333. [2 ] T. Tamir and H.L. Bertoni,J. Opt. Soc. Am. 61 ( 1971 ) 1397; O. Costa de Beauregard, C. Imbert and Y. Levy, Phys. Rev. D 15 (1977) 3553. [31 G. Abbate, P. Maddalena, E. Santamato, P. Mormile and G. Pierattini, J. Mod. Optics 35 (1988) 1257. [4] R.H. Renard, J. Opt. Soc. Am. 54 (1964) 1190. [5] S.L. Chuang, J. Opt. Soc. Am. A 3 (1986) 593. [6] E. Santamato and F. De Martini, Nuovo Cim. B 59 (1980) 223.
OPTICS COMMUNICATIONS
Experimental investigation of lateral wave contribution to the shift of a reflected beam at surface plasmon resonance P. Maddalena a G. Abbate a, p. Mormile b, G. Pierattini b and E. Santamato a a Dipartimento di Scienze Fisiche, Universit& di Napoli, Pad. 20, Mostra d'Oltremare, 80125 Napoli, Italy b Istituto di Cibernetica del C.N.R., Via Toiano n. 6, 80072Arco Felice (NA), Italy
Received 25 September 1992
Reflected field intensity distributions are reported for surface plasmon wave excitation in an attenuated total internal reflection configuration for different metal film thicknesses. The measured lateral shift is compared with theoretical predictions.
1. Introduction A light beam, when totally reflected at a dielectric interface, undergoes a lateral shift which is usually of the order of a few wavelengths [ 1 ]. Amplification of this shift can be achieved when the beam is reflected by multilayered media [ 2 ]. In particular, when thin metal films are present in layered structures, the beam can undergo even larger displacements if the reflection occurs near a surface plasmon (SP) resonance. In this case observation of an enhanced lateral shift o f several ~tm in the visible region was reported [3]. The SP was excited in a Kretschmann attenuated total reflection (ATR) configuration (e.g. glass p r i s m - m e t a l - a i r ) . The experimental results were in good agreement with a simple theoretical model, due to Renard, based on energy-flux conservation for bounded light beams [4]. At resonance, indeed, there is an energy flow associated to the SP wave in the dielectric, which is parallel to the metal dielectric interface. Consequently, a lateral shift o f the beam must occur if energy has to be conserved. In that case, however, the transmitted and reflected field distributions were calculated by means of a leaky-wave theory in which the reflection coefficient o f the layer structure was expanded near the pole of the leaky SP mode. It must be noted that the series expansion of the reflection coefficient around the pole cannot be assumed in general since contributions from other singularities,
such as branch points, can be important [ 5 ]. This is true especially if Kretschmann configurations are studied in which the metallic film is very small with respect to the light wavelength. It is, then, necessary to proceed to a direct numerical integration of the equations for the fields in order to have the reflected intensity distribution of the beam. In this work the contribution of lateral waves (due to the presence of a branch point) to the beam displacement near a SP resonance is experimentally investigated for different film thicknesses and the observed results are compared with theory.
2. Experimental results and discussion In our experiment, an aluminum film was grown on the base of a glass prism. The film had a stepgraded thickness ranging from 40 ~, to 520 A in steps of 40 A. A linearly polarized HeNe laser was focused to a spot size of 8 g m by a cylindrical lens at the SP resonance angle on the prism base. The reflected beam was enlarged by a microscope and sent to a photodiode via a rotating mirror driven by a stepping motor. The electrical output signal was recorded by a personal computer for display and data analysis. A translation of the rotating base supporting the prism coupler allowed signal recording for each film thickness. The experimental layout is shown in fig. 1 to-
0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
221
Volume 96, number 4,5,6
OPTICS COMMUNICATIONS •
glass
Z
laser
with
prism
+oo
~ Hl(fl) = ~
beam AI f
i
l
m
~
~
15 February 1993
\"
~ X
I
H,(x) exp(-ikoflx) dx,
(3)
the reflected field is given by +oo
I
~
H~(x)=(koW/2x/~) I R(B)
MS
HE-NE
-oo
M
dB,
×exp[-kgw2(l?-B~)2/4+ikoBx]
I Fig. 1. Experimental lay-out. P: polarizer; 2/2: halfwave plate; CA: coupling assembly; MS: microscopy; RM: rotating mirror; PM: photomultiplier; PC: personal computer. The insert shows the coupling assembly in greater detail. gether with an enlarged view of the coupling assembly. The half-wave plate behind the laser allowed polarization switching between the s- and p- state. Since SP waves are excited only by p-polarized light, the s-polarized reflected beam provided the zero reference in the shift measurements. Proper calibration of the recorded signal in absolute spatial units along the prism base was achieved by means of a reticle scale attached to the prism ~1 Let us refer to a theoretical model based on planewave expansion and consider a p-polarized gaussian beam incident at an angle 0~ whose amplitude (at the prism base) is
where R (fl) is the reflection coefficient of the whole layered medium. If a direct numerical integration in eq. (4) is performed, one obtains the curves of fig. 2 which show the reflected field intensity at the prism
!
I
I
• 520 a 480 440 - - - 400 ....... 360 ....... 320° ....
~F-~, r,:' ~'~ ~
0.6 o*
0.2
(A)
-lO
o
10
30
20
x (~m) !
I
( 1)
where x is taken along the propagation direction o f the SPW (see insert of fig. 1 ). In the preceding equation, w is the beam waist, ko= 2n/2 is the wavenumber (2 is the laser wavelength in v a c u u m ) and fl~= ~ sin 0~, ~ being the dielectric constant o f the glass prism. Using the plane wave spectrum of the incident field,
I
• --
I
HI(x) = e x p ( - x 2 / w 2 +ikofli x) ,
(4)
I
• -- • -
-
-
........ 0 . 6 -
/-\ I
~'
280 ?, 240 ~, 200,~ 160,~ 120° 80,~ 40,~
."" ".."
_.
~
"
// • ,~\ ",.. ,/., J/'. x., ",,.. //., ../- ~,~a "\ /}," .;<'~ '.\~"- ' 0.2
#, ///
\ \*~ ....."<', %,
//,)~7
[B]
+oo /I
Hi(x) =
j H i ( r ) exp(ik0flx) d r ,
(2)
-10
0
10
20
30
× O,m)
--oo
~ A more detailed description of the experimental apparatus and of the calibration procedure can be found in ref, [ 3 ]. 222
Fig. 2. Reflected field intensity distribution p(x) at the prism base for different values of the metallic film thickness d computed by exact theory.
Volume 96, number 4,5,6
OPTICS COMMUNICATIONS
base for an incident field of unit amplitude at various film thicknesses. In the computation a refractive index n o = x / ~ t = 1.515 for the glass prism and a dielectric constant eA~= ( - - 2 9 . 8 + i 1 1 . 6 ) for the aluminum film are used. Moreover, according to the experimental configuration, the incident beam wavelength is 2 = 0 . 6 3 2 8 pm and w = 8 p,m is the waist. For 40 A film thickness, the lateral shift is of the order of 2 pm. A m a x i m u m value o f the shift of about 4 p m is reached at 120 ~,. For thicker films, the shift rapidly decreases to zero as shown by the solid curve of fig. 3. This is to be expected since the coupling between the incident radiation and the surface plasmon field, which is localized at the metalair interface, is low for a large film thickness. Consequently, there is no amplification of the lateral shift due to surface plasmon resonance. In this limit, the reflected field distribution is mainly due to the reflection at the prism-metal interface which, as is well known, shows no lateral shift. In fig. 3 we have also reported the experimental values of the shift. They were obtained by measuring the spatial distance between the maxima o f the reflected intensity distributions at the prism base for the s- and p-polarized light. The agreement between the experiment and the theoretical prediction is good. Moreover, the shape of the observed distributions closely resembles the theoretical one. In order to point out the lateral wave contribution to the shift, we have also reported in fig. 4 the in-
I
I
|
I
I
¢2
o 0
0
0
O,
o
o
o
0
I
I
I
I
• -- -- •-
_
L,{f/'-). "'~
......... - --
....... "~,}. ~,........,:{
0.6
520 4 8 0 ,~ 440~, 400,: 360,~ 3 2 0 ~,
x
l: 0.2 -
:::,}
!
(A)
I
0
-10
I
10
x (.m /
I
l
I -
---
-
-.... ---....
--
..........
0.6 x
3O
20
I
280
2 4 0 ,~ 200 160~ 120,~ 8 0 ,~
40
I' \~..
B
/
. ~ \~ i'1.1 '\ II .-...
0.2 -
2~.'"
-10
",~
'
",
0
10
(B)
20
30
x( m)
Fig. 4. Reflected field intensity distribution p(x) at the prism base for different values of the metallic film thickness d computed by the approximate leaky-wavetheory. tensity profiles referring to a simplified model in which only contributions to the reflected beam distribution from the SP mode are considered. The curves refer, indeed, to a leaky-wave theory in which the reflection coefficient o f the layered structure is expanded near the pole of the leaky SP mode [6]. In that case, it can be shown that the reflected field is expressed by
E 4
¢n
15 February 1993
n
HR(X) = r12 [HI (x) - ( 2/lr)Hw(x) ] ,
(5)
0
1
100
I
I
I
300 thickness
I
500
(A)
Fig. 3. Lateral shift of the reflected beam versus the aluminum film thickness. The solid curve refers to the theory; circles to measured values•
where H i ( x ) is the incident field amplitude given by eq. (1) and
HT(X) = ~ ] 2 w
exp [w2/ ( 4l 2) --x/lc + i k o k x ]
X {l +erf[x/w-w/
(2lc) ]}
(6) 223
Volume 96, number 4,5,6
OPTICS COMMUNICATIONS
is the transmitted field amplitude at the prism base. In the above formulas lc and lr are the coupling and radiative lengths respectively and depend on the coupling system constants. The former is the length at which the SP wave decays to the fraction 1/e and the latter describes the energy leakage out of the prism, r12 is the Fresnel reflection factor of the interface p r i s m - a l u m i n u m film. It can be seen from eq. (5), that the reflected field intensity is due to the contribution of the c o n t r i b u t i o n of two terms: direct reflection of the incident beam at the prism base and the field leaked out of the SP wave back into the prism. Referring to fig. 4, interference of these terms accounts for the characteristic double peak structure shown in figure when a thickness in the range 80280 g m is considered. For sake of comparison, in fig. 5 we reported both the theoretical curves and the experimental one giving the reflected field distribution at 240 A film thickness. The curves are normalized to the maxim u m amplitude of the corresponding ones obtained for 520 A thick film, in order to account for energy loss at the prism input face. The agreement between the experimental curve and the theoretical one given by direct numerical inte-
I
I
I
gration is good. Their shape is similar while the maxi m u m amplitude and the lateral shift are of the same order of magnitude. Differences can be ascribed to slight variations between the thickness values considered in the experiment and in theoretical calculations. The curve obtained from approximate leakywave theory shows a complex structure which was not observed in the experiment. Moreover the lateral shift is overestimated. We think that these discrepancies come out since lateral wave effects are not taken into account by the approximate leaky-wave theory: for very thin metallic films, indeed, part of the energy from the incident beam is coupled to the lateral wave and is subtracted to the surface-plasmon mode. This effect results in a reduced SP wave propagation length, that is in a reduction of the lateral shift according to what is observed experimentally. At higher film thicknesses ( > / 4 0 0 / k ) , where the lateral wave contribution is negligible, either the approximate theory or the direct numerical calculations give the same predictions.
Acknowledgements
This work was supported by the Ministero dell'Universit/: e della Ricerca Scientifica e Tecnologica and by Consiglio Nazionale delle Ricerche.
I d = 240 /~
<
15 February 1993
~6 z klJ
I---
References
z _.1 t.i.. 1.1.1
.- ~ 1 " ' . ~ " -10
0
10 x (,am)
~=':":" :; :~~ ' ' ~ ' ~ ' ~
........
20
30
Fig. 5. Reflected field intensity distribution at the prism base for a metallic film thickness d=240 A. Solid line refers to the experimental curve, dotted to approximate leaky-wavetheory, dashed to direct numerical integration.
224
[ 1] F. Goos and H. H~inchen,Ann. Physik 1 ( 1947 ) 333. [2 ] T. Tamir and H.L. Bertoni,J. Opt. Soc. Am. 61 ( 1971 ) 1397; O. Costa de Beauregard, C. Imbert and Y. Levy, Phys. Rev. D 15 (1977) 3553. [31 G. Abbate, P. Maddalena, E. Santamato, P. Mormile and G. Pierattini, J. Mod. Optics 35 (1988) 1257. [4] R.H. Renard, J. Opt. Soc. Am. 54 (1964) 1190. [5] S.L. Chuang, J. Opt. Soc. Am. A 3 (1986) 593. [6] E. Santamato and F. De Martini, Nuovo Cim. B 59 (1980) 223.