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Surface-enhanced second-harmonic generation in C60-coated silver island films
PhysicsLettersA 179 (1993) 149—153 North-Holland
PHYSICS LETTERS A
Surface-enhanced second-harmonic generation in C60-coated silver island films O.A. Aktsipetrov ‘, 0. Keller, K. Pedersen Institute of Physics, University ofAalborg, Pontoppidansirude, DK-9220 Aalborg øst, Denmark
A.A. Nikulin, N.N. Novikova and A.A. Fedyanin Physics Department, Moscow State University, Moscow 119899, Russian Federation Received 28 May 1993; accepted for publication 5 June 1993 Communic~atedby V.M. Agranovich
Surface-enhanced generation ofthe diffuse and depolarized optical second harmonic (SH) upon reflection of laser radiation from Cse-coated silver island films is observed. An order of magnitude relative enhancement ofthe SH response from the coated films with tespect to the uncoated ones is found. The nature ofthe observed effects is discussed.
1.
Introduction
The use of reflected optical second-harmonic generation (SHG) has proved to be an effective way of studying surfai~esand interfaces in numerous physical systems, e.g. semiconductors [1], metals [21, island [3—5] and cold-deposited [61 metal films, electrochemically etched metal electrodes [7,8], semiconductor quantum dots [91,etc. The characteristics of the reflected second-harmonic (SH) radiation (such as intensity, wave polarization and scattering indicatrix) are very sensitive to the surface properties of the systems. As a consequence, SH measurements become much more informative if they are combirted with a calibrated variation of the parameters determining the surface properties. This approach has been realized, for instance, in ref. [5] by using silver~island films deposited onto a dielectric wedge on a semiconductor substrate. Such a structure allows one to control the surface enhancement of SHG by shifting the resonance frequencies originating in excitation of the local plasmon modes To whom correspondence should be addressed. Permanent address: InternBtional Laser Center, Moscow State University, Moscow 119899, Russian federation.
of the islands. If special emphasis is put on the role of interface phenomena in SHG, then another way of affecting the nonlinear optical response of island films is effective, namely the deposition of dielectric coatings onto the films. In this Letter we report results of SHG experiments in C60- and SiO~-coatedAg island films, and propose a theoretical interpretation of the experimental data. The choice of C60 (more traditional SiOx is used as a reference material) is of topical interest since a better understanding of the physical properties of the buckminster-fullerenes (“magic number” cluster modifications of carbon [10]) is of importance from both a fundamental and an applied point of view. Thus, we hope that the present communication stimulates the use of optical techniques for studying C60.
2. Experimental We prepared island films (with Ag mass thickness 150 A, filling factor 0.6, and mean radius of the islands 200 A) in a vacuum chamber at a residual pressure ~ 10—6 Torr by deposition of pure (0.9999) silver onto quartz substrates preliminarily cleaned
0375-960 1/93/$ 06.00 ~ 1993 Elsevier Science Publishers B.V. All rights reserved.
149
Volume 179, number 2
PHYSICS LE’flERS A
dichromate. The SiO~coating of thickness 500 A was also deposited in vacuum at the same residual pressure. The C60 powder was obtained by sublimation from with potassium
soot produced via an arc discharge between graphite electrodes in an inert gas. After dissolving C60 in toluene, a drop of the solution was placed onto the sample. The thickness of the C60 layer precipitated on the sample surface after evaporation of toluene was
lo~A.
Since various combinations of the described preparation procedures were used for distinct macroscopic areas ofthe same substrate, the obtained samplc has spatially separated regions of different crosssectional structure (fig. 1). Thus a comparative study of the various structures could be carried out by scanning the sample surface with the pump beam. In the SHG experiment the samples were 3~laser illuminated by a beam from a Q-switched YAG : Nd with a 1064 nm wavelength, a pulse duration time 10—20 ns, a repetition rate 12.5 Hz,SH andsignal a power 2. The reflected wasdendesity —~ 1 MW/cm tected with an analog-to-digital system described elsewhere [11]. The SH signals from the pure SiO~and C 60 coatings as well as from the substrate (i.e. in the absence of Ag islands) were negligibly small. The SH radiation generated by the island films (both with and without coatings) was diffuse, i.e. practically iso-
2 August 1993
tropic within a solid angle of 2x sr, and strongly depolarized. The corresponding values of the intensity of the s- and p-polarized components selected from the depolarized SH signal driven by a p-polarized pump are given in table 1.
3. Theory Since the Ag particle size is much smaller than the pump wavelength A, the island film can be considered as a two-dimensional array of electric-point dipoles of moment d~,j(r,) (where r1 is the coordinate of the lth dipole, and w is the pump frequency) embedded in a layered dielectric medium (fig. 2a) and oscillating at the SH frequency 2w. We use the superscripts i = 1, 2, 3 throughout the paper to denote the values pertaining to the cases of uncoated, C 60-, and SiO~-coatedfilms, respectively. In agreement with the experimental data we neglect the optical of the film of substrate coating.is Thenonlinearity strong depolarization the SHand radiation an evidence of the breaking of the usual polarization selection rules [12] which forbid the generation of an s-polarized SH component upon reflection of light from a macroscopically centrosymmetric medium with a smooth and flat boundary. The diffuseness and
c=1
________
SIO,
A
~
C~
2
(I.) 2~..
______________________________________
a
I
~ ~
Fig. 1. The structure of the sample. E2 Table 1 The measured intensities ofthe p- and s-polarized SH components (expressed in arbitrary units).
- -
___________________
—
i
— —
b p s
150
Uncoated Ag 1.0 0.9
C~,-coatedAg 1.0 1.7
SiO~-coatedAg 1.8 1.3
Fig. 2. The geometry of the model system studied in section 3. The insert illustrates the approximation used for the nonlinear surface current.
Volume 179, number 2
PHYSICS LETFERS A
depolarization of the SH radiation indicates that its sources have large spatial fluctuations with a correlation length much smaller than A and that the regular part of d~responsible for the generation of the specular and p-polarized SH component is negligibly small, i.e.
2 August 1993
d~I?~=$iL: L”~(w)L~(w):E~E~, a~J~ is the second-order polarizability tensor of the particle, E~’~ is the electric field amplitude of the pump wave transmitted through the air/coating interface (the outer boundary of the system):
semble of realizations. For simplicity we postulate that (i) = 0, (ii) the dipole moments are ö-correlated and (iii) the system is statistically ho-
IE~I =t~’~ IE~I,whereE~isthe incident pump amplitude in the air, tu)=1, t~°
mogeneous and isotropic in the film plane, viz,
expression for ~
~ < Id~2(ri)I2>1~’2,
(1)
where < > denote averaging over the statistical en-
reads a=~L,II~
~
(a,fi=x,y,z),
(2)
where D~=D~mD1, for plane. the z-axis normal and xy-plane parallelD~ED1, to the film Using these assumptions we obtain the following expressions forthe intensity ofthe s-and p-polarized components selected from the depolarized and diffuse SH signal,
~
xK”~I 1
I 2D~°
—
where
2>
DQ1~
DUL~ = <~ df..IL~ 2> L~ L~° = ,
The LFF component ~ lowing form,
may be written in the fol-
(3)
,
Lt1~ (L~’~1 +P~’~ +I~~)’ —
I~jpcxKU)(cos2l~l—K”~I2D~~~ +sin26 I 1 +,c~I2DS~),
—
(4)
where ~9is the angle between the normal to the film plane and the observation direction, 1 K~°=‘ +e~(2w)I2’ =
e
1>(2w)
~
=
1
1(2w)—~ and e~and ~ (i= 2, 3) are the dielectric constants ofthe substrate and the coating, respectively. In eqs. (3) and (4) the dielectric screening of the dipoles is taken into account by introducing the factor ~ whereas K~ describes the linear polarization of the substrate at frequency 2w, i.e. image dipoles induced in the substrate by d~J(r,). It is convenient to express the particle dipole moment d~J~ in the following form, =
where
L~° (2w )d~,
(6)
(5)
,
(7)
a
where L~jis the LFF component ofa single particle, and the terms P~ and If,’) describe the electrostatic interaction of the particles with each other and with the substrate, respectively. For a small metallic particle the radial inhomogeneity of its surface properties stemming from a nonuniform spatial distribution of the electron density can be taken into account using a transverse self-field approach [13]. By assuming that the optical diamagnetic effect dominates the interaction one obtains [131 ________
L~~
~+2
d3r,
(8)
where e~ ( r) is the local position-dependent dielectric constant of the particle. The integration in eq. (8) extends over the particle domain of volume V. In the system under study, however,the effect of the particle radial inhomogeneity on the local field is neglected since it is expected to be small when as here the typical particle size is about 200 A. Thus we shall use the bulk value of e 0 and consider the particles as 151
Volume 179, number 2
PHYSICS LETTERS A
homogeneous spheroids of the same size, shape and orientation (fig. 2b). In this case L~j is given by [14] = [e~~+ (e L~1i~ 0 ~)Na(fl) ] —l (9)
2 August 1993
curvature of rTF is the Thomas—Fermi screening radius). This in turn means that one can neglect the boundary curvature by putting ~,
~
—
‘(i fIat
JN~(r~)_JNLfl
where Na(fl) is the depolarization factor [14], /J= b/a, a and b being the spheroid semiaxes. In the electrostatic dipole approximation we obtam for P~jand J~,1) [5] p(i) a
— —
ji)
=
(~‘~ — e 0/ ~‘
(~
—
X [(4/32)
~
‘10
a~
)K~
—‘ —
I
v/3( 1 + $2) _3/2]I a
(11) ‘
2, n being the number where o~ = a~= v= itna of particles per unit area. A resonance of ~ (due to the excitation of dipole-active surface plasmon modes of the particles) exists at the frequency Q~) for which Re [L~~ ~ (Q~,i))]= 0. In the system under study ~2) ~ 1 and 2w—~Q~whereas w is sufficiently far from the resonant values to neglect the dependence of L~(w) (in contrast with ~ (2w)) on the coating material, — ~,
~,
L”~ L a(2) (to) a (w)
L a(3) (w)
out
where j~~t is the nonlinear surface current corresponding to a flat interface between the same materials as above and E~,,(r~”)is the value of the local field the at the pump frequency, in a point outside metal selvedge (see taken the insert of fig. just 2). The subscript n denotes the vector component normal to the interface. The tangential component of the current and the local field can be neglected if w~0.lw~, [15,16], where w~is the bulk plasma frequency of the metal (in our case w—~0.lw~).In such an approximation the nonlinear surface current can be represented in a factorized form j~( r~)= Jwf(rz)n(r~), where the factor J~ describes the dependence on the coating material, n (rz) is the Unit vector normal to the surface, and the functionf(rz) is determined exclusively by the particle shape. The result leads to eqs. (13). The two conditions given by eqs. (13) allow us to
(12)
calculatethetwo unknown parameters namely dielectric constant e~2~ of Cof the system, 60 and the pa-
Therefore, in dNL such a dependence is determined by the effect of the coating on the nonlinear polarizability UNL. This allows us to use D~j~a as a measure ofatthe fluctuations of UNL,the i.e.influence the values of D~a i= 1, 2, 3 characterize of the coating on the optical nonlinearity of the particles. At the same time the value of the ratio OWm DW,~/D,~J~, 11 is supposed to be independent of the coating material, 1)_o(2)_o(3) (13) o( This hypothesis seems to be reasonable from a microscopic point of view. In fact
rameter /3= b/a characterizing the particle shape. Using the data given in table 1, and taking into account that 3~(2w)=2, in our system ~0(2w)we = —58 + iO.6 1, and v=0.6, obtain from e1(2w)=e~ eqs. (2 )—( 13): ~ (2w) = 2.9 and /3=0.4. The effect of the coating on the nonlinear-response of the particles can be characterized by two enhance-
‘
a=
(1)
(E~,~(rz))
‘
.
ment factors, ~
K< Id~ d~Jj2> 2> <
~I;
2 2
(14) 1=2,3.
(15)
d~ij~cicIj~jL(r.r)dSz 1
For the given values of the expenmental parameters weobtainfromeqs. (2)—(9):y~)=ll.5,y~j=32.5
whereJ~(rz)is the effective nonlinear surface cur-
for the C
rent induced by the pumping in the point rz on the particle boundary An integration is carried out over this surface which is supposed to be so smooth that ps>> rTF (p~is the typical value of the radius of
60 coating, and y~]= 9.3, y~ = 24.6 for the SiO~,coating. It is worth noting that y~ and y~pertam to the response of the pure silverislands, whereas the experimentally observed enhancement is reduced because of screening by the coating and the
~.
152
Volume 179, number 2
PHYSICS LETTERSA
pump attenuation due to the partial reflection from the air/coating interface.
4. Discussion For the experimental parameter values of our model yfJ~.> y~ (i.e. the coating-caused enhancement of the particle nonlinearity is larger than that of the total particle response at the SH frequency) because the increase in the nonlinearity is partially compensated by the LFF decrease. The latter, in turn, is due to the factthat in the uncoated film the surface plasmon resonance in L~’~ (2w) is excited, since 2w Q I) The coating deposition (formally obtamed by replacing e~ = 1 with 1=2, 3) shifts the resonance frequency away from 2w and, as a resuit, reduces the LFF. The calculated value of/i (/3=0.4, i.e. the particles are oblate spheroids with a semiaxis ratio 0.4) is consistent with the silver island film morphology. Another calculated parameter value, namely the di~
electric constant of C60 ~2) (2w) = 2.9, is smaller than the experimental value e~(2w) 4 obtained in ref. [17] by ellipsometric measurements on C60 films deposited in a diffusion-pumped chamber. This can be explained by assuming that our preparation technique provides C60 coatings of a lower density and, consequently, with a smaller value of the effective dielectric constant.
Acknowledgement We wish to thank A.A. Puretskii for supplying C60
2 August 1993
and for critical remarks and T.V. Murzina for assistance in carrying out the experiment. We also gratefully acknowledge helpful discussions with L.V. Keldysh, P.V. Elyutin, and A. Liu. These studies were supported by the “Laser systems” and “Low-dimensional systems” programs.
References [1]Y.R. Shen, J. Vac. Sci. Technol. B 3 (1985) 1464. [2] G.L. J.M.1. Robinson and V.L. Shannon, Prog. Suil’. Richmond, Sci. 28 (1988) [3] A. Wokaun et al., Phys. Rev. B 24 (1981) 849. [4]O.A. Aktsipetrov et al., Phys. Lett. A 117 (1986) 239.
[5] O.A. Aktsipetrov
et al., Solid State Commun. 70 (1989) 1021. [6]O.A. Aktsipetrov et al., Solid State Commun. 73 (1990) 411. [7] C.K. Chen, A.R.B. de Castro and Y.R. Shen, Phys. Rev. Lett. 46 (1981) 145. [8] O.A. Aktsipetrov et al., Solid State Commun. 76 (1990) 55. [9]O.A. Aktsipetrov, A.I. Ekimov and A.A. Nikulin, Pis’ma Zh. Eksp. Teor. Fiz. 55 (1992) 427 [JETPLett. 55 (1992) 435]. [10]H. Kroto, Science 242 (1988) 1139. [11] O.A. Aktsipetrov et al., Soy. Phys. JETP 62 (1986) 524. [12] O.A. Aktsipetrov, I.M. Baranova and Yu.A. Il’inskii, Soy. Phys.JETP64 (1986) 167. [13]0. Keller, tobe published; 0. Keller, M. Xiao and S. Bozhevolnyi, Opt. Commun., to be published. [14] L.D. Landau and E.M. Lifshitz, Electrodynamics of continuous media (Nauka, Moscow, 1982) p. 43 [in Russian]. [15] M. Weber and A. Liebsch, Phys. Rev. B 35 (1987) 7411. [16] M.G. Weber and A. Liebsch, Phys. Rev. B 36 (1987) 6411. [17] S.L. Ben et al., Appi. Phys. Lett. 59 (1991) 2678.
153
PHYSICS LETTERS A
Surface-enhanced second-harmonic generation in C60-coated silver island films O.A. Aktsipetrov ‘, 0. Keller, K. Pedersen Institute of Physics, University ofAalborg, Pontoppidansirude, DK-9220 Aalborg øst, Denmark
A.A. Nikulin, N.N. Novikova and A.A. Fedyanin Physics Department, Moscow State University, Moscow 119899, Russian Federation Received 28 May 1993; accepted for publication 5 June 1993 Communic~atedby V.M. Agranovich
Surface-enhanced generation ofthe diffuse and depolarized optical second harmonic (SH) upon reflection of laser radiation from Cse-coated silver island films is observed. An order of magnitude relative enhancement ofthe SH response from the coated films with tespect to the uncoated ones is found. The nature ofthe observed effects is discussed.
1.
Introduction
The use of reflected optical second-harmonic generation (SHG) has proved to be an effective way of studying surfai~esand interfaces in numerous physical systems, e.g. semiconductors [1], metals [21, island [3—5] and cold-deposited [61 metal films, electrochemically etched metal electrodes [7,8], semiconductor quantum dots [91,etc. The characteristics of the reflected second-harmonic (SH) radiation (such as intensity, wave polarization and scattering indicatrix) are very sensitive to the surface properties of the systems. As a consequence, SH measurements become much more informative if they are combirted with a calibrated variation of the parameters determining the surface properties. This approach has been realized, for instance, in ref. [5] by using silver~island films deposited onto a dielectric wedge on a semiconductor substrate. Such a structure allows one to control the surface enhancement of SHG by shifting the resonance frequencies originating in excitation of the local plasmon modes To whom correspondence should be addressed. Permanent address: InternBtional Laser Center, Moscow State University, Moscow 119899, Russian federation.
of the islands. If special emphasis is put on the role of interface phenomena in SHG, then another way of affecting the nonlinear optical response of island films is effective, namely the deposition of dielectric coatings onto the films. In this Letter we report results of SHG experiments in C60- and SiO~-coatedAg island films, and propose a theoretical interpretation of the experimental data. The choice of C60 (more traditional SiOx is used as a reference material) is of topical interest since a better understanding of the physical properties of the buckminster-fullerenes (“magic number” cluster modifications of carbon [10]) is of importance from both a fundamental and an applied point of view. Thus, we hope that the present communication stimulates the use of optical techniques for studying C60.
2. Experimental We prepared island films (with Ag mass thickness 150 A, filling factor 0.6, and mean radius of the islands 200 A) in a vacuum chamber at a residual pressure ~ 10—6 Torr by deposition of pure (0.9999) silver onto quartz substrates preliminarily cleaned
0375-960 1/93/$ 06.00 ~ 1993 Elsevier Science Publishers B.V. All rights reserved.
149
Volume 179, number 2
PHYSICS LE’flERS A
dichromate. The SiO~coating of thickness 500 A was also deposited in vacuum at the same residual pressure. The C60 powder was obtained by sublimation from with potassium
soot produced via an arc discharge between graphite electrodes in an inert gas. After dissolving C60 in toluene, a drop of the solution was placed onto the sample. The thickness of the C60 layer precipitated on the sample surface after evaporation of toluene was
lo~A.
Since various combinations of the described preparation procedures were used for distinct macroscopic areas ofthe same substrate, the obtained samplc has spatially separated regions of different crosssectional structure (fig. 1). Thus a comparative study of the various structures could be carried out by scanning the sample surface with the pump beam. In the SHG experiment the samples were 3~laser illuminated by a beam from a Q-switched YAG : Nd with a 1064 nm wavelength, a pulse duration time 10—20 ns, a repetition rate 12.5 Hz,SH andsignal a power 2. The reflected wasdendesity —~ 1 MW/cm tected with an analog-to-digital system described elsewhere [11]. The SH signals from the pure SiO~and C 60 coatings as well as from the substrate (i.e. in the absence of Ag islands) were negligibly small. The SH radiation generated by the island films (both with and without coatings) was diffuse, i.e. practically iso-
2 August 1993
tropic within a solid angle of 2x sr, and strongly depolarized. The corresponding values of the intensity of the s- and p-polarized components selected from the depolarized SH signal driven by a p-polarized pump are given in table 1.
3. Theory Since the Ag particle size is much smaller than the pump wavelength A, the island film can be considered as a two-dimensional array of electric-point dipoles of moment d~,j(r,) (where r1 is the coordinate of the lth dipole, and w is the pump frequency) embedded in a layered dielectric medium (fig. 2a) and oscillating at the SH frequency 2w. We use the superscripts i = 1, 2, 3 throughout the paper to denote the values pertaining to the cases of uncoated, C 60-, and SiO~-coatedfilms, respectively. In agreement with the experimental data we neglect the optical of the film of substrate coating.is Thenonlinearity strong depolarization the SHand radiation an evidence of the breaking of the usual polarization selection rules [12] which forbid the generation of an s-polarized SH component upon reflection of light from a macroscopically centrosymmetric medium with a smooth and flat boundary. The diffuseness and
c=1
________
SIO,
A
~
C~
2
(I.) 2~..
______________________________________
a
I
~ ~
Fig. 1. The structure of the sample. E2 Table 1 The measured intensities ofthe p- and s-polarized SH components (expressed in arbitrary units).
- -
___________________
—
i
— —
b p s
150
Uncoated Ag 1.0 0.9
C~,-coatedAg 1.0 1.7
SiO~-coatedAg 1.8 1.3
Fig. 2. The geometry of the model system studied in section 3. The insert illustrates the approximation used for the nonlinear surface current.
Volume 179, number 2
PHYSICS LETFERS A
depolarization of the SH radiation indicates that its sources have large spatial fluctuations with a correlation length much smaller than A and that the regular part of d~responsible for the generation of the specular and p-polarized SH component is negligibly small, i.e.
2 August 1993
d~I?~=$iL: L”~(w)L~(w):E~E~, a~J~ is the second-order polarizability tensor of the particle, E~’~ is the electric field amplitude of the pump wave transmitted through the air/coating interface (the outer boundary of the system):
semble of realizations. For simplicity we postulate that (i)
IE~I =t~’~ IE~I,whereE~isthe incident pump amplitude in the air, tu)=1, t~°
mogeneous and isotropic in the film plane, viz,
expression for ~
~ < Id~2(ri)I2>1~’2,
(1)
where < > denote averaging over the statistical en-
reads a=~L,II~
~
(a,fi=x,y,z),
(2)
where D~=D~mD1, for plane. the z-axis normal and xy-plane parallelD~ED1, to the film Using these assumptions we obtain the following expressions forthe intensity ofthe s-and p-polarized components selected from the depolarized and diffuse SH signal,
~
xK”~I 1
I 2D~°
—
where
2>
DQ1~
DUL~
The LFF component ~ lowing form,
may be written in the fol-
(3)
,
Lt1~ (L~’~1 +P~’~ +I~~)’ —
I~jpcxKU)(cos2l~l—K”~I2D~~~ +sin26 I 1 +,c~I2DS~),
—
(4)
where ~9is the angle between the normal to the film plane and the observation direction, 1 K~°=‘ +e~(2w)I2’ =
e
1>(2w)
~
=
1
1(2w)—~ and e~and ~ (i= 2, 3) are the dielectric constants ofthe substrate and the coating, respectively. In eqs. (3) and (4) the dielectric screening of the dipoles is taken into account by introducing the factor ~ whereas K~ describes the linear polarization of the substrate at frequency 2w, i.e. image dipoles induced in the substrate by d~J(r,). It is convenient to express the particle dipole moment d~J~ in the following form, =
where
L~° (2w )d~,
(6)
(5)
,
(7)
a
where L~jis the LFF component ofa single particle, and the terms P~ and If,’) describe the electrostatic interaction of the particles with each other and with the substrate, respectively. For a small metallic particle the radial inhomogeneity of its surface properties stemming from a nonuniform spatial distribution of the electron density can be taken into account using a transverse self-field approach [13]. By assuming that the optical diamagnetic effect dominates the interaction one obtains [131 ________
L~~
~+2
d3r,
(8)
where e~ ( r) is the local position-dependent dielectric constant of the particle. The integration in eq. (8) extends over the particle domain of volume V. In the system under study, however,the effect of the particle radial inhomogeneity on the local field is neglected since it is expected to be small when as here the typical particle size is about 200 A. Thus we shall use the bulk value of e 0 and consider the particles as 151
Volume 179, number 2
PHYSICS LETTERS A
homogeneous spheroids of the same size, shape and orientation (fig. 2b). In this case L~j is given by [14] = [e~~+ (e L~1i~ 0 ~)Na(fl) ] —l (9)
2 August 1993
curvature of rTF is the Thomas—Fermi screening radius). This in turn means that one can neglect the boundary curvature by putting ~,
~
—
‘(i fIat
JN~(r~)_JNLfl
where Na(fl) is the depolarization factor [14], /J= b/a, a and b being the spheroid semiaxes. In the electrostatic dipole approximation we obtam for P~jand J~,1) [5] p(i) a
— —
ji)
=
(~‘~ — e 0/ ~‘
(~
—
X [(4/32)
~
‘10
a~
)K~
—‘ —
I
v/3( 1 + $2) _3/2]I a
(11) ‘
2, n being the number where o~ = a~= v= itna of particles per unit area. A resonance of ~ (due to the excitation of dipole-active surface plasmon modes of the particles) exists at the frequency Q~) for which Re [L~~ ~ (Q~,i))]= 0. In the system under study ~2) ~ 1 and 2w—~Q~whereas w is sufficiently far from the resonant values to neglect the dependence of L~(w) (in contrast with ~ (2w)) on the coating material, — ~,
~,
L”~ L a(2) (to) a (w)
L a(3) (w)
out
where j~~t is the nonlinear surface current corresponding to a flat interface between the same materials as above and E~,,(r~”)is the value of the local field the at the pump frequency, in a point outside metal selvedge (see taken the insert of fig. just 2). The subscript n denotes the vector component normal to the interface. The tangential component of the current and the local field can be neglected if w~0.lw~, [15,16], where w~is the bulk plasma frequency of the metal (in our case w—~0.lw~).In such an approximation the nonlinear surface current can be represented in a factorized form j~( r~)= Jwf(rz)n(r~), where the factor J~ describes the dependence on the coating material, n (rz) is the Unit vector normal to the surface, and the functionf(rz) is determined exclusively by the particle shape. The result leads to eqs. (13). The two conditions given by eqs. (13) allow us to
(12)
calculatethetwo unknown parameters namely dielectric constant e~2~ of Cof the system, 60 and the pa-
Therefore, in dNL such a dependence is determined by the effect of the coating on the nonlinear polarizability UNL. This allows us to use D~j~a as a measure ofatthe fluctuations of UNL,the i.e.influence the values of D~a i= 1, 2, 3 characterize of the coating on the optical nonlinearity of the particles. At the same time the value of the ratio OWm DW,~/D,~J~, 11 is supposed to be independent of the coating material, 1)_o(2)_o(3) (13) o( This hypothesis seems to be reasonable from a microscopic point of view. In fact
rameter /3= b/a characterizing the particle shape. Using the data given in table 1, and taking into account that 3~(2w)=2, in our system ~0(2w)we = —58 + iO.6 1, and v=0.6, obtain from e1(2w)=e~ eqs. (2 )—( 13): ~ (2w) = 2.9 and /3=0.4. The effect of the coating on the nonlinear-response of the particles can be characterized by two enhance-
‘
a=
(1)
(E~,~(rz))
‘
.
ment factors, ~
K< Id~ d~Jj2> 2> <
~I;
2 2
(14) 1=2,3.
(15)
For the given values of the expenmental parameters weobtainfromeqs. (2)—(9):y~)=ll.5,y~j=32.5
whereJ~(rz)is the effective nonlinear surface cur-
for the C
rent induced by the pumping in the point rz on the particle boundary An integration is carried out over this surface which is supposed to be so smooth that ps>> rTF (p~is the typical value of the radius of
60 coating, and y~]= 9.3, y~ = 24.6 for the SiO~,coating. It is worth noting that y~ and y~pertam to the response of the pure silverislands, whereas the experimentally observed enhancement is reduced because of screening by the coating and the
~.
152
Volume 179, number 2
PHYSICS LETTERSA
pump attenuation due to the partial reflection from the air/coating interface.
4. Discussion For the experimental parameter values of our model yfJ~.> y~ (i.e. the coating-caused enhancement of the particle nonlinearity is larger than that of the total particle response at the SH frequency) because the increase in the nonlinearity is partially compensated by the LFF decrease. The latter, in turn, is due to the factthat in the uncoated film the surface plasmon resonance in L~’~ (2w) is excited, since 2w Q I) The coating deposition (formally obtamed by replacing e~ = 1 with 1=2, 3) shifts the resonance frequency away from 2w and, as a resuit, reduces the LFF. The calculated value of/i (/3=0.4, i.e. the particles are oblate spheroids with a semiaxis ratio 0.4) is consistent with the silver island film morphology. Another calculated parameter value, namely the di~
electric constant of C60 ~2) (2w) = 2.9, is smaller than the experimental value e~(2w) 4 obtained in ref. [17] by ellipsometric measurements on C60 films deposited in a diffusion-pumped chamber. This can be explained by assuming that our preparation technique provides C60 coatings of a lower density and, consequently, with a smaller value of the effective dielectric constant.
Acknowledgement We wish to thank A.A. Puretskii for supplying C60
2 August 1993
and for critical remarks and T.V. Murzina for assistance in carrying out the experiment. We also gratefully acknowledge helpful discussions with L.V. Keldysh, P.V. Elyutin, and A. Liu. These studies were supported by the “Laser systems” and “Low-dimensional systems” programs.
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