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Optical second-harmonic generation from silver films with long-range surface-plasmon excitation
579
Surface Science 216 (1989) 579-586 North-Holland, Amsterdam
OPTICAL SECOND-HARMONIC GENERATION FROM SILVER FILMS WITH LONG-RANGE SURFACEPLASMON EXCITATION Chin-Ching TZENG Department
and Juh Tzeng LUE
of Physics, National
Tsing Hua University, Hsinchy
Taiwan, ROC
Received 20 October 1988; accepted for publication 7 February 1989
In this work, we have derived an expression for the second-harmonic generation from metal surfaces under the modified Kretschmann geometry (or Grid’s geometry) based on the hydrodynamic theory of a free electron gas. Numerical calculation shows that the harmonic generation is more than 2 orders of magnitude larger than that due to a single-boundary surface plasmon, if a long-range surface plasmon is excited on both sides of the thin silver film which is bounded by a glass substrate and an index-matched liquid. Resonant surface plasmons excited at some specific internal incident angles emanate a nonlinear wave with an intensity of 5 orders of magnitude greater than that due to long-range surface plasmon.
1. Introduction Recent studies [l] on the properties of long-range surface plasmons (LRSP) excited on both boundaries of a very thin metal film bounded by index-matched dielectrics have stimulated theoretical and experimental interest in nonlinear optics. Excitation of the LRSP mode on semiconductors in the infrared region is believed to be able to enhance the generation of three- and four-wave optical mixings [2] and to increase the nonlinear propagation distance for surface modes [3]. The enhancement of optical second-harmonic generation (SHG) due to the fundamental LRSP mode excited on this silver films deposited on a quartz crystal has been reported [4]. The harmonic intensity is hundred times larger than that due to thick films. The sources of the SHG on a metal surface consist of a “volume” current density extending over a skin depth and a “surface” current density with normal and tangential components within only a few Fermi wavelengths beneath the metal surface. The hydrodynamic theory [5] of an electron gas has been proved successfully by some experiments [6,7] in demonstrating the SHG from noble metals and alumina films through the excitation by a p-polarized Nd : YAG laser. Rudnick and Stern [8] first pointed out the limitations of the free-electron model in describing the SHG surface-current sources and proposed two phenomenological parameters a and b to estimate the size of the 0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
580
C.-C. Tzeng, J. T. Lue / Optical second-harmonic generation from silver films
normal and tangential components of the SH surface current. Sipe et al. [6] and Quail et al. [6] have given an explicit expression for these parameters with a free-electron hydrodynamic model with the introduction of an effective plasma frequency. They have done calculations with b = - 1 for a smooth silver film, allowing the parametor u to be determined experimentally. Second harmonic generation from a modified Kretschmann configuration in which the metal film was surrounded by nonlinear quartz media had been reported by Deck and Sarid [7]. A free long-range transverse-mode (TM) wave was predicted to be excited due to interference of surface plasmons on both sides of the thin metal films. Additional proof of the SHG from a metal film with LRSP excitation has been reported recently by Chen et al. [9]. However, their results are in arbitrary units and do not take into account the contribution from bound electrons. They also assumed an air gap existing between the metal film and the media. In this work, we have assumed that the boundary media have a negligible nonlinear effect and that the SH waves are essentially generated in the bulk and selvedge of the metal film. Due to the high dielectric constant inside the metal, the fundamental and the subsequent SH fields are expected to be smaller in the metal film than those inside the quartz media as predicted in ref. [7]. We have also derived a formula for the evaluation of the SHG from a metal film under the modified Kretschmann geometry based on the hydrodynamic theory. The absolute value of R is calculated by including the bound electrons in the intimate contact media. An anomalously large nonlinear reflectance is found at some specific angles of incidence. The possible sources for such an enormous enhancement with such extremely narrow angular width are discussed. 2. Theory The hydrodynamic theory was firstly developed by Sipe et al. [5] in describing the SHG of light on metal surfaces. In view of a p-polarized wave illuminating a metal film of thickness d, through the geometries as shown in fig. la (ATR) and fig. lb (Sarid’s geometry), a free transverse-mode (TM) wave can be excited in the tin metal film obeying the dispersion relation which is deduced from the law of momentum conservation and boundary conditions as given by w3d, = taC1&,
+ tan-‘&,
+ mm,
(1)
where
(2)
C.-C. Tzeng, J. T. Lue / Optical second-harmonic
r (a)
generation from silver films
X
581
index-matched
(b)
Fig. 1. Two prism-coupling geometries for exciting a surface-plasma wave: (a) and (b) correspond to the Kretschmann and modified Kretschmann (or Sarid’s) geometries, respectively.
m is the mode number (a positive integer), Oi = w/c[~~(w)]“~ is the wave vector in the ith medium with dielectric constant ei( w), and k,, = k& + ik& is the propagation wave vector of the guided mode. Eq. (1) can be used to solve the effective index k,,/c. The wave with large value of k& can propagate only a short distance within the metal film and is called the short-range surface plasmon (SRSP), while that with small value of k& is called the long-range surface plasmon. The nonlinear reflection coefficient R defined as the ratio of the reflected SHG irradiance to the square of the incident fundamental irradiance can be written as R=$>,A,2T, 1
where n, and Nr are the refractive indices of the prism at frequencies w and 2w, respectively, and A is the ratio of the second-harmonic electric field to the square of the fundamental electric field inside the prism and is expressed as A = A, + A, + A,. The three terms are the SHG contributions from the bulk metal, the liquid/front-metal selvedge, and the back-metal/glass-substrate interface for Sarid’s geometry (or ATR geometry), respectively. The factor T contains the Fresnel and geometrical factors describing the coupling of the fundamental waves from air into the prism and the exiting of the secondharmonic beam from the prism back into the air. The explicit expressions of T, A,, A,, and A, for ATR geometry have been published previously by the present authors [lO,ll]. The SHG from bulk metal, liquid layer-metal selvedge and metal-glass substrate interfaces for &rid’s geometry including the contribution from
582
C.-C. Tzeng, J. T. Lue / Optical second-harmonic generation from silver films
bound electrons is
X { K(q/m,)[e,(20) x ( O+%)e
- l]/ic*W$&}
i(2w+,+ W3d3)[ /P(l + ‘34)2 + wi(l
-( 1 + R,, e2iw3d3)[ k*(l
+ r34 e2iw3d3)2+ w:(l
A, = 2riM12s, T321 [ (K&/W,)(l + ( fi2/6,)(1
- $)*I - rs4 ei2w3d3)2]},
(4)
+ R,, e2iw3d3)Qz
- Rj4 e2iw3d3)Qt],
(5)
and A, = 2niM,,,,T,,,T,,
eiWJd3[(~~dK)Q:+
(fi’/%)Qi]~
(6)
respectively, where m1234= ( 1 + r12r234 e2iw2d2)-1,
MI234 = (1 + R,,R,,,
e2iw2d3)M1,
(7)
are the modification factors due to multiple reflection in the films at o and 2w, respectively. The free space wave vector is 3 = w/c, and the normal component of the wave vector in the i th medium is wi = (3: - k*)l/*. The factor Ts2, in the above equations represents the transmission from the 3rd layer to the 1st layer at 2w, and r234 is the reflection factor due to the 2nd, 3rd and 4th layer at w. They are expressed as T321= M321T32T21eiWzdz,
r,,, = m234 ( r23 + r3, e2iw3d3),
(8)
respectively, where M321 = (1 + R,,R,,
eZiWzd2
‘,
m2,, =
The Fresnel coefficients for reflection wave are given 7 respectively) 2as
W$/ + wjc; ’
and transmission
tij =
wicj + wjci
(9)
of a p-polarized
2( Ei’i)1’2W,
w,c, - wjc;
riJ =
(1 + r23r34 e2iw3d3)M1.
(10)
.
We use capital letters to indicate the corresponding quantities evaluated at 52 = 20 and K = 2 k, where o is the angular frequency of the fundamental wave and k is the tangential component of the incident wave vector with subscripts 1, 2, 3, and 4 to denote the prism, index-matched liquid layer with thickness d,, metal with thickness d,, and glass substrate, respectively. Here Q is the dipole moment per unit area of the harmonic current sheets. The tangential and normal components for the liquid layer-metal selvedge are Q,” =
bFkw,( rt4 e4iw3d3 - l),
Qi = aF( k*/2)(
r34 e2iw3d3 + 1)2,
(11)
C.-C. Tzeng, J. T. Lue / Optical second-harmonic
respectively, become
while at the metal-glass
Q,” = -bF,b~,(r~~
substrate
selvedge,
the components
+ 1)2 e2iw3d3, (12)
Q; = -aF(1?~/2)(r~~
- 1) e2iw3d3,
583
generation from silver fihns
where the common factor F is
[c3(o) - ‘I( m,234m23,t,2t23 eiw2d2)29 8nw2L?:
F = 0,
03)
is the charge of an electron, m, is the mass of an electron, e3(w) is the metal dielectric constant at the fundamental frequency, and a and b are the phenomenological parameters. q
3. Theoretical results and conclusions The optical constants
used for numerical calculations
are /m
= n, =
1.908 and /m = Nt = 1.970 for the SF-59 glass prism [12], Ed = Ed = 2.1016 and e2(2a) = r,(2w) = 2.1339 for the index-matched liquid layer and glass substrate [13], Ed = -67.03 + i2.44 and es(2w) = - 11.9 + i0.33 for the silver film [14], respectively. Fig. 2 shows the nonlinear reflection coefficient R with fundamental LRSP excitation at X = 1.06 pm as function of internal angle of incidence in &rid’s geometry. For d, = 100 A, the secondharmonic intensity with LRSP excitation is over 2 orders of magnitude larger -13
‘O’ -15 10 +400X
z
z
d,=4.90W -17
E ” z -19 10
w’
10-21 i 49.4
496
49.0 Internal
Incident
50
50.2
Angle(Degree)
Fig. 2. Second-harmonic reflection coefficient as a function of internal incident angle in Sarid’s geometry with LRSP excitation at sets of silver film and index-matched liquid layer thickness.
584
C.-C. Tzeng, J. T Lue / Optical second-harmonic 3
generation from silver films
03=400 Angstrom e1=49.965806Deg.
lE-15,
lE-16 1E 1
1E 2
02
(An&om)
1E 4
Fig. 3. The variation of R versus d,.
than that from simple SP excitation. An unusual sharp peak occurs at the vicinity of 8, = 49.965 which implies a SHG of R larger than lop9 cm2/watt for the case of d, = 400 A and d, = 1.75 pm. To investigate the possible sources of this anomalously large nonlinear reflectance, we have calculated the changes of R with respect to a small 02=1.75 Microm 81=49.965806Deg.
Fig. 4. The variation R versus d,.
C. -C. Tzeng, J. T. Lue / Optical second-harmonic
D2=1.75 Micron 03=400 Angstron eo=49.%m6l5207
IE-lq] -5
-L
-3
-2
Deg.
(
-1
0
585
generation from silver films
1
2
3
&
5
81-80(1E-9 Deg.) Fig. 5. The change of R and
1Ml2341* as function of the deviation of 8, from its resonance value 4.
variation in layer thickness, and angles of incidence. Fig. 3 is the variation of R versus the thickness ofOthe index-matched liquid layer d, by keeping the silver thickness d, = 400 A and the incident angle 8, at the critical value of 19,= 49.965806’. We find that the variation of R is not large but suddenly drops to zero for d, > 2 pm and then the coupling of incident wave to the metal vanishes. The variation of R as function of metal thickness d, at specified d, and 8i is shown in fig. 4. At d, = 357 A, the excitation of the LRSP is maximum inferring a largest R. The change of R due to a small deviation of the incident angle 8, to the resonance angle 8, = 0, is shown in fig. 5. In the same chart, we have plotted the multiple reflection coefficient 1Ml234 12 of the SHG in the bulk and selvedge region of the metal film. Mi2+, is not sensitive to the variation of the thickness d, and d,. This resonance peak cannot simply be explained by the usual interference effect, since the generation of the SH wave by the excitation of the LRSP is also very sensitive to the angle of incidence. The coupling of these two complex effects results in the extremely narrow angular dependence. It is difficult to observe this phenomenon experimentally, since the angular width is usually much narrower than the divergent angle of the available laser beams. Acknowledgement This work is supported by the National Science Council of the Republic of China.
586
C.-C. Tzeng, J.T. Lue / Optical second-harmonic generation from silver films
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13]
D. Sarid, Phys. Rev. Letters 47 (1981) 1927. G. Stegeman, J.J. Burke and D.G. Hall, Appl. Phys. Letters 41 (1982) 906. D. Sarid, R.T. Deck and J.J. Fasano, J. Opt. Sot. Am. 72 (1982) 1345. J.C. Quail, J.G. Rako, H.J. Simon and R.T. Deck, Phys. Rev. Letters 50 (1983) 1987. J.E. Sipe, V.C.Y. So, M. Fukui and G.I. Stegema, Phys. Rev. B 21 (1980) 4389. J.C. Quail and H.J. Simon, Phys. Rev. B 31 (1985) 4900. R.T. Deck and D. Sarid, J. Opt. Sot. Am. 72 (1982) 1613. J. Rudnick and E.A. Stern, Phys. Rev. B 4 (1971) 4274. E. Chen, J. Zheng, W. Wang and E. Ehang, Chinese Phys. 6 (1986) 450. CC. Tzeng and J.T. Lue, Surface Sci. 192 (1987) 491. CC. Tzeng and J.T. Lue, Phys. Rev. A, in press. Optical Glass Catalog, Schott Optical Glass Inc., Duryea PA 18642. D. Palik, Ed., Handbook of Optical Constants of Solids (Academic Press, New York, 1985) p. 760. (141 P.B. Johnson and R.W. Christy, Phys. Rev. B 6 (1972) 4370.
Surface Science 216 (1989) 579-586 North-Holland, Amsterdam
OPTICAL SECOND-HARMONIC GENERATION FROM SILVER FILMS WITH LONG-RANGE SURFACEPLASMON EXCITATION Chin-Ching TZENG Department
and Juh Tzeng LUE
of Physics, National
Tsing Hua University, Hsinchy
Taiwan, ROC
Received 20 October 1988; accepted for publication 7 February 1989
In this work, we have derived an expression for the second-harmonic generation from metal surfaces under the modified Kretschmann geometry (or Grid’s geometry) based on the hydrodynamic theory of a free electron gas. Numerical calculation shows that the harmonic generation is more than 2 orders of magnitude larger than that due to a single-boundary surface plasmon, if a long-range surface plasmon is excited on both sides of the thin silver film which is bounded by a glass substrate and an index-matched liquid. Resonant surface plasmons excited at some specific internal incident angles emanate a nonlinear wave with an intensity of 5 orders of magnitude greater than that due to long-range surface plasmon.
1. Introduction Recent studies [l] on the properties of long-range surface plasmons (LRSP) excited on both boundaries of a very thin metal film bounded by index-matched dielectrics have stimulated theoretical and experimental interest in nonlinear optics. Excitation of the LRSP mode on semiconductors in the infrared region is believed to be able to enhance the generation of three- and four-wave optical mixings [2] and to increase the nonlinear propagation distance for surface modes [3]. The enhancement of optical second-harmonic generation (SHG) due to the fundamental LRSP mode excited on this silver films deposited on a quartz crystal has been reported [4]. The harmonic intensity is hundred times larger than that due to thick films. The sources of the SHG on a metal surface consist of a “volume” current density extending over a skin depth and a “surface” current density with normal and tangential components within only a few Fermi wavelengths beneath the metal surface. The hydrodynamic theory [5] of an electron gas has been proved successfully by some experiments [6,7] in demonstrating the SHG from noble metals and alumina films through the excitation by a p-polarized Nd : YAG laser. Rudnick and Stern [8] first pointed out the limitations of the free-electron model in describing the SHG surface-current sources and proposed two phenomenological parameters a and b to estimate the size of the 0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
580
C.-C. Tzeng, J. T. Lue / Optical second-harmonic generation from silver films
normal and tangential components of the SH surface current. Sipe et al. [6] and Quail et al. [6] have given an explicit expression for these parameters with a free-electron hydrodynamic model with the introduction of an effective plasma frequency. They have done calculations with b = - 1 for a smooth silver film, allowing the parametor u to be determined experimentally. Second harmonic generation from a modified Kretschmann configuration in which the metal film was surrounded by nonlinear quartz media had been reported by Deck and Sarid [7]. A free long-range transverse-mode (TM) wave was predicted to be excited due to interference of surface plasmons on both sides of the thin metal films. Additional proof of the SHG from a metal film with LRSP excitation has been reported recently by Chen et al. [9]. However, their results are in arbitrary units and do not take into account the contribution from bound electrons. They also assumed an air gap existing between the metal film and the media. In this work, we have assumed that the boundary media have a negligible nonlinear effect and that the SH waves are essentially generated in the bulk and selvedge of the metal film. Due to the high dielectric constant inside the metal, the fundamental and the subsequent SH fields are expected to be smaller in the metal film than those inside the quartz media as predicted in ref. [7]. We have also derived a formula for the evaluation of the SHG from a metal film under the modified Kretschmann geometry based on the hydrodynamic theory. The absolute value of R is calculated by including the bound electrons in the intimate contact media. An anomalously large nonlinear reflectance is found at some specific angles of incidence. The possible sources for such an enormous enhancement with such extremely narrow angular width are discussed. 2. Theory The hydrodynamic theory was firstly developed by Sipe et al. [5] in describing the SHG of light on metal surfaces. In view of a p-polarized wave illuminating a metal film of thickness d, through the geometries as shown in fig. la (ATR) and fig. lb (Sarid’s geometry), a free transverse-mode (TM) wave can be excited in the tin metal film obeying the dispersion relation which is deduced from the law of momentum conservation and boundary conditions as given by w3d, = taC1&,
+ tan-‘&,
+ mm,
(1)
where
(2)
C.-C. Tzeng, J. T. Lue / Optical second-harmonic
r (a)
generation from silver films
X
581
index-matched
(b)
Fig. 1. Two prism-coupling geometries for exciting a surface-plasma wave: (a) and (b) correspond to the Kretschmann and modified Kretschmann (or Sarid’s) geometries, respectively.
m is the mode number (a positive integer), Oi = w/c[~~(w)]“~ is the wave vector in the ith medium with dielectric constant ei( w), and k,, = k& + ik& is the propagation wave vector of the guided mode. Eq. (1) can be used to solve the effective index k,,/c. The wave with large value of k& can propagate only a short distance within the metal film and is called the short-range surface plasmon (SRSP), while that with small value of k& is called the long-range surface plasmon. The nonlinear reflection coefficient R defined as the ratio of the reflected SHG irradiance to the square of the incident fundamental irradiance can be written as R=$>,A,2T, 1
where n, and Nr are the refractive indices of the prism at frequencies w and 2w, respectively, and A is the ratio of the second-harmonic electric field to the square of the fundamental electric field inside the prism and is expressed as A = A, + A, + A,. The three terms are the SHG contributions from the bulk metal, the liquid/front-metal selvedge, and the back-metal/glass-substrate interface for Sarid’s geometry (or ATR geometry), respectively. The factor T contains the Fresnel and geometrical factors describing the coupling of the fundamental waves from air into the prism and the exiting of the secondharmonic beam from the prism back into the air. The explicit expressions of T, A,, A,, and A, for ATR geometry have been published previously by the present authors [lO,ll]. The SHG from bulk metal, liquid layer-metal selvedge and metal-glass substrate interfaces for &rid’s geometry including the contribution from
582
C.-C. Tzeng, J. T. Lue / Optical second-harmonic generation from silver films
bound electrons is
X { K(q/m,)[e,(20) x ( O+%)e
- l]/ic*W$&}
i(2w+,+ W3d3)[ /P(l + ‘34)2 + wi(l
-( 1 + R,, e2iw3d3)[ k*(l
+ r34 e2iw3d3)2+ w:(l
A, = 2riM12s, T321 [ (K&/W,)(l + ( fi2/6,)(1
- $)*I - rs4 ei2w3d3)2]},
(4)
+ R,, e2iw3d3)Qz
- Rj4 e2iw3d3)Qt],
(5)
and A, = 2niM,,,,T,,,T,,
eiWJd3[(~~dK)Q:+
(fi’/%)Qi]~
(6)
respectively, where m1234= ( 1 + r12r234 e2iw2d2)-1,
MI234 = (1 + R,,R,,,
e2iw2d3)M1,
(7)
are the modification factors due to multiple reflection in the films at o and 2w, respectively. The free space wave vector is 3 = w/c, and the normal component of the wave vector in the i th medium is wi = (3: - k*)l/*. The factor Ts2, in the above equations represents the transmission from the 3rd layer to the 1st layer at 2w, and r234 is the reflection factor due to the 2nd, 3rd and 4th layer at w. They are expressed as T321= M321T32T21eiWzdz,
r,,, = m234 ( r23 + r3, e2iw3d3),
(8)
respectively, where M321 = (1 + R,,R,,
eZiWzd2
‘,
m2,, =
The Fresnel coefficients for reflection wave are given 7 respectively) 2as
W$/ + wjc; ’
and transmission
tij =
wicj + wjci
(9)
of a p-polarized
2( Ei’i)1’2W,
w,c, - wjc;
riJ =
(1 + r23r34 e2iw3d3)M1.
(10)
.
We use capital letters to indicate the corresponding quantities evaluated at 52 = 20 and K = 2 k, where o is the angular frequency of the fundamental wave and k is the tangential component of the incident wave vector with subscripts 1, 2, 3, and 4 to denote the prism, index-matched liquid layer with thickness d,, metal with thickness d,, and glass substrate, respectively. Here Q is the dipole moment per unit area of the harmonic current sheets. The tangential and normal components for the liquid layer-metal selvedge are Q,” =
bFkw,( rt4 e4iw3d3 - l),
Qi = aF( k*/2)(
r34 e2iw3d3 + 1)2,
(11)
C.-C. Tzeng, J. T. Lue / Optical second-harmonic
respectively, become
while at the metal-glass
Q,” = -bF,b~,(r~~
substrate
selvedge,
the components
+ 1)2 e2iw3d3, (12)
Q; = -aF(1?~/2)(r~~
- 1) e2iw3d3,
583
generation from silver fihns
where the common factor F is
[c3(o) - ‘I( m,234m23,t,2t23 eiw2d2)29 8nw2L?:
F = 0,
03)
is the charge of an electron, m, is the mass of an electron, e3(w) is the metal dielectric constant at the fundamental frequency, and a and b are the phenomenological parameters. q
3. Theoretical results and conclusions The optical constants
used for numerical calculations
are /m
= n, =
1.908 and /m = Nt = 1.970 for the SF-59 glass prism [12], Ed = Ed = 2.1016 and e2(2a) = r,(2w) = 2.1339 for the index-matched liquid layer and glass substrate [13], Ed = -67.03 + i2.44 and es(2w) = - 11.9 + i0.33 for the silver film [14], respectively. Fig. 2 shows the nonlinear reflection coefficient R with fundamental LRSP excitation at X = 1.06 pm as function of internal angle of incidence in &rid’s geometry. For d, = 100 A, the secondharmonic intensity with LRSP excitation is over 2 orders of magnitude larger -13
‘O’ -15 10 +400X
z
z
d,=4.90W -17
E ” z -19 10
w’
10-21 i 49.4
496
49.0 Internal
Incident
50
50.2
Angle(Degree)
Fig. 2. Second-harmonic reflection coefficient as a function of internal incident angle in Sarid’s geometry with LRSP excitation at sets of silver film and index-matched liquid layer thickness.
584
C.-C. Tzeng, J. T Lue / Optical second-harmonic 3
generation from silver films
03=400 Angstrom e1=49.965806Deg.
lE-15,
lE-16 1E 1
1E 2
02
(An&om)
1E 4
Fig. 3. The variation of R versus d,.
than that from simple SP excitation. An unusual sharp peak occurs at the vicinity of 8, = 49.965 which implies a SHG of R larger than lop9 cm2/watt for the case of d, = 400 A and d, = 1.75 pm. To investigate the possible sources of this anomalously large nonlinear reflectance, we have calculated the changes of R with respect to a small 02=1.75 Microm 81=49.965806Deg.
Fig. 4. The variation R versus d,.
C. -C. Tzeng, J. T. Lue / Optical second-harmonic
D2=1.75 Micron 03=400 Angstron eo=49.%m6l5207
IE-lq] -5
-L
-3
-2
Deg.
(
-1
0
585
generation from silver films
1
2
3
&
5
81-80(1E-9 Deg.) Fig. 5. The change of R and
1Ml2341* as function of the deviation of 8, from its resonance value 4.
variation in layer thickness, and angles of incidence. Fig. 3 is the variation of R versus the thickness ofOthe index-matched liquid layer d, by keeping the silver thickness d, = 400 A and the incident angle 8, at the critical value of 19,= 49.965806’. We find that the variation of R is not large but suddenly drops to zero for d, > 2 pm and then the coupling of incident wave to the metal vanishes. The variation of R as function of metal thickness d, at specified d, and 8i is shown in fig. 4. At d, = 357 A, the excitation of the LRSP is maximum inferring a largest R. The change of R due to a small deviation of the incident angle 8, to the resonance angle 8, = 0, is shown in fig. 5. In the same chart, we have plotted the multiple reflection coefficient 1Ml234 12 of the SHG in the bulk and selvedge region of the metal film. Mi2+, is not sensitive to the variation of the thickness d, and d,. This resonance peak cannot simply be explained by the usual interference effect, since the generation of the SH wave by the excitation of the LRSP is also very sensitive to the angle of incidence. The coupling of these two complex effects results in the extremely narrow angular dependence. It is difficult to observe this phenomenon experimentally, since the angular width is usually much narrower than the divergent angle of the available laser beams. Acknowledgement This work is supported by the National Science Council of the Republic of China.
586
C.-C. Tzeng, J.T. Lue / Optical second-harmonic generation from silver films
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13]
D. Sarid, Phys. Rev. Letters 47 (1981) 1927. G. Stegeman, J.J. Burke and D.G. Hall, Appl. Phys. Letters 41 (1982) 906. D. Sarid, R.T. Deck and J.J. Fasano, J. Opt. Sot. Am. 72 (1982) 1345. J.C. Quail, J.G. Rako, H.J. Simon and R.T. Deck, Phys. Rev. Letters 50 (1983) 1987. J.E. Sipe, V.C.Y. So, M. Fukui and G.I. Stegema, Phys. Rev. B 21 (1980) 4389. J.C. Quail and H.J. Simon, Phys. Rev. B 31 (1985) 4900. R.T. Deck and D. Sarid, J. Opt. Sot. Am. 72 (1982) 1613. J. Rudnick and E.A. Stern, Phys. Rev. B 4 (1971) 4274. E. Chen, J. Zheng, W. Wang and E. Ehang, Chinese Phys. 6 (1986) 450. CC. Tzeng and J.T. Lue, Surface Sci. 192 (1987) 491. CC. Tzeng and J.T. Lue, Phys. Rev. A, in press. Optical Glass Catalog, Schott Optical Glass Inc., Duryea PA 18642. D. Palik, Ed., Handbook of Optical Constants of Solids (Academic Press, New York, 1985) p. 760. (141 P.B. Johnson and R.W. Christy, Phys. Rev. B 6 (1972) 4370.