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Polarization studies of radiation emitted by surface plasmons in silver
Volume
7, number
4
OPTICS COMMUNICATIONS
POLARIZATION EMITTED
April 1973
STUDIES OF RADIATION
BY SURFACE
PLASMONS
IN SILVER
D.C. HALL *t and A.J. BRAUNDMEIER
Jr.
Physics Department, Southern Illinois University, EdLclardsville,Illinois 62025, USA
Revised
Received manuscript
24 October 1972 received 5 December
1972
Measurements are reported on the polarization of radiation emitted by the roughness induced decay of nonradiative surface plasmons optically excited by light in thin Ag films. This radiation is of mixed polarization when the incident light is p-polarized. The s-polarized component of the radiation is observed to be considerably less intense than the p-polarized component.
1. Introduction In 1968, Otto [l] reported that nonradiative surface plasma waves, Ritchie modes, could be excited in Ag by the method of frustrated total reflection. His experimental arrangement consisted of a silver film separated from a quartz prism by a thin space layer of air. He observed a minimum in the ratio of reflectivities for transverse magnetic (p-polarized) to transverse electric (s-polarized) light which depended on the angle of incidence of the light in the prism, the wavelength of the incident light, and the thickness of the space layer. This study was primarily a study of surface plasmon absorption of light by optically coupling the incident light directly to the Ritchie modes. Surface roughness is not required for the coupling since k-conservation is achieved in this configuration. A modification of Otto’s experiment was performed by Kretschmann and Raether [2] later in 1968. They deposited an Ag film directly onto a quartz prism and * This research is based in part on a thesis submitted by D.G. Hall to Southern Illinois University in partial fulfilment of the requirements for the MS. degree. “r Present address: Optical Sciences Center, University of Arizona, Tucson, Arizona 85721, USA.
looked at the intensity of the light transmitted through the film as a function of both wavelength and angle of incidence of the exciting light. Their observation was that the Ritchie modes could only be excited by p-polarized light at angles beyond the critical angle of the quartz prism. There were no reported measurements of the polarization characteristics of this plasma resonance emission. Further studies by Otto [3] included the measurement of the polarization of radiation emitted during the decay of Ritchie modes on a rough surface of Ag. He found that light of both p- and s-polarization could excite the Ritchie modes but the radiation from their subsequent decay was always p-polarized. In the following paper further experiments on Ag films are described and the existence of s-polarized surface plasmon radiation is reported.
2. Experimental
procedure
Silver films were prepared at a pressure of = 10e6 torr by evaporating 99.9% pure Ag wire onto the flat surface of a semi-cylindrical quartz substrate. A quartz crystal monitor was mounted in the evaporator to measure the thickness of the films as they were prepared. After preparation of the film the substrate 343
Volume
7, number
4
OPTICS COMMUNICATIONS
April 1973
was removed from the vacuum chamber and placed on a rotary table. The placement of the substrate was such that the 6328 A wavelength light from a He--Ne laser intersected the Ag film at the axis of rotation of the rotary table. The intensities were measured by a photomultiplier tube driving the standard picoammeter-recorder arrangement. The polarization of the incident and plasmon resonance radiation in the plane of incidence was determined by sheet polarizers in the light paths. The basic experimental arrangements are depicted in fig. 1. In one case light approached the silver film from the substrate side whereas in the second arrangement the incident light struck the air/ silver interface. The angle 0 can be changed by rotating the substrate.
3. Results and discussion
44
45
46
8 (DEGREES)
The first study was conducted using the apparatus as depicted in fig. la. The photomultiplier was positioned such that it observed light ernitted normal to the Ag/air interface and in the plane of incidence. It was observed that p-polarized incident light produced
(4
(b)
Fig. 1. Experimental arrangements for first study (a) and second study (b) showing semicylindrical substrate with thin silver film, light source L, and photomultiplier tube PMT. 0 is the angle of incidence.
344
Fig. 2. Intensity of surface plasmon radiation, as measured with the arrangement of fig. la, plotted as a function of angle of incidence 0.
an intense resonance peak at the Ag/air interface when 8 was increased to just beyond the substrate’s critical angle (= 44”). A typical plot of the intensity of the resonance radiation excited by p-polarized incident light is shown in fig. 2. This plasmon radiation was observed to contain both a p-polarized and an s-polarized component. We know of no previous observation of this s-polarized component. When the incident light was s-polarized no resonance peaks of either polarization were observed. Fig. 3 shows the intensity of the p- and s-polarized components of the plasmon radiation as a function of film thickness. The curve representing the s-polarized intensity has been increased by a factor of two relative to the p-polarized intensity curve. The behavior of the relative intensities as the film thickness is varied is not understood at present and is being studied. A recent paper by Kretschmann [4] presents his calculations of the polarization of light emitted by surface plasmons on metals due to surface irregularities. He finds that for the case where the plane of incidence and the plane of observation are equal the s-polarized scattered intensity is zero. Our experiments do not confirm this since we always observed an s-polarized
Volume
7, number
OPTICS COMMUNICATIONS
4
April
1973
1,o -
.a 0
f
q -4 .2 -
"23
I’ _’
’
I-.
/’
‘\
‘\ \
4
567
2 3 4 ctik (CV)
5
Fig. 4. Plot of dispersion relations for Ritchie modes at the Ag/air and Ag/quartz interface of an Ag film deposited onto a quartz substrate. Also shown are the dispersion relation\ for photons in vacuum and quartz. Ritchie modes at the A@ air interface have the proper momentum to couple with photons propagating in quartz.
\
\
1
\
a
9
10
FILMTIIICKJ~ESS(130~)
Fig. 3. Relative intensities of p- and s-polarized surface plasmon radiation from Ag versus film thickness. The solid curve is the intensity of the p-polarized radiation whereas the dashed curve depicts the s-polarized radiation and has been nultiplied by a factor of two. The data were taken with the arrangement of fig. la. radiation peak along with a p-polarized radiation peak. Further experiments in this area are being conducted by the authors. The second study was made by reversing the positions of the light source and photomultiplier tube so that the incident light strikes the Ag/air interface at normal or near-normal incidence while the photomultiplier tube looks at light radiated into the quartz as a function of the angle 0 from the film normal (see fig. 1b). With either p- or s-polarized incident laser light a p-polarized radiation peak was observed by the photomultiplier tube at the same value of 0 as seen in fig. 2. An s-polarized radiation peak was never observed and was not expected. This is of course quite consistent. The explanation of these results is based on the availability of two mechanisms which enable surface plasmons to couple with photons: (1) optical coupling or k-conservation and (2) roughness coupling or nonk-conservation. Optical coupling requires that only the momentum parallel to the film surface and the energy be conserved between the indicent photon and the plasmon; roughness at the interface is not required.
The familiar dispersion of surface plasmons shown in fig. 4 forbids a photon travelling in vacua from cou-
pling with a surface plasmon at a plane, smooth boundary. However, if a photon is incident upon a silver fflrn from a medium of refractive index II (n > 1) at an angle 0 from the film normal, then the momentum of the incident photon parallel to the interface is increased and given by the expression P,, = tzA(w/c) sin 8. By properly adjusting 0, PII can be made to match the momentum of a surface plasmon of the same energy at the Adair interface and coupling can occur. The polarization of the incident light must now be considered since only p-polarized light is observed to couple optically with plasmons. For incident light of purely s-polarization the electric field is, for all angles of incidence parallel to the plane containing the quartz/Ag interface. This means that by varying the angle 0 one does not alter the component of the electric field parallel to this interface. The direction of the incoming electric field defines the direction of initial motion of the electrons contained in the film and for s-polarized light the force on the electrons is transverse to the component of the photon momentum along the interface for all angles of incidence Thus s-polarized light tends to create transverse electronic oscillations not longitudinal oscillations. When one considers p-polarized light it is apparent that an incoming photon approaching the quartz/Ag interface of fig. la has electric field components parallel and perpendicular to the interface, both of which vary with the angle of incidence. The parallel component tends to produce a longitudinal wave of the type associated with surface plasmons. Hence one expects only p-polarized photons to be able to optically couple with plasmons. 345
Volume
7, number
4
OPTICS COMMUNICATIONS
After the plasmons have been created by p.polarized photons incident through the quartz they again have two possible mechanisms for coupling to photons. Optical coupling to photons in vacua at the Ag/air interface is not available however, due to the dispersion of the plasmon oscillations. If roughness is present on the Ag/air interface a surface plasmon can be scattered by the surface roughness into a new momentum state where the energy and lkl are unchanged [ 51. Hence the magnitude and direction of k along the surface, k,,, can be altered by these scattering interactions. It is conceivable then that due to these scattering events not only will the plasmon be able to couple with photons but the resulting photons may be of mixed polarization. Plasmons whose wavevector klay entirely in the plane of incidence before the scattering may have a component of k perpendicular to the plane of incidence after the scattering. The resultant radiation would then be expected to have both polarization components present with the relative magnitude of the intensity of the two components dependent on the surface roughness. The decay of a plasmon from a smooth film by reradiation back into the quartz substrate (decay by optical coupling) is not observed since the plasmon can contribute very little momentum normal to the fdrn surface. This then is why one finds decreased specular reflectance from a smooth film at the plasmon angle, i.e., the incident light can optically couple to produce a plasmon but the plasmon cannot readily couple back to launch a photon in the specular beam. A summary of our results and the results from the experiments of Otto [3] and Kretschmann and Raether [2] is presented in fig. 5. The Feynman diagrams depict the coupling processes involved in all of these experiments. One notices that whereas opticalroughness and roughness-optical coupling have been observed roughness-roughness coupling has not been reported. We would expect this type of creation-decay process to produce very weak plasmon radiation from surface irregularities randomly distributed. Regularly structured surfaces may induce greater intensities from this type of coupling and is most likely evidenced by the recent work on Wood’s Anomalies [6]. 4. Summary The absorption
346
and reradiation
of light by surface
April 1973
KRETSCHNANN & RAETHER
OTTO
s
s
P
P
s
IP I
PRESENT WORK
I
P
1-
-I=
0
3;:’
x
f
3;=:
X x
I
PRESENT WORK
-f! -== X 7 *=== x I I
I
s
s
--a
NICI)
PHOTON
PIASMON
-__ ___x SURFACE
Fig. 5. Feynman diagrams of possible photon-plasmon interactions for the experimental arrangements used by Otto [ 31, Kretschmann and Raether [ 21, and the present work. P and S indicate the polarization of the photons whereas N indicates interactions specifically sought but not observed. Those not observed require multiple coupling to the surface roughness. Roughness coupling is indicated by a X while an 0 indicates optical coupling.
plasmons at a metal/dielectric interface has been shown to depend on the nature of the coupling mechanism. Light polarized parallel to the plane of incidence is observed to exhibit both optical coupling and roughness coupling with surface plasmons whereas light polarized perpendicular to the plane of incidence can couple with the plasma modes only by interaction with surface roughness. The observation of s-polarized light due to the scattering of surface plasmons by roughness is reported.
References
111A. Otto, 2. Physik 216 (1968) 389. f21 E, Kretschmann and H. Raether, Z. Naturforsch.
23a (1968)2135. 131 A. Otto, Z. Physik 224 (1969) 6.5. Opt. Commun. 5 (1972) 331. [41 E. Kretschmann, [51 J.M. Elson and R.H. Ritchie, Phys. Rev. B4 (1971) 4129. I61 J.J. Cowan and E.T. Arakawa, Z. Physik 235 (1970) 97; Phys. Stat. Sol. 1 (1970) 695.
7, number
4
OPTICS COMMUNICATIONS
POLARIZATION EMITTED
April 1973
STUDIES OF RADIATION
BY SURFACE
PLASMONS
IN SILVER
D.C. HALL *t and A.J. BRAUNDMEIER
Jr.
Physics Department, Southern Illinois University, EdLclardsville,Illinois 62025, USA
Revised
Received manuscript
24 October 1972 received 5 December
1972
Measurements are reported on the polarization of radiation emitted by the roughness induced decay of nonradiative surface plasmons optically excited by light in thin Ag films. This radiation is of mixed polarization when the incident light is p-polarized. The s-polarized component of the radiation is observed to be considerably less intense than the p-polarized component.
1. Introduction In 1968, Otto [l] reported that nonradiative surface plasma waves, Ritchie modes, could be excited in Ag by the method of frustrated total reflection. His experimental arrangement consisted of a silver film separated from a quartz prism by a thin space layer of air. He observed a minimum in the ratio of reflectivities for transverse magnetic (p-polarized) to transverse electric (s-polarized) light which depended on the angle of incidence of the light in the prism, the wavelength of the incident light, and the thickness of the space layer. This study was primarily a study of surface plasmon absorption of light by optically coupling the incident light directly to the Ritchie modes. Surface roughness is not required for the coupling since k-conservation is achieved in this configuration. A modification of Otto’s experiment was performed by Kretschmann and Raether [2] later in 1968. They deposited an Ag film directly onto a quartz prism and * This research is based in part on a thesis submitted by D.G. Hall to Southern Illinois University in partial fulfilment of the requirements for the MS. degree. “r Present address: Optical Sciences Center, University of Arizona, Tucson, Arizona 85721, USA.
looked at the intensity of the light transmitted through the film as a function of both wavelength and angle of incidence of the exciting light. Their observation was that the Ritchie modes could only be excited by p-polarized light at angles beyond the critical angle of the quartz prism. There were no reported measurements of the polarization characteristics of this plasma resonance emission. Further studies by Otto [3] included the measurement of the polarization of radiation emitted during the decay of Ritchie modes on a rough surface of Ag. He found that light of both p- and s-polarization could excite the Ritchie modes but the radiation from their subsequent decay was always p-polarized. In the following paper further experiments on Ag films are described and the existence of s-polarized surface plasmon radiation is reported.
2. Experimental
procedure
Silver films were prepared at a pressure of = 10e6 torr by evaporating 99.9% pure Ag wire onto the flat surface of a semi-cylindrical quartz substrate. A quartz crystal monitor was mounted in the evaporator to measure the thickness of the films as they were prepared. After preparation of the film the substrate 343
Volume
7, number
4
OPTICS COMMUNICATIONS
April 1973
was removed from the vacuum chamber and placed on a rotary table. The placement of the substrate was such that the 6328 A wavelength light from a He--Ne laser intersected the Ag film at the axis of rotation of the rotary table. The intensities were measured by a photomultiplier tube driving the standard picoammeter-recorder arrangement. The polarization of the incident and plasmon resonance radiation in the plane of incidence was determined by sheet polarizers in the light paths. The basic experimental arrangements are depicted in fig. 1. In one case light approached the silver film from the substrate side whereas in the second arrangement the incident light struck the air/ silver interface. The angle 0 can be changed by rotating the substrate.
3. Results and discussion
44
45
46
8 (DEGREES)
The first study was conducted using the apparatus as depicted in fig. la. The photomultiplier was positioned such that it observed light ernitted normal to the Ag/air interface and in the plane of incidence. It was observed that p-polarized incident light produced
(4
(b)
Fig. 1. Experimental arrangements for first study (a) and second study (b) showing semicylindrical substrate with thin silver film, light source L, and photomultiplier tube PMT. 0 is the angle of incidence.
344
Fig. 2. Intensity of surface plasmon radiation, as measured with the arrangement of fig. la, plotted as a function of angle of incidence 0.
an intense resonance peak at the Ag/air interface when 8 was increased to just beyond the substrate’s critical angle (= 44”). A typical plot of the intensity of the resonance radiation excited by p-polarized incident light is shown in fig. 2. This plasmon radiation was observed to contain both a p-polarized and an s-polarized component. We know of no previous observation of this s-polarized component. When the incident light was s-polarized no resonance peaks of either polarization were observed. Fig. 3 shows the intensity of the p- and s-polarized components of the plasmon radiation as a function of film thickness. The curve representing the s-polarized intensity has been increased by a factor of two relative to the p-polarized intensity curve. The behavior of the relative intensities as the film thickness is varied is not understood at present and is being studied. A recent paper by Kretschmann [4] presents his calculations of the polarization of light emitted by surface plasmons on metals due to surface irregularities. He finds that for the case where the plane of incidence and the plane of observation are equal the s-polarized scattered intensity is zero. Our experiments do not confirm this since we always observed an s-polarized
Volume
7, number
OPTICS COMMUNICATIONS
4
April
1973
1,o -
.a 0
f
q -4 .2 -
"23
I’ _’
’
I-.
/’
‘\
‘\ \
4
567
2 3 4 ctik (CV)
5
Fig. 4. Plot of dispersion relations for Ritchie modes at the Ag/air and Ag/quartz interface of an Ag film deposited onto a quartz substrate. Also shown are the dispersion relation\ for photons in vacuum and quartz. Ritchie modes at the A@ air interface have the proper momentum to couple with photons propagating in quartz.
\
\
1
\
a
9
10
FILMTIIICKJ~ESS(130~)
Fig. 3. Relative intensities of p- and s-polarized surface plasmon radiation from Ag versus film thickness. The solid curve is the intensity of the p-polarized radiation whereas the dashed curve depicts the s-polarized radiation and has been nultiplied by a factor of two. The data were taken with the arrangement of fig. la. radiation peak along with a p-polarized radiation peak. Further experiments in this area are being conducted by the authors. The second study was made by reversing the positions of the light source and photomultiplier tube so that the incident light strikes the Ag/air interface at normal or near-normal incidence while the photomultiplier tube looks at light radiated into the quartz as a function of the angle 0 from the film normal (see fig. 1b). With either p- or s-polarized incident laser light a p-polarized radiation peak was observed by the photomultiplier tube at the same value of 0 as seen in fig. 2. An s-polarized radiation peak was never observed and was not expected. This is of course quite consistent. The explanation of these results is based on the availability of two mechanisms which enable surface plasmons to couple with photons: (1) optical coupling or k-conservation and (2) roughness coupling or nonk-conservation. Optical coupling requires that only the momentum parallel to the film surface and the energy be conserved between the indicent photon and the plasmon; roughness at the interface is not required.
The familiar dispersion of surface plasmons shown in fig. 4 forbids a photon travelling in vacua from cou-
pling with a surface plasmon at a plane, smooth boundary. However, if a photon is incident upon a silver fflrn from a medium of refractive index II (n > 1) at an angle 0 from the film normal, then the momentum of the incident photon parallel to the interface is increased and given by the expression P,, = tzA(w/c) sin 8. By properly adjusting 0, PII can be made to match the momentum of a surface plasmon of the same energy at the Adair interface and coupling can occur. The polarization of the incident light must now be considered since only p-polarized light is observed to couple optically with plasmons. For incident light of purely s-polarization the electric field is, for all angles of incidence parallel to the plane containing the quartz/Ag interface. This means that by varying the angle 0 one does not alter the component of the electric field parallel to this interface. The direction of the incoming electric field defines the direction of initial motion of the electrons contained in the film and for s-polarized light the force on the electrons is transverse to the component of the photon momentum along the interface for all angles of incidence Thus s-polarized light tends to create transverse electronic oscillations not longitudinal oscillations. When one considers p-polarized light it is apparent that an incoming photon approaching the quartz/Ag interface of fig. la has electric field components parallel and perpendicular to the interface, both of which vary with the angle of incidence. The parallel component tends to produce a longitudinal wave of the type associated with surface plasmons. Hence one expects only p-polarized photons to be able to optically couple with plasmons. 345
Volume
7, number
4
OPTICS COMMUNICATIONS
After the plasmons have been created by p.polarized photons incident through the quartz they again have two possible mechanisms for coupling to photons. Optical coupling to photons in vacua at the Ag/air interface is not available however, due to the dispersion of the plasmon oscillations. If roughness is present on the Ag/air interface a surface plasmon can be scattered by the surface roughness into a new momentum state where the energy and lkl are unchanged [ 51. Hence the magnitude and direction of k along the surface, k,,, can be altered by these scattering interactions. It is conceivable then that due to these scattering events not only will the plasmon be able to couple with photons but the resulting photons may be of mixed polarization. Plasmons whose wavevector klay entirely in the plane of incidence before the scattering may have a component of k perpendicular to the plane of incidence after the scattering. The resultant radiation would then be expected to have both polarization components present with the relative magnitude of the intensity of the two components dependent on the surface roughness. The decay of a plasmon from a smooth film by reradiation back into the quartz substrate (decay by optical coupling) is not observed since the plasmon can contribute very little momentum normal to the fdrn surface. This then is why one finds decreased specular reflectance from a smooth film at the plasmon angle, i.e., the incident light can optically couple to produce a plasmon but the plasmon cannot readily couple back to launch a photon in the specular beam. A summary of our results and the results from the experiments of Otto [3] and Kretschmann and Raether [2] is presented in fig. 5. The Feynman diagrams depict the coupling processes involved in all of these experiments. One notices that whereas opticalroughness and roughness-optical coupling have been observed roughness-roughness coupling has not been reported. We would expect this type of creation-decay process to produce very weak plasmon radiation from surface irregularities randomly distributed. Regularly structured surfaces may induce greater intensities from this type of coupling and is most likely evidenced by the recent work on Wood’s Anomalies [6]. 4. Summary The absorption
346
and reradiation
of light by surface
April 1973
KRETSCHNANN & RAETHER
OTTO
s
s
P
P
s
IP I
PRESENT WORK
I
P
1-
-I=
0
3;:’
x
f
3;=:
X x
I
PRESENT WORK
-f! -== X 7 *=== x I I
I
s
s
--a
NICI)
PHOTON
PIASMON
-__ ___x SURFACE
Fig. 5. Feynman diagrams of possible photon-plasmon interactions for the experimental arrangements used by Otto [ 31, Kretschmann and Raether [ 21, and the present work. P and S indicate the polarization of the photons whereas N indicates interactions specifically sought but not observed. Those not observed require multiple coupling to the surface roughness. Roughness coupling is indicated by a X while an 0 indicates optical coupling.
plasmons at a metal/dielectric interface has been shown to depend on the nature of the coupling mechanism. Light polarized parallel to the plane of incidence is observed to exhibit both optical coupling and roughness coupling with surface plasmons whereas light polarized perpendicular to the plane of incidence can couple with the plasma modes only by interaction with surface roughness. The observation of s-polarized light due to the scattering of surface plasmons by roughness is reported.
References
111A. Otto, 2. Physik 216 (1968) 389. f21 E, Kretschmann and H. Raether, Z. Naturforsch.
23a (1968)2135. 131 A. Otto, Z. Physik 224 (1969) 6.5. Opt. Commun. 5 (1972) 331. [41 E. Kretschmann, [51 J.M. Elson and R.H. Ritchie, Phys. Rev. B4 (1971) 4129. I61 J.J. Cowan and E.T. Arakawa, Z. Physik 235 (1970) 97; Phys. Stat. Sol. 1 (1970) 695.