Surface Plasmon Resonance Spectroscopy Based on Evanescent

Dec 20, 2003 - imaginary part of the dielectric constant of all absorbing media. The evanescent field in the metal film consists of two fields, one or...
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Anal. Chem. 2004, 76, 561-568

Surface Plasmon Resonance Spectroscopy Based on Evanescent Field Treatment Sanong Ekgasit,*,†,‡ Chuchaat Thammacharoen,† and Wolfgang Knoll‡

Department of Chemistry, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand, and Max-Planck-Institut fu¨r Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany

The reflectance in a surface plasmon resonance (SPR) curve can be expressed in terms of the integration of the product between the evanescent electric field and the imaginary part of the dielectric constant of all absorbing media. The evanescent field in the metal film consists of two fields, one originating at the prism/metal interface and the other at the metal/dielectric interface. Near the resonance angle, the evanescent field strength at the metal/dielectric interface is much greater than that at the prism/metal interface. The evanescent field in dielectric medium has a single origin at the metal/dielectric interface. Due to the optical enhancement at the interface, the amplitude of the evanescent electric field in the dielectric medium is much greater than that in the metal film. This field, however, is not being utilized in conventional SPR where changes in the refractive index of the nonabsorbing dielectric media are of interest. In a system with an absorbing dielectric medium, the absorption of the medium is enhanced by the strong evanescent electric field. The evanescent field distributions in the metal film and in the dielectric medium are significantly altered by the absorbing dielectric, which results in shifting of the resonance angle, increasing of the reflectance, and broadening of the SPR curve. Since the absorption contribution from the absorbing dielectric can be separated from that of the metal film via knowledge of evanescent field distribution, an in-depth analysis of the SPR curve of an absorbing medium and its relationship with the material characteristics are possible. Surface plasmon resonance (SPR) spectroscopy is a surface characterization technique that takes advantage of the enhanced evanescent field at the surface of a thin noble metal film for probing thin dielectric film deposited on the metal surface. Near the resonance angle, an extremely strong evanescent field is generated at the metal/dielectric interface by the surface plasmon wave. Its properties (i.e., strength, distribution, and decay characteristic) are governed by the experimental parameters (i.e., polarization and wavelength of the incident radiation) and material characteristics (i.e., dielectric constants of prism, metal film and * To whom correspondence should be addressed: (e-mail) sanong.e@ chula.ac.th. † Chulalongkorn University. ‡ Max-Planck-Institut fu ¨ r Polymerforschung. 10.1021/ac035042v CCC: $27.50 Published on Web 12/20/2003

© 2004 American Chemical Society

dielectric medium, and the metal film thickness).1-3 The unique characteristic of the surface plasmon wave-generated evanescent field, where the field amplitude is greatest at the interface and exponentially decays as a function of distance from the metal/ dielectric interface, makes the SPR signal very sensitive to changes at the vicinity of the metal surface. In general, physical or chemical changes of the dielectric medium at the metal surface involve refractive index or thickness variation. Once the refractive index, the thickness of the dielectric medium at the vicinity of the metal surface, or both, are changed, the resonance position of the SPR curve is shifted. The magnitude of the changes of the SPR reflectance and shift of the resonance angle can be correlated to the physicochemical phenomena. The kinetics and mechanism of the reaction as well as properties of the dielectric medium on the metal surface are then interpreted from the observed SPR curve.2,4 The SPR technique is so sensitive that a minor change in the refractive index of the dielectric material as small as ∆n ) 5 × 10-7 has been detected.5 Due to its highly sensitive nature, SPR spectroscopy became a powerful analytical technique for sensing chemical and biochemical reactions at the surface and interface. Various application of the SPR technique can be found in life science and physical science research such as antibodyantigen, protein-protein, DNA-protein, and DNA-DNA interactions,6 biomembrane interactions,7 imaging,8 microscopy,9 properties of thin films,10 and enhancement of the photoelectric effects.11 Although the high sensitivity of the SPR technique is sufficient for monitoring most of the interfacial reactions of interest, only insignificant changes in the SPR signal are observed if the reactions involve small molecules such as protein fragments or low molecular weight drugs. Novel techniques such as colloidal gold-enhanced SPR,12 gold and silver nanoparticle-enhanced SPR,13,14 and surface plasmon field-enhanced fluorescence spectroscopy15 have been employed to improve sensitivity of the SPRbased surface characterization techniques. However, the quantitative analysis of those techniques becomes more complex since both, the metal film and the dielectric medium, are absorbing. Changes in the SPR signal are not linearly related to the physical (1) Raether, H. Surface Plasmon on Smooth and Rough Surfaces and on Gratings; Springer-Verlag: Berlin, 1988; Vol. 111. (2) Knoll, W. Annu. Rev. Phys. Chem. 1998, 49, 569-638. (3) Homola, J.; Yee, S. S.; Gauglitz, G. Sens. Actuators, B 1999, 54, 3-15. (4) Salamon, Z.; Macleod, H. A.; Tollin, G. Biochim. Biophys. Acta 1997, 1331, 117-129. (5) Nelson, S. G.; Johnston, K. S.; Yee, S. S. Sens. Actuators, B 1996, 35-36, 187-191.

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parameters of the dielectric medium (i.e., refractive index and thickness) as they are in the conventional SPR. There are numerous theoretical models that describe the relationship between the SPR reflectance and physical parameters of the dielectric media. A complex and nonlinear relationship based on the Fresnel reflection and transmission coefficients is normally observed.1,14,16 This paper introduces the quantitative expression that describes the relationship between the SPR signals and dielectric constants of the involved materials. We will show that, based on the evanescent field treatment, a quantitative analysis of the SPR reflectance of absorbing dielectric media is possible. First, the conventional SPR of the nonabsorbing dielectric medium will be treated. Then, the SPR of the absorbing dielectric medium will be discussed. THEORY For a stratified medium with plane boundaries consisting of N isotropic layers, the medium is placed between a high refractive index prism and a dielectric substrate. A schematic illustration of the system is shown in Figure 1. The prism is transparent and has a dielectric constant of p. Τhe dielectric substrate with a semiinfinite thickness has a complex dielectric constant of ˆ D. The jth layer of the stratified medium has a thickness of dj and a complex dielectric constant of ˆ j. When an incident beam of wavelength λ impinges at the prism/multilayer interface with an angle of (6) Fivash, M.; Towler, E. M.; Fisher, R. J. Curr. Opin. Biotechnol. 1998, 9, 97-101. (7) (a) Kuziemko, G. M.; Stroh, M.; Stevens, R. C. Biochemistry 1996, 35, 63756384. (b) Cooper, M. A.; Hansson, A.; Lofas, S.; Williams, D. H. Anal. Biochem. 2000, 277, 196-205. (c) Mozsolits, H.; Aguilar, M. I. Biopolymers 2002, 66, 3-18. (8) (a) Jordan, C. E.; Frutos, A. G.; Thiel, A. J.; Corn, R. M. Anal. Chem. 1997, 69, 4939-4947. (b) Steiner, G.; Sablinskas, V.; Hubner, A.; Kuhne, C.; Salzer, R. J. Mol. Struct. 1999, 509, 265-273. (c) Wegner, G. J.; Lee, H. J.; Corn, R. M. Anal. Chem. 2002, 74, 5161-5168. (d) Smith, E. A.; Thomas, W. D.; Kiessling, L. L.; Corn, R. M. J. Am. Chem. Soc. 2003, 125, 6140-6148. (9) (a) Yeatman, E. M. Biosens. Bioelectron. 1996, 11, 635-649. (b) Zhou, W.; Caide, X.; Sui, S. F. Mol. Cryst. Liq. Cryst. 1999, 337, 61-64. (c) Somekh, M. G.; Liu, S. G.; Velinov, T. S.; See, C. W. Appl. Opt. 2000, 39, 62796287. (d) Zhang, T.; Morgan, H.; Curtis, A. S. G.; Riehle, M. J. Opt. A 2001, 3, 333-337. (10) (a) Steiner, G.; Sablinskas, V.; Hubner, A.; Kuhne, C.; Salzer, R. J. Mol. Struct. 1999, 509, 265-273. (b) Tamada, K.; Ishida, T.; Knoll, W.; Fukushima, H.; Colorado, R.; Graupe, M.; Shmakova, O. E.; Lee, T. R. Langmuir 2001, 17, 1913-1921. (c) Tawa, K.; Knoll, W. Macromolecules 2002, 35, 70187023. (d) Zhang, Z.; Menges, B.; Timmons, R. B.; Knoll, W.; Forch, R. Langmuir 2003, 19, 4765-4770. (11) Kato, K.; Tsuruta, H.; Ebe. T.; Shinbo, K.; Kaneko, F.; Wakamatsu, T. Mater. Sci. Eng. C 2002, 22, 251-256. (12) (a) Gu, J. H.; Lu ¨ , H.; Chen, Y. W.; Liu, L. Y.; Wang, P.; Ma, J. M.; Lu, Z. H. Supramol. Sci. 1998, 5, 695-698. (b) Lyon, L. A.; Musick, M. D.; Natan, M. J. Anal. Chem. 1998, 70, 5177-5183. (c) Lyon, L. A.; Pen ˜a, D. J.; Natan, M. J. J. Phys. Chem. B. 1999, 103, 5826-5831. (d) He, L.; Musick, M. D.; Nicewarner, S. R.; Salinas, F. G.; Benkovic, S. J.; Natan, M. J.; Keating, C. D. J. Am. Chem. Soc. 2000, 122, 9071-9077. (13) Kume, T.; Hayashi, S.; Yamamoto, K. Mater. Sci. Eng. A 1996, 217, 171175. (14) (a) Hutter, E.; Cha, S.; Liu, J.-F.; Park, J.; Yi, J.; Fendler, J. H.; Roy, D. J. Phys. Chem. B 2001, 105, 8-12. (b) Hutter, E.; Fendler, J. H.; Roy, D. J. Phys. Chem. B 2001, 105, 11159-11168. (15) (a) Liebermann, T.; Knoll, W. Colloids Surf. A 2000, 171, 115-130. (b) Neumann, T.; Johansson, M. L.; Kambhampati, D.; Knoll, W. Adv. Funct. Mater. 2002, 12, 575-586. (c) Liebermann, T.; Knoll, W. Langmuir 2003, 19, 1567-1572. (d) Baba, A.; Knoll, W. J. Phys. Chem. B 2003, 107, 77337738. (e) Yu, F.; Yao, D. F.; Knoll, W. Anal. Chem. 2003, 75, 2610-2617. (16) (a) Roy, D. Opt. Commun. 2001, 200, 119-130. (b) Roy, D. Appl. Spectrosc. 2001, 55, 1046-1052. (c) Kurihara, K.; Suzuki, K. Anal. Chem. 2002, 74, 696-701. (d) Kurihara, K.; Nakamura, K.; Hirayama, E.; Suzuki, K. Anal. Chem. 2002, 74, 6323-6333.

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Figure 1. Schematic illustration shows the interaction between a plane wave and a stratified medium. Sign conventions for parallel (|) and perpendicular (⊥) polarized radiation are illustrated.

incidence θ, the Fresnel reflection and transmission coefficients of the system are given by17

r|.⊥ ) t|.⊥ )

(M11 + M12qD)qP - (M21 + M22qD) (M11 + M12qD)qP + (M21 + M22qD) 2qP (M11 + M12qD)qP + (M21 + M22qD)

(1)

(2)

where | indicates parallel-polarized radiation and ⊥ indicates perpendicular-polarized radiation. Mmn is an element of the characteristic matrix M(2 × 2) of the plane boundary stratified layers. This matrix M is given in terms of material characteristics and experimental parameters by N

M)

∏ j)1

[

-i

sin(kzjdj) qj -iqj sin(kzjdj) cos(kzjdj)

cos(kzjdj)

]

(3)

where i ) (-1)1/2, qj ) kzj/ˆ j for parallel-polarized radiation, and qj ) kzj for perpendicular- polarized radiation. kzj is the z-component of the wavevector in the jth layer and is given by kzj ) [(2π/λ)2ˆ j 2 - kxP ]1/2. kxP is the x-component of the wavevector in prism and is given by kxP ) (2π/λ)[P sin2 θ]1/2. The reflectance and transmittance are given in terms of the Fresnel reflection and transmission coefficients, respectively, according to17

R| ) |r||2 and T| )

Re[kzD/ˆ D] 2 |t|| kzP/P for parallel polarization (4)

R⊥ ) |r⊥|2 and T⊥ )

Re[kzD] 2 |t⊥| kzP for perpendicular polarization (5)

The electromagnetic fields (the magnetic field and the electric field) at a distance z from the prism, which are located within the lth layer of the stratified medium, are given in terms of the wavevector and the Fresnel reflection and transmission coefficients by the following expressions.17

For parallel polarization: 2

2

〈Hyz 〉 ) |U|z|2, 〈Exz 〉 )

P

|V|z|2, 〈E2zz〉 ) (2π/λ)2 kxP2

|U|z|2 (6)

(2π/λ)2|ˆ j|2 with

[ ]

U|z V|z )

[

ˆ l i (kzl∆z) kzl

cos(kzl∆z) i

kzl ˆ l

[

sin(kzl∆z) cos(kzl∆z)

N

∏ j)l

cos(kzjdj) -i

kzj ˆ j

]

×

ˆ j -i sin(kzjdj) kzj

sin(kzjdj) cos(kzjdj)

][ ]

t| kzD H i | t| ˆ D

For perpendicular polarization: 2

〈Hxz 〉 )

kxP2 1 2 2 2 |V | , 〈H 〉 ) |U⊥z|2, 〈Eyz 〉 ) ⊥z zz (2π/λ)2 (2π/λ)2 |U⊥z|2 (7)

with

[

]

i sin(kzl∆z) U⊥z cos(kzl∆z) × kzl V⊥z ) ikzl sin(kzl∆z) cos(kzl∆z)

[ ]

N

∏ j)l

[

-i sin(kzjdj) kzj -ikzj sin(kzjdj) cos(kzjdj)

cos(kzjdj)

]

[ ]

t⊥ i kzDt⊥ E⊥

where ∆z is the distance of z from the lth/(l - 1)th interface (i.e., l-1 ∆z ) z - Σj)1 dj, see Figure 1), H i| is the magnetic field of the incident radiation with parallel polarization, and E i⊥ is the electric field of the incident radiation with perpendicular polarization. For parallel-polarized radiation, H i| is given in terms of Ei| by H i| ) (P)1/2E i|.17 Since the surface plasmon resonance phenomena can only be observed with a parallel-polarized radiation, eqs 4 and 6 will be employed for the calculations of the reflectance and the electromagnetic field of the system. RESULTS AND DISCUSSION SPR of a Nonabsorbing Dielectric Medium. The most simple and widely employed experimental setup for excitation of (17) Hansen, W. N. J. Opt. Soc. Am. 1968, 58, 380-390.

Figure 2. Conventional angle-scan SPR curves. θC and θSPR indicate the critical angle and the surface plasmon resonance angle, respectively. A comparison between SPR curves obtained via Fresnel equation (solid line) and that via evanescent field integration, eq 11, (dashed line) is shown. Both curves are exactly the same except at an angle of incidence smaller than the critical angle.

the surface plasmon wave at the metal/dielectric interface is the setup according to the Kretschmann-Raether attenuated total reflection (ATR) configuration. In this configuration, a thin noble metal film (i.e., gold or silver with or without an adhesion promoter, for example, chromium or titanium) is deposited to the surface of a high refractive index (i.e., higher than that of the dielectric medium) prism. A nonabsorbing dielectric medium is then brought into contact with the metal film. A parallel-polarized laser beam of the desired wavelength is coupled to the system from the prism side, and the reflected beam is monitored by a detector. The angle of incidence is varied in order to adjust the momentum of the wavevector of the coupled radiation. The surface plasmon wave at the metal/dielectric interface is excited if the wavevector of the coupled beam matches that of the surface plasmon wave. When the surface plasmon wave is excited, a substantial decrease in reflectance is observed at the surface plasmon resonance angle, θSPR.1-3 In a three-phase system consisting of prism/metal film/ nonabsorbing dielectric with P ) 3.4069, ˆ M ) -12.1 + i1.3, dM ) 50 nm, and ˆ D ) 1.778, a conventional angle-scan SPR curve at λ ) 632.8 nm is shown Figure 2. At a small angle of incidence, a large reflection loss is caused by the absorption of the metal film and the transmission of the incident radiation into the dielectric substrate. As the angle of incidence is increasing, the onset of the ATR phenomenon is observed, as the reflectance almost reaches unity, at the critical angle, θC. The critical angle is governed by the refractive indices of prism and dielectric medium and is given by θC ) sin-1[(Re[ˆ D]/P)1/2]. At an angle slightly above the critical angle, a small reflection loss is observed. The reflection loss, in this case, is due to the absorption of the metal film under ATR conditions. As the angle of incidence approaches the resonance angle, a substantial reflection loss is observed due to the surface plasmon resonance phenomenon. For the experimental setup specified above, the resonance angle is θSPR ) 51.56°. Under the ATR condition, evanescent fields are generated at the prism/metal and metal/dielectric interfaces. The evanescent fields are strongest at the interfaces and exponentially decay as a function of the distance from the interface into the metal film and into the dielectric medium, respectively. The evanescent fields associated with the parallel-polarized radiation (i.e., the evanescent magnetic field and the evanescent electric field) at the resonance Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

563

Figure 3. Depth-dependent mean square evanescent fields at the 2 resonance angle of the SPR curve in Figure 2. 〈Hy 〉 is the mean 2 square magnetic field, 〈Ex 〉 is the mean square electric field in the 2 x-direction, 〈Ez 〉 is the mean square electric field in the z-direction, 2 and 〈E| 〉 is the mean square electric field of parallel-polarized 2 2 radiation; 〈E2| 〉 ) 〈Ex 〉 + 〈Ez 〉. Note: The field amplitudes are normalized to the electric field amplitude of the incident radiation. Figure 5. Mean square electric fields of a parallel-polarized radiation at the interfaces (A). z ) 0+ indicates the metal side of the prism/ metal interface while z ) dM- indicates the metal side of the metal/ dielectric interface. A contour plot of the mean square electric field within the metal film (B). The numbers indicate field amplitudes. An integration of the mean square electric field within the metal film (C). The shaded area indicates the angular region to which a very weak mean square electric field at the prism/metal interface is observed.

Figure 4. Evanescent field ratio within the metal film and within the dielectric medium.

angle are shown in Figure 3. The electric field consists of two components: the electric field in the x-direction and the electric field in the z-direction. The magnetic field and the electric field in the x-direction are continuous at the interface. A strong enhancement of the electric field in the z-direction is observed at the metal/ dielectric interface due to the smaller |ˆ D| compared to |ˆ M| (see eq 6). This strong enhancement also makes the electric field in the z-direction discontinuous at the metal/dielectric interface. Figure 4 shows the 〈E 2| 〉/〈H 2y 〉 ratio within the metal film and the dielectric medium at the resonance angle. The ratio within the dielectric medium is constant while that within the metal film varies as a function of the distance from the prism. The evanescent field within the metal film is a convolution of two evanescent fields; one is generated at the prism/metal interface and the other at the metal/dielectric interface. The small evanescent field at the prism/metal interface generated under ATR conditions is constant throughout the angular region except in the vicinity of the resonance angle. The stronger evanescent field generated at the metal/dielectric interface via surface plasmon resonance, on the other hand, varies considerably. Its strength at the interface is greatest near the resonance angle while that at the angle far away from the resonance angle is very small (see Figure 5A). The existence of two evanescent fields within the metal film can be recognized by a nonzero evanescent field at the prism/metal interface and a small dip of the magnetic field near the prism/ metal interface (see Figure 3). Both magnetic field and electric field have the maximums at their respective interfaces of origins and decay exponentially as a function of distance from the 564

Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

interfaces. The evanescent field decay within the metal film is complicated since it is governed not only by the evanescent nature of the field but also by the absorption and the thickness of the metal film. Due to the convolution of the two fields and the absorption of metal film, the 〈E 2| 〉/〈H 2y 〉 ratio within the metal film is not constant. The evanescent field within the metal film can be calculated when the thickness and the dielectric constants of all media are known. The evanescent field in the dielectric medium, on the other hand, has a single origin at the metal/dielectric interface. Its decay characteristic can be expressed in terms of the wavevector and the evanescent field amplitude at the metal/dielectric interface by 2

〈Hyz 〉 2 〈H y,z)d 〉 M+

2

)

〈Exz 〉 2 〈E x,z)d 〉 M+

2

)

〈Ezz 〉 2 〈E z,z)d 〉 M+

)

e-2Im[kzD](z-dM) ) e-2(z-dM)/dP (8) 2 2 2 where 〈H x,z)d 〉, 〈E z,z)d 〉, and 〈H y,z)d 〉 are the mean square M+ M+ M+ evanescent fields at the metal/dielectric interface (on the dielectric 2 2 2 side) and 〈Exz 〉, 〈Exz 〉, and 〈Hyz 〉 are those at a distance z from the prism/metal interface. According to eq 6, the mean square evanescent fields at the metal/dielectric interface (on the dielectric side) are given in terms of the Fresnel transmission coefficient by

xPkzD t |2, 2 2 〉 ) |t||2, 〈E x,z)d 〉)| 〈H y,z)d M+ M+ (2π/λ)D | kxP 2 〈E z,z)d 〉)| t |2 (9) M+ (2π/λ)ˆ D |

The penetration depth, dp, can be expressed in terms of the dielectric constants by

dp )

λ 2π(P sin θ - Re[ˆ D])1/2 2

(10)

For conventional SPR with a nonabsorbing dielectric, the only absorbing medium in the system is the metal film (i.e., Im[ˆ M] * 0). According to the principle of energy conservation (i.e., R + T + A ) 1) and if there is no other cause of energy loss in the system beside absorption by the metal film, the reflectance R is given in terms of the mean square electric field and material characteristics by18

R)1-A)1-

(2πλ) k1 ∫ 2

dM

zP

0

Im[ˆ M]〈E|z2〉 dz

(11)

where A is the absorption of the metal film in absorptance unit. Note: Under ATR conditions, the transmittance T always equals zero. In the conventional SPR, the reflectance is governed by the strength and decay characteristic of the evanescent field within the metal film and the imaginary part of the dielectric constant of the metal at the excitation wavelength. Figure 5 shows strengths and decay characteristic of the mean square electric field of the system given in Figure 2. According to eq 11, and the depthdependent nature of the evanescent field (see Figure 3), the surface plasmon wave-generated evanescent field is responsible for most of the reflection loss in the vicinity of the resonance angle. The evanescent field generated under ATR conditions, on the other hand, induces a negligible reflection loss near the resonance angle. A small reflection loss due to the ATR-generated evanescent field at the angle far away from the resonance angle is observed as the baseline of the SPR curve. According to Figure 5A, the electric field at the metal/dielectric interface (on the metal side) is asymmetric about the angle with the maximum electric field amplitude, θEF, in the same fashion as that of the SPR curve about the resonance angle, θSPR. However, the angle with the maximum mean square electric field is slightly smaller than the resonance angle. This discrepancy is due to the fact that the reflection loss is governed by not only the mean square electric field at the metal/dielectric interface but also its decay characteristic within the metal film. Figure 5B indicates that the mean square electric field at the angle greater than θEF decays slower than that smaller than θEF. The slower field decay is identified by a larger separation between contour lines with contour maximums tailing toward a greater angle. This unique characteristic of the evanescent field decay within the metal film makes the field integration having the maximum at an angle slightly greater than θEF (see Figure 5C). The angle with maximum field integration is, in fact, θSPR. The absorptance defined in eq 11 is the product of the field integration, the imaginary part (18) (a) Harrick, N. J. Internal Reflection Spectroscopy; Harrick Scientific Corp.: New York, 1987. (b) McIntyre, J. D. E. In Optical Properties of Solids: New Developments; Seraphin, B. O. Ed.; North-Holland Publishing Co.: Amsterdam, 1967; pp 555-630. (c) Ekgasit, S. Appl. Spectrosc. 1998, 52, 773776. (d) Ekgasit, S. Appl. Spectrosc. 2000, 54, 756-758. (e) Ekgasit, S.; Padermshoke. A. Appl. Spectrosc. 2001, 55, 1352-1359.

Figure 6. Angle-scan SPR curves with different thicknesses of chromium adhesion-promoting layers. The shaded area (corresponding to that in Figure 5) indicates the angular region to which a relatively unchanged reflectance is observed.

of the dielectric constant of the metal, and a constant (2π/λ)2. The mean square electric field at the interfaces and its decay characteristics within the metal film make the SPR curve asymmetric where tailing is observed at angles greater than θSPR. A comparison between SPR curves calculated via evanescent field integration (i.e., via eq 11) and that via the Fresnel reflection coefficient (i.e., via eq 4) is shown in Figure 2. There is no difference between both curves at an angle greater than the critical angle. At an angle below the critical angle, however, there is a significant difference between both curves. This is due to the validity of eq 11 that it can only be applied under the condition where an evanescent field exists. The evanescent field does not exist below the critical angle. The strong surface plasmon wave-generated evanescent field is governed by experimental parameters and material characteristics. The magnitudes of the evanescent field and the resonance angle are very sensitive to changes in any of the governing parameters. This unique characteristic makes SPR an exceptionally sensitive technique for the determination of changes of the dielectric medium in contact with the metal film. As a result, SPR became a powerful surface-sensing technique for detecting and monitoring any chemically or physically related phenomena that can induce refractive index variations of the medium in contact with the metal surface. A very high field strength at the metal/dielectric interface compared to that at the prism/metal interface and the exponential decay characteristic of the evanescent field make the SPR signal at the vicinity of the resonance angle less sensitive to properties of the metal film near the prism/metal interface. Since the absorption of metal at a distance z is proportional to the mean square electric field at that distance, the metal near the prism/ metal interface contributes a much smaller absorption to the SPR curve compared to that near the metal/dielectric interface. This unique characteristic makes reflectance near θSPR of systems with different thickness of the additional adhesion-promoting metal film almost the same (Figure 6). Figure 5A indicates that the evanescent field at the prism/metal interface is very small near the resonance angle, especially at the angular region slightly lower than the resonance angle. In other words, within this angular region, the strong evanescent field generated at the metal/ dielectric interface does not see the additional metal film on the surface of the prism. As a result, within the shaded angular region shown in Figures 5 and 6, a small difference in thickness of the Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

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adhesion-promoting metal films does not make a significant discrepancy in the observed SPR signals. Absorption of the adhesion-promoting metal film (in this case chromium) is characterized by a shift of the baseline of the SPR curve (see Figure 6). The shift is greater as the binding layer become thicker. Although this adhesion-promoting layer is thin and the mean square electric field at the prism/metal interface is small, a large imaginary part of the dielectric constant of the adhesion-promoting metal film makes its absorption large enough and causes a significant shift of the baseline. The absorption of the adhesion-promoting metal film is the major cause for reflection loss in the SPR curve at an angle far from the resonance angle where the evanescent field at the prism/metal interface is greater than that at the metal/dielectric interface. A small decrease in reflection loss and a minor resonance angle shift to a greater angle are observed if the thickness of the adhesion-promoting layer is increased. As the thickness of the layer is increasing from 0 to 1.5 nm, the minimum reflectance changes from 0.0124 to 0.0172 and the resonance angle shifts from 51.56° to 51.58°. SPR of an Absorbing Dielectric Medium. One of the prominent features of the evanescent field distribution in an SPR system is the exceptionally strong evanescent field in the vicinity of the metal/dielectric interface (see Figure 3). The mean square electric field at the metal/dielectric interface on the dielectric side is greater than that on the metal side due to the smaller |ˆ D| compared to |ˆ M|. In conventional SPR, in which changes in refractive index of nonabsorbing dielectric media on the metal surface are of interest, the high electric field in the dielectric medium is not being utilized. Although the nonabsorbing dielectric medium does not have any contribution to the reflection loss of the SPR curve because of its zero absorption coefficient, a minute change in its refractive index does alter the evanescent field distribution within the metal film and within the dielectric medium itself. This alteration results in a shift of the resonance angle but not in a change of the reflectance at the resonance angle. Techniques for enhancing SPR sensitivity are being explored by employing absorbing dielectric media such as gold and silver nanoparticles in nanoparticle-assisted SPR12-14 or by using fluorophores in surface plasmon field-enhanced fluorescence spectroscopy.15 The system becomes more complicated and the quantitative analysis more difficult because both the metal film and the dielectric medium are absorbing. Moreover, the evanescent field distribution within the metal film and the dielectric medium is significantly altered by the absorbing dielectric. This feature is noted by a shift of the resonance angle, a decrease of reflection loss, and a broader SPR curve.12,14 In an SPR setup involving an absorbing dielectric medium (AD) with a system configuration consisting of prism/chromium binding layer/gold film/absorbing dielectric/nonabsorbing dielectric substrate with P ) 3.4069, ˆ Cr ) -4.0 + i18, dCr ) 1.5 nm, ˆ Au ) -12.1 + i1.3, dAu ) 50 nm, ˆ AD ) 2.125 + i0.66, and ˆ D ) 1.813, the simulated SPR curves based on these dielectric constants with different thicknesses of absorbing dielectric film are shown in Figure 7A. The resonance angle shifts to a greater value and the reflection loss is smaller while the SPR curve becomes broader as a thicker film of the absorbing dielectric is employed. The resonance angles and the minimum reflectance are 52.46°, 53.06°, 53.68°, and 54.31° and 0.020, 0.153, 0.260, and 0.337, respectively, 566

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Figure 7. Angle-scan SPR curves with different thicknesses of absorbing dielectric film (A) and those of nonabsorbing dielectric film (B).

with thicknesses of the absorbing dielectric of 0, 5, 10, and 15 nm. The resonance angle becomes less obvious as the thickness of the absorbing medium increases. For comparison, SPR curves of a nonabsorbing dielectric film of the same refractive index and layer architecture are shown in Figure 7B. The resonance angle increases while the reflectance minima at the resonance angles and the shape of the SPR curves stay the same as the thickness of the nonabsorbing dielectric increases. The resonance angle increases linearly with the thickness of the nonabsorbing dielectric film. The resonance angles and the minimum reflectance are 52.46°, 52.83°, 53.20°, 53.57° and 0.020, 0.020, 0.020, 0.020, respectively, with the thickness of the nonabsorbing dielectric of 0, 5, 10, and 15 nanometers. The magnitude of the resonance angle shift in the system with a nonabsorbing dielectric film is slightly smaller than that with an absorbing dielectric film. According to the SPR curves in Figure 7A, due to the presence of additional absorbing films, the reflectance of the system can be expressed in terms of the mean square electric field and the dielectric constants of all absorbing media by18

R(θ) ) 1 -

(2πλ) k1 {∫ 2

zP

∫

dCr

0

Im[ˆ Cr]〈E|z2(θ)〉 dz +

dCr+dAu

Im[ˆ Au]〈E|z2(θ)〉 dz +

dCr

∫

dCr+dAu+dAD

dCr+dAu

Im[ˆ AD]〈E|z2(θ)〉 dz} (12)

In Figure 7A, a smaller reflection loss with a thicker film of the absorbing dielectric can be explained via electric field alteration due to the absorbing dielectric film. Since the electric field near the resonance angle is very sensitive to changes at the metal/dielectric interface, a minor change of the thickness, dielectric constant, or both of the absorbing dielectric film can significantly alter the electric field amplitude at the interface and its decay pattern, as shown in Figure 8A. The interface between two media (i.e., chromium/gold, gold/absorbing dielectric, and

Figure 8. Depth-dependent mean square electric fields at the corresponding resonance angles of SPR curves in Figure 7: absorbing dielectric film (A) and nonabsorbing dielectric film (B). In (B), the mean square electric fields in the metal film with different thicknesses of nonabsorbing dielectric films cannot be differentiated by the graphical illustration. Note: The field amplitudes are wavevector corrected.

absorbing dielectric/nonabsorbing dielectric) can be identified by a discontinuity of the mean square electric field due to the change of the dielectric constant at the interface. The mean square electric field (on the dielectric side) is greatly enhanced at the metal/ dielectric interface. However, the magnitude of enhancement decrease significantly as the thickness of the absorbing dielectric (and hence the absorption) is increasing. The field amplitude within the metal film and the dielectric media decrease significantly as the absorbing dielectric with greater absorption present. The greater the absorption, the smaller the mean square electric field. Although the thickness of the absorbing dielectric is increasing, the product between the mean square electric field and the imaginary part of the dielectric constant, as defined in eq 12, is getting smaller. As a result, the reflectance at the resonance angle increases as the absorbing dielectric film becomes thicker. A shift of the resonance angle to a greater value is due largely to the increase in thickness of the dielectric film. However, insignificant changes of the evanescent field at the prism/chromium and chromium/gold interfaces are observed as the thickness of the absorbing dielectric increases. Figure 8B shows the corresponding electric field decays at the resonance angles of the SPR curves in Figure 7B. The electric field (on the dielectric side) is greatly enhanced at the metal/ dielectric interface. A smaller enhancement is observed when the nonabsorbing dielectric film (with higher refractive index) is present. Similar to that of the absorbing dielectric film, the thickness of the nonabsorbing dielectric film can be noted by a step increase of the mean square electric field due to a decrease of the dielectric constant at the interface. The strong electric field in the nonabsorbing dielectric media does not have any contribution to the reflection loss in the SPR curve. The presence of the nonabsorbing dielectric film does not significantly change the amplitude and decay pattern of the electric field within the metal film. However, the resonance angle shifts to a greater value as

Figure 9. SPR absorption curves of all absorbing media at different thicknesses of the absorbing dielectric film in Figure 7A: adhesionpromoting chromium film (dotted lines), gold film (solid lines), and absorbing dielectric film (dashed lines).

the thickness of the nonabsorbing dielectric film increases. As a result, the SPR curve still possesses the same peak shape and reflectance minimum at the resonance angle. The reflectance minimum insignificantly increases as the thickness of the nonabsorbing dielectric film increases. The absorption of each absorbing layer that contributes to the reflection loss of the SPR curve is shown in Figure 9. In the system without the absorbing dielectric film (Figure 9A), the major cause of reflection loss is the absorption of the gold film. The chromium layer, although having a larger imaginary part of the dielectric constant compared to that of gold, possesses a very small absorption due to its small thickness and the weak mean square electric field near the prism/chromium interface. However, the absorption of chromium can be noticed at angles far away from the resonance angle. Due to the relatively constant mean square electric field at the prism/chromium interface (see Figure 8A), the absorption of the chromium layer does not change significantly as the thickness of the absorbing dielectric increases. As the thickness of the absorbing dielectric film increases, the absorption of the dielectric increases while that of gold film becomes smaller. The decrease of the absorption of gold is due to the smaller mean square electric field within the gold film. The absorption of the absorbing dielectric at the resonance angle reaches a maximum value before it starts to decrease again (Figure 9B-D). This is due to the decrease of the mean square electric field within the absorbing dielectric film as the thickness of the film is increasing. The angle with maximum absorption of the absorbing dielectric film is slightly smaller than that of the metal film. This difference is a contributing factor to the broadening of the SPR curve of the absorbing dielectric film (as shown in Figure 7A). Although the imaginary part of the dielectric constant of gold is much greater than that of the absorbing dielectric, its absorption Analytical Chemistry, Vol. 76, No. 3, February 1, 2004

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is smaller if the absorbing dielectric is thick enough (but still thinner than that of gold). This is due to the optical enhancement of the mean square electric field at the metal/dielectric interface and the slow evanescent field decay within the dielectric medium. This unique characteristic makes SPR very sensitive to absorbing media, although the film thickness of the absorbing medium is very thin or consists of objects (nanoparticles, molecules, etc.) of low concentration. The exceptionally high mean square electric field in dielectric medium is responsible for the extremely high sensitivity of surface plasmon field-enhanced fluorescence and nanoparticle-assisted SPR.12-14 From Figure 9, the angle at which the absorption of the absorbing dielectric film reaches a maximum is slightly smaller than that of the gold film (and the resonance angle). The phenomenon is more obvious if the absorption of the dielectric medium is small. This unique characteristic can be observed experimentally in surface plasmon field-enhanced fluorescence experiments where the angle of the peak maximum of the fluorescence curve is slightly lower than the resonance angle.15 The phenomenon can be attributed to the angle-dependent nature of the exciting wavevector of the incident radiation as it travels from prism through the metal film and the dielectric media and due to the evanescent field decay within the media. CONCLUSIONS The reflection loss seen in the SPR curve can be assigned to the absorption of all absorbing media in the system. It can be quantified in terms of the product between the mean square electric field and the dielectric constant of the absorbing media. The evanescent field within the meal film consists of two fields:

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a weak evanescent field at the prism/metal interface generated under ATR conditions and a strong evanescent field at the metal/ dielectric interface generated by the surface plasmon wave. The mean square electric field within the dielectric medium is much greater than that in the metal film due to the optical enhancement at the metal/dielectric interface. This unique characteristic enables further enhancement of the sensitivity and improvement of the detection limit of SPR-based sensors by incorporation of an absorbing medium. For a nonabsorbing dielectric medium, the refractive index variation or thickness change does not significantly alter the amplitude and decay profile of the evanescent field but shifts the angle with field maximum (and hence the resonance angle). Peak shape of the SPR curve and the reflectance minimum at the resonance angle stay the same as the thickness, refractive index, or both of the nonabsorbing dielectric changes. An absorbing dielectric medium, on the other hand, significantly decreases the evanescent field amplitude and alters its decay profile. The SPR curve becomes broader, and the minimum reflectance at the resonance is larger as an absorbing medium with a greater absorption is employed. ACKNOWLEDGMENT S.E. gratefully acknowledges support from the Thailand Research Fund (TRF Contract RSA/07/2545) and a research fellowship from the Alexander von Humboldt (AvH) Foundation.

Received for review September 5, 2003. Accepted October 9, 2003. AC035042V