3456 OPTICS LETTERS / Vol. 32, No. 23 / December 1, 2007

Full-field and real-time surface plasmon resonanceimaging thermometry

Il Tai Kim and Kenneth David Kihm*Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville,

Tennessee 37996, USA*Corresponding author: kkihm@utk.edu

Received September 7, 2007; revised October 28, 2007; accepted October 31, 2007;posted November 6, 2007 (Doc. ID 87335); published November 29, 2007

The feasibility of surface plasmon resonance (SPR) imaging thermometry is tested as a potential tool forfull-field and real-time temperature field mapping for thermally transient liquid mediums. Using the well-known Kretschmann’s analysis [Physik 241, 313 (1971)]. parametric examinations are performed to delin-eate the effects of important optical properties, including seven different prism materials with different re-fractive index values and seven different measured dielectric constants for thin gold (Au) films(approximately 47.5 nm in thickness), on the temperature dependence of SPR reflectance intensity varia-tions. Furthermore, a laboratory-implemented real-time SPR thermometry system demonstrates the full-field mapping capabilities for transient temperature field developments in the near-wall region when a hotwater droplet �80°C� contacts the Au metal surface �20°C� and spreads either in an air- or in a water-surrounded environment. © 2007 Optical Society of America

OCIS codes: 240.6680, 120.6780.

Despite the known best sensitivity of SPR to the re-fractive index of the contacting medium [as fine as10−8 refractive index units (RIU) [1]], the SPR ther-mometry technique utilizing the refractive index–temperature (T) correlation has not been well ex-ploited to date. Limited SPR thermometry tests havebeen conducted to examine a single-point tempera-ture detection of thin metal films [2–5]. None of theseresults, however, supplies temperature measure-ments in a full-field and real-time manner. Note thatneither incident-angle scans [2,3] nor incident-wavespectral scans [5,6] can provide a “real-time” detec-tion of transient test fields. At present, SPR imagingat a fixed angle is devised to allow real-time record-ing of transient thermal phenomena.

The refractive index of the prism and the refractiveindex of the thin Au film coated on the prism are ex-amined using the Fresnel theory [7] to determinetheir effects on the temperature dependence of SPRreflectance intensity. Based on the examinations, themost desirable selection of design parameters is pro-posed for improved measurement sensitivities forSPR thermometry.

The SPR reflectance R, for a three-layer configura-tion [Fig. 1(a)] with the prism (1), the thin metal film(2), and a test medium (3), is given as

R�T� = R�n1�T�,n2�T�,n3�T�,d2,�I,��, �1�

where n is the refractive index, d2 is the Au filmthickness, �I is the incident ray wavelength, and � isthe incident ray angle. For the case of fixed d2�=47.5 nm� and �I �=632.8 nm�, R varies exclusivelywith the refractive indices of n1, n2, and n3.

The temperature dependence of the refractive in-dex of the prism, n1, is assumed to be negligibly small[5]. The refractive index of a thin metal film, n2, isgiven by the Drude model [8] as

0146-9592/07/233456-3/$15.00 ©

n2�T� = nr + ini = ��2 =�1 −�p

2

��� + i�c�, �2�

where � is the angular frequency of the incident-wave field and �p�T� and �c�T� are the plasmon fre-quency [9] and the collision frequency [10] of the thinmetal film material, respectively. Note that bothtemperature-dependent frequencies �p and �c alterthe resulting SPR reflectance R. The temperature de-pendence of the test medium n3�T� of water is pro-vided from the CRC Handbook [11].

Fig. 1. SPR reflectance R as a function of water tempera-ture for seven different prism materials using the dielectricconstant of Kolomenskii et al. [12] for a thin Au film of

47.5 nm thickness.

2007 Optical Society of America

December 1, 2007 / Vol. 32, No. 23 / OPTICS LETTERS 3457

Figures 1(b) and 1(c) show the temperature depen-dence of SPR reflectance for the seven differenttested prism materials using water as the test me-dium. The SPR optimum angle is set for water at80°C. The plasma frequency �p0 needs to be experi-mentally determined using at least one refractive in-dex value measured at a specified temperature tocomplete the calculations. The data from Kolomen-skii et al. [12] are selected to calculate �p0 and deter-mine n2�T�, and successively R�T� from Eq. (1).

The BK 7 prism shows the steepest gradients andthe highest SPR reflectance intensity, whereas theSF 11 prism shows the lowest SPR reflectance inten-sity. As the refractive index of the prism, n1, in-creases, R decreases consistently. Among the sevenmaterials tested, the BK 7 prism seems to show thehighest sensitivity for the temperature dependence ofSPR reflectance when water is the test medium.

Figure 2(a) shows the R–T correlations for sevendifferent sets of published refractive index data forthin Au films with thicknesses ranging from45 to 48 nm (except for Palik’s case for 10–25 nmthicknesses), and Fig. 2(b) shows the correspondingnormalized R–T correlations. The seven measuredrefractive index values [12–18] for thin Au films ofapproximately the same thickness show deviationsbetween them that may be attributed to differentmeasurement techniques and the preparation of thespecimens, such as differences in surface roughness,dimensional uncertainties, and differences in fabrica-

Fig. 2. SPR reflectance R as a function of water tempera-ture for seven different refractive index values measuredfor thin metal films of approximately 47.5 nm thickness,

coated on the top surface of a BK 7 prism �n2=1.515�.

tion processes. The largest deviation of �2r is approxi-mately 15% [12] over the average, while the largestdeviation of �2i is up to 50% [18] above the average.On the other hand, the SPR optimum angle �SPRshows a mere ±2.5% deviation, and this can be par-tially attributed to the dominating dependence of�SPR on �2r, with its relatively narrower deviationrange, compared with �2i [19].

The R–T correlation gradient, �R /�T, representsthe sensitivity of the SPR reflectance change corre-sponding to a unit temperature change; thus, thesteepest gradient shown for the Kolomenskii et al.data [Fig. 2(a)] is expected to provide the highestmeasurement sensitivity. The data from both Snopoket al. [17] and Peterlinz et al. [18] are considered in-appropriate because of the deflections occurring forT�60°C [more clearly visible in Fig. 2(b)].

The experimental setup for full-field and real-timeSPR reflectance imaging thermometry [Fig. 3(a)] isdesigned and fabricated based after Kretschmann’sconfiguration of [7]. The system uses a BK 7 prismwith 47.5 nm thick Au film coated on its top surface.Example results of SPR thermometry measurementsare presented for dynamic temperature field develop-ments when a hot water droplet at 80°C contacts theAu film surface at 20°C and spreads either in an airenvironment [Fig. 3(b)] or a water environment [Fig.3(c)]. The most favored R–T correlation, based on theKolomanskii et al.’s n2, is used to convert the re-corded SPR image intensity distributions into corre-sponding temperature fields. The gradual heat andenergy transport under the air environment allowsthe contact surface shape to remain circular andspread concentrically, and the surface temperaturegradually decreases to the environmental level after16 s. In the cold-water environment, however, the ag-gressive single-phase mass and energy diffusion ofhot water deforms the contact surface shape andspread, and the contact surface temperature rapidlyapproaches the environmental level in the relativelyshort time period of 1 s.

The temporal resolution of SPR thermometry de-pends exclusively on the data acquisition rate of theCCD camera recording system (6.4 ms or156 frames/s for the present condition), while thespatial resolution is known to be specified equivalentto the propagation length of a surface plasmon wave,which is a function of the incident ray’s wavelength,the dielectric constant of the thin metal film, and thedielectric constant of the test medium [20]. For thepresent experiment, the theoretically minimum spa-tial resolution is estimated to be approximately4.5 �m.

Using the Klein–McClintock analysis [21] consider-ing the elementary uncertainties [22], the overallmeasurement uncertainty of T is estimated tobe±1.85°C (3.3% in R) at 20°C and ±1.41°C (9.8%in R) at 70°C. The relative large uncertainty levelsare mainly attributed, firstly, to the excessive el-ementary uncertainties of the dielectric constant ofthe Au film and, second, to the fabrication uncertain-ties of the Au film thickness. The elementary uncer-

tainty for the fluctuation of light intensity of highly

3458 OPTICS LETTERS / Vol. 32, No. 23 / December 1, 2007

DC regulated power supply is considered negligiblysmall.

The present real-time SPR thermometry at a fixedSPR angle tends to increase the measurement uncer-tainties at the lower temperature range, and its mea-surement accuracy critically depends upon the thick-ness and dielectric constant of the Au thin film.Therefore it is recommended that the dielectric con-stant of Au film be more accurately determined andthat the film thickness be more precisely fabricated.

References

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Fig. 3. Full-field and real-time mapping of transient tem-perature fields when a hot water droplet �80°C� falls on thecold Au surface �20°C� in (a) air environment and(b) water environment.

2. H.-P. Chiang, H.-T. Yeh, C.-M. Chen, J.-C. Wu, S.-Y. Su,

R. Chang, Y.-J. Wu, D. P. Tsai, S. U. Jen, and P. T.Leung, Opt. Commun. 241, 409 (2004).

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7. E. Z. Kretschmann, Physik 241, 313 (1971).8. H. P. Chaing, P. T. Leung, and W. S. Tse, J. Chem.

Phys. 108, 2659 (1998).9. �p=�p0�1+3��T−T0��−1/2, where �p0 is the plasma

frequency at reference temperature T0 and � is thethermal linear expansion coefficient of thin metalfilm.

10. �c=�cp+�ce, where the photon–electron scatteringfrequency is defined as �cp�T�=�0�2/5+4�T /TD�5��0

TD/Tz4 /ez−1dz and the electron–electronscattering frequency is �ce�T�=1/64� /hEF��kBT�2

+ �h� /42�2�. Parametric values used forcalculations throughout are constant coefficient �0=1.438�10−14 rad/s, Debye temperatureTD=170 K, Fermi energy EF=5.53 eV, Boltzmannconstant kB=1.3807�10−23 J/K, and scatteringprobability =0.55, Fractional Umklapp scatteringcoefficient �=0.77, Planck constant h=6.262620�10−34 Js, and thermal linear expansion coefficient�=1.42�10−5 K−1

11. D. R. Lide, CRC Handbook of Chemistry and Physics(CRC Press, 2005).

12. A. A. Kolomenskii, P. D. Gershon, and H. A.Schuessler, Appl. Opt. 36, 6539 (1997).

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18. K. A. Peterlinz and R. Georgiandis, Langmuir 12, 4731(1996).

19. The optimum SPR angle is given as �spr=sin−1�1/np��m�s /�m+�s�1/2� from the Kretschmanntheory [7].

20. C. E. H. Berger, R. P. H. Kooyman, and J. Greve, Rev.Sci. Instrum. 65, 2829 (1994).

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22. Estimated elementary uncertainties: �dm=47.5 nm

� ±1.25% �=±0.59375 nm�, ��m= ±0.002115

+ ± i0.081 ��m=−13.2+ i1.25�, ��= ±1.0/60°= ±0.0167°, ��= ±1.5 nm, �T= ±0.1°C where dm isthe thickness of the Au layer �47.5 nm�, � is theincident SPR angle optimized for water temperatureof 80°C (69.47°), and � is the incident wavelength

�632.8 nm�.