A spectral method based on surface plasmon resonance (SPR) in air is used to measure the dielectric function of a thin metal film. The method utilizes the spectral dependence of the ratio of the reflectances of p- and s-polarized waves measured in the Kretschmann configuration at different angles of incidence. By processing these dependences in the vicinity of a dip, or equivalently near the resonance wavelength, and using the dispersion characteristics of a metal film according to a proposed physical model, the real and imaginary parts of the dielectric function of the metal can be determined. The corresponding dielectric function of the metal is obtained by a least squares method for such a thickness minimizing the difference between the measured and theoretical dependence of the resonance wavelength on the the angle of incidence. The feasibility of the method is demonstrated in measuring the dielectric function of a gold film of an SPR structure comprising an SF10 glass prism and a gold coated SF10 slide with an adhesion film of chromium. The dielectric function according to the Drude⁻Lorentz model with two additional Lorentzian terms was determined in a wavelength range from 534 to 908 nm, and the results show that the gold film is composed of homogenous and rough layers with thicknesses 42.8 nm and 2.0 nm, respectively. This method is particularly useful in measuring the thickness and dielectric function of a thin metal film of SPR structures, directly in the Kretschmann configuration.

Department of Physics Technical University Ostrava 17 listopadu 15 708 33 Ostrava Poruba Czech Republic

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Kretschmann E., Raether H. Radiative decay of nonradiative surface plasmons excited by light. Z. Naturforsch. 1968;A23:2135–2136.

Otto A. Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection. Z. Phys. 1968;216:398–410. doi: 10.1007/BF01391532. DOI

Raether H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings. Springer; New York, NY, USA: 1988.

Manuel M., Vidal B., Lopéz R., Alegret S., Alonso-Chamarro J., Garces I., Mateo J. Determination of probable alcohol yield in musts by means of an SPR optical sensor. Sens. Actuators B. 1993;11:455–459. doi: 10.1016/0925-4005(93)85287-K. DOI

Homola J. Surface Plasmon Resonance Based Sensors. Springer; New York, NY, USA: 2006.

Pitarke J.M., Silkin V.M., Chulkov E.V., Echenique P.M. Theory of surface plasmons and surface-plasmon polaritons. Rep. Prog. Phys. 2007;70:1–87. doi: 10.1088/0034-4885/70/1/R01. DOI

Nikitin P., Beloglazov A., Kochergin V., Valeiko M., Ksenevich T. Surface plasmon resonance interferometry for biological and chemical sensing. Sens. Actuators B. 1999;54:43–50. doi: 10.1016/S0925-4005(98)00325-6. DOI

Liedberg B., Nylander C., Lundström I. Principles of biosensing with an extended coupling matrix and surface plasmon resonance. Sens. Actuators B. 1993;11:63–72. doi: 10.1016/0925-4005(93)85239-7. DOI

Dostálek J., Vaisocherova H., Homola J. Multichannel surface plasmon resonance biosensor with wavelength division multiplexing. Sens. Actuators B. 2005;108:758–764. doi: 10.1016/j.snb.2004.12.096. DOI

Gwon H.R., Lee S.H. Spectral and angular responses of surface plasmon resonance based on the Kretschmann prism configuration. Mater. Trans. 2010;51:1150–1155. doi: 10.2320/matertrans.M2010003. DOI

El-Gohary S.H., Choi M., Kim Y.L., Byun K.M. Dispersion curve engineering of TiO2/silver hybrid substrates for enhanced surface plasmon resonance detection. Sensors. 2016;16:1442. doi: 10.3390/s16091442. PubMed DOI PMC

Meng Q.Q., Zhao X., Lin C.Y., Chen S.J., Ding Y.C., Chen Z.Y. Figure of merit enhancement of a surface plasmon resonance sensor using a low-refractive-index porous silica film. Sensors. 2017;17:1846. doi: 10.3390/s17081846. PubMed DOI PMC

Shalabney A., Abdulhalim I. Figure-of-merit enhancement of surface plasmon resonance sensors in the spectral interrogation. Opt. Lett. 2012;37:1175–1177. doi: 10.1364/OL.37.001175. PubMed DOI

Hlubina P., Duliakova M., Kadulova M., Ciprian D. Spectral interferometry-based surface plasmon resonance sensor. Opt. Commun. 2015;354:240–245. doi: 10.1016/j.optcom.2015.06.011. DOI

Suvarnaphaet P., Pechprasarn S. Quantitative crossp-platform performance comparison between different detection mechanisms in surface plasmon sensors for voltage sensing. Sensors. 2018;18:3136. doi: 10.3390/s18093136. PubMed DOI PMC

Hlubina P., Ciprian D. Spectral phase shift of surface plasmon resonance in the Kretschmann configuration: Theory and experiment. Plasmonics. 2017;12:1071–1078. doi: 10.1007/s11468-016-0360-9. DOI

Kaňok R., Ciprian D., Hlubina P. Sensing of liquid analytes via the phase shift induced by surface plasmon resonance. Proc. SPIE. 2018;10680:106801Q.

de Bruijn H.E., Kooyman R.P.H., Greve J. Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment. Appl. Opt. 1990;29:1974–1978. doi: 10.1364/AO.29.001974. PubMed DOI

Pokrowsky P. Optical methods for thickness measurements on thin metal films. Appl. Opt. 1991;30:3228–3232. doi: 10.1364/AO.30.003228. PubMed DOI

Posudievsky O., Samoylov A., Surovtseva E., Khristosenko R., Kukla A., Shirshov Y. Extraction of optical constants of polyaniline thin films by surface plasmon resonance. Thin Solid Films. 2008;515:6104–6109. doi: 10.1016/j.tsf.2007.11.010. DOI

Fujiwara H. Spectroscopic Ellipsometry: Principles and Applications. John Wiley and Sons Ltd.; Chichester, UK: 2007.

Zhang M.Y., Wang Z.Y., Zhang T.N., Zhang Y., Zhang R.J., Chen X., Sun Y., Zheng Y.X., Wang S.Y., Chen L.Y. Thickness-dependent free-electron relaxation time of Au thin films in near-infrared region. J. Nanophotonics. 2016;516:033009. doi: 10.1117/1.JNP.10.033009. DOI

Hu E.T., Cai Q.Y., Zhang R.J., Wei Y.F., Zhou W.C., Wang S.Y., Zheng Y.X., Wei W., Chen L.Y. Effective method to study the thickness-dependent dielectric functions of nanometal thin film. Opt. Lett. 2016;41:4907–4910. doi: 10.1364/OL.41.004907. PubMed DOI

Sun X., Hong R., Hou H., Fan Z., Shao J. Thickness dependence of structure and optical properties of silver films deposited by magnetron sputtering. Thin Solid Films. 2007;515:6962–6966. doi: 10.1016/j.tsf.2007.02.017. DOI

Qi Z.M., Wei M., Matsuda H., Honma I., Zhou H. Broadband surface plasmon resonance spectroscopy for determination of refractive index dispersion of dielectric thin films. Appl. Phys. Lett. 2007;90:181112. doi: 10.1063/1.2734898. DOI

Yan H., Hong-An Y., Song-Quan L., Yin-Feng D. The determination of the thickness and the optical dispersion property of gold film using spectroscopy of a surface plasmon in the frequency domain. Chin. Phys. B. 2013;22:027301.

Kanso M., Cuenot S., Louarn G. Roughness effect on the SPR measurements for an optical fiber configuration: Experimental and numerical approaches. J. Opt. A Pure Appl. Opt. 2007;9:586–592. doi: 10.1088/1464-4258/9/7/008. DOI

Born M., Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th ed. Cambridge University Press; Cambridge, UK: 1999.

Yeh P. Optical Waves in Layered Media. John Wiley and Sons, Inc.; New York, NY, USA: 1988.

Bach H., Neuroth N., editors. The Properties of Optical Glass. Springer; Berlin/Heidelberg, Germany: 1998.

SCHOTT Technical Information, TIE-29: Refractive Index and Dispersion. [(accessed on 15 October 2018)]; Available online: https://www.us.schott.com.

SCHOTT Technical Information, TIE-29: Temperature Coefficient of the Refractive Index. [(accessed on 15 October 2018)]; Available online: https://www.us.schott.com.

Vial A., Laroche T. Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method. J. Phys. D Appl. Phys. 2007;40:7152–7158. doi: 10.1088/0022-3727/40/22/043. DOI

Vial A., Grimault A.S., Macías D., Barchiesi D., de la Chapelle M.L. Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method. Phys. Rev. B. 2005;71:085416. doi: 10.1103/PhysRevB.71.085416. DOI

Yang Z., Gu D., Gao Y. An improved dispersion law of thin metal film and application to the study of surface plasmon resonance phenomenon. Opt. Commun. 2014;329:180–183. doi: 10.1016/j.optcom.2014.05.014. DOI

Watad I., Abdulhalim I. Spectropolarimetric surface plasmon resonance sensor and the selection of the best polarimetric function. IEEE J. Sel. Top. Quant. Electr. 2017;23 doi: 10.1109/JSTQE.2016.2575543. DOI

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