646 OPTICS LETTERS / Vol. 27, No. 8 / April 15, 2002

Photonic crystal sensor based on surface waves forthin-film characterization

F. Villa and L. E. Regalado

Centro de Investigaciones en Óptica, Loma del Bosque 115, Lomas del Campestre 37150, León, Guanajuato, Mexico

F. Ramos-Mendieta and J. Gaspar-Armenta*

Centro de Investigación en Física de la Universidad de Sonora, Apartado Postal 5-088, Hermosillo, Sonora, Mexico

T. Lopez-Ríos

Centre National de la Recherche Scientifique, Laboratoire d’Etudes des Propriétés Electroniques des Solides,25, Avenue des Martyrs, B.P. 166 38042 Grenoble Cedex 9, France

Received October 26, 2001

A new sensor based on optical surface waves in truncated one-dimensional photonic crystals is proposed foruse in determining the optical properties of metallic or dielectric thin films and bulk media. Specifically,the method of optical characterization takes into account the changes that the surface waves of a layeredstructure undergo when either a thin film of arbitrary material is added at the surface or the optical propertiesof transmission medium change. For the surface-wave excitation the Kretschmann configuration used inattenuated total ref lectance is employed. © 2002 Optical Society of America

OCIS codes: 240.0240, 230.4110, 310.0310, 240.0310, 240.6680, 240.6690.

The study of electromagnetic surface waves (SWs)has grown in the past few years because they con-stitute a natural mechanism for energy loss—viatunneling—of localized bulk excitations.1 Thesenonradiative electromagnetic waves can exist in trun-cated one-dimensional photonic crystals1 –3 (1D-PCs)and propagate along the crystal–air interface, withevanescent fields in the perpendicular direction awayfrom the surface plane. From a technological point ofview, electromagnetic SWs could be highly relevant inthe design of optical devices as sensors, modulators,and mirrors.4 – 9

An interesting characteristic of SWs that is notpresent in surface plasmon–polaritons in metallicsurfaces is their high sensitivity to the termination ofthe structure.1 Their dispersion curve (wave vectorversus frequency) and confining distance could differwhen the truncation leaves one or the other layer atthe surface (the 1D-PC is composed of two alternatedielectric layers of thicknesses A and B). The highsensitivity of SWs was also proved for truncationsthat left incomplete layers at the surface.1 Indeed, asmall optical thickness variation of the last layer maymodify strongly both the frequency and the intensity ofthe wave. As we demonstrate in this Letter, the highsensitivity of SWs makes these excitations potentiallyuseful for sensor applications.

With the periodic system supporting SWs, we foundsignificant variations of the attenuated ref lectivitywhen the sample, a solid layer or a bulk medium, wasadded to the structure. Such a response is easilyassociated with the thickness and optical properties ofthe sample. An appreciable change in the response ofour sensor is also produced by variation of the opticalproperties of the transmission medium.

0146-9592/02/080646-03$15.00/0

Let us consider a 1D-PC with the band structureshown in Fig. 1 for TE polarization. The refractiveindices of materials considered for this system arenA � 2.22 and nB � 1.46, with a thickness relationB � 0.5A. The dispersion curves of the surface modes

Fig. 1. Band structure of the TE polarization of aninfinite periodic system. In this case, v and b aregiven in reduced units, vd�2pc and bd�2p, respectively.The light lines for vacuum (the transmission medium)and for BK7 glass (the incident medium) at an angleof incidence of 85± are given by the upper and lowerdashed–dotted lines, respectively. The area limitedby these lines represents the region where it is pos-sible to excite SWs by total internal ref lection with a BK7prism. The surface modes are indicated by dashed lines.The squared electric f ield amplitude is shown in theinset for the SW in the f irst gap �v � 0.358, b � 0.511�,indicated by a diamond.

© 2002 Optical Society of America

April 15, 2002 / Vol. 27, No. 8 / OPTICS LETTERS 647

(determined with the supercell method2) are shownin Fig. 1 by dotted lines appearing in only the f irstand third bandgaps when the crystal is truncated in alayer of material nA with a thickness of 0.4A.

Although TM modes are amenable to being usedin much the same way as the TE modes, they arenot equally interesting for sensing purposes. The TMbandgaps narrow at the Brewster angle,1 closing theeffective sensing window in the spectrum or in theangle-of-incidence range.

It is known that surface modes can be excitedby use of Kretschmann and Otto conf igurations9

in very much the same way as surface plasmonsare excited.10 From a practical point of view, theKretschmann configuration is more suitable as asensor. Let us consider a specif ic truncated crystalwith the configuration shown in Fig. 2, whose struc-ture can be expressed by g 2 �AB�3 2 tA 2 a, whereg is the incidence medium, which is a prism ofBK7 glass (used to gain access to the region beyondthe light line in vacuum; see Fig. 1); A � 150 nmrepresents the thickness of a layer with refractiveindex nA, B � 0.5A represents the thickness of alayer with refractive index nB , and the exponentassociated with the parentheses means the numberof times that this period is repeated. The parametert [ �0, 1� stands for a factor of truncation of thelast layer, A, which will support the SW. Finally,a represents the air medium (transmission medium).

Since the surface modes are highly conf ined to thelast layer, we found that a system with a few periodsbehaves very well, closely following the theory. It isworthwhile to emphasize the approximated behaviorin this case, since with few periods the boundaries ofbandgaps cannot be precisely defined and are seem towiden. The extraordinary fact is that surface modescan be observed even with such diffuse conditions ifone follows the rule that the effect must be concen-trated within only two or three periods of the pho-tonic crystal.1 This fact is evident from the inset inFig. 1, in which the squared amplitude of the electricfield profile is given for the mode in the f irst bandgap�v � 0.358, b � 0.511�, indicated by a diamond in thedispersion diagram.

The potential application of the SWs in a sensingdevice can be appreciated from the results shown inFig. 3. Ref lectance curves are shown as a function ofthe wavelength for the SW in the first gap of Fig. 1.All the curve minima correspond to the same modedisplaced within the gap as the parameter t varies.Because of this high sensitivity to the variation of thethickness, tA, similar modification of the ref lectancepeaks is expected when any material is added to thesurface of the truncated film, independently of thetransmission medium.

Another important case can be considered if we takeas a test layer T a discontinuous thin f ilm attached tothe system given in an example, presented above, witha truncation factor of t � 0.4 (indicated by a diamondin Fig. 1). It is well known that thin films of metal-lic materials grow as discontinuous f ilms, the opticaland physical properties of which vary with thickness,until the percolation threshold is achieved.11,12 Let us

consider, for example, an ultrathin film of gold whoseoptical properties and thickness were estimated by aMaxwell–Garnett effective medium model13 based onelectron micrography.12 The surface mode response isshown in Fig. 4 for different f ilm thicknesses and dif-ferent filling fractions. As can be seen, the SW sensi-tivity is enough that thickness variations of the orderof few nanometers can be detected in the sample. Inthis case it is assumed that all dielectric layers are freeof absorption.

The sensitivity of our proposed sensor can also be ev-idenced by analysis of the change in the response or theposition of the mode when the optical properties ofthe transmission medium vary.14 In Fig. 5, we showthe natural mode of the same system used in the lastexample (solid line with t � 0.4). If we change thetransmission medium air to water with index of refrac-tion ns � 1.332, the peak displaces more than 30 nmin wavelength (dotted curve). By considering thinfilms of the sensor to be free of losses and increasingthe absorption of the water try to simulate a varyingconcentration of a saline substance, we damp the mode

Fig. 2. Kretschmann configuration and multilayer sys-tem for three periods for measuring SWs. Ref lectance canbe measured by variation of wavelength while either theangle of incidence or R�u, l� is kept constant. jEj2 is thesquared electric f ield amplitude.

Fig. 3. Surface mode of the first bandgap observed at thefixed angle of u � 70± for different thicknesses t (in mil-limeters) of the truncated layer, tA.

648 OPTICS LETTERS / Vol. 27, No. 8 / April 15, 2002

Fig. 4. Surface mode of the f irst bandgap observed atthe fixed angles of u � 70± with the truncated crystalg 2 �AB�30.4A 2 T 2 a, considering as a test overlayerT and ultrathin discontinuous f ilm of gold with differ-ent thicknesses T and filling fractions f . For T � 1 nm,f � 0.0092 (curve with spheres), the complex refractive in-dex is l � 632.8 nm and NT � 1.025 2 i0.002538. For T �3 nm, f � 0.045 (triangles), NT � 1.122 2 i0.013. For T �10 nm, f � 0.138 (solid curve), NT � 1.402 2 i0.047. ForT � 20 nm, f � 0.295 (dashed curve), NT � 2.055 2 i0.17.

Fig. 5. Surface mode of the f irst bandgap observed at anangle of incidence u � 70± with the system g 2 �AB�30.4A 2a. The natural mode with air as a transmission medium isshown by the solid curve. If a saline water solution is sub-stituted for air, the peak is displaced close to l � 690 nm.Curve with spheres, refractive index of a saline solution,ns 2 iks � 1.332 2 i2 3 1024; curve with diamonds, ks �2 3 1023; dashed curve, ks � 1021.

while the peak corresponding to the mode stays in thesame position (in wavelength) shown in Fig. 5.

In conclusion, we have shown the potential applica-tion of the attenuated total ref lectance technique for

optical characterization by exciting the surface wavesin a truncated 1D-PC. Contrary to the assumptionthat many periods are necessary to calculate and mea-sure surface modes,9 we found that only a few are suffi-cient for observing SW effects in the spectral response.An important advantage offered by photonic crystalsis the possibility of designing and manipulating sen-sor sensitivity to characterize the optical properties ofmaterials and thin f ilms in wide regions of the electro-magnetic spectrum. Extraordinary application poten-tial and, eventually, a good alternative to the use of theattenuated total ref lectance technique for optical char-acterization are possible, since most of dielectrics havea number of advantages over metallic thin films suchas gold and silver, which are expensive and quickly de-graded by the environmental or by chemical attack dur-ing measurements.

F. Villa’s e-mail address is fvilla@foton.cio.mx.*On sabbatical at Centro de Investigaciones en

Óptica.

References

1. F. Ramos-Mendieta and P. Halevi, J. Opt. Soc. Am. B14, 370 (1997).

2. P. Yeh, A. Yariv, and Ch.-S. Hong, J. Opt. Soc. Am. 67,423 (1977).

3. P. Yeh, Optical Waves in Layered Media (Wiley,New York, 1988).

4. N. J. Tao, S. Boussaad, W. L. Huang, R. A. Arecha-baleta, and J. D’Agnese, Rev. Sci. Instrum. 70, 4656(1999).

5. C. G. Ribbing and O. Staaf, Proc. SPIE 4103, 116(2000).

6. E. Fontana, R. H. Pantell, and S. Strober, Appl. Opt.29, 4694 (1990).

7. T. Okamoto, T. Kamiyama, and I. Yamaguchi, Opt.Lett. 18, 1570 (1993).

8. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, andV. Gaponenko, J. Lightwave Technol. 17, 2018 (1999).

9. W. M. Robertson, J. Lightwave Technol. 17, 2013(1999).

10. H. Raether, Surface Plasmons on Smooth and RoughSurfaces and on Gratings (Springer, New York, 1986).

11. N. Kaiser, in Optical Inteference Coatings, Vol. 63of OSA Trends in Optics and Photonics Series (Op-tical Society of America, Washington, D.C., 2001),paper MA1-1.

12. Z. M. Meiksin, Phys. Thin Films 8, 99 (1975).13. D. E. Aspnes, Thin Solid Films 89, 249 (1982).14. T. Okamoto, M. Yamamotot, and I. Yamaguchi, J. Opt.

Soc. Am. A 17, 1880 (2000).