Focused-beam attenuated total-reflectiontechnique on absorptive film in Kretschmann'sconfiguration

Keh-su Chang, Chien Chou, and Chin-hwa Lin

The conventional algorithm for obtaining the p-ray reflectance (R) of a metal in an attenuatedtotal-reflection (ATR) experiment is to normalize thep-ray reflecting power of the metal (Ip) with its s-rayreflecting power (Is). We found that for these ATR experiments in Kretschmann's configuration, twoconditions will make Is less than Ip. In the first condition the film itself is absorptive; in the second thefilm is weakly absorptive but has thin thickness. When I < I, the conventional algorithm is notapplicable anymore; otherwise, the measured reflectance will be greater than one. With a modifiedfocused-beam ATR experiment, we demonstrated that the above hindrance can be overcome by taking theintensity distribution of the incidentp ray as the normalizing signal. The reflectance of the bare prism atincident angles greater than the critical angle is also suggested to be taken as a proper normalizationfactor.

Key words: Surface plasma wave, attenuated total reflection, absorptance, transmittance.

Introduction

Because of successful applications in many areas, thesurface-plasma wave (SPW)' has secured strong atten-tion in recent years. Typical applications of thewave are optical property measurements of metallicfilms,2 3 optical chemical sensors,4 5 and surface non-linear optics.6 8 The measurement technique usedin SPW experiments is the attenuated total-reflection(ATR) technique.9 Two ATR configurations havebeen commonly adopted: the Otto9 and the Kretsch-mann.' 0 There are several features common to bothconfigurations. First, the incident light is p polar-ized because the SPW itself is a p-polarized surfaceelectromagnetic wave. Second, a coupling prism isadopted to match the momenta of the incident lightand the SPW. Third, a surface-active medium thathas a negative dielectric constant is required forexciting the SPW. Within the spectrum of visiblelight, good conductors with complex dielectric con-stants (E = Er + Ei, Er < 0) such as silver, gold, copper,

K.-S. Chang and C.-H. Lin are with the Department of AppliedPhysics, Chung Cheng Institute of Technology, Tashi, Taoyuan,Taiwan, China. C. Chou is with the School of Medical Technology,National Yang Ming Medical College, Shihpai, Taipei, Taiwan,China.

Received 31 May 1991.0003-6935/93/162957-06$06.00/0.© 1993 Optical Society of America.

and aluminum have been used as the surface-activemedia for exciting the SPW. Among those metals,silver is weakly absorptive (I Er >> E), and has beenadopted extensively in ATR experiments. In con-trast, aluminum is an absorptive material (I Er I Ei)and has not been commonly used in ATR experiments.However, because aluminum film is sturdy and dura-ble when it is in a rugged or chemical environment,the application of aluminum film as a chemical sensorhas valuable potential. Moreover, in the infraredspectrum the materials suitable for ATR experimentsare highly absorptive (Er << Ei or Er= 0).1Therefore, the application of the ATR technique onabsorptive materials should be worth studying.

In an angular scan ATR experiment, the incident pray is collimated and the propagation constant of theincident light is fixed. Varying the incident angle,we see that the propagation constant of the incidentlight is altered and the reflectance of the metal ischanged. At the resonant angle of the SPW, theenergy of incident light couples to the field energy ofthe SPW that is eventually converted into heat, andthe reflectance of the metal is reduced to approxi-mately zero. A curve of reflectance is obtained byscanning the incident angle and measuring the reflec-tance of the metal at each incident angle. From thiscurve the propagation properties of the SPW and theoptical properties of the metal can be deduced.

To have the reflectance R of the metal, one needs to

1 June 1993 / Vol. 32, No. 16 / APPLIED OPTICS 2957

measure not only the intensity of the light reflectedby the metal, Ip, but also the intensity of the lightincident on it, Ii. As the SPW cannot be excited bythe s ray, the incident s ray will be totally reflected bythe metal at incident angles (0) greater than thecritical angle of the prism (0,). Therefore, Ii can besimulated by measuring the intensity of the s rayreflected by the metal, Is, at 0 2 0. In this way the Rcan be calculated by normalizing the Ip with the Ismeasured at 0 O. However, we found that if theATR experiment is arranged in Kretschmann's config-uration, an evident reduction of Is may occur andthere will be error in the measuring results. In somecases I becomes less than Ip at 0 O , which makesthe former normalization algorithm yield a reflec-tance greater than one.

In collimated-beam ATR experiments, Ii can bemeasured directly. However, measuring Ii in a fo-cused-beam ATR experiment is not a simple taskbecause the experimental setup cannot be disar-ranged during the measurement; the measurment ofI, is thus essentially required. The advantage ofusing a focused beam in an ATR experiment is thatthe measurement procedure is greatly simplified.A range of incident angles is included in a focusedincident beam, and the reflectance of metal at thesedifferent incident angles is presented simultaneouslyin the reflected beam. To our knowledge, Kretsch-mann12 was the first person to use a focused beam toexcite the SPW. Matsubara 3 designed a focused-beam, ATR-based chemical sensor in which a 1024-element linear detector array was used to record theintensity distribution of the reflected light. Theintensity measured by each detector is the p (or Is) atthe corresponding incident angle. This featuremakes the measurement easier and faster than thatused in a collimated-beam case. However, it is impor-tant that in a focused-beam ATR experiment the sizesof the light cones must be identical to one another, asthey are incident upon the detector array. Other-wise, the angular distribution of the recorded lightcones will be different, and the normalization resultwill be meaningless. In Kretschmann's and Matsu-bara's experiments, the surface film was silver andthe normalization factor was I A linear polarizerwas used in their experiments to set the polarizationstate of the incident light; thus the sizes of thereflected light cones were essentially identical. How-ever, when absorptive materials are considered, the I,is not available for the normalization factor anymore;thus a modification is required.

Reflectance Functions of Metal Film

In the Fresnel theory, the reflectance function R(0) ofa three-layer (prism-metal-air) system is expressedas

r0 + r 2 exp(2ik~ld) 21 + rr 12 exp(2ikzld) (

where 0 is the incident angle of light at the prism-

metal interface, k is the normal component of thewave vector of the light propagating in the metal, andd is the thickness of the metal film. In Eq. (1) rmn isthe Fresnel reflection coefficient for ap-pay incidenceat the interface between the mth and the nth me-dium:

Enkzm - Emkznr mn =Enkzm + Emkzn

(2)

In Eq. (2) Em is the dielectric constant of the mthmedium, and kzm is the normal component of thewave vector of the light propagating in the mthmedium. Here kzm is related to the vacuum wavenumber of the incident light ko by

kzm = kO[Em - np2 sin2(0)]1/2 , (3)

where np is the refraction index of the coupling prism.In the following simulations the incident wavelengthis 0.6328 m. At this wavelength, np = 1.515 (BK-7optical glass), the dielectric constants of silver andaluminum are -18 + 0.47i and -47 + 18i, respective-ly.14

To demonstrate the fact that the measured s-rayreflectance (Is) of an absorptive film is less than itsp-ray reflectance (Ip) at incident angles near thecritical angle of the prism, we calculate reflectancefunctions of the p ray (Rp) and the s ray (R,).Equation (1) is employed in calculating R,, but Eq. (2)is replaced by

kzm -kzn

rmn - kzm + kz(

Figure 1 shows the results. The surface film used inFigs. 1(a) and 1(c) is silver; Figs. 1(b) and 1(d), it isaluminum. Although the Rp curves in Fig. 1 haveevident dips at the resonant angles, the Rs curves arerelatively flat lines. In Fig. 1(a) the values of Rs aregreater than those of Rp at all incident angles, but inFig. 1(b) the values of Rs are less than those of Rp atincident angles near the critical angle of the prism(41.3°). Besides, it is notable that the thinner themetal film, the less the value of R,. This effect canbe observed not only in Fig. 1(b) but also in Fig. 1(c),where the thickness of the silver film is half of that inFig. 1(a). Just as in Fig. 1(b), some values of Rs areless than those of Rp in Fig. 1(c). However, it isimportant to realize that this phenomenon, i.e., R <Rp at 0 0, will never happen if the experiment isarranged in Otto's configuration. Figure 1(d) showsthe result in which the s ray is totally reflected at allincident angles.

We have concluded that there are two reasons forthe reduction of Rs in Figs. 1(b) and 1(c). The firstreason is that the evanescent s ray is partially ab-sorbed by the film. This absorption explains whythe reduction of R occurs only in Kretschmann'sconfiguration. In Otto's configuration the evanes-cent wave is in the air, which does not absorb energy,and the s ray is totally reflected at the prism-air

2958 APPLIED OPTICS / Vol. 32, No. 16 / 1 June 1993

(4)

Ag

s ray

p ray

0.9

a)

d=0.06gm CD

a)

0.8

0.7

0.6

0.5l e l l l i l e l

42 43 44 45 46

incident angle (degree)(a)

Al

I.............I.......................d=0.006gm

40 41 42 43 44 45 46

incident angle (degree)(b)

l . . . . . . . . . .

------ .......

- : &0.01gm

- : d=0.006gm

..2 .... .........................

--------- 4 ..............

Ag1

I

0.8

a)au 0.6COUCD- 0.42

0.2

;

d=0.03g1m

o

0

4( 41 40 41 42 43 44 45 46

incident angle (degree)(C)

Al1

0.8

(D11 0.6Ca0CD- 0.40L_

0.2

0

0.8

4)au 0.620a)- 0.42

0.2

0

Ofto's configuration

d=0.7,um

d=0.9gm

40 41 42 43 44 45 46

incident angle (degree)(d)

Fig. 1. Simulated reflectance curves of ATR experiments. The surface films are (a), (c) silver and (b), (d) aluminum. They are simulatedwith Kretschmann's configuration in (a), (b), and (c) and with Otto's configuration in (d). The solid curves are R and the dotted curves areR.,. In (a), (b), and (c), d is the thickness of the films; in (d) it is the air gap. The ordinate scale in (c) is different from that in (a), (b), and (d).

Al

s ray

interface. The second reason for the reduction of R,0.4 is that some of the evanescent s ray transmits through

the film. This transmittance can be interpreted bychecking the value of kj in Eq. (1). Although kj is apure imaginary in Otto's configuration, it is a com-

0.3- plex in Kretschmann's configuration. For example,0 when X0 = 06328 pm, the value of kj in Kretsch-

0.15

3W0

0.2 CD

0 0.10Ua.2CL00MCU 0.05

0.00

prism

focusing lensI

40 41 42 43 44 45 46

nqI

screenincident angle (degree)

Fig. 2 Simulated s-ray absorptance curves (left ordinate) andtransmittance curves (right ordinate) of aluminum in Kretsch-mann's configuration. The transmittance of the s ray is more in athin film than in a thick film. The absorptance of the s ray isnearly zero at = 0, for an aluminum film with a thickness of 0006PM.

details of the prism CCD (512 x 512)

Fig. 3 Setup of a focused-beam ATR experiment.

1 June 1993 Vol. 32, No. 16 APPLIED OPTICS 2959

632.8 nm w-�

>1

C

(a)

100

80

CZ0)

.040 ~ ~~~~ m00

0 0

30 0 00 00 0 0 1 1 0( 0 0 0

0 0001111 000 a 001o= 110000 a 0m° go~0 [10 00 0ar

own cnm~. o o0 C.

0 0 0 0 m1 1 0 0 1 ) 0

0: 0111 1

1 0= m0

L0 0 10 20o 30o 40o 50

pixel number(c)

03

00

BOd

a

26o 300 400 500

60

40. i

0 100

pixel number(b) (d)

Fig. 4. (a) Pattern of the beam reflected from the aluminum film. (b) Pattern of the beam reflected from the front-surface mirror. (c),(d) Intensity distribution of the central horizontal line in (a) and (b), respectively.

mann's configuration is approximately 0.5 + 43.6i insilver and 12.8 + 70.5i in aluminum. The realcomponent of kzj provides the evanescent s ray with achance to grow into a traveling wave again, i.e., tobecome a transmitted wave. The values of kzj indi-cate that the evanescent s ray has a better chance inaluminum than in silver to penetrate the film.However, because the imaginary components of kzjare large, the thickness of film is the determinant forthe penetration of the s ray: The thinner the film,the more penetrative the evanescent s ray, and themore reductive the Rs curve. This fact is shown inFig. 1(b). R < R may even occur in weakly absorp-tive media (e.g., silver) when the film is thin enough,as shown in Fig. 1(c).

To interpret the causes for the reduction of R in

ATR experiments further, we simulated the absorp-tance and transmittance of the s ray in Kretschmann'sconfiguration with different thicknesses of aluminumfilms. Figure 2 shows the result: The thinner thefilm, the greater the transmittance, but the less theabsorptance. (Note that the absorptance of 0.006-jLmaluminum film at 0 0, is nearly zero.) Thisphenomenon means that it is the transmission of theevanescent s ray that brings the Rs curves in Figs.1(b) and 1(c) to a lower level. In a weakly absorptivemedium (e.g., silver), the reduction of Rs can beprecluded by a thicker film (e.g., 0.06 jm). However,in an absorptive medium (e.g., aluminum), the absorp-tance is so strong that the phenomenon R < Rp at0 0, cannot be cured by a thicker film.

2960 APPLIED OPTICS / Vol. 32, No. 16 / 1 June 1993

4

2:

i

0o

leI

Experimental Results and Discussion

In our experiments we used the ATR technique tomeasure the thickness and the complex dielectricconstant of a thin aluminum film (d < 0.01 ji.m).

The setup is shown in Fig. 3. Ap-polarized He-Nelaser ( = 0.6328jim) whose diameter of beam () hadbeen expanded to 19 mm was taken to be the lightsource in a focused-beam ATR experiment and acollimated-beam ATR experiment. In the focused-beam ATR experiment, the collimated laser beam wasfocused by an achromatic lens (f = 64 mm). Anachromatic lens was required in this experiment;otherwise, the spherical aberration of a simple lenswould cause an ambiguity in defining the range ofincident angle covered in the light cone. The rangeof angle covered in the incident light cone wascalculated as 2a = tan-'(l/2f). With the abovevalues, we had at = 8.44. Supposing that the opticalaxis of the incident light cone was perpendicular tothe entrance surface of the prism, we found that therange of incident angle was 0 = r/4 + sin- [sin(0)/np ]when the light cone was incident upon the base planeof the prism. If a = 8.440, then 0 = (45 5.56)°.The beam reflected from the prism was projected ontoa screen. A CCD camera (512 x 512 pixels) caughtthe pattern appearing on the screen, and a framegrabber converted this pattern into gray levels imme-diately afterward.

Because I is no longer available as the normalizingfactor for aluminum, our task was to find an alterna-tive for recording the incident light cone. Our solu-tion was to coat an aluminum film on the lower half ofthe base plane of a right-angle prism (np = 1.515) andto glue a front-surface reflecting mirror to the bareupper half of the prism (see the inset of Fig. 3). Theprism was placed on a vertical translation stage.After the beam reflected from the film was recorded,the prism was lowered down until the light cone wasincident upon the mirror directly. Locations andsizes of the two reflected beams were identical as theywere incident on the CCD. The latter beam is thenormalization factor to the former beam. Figure4(a) shows the reflection pattern of the film, and Fig.4(b) shows the mirror. In Fig. 4(a) the intensitydistributions in the horizontal direction show thefeature of the reflectance curves of the SPW, whereasin Fig. 4(b) a two-dimensional Gaussian distributionof the laser beam is shown.

After being digitized by a frame grabber, the cen-tral horizontal intensity distributions of Figs. 4(a)and 4(b) are shown in Figs. 4(c) and 4(d), respectively.Although there is no dip in Fig. 4(d), a dip in Fig. 4(c)marks the excitation of the SPW. The second peakin Fig. 4(c) is the intrinsic Gaussian distribution ofthe laser beam. Only pixels within the borders ofthe beams are effective in calculating the correspond-ing incident angles of the pixels in Figs. 4(c) and 4(d).The translation of the xth effective pixel tothe corresponding incident angle is 0(x) = min +

(Omax - Omin)X/m, where m is the total number of theeffective pixels and Oma, and Omin are the maximum

and the minimum incident angle, respectively. Thegray level of each effective pixel in Fig. 4(c) is normal-ized with that in Fig. 4(d) and yields a reflectancecurve of the SPW that is illustrated in Fig. 5(a).However, for accuracy of calculation, only the parts ofthe effective pixel that ranged from 410 to 48° areconsidered in Fig. 5(a). A least-squares-mean pro-gram is applied to fit the data in Fig. 5(a) with Eq. (1).The fitted parameters of the film are (Er, Ei, d) =(-47, 12, 8.0 nm). The fitted dielectric constant ofthe aluminum film agrees with the value cited in theprevious section. Figure 5(a) also shows reflectancecurve calculated by substituting these parametersinto Eq. (1). To demonstrate the reduction of I, wemeasured and processed the reflection pattern of thefilm with an incident s ray. Because this pattern issimilar to the pattern in Fig. 4(b), it is not presentedhere. Figure 5(b) shows the results obtained bynormalizing the data in Fig. 4(c) with that of the s ray.Apparently the values of the reflectance normalizedin this manner are greater than one at 0 = 0.

- : experimental data

0.8

a)0 0.6inCu

a)-0.4

0.2

0

:theoretical fitted data

(er, E , d) = (-47, 12, 0.008m)

I

41

an)

a)a)

1.4

1.2

I

0.8

0.6

0.4

0.2

0

42 43 44 45 46 47 48

incident angle (degree)(a)

,: experimental data

- :theoretical fitted data

41 42 43 44 45 46 47 48

incident angle (degree)(b)

Fig. 5. (a) Squares are obtained by taking ratios of the gray levelsin Figs. 4(c) and 4(d); the solid curve is the theoretical reflectancecurve calculated by substituting parameters of the film, (e,, i, d) =(-47, 12, 8.0 nm), into Eq. (1). (b) Normalization result of thegray levels in Fig. 4(c) with that of I,.

1 June 1993 / Vol. 32, No. 16 / APPLIED OPTICS 2961

l I . . . . . . . . . . .

0.8

c 0.6

a)E0.4

0.2

0 I I I I

41 42 43 44 45 46 47 48

incident angle (degree)Fig. 6. Results of a collimated-beam ATR experiment. Thesquares are experimental data; the fitted parameters of the film are-51, 13, and 8.0 nm; the solid curve is the reflectance curveobtained by substituting these parameters into Eq. (1).

The result of the focused-beam experiment wascompared with that of a collimated-beam experiment,in which the focusing lens was replaced by a beam-slitter and the reflecting mirror was removed. Thebeam splitter and a monitoring power meter wereused to monitor the intensity fluctuation of theincident light. The intensity of the light reflectedfrom the aluminum film, which was measured with apower meter, was normalized by the monitoringsignal to obtain the Ip of the film. By rotating theprism, we measured the Ip at each incident angle.The reflectance of the bare prism (Ib), measured at anangle greater than the critical angle of the prism, wasused to normalize Ip to obtain the reflectance(R = Ip/Ib) of the film. The reflectance curve ispresented in Fig. 6. The curve-fitting program wasapplied to these data to find the parameters of thefilm. The result shows (Er, Ei, d) = (-51, 13, 8.0nm). A theoretical reflectance curve of a film withthese parameters is also presented in Fig. 6.

Although the measured dielectric constants of thefilm in these two experiments were different (devia-tion < 7%), the thicknesses of the film in the measure-ments were identical. The discrepancy in the mea-sured dielectric constants might be attributed to thefact that the intensity distributions of the horizontallines were not identical, as shown in Fig. 4(a). Thereis no criterion for choosing a proper horizontal line asthe actual reflectance, and the central horizontal linein Figs. 4(a) and 4(b) were chosen for the calculations.Replacing the achromatic lens with a cylindrical lensmay solve this problem, but the spherical aberrationof the cylindrical lens should be corrected. Althoughthere is a small difference between the two experimen-tal results, they agree well with the values presentedin other studies.14,15

Conclusion

The evident reduction of I in an ATR experimentarranged in Kretschmann's configuration is caused

by the absorption of the evanescent s ray by anabsorptive surface film and by the transmission of theevanescent s ray through a thin surface film. It isnoteworthy that the reduction of I, is not limited toabsorptive materials. It may also occur in weaklyabsorptive media such as silver if the film is thinenough. If the reduction of I, occurs, the conven-tional measuring algorithm is no longer applicable.A remedy for this algorithm is therefore suggested:the p-ray reflectance of a mirror or a bare prism canbe used as a replacing normalization factor for themeasurement of R in a focused-beam ATR experi-ment.

This research was partially supported by the Na-tional Science Council of the Republic of China undercontract NSC81-0417-E-010-01.

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surfaces and interfaces," in Surface Polaritons, V. M. Agranovichand D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap. 6.

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8. C. K. Chen, A. R. B. de Castro, and Y. R. Shen, "Surfacecoherent anti-Stokes Raman spectroscopy," Phys. Rev. Lett.43, 946-949 (1979).

9. A. Otto, "Excitation of nonradiative surface plasma waves insilver by the method of frustrated total reflection," Z. Phys.216, 398-410 (1968).

10. E. Kretschmann, "The determination of the optical constantsof metals by excitation of surface plasmons," Z. Phys. 241,313-324 (1971).

11. G. P. Bryan-Brown, F. Yang, G. W. Bradberry, and J. R.Sambles, "Prism and grating coupling to long-range coupled-surface exciton-polaritons," J. Opt. Soc. Am. B 8, 765-769 (1991).

12. E. Kretschmann, "The ATR method with focused light-application to guided waves on a grating," Opt. Commun. 26,41-44(1978).

13. K. Matsubara, S. Kawata, and S. Minami, "Optical chemicalsensor based on surface plasmon measurement," Appl. Opt.27, 1160-1163 (1988).

14. J. C. Quail, J. G. Rako, and H. J. Simon, "Long-rangesurface-plasmon modes in silver and aluminum films," Opt.Lett. 8, 377-379 (1983).

15. H. Kitajima, K. Hieda, and Y. Suematsu, "Optimum condi-tions in the attenuated total reflection technique," Appl. Opt.20,1005-1010 (1981).

2962 APPLIED OPTICS / Vol. 32, No. 16 / 1 June 1993