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Dvoynenko et al. Vol. 23, No. 9 /September 2006 /J. Opt. Soc. Am. A 2315

Suppressed light transmission through corrugatedmetal films at normal incidence

Mykhaylo M. Dvoynenko

Institute of Atomic and Molecular Sciences, Academia Sinica, P. O. Box 23-166, Taipei 106, Taiwan

Ivan I. Samoylenko

Physics Department, National Taiwan Normal University, Taipei 117, Taiwan, and Institute of Crystallography,Russian Academy of Sciences, Moscow 117333, Russia

Juen-Kai Wang

Center for Condensed Matter Sciences, National Taiwan University and Institute of Atomic and Molecular Sciences,Academia Sinica, P. O. Box 23-166, Taipei 106, Taiwan

Received January 27, 2006; accepted February 12, 2006; posted March 8, 2006 (Doc. ID 67508)

In the study of light transmission through corrugated metallic film, it has been shown that along with theenhancement of light transmission, suppression may take place at specific values of the period and magnitudeof corrugation for normal light incidence. Suppression was found to be due to the interplay between symmetricand assymetric surface plasmon polariton modes at their simultaneous excitation. © 2006 Optical Society ofAmerica

OCIS codes: 240.6680, 240.0310.

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here has been considerable interest recently in surfacelasmon polaritons (SPPs) owing to the possibilities foroncentrating and channeling light wave using subwave-ength structures.1 Enhanced light transmission through

etal film containing periodic hole arrays2 is a good ex-mple that can have many potential applications.1 Fur-hermore, anomalous transmission behavior was found toe associated not only with apertures but also with struc-ures on continuous metal films.3–6 Along with enhancedransmission, suppressed transmission at SPP resonanceas also predicted.7–9 For example, it was found theoreti-

ally by Cao and Lalanne7 that SPPs can suppress lightransmission through a metal film with periodic slits.ince both aperture (slit) structures and SPP excitation

nfluence light transmission, the physical interpretationf their results can be rather complicated. Corrugatedontinuous metal films therefore serve as a basic struc-ure in the investigation of SPP-assisted mechanisms ofuppressed light transmission. Using a continuous filmith stepped corrugation, Zayats and coworkers showed

hat the interplay between different symmetries of SPPsnd Bloch modes may result in suppression of lightransmission.8,9 They predicted, however, that suppres-ion would occur only at oblique light incidence. Further-ore, since the structure parameters (corrugation depth

nd period) in their studies were not varied, it is not clearow suppression depends on these parameters in corru-ated continuous films. In this study, we investigatedight transmission in continuous metal films with har-

1084-7529/06/092315-5/$15.00 © 2

onic corrugation, which allows us to illustrate the fun-amental role of SPPs in light transmission.The system of interest is a silver film in vacuum with

oth upper and lower surfaces harmonically modulated inhe x direction [inset in Fig. 1(a)]. The surface landscapesf the film are defined by zl�x�=−� cos�2�x /�� for theower (incident) side and zu�x�=h+� cos�2�x /�+�� forhe upper (transmitted) side, with � being the period ofodulation, h the average thickness, � the phase shift be-

ween the upper and lower modulated surfaces, and � theodulation magnitude. The bulk dielectric function of sil-

er at the wavelength of the incident light wave �460 nm�s taken as �=��+ i��=−6.5+ i0.27.10 The wavelength ishosen such that �� is negative, and therefore SPPs can bexcited. The electrical field E��x ,z� for the corrugated filman be found from the Lippmann–Schwinger equation,hich is written in the following form:6

E��x,z� = E�0�x,z� + �� − 1�k02�

−�

�

dx��−� cos�2�x/��

h+� cos�2�x/��

dz�

�GJ�x,x�,z,z��E��x�,z��, �1�

here Ex0�x ,z�=cos � exp�ik0�x sin �+z cos ���, Ey

0�x ,z�=0,nd Ez

0�x ,z�=−sin � exp�ik0�x sin �+z cos ��� are the com-onents of the p-polarized plane wave incident on the filmt an angle �; k0 is the wave vector in vacuum; and�x ,z ,x ,z � is the electrodynamic vacuum Green’s ten-

� �

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2316 J. Opt. Soc. Am. A/Vol. 23, No. 9 /September 2006 Dvoynenko et al.

or. The field can be expressed in the form of the planeave expansion

E��x,z� = �n=−�

�

exp�i�k0 sin � + 2�n/��x��A�n exp�i2,nz�

+ B�n exp�− i2,nz��, �2�

here 2,n=��k02− �k0 sin �+2�n /��2. A�n and B�n are un-

nown coefficients. Substituting Eq. (2) into Eq. (1), onean derive a system of linear equations for the unknownoefficients. A detailed description of the solution of Eq.1) can be found in Ref. 6. If the coefficients A�n and B�n arenown, the transmission �T� and reflection coefficientsR� can be determined by the transmitted and reflectedelds calculated from Eq. (1). Furthermore, the absorp-ance �A� can be evaluated by taking the ratio betweenhe absorbed power �Pabs� and the incident power �Pinc� ofhe light wave as follows:11

A =Pabs

Pinc=

2����0

�

dx�−� cos�2�x/��

h+� cos�2�x/�+��

dz�E��x,z��2

� cos ��E�0�2. �3�

ince the film is a two-dimensional periodic system, thentegration along the x direction is performed over one pe-

ig. 1. Transmission coefficient of a symmetrically corrugatedlm of h=0.1 �m at different values of �. The solid horizontal

ine in (a) shows the transmission value of the corresponding flatlm. The result of �=2 nm multiplied by 100 in (b).

iod of modulation, while the integration along the y axiss neglected. In this study, the expansion of

exp�i2,n� cos�2�x/��� �m=−N

N

imJm�2,n��exp�i2�nx/��,

nstead of the less accurateexp�i2,n� cos�2�x /���1i2,n� cos�2�x /��,6 is applied to the calculation, wherem is the Bessel function of the first kind. The summationas limited to a certain number N of diffracted orders.ecause of the dependence of SPP resonance coupling on

he ratio of the wavelength and the period and on the dis-ersive properties of noble metals, the zero-order trans-ission coefficient �T� of a normally incident p-polarized

ight is calculated as a function of �. It was found that forhe modulated magnitudes of interest the calculated re-ults vary insignificantly with N�1. We thus limit thealculation order to N=3.

For symmetrically corrugated films ��=0� with h0.1 �m, the transmission coefficients �T� at different �s a function of � are presented in Fig. 1. The period �aries in the vicinity of semi-infinite SPP resonance �00.423 �m. Two weakly enhanced transmission featurest �1=0.419 �m and �2=0.427 �m are found for smallodulated magnitudes �� 5 nm�, as shown in Fig. 1(a).or larger modulated magnitudes ���5 nm�, the featuresre no longer resolved and are replaced by one broadenedransmission peak [Fig. 1(b)]. The broadening is causedy diffractive and absorption losses that grow with theodulation magnitude � as a result of higher coupling. In

he absence of absorption loss ���=0� and at small �,hese two features approach two � functions6 that are lo-ated approximately at the same modulation periods. Ashown in the dispersion relation of SPP film modes,12

here exist two SPP film modes: asymmetric ��1� andymmetric ��2�. As � approaches zero, the two resonanceeatures in Fig. 1(a) match the two film modes. We thusssign the corresponding modes in our system to be asym-etric and symmetric modes as well. The transmission at

he valley between the two resonance modes aroundmin=0.4239 �m is lower than that of the correspondingat film (T0=0.17% at h=0.1 �m). The transmission atmin decreases with the modulation magnitude, reaches ainimum value Tmin=6.8�10−6% at �=2 nm, and then

ig. 2. Dependence of the minimal transmission coefficient onhe modulation magnitude.

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Dvoynenko et al. Vol. 23, No. 9 /September 2006 /J. Opt. Soc. Am. A 2317

ncreases [see Fig. 2]. We note that the value of Tmin ishanged only by about 0.001% when N is increased from 3o 10. This confirms that Tmin is dominated by the firsthree diffraction orders. To further verify the consistencyf our calculations, T, R, and A were calculated to checkhe energy conservation law. The resultant value of 1−RT−A is varied from about 10−7 for N=2, 10−10 for N=3,nd 10−15 for N=5 with �=2 nm for all the periods of in-erest. At normal light incidence, the corrugated struc-ures can thus introduce a drop in the transmission ofour orders of magnitude compared with that of the corre-ponding flat film. Finally, we notice that the peak trans-ission coefficient at the two resonance features in-

reases with the modulation amplitude in this range.As shown in Fig. 1, suppression at normal incidence oc-

urs only at small �. This can be explained by the domi-ant interaction between symmetric and asymmetric SPPodes that have pronounced phase behaviors, such as

hat for the flat film. Interference between the two simul-aneously excited modes can produce suppression in theight transmission, but not completely, because of the

odes’ different propagation lengths. The degree of in-ompleteness of the suppression depends on the values ofhe modulation period � and the modulation magnitude. Such suppression may take place at certain values of

ig. 3. Dependence of (a) the reflection coefficient R and (b) thebsorptance A on the modulation period for a symmetrically cor-ugated film �h=0.1 �m� at �=2 nm. The dotted horizontal linen (a) shows the reflection coefficient (97.2%) of the correspondingat film, and the one in (b) shows the corresponding absorptance

2.80%).

he modulation magnitude only, as shown Fig. 2. Thisuppression effect is accompanied by transmission loss,hich depends on the ratio of the film thickness and the

kin depth. The diminished transmission corresponds tohe valley between the peaks of the reflection coefficientFig. 3(a)] and absorptance [Fig. 3(b)] in the same modu-ation period. The two sharp features in reflection and ab-orption behaviors clearly show excitation of asymmetricnd symmetric SPP modes at �1=0.419 �m and �20.427 �m, respectively. It is seen also that the absorp-

ance at �min=0.4239 �m is higher for the corrugated filmhan the one for the flat film, while the corresponding re-ection coefficient is lower for the corrguated film thanhat for the flat film.

To illustrate the physical explanation of the observeduppression in normal transmission, the intensity andhase distributions of the x component of the field werealculated. Only the x component of the field is calculated,s shown in Fig. 4, because it contributes to the zero-rder transmission coefficient at �=0 according to Eq. (1).t resonance, SPP characters appear on both the lowernd the upper sides of the film, indicating the field tun-eling effect. Notice that a strong field appears at thevalley” �x=0.212 �m� and the “hill” �x=0.4239 �m� of thepper side with comparable amplitudes. On the otherand, the corresponding phase distribution of the x com-

ig. 4. Intensity (a) and phase (b) distribution of the x compo-ent of the field inside the corrugated film at �=2 nm and �0.4239 �m for =0.46 �m.

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2318 J. Opt. Soc. Am. A/Vol. 23, No. 9 /September 2006 Dvoynenko et al.

onent of the field exhibits an almost opposite phase re-ation at these two locations. Because it is expected fromangential boundary conditions that such properties ofhe intensity and the phase will be kept above the upperide of the film in air for small modulation amplitudes,hey diminish the zero-order transmission coefficient toero. Meanwhile, the enhanced excitation of the field onoth sides of the corrugated film at resonance can also in-uce more absorption than in the case of the flat film.his is reflected by the enhanced absorption at the reso-ance shown in Fig. 3(b).These results are related to the study by Zayats and

oworkers,8,9 where large � was adopted and resonantuppression was found only at oblique incidence. We alsobserved (not shown here) that �min decreases with meanlm thickness h. For example, �min1 nm at h=0.2 �mT01.6�10−4% �, while �min is about 10 nm at h0.05 �m �T05.5% �. This can be explained on the basisf the following two facts. First, the splitting between thewo modes decreases with the film thickness. This causesn increase in the overlap between the two modes. Sec-nd, the mode broadening increases with the modulationmplitude. To achieve minimum transmission, the modu-ation amplitude needs to be decreased. �min therefore de-reases with the film thickness. We also investigated theransmission of the corrugated metal film that is embed-ed inside a dielectric medium. It was found that the be-avior is similar and that the corresponding modulation

ig. 5. Transmission coefficient of the bending-like ��=�� cor-ugated film �h=0.1 �m� at different values of �.

mplitude and period (�min and �min) that produce theinimum transmission decrease.Consider the case of bending-like corrugation ��=�� in

omparison with the symmetrical corrugation ��=0� dis-ussed above. The corresponding transmission coefficientxhibits two overlapping features for small modulationmplitudes, as shown in Fig. 5(a). As � increases, the twoeatures become blurred and one prominent transmissioneak emerges [Fig. 5(b)]. This is consistent with the ex-erimental observation by Bai et al.13 In contrast to thetudy by Gérard et al.,14 they investigated enhancedransmission of a corrugated continuous metal film with aeriodic structure of ridges on both top and bottom sides,hich is complementary to our structure. In the case of

wo extreme phase differences between top and bottomidge periodic structures (�=0 and �), they observed aimilar relationship between the light wavelength andhe period of the structure in the transmission. In con-rast to the case of the symmetrically corrugated film, theransmission value is larger, and no extreme transmis-ion suppression exists for all modulated magnitudes. Inhis case, because the geometric symmetry is broken foronsymmetric films ���0�, the SPP field cannot be fur-her taken as a sum of symmetric and asymmetric modes.he reasoning in the case of symmetric films is not appli-able to analysis of light propagation through nonsym-etric films. The two modes are thus entangled to pro-

uce one broadened transmission feature with twondistinct peaks. We note that Hooper and Sambles alsotudied surface plasmon polaritons of nonsymmetricallyorrugated silver films, although no discussion on sup-ressed transmission was given.15

In conclusion, we found that suppressed light transmis-ion, less than 10−7, can be observed along with enhancedight transmission through a symmetrically corrugated

etal film at a specific modulation amplitude and period.he suppression is caused by a simultaneous excitation ofsymmetric and symmetric SPPs film modes that exitnly in a certain range of the modulation magnitude. Onhe other hand, the transmission coefficient for asym-etrically corrugated films does not show such extreme

uppression.

CKNOWLEDGMENTShis study was supported by the National Science Council

grant NSC 94-2120-M-001-002) and Academia Sinica ofaiwan.

Juen-Kai Wang’s e-mail address is jkwangccms.ntu.edu.tw.

EFERENCES1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface

plasmon subwavelength optics,” Nature 424, 824–830(2003).

2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A.Wolf, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).

3. N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière,“Resonant optical transmission through thin metallic filmswith and without holes,” Opt. Express 11, 482–490 (2003).

4. S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical

1

1

1

1

1

1

Dvoynenko et al. Vol. 23, No. 9 /September 2006 /J. Opt. Soc. Am. A 2319

theory of optical transmission through periodicallystructured metal films via tunnel-coupled surface polaritonmodes,” Phys. Rev. B 70, 075103-1–075103-9 (2004).

5. I. Avrutsky, Y. Zhao, and V. Kochergin, “Surface plasmon-assisted resonant tunneling of light through a periodicallycorrugated thin metal film,” Opt. Lett. 25, 595–597(2000).

6. T.-R. Yang and M. M. Dvoynenko, “Influence of small losseson light transmission through corrugated metal film,” Opt.Commun. 227, 25–35 (2003).

7. Q. Cao and P. Lalanne, “Negative role of surface plasmonsin the transmission of metallic gratings with very narrowslits,” Phys. Rev. Lett. 88, 057403-1–057403-4 (2002).

8. D. Gérard, L. Salomon, F. de Fornel, and A. Zayats,“Analysis of the Bloch mode spectra of surface polaritoniccrystals in the weak and strong coupling regimes: grating-enhanced transmission at oblique incidence andsuppression of SPP radiative losses,” Opt. Express 12,3652–3663 (2004).

9. D. Gérard, L. Salomon, F. de Fornel, and A. Zayats,

“Suppression of radiative losses of surface polaritons onnanostructured thin metal films,” Opt. Lett. 30, 780–782(2005).

0. P. B. Johnson and R. W. Christy, “Optical constants of thenoble metals,” Phys. Rev. B 6, 4370–4379 (1972).

1. W. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley,1999).

2. H. Raether, Surface Plasmons on Smooth and RoughSurfaces and on Gratings (Springer-Verlag, 1988).

3. B. Bai, L. Li, and L. Zeng, “Experimental verification ofenhanced transmission through two-dimensionallycorrugated metallic films without holes,” Opt. Lett. 30,2360–2362 (2005).

4. D. Gérard, L. Salomon, F. de Fornel, and A. V. Zayats,“Ridge-enhanced optical transmission through acontinuous metal film,” Phys. Rev. B 69, 113405-1–113405-4 (2004).

5. I. R. Hooper and J. R. Sambles, “Coupled surface plasmonpolaritons on thin metal slabs corrugated on both surfaces,”Phys. Rev. B 70, 045421-1–045421-14 (2004).