Bragg scattering of surface plasmon polaritons on extraordinary transmission through silver periodic perforated hole arrays Ming-Wei Tsai, Tzu-Hung Chuang, Hsu-Yu Chang, and Si-Chen Lee Citation: Applied Physics Letters 88, 213112 (2006); doi: 10.1063/1.2206553 View online: http://dx.doi.org/10.1063/1.2206553 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/88/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Strong coupling between surface plasmon polariton and laser dye rhodamine 800 Appl. Phys. Lett. 99, 051110 (2011); 10.1063/1.3619845 Exploring magnetic plasmon polaritons in optical transmission through hole arrays perforated in trilayer structures Appl. Phys. Lett. 90, 251112 (2007); 10.1063/1.2750394 Multiple transmission bands through metal films perforated with two periodic arrays of apertures Appl. Phys. Lett. 89, 221108 (2006); 10.1063/1.2397540 Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice Appl. Phys. Lett. 89, 093102 (2006); 10.1063/1.2338886 Characterization of long-range surface-plasmon-polariton waveguides J. Appl. Phys. 98, 043109 (2005); 10.1063/1.2008385 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 95.47.162.6 On: Fri, 11 Apr 2014 08:43:58
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Bragg scattering of surface plasmon polaritons on extraordinary transmission throughsilver periodic perforated hole arraysMing-Wei Tsai, Tzu-Hung Chuang, Hsu-Yu Chang, and Si-Chen Lee
Citation: Applied Physics Letters 88, 213112 (2006); doi: 10.1063/1.2206553 View online: http://dx.doi.org/10.1063/1.2206553 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/88/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Strong coupling between surface plasmon polariton and laser dye rhodamine 800 Appl. Phys. Lett. 99, 051110 (2011); 10.1063/1.3619845 Exploring magnetic plasmon polaritons in optical transmission through hole arrays perforated in trilayerstructures Appl. Phys. Lett. 90, 251112 (2007); 10.1063/1.2750394 Multiple transmission bands through metal films perforated with two periodic arrays of apertures Appl. Phys. Lett. 89, 221108 (2006); 10.1063/1.2397540 Dispersion of surface plasmon polaritons on silver film with rectangular hole arrays in a square lattice Appl. Phys. Lett. 89, 093102 (2006); 10.1063/1.2338886 Characterization of long-range surface-plasmon-polariton waveguides J. Appl. Phys. 98, 043109 (2005); 10.1063/1.2008385
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 95.47.162.6
Metal films with two-dimensional subwavelength peri-odic perforated hole arrays exhibit extraordinary opticaltransmission.1,2 When a single slit in a metallic film is sur-rounded by periodic surface corrugations, the emitted lightfield from the slit concentrates in a specific direction with aconstrained range of angles, instead of diverging in all direc-tions, which supports the directional beaming nature of thesurface plasmon.3,4 If the period of the corrugation is appro-priate, then the surface plasmon plaritons �SPPs� can Braggreflect and an energy gap opens up in the SPP dispersionrelation.5,6 Recent work on the conservation of surfaceplasmons and light through periodic perforated hole arrays7
has elucidated the propagation of surface plasmons. Extraor-dinary optical transmission in the middle and far infraredregion has been demonstrated.8–10 They have potential appli-cations in optical filters and optical modulators. This workinvestigates how hole size affects extraordinary transmissionthrough a two-dimensional periodically perforated Ag film inthe far infrared region. SPP dispersion relations with vari-ously sized square holes are measured to discuss the varioussurface charge displacements on periodic perforated Ag film.
After the photoresist was spun onto a silicon wafer andfollowing pattern transfer, 50 nm thick Ag metal films withsquare holes of various sizes were deposited and lifted off. ABruker IFS 66 v/s system was adopted to measure zero-order transmission spectra. The sample is defined to lie in the�x ,y� plane, and is rotated about the y axis in 1° incrementsup to �=50°. The light is incident in the z direction, allowingthe dispersion relation in the kx direction to be studied. Thewave number resolution of the measurement was 8 cm−1.
The conservation of momentum for surface plasmons1 isgiven by
ksp = kx + iGx + jGy , �1�
where ksp is the surface plasmon wave vector given by
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�ksp� =�
c� �1�2
�1 + �2�1/2
, �2�
where � is the frequency of surface plasmon that is excitedby the incident radiation with frequency �; kx= �k0�sin �;�k0�=2� /� is the wave vector of the incident radiation, and �is the wavelength in vacuum. �1 is the dielectric constant ofthe interface medium, and �2 is that of the metal. Gx and Gyare the reciprocal lattice vectors of a square lattice with�Gx�= �Gy�=2� /a, and i and j are integers. For normal inci-dent light,kx=0, Eq. �2� reduces to
�i2 + j2�1/2� = a� �1�2
�1 + �2�1/2
, �3�
The real part of the dielectric constants of Ag at 18, 22, 24,and 30 �m are −1.59�104, −2.31�104, −2.71�104, and−3.98�104,11 respectively. That of Si is 11.7 at all of thesewavelengths. Figures 1 and 2 show the zero-order transmis-sion spectra at normal incidence with variously sized holes.The lattice constant a is 7 �m; the square length L variesfrom 3.8 to 4.5 �m in Fig. 1. In Fig. 2, the square length L
FIG. 1. �Color online� Zero-order transmission spectra at normal incidencewith different squared hole size L. The Ag film thickness is 50 nm and the
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varies from 3.3 to 5.8 �m, and a is 9 �m. Figure 1 clearlyshows that when the square hole is larger than half of thelattice constant a /2, L�4.1 �m, the degenerate �±1,0�Ag/Si and �0, ±1� Ag/Si modes split into two peaks at 24and 25 �m, respectively. At L=3.8 �m, the split in the de-generate modes can barely be seen. The structure with a
FIG. 2. �Color online� Zero-order transmission spectra at normal incidencewith different squared hole size L. The Ag film thickness is 50 nm and thelattice constant a is 9 �m.
FIG. 3. Energy dispersion relation of SPPs as a function of kx, the transmiss copyrighted as indicated in the article. Reuse of AIP content is subjec
5.3 �m, �c� 4.7 �m, and �d� 4.3 �m, and the lattice constant of the hole array a
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different lattice constant a=9 �m yields similar results, asshown in Fig. 2. The split double peaks represent degeneratemodes that are composed of �0, ±1� Ag/Si and �±1,0�Ag/Si modes, because when the normal incident light propa-gates through the sample, Bragg scattering of SPPs on theperiodic perforated square hole arrays yields two standingwaves ��+ and �−�—each with its own surface chargeenergy5,6—and splits into two peaks. The photonic band gapopens up when the size of the squared hole exceeds a halflattice constant a /2. The transmission intensity of �+ be-comes larger than �− as the size of holes increases, becauseas the size of the holes increases, such that the metal line-width decreases, the �+ mode more easily increases the sur-face charge density with a single polarity in the metal line toa value that exceeds that required to form a charge dipole inthe �− mode. Figures 3�a�–3�d� display the SPP dispersionrelation of the periodic arrays of square holes with latticeconstant a=9 �m and squared hole sizes L=6, 5.8, 4.7, and4.3 �m, respectively. At normal incidence ��=0° �, fourfolddegeneracy is evident at 0.04 and 0.058 eV, which comesfrom Ag/Si �±1,0� plus Ag/Si �0, ±1� and Ag/Si �±1, ±1�,respectively. In the �1,0� Ag/Si mode, the transmission con-trast is weak and the bright line that represents the transmis-sion peak moves to higher energy as kx increases. Figures4�a� and 4�b� present the detailed transmission spectra at dif-ferent incident angles of light. The lattice constant a is 9 �m,
tensity is depicted with gray scale. The square hole length are �a� 6 �m, �b�he terms at: http://scitation.aip.org/termsconditions. Downloaded to IP
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213112-3 Tsai et al. Appl. Phys. Lett. 88, 213112 �2006�
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and the square length L varies from 4.3 to 6 �m. When thelight incident angle or kx increases, as shown in Figs. 4�a�and 4�b�, �0, ±1� Ag/Si, �−1,0� Ag/Si, and �1,0� Ag/Simodes separate, because ksp �0, ±1� lies in the �x ,y� planewhose magnitude differs from that of the ksp �−1,0� and ksp
�1,0� modes which lie in the x axis. The vector kx increaseswith the incident angle of the light that moves in the positivex direction; ksp �−1,0� in the negative x direction becomeless negative, according to Eq. �1�, and ksp �1,0� becomesmore positive. These results suggest that the �−1,0� Ag/Simode shift to longer wavelength and lower energy, but the�1,0� Ag/Si mode does the opposite. The vectors ksp �0, ±1�lie in the �x ,y� plane, and the �0, ±1� Ag/Si mode moves toshorter wavelength and higher energy. At a small incidentangle, Bragg scattering in the x direction causes both forwardand backward SPP waves to interfere with each other and setup two standing waves. Besides, strong scattering of the in-cident light makes the ksp �1,0� mode weaker than the ksp�−1,0� mode. At an incident angle of � from the x direction,the electric field polarized in y direction exceeds that polar-ized in the x direction. k �0, ±1� was excited by an electric
FIG. 4. �Color online� Transmission spectra of a periodic squared hole arraywith lattice constant a of 9 �m and square length L of �a� 6 �m and �b�4.3 �m at various incident angles.
sp
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field polarized in the y direction, so the transmission inten-sity of ksp �0, ±1� exceeded that of ksp �−1,0�. Figure 4�b�shows the transmission spectra when the square holes aresmaller than a half lattice constant a /2, and the �0, ±1�Ag/Si and �−1,0� Ag/Si modes split, such that the intensityof �−1,0� Ag/Si exceeds that of �0, ±1� Ag/Si at �10°.When �12°, the intensity of the �0, ±1� Ag/Si mode ex-ceeds that of the �−1,0� Ag/Si and �1,0� Ag/Si modes, be-cause incident light at a small incident angle underwentstrong scattering, resulting in the very high transmission in-tensity of backward SPP waves. However, transmission in-tensity of forward SPP waves increases with larger projec-tion quantity in the direction of propagation direction. Thetransmission intensity of the backward ksp �−1,0� mode issimultaneously lower than that of the ksp �0, ±1� mode. The�1,0� Ag/Si mode is observed at a smaller angle in Fig. 4�b�than that associated with the larger hole size in Fig. 4�a�. Asurface charge field of a larger hole in the ksp �1,0� modeforms less easily than a smaller square hole, so a larger kx,and thus �, is required to the support ksp �1,0� mode. Forsome range of �, the ksp �−1,0� mode forms more easily thanthe ksp �0, ±1� mode, indicating that the surface charge fieldchanges between the �0, ±1� Ag/Si mode and the �−1,0�Ag/Si mode.
In conclusion, when normal incident light propagatesthrough the sample, the Bragg scattering of SPP on periodicperforated hole arrays generates two standing waves ��+ and�−� and the photonic band gap. The SPP dispersion relationswith variously sized square holes were measured to investi-gate the surface charge field at the periodic metal array. Theintensity of the �0, ±1� Ag/Si mode exceeds that of the�−1,0� Ag/Si when the hole size is sufficiently large. Thesurface charge density of the �0, ±1� Ag/Si mode exceedsthat of the �−1,0� Ag/Si mode with a smaller metal linewidth, explaining why transmission intensity is higher.
This work is supported by the National Science Councilof Republic of China under Contact No. NSC 94-2215-E-002-042.
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