Surface plasmon polaritons (SPPs) and Rayleigh anomalies (RAs) are two characteristic phenomena exhibited by periodic grating structures made of plasmonic materials. For Au subwavelength hole arrays, SPPs and RAs from opposite sides of the film can interact under certain conditions to produce highly intense, narrow spectral features called RA-SPP resonances. This paper reports how RA-SPP effects can be achieved in subwavelength hole arrays of Pd, a weak plasmonic material. Well-defined resonances are observed in measured and simulated optical transmission spectra with RA-SPP peaks as narrow as 45 nm (FWHM). Dispersion diagrams compiled from angle-resolved spectra show that RA-SPP resonances in Pd hole arrays shift in wavelength but do not decrease significantly in amplitude as the excitation angle is increased, in contrast with RA-SPP peaks in Au hole arrays. The apparent generality of the RA-SPP effect enables a novel route to optimize resonances in non-traditional plasmonic media.
© 2009 Optical Society of America
Surface plasmon polaritons (SPPs) are collective oscillations of conduction electrons trapped at metal-dielectric interfaces. Because the real part of the electric permittivity ε′ (complex permittivity of the metal εm = ε′+iε′′) changes sign at the metal-dielectric interface, evanescent SPP fields are highly concentrated at the boundary. For noble metals such as Au and Ag, the small imaginary part of the dielectric constant (ε′′ << |ε′|) at visible wavelengths  results in small ohmic energy dissipation, which gives rise to narrow plasmon resonance. In contrast, metals such as Pd have relatively large ε′′ values  and are categorized as weak plasmonic materials . Manipulating confined electromagnetic fields and tailoring the SPP resonances in different plasmonic media are crucial for developing negative index materials , nanoscale optical switches , and label-free chemical/biological sensors [6, 7]. To improve the performance of plasmonic devices, significant effort has been devoted toward optimizing the quality of SPPs (e.g. producing intense and narrow resonances) as well as their tunability. For example, we have demonstrated that well-defined SPP-Bloch wave (SPP-BW) modes can be achieved in microscale arrays of nanoholes  and nanohole patches , and that unexpected sharp and strong Rayleigh anomaly-SPP (RA-SPP) resonances can be formed in Au subwavelength hole arrays .
When light is incident on a 2D square array of subwavelength holes with lattice constant a0, photons can gain additional momentum in integer multiples of |Gx| = |Gy| = 2π/a 0 , and SPP-BW modes are generated under the Bragg coupling condition 
where ω, c, and k 0 are the angular frequency, speed, and momentum of free-space light, and εd is the relative permittivity of the adjacent dielectric material, which can be expressed in terms of refractive index (n 2 = εd) for non-absorbing materials. Integer index pairs (i, j) denote specific SPP modes, and θ is the excitation angle. If the metal hole arrays are sandwiched between a dielectric substrate (sub) and superstrate (sup), SPP-BWs excited at the metal-sub interface can efficiently tunnel through the nanoholes to the metal-sup interface, where they are scattered back into plane waves, which then contribute to the overall light transmission (i.e. enhanced optical transmission, or EOT). The coupling of SPPs on opposite sides of the metal film can also occur [12, 13], and we found that coupled SPPs on Au films supported on glass  can produce a lower energy symmetric mode and a higher energy antisymmetric mode.
Besides SPP waves, another optical phenomenon is the RA (sometimes referred to as a Wood anomaly or Rayleigh-Wood anomaly), which is associated with light diffracted parallel to the grating surface. RAs occur when
which is related to εd and the grating pitch but not the grating material (i.e., no dependence on εm). The wavelength of the RA occurs at the onset of the (i, j) diffraction order, above which free-space light diffraction is forbidden in the order. Although a RA is a non-resonant spectral feature, the interplay between RAs and SPPs on opposite sides of the metal film (the RA-SPP effect) can lead to narrower spectral features  and sometimes a higher EOT. Unlike the coupling between SPPs, we have demonstrated that the coupling between RAs and SPPs only occurs for a range of film thicknesses .
Here, we investigated the optical properties of Pd subwavelength hole arrays and observed well-defined SPP resonances associated with EOT. The most narrow and intense resonances, however, were RA-SPP resonances; the broad, long wavelength peak obscured SPP coupling on opposite sides of the Pd film. Importantly, the RA-SPP resonances in Pd hole arrays could be tuned over a large spectral range either by changing the surrounding dielectric environment or the excitation conditions. Different from those observed in Au hole arrays, the RA-SPP features in Pd occurred at high angles of excitation without significant changes in peak amplitude or peak width.
Large-area (> 1 in2) Pd subwavelength hole arrays were fabricated by a combination of SIL and PEEL techniques . SIL was used to generate square arrays of photoresist posts (diameter d = 160 nm, pitch a 0 = 400 nm) on a Si (100) substrate, which were then transferred into subwavelength hole arrays with film thickness t = 55 nm using PEEL (Fig. 1(a), inset). Zero-order transmission spectra were obtained using a home-built rotational stage. Pd hole arrays sandwiched between glass substrates and oil superstrates were illuminated with collimated white light (Thorlabs OSL1 180-W fiber coupled halogen lamp, beam diameter ≈ 2 mm, divergence angle < 0.4°). The transmitted light was collected by a fiber coupler through a 0.5-mm iris located about 20 cm behind the sample. Figure 1(a) shows that Pd subwavelength hole arrays in air (nsub = 1.523, nsub = 1.00) exhibit transmission intensities up to 18% at 665 nm. The transmission through a 55-nm thick solid Pd film was very weak at most wavelengths except for a broad peak around 900 nm with maximum intensity of 3% (Fig. 1(a), dashed line). Considering that the geometric open area of the hole array films was 12%, we found that EOT was obtained in this relatively weak plasmonic metal. The EOT observed in these Pd hole arrays was found to be closely related to the excitation of SPP-BW modes.
As predicted by Eq. (1), maxima and minima in the transmission spectra were red-shifted with increasing nsub. The resonance features in the transmission spectra exhibited a Fano profile , corresponding to a sharp minimum followed by an adjacent maximum . The minima in the experimental spectra were closer to the predictions of Eq. (1). Zero-order transmission spectra of Pd hole arrays under normal incidence were also simulated using the finite-difference time-domain (FDTD) method  with nsub = 1.00 to 1.70 (Fig. 1(b)). The calculated spectral features and experimental data showed excellent agreement regarding the frequencies of resonances. Slight differences in transmission amplitude were most likely because of minor yet unavoidable imperfections in the Pd samples (such as variations in hole size, film thickness, and surface roughness).
As nsub was increased past an index value of 1.55, the (±1, 0)sub RA wavelength approached the (±1, 0)sub SPP mode, and a distinct peak as narrow as 45 nm appeared at 670 nm (Fig. 1, ). Because ∣ε′Pd∣ > ∣ε′Au∣ (ε′Pd = -16.7, ε′Au = -14.4 at 670 nm), plasmon resonances on Pd occurred at bluer wavelengths, and the RA-SPP peak was also blue-shifted by ca. 20 nm. When nsup approached 1.29, the RA-SPP resonances occurred as (±1, 0)sup SPPs overlapped with (±1, 0)sub RAs. Because Pd films attenuate the propagation of SPP waves more strongly than Au at optical wavelengths, the RA-SPP peak at 670 nm from Pd hole arrays was broader and less intense compared to the same RA-SPP mode on Au at 690 nm (FWHM = 34 nm) . However, these RA-SPP spectral features are more well-defined and much narrower compared to previous reports that did not observe strong resonances from Pd substrates . Furthermore, because ε′′Pd becomes smaller with decreasing wavelength (a somewhat unusual feature) , Pd becomes more free electron-like at shorter wavelengths, and the plasmon resonances therefore can be very distinct in the blue region of the visible spectrum.
The strongest RA-SPP peak for nsup > 1.55 occurred at a wavelength that was slightly longer than the RA condition at the Pd-sub interface but shorter than the SPP resonance at the Pd-sup interface. In this case, first order diffraction is a virtual process, which means that SPP excitation associated with the bottom of the film can temporarily populate the virtual diffraction channel before ultimately scattering to the zero-order channel. This pathway operates in parallel with normal zero-order scattering to enhance transmission. When the wavelength is reduced further to allow first order diffraction, scattering to the zero-order channel stops, leading to a sharp cutoff in the RA-SPP peak on the short wavelength side. Therefore, sharp features in the transmission spectra can be observed even though Pd has a large ε′′ at these wavelengths. An analogous process happens for nsup < 1.55 except that the roles of the Pd-sup and Pd-sub interfaces are reversed.
Strong variations in the transmission amplitude from the RA-SPP effect were observed in FDTD calculations near 606 nm when nsup = 1.293 and near 685 nm when nsup = 1.70 (Fig. 1(b), ). To verify coupling between the (±1, 0)sub SPP and the (±1, 0)sup RA, we plotted the Fourier transformed field intensity ∣Ez∣2 at 628 nm for nsup = 1.70, near the minimum in the zero-order transmission spectrum associated with the RA-SPP peak (Fig. 2). Figure 2(a) shows that the SPP has greatest intensity at the Pd-sub interface, but intensity was also noticeable on the superstrate side. The RA is also present along with the SPPs but cannot be resolved because of its low intensity relative to the SPP. Figure 2(b) shows the field at z > 200 nm above the hole where the SPP fields have significantly decayed and the electromagnetic characteristics of the RA are evident (i.e., a propagating plane wave with infinite extent) .
The identification of specific SPP modes from normal-incidence spectra can be difficult when there are degeneracies or when multiple broad and weak maxima/minima overlap with each other. Such challenges can be overcome using angle-resolved transmission spectroscopy because SPP modes that are degenerate when θ = 0° (kx = 0) will split at other angles (kx ≠ 0) (Eq. (1)). Taking advantage of our large-area samples, we mapped out the SPP band structures of Pd hole arrays out to high angles (θ = 70°) and converted them into E-kx dispersion diagrams (Fig. 3), where E is the photon energy, kx is the in-plane wavevector of the incident light in air. The grayscale represents the transmission intensity. Two sets of plasmonic (SPP) and photonic (RA) bands were observed at the Pd-sub interface (Fig. 3, dashed lines from Eq. (1) and (2)) and the Pd-sup interface (Fig. 3, solid lines). As expected, when nsup increased, the Pd-sub modes did not change while the Pd-sup modes shifted to lower E. Good agreement was found between the predicted modes and the dispersion diagrams, which verified the spectral features originated from SPP-BWs.
The dispersion diagrams of Pd hole arrays show distinct differences from Au hole arrays (Fig. 3(b)): (1) Pd SPP resonances are observed at shorter wavelengths because the interband transitions of Pd occur near 3.6 eV (ca. 344 nm) , but Au plasmon resonances are obscured by the intrinsic interband transitions around 2.5 eV (ca. 500 nm) ; (2) the (-1, 0) SPP band of the Pd hole arrays is nearly linear and parallel to the RA line because ε′Pd changes more slowly than ε′Au throughout the optical regime [1, 2], whereas the SPP bands of Au hole arrays exhibit slopes different from the RA curves; and (3) the bright RA-SPP bands of the Pd hole arrays remain intense with increased kx (Fig. 3(a), nsup = 1.70, inset), while the equivalent band in Au becomes weak at large wavevectors (Fig. 3(b), nsup = 1.70).
Since both SPPs and RAs are angle dependent, RA-SPP peaks also shift with incident angle. The required condition for the RA-SPP effect—overlap between the (-1, 0)sub SPP mode and the (-1, 0)sup RA mode—in Pd occurred not only at normal incidence (θ = 0°) but also out to large angles without changes in nsup because SPP and RA bands have similar slopes as function of θ. Figure 4(a) shows that the RA-SPP peak of Pd hole arrays exhibits nearly the same amplitude and FWHM at angles from 0° to 60°. In contrast, the amplitude of the RA-SPP peak of Au hole arrays decreases dramatically with increased θ when nsup = 1.70 (Fig. 4(b)) because the (-1, 0)sub SPP band deviates significantly from the (-1, 0)sup RA one at large angles. Therefore, changing the excitation angle presents another effective approach to tune RA-SPP resonances to desirable wavelengths in Pd without compromising the spectral quality.
In summary, we have shown that Pd subwavelength hole arrays exhibit both EOT and RA-SPP resonances that were previously observed only in Au hole arrays. There are at least three important implications of this work: (1) RA-SPP resonances are a general effect that may be observed in plasmonic materials under the proper conditions; (2) hole arrays or related structures created from weak plasmonic materials offer new prospects for constructing plasmonic components; and (3) the design of SPP-based sensors and surface-enhanced Raman scattering substrates that require short wavelengths for efficient excitation can be improved.
This work was supported by the National Science Foundation (NSF) under DMR-0705741, the NSF-NSEC (EEC-0647560), the NSF-MRSEC (DMR-0520513), and the DOE BES (DE-AC02-06CH11357). This work made use of the NSERC computation facilities, supported by DOE, and the NUANCE Center facilities, supported by NSF-MRSEC, NSF-NSEC and the Keck Foundation.
References and links
1. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,“ Phys. Rev. B 6, 4370 (1972). [CrossRef]
2. P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,“ Phys. Rev. B 9, 5056–5070 (1974). [CrossRef]
3. H. Gao, J. Henzie, M. H. Lee, and T. W. Odom, “Screening plasmonic materials using pyramidal gratings,“ Proc. Natl. Acad. Scie. 105, 20146–20151 (2008). [CrossRef]
4. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three Dimensional Optical Metamaterial Exhibiting Negative Refractive Index,“ Nature 455, 376 (2008). [CrossRef] [PubMed]
5. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,“ Nature Photon. 1, 402–406 (2007). [CrossRef]
7. R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,“ Accts. Chem. Res. 41, 1049–1057 (2008). [CrossRef]
9. J. Henzie, M. H. Lee, and T. W. Odom, “Multiscale Patterning of Plasmonic Metamaterials,“ Nature Nanotech. 2, 549–554 (2007). [CrossRef]
10. J. M. McMahon, J. Henzie, T. W. Odom, G. C. Schatz, and S. K. Gray, “Tailoring the Sensing Capabilities of Nanohole Arrays in Gold Films with Rayleigh Anomaly-Surface Plasmon Polaritons,“ Opt. Express 15, 18119–18129 (2007). [CrossRef] [PubMed]
11. W. L. Barnes, A. W. Murray, J. Dintinger, E. Devaux, H. J. Lezec, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of sub-wavelength holes in a metal film,“ Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]
12. D. Sarid, “Long-Range Surface-Plasma Waves on Very Thin Metal Films,“ Phys. Rev. Lett. 47, 1927–1930 (1981). [CrossRef]
13. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen,“Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,“ Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]
14. G. C. Schatz, J. M. McMahon, and S. K. Gray, “Tailoring the parameters of nanohole arrays in gold films for sensing applications,“ Proc. SPIE 6641, 664103/664101–664103/664108 (2007).
15. C. Genet, M. P. v. Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,“ Opt. Commun. 225, 331–336 (2003). [CrossRef]
16. S.-H. Chang, S. K. Gray, and G. C. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,“ Opt. Express 13, 3150–3165 (2005). [CrossRef] [PubMed]
17. O. M. Piciu, M. W. Docter, M. C. v. d. Krogt, Y. Garini, I. T. Young, P. M. Sarro, and A. Bossche, “Fabrication and optical characterization of nano-hole arrays in gold and gold/palladium films on glass “ Proc. Inst. Mech. Engin. Part N: J. Nanoengin. Nanosyst. 221, 107–114 (2007). [CrossRef]
18. J. Steele, C. Moran, C. Aguirre, A. Lee, and N. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,“ Phys. Rev. B 68, 205103 (2003). [CrossRef]
19. R. C. Vehse, E. T. Arakawa, and M. W. Williams, “Optical and Photoemissive Properties of Palladium in the Vacuum Ultraviolet Spectral Region,“ Phys. Rev. B 1, 517–522 (1970). [CrossRef]