Letter pubs.acs.org/NanoLett
Deep-Subwavelength Plasmonic Nanoresonators Exploiting Extreme Coupling Rasoul Alaee,*,† Christoph Menzel,‡ Uwe Huebner,§ Ekaterina Pshenay-Severin,‡ Shakeeb Bin Hasan,† Thomas Pertsch,‡ Carsten Rockstuhl,† and Falk Lederer† †
Institute of Condensed Matter Theory and Solid State Optics and ‡Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany § Institute of Photonic Technology (IPHT), 07702 Jena, Germany S Supporting Information *
ABSTRACT: A metal−insulator−metal (MIM) waveguide is a canonical structure used in many functional plasmonic devices. Recently, research on nanoresonantors made from finite, that is, truncated, MIM waveguides attracted a considerable deal of interest motivated by the promise for many applications. However, most suggested nanoresonators do not reach a deep-subwavelength domain. With ordinary fabrication techniques the dielectric spacers usually remain fairly thick, that is, in the order of tens of nanometers. This prevents the wavevector of the guided surface plasmon polariton to strongly deviate from the light line. Here, we will show that the exploitation of an extreme coupling regime, which appears for only a few nanometers thick dielectric spacer, can lift this limitation. By taking advantage of atomic layer deposition we fabricated and characterized exemplarily deep-subwavelength perfect absorbers. Our results are fully supported by numerical simulations and analytical considerations. Our work provides impetus on many fields of nanoscience and will foster various applications in high-impact areas such as metamaterials, light harvesting, and sensing or the fabrication of quantum-plasmonic devices. KEYWORDS: Nanoresonators, plasmonics, perfect absorbers, extreme coupling, deep-subwavelength metal−insulator−metal (MIM), atomic layer deposition
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advantage consist in their potentially direct connection with electrical circuits permitting many electro-optical devices and, perspectively, even room-temperature electrically pumped nanolasers.20 Furthermore, nanoresonators made from MIM waveguides have potential applications in, for example, thermal emitters,21−24 plasmonic sensors25,26 and solar cells.27,28 However, thus far most of the respective nanoresonators have a fairly thick dielectric spacer, that is, in the order of a few tens of nanometers.25,29−31 If the dielectric spacer is rather thick, the propagation constant of the surface plasmon polariton remains close to the light line of the dielectric medium and the achievable nanoresonators are only slightly smaller than half the wavelength in the dielectric. Previously the technological challenges to fabricate homogeneous and thin dielectric layers prevented the fabrication of structures with an ultrathin dielectric spacer. Hence, it was the major limitation to achieve the deep-subwavelength resonators. To significantly shrink nanoresonators a geometry is required where the propagation constant of the SPP is much larger than that in the free space. Generally, this can be achieved by “extreme coupling” of the surface plasmon polaritons of the
uring the past decade plasmonics has sparked enormous research interest because of the potential control of lightmatter-interactions at the nanoscale.1,2 Light confinement and local-field enhancement are the two most remarkable properties that can be exploited.3−6 In general, optical nanoresonators are used to achieve these properties. In optical nanoresonators, also called optical nanoantennas, concepts from ordinary resonators are transferred to the nanoscale by exploiting surface plasmon polaritons.7 At their heart, optical nanoresonators consist of truncated metallic waveguides. This causes the propagating plasmon polariton, as sustained by the waveguide, to bounce back and forth in the nanoresonator.8−12 In resonance, that is, if the phase accumulation per round trip is a multiple of 2π, the cavity field is hugely enhanced. Moreover, a small cavity in both transverse and longitudinal directions leads to a small effective mode volume.13,14 This entails many advantages that can be illustrated in the context of various applications. As far as sensors are concerned it occurs that, for example, the smaller the structure the faster the response time, the lower the electrical energy consumption, and the higher the signal-tonoise ratio.15 Such a concept of an optical nanoresonator is universal and many different waveguiding structures can be used for its implementation. However, very likely, the majority relies on metallic nanowires.16−19 Even better light localization can be achieved by using metal−insulator−metal (MIM) waveguides. Their additional © XXXX American Chemical Society
Received: March 1, 2013 Revised: June 21, 2013
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reflection across an extended angular domain around a design frequency. By invoking the concept of critical coupling, the entire incoming electromagnetic energy is dissipated by the structure.34,38−40 Although demonstrated here at the example of a perfect absorber, many other plasmonic applications will equally benefit from the extreme coupling regime. Generally, the eigenmodes of the plasmonic nanostructure are much stronger localized which also causes them to couple less to free space radiation. The strongly reduced radiative losses and the associated much larger field enhancement are beneficial for all applications where, for example, quantum emitters are coupled to those nanoresonators.24,41 Eventually, upon reaching the extreme coupling limit a novel class of quantum optical components such as logical quantum gates and quantum communication devices can be achieved with reasonable efficiencies by proper design of the plasmonic nanoresonators.42,43 Alternatively and probably more immediate, with the availability of plasmonic nanostructures that sustain deepsubwavelength resonances truly homogeneous metamaterials can be achieved.32,44 Thus far, it remains distracting that the nanostructures used to build optical metamaterials are in most cases only smaller than the wavelength but not much smaller. Consequently, light probes the periodicity of the material that no longer appears as homogeneous. All these detrimental aspects can be lifted if the unit cells of the metamaterials can be made much smaller than the operating wavelength. Experimental and Numerical Results. The MIM nanoresonator we consider consists of an array of metallic nanopatches on top of a gold metallic ground plate. They are separated by a thin dielectric spacer. A sketch of the actual structure as well as a SEM image of a fabricated sample are shown in Figure 2a,b. The geometrical parameters are given in
isolated interfaces. Extreme coupling occurs whenever the coupled plasmonic nanostructures have an ultrathin dielectric spacer, that is, in the order of few nanometers, such that the coupling leads to an excessively large resonance splitting.32 If the metallic interfaces are brought in such close proximity, the coupling among the surface plasmon polaritons sustained at each interface is largely increased and thus the propagation constant of the guided plasmonic eigenmode gets very large. This huge wavevector allows the achievement of nanoresonators deep in the subwavelength domain, as has been recently shown for one-dimensional resonator geometries.18,19 However, they cannot be used to achieve field localization in all three dimensions. Recently, two-dimensional MIM nanoresonators have been realized by using chemical deposition techniques that exploit bottom-up approaches.3,4,33,34 However, these structures also suffering from inherent disadvantages with respect to a top-down approach, for example, the inhomogeneous broadening of the resonances as well as limited control over the optical properties of nanoresonators. Here, we realize for the first time a two-dimensional deepsubwavelength MIM plasmonic nanoresonator that operates in the extreme coupling regime. The necessary ultrathin dielectric spacer as required to achieve this regime has been fabricated by using atomic layer deposition (ALD) techniques.35 An artistic view of the device is shown in Figure 1. The application we
Figure 1. Schematic of the extremely coupled MIM nanoresonator. Each nanoresonator consists of a metallic nanopatch deposited on a metallic ground plate from which it is separated by an ultrathin dielectric spacer. For convenience, the nanoresonator is fabricated as an array. The ultrathin dielectric spacer as fabricated with ALD leads to deep-subwavelength resonances. In addition to a lowest order resonance that occurs at the longest wavelength (indicated with the red color), higher order modes are equally excited at increasing frequencies. The figure shows the corresponding current distribution of selected eigenmodes. A TEM image of a cross section of the fabricated spacer is shown in the inset to highlight the presence of the ALD fabricated dielectric layer.
Figure 2. (a) Schematic view of the plasmonic absorber with an extremely thin dielectric spacer. (b) SEM image of a fabricated absorber. Geometrical parameters are chosen as P = 250 nm, L = 100− 200 nm, tfilm = 200 nm, tALD = 3−8 nm, tNP = 30 nm.
the figure caption. We have chosen the geometry such that it sustains well-pronounced resonances with large absorption across a broad angular range. Moreover, the nanoresonator shall not just support the lowest order longitudinal resonance but also a few higher-order ones. The structure is periodic in both lateral directions with a period of 250 nm. Fused silica (ε = 2.25) serves as dielectric spacer and was deposited onto the metallic ground plate with ALD. Gold was used for all metallic constituents from which data for the permittivity were taken.45 We used the Fourier model method (FMM) to simulate all optical properties of the structure.46 The resonance features can also be studied analytically by taking advantage of a Fabry− Perot model. Details of the model are documented in the Supporting Information. In passing, we note that on purpose we avoid dielectric spacers that are thinner than 1 nm to avoid
concentrate on is a perfect absorber.31 The functional simplicity of a perfect absorber allows the study of the peculiarities of our device and the unique features of the extreme coupling regime. The perfect absorber is a device that has been studied across the entire spectral range at microwave, terahertz, infrared, and visible frequencies.30,31,36−38 It consists of a metallic nanostructure deposited on a metallic ground plate from which it is separated by a dielectric spacer. Since transmission is entirely suppressed, perfect absorption is achieved by suppressing B
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the emergence of quantum plasmonic effects. Beside being welldocumented by now,4,47−49 they will obscure the interpretation as well as the functionality of the structure. Nevertheless, we will see that the limiting factor of the suggested nanoresonators are actually not quantum constraints but rather the unavoidable surface roughness that contributes to a degradation of resonances. The fabrication of the structure starts on wafer-level by using a fused-silica wafer. At first, the 200 nm thick gold ground plates were prepared by using electron beam lithography, thermal evaporation and lift-off-technique. Sliced in chips the samples were individually coated with ultrathin SiO2-films (in the range of 3−8 nm) by means of ALD. Eventually, the thin 2D gold grating nanostructure was prepared on top of the ALD layer by using aligned electron beam lithography, Ti/Au, evaporation and lift-off-technique. The gold films have a 3 nm thick titanium adhesion-underlayer that, however, does not affect the properties of interest. The optical measurements were performed by a FTIR Bruker spectrometer connected to a microscope in reflection mode. The measured and simulated reflection spectra for the structure with a gap of only 3 nm and a length of the nanopatch of L = 195 nm are shown in Figure 3a,b for normal as well as oblique incidence (θ = 70°) for TM polarization, respectively. The thin dielectric spacer between the metallic plates of the structure leads to a large propagation constant and, hence, effective index. Thus the nanoresonator supports multiple
resonances in the investigated spectral range. At normal incidence, only even order modes with an even number of nodes in the current parallel to the ground plate can be excited by an incoming plane wave50 (see Figure 3e, the fundamental mode (FM) and second order mode). Breaking the symmetry by an oblique illumination allows for the excitation of odd modes as well. The first three modes, that is, the fundamental, the first, and the second order mode, appear at 135, 250, and 320 THz, respectively, with negligible dependency on the incidence angle (see Figure 3a,b). The extreme near-field coupling shifts the fundamental mode toward a free space wavelength of roughly 2.25 μm. This renders the nanoresonator to be deep-subwavelength with an impressive aspect ratio of resonance wavelength to period of 9. This is huge when compared to traditional MIM-nanoresonators. Typical values for this ratio as achievable with a spacer of 30 nm are 3.25 The results show that the measured reflection is in excellent agreement with the simulations especially at lower frequencies. The measured reflection at higher frequencies is generally smaller and the resonances are less pronounced and broader. These discrepancies can however be entirely explained by the surface roughness of the thick metallic ground plate. This is discussed in detail in the Supporting Information. The absorption for the FM at normal and oblique incidence is A > 0.75. For higher order modes, that is, first and second mode, the resonances are less pronounced. The current distribution of the first three resonant modes are shown in Figure 3e. From these current distributions, it is seen that all resonances supported by the nanoresonator are based on the fundamental mode of the MIM-waveguide. This fundamental MIM-waveguide mode is antisymmetric with respect to the current in the upper and the lower metallic plate and sometimes called the magnetic dipolar one.51 Resonances of the nanoresonantor that are based on the symmetric MIM-waveguide mode and that are usually identified with the electric dipolar modes appear at much larger frequencies if at all. Figure 3c,d shows the measured and simulated reflection spectra of the structure with a thicker dielectric spacer fabricated with ALD that is, tALD = 8 nm and a length of the nanopatch of L = 200 nm at normal and oblique incidence (θ = 70°), respectively. There is an excellent agreement between measured and simulated reflection spectra (see Figure 3c,d) at all frequencies of interest. This better agreement, as supported by the analysis documented in the Supporting Information, can unambiguously be attributed to the marginal impact of the surface roughness for a larger spacer. However, it has to be stressed that the roughness remains the same when compared to the previous sample with the thinner spacer. But the evanescent waves associated with the surface roughness with a critical dimension of only a few nanometers have an extremely small decay length. For slightly thicker spacers evanescent waves at adjacent interfaces do not couple and their effect almost disappear. Therefore, rough surfaces cease to be perceived optically. This finding emphasizes the importance of flat surfaces free of any spurious roughness if the last nanometer shall be conquered in the coupling distance between adjacent plasmonic nanostructures. Because of the larger spacer, the effective index of the waveguide decreases, the resonances shift to larger frequencies, and a smaller number of modes can be excited in the investigated spectral range. Nonetheless, we can clearly identify
Figure 3. (a,b) Experimental and numerical reflection spectra for L = 195 nm with 3 nm gap at normal and oblique incidence (θ = 70°), respectively. (c,d) Experimental and numerical reflection spectra for L = 200 nm with 8 nm gap at normal and oblique incidence, respectively. (e) Current distribution (x-component) of the fundamental, first, and second modes for L = 195 nm with 3 nm gap. The structure is illuminated by a TM polarized plane wave with magnetic field along the y-direction. C
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the fundamental, the first, second, and third one in the measured spectra at 180, 335, 415, and 480 THz, respectively. The measured absorption for the fundamental mode is roughly 0.9 at normal incidence. Similar spectra to those shown in Figure 3 were measured at normal incidence for nanoresonators with a different length L while maintaining the spacer thickness. The dependence of the resonance positions of the fundamental and the second order mode obtained from the measured and simulated spectra as a function of the length of the MIM nanoresonator (L) for tALD = 3 nm and tALD = 8 nm are shown in Figure 4, respectively. The
Figure 5. (a) The 2D MIM absorber. (b) The simulated absorption as a function of particle size and frequency at normal incidence. Whitedotted curves show estimated resonance positions of all supported modes by the structure based on the semianalytical model. Geometrical parameters are chosen as P = 250 nm, L = 100−240 nm, tfilm = 200 nm, tALD = 3 nm, tNP = 30 nm.
model are indicated by white dotted lines. As expected, the resonance frequencies of all modes shift to lower frequencies by increasing the width L as observed in Figure 4. The estimated resonance frequencies of the excited modes based on a semianalytical model show perfect agreement with simulated absorption peaks. Note, that at normal incidence only the even modes are excited by the structure whereas the odd modes can be excited just at oblique incidence. However, the semianalytical model predicts all even and odd modes simultaneously (see Figure 5b). Combined with the excellent agreement between the measured and simulated absorption (see Figure 4), we conclude that the Fabry−Perot model properly predicts all spectral positions of the resonances. It should be noted that the excellent agreement holds for the parameter range of studied sample. Conclusion. To conclude, we have experimentally studied the extreme coupling in MIM plasmonic nanoresonators with a dielectric spacer in the order of few nanometers. The structures only became achievable by taking advantage of atomic layer deposition as a fabrication technique for the dielectric spacer. We have clearly shown that the resonance frequencies of the structure are shifted to extremely low frequencies with a ratio of resonance wavelength to period of λ/P ≈ 2.25 μm/0.25 μm = 9. We have explained our findings by using a semianalytical approach based on a Fabry−Perot model, which describes very well the observed resonance behavior of the structure. We have shown that slight deviations between experimental and numerical results for thin dielectric spacers can be explained by the surface roughness introduced by the ground layer. We believe that our research will open up new perspectives to fabricate deep-subwavelength plasmonic nanostructures by ALD. This strategy has the potential to enable many applications such as truly homogeneous metamaterials, omnidirectional perfect absorbers and to obtain an ultimate field enhancement as a required for many applications where quantum objects are coupled to plasmonic entities.
Figure 4. (a) The measured (dots) and simulated (solid lines) resonance frequencies of the MIM nanoresonator as a function of its length (L) for the fundamental and second order mode. (a) 3 nm spacer; (b) 8 nm spacer.
resonance frequency ωres decreases by increasing the length of the MIM nanoresonator (ωres ∝ 1/L). Our results reveal an astonishing agreement between the predictions of the numerical simulations and the experimentally measured resonance frequencies for thick as well as very thin spacers. For the small ALD gap of 3 nm, the resonance frequency of the fundamental mode shifts to extremely long wavelength when compared to the particle size. Discussion of the Results. To explain the optical properties of the nanoresonators, we employ a semianalytical model to estimate the resonance frequencies. It has been previously shown that the experimental and numerically estimated resonance frequencies of a two-dimensional structure are almost identical to the three-dimensional one.34,38 Hence, for simplicity we focus on a two-dimensional structure in the following where the upper metallic nanopatches are assumed to be infinitely extended into y-direction. The physical behavior of the three-dimensional structure, however, is equivalent to the two-dimensional one. Figure 5a shows a schematic view of the periodically arranged 2D MIM nanoresonators. The geometrical parameters are indicated in the figure caption. Our semianalytical approach explains the resonances using a Fabry−Perot model.9−12,52 This is in particular versatile to study MIM-waveguides in the extreme coupling regime. The details of the model and all computational aspects are documented in the Supporting Information. In short, we calculate the dispersion relation of the guided eigenmodes (neff(ω)) and the complex reflection coefficient at the interface of the MIM waveguide to an ambient material. The resonances are predicted for an isolated nanoresonator and not for an array. The resonances of the nanoantenna occur whenever the phase accumulation per round trip due the propagation and the reflection is a multiple of 2π (see Supporting Information). The simulated absorption upon TM-polarized plane wave excitation at normal incidence for the actual device as a function of frequency and wire width (L) is shown in Figure 5b. The resonance frequencies estimated by the semianalytical
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ASSOCIATED CONTENT
S Supporting Information *
Optical measurement, semianalytical model to explain the absorber resonance frequencies, and surface roughness effects. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. D
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Notes
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was partially supported by the German Federal Ministry of Education and Research (Metamat and PhoNa) and by the Thuringian State Government (MeMa). The authors thank Mario Ziegler for providing the AFM measurement, Stephan Fahr for surface roughness modeling, and Karsten Verch for the visualization in Figure 1.
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