Here we numerically and experimentally explore the rich phenomena in the optical responses and local electromagnetic fields of a MIM absorber mediated by the dispersive spacer. We first show that the line shape of the spectral absorption is strongly modified by the interaction between the plasmonic resonances and the optical phonons in the silicon dioxide spacer. Importantly, broadening the spectral absorption in the long wave infrared range is achieved by tuning the strength of coupling. Modification to the local electromagnetic field distribution in the epsilon-near-zero region is also numerically studied. The incident-angle dependence and polarization dependence of the broadened absorption spectrum are evaluated. We also show that the spectral broadening mechanism can be generalized to other frequency bands by employing different spacing materials such as silicon nitride and polydimethylsiloxane. Our results can be useful for designing spectrally selective thermal detectors and thermal emitters.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Plasmonic metamaterial absorbers (PMA) are arrays of engineered metallic subwavelength elements which can localize the incoming electromagnetic waves and produce strong near fields via the localized surface plasmon resonances (LSPR) [1–4]. The localized optical energy in the LSPRs is then converted into heat via the free carrier absorption in the nanostructured metals [5,6]. Since the geometric size and pattern of subwavelength elements (also called meta-atoms  or nanoantennas ) can be customized, optical responses of PMAs can be artificially tailored to adapt to a wide range of applications where light trapping and near field enhancement are needed [3,5–12]. One very typical PMA is the metal-insulator-metal (MIM) absorber which consists of a 2-D array of metallic nanoantennae on top of a thin dielectric spacer backed by a metallic backmirror [13–16]. The MIM absorber can strongly concentrate the electromagnetic field and thus achieve near unity absorption by resonantly exciting both electric and magnetic dipoles in a three layer stack with a total thickness much smaller than the resonant wavelength [17,18]. The ultra-thinness makes the MIM absorber ideal for applications such as thermal photovoltaic and thermal detection [19,20]. In most of the published work on MIM absorbers, the dielectric constants of the spacers are treated as constants (non-dispersive) and the optical resonances are mainly tailored by tuning the geometric structure and dimensions of the nanoantenna, the lattice constant of the antenna array and the thickness of the spacer. Also, the resonantly enhanced spectral absorption is usually narrowband, unable to cover the infrared atmospheric window from 8 μm to 14 μm. In the infrared regime, common polar dielectrics such as silicon dioxide [21–28], silicon nitride , silicon carbide  and aluminum arsenide  have intrinsic vibrational modes (optical phonons) in the mid-wave infrared (MWIR) and long-wave infrared (LWIR) range. The terminology “epsilon-near-pole” (ENP) has been established for the dielectric function at each vibrational mode . The imaginary part of the dielectric function Im(ε) exhibits a Lorentz line shape in each ENP region along with a distinct peak, which indicates the loss feature associated with the mode . Also, cross-over points between positive Re(ε) and negative Re(ε) exist in the dielectric functions of these materials, resulting in the “epsilon-near-zero” (ENZ) regions where Re(ε) ~0 . The ENP and ENZ regions in the dielectric functions of these materials provide a fundamentally new alternative for tailoring light-matter interactions at the nanoscale. Specifically, the optical responses and the resonant mode profile of plasmonic nanoantennae atop ENP and ENZ materials such as Ga doped ZnO and Al doped ZnO, 4H-SiC, GaAs and AlAs can be significantly altered by the optical phonons in the substrates [30,31,35,36]. However, the modification to the optical responses and the distribution of local electromagnetic fields caused by the coupling of the resonantly excited electric dipoles and magnetic dipoles in the MIM absorbers to the optical phonons in the spacers have yet been systematically explored.
In this paper, we numerically and experimentally investigate the role of ENP and ENZ spacers in tailoring the near field distribution and the optical spectra of the MIM absorbers. We first choose silicon dioxide, a commonly used dielectric material as the spacer and explore the interaction between the antenna resonances and the infrared phonons in silicon dioxide. We show that interesting features in the spectral absorption can emerge in the coupled system. The strength of the emerged new spectral features can be engineered by the designs of the antenna and the thickness of the spacer. In particular, we demonstrate that the coupling of the antenna resonances to the symmetric stretching mode of the silicon dioxide spacer contributes to a broadened high absorption band in the LWIR. The measured absorption of MIM absorber with a top layer of single-sized nanodisk array is over 75% from 11.5 μm to 13.8 μm, with a full width at half maximum (FWHM) of 2.8 μm. The total thickness of the MIM tri-layer stack is 660 nm, about 1/20 of the working wavelength (~12 μm). We also numerically examine the modifications to the local electromagnetic fields caused by the ENZ region at 8 μm. We then show that the broadband absorption of the nanodisk array based MIM absorber is polarization-independent, and a high absorption can be maintained when the incident angle is less than 40°. As a comparison, the polarization selective version of MIM absorber based on a top layer of single sized nanorod array is also simulated, fabricated and measured. Finally, we show by numerical simulation that the proposed method of spectral tailoring of MIM absorber can be extended to other frequency bands by properly selected spacer materials such as silicon nitride and polydimethylsiloxane (PDMS).
2. Results and discussion
Figure 1(a) shows the configuration of the studied absorber with a typical MIM structure which consists of a top layer of single-sized gold nanodisk antenna array, a silicon dioxide dielectric spacer in the middle and a gold backplate at the bottom. An example of fabricated gold nanodisk antenna array is also shown in the inset. Numerical simulations were carried out assuming a plane wave excitation at normal incidence using the FDTD Solutions from Lumerical Inc. Due to the periodicity of the structure, the simulation is reduced to one unit cell with periodic boundary conditions applied at the four sides of the unit cell. As presented by Fig. 1(b), both the real part Re(ε) and the imaginary part Im(ε) of the dielectric function of silicon dioxide are highly dispersive from 6 μm to 15 μm. The peak of Im(ε) between 9.0 μm and 9.5 μm labeled as ENP1 is attributed to the asymmetric stretching vibration while the peak of Im(ε) at ~12.5 μm labeled as ENP2 is due to the symmetric stretching vibration . The cross-over point between positive Re(ε) and negative Re(ε) at ~8 μm where Re(ε) ~0 is labeled as ENZ. (See Appendix A for details about the dielectric function of silicon dioxide and other configurations used in the simulation).
To illustrate the modulation effect of the highly dispersive silicon dioxide spacer on the optical responses of the MIM absorber, we plot in Fig. 2(a) the simulated spectral absorption of the MIM absorber with 500 nm thick silicon dioxide spacer as a function of the nanodisk radius R. As a comparison, we also plot the monotonically increasing resonant wavelength of the fundamental mode (FM) in the MIM absorber with a 500 nm thick fixed index spacer (ε = 1.452 = 2.1025) using the black dotted line (See Appendix B for detailed comparison). Obviously, the spectral absorption of the MIM absorber is significantly modulated by the highly dispersive silicon dioxide spacer, splitting into multiple variants of the fundamental modes  in the wavelength range from 6 μm to 16 μm. In fact, the Coulomb interaction between the electron-hole dipoles (plasmons) and the lattice vibrations (phonons) leads to the strong dependence of the plasmon wavelength on the dielectric functions of the surrounding media. Hence, the rapid change of the SiO2 dielectric constant near its phonon frequencies further compresses the plasmons in space, allowing the gold nanodisk to support additional low energy plasmon oscillations [29,37,38]. For verification, we fabricated a variety of MIM absorbers with 500 nm thick silicon dioxide spacer, each of which has a distinct nanodisk radius R. The measured spectral absorption as a function of R shown in Fig. 2(b) agrees well with the simulated results. To further reveal the influences on the multiple optical resonances of the MIM absorber caused by the dispersion in silicon dioxide spacer, we plot in Fig. 2(c) the resonant wavelengths of the two optical resonances in the 6 μm–8 μm range and 9.3 μm–12 μm range as a function of R, respectively. The resonant wavelength of the fundamental mode in the MIM absorber with a 500 nm thick fixed index spacer (ε = 1.452 = 2.1025) is also plotted for comparison. It can be seen that in the 6 μm–8 μm range, when the resonance approaches the ENZ point with the increase of R, the rate of the resonant wavelength shift slows downs caused by the corresponding reduction in the refractive index of SiO2. Similarly, when the resonance moves from 12 μm towards the ENP1 point, the resonance shift rate also slows down, and this is because the corresponding increase in the refractive index compensates the decrease of R. We then focus on the modified optical responses in the ENP2 region. From Fig. 2(a) we see that as R increases from 1500 nm to 2100 nm, the strong coupling between the plasmonic resonance and the phonon leads to a broadened spectral absorption in the ENP2 region. (See Appendix C for detailed analysis about the dual peak in the spectral line shape). In Fig. 2(d) we plot the simulated and measured spectral absorption of the MIM absorber with silicon dioxide spacer assuming t2 = 500 nm and R = 1750 nm, respectively. The two peaks in the measured absorption spectrum are 86.3% at 11.75 μm and 96.7% at 13.22 μm, respectively. The FWHM is found to be 3 μm, assuming we take 12.95 μm as the center wavelength of the absorption band. For comparison, we also plot the simulated spectral absorption of the MIM absorber with fixed index spacer assuming t2 = 200 nm and R = 1750 nm and the corresponding FWHM is found to be 1.5 μm only. We emphasize that previous publications on the strong coupling between the plasmonic resonances and the optical phonons in silicon dioxide mainly focus on the ENP1 region [21–25]. While our results show that the coupling in the ENP2 region can also lead to useful spectral features. We also note that in order to broaden the spectral absorption of the MIM absorber, several other methods have been proposed. One method is to geometrically construct a top layer of nanoantennas with a variety of sizes and hence resonant wavelengths to generate a broadened absorption band [14,39,40]. Another method is to replace the noble metals in the MIM absorber such as gold with metals with higher optical losses (high-ε” metals) such as tungsten (W), titanium (Ti), chromium (Cr) and nickel (Ni) [41,42]. Compared to these methods, our method of broadening the spectral absorption via the optical phonons in the spacer requires only a single-sized nanoantenna array and noble metals, thus simplifying the design process.
Besides the modification to the spectral line shape, the dispersion in the spacer can also influence the near-field distribution in the MIM structure. Figure 3(a) shows Re(ε) and Im(ε) of silicon dioxide and the corresponding spectral absorption from 6 μm to 9 μm. The local electric fields at eight wavelengths in this band are plotted in Fig. 3(b)-(i). It can be seen that as the real part Re(ε) of silicon dioxide is reduced from 1.5 at λ = 6.45 μm to −4.0 at λ = 8.97 μm, the air becomes more and more “denser”, i.e. with higher relative permittivity, than silicon dioxide. Consequently, the resultant pattern of the local electric field |E| gradually shifts back from the spacer to the air. In the meantime, the imaginary part Im(ε) of silicon dioxide increases from 0.016 at λ = 6.45 μm to 1.93 at λ = 8.97 μm. The increased loss of silicon dioxide causes the local electric field |E| to diminish at above 8 μm.
Since an effective absorber should maintain a high absorption within a wide range of incident angle, we now inspect the spectral absorption as a function of the incident angle of the plane wave excitation. As shown by Fig. 4(a), in TE polarization case, the E component is aligned in the x-y plane while the incident angle is the angle between H component and z axis. While in the TM polarization case as shown by Fig. 4(b), the H component is aligned in the x-y plane while the incident angle is the angle between E component and z axis. The simulated results in Fig. 4(c) and 4(d) show that in both TE polarization case and TM polarization case, the broadened high absorption in the ENP2 region can be maintained from 0° to 40° while in TM case the high absorption can be maintained up to 60°. This is consistent with previously reported results from MIM absorbers with single peak geometrical resonances [13,17,20,43,44]. We also note that in the TM case, as the incident angle is above 15°, new high absorption bands emerge in the contour near 8 μm and this is attributed to the excitation of Berreman mode and ENZ mode [24,45].
To demonstrate that our design concept can be extended to polarization selective configurations, we also fabricated MIM absorbers with nanorod antennas as the top layer. Figure 5(a) shows the SEM image of one fabricated MIM absorber with nanorod antennas and relevant geometric parameters. The measured absorption spectrum of the structure using non-polarized light is shown in Fig. 5(b) with blue solid line. As a comparison, the simulated absorption spectra under normally incident TE polarized light (black solid line) and TM polarized light (red solid line) are also plotted. It can be seen that the nanorod antennas based MIM absorber mainly absorbs the TE polarized light while it only absorbs a small portion of the TM polarized light. When measured using non-polarized light, the absorption is the average value (purple dash-dotted line) of the absorption spectra of TE and TM cases. From the comparison between the purple dash-dotted line and the blue solid line, a good agreement is found between the simulation and the experiment. We also fabricated and measured a series of MIM absorber structures with nanorod length L ranging from 2700 nm to 3300 nm and W fixed at 1000 nm. Again, we find a good agreement between the contour plots of the simulated and measured absorption spectra assuming normally incident unpolarized light, as shown in Fig. 5(c) and 5(d), respectively.
Finally, we numerically show that the design concept can be extended to other frequency band by properly selecting the spacing material of the MIM absorber. We choose two representative materials: silicon nitride with optical phonons in the 20–30 μm range and PDMS with optical phonons from 8.5 μm to 10.5 μm, as shown in Fig. 6(a) and 6(c). By varying the geometric parameters of the MIM structure (R, t2 and P) to couple the plasmonic resonance to the optical phonons in the spacer, a broadened absorption band can be obtained in the corresponding frequency bands. Figure 6(b) and 6(d) illustrate how to achieve the broadened spectral line shape of A(ω) of the MIM absorber with silicon nitride spacer and PDMS spacer by varying the nanodisk radius R. The optimized spectral line shapes are plotted in Fig. 6(a) and 6(c), respectively.
In conclusion, we comprehensively investigated the role of optical phonon of polar dielectric spacers in tailoring the patterns of the local fields and the line shape of the spectral absorption of the MIM absorbers. The strength of spectral modulation can be controlled via the antenna geometric design and the thickness of the spacer. Slowing down of resonance shift as a function of nanodisk radius caused by the dispersion in the spacer is also observed. Broadened spectral line shape can occur when two resonant peaks are tuned to be close enough to each other. The broadened absorption can maintain at a high value when the incident angle is less than 40°. Both polarization insensitive and polarization sensitive configurations have been demonstrated. Extension of the design concept to other frequency band is numerically discussed by using different spacing materials such as silicon nitride and PDMS. The demonstrated spectral broadening mechanism does not require complicated design of mult-resonant elements on the top layer, neither does it require high-ε” metals for the plasmonic nanoantennas. Therefore it is suitable for large-scale production with noble metals. The demonstrated “band-pass” type of absorption spectrum is located at the long wave infrared atmospheric window (8–14 μm) and can be extended to longer wavelength range. We therefore envision the demonstrated method to have a wide range of potential applications such as spectral and polarization selective thermal detection, thermal emission .
Numerical Simulation and Analysis. The periodic structure is studied by simulating a unit cell with periodic boundary conditions applied at the x- and y- boundaries and perfectly matched layers (PMLs) applied at the z-boundaries. A plane wave source is used to excite the structure and a power monitor is used to collect the reflected waves. Since the transmission is eliminated by the gold backplate, the calculation of absorption is simplified to A(ω) = 1 – R(ω). The dispersive complex dielectric constants of gold (Au) is obtained from . The Re(ε) and Im(ε) of silicon nitride is measured by ellipsometry (IR-Vase II from J.A. Woollam). The Re(ε) and Im(ε) of silicon dioxide and PDMS are from  and , respectively.
Fabrication. The substrate used for the absorber is a single-sided polished 500 μm silicon substrate. First, a 10nm titanium adhesion layer was evaporated on the substrate followed by a 100nm gold film, which serves as the metal back plate of the MIM structure. Thereafter, a layer of 500nm thick SiO2 was deposited on the gold layer as the dielectric spacer by plasma enhanced chemical vapor deposition (PECVD). Then, a layer of e-beam resist (PMMA AR-P 679.04 950K) was spin coated on the SiO2 dielectric spacer. The sample was then exposed by electron beam lithography (EBL) according to the designed patterns of the nanoantenna array with a dose of 1350μC/cm2 at a current of 10 nA. After exposure, the sample is developed in a mixed solution of methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) of MIBK:IPA = 1:3 to generate the patterns. Then, an adhesion layer of 10nm nickel and a 50 nm gold film were evaporated onto the patterned resist. Finally, a standard lift-off process was used to remove the resist and the excessive gold.
Characterization of Samples. The reflectance spectra of the fabricated MIM absorbers are measured using microscope coupled Fourier transform infrared (FTIR) spectrometer (VERTEX 70 from Bruker). The area of each nanoantenna array on top of the absorber is 450 μm × 450 μm, and the aperture size of the FTIR is 250 μm × 250 μm. Since the metal back plate (100 nm) is thick enough to block the transmitted light, the transmittance of the absorber is considered to be zero. A gold mirror from Thorlabs Inc. is used as the reference for measuring and calculating the reflectance of the MIM absorber.
Appendix A Details about the dielectric function of silicon dioxide and other configurations used in the simulation
The dielectric function is the square of the complex refractive index and can be modeled by a superposition of many Lorentzian oscillators (see Fig. 7).
where , is a real constant, N is the number of oscillators (N = 3), and , , and are the strength, the width, and the center wave number of the oscillator, respectively. Note that is almost equal to the square of the refractive index at 6000 , represents the effect of all oscillators well removed to higher frequencies, so we take = 2.1. Each oscillator corresponds to an absorption band, with its center wave number located at the absorption peak.
The simulation time is 1000 fs and the convergence criteria were set to be with auto shutoff min of 1e−5. In order to reduce the simulation time, we set the mesh size to be 50 nm along x- and y-axes and 5 nm along z-axis. During the meshing process, we further verified that the reflection spectrum did not change with the denser mesh. The coefficient numbers for silicon dioxide was 10 and the root-mean-square (RMS) errors of the approximation for silicon dioxide was 0.0674. The coefficient numbers for silicon nitride was 13 and the RMS errors of the approximation for silicon nitride was 0.0095. The coefficient numbers for PDMS was 14 and the RMS errors of the approximation for PDMS was 0.0431. The coefficients number for Au fitting is 5 with RMS error of the approximation to be 0.0214. The cross-section of the electric field and magnetic field distribution was detected by a 2D field profile monitors in x-y plane and x-z plane, respectively (see Table 1).
Appendix B The spectral absorption as a function of the dielectric function and thickness of the spacer
To reveal the influences of the dielectric function and thickness of the spacer on the spectral absorption, we first plot in Fig. 8(a) the simulated spectral absorption of the MIM absorber with a 500 nm thick fixed index spacer. As the nanodisk radius R increases from 700 nm to 2200 nm, the resonant wavelength of the fundamental mode (FM) almost increases monotonically from 6 μm to 16 μm. Higher order resonance (HM) is only excited when R is above 2000 nm. We then plot the simulated spectral absorption of the MIM absorber with a 250 nm thick, 500 nm thick and 750 nm thick silicon dioxide spacer in Fig. 8(b), (c) and (d), respectively. It can be seen that the high dispersion in the silicon dioxide spacer cause the spectral absorption of the fundamental mode to split into multiple peaks. The relative strength of each peak can be tuned by varying the thickness of the spacer.
Appendix C Detailed analysis of the mode profile at each resonance
To further understand the nature of the spectral absorption mediated by the dispersion in the silicon dioxide spacer, we first choose two resonant wavelengths labeled as FM1 and FM2 in Fig. 9(c) to plot the local electromagnetic fields. From Fig. 9(a)-(d) it is seen that the distribution of the local electromagnetic fields displays the same profile at FM1 and FM2. This confirms that the multiple peaks in the spectral absorption of the MIM absorber with silicon dioxide spacer are the variants of the same fundamental mode. We then look into the local electromagnetic fields at the higher order mode labeled as HM in Fig. 9(c). From Fig. 9(e) and (f), we can see that the profile of the higher order mode has two maxima in the |H| field at the two edges of the nanodisk, which is distinctly different from the profile of the fundamental mode.
National Natural Science Foundation of China (NSFC) (11604110, 11774112); National Key Research and Development Program of China (2016YFC0201300); The Innovation Foundation of Shenzhen Government (JCYJ20160429182829578); The Fundamental Research Initiative Funds for Huazhong University of Science and Technology (2017KFYXJJ031).
We thank Li Pan engineer in the Center of Micro-Fabrication and Characterization (CMFC) of WNLO for the support in PECVD fabrication. We thank Zeng Tiantian engineer in the Huazhong University of Science & Technology Analytical & Testing Center for the support in FTIR test. We thank the technical support from Experiment Center for Advanced Manufacturing and Technology in School of Mechanical Science & Engineering of HUST.
References and links
1. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial Electromagnetic Wave Absorbers,” Adv. Mater. 24(23), OP98–OP120 (2012). [PubMed]
2. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]
3. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94(7), 4632–4642 (2003). [CrossRef]
4. Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014). [CrossRef]
5. G. Baffou and R. Quidant, “Thermo-plasmonics: using metallic nanostructures as nano-sources of heat,” Laser Photonics Rev. 7(2), 171–187 (2013). [CrossRef]
9. H. Zhu, F. Yi, and E. Cubukcu, “Nanoantenna Absorbers for Thermal Detectors,” IEEE Photonic Tech L 24(14), 1194–1196 (2012). [CrossRef]
10. D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004). [CrossRef] [PubMed]
11. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the Blackbody with Infrared Metamaterials as Selective Thermal Emitters,” Phys. Rev. Lett. 107(4), 045901 (2011). [CrossRef] [PubMed]
13. C. Wu, I. Burton Neuner, G. Shvets, J. John, A. Milder, B. Zollars, and S. Savoy, “Large-area wide-angle spectrally selective plasmonic absorber,” Phys. Rev. B 84(7), 075102 (2011). [CrossRef]
14. A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492(7427), 86–89 (2012). [CrossRef] [PubMed]
15. A. Ghobadi, H. Hajian, M. Gokbayrak, S. A. Dereshgi, A. Toprak, B. Butun, and E. Ozbay, “Visible light nearly perfect absorber: an optimum unit cell arrangement for near absolute polarization insensitivity,” Opt. Express 25(22), 27624–27634 (2017). [CrossRef] [PubMed]
16. Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically Tunable Metasurface Perfect Absorbers for Ultrathin Mid-Infrared Optical Modulators,” Nano Lett. 14(11), 6526–6532 (2014). [CrossRef] [PubMed]
18. P. T. Bowen, A. Baron, and D. R. Smith, “Theory of patch-antenna metamaterial perfect absorbers,” Phys. Rev. A 93(6), 063849 (2016). [CrossRef]
19. J. Y. Suen, K. Fan, J. Montoya, C. Bingham, V. Stenger, S. Sriram, and W. J. Padilla, “Multifunctional metamaterial pyroelectric infrared detectors,” Optica 4(2), 276–279 (2017). [CrossRef]
20. C. Wu, B. Neuner III, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J Opt. 14(2), 024005 (2012). [CrossRef]
21. J. A. Mason, G. Allen, V. A. Podolskiy, and D. Wasserman, “Strong Coupling of Molecular and Mid-Infrared Perfect Absorber Resonances,” IEEE Photonic Tech L 24(1), 31–33 (2012). [CrossRef]
22. D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale Metamaterials and Phonons,” Nano Lett. 11(5), 2104–2108 (2011). [CrossRef] [PubMed]
23. C. Huck, J. Vogt, T. Neuman, T. Nagao, R. Hillenbrand, J. Aizpurua, A. Pucci, and F. Neubrech, “Strong coupling between phonon-polaritons and plasmonic nanorods,” Opt. Express 24(22), 25528–25539 (2016). [CrossRef] [PubMed]
24. Y.-B. Chen and F.-C. Chiu, “Trapping mid-infrared rays in a lossy film with the Berreman mode, epsilon near zero mode, and magnetic polaritons,” Opt. Express 21(18), 20771–20785 (2013). [CrossRef] [PubMed]
25. F. Liu, T. Zhan, A. Y. Zhu, F. Yi, and W. Shi, “Band structure and dispersion engineering of strongly coupled plasmon-phonon-polaritons in graphene-integrated structures,” Opt. Express 24(2), 1480–1494 (2016). [CrossRef] [PubMed]
26. I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, and G. R. Nash, “Strong Coupling in the Far-Infrared between Graphene Plasmons and the Surface Optical Phonons of Silicon Dioxide,” ACS Photonics 1(11), 1151–1155 (2014). [CrossRef]
27. M. K. Gunde, “Vibrational modes in amorphous silicon dioxide,” Physica B 292(3-4), 286–295 (2000). [CrossRef]
28. R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. 46(33), 8118–8133 (2007). [CrossRef] [PubMed]
29. Q. Guo, F. Guinea, B. Deng, I. Sarpkaya, C. Li, C. Chen, X. Ling, J. Kong, and F. Xia, “Electrothermal Control of Graphene Plasmon-Phonon Polaritons,” Adv. Mater. 29(31), 1700566 (2017). [CrossRef] [PubMed]
30. J. Kim, A. Dutta, G. V. Naik, A. J. Giles, F. J. Bezares, C. T. Ellis, J. G. Tischler, A. M. Mahmoud, H. Caglayan, O. J. Glembocki, A. V. Kildishev, J. D. Caldwell, A. Boltasseva, and N. Engheta, “Role of epsilon-near-zero substrates in the optical response of plasmonic antennas,” Optica 3(3), 339–346 (2016). [CrossRef]
31. S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-Near-Zero Modes for Tailored Light-Matter Interaction,” Phys. Rev. Appl. 4(4), 044011 (2015). [CrossRef]
32. S. Molesky, C. J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21(S1Suppl 1), A96–A110 (2013). [CrossRef] [PubMed]
33. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer New York, 2010).
34. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017). [CrossRef]
35. S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93(6), 063846 (2016). [CrossRef]
36. Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-Near-Zero Strong Coupling in Metamaterial-Semiconductor Hybrid Structures,” Nano Lett. 13(11), 5391–5396 (2013). [CrossRef] [PubMed]
37. V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly Confined Tunable Mid-Infrared Plasmonics in Graphene Nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013). [CrossRef] [PubMed]
38. V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid Surface-Phonon-Plasmon Polariton Modes in Graphene/Monolayer h-BN Heterostructures,” Nano Lett. 14(7), 3876–3880 (2014). [CrossRef] [PubMed]
40. Y. X. Cui, J. Xu, K. H. Fung, Y. Jin, A. Kumar, S. L. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett. 99(25), 253101 (2011).
41. W. Wang, Y. Qu, K. Du, S. Bai, J. Tian, M. Pan, H. Ye, M. Qiu, and Q. Li, “Broadband optical absorption based on single-sized metal-dielectric-metal plasmonic nanostructures with high-ε” metals,” Appl. Phys. Lett. 110(10), 101101 (2017). [CrossRef]
42. W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014). [CrossRef] [PubMed]
43. J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
44. J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83(16), 165107 (2011). [CrossRef]
46. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]
47. Z. M. Zhang, G. Lefever-Button, and F. R. Powell, “Infrared Refractive Index and Extinction Coefficient of Polyimide Films,” Int. J. Thermophys. 19(3), 905–916 (1998). [CrossRef]
48. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).