Abstract
This work develops and analyzes a planar subwavelength device with the ability of onedimensional resolution at visible frequencies that is based on alternately arranged insulatormetal (IM) and insulatorinsulatormetal (IIM) composite structures. The mechanism for the proposed device to accomplish subwavelength resolution is elucidated by analyzing the dispersion relations of the IMIIM composite structures. Electromagnetic simulations based on the finite element method (FEM) are performed to verify that the design of the device has subwavelength resolution. The ability of subwavelength resolution of the proposed device at various visible frequencies is achieved by slightly varying the constituent materials and geometric parameters. The proposed devices have potential applications in multifunctional material, realtime superresolution imaging and highdensity photonic components.
Introduction
The demand for highdensity photonics components has recently increased significantly. Surface plasmonpolaritons (SPPs) have attracted much attention because they can be confined on a subwavelength scale, helping to meet the requirement of high density^{1}. The practicability of plasmonic based components must be determined. Comparing to the totally three dimensional fabrications, a class of novel optical devices named metasurface with a reduced dimensionality can be used to control the propagation of light^{2,3}. Such optical devices have great potential for use in fabricating the nextgeneration highdensity photonics components for their ease of fabrication. Actually, the multilayer hyperbolic metamaterials (MHMs) that consist of a few pairs of Ag and dielectric layers with the thickness of 10 nm have been fabricated by using such as focused ion beam (FIB)^{4}, ebeam lithography system^{5,6,7} and physical vapor deposition (PVD)^{4,5,6} with high reliability and accuracy. The recent literature has proposed many planar photonics components. These include the optical vortex plate^{8}, broadband quarterwave plate^{9,10}, plasmonics lens^{11}, optical antenna^{12,13}, graphene devices that use transformation optics^{14}, the gradient metasurface^{15} and subwavelength imaging components^{16,17,18}. As well as a lowcost of manufacture, tunability is critical.
Super and hyperlenses have been extensively studied owing to their ability of achieving subwavelength resolution^{19,20}. Very recently, the hybridsuperlenshyperlens was developed and demonstrated to exhibit superresolution^{21,22,23}. This device consists of both planar and concave metaldielectric metamaterials. It overcomes the disadvantages of traditional nearfield scanning optical microscopy, including low throughput, poor compatibility with samples and an inability to obtain a complete image in a single scan. However, the range of materials that can be used to break optical diffraction is severely limited and their operating bands may not be changed arbitrarily. Additionally, since they are threedimensional structures, they are difficult to be integrated with other ultrathin photonic components.
This work proposes a planar subwavelengthresolved system that is based on alternately arranged insulatormetal (IM) and insulatorinsulatormetal (IIM) composite structures. The dispersion relations of the alternately staked IMIIM composite structures are studied. The ability of subwavelength resolution of the proposed structures is demonstrated by running electromagnetic simulations using the finite element method (FEM). This work develops the conceptual basis of a tunable flat photonics device that overcomes the optical diffraction limit. The proposed structure can be fabricated by using the same techniques for MHMs.
Results
Figure 1(a) presents the investigated structure, which consists of a few pairs of alternately arranged insulatormetal (IM) and insulatorinsulatormetal (IIM) semiinfinite components with relative permittivities of ε_{1}/ε_{m} and ε_{2}/ε_{3}/ε_{m} respectively. In Fig. 1(a), d_{1} and d_{2} denotes the lengths of IM and IIM in the x direction, respectively and t is the thickness of the middle insulator in IIM (ε_{3}). (The number of pairs is varied according to the operation conditions, as presented in Table 1.) Generally, SPPs in both IM and IIM structures are vertically confined (in the zdirection), but extended in the xyplane. The effective refractive index of the IM or the IIM structure, n, is given by the formula, n = c·Re[k]/ω, where k is the wavevector of the excited SPPs and can be determined by measuring the wavelength of the SPPs. (However, the sign of n is determined from the slope of the dispersion curve of the SPPs.) Therefore, the developed system (Fig. 1(a)) is viewed as an alternately stacked periodic system with an effective refractive index of n_{e}_{1} (n_{e}_{2}), as presented in Fig. 1(c).
The dispersion relation of the equivalent structure (Fig. 1(c)), which can be obtained using the transfer matrix method^{24}, is
where and are the xdirectional component of wavevectors in the materials with effective refraction indices of n_{e}_{1} and n_{e}_{2}, respectively (and is the y and zdirectional wavevectors); Λ = d_{1} + d_{2} is the period of the alternately stacked system. Since (with μ = 1), the long wave approximation ( where λ is the wavelength of the incident source) and expansion of Eq. (1) to second order, the dispersion relation will be simplified to
where and are the effective relative permittivities in the perpendicular (x) and parallel (z) directions, respectively and k_{0} is the free space wave vector. (See Appendix A of supplementary information) Superresolution applications that use the periodic layered system as shown in Fig. 1(c) require and ^{25}. Considering ε_{e}_{1}·ε_{e}_{2} < 0, these criteria can be met. Therefore, an imaging device with the ability of onedimensional subwavelength resolution can be realized by combining IM and IIM components.
Since the used components (IM or IIM) support SPPs at the dielectricmetal interface (as shown in the inset (i) in Figs. 2(a) and (b)), the structure in Fig. 1(a) can be regarded as a SPPsbased waveguide. First, the dispersion relations (frequency vs. wavevector, f – k diagrams) of IM and IIM are determined by simulation. Figures 2(a) and 2(b) present the simulated dispersion relations of the IM and IIM structures, respectively (The metal substrate is Cu, ε_{1} = 2, ε_{2} = 1, ε_{3} = 4 and t = 5 nm.) Figure 2(a) reveals that the slopes (f/k_{x}) of the dispersion curve in all of wavevectors are positive. Hence, the IM structures have positive effective refractive indices. The wavelength of the excited SPPs falls as the operating frequency increase as shown in the inset in Fig. 2(a). Figure 2(b) indicates both positive and negative slopes of the dispersion relation in different wavevector regions. Between the two dashed lines in Fig. 2(b), one frequency corresponds to two wavevectors, indicating that two kinds of SPPs would be excited at this frequency. The excited SPPs with the larger (smaller) wavelength are associated with the lowerk (higherk) mode. The lowerk (higherk) mode has a positive (negative) slope, so the IIM structure has a positive (negative) refractive index in that mode. Notably, in the higherk mode, the wavelength of the excited SPPs increases with the operating frequency (as shown in the insets in Fig. 2(b)). This relationship is a characteristic of a material with an effective negative refractive index^{26,27}.
f − k diagrams.
(a) IM (b) IIM structures. Insets (i) in (a) and (b): simulated structures and Hy field contours around insulatormetal interface (as shown in Fig. S2) Insets (ii) ~ (iv) in (a): magnetic field (Hy) contours at 300, 350 and 400 THz, respectively (in region where f − k diagram has a positive slope). Insets (ii) ~ (iv) of (b): magnetic field (Hy) contours at 370, 390 and 400 THz, respectively (in region where f − k diagram has both positive and negative slopes). Metal substrate is Cu. ε_{1} = 2, ε_{2} = 1, ε_{3} = 4 and t = 5 nm.
The insets in Fig. 2(b) reveal that the propagation loss of the higherk mode is very strong (meaning that this mode can only propagate a short distance.) The propagation loss declines as the operating frequency increases. For the higherk mode, the relationship between the effective refractive index and the effective permittivity is The real and imaginary parts of the effective refractive index are determined by measuring the excited wavelength and propagation length of the higherk mode, (n = n_{r} + in_{i}; here n_{i} < n_{r}) The corresponding relative permittivity is (between the two dashed lines in Fig. 2(b)). (See Appendix B of supplementary information.) The effective refractive index and the relative permittivity of the IM structure (both of which are positive) are also determined from this measurement. Based on Figs. 2(a) and 2(b), the composite structure of alternatively arranged IM (with a positive relative permittivity) and IIM (with a negative relative permittivity) satisfies the requirement for subwavelengthresolved applications in particular frequency ranges.
To demonstrate further the tunability with subwavelengthresolved ability over whole visible region, the effects of changing the relevant parameters (such as: ε_{m}, ε_{2}, ε_{3} and t) on the f − k diagrams of IM and IIM are considered. Figure 3(a) displays the f − k diagrams of the IM structure with Ag (blue line) and Cu (red line) metal substrates (ε_{1} = 2). The f − k diagrams approach different asymptotes (dashed lines) in Fig. 3(a). The asymptote frequency (the surface plasma frequency, ω_{sp}), is estimated using the formula, ^{28} and is proportional to the plasma frequency of the metal. Clearly, ω_{sp} decreases as ε_{1} increases. Figure 3(b) shows the f − k diagrams of IM structure for various values of ε_{1} which verify the relation between ω_{sp} and ε_{1} The yellow region in Fig. 3(b) is the range of frequencies at which the dispersion diagrams of IM and IIM intersect each other. The proposed subwavelengthresolved structure operates in this region. Figures 3(a) and 3(b) also reveal that a metal with a larger ω_{sp} and a dielectric with a smaller ε_{1} are required as the frequency of the incident light increases. Notably, to provide good resolution, the isofrequency dispersion curve of the alternately arranged structure should have a hyperbolic form and the hyperbola must be as flat as possible (as shown in the inset in Fig. 3(b))^{29}.
(a)–(d): f − k diagrams. (a) IM structure of Cu (red line) and Ag (blue line) metal substrate withε_{1} = 2 Dashed lines are asymptotes of ω_{sp} (b) IM structure for different values of ε_{1} with Cu metal substrate. Purple line is dispersion diagram of IIM structure with Cusubstrate, ε_{2} = 1, ε_{3} = 4 and t = 8 nm. Inset: shows Hyperbolic isofrequency curve (Eq. (2)) when alternately arranged IMIIM structure fulfills the requirements for subwavelength resolution, which is that the point of intersection in yellow region. (c) IIM structure for different values of t with Cu metal substrate, ε_{2} = 1, ε_{3} = 4. (d) IIM structure for various values of ε_{3} with Cu metal substrate, ε_{2} = 1 and t = 8 nm.
Figure 3(c) presents the f − k diagrams of the IIM structure for ε_{3} layer with various values of t, a Cu metal substrate, ε_{2} = 1 and ε_{3} = 4 Figure 3(c) indicates that the f − k diagrams in the higherk mode in the negative slope region become flatter as t increases. The simulation results reveal that the feature of negative slope disappears once t increases to 28 nm (not shown here). This effect follows from the gradual increase in the propagation losses of the higherk (negative slope) mode^{26} and implies that the thickness of the ε_{3} layer provides a means of cutting off the negative slope of the higherk mode. Figure 3(d) plots f − k diagrams of the IIM structure for various ε_{3} with the Cu metal substrate, ε_{2} = 1 and t = 8 nm. Figure 3(d) shows that the frequency of the SPPs in the IIM structure in the negative slope region decreases as the value of ε_{3} increases. Figure 3(d) indicates that the operating frequency of the IIM structure can be finetuned by varying the material parameter ε_{3}. In the following, this characteristic is exploited to modulate the operating frequency to meet the requirements for subwavelength resolution.
Next, the ability of subwavelength resolution of the proposed IM and IIM composite structure is demonstrated. Figure 4 plots the simulated structure. In Fig. 4, a chromium (Cr) mask with two holes is the object, which is in contact with the composite structure of alternately arranged IM and IIM. Two operating frequencies in the visible regime are considered – those of red light and violet light. The radius and the centertocenter distance of the two holes in red (violet) light are 35 nm and 320 nm (40 nm and 205 nm), respectively. Linearly polarized light (polarized in the xz plane) is incident on the Cr mask. Owing to the superresolution, the light that is diffracted from the tiny holes excites the SPPs and propagates through the proposed device. Finally, the subwavelength features are resolved at the end of the composite structure (Fig. 5).
Figures 5(a) and 5(b) present the simulated timeaveraged power flow contours and the corresponding isofrequency dispersion curves for the structure in Fig. 4 at incident frequencies of 432.9 THz and 431.63 THz (red light), respectively. (Table 1 presents the material and geometric parameters of the IM and IIM structures.) For comparison, Fig. 5(c) plots the contours and isofrequency dispersion curve at 432.9 THz for the imaging system that includes only the IM structure (i.e. the dielectric materials (ε_{2} and ε_{3}) of the IIM structure are removed). These contours are extracted in the xy plane and 2.5 nm above the top metal substrate. Figures 5(a) and 5(b) reveal that the two tiny holes are resolved at the end of the proposed system with the alternate components. The isofrequency dispersion curves in these figures satisfy the requirements for subwavelength resolution, as they are hyperbolic. Conversely, Fig. 5(c) shows that, when only the IM structure is utilized, the light that is diffracted from one of the two tiny holes (in the form of SPPs) interferes with that from the other in the system. These holes cannot be resolved at the end of the system. The isofrequency dispersion curve becomes elliptical. Figure 5(d) displays the timeaveraged power flow contours and the isofrequency dispersion curve obtained using the same structure as in Figs. 5(a) and (b) but with an incident frequency of 350 THz. Figure 5(d) shows that the diffraction occurs and the holes cannot be resolved at the end of the system because the requirements for subwavelength resolution are not met, as mentioned above (since the sofrequency dispersion curve is elliptical). Finally, Fig. 5(e) plots the simulated timeaveraged power flow contours and the isofrequency dispersion curve for the structure in Fig. 4 but with an incident frequency of 732.52 THz (violet light) and with various material and geometric parameters also given in Table 1. Figure 5(e) clearly reveals that the metal substrate and geometric parameters can be changed to resolve the two tiny holes with a centertocenter distance of less than half of the incident wavelength in the violet light region. It's also worth mentioning that, for above successfully resolved cases (Figs. 5(a), 5(b) and 5(e)), the two holes on the Cr mask still can be resolved when their zdirectional positions are changed. It is originated from that the SPPs on the IM structure can be excited by the evanescent waves that emit from the objects and the above mentioned mechanism still work. As an example, considering two holes with centers locating at 30 nm and 80 nm, respectively, above the metal top (the other conditions are the same as Fig. 5(e)), our simulation results reveal that both holes can be resolved at the end of the proposed device. (See Appendix C of supplementary information) This feature enables the proposed structure to transform the twodimensional objects into the onedimensional image.
Table 1 further indicates that small changes in the material and geometric parameters change the frequency at which subwavelength resolution is obtained. For example, in Figs. 5(a) and 5(b), small changes in ε_{1} (from 2 to 2.25) and t (from 8.5 nm to 8 nm) change the operating frequency of subwavelength resolution from 432.9 THz to 413.63 THz, revealing that more parameters of the proposed structure can be adjusted to achieve superresolution function for a light source with various frequency. The fabrication tolerances of the designed geometric parameters d_{1}, d_{2} and t are also examined. For d_{1} and d_{2}, according to Ref. 5, the thickness error of sputtered film (10 nm Ag and 10 nm Si) for the MHMs is not larger than 1 nm. With this thickness error, Eq. (2) shows that the isofrequency dispersion relation in Figs. 5(a), 5(b) and 5(e) still have the hyperbolic form. Hence, the objects (two holes) can still be resolved. That is to say, the error in thickness of the multilayers that is caused by the stateofart technology has little effect on the designed parameters d_{1} and d_{2}. Conversely, for the designed parameter t = 8 nm in Fig. 5(a), an error of 3 nm in t will cause a deviation of 22 THz (about 5%) from the operation frequency designed at 433 THz. (See Appendix D of supplementary information.) Based on these analyses, the proposed design is practical for the stateofart technology.
Notably, the structure that is proposed herein is better than those developed elsewhere^{21,22,23}, in occupying less space, being easier to fabricate and having a flexible design with superresolution. Our investigations exhibit that, by designing the isofrequency dispersion curve (i.e. , as shown in Fig. 5), the propagating waves in the IMIIM composite structures can be manipulated. By suitably controlling the incident angles and positions of launched sources, the planar subwavelength focusing of surface plasmon beam can be achieved by using the proposed structure^{30}. Some other fantastic phenomena that are based on the SPPs wave, such as the feature of scatteringfree^{31}, totalexternalreflection^{27}, allangle negative refractive^{32} and spatial plasmonic Bloch oscillations^{33}, can also be implemented by using the proposed structure. Moreover, the typically resolvable size depends on the geometry and material parameters and hence can be deigned. (For example, this size is about 200 nm for the incident frequency of 723.52 THz in the design of Fig. 5(e).) Therefore, the proposed planar structures have a wide range of potential applications in different fields (owing to their periodic construction) such as in hyperbolic materials^{34,35}, nearzero materials^{36,37} and highly efficient nanoscale mirrors^{27}.
Discussion
A planar subwavelengthresolved device (at the visible frequencies) that is based on alternately arranged IM and IIM composite structures is proposed and analyzed. The IM and IIM components in the proposed device can be viewed as forming an effective optical medium with positive and negative refractive indices, respectively. The isofrequency dispersion curves of the alternately arranged IMIIM composite structures are hyperbolic form. The FEM electromagnetic simulations confirm that the device has a subwavelength resolution. The subwavelength resolution of the proposed device can be achieved at different visible frequencies by slightly changing the constituent materials and geometric parameters. More importantly, the constituent materials that satisfy the criteria for overcoming limits on optical diffraction are available in nature. The device that is developed herein has potential applications in realtime subwavelength imaging and highdensity photonic components.
Methods
All simulations herein are conducted in the commercial electromagnetic software COMSOL Multiphysics, using the finite element method. The metals in Fig. 1(a) and Fig. 4 are copper (Cu) and silver (Ag). The Drude model applies as follows^{28,38,39},
where ω is the angular frequency; ω_{p}_{1} = 5 × 10^{15} rad/s and ω_{p}_{2} = 1.5 × 10^{16} rad/s are the bulk plasma frequencies of Cu and Ag, respectively and γ_{1} = 5 × 10^{13} rad/s (γ_{2} = 7.73 × 10^{13} rad/s) is the damping constant of Cu (Ag). Here, the material with dielectric constant ε_{1} (ε_{2} and ε_{3}) in Fig. 5(a) and 5(b) is SiO_{2} (Air and HfO_{2})^{40}. And the material with dielectric constant ε_{1} (ε_{2} and ε_{3}) for operating in higher frequency (Fig. 5(e)) is Y_{2}O_{3} (Air and Nb2O5)^{40}. To suppress the noise reflected from the simulated boundaries, perfectly matched layers are used outside the structure. To excite the SPPs of interest, a linearly polarized plane source whose electric field oscillates in the xzplane is launched at x = 0 (as in the endfire method)^{41,42}, producing the nonradiation mode SPPs on the IM (IIM) interface^{26}.
References
Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003).
Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Planar photonics with metasurfaces. Science 339, 1232009 (2013).
Zhang, J., Xiao, S., Wubs, M. & Mortensen, N. A. Surface plasmon wave adapter designed with transformation optics. ACS Nano 5, 4359–4364 (2011).
Poddubny, A., Iorsh, I., Belov, P. & Kivshar, Y. Hyperbolic metamaterials. Nat. Photon. 7, 948–957 (2013).
Lu, D., Kan, J. J., Fullerton, E. E. & Liu, Z. Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials. Nature Nanotech. 9, 48–53 (2014).
Yang, X., Yao, J., Rho, J., Yin, X. & Zhang, X. Experimental realization of threedimensional indefinite cavities at the nanoscale with anomalous scaling laws. Nat. Photon. 6, 450–454 (2012).
Yang, J. K. W. & Berggren, K. K. Using highcontrast salty development of hydrogen silsesquioxane for sub10nm halfpitch lithography. J. Vac. Sci. Technol. B 25, 2025–2029 (2007).
Litchinitser, N. M. Applied Physics. Structured light meets structured matter. Science 37, 1054–1055 (2012).
Yu, N. et al. Broadband backgroundfree quarterwave plate based on plasmonic metasurfaces. Nano Lett. 12, 6328–6333 (2012).
Roberts, A. & Lin, L. Plasmonic quarterwave plate. Opt. Lett. 37, 1820–1822 (2012).
Liu, Y., Zentgraf, T., Bartal, G. & Zhang, X. Transformational plasmon optics. Nano Lett. 10, 1991–1997 (2010).
Ni, X., Emani, N. K., Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Broadband light bending with plasmonic nanoantennas. Science 335, 427 (2012).
Yu, N. et al. Flat photonics: Controlling wavefronts with optical antenna metasurfaces. IEEE J. Sel. Top. Quantum Electro. 19, 4700423 (2013).
Vakil, A. & Engheta, N. Transformation optics using grapheme. Science 332, 1291–1294 (2011).
Sun, S. L. et al. Gradientindex metasurfaces as a bridge linking propagating waves and surface waves. Nat. Mater. 11, 426–431 (2012).
Smolyaninov, I. I., Hung, Y.J. & Davis, C. C. Magnifying superlens in the visible frequency range. Science 315, 1699–1701 (2007).
Smolyaninov, I. Twodimensional metamaterial optics. Laser Phys. Lett. 7, 259–269 (2010).
Li, P. & Taubner, T. Broadband subwavelength imaging using a tunable graphenelens. ACS Nano 6, 10107–10114 (2012).
Bloemer, M. J., D′Aguanno, G., Scalora, M., Mattiucci, N. & Ceglia, D. de. Energy considerations for a superlens based on metal/dielectric multilayers. Opt. Express 16, 19342–19353 (2008).
Lee, H., Liu, Z., Xiong, Y., Sun, C. & Zhang, X. Development of optical hyperlens for imaging below the diffraction limit. Opt. Express 15, 15886–15891 (2007).
Cheng, B. H., Ho, Y. Z., Lan, Y. C. & Tsai, D. P. Optical hybridsuperlenshyperlens for super resolution imaging. IEEE J. Sel. Top. Quantum Electron. 19, 4601305 (2013).
Wang, Y. T. et al. Gainassisted hybridsuperlenshyperlens for nano imaging. Opt. Express. 20, 22953–22960 (2012).
Cheng, B. H., Lan, Y. C. & Tsai, D. P. Breaking optical diffraction limitation using optical hybridsuperlenshyperlens with radically polarized Light. Opt. Express 21, 14898–14906 (2013).
Yariv, A. & Yeh, P. Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, Oxford, 2006).
Salandrino, A. & Engheta, N. Farfield subdiffraction optical microscopy using metamaterial crystals: theory and simulations. Phys. Rev. B 74, 075103 (2006).
Dionne, J. A., Verhagen, E., Polman, A. & Atwater, H. A. Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries. Opt. Express 16, 19001–19017 (2008).
Stockman, M. I. Slow propagation, anomalous absorption and total external reflection of surface plasmon polaritons in nanolayer systems. Nano Lett. 6, 2604–2608 (2006).
Karalis, A., Lidorikis, E., Ibanescu, M., Joannopoulos, J. D. & Soljacić, M. Surfaceplasmonassisted guiding of broadband slow and subwavelength light in air. Phys. Rev. Lett. 95, 063901 (2005).
Wood, B., Pendry, J. B. & Tsai, D. P. Directed subwavelength imaging using a layered metaldielectric system. Phys. Rev. B 74, 115116 (2006).
Verslegers, L., Catrysse, P. B., Yu, Z. & Fan, S. Deepsubwavelength focusing and steerging of light in an aperiodic metallic waveguide array. Phys. Rev. Lett. 103, 033902 (2009).
Elser, J. & Podolskiy, V. A. Scatteringfree plasmonic optics with anisotropic metamaterials. Phys. Rev. Lett. 100, 066402 (2008).
Fan, X., Wang, G. P., Lee, J. C. W. & Chan, C. T. Allangle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstation. Phys. Rev. Lett. 97, 073901 (2006).
Lin, W., Zhou, X. & Wang, G. P. Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays. Appl. Phys. Lett. 91, 243113 (2007).
Zhukovsky, S. V., Kidwai, O. & Sipe, J. E. Physical nature of volume plasmonpolaritons in hyperbolic metamaterials. Opt. Express 21, 14982–14987 (2013).
Guo, Y. & Jacob, Z. Thermal hyperbolic metamaterials. Opt. Express 21, 15014–15019 (2013).
Engheta, N. Pursuing NearZero Response. Science 340, 286 (2013).
Ourir, A., Maurel, A. & Pagneux, V. Tunneling of electromagnetic energy in multiple connected leads using nearzero materials. Opt. Lett. 38, 2092–2094 (2013).
Johnson, P. B. & Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 74, 4370–4379 (1972).
Kittel, C. Introduction to Solid State Physics, 7th ed. (John Wiley & Sons, New York, 1996).
Polyanskiy, M. RefractiveIndex,INFO. (2008) Available at: http://refractiveindex.info. (Date of access: 6th December 2014).
Stegeman, G. I., Wallis, R. F. & Maradudin, A. A. Excitation of surface polaritons by endfire coupling. Opt. Lett. 8, 386–388 (1983).
Leosson, K., Nikolajsen, T., Boltasseva, A. & Bozhevolnyi, S. I. Longrange surface plasmonpolariton nanowire waveguides for device applications. Opt. Express 14, 314–319 (2006).
Acknowledgements
The authors acknowledge financial support from Ministry of Science and Technology, Taiwan (Grant Nos. 1012112M006002MY3, 1032745M002004ASP, 1022911I002505 and 1032911I002594) and Academia Sinica (Grant No.AS103TPA06). They are also grateful to National Center for Theoretical Sciences, Taipei Office, Molecular Imaging Center of National Taiwan University, National Center for HighPerformance Computing, Taiwan and Research Center for Applied Sciences, Academia Sinica, Taiwan for their support.
Author information
Authors and Affiliations
Contributions
B.H.C. and K.J.C. jointly conceived the idea. B.H.C. and K.J.C. designed and performed the calculations. Y.C.L. and D.P.T. assisted in the analyzing and discussion of the results. B.H.C., Y.C.L. and D.P.T. prepared the manuscript. Y.C.L. and D.P.T. supervised and coordinated all the work. All authors commented on the manuscript.
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Electronic supplementary material
Supplementary Information
Supplementary Information
Rights and permissions
This work is licensed under a Creative Commons AttributionNonCommercialNoDerivs 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/byncnd/4.0/
About this article
Cite this article
Cheng, B., Chang, K., Lan, YC. et al. Achieving planar plasmonic subwavelength resolution using alternately arranged insulatormetal and insulatorinsulatormetal composite structures. Sci Rep 5, 7996 (2015). https://doi.org/10.1038/srep07996
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/srep07996
This article is cited by

Tunable tapered waveguide for efficient compression of light to graphene surface plasmons
Scientific Reports (2016)

Extreme stiffness hyperbolic elastic metamaterial for total transmission subwavelength imaging
Scientific Reports (2016)

Robustly Efficient Superfocusing of Immersion Plasmonic Lenses Based on Coupled Nanoslits
Plasmonics (2016)

Magnetically controlled planar hyperbolic metamaterials for subwavelength resolution
Scientific Reports (2015)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.