Plasmonics has achieved many unique optical properties by exploiting the surface plasmon polaritons, or the collective oscillation of free charges strongly coupled to light, that exhibit subwavelength modes with extremely enhanced electric field intensities1,2,3. Taking advantage of such properties, two-dimensional ensembles of plasmonic nanostructures have been arranged for surface-enhanced Raman scattering substrates4,5,6, metamaterials7,8,9, and nonlinear optics10,11. The localized surface plasmon resonance strongly depends on the structural geometry, and a variety of optical properties have been realized by metallic nanostructures12,13.

One of the most interesting applications of nanoplasmonics is the fundamental control of the electromagnetic properties by using a metamaterial. This effectively homogeneous material has demonstrated many extraordinary optical properties, such as artificial magnetism14,15,16, a negative refractive index17,18,19,20, strong artificial optical activity21,22, and perfect absorption23,24,25,26. However, the realization of these properties often requires a magnetic response that is introduced through the fabrication of complex three-dimensional (3D) architectures, for instance, split-ring resonators27, core shells28,29, and vertically stacked rods30. Well-defined complex nanostructures with a magnetic response are usually prepared by top–down approaches, including direct laser writing31, multiple e-beam lithography32, and membrane projection lithography33. Gansel et al.34 achieved broadband circular dichroism in a gold helix photonic metamaterial fabricated through direct-write 3D laser lithography, but the operating window of this material was limited to the near-infrared (NIR) regime due to its large feature size (2 μm). Liu et al.35 demonstrated a negative permeability with a stack of four split-ring resonators fabricated through multiple e-beam lithography, but large-scale device fabrication of this structure is practically impossible.

Table 1 Molecular characteristics of SML-51, PS-ran-PMMA, and PS homopolymer

The realistic application of plasmonic metamaterials with complex geometries requires large-area fabrication and feature sizes below 100 nm to have a working regime of visible to NIR wavelengths. The bottom-up approach, particularly the self-assembly of a block copolymer (BCP), could satisfy these two requirements for the fabrication of complex plasmonic nanostructures over a large area36,37,38. BCPs self-assemble into various nanodomains, such as lamellae, gyroids, cylinders, and spheres, depending on the volume fraction of each block39. Although these nanodomains in their bulk states do not align to form complex nanostructures, the confinement of nanodomains inside a constrained geometry can provide uncommon architectures, such as single40 and double helixes41 and toroid shapes42, that have not been observed in the bulk state. Anodized aluminum oxide (AAO) templates with tunable sub-100 nm pore sizes have been widely applied in the preparation of bulk metamaterials43,44. Here we combined BCP self-assembly and an AAO template to form a unique complex nanostructure. We focused on stacked lamellar nanostructures45, where each nanodomain is alternatively stacked along the direction of the nanorod.

This paper demonstrates the fabrication of sophisticated nanostructures that are difficult to realize through the top–down process in a large optical device by taking advantage of BCP self-assembly. Specifically, we fabricated a high-density array of 3D plasmonic nanostructures on the centimeter scale through the confinement of lamellar nanodomains of BCP inside the cylindrical pores of an AAO template. This confinement allowed us to obtain a vertically stacked lamellar nanostructure. Once Ag was deposited on only one of the two nanodomains, a high-density array of “accordion-like” Ag nanorods was fabricated over a large area. This array shows three transmittance dips, the origins of which are explained through finite-difference time-domain (FDTD) simulations. The retrieved effective electromagnetic properties and the corresponding field patterns reveal multiple electromagnetic responses in the visible-NIR regime and their origins. Owing to these multiple modes, which include both magnetic and electric responses, this bottom–up approach based on the confinement of BCP nanodomains could be applied to the development of metamaterials for multi-analyte sensing46,47,48, imaging49,50, and invisibility cloaking51,52,53,54,55.

Materials and methods

Chemicals and AAO fabrication

PS-b-PMMA (SML-51) and PS-ran-PMMA-OH were purchased from Polymer Source Inc, (Quebec, Canada) and used as received (Table 1). Epoxy resin (Araldite resin grade 502: (50:45:5 wt/wt/wt) dodecenylsuccinic anhydride:phenol,2,4,6-tris[(dimethylamino) methyl]-[90-72-2]:bis(dimethylaminomethyl) phenol) was purchased from Polymer Source Inc. The AAO template was prepared by the well-established two-step anodization method56. The first anodization step was performed in an aqueous oxalic acid solution to obtain the perfect hexagonal pore arrangement over a large area. The center-to-center distance between two neighboring pores in this AAO membrane was 100 nm. After the irregular pores in the AAO were removed, the second anodization step was performed for 120 s. The pore diameter was controlled by adjusting the pore-widening time in a 0.1 M H3PO4 aqueous solution at 30 °C (see Sec. S1 of the SI).

Fabrication of a high-density array of accordion-like nanorods

First, PS-ran-PMMA-OH solutions in toluene (0.5 wt% in solid) were dropped on an AAO template and annealed at 180 °C for 3 days under vacuum. The non-grafted PS-ran-PMMA-OH chains were completely removed by rinsing with toluene. This treatment made the AAO pore walls neutral to both PS and PMMA chains (Fig. 1a). Then SML-51 in toluene (2 wt%) was spin-coated on the AAO template and annealed at 200 °C for 3 days in vacuum, followed by quenching to room temperature. Epoxy resin (with a thickness of 0.5 mm) was dropped on the as-annealed AAO template and cured at 60 °C for 12 h (Fig. 1b). Next, the aluminum layer on the AAO template was removed by using a CuCl2 solution (9 g of CuCl2, 20 mL of 0.1 M HCl, 100 mL of DI water), and the AAO template was removed by using a 0.4 M sodium hydroxide aqueous solution for 120 min (Fig. 1c). Finally, 5-nm-thick Ag was selectively deposited on the PS nanodomains of all the nanorods by thermal evaporation57 at a rate of 0.01 nm s−1 under high vacuum (Fig. 1d).

Fig. 1: Schematic of the fabrication of a high-density array of “accordion-like” Ag nanorods over a large area.
figure 1

a An AAO template was grafted by a neutral brush of PS-ran-PMMA-OH. b PS-b-PMMA was spin-coated to fill the AAO template and thermally annealed. Then epoxy resin was drop casted on the top of the AAO template. c Both the aluminum layer and the AAO template were removed. d Ag was selectively deposited on only the PS nanodomains

The arrangement of the PS-b-PMMA nanodomains confined in the AAO template was examined via transmission electron microscopy (TEM; S-7600: Hitachi Ltd., operating at an accelerating voltage of 80 kV). To make a sample for the TEM, epoxy resin was first embedded on the AAO template containing PS-b-PMMA. After removal of the aluminum and AAO template, epoxy resin was again dropped on the array of PS-b-PMMA nanorods and cured. After ultrathin sections were prepared using a Leica Ultracut Microtome (EM UC6 Leica Ltd.) equipped with a diamond knife, the samples were stained with ruthenium tetroxide (RuO4), a staining agent selective for the PS nanodomains. The vertical alignment of the nanorods on the epoxy substrate after removing the AAO template was examined via field emission scanning electron microscopy (FE-SEM; Hitachi S-4800). Transmittance spectra were measured via an Fourier transform-infrared spectrometer (Bruker Vertex 70) equipped with a microscope (Bruker Hyperion 2000).

FDTD simulations

3D full-wave numerical simulations were conducted to analyze the electromagnetic properties of the hexagonally packed Ag accordion nanorod array. A commercial-grade simulator (Lumerical) based on the FDTD method was used to calculate the electromagnetic field. The simulation model was designed by SEM/TEM observations (see Sec. S2 of the SI), and the simulation mesh size was set to <0.3 nm to account for the small feature size. The electromagnetic field was calculated with polarized incident light. The refractive index of PS-b-PMMA and the epoxy resin was 1.53, as measured using ellipsometry, and the Ag permittivity was taken from Johnson and Christy58.



The versatile tunability of the AAO template is illustrated in the cross-sectional TEM images of SML-51 confined in AAO templates with various pore diameters ranging from 30 to 80 nm (Fig. 2). Alternatingly stacked lamellae of PS and PMMA nanodomains are clearly observed in the TEM images independent of the AAO pore diameter. In general, the PS and PMMA nanodomains on a flat surface are vertically oriented when treated by a neutral brush59. Although the substrate (the AAO wall) in this study was not flat, the neutrality of the AAO walls allowed the PS and PMMA chains to align well along the wall. While the vertical orientation of the lamellae-forming PS-b-PMMA was achieved on a flat surface with the neutral brush for a range of film thicknesses (H) (0.3–1.4 H/L0)59, stacked lamellae are observed inside the AAO for D/L0 values between 0.91 and 2.31 (D is the diameter of the AAO pore).

Fig. 2: Cross-sectional TEM images of SML-51 confined in AAO templates with various pore diameters.
figure 2

a 80 nm, b 70 nm, c 50 nm, and d 30 nm. The dark stripes represent the PS nanodomains stained with RuO4

A high-density array of vertically oriented nanorods was successfully fabricated over a large area (2.5 × 2.5 cm2) (see Sec. S3 of SI), and the BCP nanorods were clearly observed by removing the AAO template (Fig. 3a, b). PS and PMMA nanodomains are alternatively stacked along the nanorod direction (Fig. 3c). Thermal evaporation of Ag onto the array resulted in the deposition of Ag on only the PS nanodomains (Fig. 3d). This selective deposition comes from the higher affinity of Ag for PS than the PMMA nanodomains57,60. Based on the SEM images, the center-to-center distance of the Ag stripes was determined to be 30 nm, which is consistent with the L0 of PS-b-PMMA (32.9 nm). Thus a high-density array of “accordion-like” Ag nanorods were successfully fabricated over a large area.

Fig. 3: FE-SEM images of the PS-b-PMMA nanorods.
figure 3

a Top and (b) 80°-tilted side views (the inset is an enlarged image) after removal of the AAO template. c Cross-sectional TEM image showing the inner stacked lamellae in the nanorods. d 80°-tilted view SEM image showing the Ag accordion nanostructure

Optical properties and FDTD simulations

The high-density array of accordion-like Ag nanorods exhibited three transmittance (T) dips at 600, 800, and 1200 nm (Fig. 4a), while an array of PS nanorods with uniformly deposited (not accordion-shaped) Ag showed only one dip at 450 nm (see Sec. S5 of the SI). This result indicates that the multiple T dips result from the accordion-like shape of the nanorods with periodic Ag side rings that are vertically displaced by the lamella thickness of the PMMA block in SML-51. The simulated FDTD results (Fig. 4b) show three T dips at positions that are consistent with the experimentally measured spectra. This consistency in the experimental and simulated T spectra allows us to proceed to calculate the effective electromagnetic parameters of the array (Fig. 4c, d). The major T dips at 800 and 1200 nm correspond to electric responses (Fig. 4c), while the other dip at 600 nm corresponds to a magnetic response (Fig. 4d). The other magnetic response at 1150 nm could not produce a T dip, possibly due to its spectral closeness to the electric response at 1300 nm, which compensates for the effect on the wave impedance (see Sec. S4.2 of the SI).

Fig. 4: Transmission spectra and effective permittivity and permeability spectra of the high-density array of accordion-like silver nanorods.
figure 4

a Experimentally observed and b simulated transmission spectra of the array. Retrieved effective electromagnetic parameters of the c permittivity and d permeability. e Schematic simulation model of an accordion-like Ag nanorod. Field intensity patterns calculated from FDTD based on the electric responses at f 800 nm and g 1300 nm and the magnetic responses at h 600 nm and i 1150 nm

The origin of each response was analyzed from the corresponding electromagnetic field patterns of the Ag accordion nanostructure. Here we consider each nanorod to have five Ag rings and one hemispherical cover (Fig. 4e) to mimic the experimentally observed accordion-like Ag nanorod (Fig. 3d). The strong electric response at 800 nm arises from the Ag hemispherical cover (Fig. 4f). The weaker electric response at approximately 1300 nm results from the Ag side rings (Fig. 4g). These two electric responses are enhanced through coupling between neighboring nanorods in the high-density array. The magnetic response at 600 nm arises from the plasmonic mode of the continuous Ag film deposited on the substrate (Fig. 4h). Another magnetic response at 1150 nm comes from the Ag hemisphere cover. This result is particularly interesting since the Ag hemisphere itself, without Ag side rings, does not exhibit any magnetic response at this wavelength (see case (5) in Fig. S6 of the SI). Thus the magnetic response possibly arises from the current loop along the hemisphere driven by the electric response of the Ag side rings. This result shows that the magnetic response of a nanostructure (i.e., a Ag hemisphere) could be induced by a nearby resonant structure (i.e., Ag side rings). The effect of each component in a single accordion-like nanorod on the electric and magnetic responses is discussed in detail in Sec. S6 of the SI. Finally, the size effect of the nanorods, for instance, the radius and height of the nanorod and the vertical gap distance, which could be tuned by altering the AAO template and the molecular weight of the BCP, on the electromagnetic responses is discussed in Sec. S7 of the SI.


In summary, a high-density array of accordion-like plasmonic Ag nanorods was successfully fabricated over a large area (~cm2) by confining lamellar nanodomains inside cylindrical AAO pores. The array showed multiple electromagnetic responses to visible and NIR wavelengths. Through FDTD simulations, the T dip at 600 nm was determined to correspond to a magnetic response, while the other T dips at 800 and 1200 nm corresponded to electric responses. Interestingly, a magnetic response at 1150 nm arose from the hemispherical cover of the nanorods. Although this hemisphere alone did not show a magnetic response at this wavelength, a magnetic response was induced by the electric resonance of the Ag side rings. This coupling between the two different structures at different resonant wavelengths could be used to engineer a metamaterial with a desired magnetic response to visible and NIR wavelengths. This realization of multiple responses in complex nanostructures through BCP self-assembly may pave the way for various practical applications, such as multi-analyte detection, and metamaterials with unique optical properties, such as a negative refractive index.