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Scalable nanofabrication of U-shaped nanowire resonators with tunable optical magnetism

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Abstract

Split ring resonators have been studied extensively in reconstituting the diminishing magnetism at high electromagnetic frequencies in nature. However, breakdown in the linear scaling of artificial magnetism is found to occur at the near-infrared frequency mainly due to the increasing contribution of self-inductance while reducing dimensions of the resonators. Although alternative designs have enabled artificial magnetism at optical frequencies, their sophisticated configurations and fabrication procedures do not lend themselves to easy implementation. Here, we report scalable nanofabrication of U-shaped nanowire resonators (UNWRs) using the high-throughput nanotransfer printing method. By providing ample area for conducting oscillating electric current, UNWRs overcome the saturation of the geometric scaling of the artificial magnetism. We experimentally demonstrated coarse and fine tuning of LC resonances over a wide wavelength range from 748 nm to 1600 nm. The added flexibility in transferring to other substrates makes UNWR a versatile building block for creating functional metamaterials in three dimensions.

© 2016 Optical Society of America

1. Introduction

Metamaterials composed of rationally designed sub-wavelength inclusions exhibit exotic and unique electromagnetic responses that cannot be found in nature [1]. They have therefore enabled a broad range of novel applications, such as sub-diffraction imaging [2,3], invisibility cloaks [4–6], negative index metamaterials (NIM) [7–9], and perfect absorbers [10]. Split ring resonators (SRRs) were first proposed as the primary building blocks that mimic the properties of orbiting electrons to produce artificial magnetism [11,12]. The SRR can be equivalently treated as an inductor-capacitor (LC) circuit with a resonant frequency ofωLC=1/LC.The induced LC resonance leads to a strongly amplified electric current along the inductor and thus, produces a spatially confined oscillating magnetic-dipole moment. The simple circuit analogy reveals an inverse scaling of the resonant frequency with respect to its size [13,14]. Thus, scaling the artificial magnetism from microwave frequencies all the way to the infrared frequencies can be accomplished by shrinking the size of SRRs [7,8,12,15,16]. However, the continuous scaling of the LC resonance was found to saturate in the near-infrared region due to the elevated contribution of self-inductance of electrons [13,14,17]. In addition, increased Ohmic loss in the metal with reduced size of the structure may further weaken the resonance at higher frequencies. Thus, it becomes practically challenging to achieve optical magnetism by simply shrinking the physical dimensions of the SRRs.

In principle, increasing the area for the induced current loop can potentially mitigate the effect of the self-inductance and the Ohmic loss and thus, continue the scaling of the LC resonance to higher frequencies [14,18,19]. For example, it has been demonstrated recently that cutting a thin slit in an individual metallic nanosphere creates a stand-alone split-ball structure as a variant from the SRR [20]. In addition, a wide range of creative designs that exploit strongly coupled plasmonic resonating elements have been investigated, such as the fish-net structure [21], paired rods [22,23], coaxial waveguide [24], ellipsoid voids [25] and gap-surface plasmon resonators [26]. In these structures, the excitation of an anti-symmetric resonance mode results in an oscillating loop current, which gives rise to an artificial magnetic moment. Similarly, nanoclusters consisting of several nanoparticles arranged in a circular pattern have also been employed to produce the magnetic-based Fano scattering resonance at optical frequencies [27–29]. However, all of these designs require deterministic patterning of plasmonic resonating elements using the time-consuming and costly nanofabrication methods, such as electron beam lithography [22,30,31], ion beam milling [20], and nanomanipulation [28]. Alternatively, optical magnetism has been realized by exciting the fundamental Mie resonance of silicon nanoparticles that are fabricated using a highly scalable bottom-up chemical synthesis process [32–34]. Other scalable fabrication methods for realizing metamaterials with optical magnetism include laser interference lithography [35] and hybrid approaching that combine direct laser writing with e-beam lithography [36].

Here we report a scalable fabrication of U-shaped nanowire resonators (UNWRs, Fig. 1) exhibiting artificial magnetism that can be widely tuned at the optical frequencies. The cross section of the UNWRs can be characterized by the height h, the gap opening g, the width of the arm ta, and the thickness of the base tb, as shown in Fig. 1. The UNWR can still be equivalently treated as a LC resonator under the transverse-magnetic (TM) polarized incidence, where the magnetic field is pointing along the length of the nanowire (y-axis in Fig. 1). Since the simplified LC circuit model fails to account for the influence of the thickness of the resonator [13], a more accurate circuit model has thus been developed to fully consider the contribution of self-inductance of electrons as well as the fringe and surface capacitances [37] (See Appendix A). Increasing of the SRR thickness results in a favorable blue shift of the LC resonance to the higher frequency. The results are further validated via numerical simulations using the commercial finite-difference time-domain (FDTD) software (FDTD Solutions, Lumerical), as shown in Fig. 6 in Appendix A. Thus, increasing the thickness of the SRRs offers a viable solution to scale the LC resonance to the higher frequencies [18,38,39]. This strategy can be conveniently implemented using UNWRs because the thickness of the conventional SRRs has been effectively extended along the length of the nanowire, as illustrated in Fig. 1. The scalable fabrication of the UNWRs is accomplished by combining the inclined metal deposition onto the soft stamp containing one-dimensional (1D) periodic gratings and the subsequent transfer to the substrate using the nanotransfer printing (nTP) process [40]. The LC resonance can be widely tuned over the wavelength range from 748 nm to 1600 nm by conveniently altering the dimensions of the UNWRs.

 figure: Fig. 1

Fig. 1 Schematic diagram of the U-shaped nanowire resonators (UNWRs) array. The UNWRs located on the epoxy surface consist of 1D array of metallic nanowires with U-shaped cross section. The inset illustrates the cross section dimensions of the UNWR. The unique structure can exhibit the evident LC resonance under excitation with TM polarization incidence and extend the scaling of artificial magnetism to the higher frequency spectrum.

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2. Materials and methods

The whole process of nTP is divided into four steps: silicon mold fabrication, soft stamp fabrication, metal deposition, and transfer printing.

2.1 Silicon mold fabrication

This step starts from generating patterns on a bare silicon wafer with a thin natural oxidation layer. Parallel groove patterns are generated by interference lithography on 100 nm thick photoresist spin-coated on the wafer. After this, 30 nm thick Cr nanowires are fabricated by performing electron beam evaporation and lift-off processes. These Cr nanowires are subsequently used as a mask to selectively etch the thin SiO2 layer on the silicon wafer by reactive ion etching to transfer patterns into silicon wafer (power: 70 W, SF6/O2/Ar flow rate: 25 s.c.c.m./25 s.c.c.m./50 s.c.c.m, pressure: 4.0 Pa, etch rate: 75 nm/min). A surfactant self-assembled monolayer, tridecafluoro-(1,1,2,2)-tetrahydrooctyl trichlorosilane (FOTS, Gelest), needs to be coated on the silicon mold to lower the surface energy. To achieve this, the mold is first cleaned by 100 W oxygen plasma for 1 minutes and immersed in a 0.5%wt solution of FOTS in heptane at 65 °C for 5 minutes. Then the mold is rinsed in pure heptane at 65 °C for 10 minutes to remove redundant surfactant. Next, the mold is thoroughly rinsed in acetone and isopropanol and baked at 100 °C for 10 minutes to improve the strength of the release layer.

2.2 Soft stamp fabrication

Similar to the conventional stamping process, the nTP process allows for a selective transfer of nanoscale structures from the soft stamp to a wide variety of substrates by controlling the surface energy of the stamp and the substrates [41–44]. In this work, poly[(mercaptopropy)methylsiloxane] (PMMS, United Chemical Technologies) is used to fabricate the soft stamps. The compliance of the PMMS stamp makes it easier to form a close and conformal contact with the substrate, which is important for successful pattern transfer with high fidelity [41]. The soft stamp material in experiments is a mixture of 6 parts PMMS, 4 parts triallyl cyanurate (Aldrich), 1 part ethoxylated bisphenol A dimethacrylate ester (SR540, Satomer), and 0.01 part 2,2-dimethoxy-2-phenylacetophenone (Aldrich). As illustrated in Fig. 2(a), to replicate nanopatterns to the stamp, the liquid PMMS resin is poured onto the silicon master mold consisting of 1D periodic gratings. The mold is subsequently placed in vacuum for degassing and promoting better mold-filling. Particularly, a quartz plate is lowered down from top to squeeze the mixture. Between the quartz plate and the silicon mold, a 1 mm thick spacer is inserted to define the thickness of the stamp. The PMMS mixture is then exposed under the ultraviolet (UV) light (Black-ray UV lamp, Ted Pella) at 4 mW/cm2 for 5 minutes from the quartz side to ensure that it is fully cured. The cured stamp can be easily separated from the silicon mold and the quartz plate in sequence. Similar to the silicon mold, the PMMS soft stamp needs to be treated by depositing a thin self-assembled monolayer of FOTS to reduce the surface energy. The stamp is first cleaned by 50 W oxygen plasma for 1 minutes and then immersed in a 0.5%wt solution of FOTS in heptane at 65 °C for 5 minutes, followed by rinsing in pure heptane at 65 °C for 10 minutes to remove redundant surfactant, and finally cleaned by isopropanol before drying by nitrogen. Unlike the silicon mold treatment, there is no acetone rinsing and 100 °C heating process involved.

 figure: Fig. 2

Fig. 2 Fabrication process flow and scanning electron microscopy images of the UNWRs. (a) To fabricate the UNWRs, the soft stamp is made by curing the liquid PMMS resin on the silicon mold. Then gold thin film is deposited at ~45 degree by thermal evaporation from two opposite directions, covering all surfaces of the soft stamp except trench bottoms due to the shadowing effect. Next, the Au-coated stamp is pressed onto a glass substrate coated with a thin layer of epoxy on the top. Following the curing, the gold structures remain on the substrate after carefully peeling off the stamp. (b) Scanning electron microscopy (SEM) images of UNWRs printed on the epoxy layer on a glass substrate and the close-up view shown in (c). The period of the UNWRs is 500 nm. The height and the width of the gap of each UNWR is 280 nm and 200 nm, respectively. The thickness of the arm and the base is 35 nm and 50 nm, respectively. Scale bar in both (b) and (c): 500 nm.

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2.3 Metal deposition

Directional metal deposition from an oblique incident angle creates a discontinuous metal film on the surface of the nanostructured stamp due to the shadowing effect from the neighboring gratings. In the experiment, directional depositions of gold are performed at approximately 45 degree incident angle from two opposite sides to form the U-shaped structures that conformally cover the surface of the 1D periodic mold. It is important to keep the metal film thickness to be less than the height of the grating structures so individual UNWRs are well separated from their neighbors. Here, the gold is deposited onto the soft stamp by thermal evaporation at the rate of 0.1 nm/s. Now the soft stamp is ready for printing.

2.4 Transfer printing

During the nTP, the epoxy layer plays an important role in providing strong adhesion to successfully transfer nanostructure from the soft stamp. In the experiment, the epoxy is a mixture of 2-(3,4-epoxycyclohexyl)ethyltrimethoxysilane (Gelest) and a photo-acid generator (PAG), p-(octyloxyphenyl)phenyliodonium hexafluoroantimonate (Gelest) that is activated by UV light or heat to initiate the crosslinking of the epoxy monomer. The weight ratio of epoxy to PAG is 93:7. Then the epoxy mixture is solved in chlorobenzene to form 3%wt solution. The solution is spin-coated on the clean glass substrate at 3000 rpm/min and baked at 80 °C for 20 seconds to form an 80 nm epoxy layer. The epoxy layer in the liquid form provides direct contact to the U-shaped gold nanowire array without the need for high external pressure. During the transfer printing, the Au-coated soft stamp (facing down) is placed onto the epoxy-coated glass substrate, between which the air is evacuated for 2 minutes. By adjusting the external pressure, a net pressure of 50 psi is generated between the substrate and stamp. The epoxy is exposed under 4 mW/cm2 UV light for 5 minutes while the pressure is on. Then the sample and PMMS stamp are baked together at 80 °C for 5 minutes. Finally, the soft stamp can be released slowly after cooling down, leaving the UNWRs being successfully transferred to the surface of the substrate. The peeling direction needs to be along the grating direction to avoid any nanostructures breaking. In the nTP, the dimensions of the UNWRs can be tailored by either altering the pitch of silicon master molds, or by controlling the duration and the angle of the metal deposition.

3. Results and discussion

Figure 2(b) shows the fabricated UNWRs with the pitch of 500 nm on a glass substrate. The highly parallel nTP technique allows the successful implementation of a large array of UNWRs with the sample area of 15 × 15 mm2, which corresponds to more than 3 × 104 UNWRs being printed in a single stamping step. The fabrication throughput is significantly higher than conventional nanofabrication processes, such as electron beam lithography and focused ion milling process, which rely on the sequential writing strategy. The magnified cross-sectional view shown in Fig. 2(c) further reveals the well-defined freestanding arms of the UNWR (h = 280 nm, g = 200 nm, ta = 35 nm and tb = 50 nm) which play vital roles in forming a circulating current. The characterization of the transmission consists of both visible and near-infrared (NIR) spectrum measurement under different polarizations (See Appendix B), and the combined spectra are shown in Fig. 3(a). Under the TE polarization where the electric field is parallel to the length of the nanowire (as shown in Fig. 1), the UNWRs can be regarded as an effective medium consisting of gold and air and exhibit a low transmission without any prominent resonances. In contrast, the transmission under the TM polarization exhibits two well-defined dips at center wavelengths of λ = 830 nm and λ = 1600 nm, respectively. The measured transmission spectra are in good agreement with the theoretical prediction that the LC resonance can only be excited under the TM polarization [8]. To better understand the physical origin of the observed transmission dips, FDTD simulations are performed to calculate the transmission spectra of the UNWRs, as shown in Fig. 3(b), and the distribution of the electric and the magnetic fields at the corresponding resonance dips are shown in Figs. 3(c)-3(f). Under the TM polarization, a pronounced LC resonance can be identified at the center wavelength of λ = 1600 nm as both electric field and magnetic field are strongly confined within the gap. Both of the x and y components of the electric field are displayed in Fig. 7 in Appendix C. A strong x component of the electric field indicates an accumulation of the field cross the gap of the UNWR, which can be equivalently understood by the concentration of electric field between the two plates of the capacitor at the LC resonance. In addition, the x and y component of the current density at λ = 1600 nm are displayed in Fig. 3(g) and 3(i), respectively. Here, the x and y components are parallel to the base and the arms of the UNWR, respectively. The different direction of the excited current in the two arms and the prominent current in the base of the U shape indicate the excitation of a strong current loop at λ = 1600 nm, which agrees well with previous study of the LC resonance [8,16]. On the other hand, the resonance found at the center wavelength of λ = 830 nm is determined by the induced electric-dipole moment along the base of the U-shaped structure [8], which results in the strongly concentrated electric field at the corners of the structure. The x and y components of the current density at λ = 830 nm are shown in Fig. 3(h) and 3(j), respectively. The formation of the electric dipole in the base of the UNWR is confirmed by the prominent x component of the current and opposite phase of the y component at the two ends of the base, while only small current is developed in the two arms. In constrast to the TM polarization, both the magnetic and electric resonances vanish under the TE polarization. Both of the electric and magnetic fields at λ = 830 nm and λ = 1600 nm are shown in Fig. 8 in Appendix C, in which both of the electric and magnetic fields are mostly distributed above the UNWRs, indicating the UNWRs serve as an effective medium consisting of gold and air and reflect most of the incoming light without prominent resonance.

 figure: Fig. 3

Fig. 3 Experimental measurement and numerical simulation for the UNWRs at the near-infrared frequencies. (a) The measured transmission spectra of the UNWRs under the TE and the TM polarization, respectively. (b) The simulated transmission spectra under the TE and the TM polarization, respectively. (c) The electric field distribution at λ = 1600 nm. (d) The electric field distribution at λ = 830 nm. (e) The magnetic field at λ = 1600 nm. (f) The magnetic field at λ = 830 nm. (g) The x component of current density at λ = 1600 nm. (h) The x component of current density at λ = 830nm. (i) The y component of current density at λ = 1600 nm. (j) The y component of current density at λ = 830 nm.

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Coarse tuning of the LC resonance into the optical frequency region is accomplished by reducing the dimension of the silicon grating mold. Figure 4(c) shows the fabricated UNWRs using the same nTP process with significant dimension reduction (h = 115 nm, g = 90 nm, ta = 35 nm, tb = 40 nm, and grating pitch = 300 nm). The experimentally measured and simulated transmission spectra under the TE and TM polarizations are plotted in Fig. 4(a) and 4(b), respectively. Two distinct resonances under the TM polarization can be observed at the center wavelength around λ = 800 nm and λ = 550 nm, which correspond to the above-mentioned LC resonance and electric resonance, respectively. The broadening of the resonance dips in the experimental curves compared with the simulation is likely caused by the additional scattering loss induced by the surface roughness. It should be noted that the resonant frequencies found in the UNWRs are in fact higher than the reported values found in the conventional in-plane SRRs with comparable cross-sectional dimensions [35], which is consistent with our theoretical expectation. Furthermore, we have fabricated a control sample consisting of flat metallic grating array with the thickness of 40 nm using the same soft stamp with the pitch of 300 nm, but keeping the metal deposition normal to the grating surface (See Fig. 9 in Appendix D). The measured transmission spectra under both TM and TE polarizations are shown in Fig. 4(d). Under the TM polarization, the grating structure only exhibits a single broadened dip between 550 nm and 650 nm. The LC resonance completely vanishes in grating structure due to the absence of the formation of equivalent inductance and capacitance.

 figure: Fig. 4

Fig. 4 Experimental measurements and numerical simulations for the UNWRs at optical frequencies. (a) The measured transmission spectra of the UNWRs under TE and TM polarization, respectively. For TM polarization, the LC resonance corresponds to the dip centered at 800 nm and the electric resonance is centered at 550 nm. For TE polarization, no resonance is observed. (b) The simulated transmission spectra under TE and TM polarization, respectively, which match with the measured spectra in (a). (c) Scanning electron microscopy (SEM) top view (scale bar: 300 nm) image of UNWRs that exhibit magnetism at optical frequencies. The inset shows the side view of UNWRs (scale bar: 500 nm). The height and width of the gap of each UNWR is 115 nm and 90 nm, respectively. The thickness of the arm and base is 35 nm and 40 nm, respectively. (d) The measured transmission spectra of the control sample that consists of gold grating on a glass substrate with the periodicity of 300 nm and thickness of 40 nm. The control sample only exhibits a single broadened dip under TM polarization rather than the two resonant dips as the UNWRs do.

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In addition to the coarse tuning of the resonance of the UNWRs from NIR towards visible spectrum by varying the dimensions of the nTP molds, fine tuning of the LC resonances can be further accomplished by altering the metal deposition time and angle, which allows for precisely controlling the geometry of the UNWRs. As an example, by extending the deposition time, the fabricated thicker UNWRs possess a reduced self-inductance and Ohmic loss [13], therefore resulting in a blue-shift in the LC resonant frequency. In addition, thicker UNWRs reduce the spacing between the neighboring resonators and form larger capacitors in series with the gap capacitor of each single UNWR. This results in a reduced equivalent capacitance in the individual UNWR, thus a higher LC resonant frequency as well [45]. While for the electric resonance, thicker UNWR have a wider base, which corresponds to a lower resonant frequency according to the scaling law of electric resonance. We have validated the tunability of both the LC and electric resonances by numerically analyzing four samples with various thicknesses but fixed dimensions h and g. The samples are numbered from 1 to 4 and their corresponding dimensions are summarized in Table 1 (See Appendix E). The simulated transmission spectra of the four samples are shown in Fig. 5(a). From sample 1 to sample 4, increasing thickness makes the center wavelength of the LC resonance in the simulation decrease by 62 nm from 810 nm to 748 nm, while the electric resonance red-shifts from 570 nm to 580 nm. The shifts of the resonance with respect to different base thicknesses of the UNWR are summarized in Fig. 10 (See Appendix E). For the validation purpose, we have fabricated sample 1 and sample 4 on glass substrates using nTP process. Their measured transmission spectra are shown in Fig. 5(b), which agree well with the simulation results. Therefore, fine tuning of the LC resonance is demonstrated through controlling the metal deposition process without the necessity of modifying the dimension of the mold. Additionally, fine tuning of the LC resonance can also be achieved by changing the angle of metal disposition to control the length and the relative thickness of the two free-standing arms.

Tables Icon

Table 1. Dimensions of the four UNWR samples with different arm and base thicknesses.

 figure: Fig. 5

Fig. 5 The influence of the metal deposition time on the resonant frequency of the UNWRs. The longer deposition time leads to thicker metal of the UNWRS. (a) The simulated transmission spectra of UNWRs with increasing gold thickness from sample 1 to sample 4. The LC resonance exhibits a blue shift with respect to the thicker gold while the electric resonance experiences a red shift. (b) Experimental transmission spectra of sample 1 and 4, which agree well with the simulation results.

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4. Conclusion

In summary, we have demonstrated the design and scalable nanofabrication of UNWRs in enabling the scaling of artificial magnetism towards the visible spectrum. The highly parallel fabrication of UNWRs with feature size as small as 35 nm have been accomplished using the nTP technique. While altering the dimension of the nanoimprint mold allows for the coarse tuning of the LC resonance over a broad wavelength range from the NIR to the visible spectrum, fine tuning of the resonant frequencies can be realized by simply controlling the metal deposition time and incident angle. With the demonstrated ability of both the coarse tuning and fine tuning of the resonance, we have created the UNWRs with the widely tunable LC resonance from 748 nm to 1600 nm. Furthermore, the highly parallel nTP technique allows for fabricating nanophotonic structures at low cost with high yield on different substrates, thereby enabling the construction of a variety of functional metamaterials, metasurfaces and devices with tunable optical magnetism.

Appendix A scaling law

Thickness dependence of the LC resonance of planar SRRs has been reported and analyzed as a way to potentially increase the resonant frequency [18,35,36]. Here, we consider planar SRRs with the length of the arm h = 150 nm, width of the arm ta = 50 nm, gap opening g = 80 nm, and out of plane thickness tU. The simulated resonant frequency against the tU with same cross-sectional dimension is shown in Fig. 6. This result is contradictory to the simple LC circuit analogy, in which the resonant frequency is independent of the thickness tU. Therefore, it calls for an improved model to further explain the phenomenon [18,35]. Corrigan et al considered the distribution of both electric and magnetic fields and implemented the nonlinear analytical equation for capacitance and inductance to fit the experimental data [35]. Taking into account the distribution of the electric field on both the fringe and surface of the structure will result into fringe capacitance Cf and surface capacitance Cs in addition to the parallel-plating capacitance [34]. Thus, the total capacitance can be formulated as:

Ctotal=ε0εr(hta)tUg+Cf+CsCf=ε0εr(tU+ta+g)Cs=2ε0(tU+ta)πlog(4hg)
Taking into account the electron self-inductanceLe=4(hta)gtUtaωp2ε0,where ωpis the plasma frequency of the metal, the resonant frequency can be written as:
ωLC=1(L+Le)Ctotal
The analytically predicted resonant frequency is also shown in Fig. 6 and the trend agrees well with the FDTD simulation.

 figure: Fig. 6

Fig. 6 Numerical and analytical analysis of the dependence of the resonant frequency on the thickness of the SRR under the modified model. Both numerical and analytical results clearly show the same trend of the rising resonant frequency with the increasing thickness.

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Appendix B optical transmission spectrum measurement

The characterization of the transmission spectrum consists of visible and NIR spectrum measurement. The grating spectrometer (Andor SR-303i) combined with the inverted microscope (Leica DMI 3000M) are employed to measure the transmission from 400 nm to 900 nm. The measurement area is 100 × 100 µm2. The Fourier transform infrared spectroscopy (FTIR, PerkinElmer Spectrum Spotlight 300) is used to measure the spectrum from 900 nm to 2500 nm with the measurement area around 6 × 6 mm2. The spectrum shown in Fig. 3 is combined by the measurements in the two separate wavelength regions. The transmission spectra are both normalized with respect to a bare glass substrate.

Appendix C FDTD simulations

The FDTD simulation is performed using the commercial software Lumerical Solutions. In the simulation, the dimensions of the UNWRs with 500 nm in pitch are h = 280 nm, g = 200 nm, ta = 35 nm and tb = 50 nm. The dimensions of the UNWRs with 300 nm in pitch are h = 115 nm, g = 90 nm, ta = 35 nm and tb = 40 nm. The optical parameters for gold are obtained from the reference [46]. In the simulation, a 100nm layer of epoxy (n = 1.56) and glass substrate are considered as an approximation to the fabricated structure by nTP process.

 figure: Fig. 7

Fig. 7 The electric field distribution under TM polarization (a) The x component of electric field at 1600 nm. (a) The x component of electric field at 830 nm. (a) The y component of electric field at 1600 nm. (a) The y component of electric field at 830 nm.

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 figure: Fig. 8

Fig. 8 The electric and magnetic field distribution under TE polarization. (a) The electric field at 1600 nm. (b) The electric field at 830 nm. (c) The magnetic field at 1600 nm. (d) The magnetic field at 830 nm.

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Appendix D control sample consisting of flat metallic grating array

 figure: Fig. 9

Fig. 9 The control sample with flat gold grating array is fabricated using nTP. The thickness of gold stripes and the grating pitch is 40 nm and 300 nm, respectively. Scale bar: 500 nm.

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Appendix E Resonant frequency v.s. Thickness of the UNWR

 figure: Fig. 10

Fig. 10 The changes of the resonant frequency of the LC resonance and electric resonance with respect to different base thicknesses of the UNWRs. A blue shift of the LC resonance and red shift of the electric resonance are observed with increasing the thickness of the metal deposition for the UNWRs.

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Acknowledgments

This work is supported by the National Science Foundation (NSF) under Grant number EEC-1530734 and DBI-1353952. We thank Dr. C. Stuart for fruitful discussion on mold fabrication process and Dr. S. Li for the help on the FTIR measurements.

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of the U-shaped nanowire resonators (UNWRs) array. The UNWRs located on the epoxy surface consist of 1D array of metallic nanowires with U-shaped cross section. The inset illustrates the cross section dimensions of the UNWR. The unique structure can exhibit the evident LC resonance under excitation with TM polarization incidence and extend the scaling of artificial magnetism to the higher frequency spectrum.
Fig. 2
Fig. 2 Fabrication process flow and scanning electron microscopy images of the UNWRs. (a) To fabricate the UNWRs, the soft stamp is made by curing the liquid PMMS resin on the silicon mold. Then gold thin film is deposited at ~45 degree by thermal evaporation from two opposite directions, covering all surfaces of the soft stamp except trench bottoms due to the shadowing effect. Next, the Au-coated stamp is pressed onto a glass substrate coated with a thin layer of epoxy on the top. Following the curing, the gold structures remain on the substrate after carefully peeling off the stamp. (b) Scanning electron microscopy (SEM) images of UNWRs printed on the epoxy layer on a glass substrate and the close-up view shown in (c). The period of the UNWRs is 500 nm. The height and the width of the gap of each UNWR is 280 nm and 200 nm, respectively. The thickness of the arm and the base is 35 nm and 50 nm, respectively. Scale bar in both (b) and (c): 500 nm.
Fig. 3
Fig. 3 Experimental measurement and numerical simulation for the UNWRs at the near-infrared frequencies. (a) The measured transmission spectra of the UNWRs under the TE and the TM polarization, respectively. (b) The simulated transmission spectra under the TE and the TM polarization, respectively. (c) The electric field distribution at λ = 1600 nm. (d) The electric field distribution at λ = 830 nm. (e) The magnetic field at λ = 1600 nm. (f) The magnetic field at λ = 830 nm. (g) The x component of current density at λ = 1600 nm. (h) The x component of current density at λ = 830nm. (i) The y component of current density at λ = 1600 nm. (j) The y component of current density at λ = 830 nm.
Fig. 4
Fig. 4 Experimental measurements and numerical simulations for the UNWRs at optical frequencies. (a) The measured transmission spectra of the UNWRs under TE and TM polarization, respectively. For TM polarization, the LC resonance corresponds to the dip centered at 800 nm and the electric resonance is centered at 550 nm. For TE polarization, no resonance is observed. (b) The simulated transmission spectra under TE and TM polarization, respectively, which match with the measured spectra in (a). (c) Scanning electron microscopy (SEM) top view (scale bar: 300 nm) image of UNWRs that exhibit magnetism at optical frequencies. The inset shows the side view of UNWRs (scale bar: 500 nm). The height and width of the gap of each UNWR is 115 nm and 90 nm, respectively. The thickness of the arm and base is 35 nm and 40 nm, respectively. (d) The measured transmission spectra of the control sample that consists of gold grating on a glass substrate with the periodicity of 300 nm and thickness of 40 nm. The control sample only exhibits a single broadened dip under TM polarization rather than the two resonant dips as the UNWRs do.
Fig. 5
Fig. 5 The influence of the metal deposition time on the resonant frequency of the UNWRs. The longer deposition time leads to thicker metal of the UNWRS. (a) The simulated transmission spectra of UNWRs with increasing gold thickness from sample 1 to sample 4. The LC resonance exhibits a blue shift with respect to the thicker gold while the electric resonance experiences a red shift. (b) Experimental transmission spectra of sample 1 and 4, which agree well with the simulation results.
Fig. 6
Fig. 6 Numerical and analytical analysis of the dependence of the resonant frequency on the thickness of the SRR under the modified model. Both numerical and analytical results clearly show the same trend of the rising resonant frequency with the increasing thickness.
Fig. 7
Fig. 7 The electric field distribution under TM polarization (a) The x component of electric field at 1600 nm. (a) The x component of electric field at 830 nm. (a) The y component of electric field at 1600 nm. (a) The y component of electric field at 830 nm.
Fig. 8
Fig. 8 The electric and magnetic field distribution under TE polarization. (a) The electric field at 1600 nm. (b) The electric field at 830 nm. (c) The magnetic field at 1600 nm. (d) The magnetic field at 830 nm.
Fig. 9
Fig. 9 The control sample with flat gold grating array is fabricated using nTP. The thickness of gold stripes and the grating pitch is 40 nm and 300 nm, respectively. Scale bar: 500 nm.
Fig. 10
Fig. 10 The changes of the resonant frequency of the LC resonance and electric resonance with respect to different base thicknesses of the UNWRs. A blue shift of the LC resonance and red shift of the electric resonance are observed with increasing the thickness of the metal deposition for the UNWRs.

Tables (1)

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Table 1 Dimensions of the four UNWR samples with different arm and base thicknesses.

Equations (2)

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C total = ε 0 ε r (h t a ) t U g + C f + C s C f = ε 0 ε r ( t U + t a +g) C s =2 ε 0 ( t U + t a ) π log( 4h g )
ω LC = 1 ( L+ L e ) C total
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