1. Introduction

Negative index metamaterials are attracting considerable interests due to their distinguishing electromagnetic properties from naturally occurring materials [1–3] and various strange potential applications such as perfect lenses [4] and invisibility cloaks [5]. To get a material with negative index and low loss, both permittivity and permeability being simultaneously negative are generally required. While most noble metals show negative permittivity in a broad optical frequency region, no natural material exhibiting negative permeability at optical frequencies is discovered so far. To produce negative permeability, diverse artificial magnetic metamaterial structures have been proposed. Typical examples include split-ring resonators [1, 2], pairs of cut wires and plates (with circular, rectangular, and square shapes) [6–10], etc. While great progress has been made by combing the above magnetic structures and noble metal materials in constructing negative index metamaterials working at microwave [11–13] and optical frequencies [3,14–16], magnetic response frequency of the most current magnetic metamaterials is generally limited within a narrow band for a given structure. Here we report experimental observation of tunable magnetic response of pairs of elliptical metal-dielectric-metal plates (PEMDMPs) in the near-infrared region. By selecting polarization direction of the incident light and varying the length of axis of the PEMDMPs simultaneously, the magnetic response wavelength can be tuned in the range of from 1.26 $\mu m$ to 2.10 $\mu m$.

2. Experiment

We employ our established single-prism holographic lithography [17, 18] to create templates for the PEMDMPs. The optical recording set-up is exactly the same as that of Refs. 17. A top-cut rectangular prism is used as a beam splitter to produce multiple beams for creating required two-dimensional elliptical hole profiles. The lengths of the major and minor axis of the elliptical holes are determined by the period of the interference profiles in the x and y directions, respectively, which are controlled by the angles between the adjacent interference beams for a given laser wavelength λ. Photosensitive emulsion used to record the interference patterns is a positive photoresist (S9918M PHOTO RESIST, Shipley Co.), which is prepared and processed according to standard procedure as described in Ref. 18. The recording light is a laser beam with wavelength$\lambda =442nm$ irradiated from a He-Cd laser ($70mW$) with a linear polarization direction perpendicular to the plane of the recording platform. Exposure dose in the recording process can be adjusted in the range of $60-90mJc{m}^{-2}$. After exposure, development, rinsing, and post baking, we can obtain a dielectric template with elliptical holes on the glass substrate. By electron-beam evaporating two $t_m=30nm$ thick Ag layers separated by a $t_d=40nm$ thick SiO₂ layer and taking a lift-off procedure, we can get an array of the PEMDMPs.

3. Results and discussion

Figures 1(b)-(d) are the oblique view of field emission scanning electron microscopy images (SEM, taken with SIRION TMP, FEI Co.) of the resultant structures with fixed minor axis a (~350 nm) but varied major axis b from 350 nm to 420 nm and 504 nm, respectively. The insets show the magnified normal view of the SEM images. Due to the deposition and lift-off process, the samples have about 20 degree sidewall angle, we determine the lengths of the axes from the SEM images through the lengths of the samples at the top surface and the sidewall angle, which leads to an error of about ± 20 nm. The transmission spectra are measured by a Fourier-transform infrared spectrometer (Nicolet 6700, Themofisher Co.) combined with a continuum infrared microscope (15 × Infinity corrected Reflachromat Objective, numerical aperture NA = 0.58, InGaAs detector, infrared polarizer, resolution 0.09 cm⁻¹). The transmittance of all the samples are normalized to that of the bare glass substrate, which are directly obtained by the tied software of the spectrometer from the measured transmittance of the samples and a bare glass substrate, respectively.

 

Fig. 1 (color online) (a) Scheme of PEMDMPs and SEM images of the fabricated PEMDMPs with fixed minor axis (a = 350 nm) but varied major axis b = (b) 350 nm, (c) 420 nm, and (d) 504 nm, respectively. Bar, $2\mu m$. Insets: magnified view. Bar, $500nm$.

Download Full Size | PDF

Figure 2 (first row) shows the measured transmittance of the above three samples as the normal incident light is with a polarization parallel to the major and minor axis of the elliptical plates, respectively. The measured results show that, as the samples are with the same length of major and minor axis (a = b, circular plates structure) as shown in Fig. 1(b), the magnetic response frequency is of around 1440 nm as the incident light is at two orthogonal polarization directions [Fig. 2(a)], which is consistent with the magnetic propose property of pairs of circular metal plates exhibited [8]. However, as the circular plates change to elliptical structures of PEMDMPs, and the major axis b gradually changes from 350 nm to 420 nm and 504 nm, the magnetic response wavelength changes from 1440 nm to 1737 nm [Fig. 2 (b), blue line] and 2005 nm [Fig. 2 (c), blue line], respectively, as the incident polarization is parallel to the major axis of the PEMDMPs. Due to the minor axis a is fixed at 350 nm, the magnetic response produced by the incident polarization parallel to the minor axis maintains unchanged around 1440 nm (Fig. 2, first row, red lines). Figure 2 (second row) shows the numerically simulated transmittance of the PEMDMPs by the finite-difference time-domain (FDTD) method, the codes of which are compiled by our group and have widely been used to calculate optical properties of different metal structures in our previous works [19,20]. The dielectric constant of silver is from a Drude model ${\epsilon }_{Ag}=1-{\omega }_p^2/[\omega (\omega +i{\omega }_c)]$ with ${\omega }_p^{}=1.37\times {10}^{16}$ Hz and ${\omega }_c^{}=8.05\times {10}^{13}$ Hz, respectively, which produces a good approximation to experimental values in the near-infrared region [21]. The refractive index of SiO₂ is $n_{Si{O}_2}=1.54$. The geometric parameters of the structures are from experimental measurements. Since the transmittance of glass substrate is removed from that of the samples in our measurements, to make sense of the comparison with the experimental results, we do not include the glass substrate in our FDTD simulations. The incident light is normal to plane of the PEMDMPs (z direction), and periodic boundary conditions are applied in the x and y directions. From the figure, we see that the simulated magnetic response frequencies match very well with the experimental measurements, and the response wavelength shows a good linear dependence on the axis length of the elliptical plates [see the inset of Fig. 2(a)], indicating that the magnetic response frequency can be effectively modulated by the length of the axis of the PEMDMPs. The physics behind the magnetic response of the PEMDMPs is similar to that of the cut-wire pairs: for normally incident light with magnetic field direction in the plane of PEMDMPs [the x - y plane, Fig. 1(a)], the oscillating magnetic field induces a circular current between the metal plate pairs, which can be regarded as an optically induced resonance in a LC circuit. The circular current produces an anti-magnetic field to the external magnetic field. As a result, a negative magnetic permeability appears [6,7]. The equivalent LC circuit model is generally employed for predicting the resonance frequency of the metamaterials [22–24]. In our structures, the inductance of two elliptical metal plates is $L_m={\mu }_{0}b{t}_d/a$ as the incident polarization is parallel to the major axis, where ${\mu }_0$ is the vacuum permeability. The capacitance between the metal plates is $C=c_1{\epsilon }_0{\epsilon }_d\pi ab/4t_d$, where ${\epsilon }_0$ is the free-space permittivity, ${\epsilon }_d$ is the permittivity of SiO₂, and $c_1$ is a numerical factor. Generally, $c_1$ ranges from 0.2 to 0.3. Due to the metal plates of PEMDMPs show sharp ends, we choose $c_1$ as 0.11. The electron self-inductance is given by $L_e=b/{\epsilon }_0{w}_p^{2}S\text{'}$, where $S\text{'}=\delta a$ is the effective cross-section area of the metal plates. $\delta =\lambda /4\pi \kappa$ is the penetration depth of silver in the near infrared frequencies, where κ is the extinction coefficient of silver [21]. δ can be set at 11 nm from the calculation. Then, the magnetic resonance frequency is given by $f_m={[2\pi \sqrt{(L_m+L_e)C}]}^{-1/2}$, which corresponds to the resonance wavelength ${\lambda }_m=c_0/f_m=b{c}_0\sqrt{c_1{\epsilon }_d{\pi }^3(1/c_0^2+1/\delta t_d{w}_p^2)}$, where $c_0$ is the speed of light in vacuum. Similar to our experimental measurements, the formula suggests that the magnetic resonance wavelength is proportional to the length of axes of the PEMDMPs along the incident polarization direction.

 

Fig. 2 (color online) (a)-(c) Measured (first row) and simulated (second row) transmittance of the PEMDMPs shown in Fig. 1(b)-(d) as the incident polarization is parallel to the major axis (blue lines) and minor axis (red lines), respectively. The inset shows the relation between the measured magnetic resonance wavelength and the length of the major axis b (darkviolet triangles: polarization parallel to the major axis; green stars: polarization parallel to the minor axis). The solid lines are obtained from the equivalent LC circuit model.

Download Full Size | PDF

On the other hand, from the above LC circuit model, we see that the thickness of SiO₂ $t_d$also influences the magnetic resonance frequency: The resonance frequency increases with the thickness of SiO₂ [25]. Additionally, the pitches of the structures will affect the coupling effect between the adjacent PEMDMPs and will finally affect the resonance frequency of the structures [22–24]. Therefore, to avoid such coupling effect, we design the distance of adjacent PEMDMPs larger than 100 nm in our experiments [24].

To further confirm the underlying mechanism, we measured the evolution of the transmission spectra of a PEMDMP (a = 360 nm, b = 540 nm) as the polarization direction of the normally incident light is changed from the major axis to the minor of the PEMDMP (see Fig. 3 ). We see that as the incident polarization is parallel to the major axis, a strong magnetic response around 2.1 $\mu m$ appears [Fig. 3, red line]. As the incident polarization gradually changes to parallel to the minor axis, the other magnetic response peak at around 1.46 $\mu m$appears and becomes stronger to stronger, accompanying by the gradual damping of the other response around 2.1 $\mu m$ and finally disappearance as the polarization is along the minor axis [Fig. 3, black line]. What should be noted is that the two response wavelengths are completely independent on the variation of the incident polarization. As the incident polarization direction is between the two axis directions, two magnetic response peaks around two fixed wavelengths 1.46 $\mu m$ and 2.10 $\mu m$ can be observed simultaneously (see Fig. 3, blue line, the angle between the incident polarization direction and the major axis of the elliptical plates is 40 degree). This can be understood that electromagnetic field of the incident light is split into the x and y directions and works on the plate pairs simultaneously in the major and minor axes. The additional peak around 1.1 $\mu m$ is attributed to the electric coupling between the structures with the incident light [10].

 

Fig. 3 (color online) Measured transmittance of a PEMDMP with a = 360 nm and b = 540 nm as the polarization of a normally incident light changes from 0° to 90° with a step of 10°.

Download Full Size | PDF

In what following, we fabricated a class of PEMDMPs with fixed period (by fixing the angle among the interference beams) but varied major and minor axes by modulating exposure dose in the recording process. Figures 4(a)-(e) show the SEM images of the resultant PEMDMPs with increased axis length gradually. Figures 4(f)-(g) show the measured (first row) and simulated (second row) transmission spectra as the polarization of normally incident light is parallel to the minor axis [Fig. 4(f)] and major axis [Fig. 4(g)], respectively. From the figures we see that the magnetic response shows obvious red shift with the length of the axis of the incident polarization direction parallel to, which is further confirmed by FDTD simulations [Figs. 4(f)-(g), second row]. For instance, as the incident polarization is parallel to the minor axis, which changes from 290 nm to 314, 330, 350, and 368 nm, the strong magnetic response around 1262, 1315, 1385, 1444, and 1495 nm occurs, respectively [see Fig. 4(f)]. While the incident polarization is parallel to the major axis, which changes from 414 nm to 446, 466, 504, and 540 nm, the corresponding magnetic response at 1731, 1810, 1905, 2005, and 2102 nm occurs, respectively [see Fig. 4(g)]. As shown in the inset of Fig. 4(f), the magnetic response also shows a good linear dependence on the length of the axis. Our results reveal that, by selecting polarization direction of the incident light and varying the axis length of the PEMDMPs, a tunable magnetic response ranging from 1.26 $\mu m$ to 2.10 $\mu m$frequencies is achieved.

 

Fig. 4 (color online) SEM images of the PEMDMPs with (a) a = 290 nm, b = 414 nm, (b) a = 314 nm, b = 446 nm, (c) a = 330 nm, b = 466 nm, (d) a = 350 nm, b = 504 nm, and (e) a = 368 nm, b = 540 nm, respectively. Bar, $500nm$. Measured (first row) and simulated (second row) transmittance of the above PEMDMPs as the incident polarization is parallel to (f) minor axis and (g) major axis, respectively. The inset of Fig. 4(f) shows the dependence of the measured magnetic response wavelength on the minor axis (red stars) and the major axis (blue stars), respectively. The solid line is obtained from the equivalent LC circuit model.

Download Full Size | PDF

Note that from the simulation results, the transmittance is monotonically decreased with the length of the axis. This is resulted from the variation of filling fraction and wavelength dependent absorption of silver. The measurements [Figs. 4(f) and 4(g), curves c, d and e] also show a good monotone change. The discrepancy of some measured transmittance [Figs. 4(f) and 4(g), curves a and b] from the monotone trend is resulted from the experimental errors in the fabrication process.

4. Conclusion

In summary, we have experimentally obtained tunable near infrared magnetic metamaterials by using a single-prism interference lithography and electron-beam evaporation and lift-off technique. The fabricated metamaterials are pairs of elliptical metal-dielectric-metal plates and exhibit linearly dependent magnetic response on the axis length of the elliptical plates. By selecting polarization direction of the incident light and varying the axis length of the elliptical plates simultaneously, we have achieved the magnetic response in a range of from 1.26 $\mu m$ to 2.10 $\mu m$. The measured results are confirmed by the FDTD numerical simulations. Our structures offer the oversimplified opportunities for robust construction of bulk photonic metamaterials for various device applications.