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We succeeded in making a silver split-ring (SR) structure of approximately 130 nm in diameter on a glass substrate using a nanosphere lithography technique. The light scattering spectrum in visible near-infrared region of a single, isolated SR was measured using a microscope spectroscopy optical system. The electromagnetic field enhancement spectrum and distribution of the SR structure were simulated by the finite-difference time-domain method, and the excitation modes were clarified. The long wavelength peak in the light scattering spectra corresponded to a fundamental LC resonance mode excited by an incident electric field. It was shown that a single SR structure fabricated as abovementioned can operate as a resonator and generate a magnetic dipole.
©2011 Optical Society of America
1. Introduction
The split-ring resonator (SRR) was first reported Pendry et al. [1] in 1999 and the structure has attracted much attention due to the “negative refractive index” property, shown theoretically by Veselago [2]. Negative refractive index materials such as the metallic rod pair [3,4] and the metallic double fish net [5,6], have also been examined. SRRs cause magnetic resonance near the LC resonance frequency and change the permeability of the SRR metamaterial [7]. The electric and magnetic fields are expected to be enhanced when LC resonance occurs in SRRs. The field enhancement effect is of value in nonlinear optics [8] and for sensors [9]. Various applications make use of metamaterials consisting of a large number of SRRs. Moreover, the potential applications of a single SRR are of considerable interest. Previous studies have reported occurrences of nonlinear optical phenomena using the electrical field enhancement of the localized surface plasmon (LSP) of a single, isolated CdS-coated silver nanoparticle [10]. An SRR that exhibits an optical nonlinearity can potentially be used as an optical information processing device on a submicron scale. In order to fabricate such devices, it is necessary to establish a low-cost method for manufacturing SRRs that operate in the visible near-infrared region.
The reduction of the operating wavelength of the SRR is a pressing issue in metamaterial applications; further, several researches have also focused on the shortening of the occurring LC resonant wavelength [11–14]. The design policy of an SRR that operated because of visible light was reported by Ishikawa et al. In addition, the study reported the miniaturization of the SRR in order for operation at high frequencies while maintaining the magnetic characteristics, the device structure, and the selection of the SRR material [12]. It is necessary to reduce the size of the SRR to around 100 nm for operation in the visible near-infrared region, however, it is technically difficult to make an SRR of this size with high accuracy. A U type SRR structure that operates in the visible near-infrared region has been examined closely. The manufacturing method relies on physical processing by electron beam lithography [7–11,13,14]. However, this method is unsuitable for mass production, the process is complex, and the system is expensive.
In 2003, Aizpurua et al. [15] developed a method for fabricating metal nanorings. They successfully produced a gold nanoring of diameter approximately 100 nm. In this technique, gold was deposited on polystyrene nanoparticles by vacuum deposition, and the gold was then processed by argon sputtering. Gold etched by the argon spatter adheres to polystyrene particles and when the polystyrene is dissolved, a gold nanoring remains. Kreiter et al. [16,17] fabricated a crescent-shaped gold nanorod in a similar manner; in addition, they tilted the substrate with the deposited polystyrene nanoparticles by a certain angle. The gold was removed by an argon ion beam incident normal to the surface. A crescent-shaped nanorod can be formed using this method. Several gold evaporations at different substrate angles are required in the formation of a split-ring (SR) structure.
These methods are known as nanosphere lithography and if put into general use, it will become possible to produce a large amount of SRRs at a comparatively low cost. However, the magnetic response via LC resonance has not yet been confirmed for a SR structure made by this method.
In this paper, we propose a simpler nanosphere lithography technique for making a silver SR structure with a small diameter. We measure the light scattering spectrum for a single isolated SR and by comparison with numerical simulations, we examine the magnetic response via LC resonance.
2. Fabrication method, measurement, and numerical calculations
2.1. Nanosphere lithography
Gold is a common choice of material for the SSR because it has a low reactivity [7,8,11,13–17]. Silver and aluminum, which have high plasma frequencies, are suitable for SRRs that operate in the visible light region [9,12,13]. In our experiment, silver was selected for the SRR material because it is expected that the conduction loss is smaller than gold and aluminum and that the resonance will be strengthened.
The SR structures were fabricated following the procedure illustrated in Fig. 1 . A colloidal solution of polystyrene spheres, 100 nm in diameter, was deposited on a Pyrex glass substrate heated to 90°C (Fig. 1(a)). The polystyrene spheres were then coated with a thin silver film, 40 nm thick, via thermal evaporation deposition (Fig. 1(b)). The substrate was titled by 43° during deposition. Next, the silver was removed by argon ion sputtering (Fig. 1(c)). For this step, the substrate was tilted to a −32° angle. Deposition and sputtering were only carried out once. The polystyrene spheres were melted and removed with acetone, (Fig. 1(d)) leaving single SRs distributed on the glass substrate. In order to avoid chemical changes to the silver SRs, an optical measurement was conducted several weeks after the SRs were fabricated.
2.2. Light scattering of single isolated SR structure
Figure 2 shows a schematic of the experimental setup for observing light scattering of a single isolated SR. Linearly polarized white light, defined as shown in the insert as Ex and Ey, passed through an objective lens and was incident in a direction normal to the substrate. The objective lens was a 100 × oil-immersion type (NA = 1.4). A filtering mask was located in the pupil plane that relayed information in confocal plane 1 to confocal plane 2. A dark-field signal was obtained at confocal plane 2 by using a filtering mask. The bright-field spectrum was obtained when the filtering mask was removed from the pupil plane.
Fig. 2 Schematic of the optical system used for the measurement of the light scattering spectrum a single isolated SR. The insert defines the polarization axes.
A light beam with a diameter of 100 μm obtained from the projected image at confocal plane 2 was routed to a multichannel spectrometer via an optical fiber. Therefore, the area of detection on the glass substrate was confined to a diameter of 1 μm due to the effect of the 100x objective lens. This made it necessary for the SRs to be separated by a minimum distance of 1μm in order to include only one SR in the detection area. The light spectra were measured using multichannel spectrometers for visible light and for the near-infrared region. Subsequently, the obtained signals were added to each other.
The dark-field spectrum from the SR is denoted by IS. Away from the SR, the dark-field and bright-field spectra are denoted by IBD and IBB respectively. Thus, the light scattering can be expressed as Isca(λ) = {IS(λ) −IBD(λ)}/IBB(λ).
2.3. Numerical calculations
We calculated the electromagnetic field distribution and enhancement spectrum of the SR by using a three-dimensional finite difference time-domain (FDTD) method. Figure 3 shows a model of the simulated structure. The glass substrate is assumed to have a refractive index of 1.515 and the size of SR, with thickness h, was obtained from FE-SEM images. The dielectric constant of silver was calculated using the Drude-Lorentz model. The Drude-Lorentz parameters were adjusted to fit the dispersion relations of the calculated dielectric function of silver to the experimentally obtained dielectric function [18] in the wavelength range from 400 nm to 2000 nm. The electric field intensity was calculated at the center of the SR gap, point g, and at a point on the axis of symmetry away from the SR, point e, as shown in Fig. 3. The magnetic field intensity was calculated at the center of the ring, point c. We calculated the electric field component parallel to the incident light direction and the magnetic field component normal to the substrate. The field enhancement was normalized to the incident electromagnetic field intensity. The field intensity distribution was obtained from snapshots using incident continuous wave light.
Fig. 3 Computational model for the FDTD simulations. h is thickness of SR. The points g and e indicate the positions where the electric field enhancement spectrum was calculated. The magnetic field enhancement spectrum was calculated at point c. The point e is at a distance 10 nm from the edge of the SR.
3. Results and discussion
3.1. Structure of the SR
Figure 4 shows dark-field microscope and field-emission scanning electron microscope (FE-SEM) images of the SR. The FE-SEM image confirms the U shape structure of the SR. Figure 4(b) is the enhanced SEM image of the square yellow area indicated in the dark field microscope image shown in Fig. 4(a). The minute structures observed in Fig. 4(b) are confirmed as U-shaped SR structures. From Fig. 4(c), the outer diameter of the SR was measured to be 132 nm, while the inside diameter is 68 nm. The width of the gap is 56 nm. The light scattering spectrum of the SR shown in Fig. 4(c) was measured.
Fig. 4 (a) Dark-field microscope and (b), (c) field-emission scanning electron microscope images of the SR.
Shumaker-Parry et al. [16] reported that when deposition and milling is performed once a crescent shaped metallic rod is formed. They, therefore, concluded that deposition needed to be performed twice, at different angles, in order to fabricate a SR structure with a narrow gap. However, in our method, a U shaped SR structure was made by depositing and sputtering the silver once only. This is because sputter redeposition occurred when the metal was milled.
3.2. Light scattering and electromagnetic field enhancement spectra of a single SR
Figure 5(a) shows the measured light scattering spectra of a single SR. We can see that the light scattering spectrum is dependent on the incident polarization. Two peaks appeared in the spectra for scattering of both Ex and Ey polarized light, which can be denoted by λx1( = 1025 nm), λx2( = 580 nm), λy1( = 720 nm), and λy2( = 450 nm), respectively. This polarization dependency is similar to the reported polarization dependency of the transmission spectrum of a U shape metal SRR array [11,14] and also similar to the polarization dependency seen in the absorbance spectrum of a crescent shape metallic array structure [17].
Fig. 5 (a) Light scattering spectra of a single SR. Scattering with incident Ex polarization is indicated by red circles and blue triangles indicate the results for Ey polarization. (b) Calculated electromagnetic field enhancement spectra of SR with a thickness of 22 nm. Other size parameters of SRR used for calculation applied the measured value in Fig. 4(c). The red and blue lines are simulation results for Ex and Ey polarization, respectively. The electric field enhancement spectrum for each polarization at point g is given by the solid line and that at point e by the dashed line. The magnetic field enhancement spectrum is indicated by points on a solid line.
Figure 5(b) shows the results of the simulations for both electric and magnetic field enhancement spectra. The two peak wavelengths in the spectra at both points g and e, denoted by Ex-g and Ex-e respectively, for Ex polarized light scattering are 1025 nm and 580 nm, as shown in Fig. 5(b). This agrees well with the measured light scattering spectra peaks λx1 and λx2. For incident Ey polarized light, the enhancement spectrum at the point e, Ey-e has two clear peaks indicated by the dashed blue line in Fig. 5(b). The peak at 710 nm also corresponded well to the measured light scattering spectrum peak λy1. The peak at 490 nm does not coincide with λy2; however, it is speculated that these peaks may be corresponding modes. The magnetic field Hz-c at point c was enhanced at a wavelength of 1025 nm for Ex polarized incident light but there was no enhancement of the magnetic field for Ey polarized incident light. The good agreement between the measured and simulated spectra leads us to conclude that the FDTD simulations accurately describe the optical response of the SR.
Because the structure of the SR was very small, it was difficult to measure its film thickness using FE-SEM and other measuring methods. Figure 6 shows the measured light scattering spectrum and the calculated electric field enhancement spectra at the point g for various film thicknesses. The observed value of the peak wavelength λx1 was in close agreement with the simulated Ex-g peak wavelength value for a thickness of 22 nm, as shown in Fig. 6. However, it is reported that the maximum near-field enhancements occur at lower energies than the maximum of the corresponding far-field spectrum [19]. In our metal SR structure, the difference in the peak wavelength of the near-field and far-field spectrum has not yet been clarified. Therefore, we assume the thickness of the SR to be 22 nm, though this estimated thickness value might be slightly more than the actual value.
Fig. 6 The measured light scattering spectrum (open circles) and calculated electric field enhancement spectra at the point g for Ex polarized incident light for various film thicknesses.
3.3. Electromagnetic near-field distribution
In the peak spectrum wavelength seen in Figs. 5(a) and 5(b), it is expected that the resonance mode is excited in the SR, and an electromagnetic field distribution unique to the resonance mode appears. In order to investigate the resonance mode of our SR, the electromagnetic field distribution in the peak wavelength was calculated. Distributions were calculated for all four Ex and Ey peak wavelengths. Stationary state electromagnetic field distributions around the SR are shown in Figs. 7 –10 . The electric field distributions correspond to the times when the electric field value outside the SR was maximum. The magnetic field distribution is shown at before one-fourth the time period of the electric field distribution. At this time period, the magnetic field around the SR takes the maximum value.
Fig. 7 Numerical results of the electromagnetic field distribution for Ex polarized incident light at a wavelength of 1025 nm. (a) The electric field distribution in the x-y plane. The magnetic field distribution in the (b) x-y, (c) x-z, and (d) y-z planes. The white arrows in indicate the vector field. The intensity is normalized to an incident intensity of unity. (e) Sketch of electric charge distribution and current in the SR. The charge concentration is indicated by red circles, the current by blue arrows, and the generated magnetic field direction in blue.
Fig. 10 Numerical results of electromagnetic field distribution for Ey polarized incident light at a wavelength of 490 nm. (a)–(e) as per Fig. 7.
Figure 7 shows the electromagnetic field distribution for incident Ex polarized light at a wavelength of 1025 nm. A strong electric field is generated in the gap of the SR and the charge is polarized at the two arms of the SR (Fig. 7(a)). The electric field strength near the arms is approximately 100 times greater than the incident electric field. A strong magnetic field along the −z direction is also generated due to an anti-clockwise current in the ring (Figs. 7(b)–7(e)). The magnetic field intensity in the ring was approximately 30 times greater than the incident light field intensity. During this time, the SR shows a behavior similar to a magnetic dipole with a magnetic moment in the −z direction. The magnetic field enhancement in the ring and the electric field enhancement in the gap alternated every one-fourth of a time period. An accumulation of magnetic and electrical energy was caused by a movement of charge. Thus, the ring and gap were seen to behave as an inductor and capacitor. The SR displays LC resonance at 1025 nm.
Figure 8 shows the electromagnetic field distribution for incident Ex polarized light at a wavelength of 580 nm. In Fig. 8(a), the electric field is also enhanced outside of the ring and not just in the gap of the SR. There were four places where a concentration of charge could be identified and three magnetic dipoles with different directions could be attributed to this magnetic field distribution. In the ring, the magnetic field existed along the −z and + z directions. However, because the sum total of the magnetic induction flux in the ring is along the –z direction, macroscopically, the SR behaves as a magnetic dipole. In this mode, LC resonance also occurs. If we assume the mode with a wavelength of 1025 nm is the fundamental LC resonance mode, then this mode is the second order LC resonance mode.
Fig. 8 Numerical results of the electromagnetic field distribution for Ex polarized incident light at a wavelength of 580 nm. (a)–(e) as per Fig. 7.
The electromagnetic field distribution for incident Ey polarized light is shown in Fig. 9 . For an incident wavelength of 710 nm, the electric field is enhanced at the outer edge of the ring opposite the gap, as shown in Fig. 9(a). In this case, the polarity of the concentrated charge in the two arms is the same. It was found that the LSP resonance mode (reported in [20]) of the electric dipole type had been formed about the SR structure when observed as a whole. The magnetic field was also enhanced in the ring with a distribution shown in Figs. 9(b)–9(d). There appears to be a local magnetic dipole, however, because the current flows to the two arms in the same direction the sum total of the magnetic induction flux through the inside of the ring is zero. Thus, a macroscopic magnetic dipole does not exist for this mode.
Fig. 9 Numerical results of electromagnetic field distribution for Ey polarized incident light at a wavelength of 710 nm. (a)–(e) as per Fig. 7.
For an incident light wavelength of 490 nm, the electric field was enhanced on the edges of the ring, as shown in Fig. 10(a). This mode showed a quadrupole type LSP resonance mode. In general, because the quadrupole mode is prohibited in plane wave incident light cases, it is not possible to excite it. However, we believe that the quadrupole mode is excited here because this SR is not symmetric in the direction parallel to the incident polarization. The peak wavelength λy2 of the measured light scattering spectrum might correspond to the quadrupole type LSP mode. We believe that the reason the peak wavelength of the electric field enhancement simulation is different from λy2 is that the computational model and the actual structure, for example, the thickness value, do not accurately describe this situation.
We can identify specific electromagnetic modes of the SR with each peak in the light scattering spectrum.
4. Conclusions
A silver SR structure approximately 130 nm in diameter was made using nanosphere lithography. The light scattering spectrum of a single isolated silver SR was observed using a dark field microscope spectroscopy technique. There was a strong polarization dependency in the peak wavelength of the light scattering spectrum in the visible near-infrared region.
The electromagnetic field spectrum and distribution were calculated by the FDTD method. The peak wavelength of the electromagnetic field enhancement spectrum coincided well with the peak in the light scattering spectrum. The electromagnetic field distribution differed for different peak wavelengths.
It was able to be specified that the peak of the light scattering spectrum in single SR was the following modes respectively. The peak wavelengths of 1025 nm and 580 nm for incident Ex polarized light were identified as LC resonance modes of the fundamental and second order, respectively. The peak wavelengths of 710 nm and 450 nm for incident Ey polarized light were identified as LSP modes of dipole and quadrupole type, respectively.
In this study, an optical measurement was conducted several weeks after the fabrication of the silver SR in order to avoid chemical change. Chemical deterioration is a factor is this study because the SR is made of silver. However, a month after the SR was fabricated, the peak of the light scattering spectrum by the LC resonance was confirmed. It will be necessary to examine the effects of deterioration of the silver SR in detail in the future.
In our SRR, a fundamental LC resonance mode was excited by light with a wavelength of about 1000 nm. Reducing the diameter of the SRR will shorten the excitation wavelength of the fundamental LC resonance mode. In principle, the size of SR structure can be reduced to the size of the polystyrene sphere. On the other hand, a surface roughness of several nanometers exists in the silver structure formed using argon ion sputtering; the formation of this roughness cannot be controlled. Therefore, there might be a limit to the miniaturization of the SR structure. At present, we have succeeded in fabricating SR structures with an approximate diameter of 80 nm by using polystyrene spheres with a diameter of 60 nm. Each SRR has a characteristic magnetic response and so it will be possible to build two-dimensional metamaterials even from random distributions of single SRRs. It is necessary to densify the SR structure in order to ensure that the metamaterial consists of a large quantity of SRs. Therefore, it is necessary to densify the structure while maintaining a reasonable distance between each polystyrene sphere. The density of polystyrene spheres on the substrate increases easily if the concentration of the colloidal solution of the polystyrene is increased. On the other hand, polystyrene spheres are coherent. The electrostatic repulsion between the polystyrene spheres can be used to maintain the required distance between them. Moreover, the array method of self-assembling the polystyrene spheres can be used to ensure the required distance. We aim to continue attempting to reduce the LC resonant wavelength via the nanosphere lithography technique and to build a two-dimension metamaterial in the future.
Acknowledgments
This study was supported by a Grant-in-Aid for Scientific Research (C) from the Japan Society for the Promotion of Science (No. 21510134) and Grant-in-Aid for Scientific Research on Innovative Areas from The Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 22109007).
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