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Herein, we will propose a new application possibility of epsilon-near-zero (ENZ) materials: high resolution wide-field imaging. We show that the resolution can be dramatically enhanced by simply inserting a thin epsilon-near-zero (ENZ) material between the sample and substrate. By performing metal half-plane imaging, we experimentally demonstrate that the resolution could be enhanced by about 47% with a 300-nm-thick SiO2 interlayer, an ENZ material at 8-μm-wavelength (1250 cm−1). The physical origin of the resolution enhancement is the strong conversion of diffracted near fields to quasi-zeroth order far fields enabled by the directive emission of ENZ materials.
© 2014 Optical Society of America
1. Introduction
For conventional optics, the lateral resolution is limited by diffraction of light, which prevents imaging of subwavelength objects. Rayleigh’s resolution criteria based on diffraction theory can be described by the following formula:
with ∆x being the minimum separation between the resolvable points and λ being the wavelength of the light [1]. The NA, the numerical aperture, is defined by NA = n·sinθ, where n is the refractive index of the medium filling between the sample and the lens, and θ is the half-angle of the maximum cone of the light that can be gathered by the lens. According to Eq. (1), a higher NA leads to better spatial resolution.Solid immersion lenses (SIL) have been widely used to increase the NA of the conventional microscope system [2, 3]. Suppose that we observe a specimen placed on a planar substrate (for example, glass or Si) under a microscope. Without SIL, high-k modes light, whose incident angle is larger than the critical angle, would undergo total internal reflection at the interface between the substrate and air (Fig. 1 (a)). For instance, the critical angle is about 17° with Si substrate (n = 3.4) at mid-IR regime (1~16 μm). The remaining propagation beams would be confined to a narrow cone around the surface normal thereby drastically reducing the NA.
Fig. 1 Diffracted light profile (a) without lens, (b) with solid immersion lens and (c) with ENZ meta-lens.
On the contrary, by placing an index-matched SIL at the bottom side of the substrate, the total internal reflection becomes frustrated as illustrated in Fig. 1 (b). In addition, thanks to the spherical geometry of the exit side of the SIL, the propagation directions are bent toward the detector when the light is passing through the SIL-air interface. These two effects give rise to significant increase in the NA. Also, the SIL can be used to guide or collect the THz waves emitted or detected at the photoconductive antennas [4]. While successful in enhancing the NA, this technique suffers from several drawbacks, including large thickness, difficulties in lens manufacture and the necessity for sophisticated alignment (the sample should be placed on the center of the flat bottom surface of the SIL).
Here, we propose a new type of a numerical aperture increasing lens (NAIL) having subwavelength thickness and planar geometry with ease of fabrication. Our meta-lens relies on an epsilon-near-zero (ENZ) material, a material with vanishingly small dielectric constant at certain wavelengths [5]. When the light is transmitted from the ENZ material to air or ordinary materials, the radiation direction is bent almost perpendicular to the interface, independent of the incident angle. Such phenomenon is known as the directive emission and can be understood by Snell’s law with high index mismatch between the two materials [6–8]. Directive emission has been demonstrated experimentally using metamaterial cavity in microwave and NIR regime [9–11]. This unusual property is the key feature enabling resolution enhancement of our proposed meta-lens.
The ENZ meta-lens can be implemented simply by inserting the ENZ material between the specimen and the substrate as illustrated in Fig. 1(c). Due to directive emission at the ENZ-substrate interface, the strongly diffracted light having large in-plane wavevectors (kx) could be converted into nearly plane waves having negligibly small kx. Now, the redirected light is able to pass through the substrate-air interface without total internal reflection because of the angle of incidence smaller than the critical angle. This could improve the NA of the system enabling the high resolution wide-field imaging. In this work, we successfully demonstrated that the imaging resolution was greatly improved, 1.5 times with 300-nm-thick SiO2 film which is an ENZ material at 8 μm. Through FDTD (Finite Difference Time Domain) simulations, we verified that the large amount of diffracted light could really be converted to quasi zero-th order far field.
2. Sample preparation and characterization
The ENZ material used in this experiment was a conventional SiO2 thin film, which was grown on a Si substrate by thermal oxidation. To find the ENZ position, we obtained the transmission spectrum of a 300-nm-thick SiO2 film on Si (normalized by bare Si) in the mid-IR regime (700 to 6000 cm−1 or 1.6–14 μm), as shown in Fig. 2(a). Strong SiO2 optical phonon absorption was clearly seen around 9.2 μm. This characteristic transmission can be described by the frequency-dependent complex dielectric constant as depicted in Fig. 2(b) [12]. The real part of dielectric constant εr crosses zero at 8.0 μm, which is slightly shorter wavelength of transmission dip. This behavior is due to an anomalous dispersion originating from the strong light-phonon interaction. Note that the corresponding imaginary part of ε is not zero and has the small value of ~0.3 at this wavelength. This observation indicates that the SiO2 thin layer can be regarded as a low lossy ENZ material at 8.0 μm.
Fig. 2 (a) Transmission spectrum of 300-nm-thick-SiO2 film on Si substrate. (b) Real part (blue line) and imaginary part (red line) of the dielectric constants of SiO2 film.
3. Result and discussion
To verify the ENZ-assisted resolution enhancement, various sizes of bar patterns, inspired by the standard USAF (United States Air Force) 1951 resolution target, were imaged with and without ENZ materials using FT-IR equipment [13]. The USAF resolution target is a universal standard for testing the resolution of imaging systems. Each element consists of three bars separated by spaces equal to the bar width. The width-to-length ratio is 1:5. Group and element numbers are assigned depending on the size of the target. The resolution of the imaging system is expressed by the group and element numbers of the smallest discernible pattern. Since our target wavelength was 8 μm (ENZ position of the SiO2 thin film), we chose the 1, 2, 3, and 4 elements in Group 6, whose widths are 7.8 μm (6-1), 7.0 μm (6-2), 6.2 μm (6-3), and 5.5 μm (6-4), respectively. The bar patterns consists of a thin Au (65 nm) film with Cr (5 nm) adhesion layer, which was fabricated on SiO2/Si or Si substrate using conventional electron-beam lithography. Figure 3(a) shows the optical microscope image of the sample. Our FT-IR imaging unit was Hyperion 3000 made by Bruker Corporation, USA. The transmission images of the samples were recorded on the focal plane array detector with a pixel resolution of 2.7 μm and a covering area of 170 μm by 170 μm. Because each pixel was able to measure total transmission/absorbance spectra, it was possible to obtain an FT-IR image at a certain wavelength. Comparing Figs. 3(b) and (c) indicates that imaging resolution is significantly improved when the SiO2 is inserted between the sample and the substrate. This result clearly implies that our meta-lens can enhance the NA of the system.
Fig. 3 (a) Microscope image of group number 6 of standard USAF 1951 resolution target. The bar widths are 7.8 μm (6-1), 7.0 μm (6-2), 6.2 μm (6-3), and 5.5 μm (6-4), respectively. Imaging of the resolution target fabricated on (b) Si and (c) SiO2/Si substrates at 8 μm.
In order to understand the resolution enhancement mechanism, two-dimensional finite-difference time-domain (FDTD) simulation (FDTD Solutions, Lumerical solutions, Inc., Canada) were performed. The simulation structures were effectively the same as the experimental structures, and all simulation parameters—film thicknesses and bar width—were set equal to those of the real samples except the thickness of the Si substrate, which was reduced to one-tenth of the sample thickness to save calculation time. Figure 4 (a) and 4(b) represent the near field power flow around the sample (a single bar in 6-4 resolution target) without and with the ENZ layer, respectively. The magnitudes of the Poynting vector were normalized so that the vectors contain only directional information. Below the bar, the power flow spreads out and forms complicated diffraction patterns without the ENZ layer (Fig. 4(a)), which results in low NA. Surprisingly, in the presence of an ENZ layer, the vectors are significantly redirected to form a quasi-plane wave immediately after the SiO2/Si interface owing to strong directional emission (Fig. 4(b)). Specifically, with the index of SiO2 (n = 0.43 + 0.43i) and Si (n = 3.4) at 8 μm, the allowed emission angle is restricted to less than 7.3° according to the Snell’s law. Such redirected light having negligibly small kx component can pass through the Si-air interface without total internal reflection resulting in high NA together with resolution enhancement, as discussed earlier in the Introduction part. Directive emission has been reported in several works. However, the radiation source in these works was positioned approximately one wavelength (~λ) from the interface [6, 8, 10]. To the best of our knowledge, our result is the first demonstration that the diffracted near field produced by subwavelength objects can contribute to directive emission, propagating into the far field almost uniformly due to ENZ materials. Remarkably, such directive emission is enabled even with ENZ thickness much less than the wavelength (~λ /20). Since our structure is in the deep subwavelength regime, the Au-SiO2 layer could be considered as the effective uniaxial media supporting hyperbolic dispersion with εx<0 and εz ~0. Such hyperlens can also deliver the high-k components into far-field and enhance the resolution without ENZ effect [14, 15]. For that reason, we should check whether our results are originated from hyperbolic dispersion effect or not. To eliminate the hyperbolic dispersion, we performed the FDTD simulation with GaAs (n = 3) dielectric instead of Au film. As shown in Fig. 6. (see Appendix), the strong directive emission is still observed at the SiO2 and Si interface. Therefore, we would like to insist that the main physical mechanism of the resolution enhancement in our experiments is ENZ effect rather than the hyperbolic dispersion.
Fig. 4 Plot of Poynting vector (a) without and (b) with the SiO2 layer. Near field distributions around the bar edge (square dotted region in (a) and (b)) (c) without and (d) with the SiO2 layer.
Fig. 5 Absorbance imaging of metal half plane (a) without and (b) with the SiO2 layer. (c) Edge-response along the white dotted lines in part (a). (d) Edge-response along the white dotted lines in part (b) at 4-μm (red line), 8-μm (green line), and 11-μm wavelength (blue line). (e) Normalized resolution (resolution/wavelength) for Si (black line) and SiO2/Si (red line) substrates.
Fig. 6 Poynting vector plot at 8-μm-wavelength passing through a GaAs strip placed on ENZ-meta lens shows strong directive emission.
The calculated near field distributions around the bar edge (dotted square regions in Figs. 4(a) and 4(b)) are displayed in Figs. 4(c) and 4(d). In both cases, the electric field enhancements at the sharp metal edges were observed, while the enhancement factors and field distributions were quite different. Without the ENZ materials, the field enhancement arises mainly from the localized surface plasmon effect [16]. Namely, the incident light coherently pushes local charges on the metal surface toward the metal edges in the region of the λ-zone and these accumulated charges make field enhancement [17]. Therefore, both x and z components of enhanced electric field (Ex and Ez in Fig. 4(c)) are strongly localized at the metal edges. On the other hand, with the ENZ materials, the enhanced Ez is not localized at the metal edges but is widely distributed in the SiO2 layer (Fig. 4(d)). In addition, the enhancement factors are greater with ENZ materials. This could be explained by the strong coupling between the surface plasmons and ENZ materials. Recently, it has been reported that the electric field can be enhanced inside a thin ENZ slab when a plane wave is propagating along the slab length direction [18, 19]. The key physical mechanism is nearly normal energy flow at the ENZ outer surface, which leads to accumulation of the electromagnetic energy and then enhancement of the electric field inside the slab. Note that such enhancement is limited to the electric field along the length direction (Ex), not along the vertical direction (Ez). It seems that the vertical electric field could also be enhanced inside the slab when considering the continuity of the displacement current at the ENZ outer surface: n1Ez1 = n2Ez2. However, as pointed out in the reference 17, the vertical electric field tends to zero as approaches to the ENZ surface causing negligible Ez field inside the ENZ slab. Nevertheless, in our case, with the help of the localized surface plasmon, the Ez field is not small, but rather large near the ENZ surface. This enhanced vertical electric field experiences further enhancement inside the ENZ due to field continuity condition. As a result, the Ez enhancement is much larger with ENZ materials than that without ENZ. Apart from the Ez field, no significant enhancement of Ex is observed inside the SiO2 layer (Fig. 4(d)) because the distribution and enhancement of the Ex field are mainly determined by the impedance mismatch and continuity of the electric field E1x = E2x between the media rather than the ENZ effect. Meanwhile, since our ENZ material and substrate are non-magnetic, the magnetic field does not show any enhancement in both cases. Finally, the power distributions are depending on the Ez field distributions, which show special characteristics of ENZ phenomena (Figs. 4(c) and 4(d)).
To quantitatively compare the resolution, we directly measured the optical resolution by evaluating the edge-response function of a metal half-plane fabricated on Si or SiO2/Si (Figs. 5(a) and 5(b)). The edge-response function describes how an optical system responds to a sharp edge and can be measured by imaging a half-metal plane [20]. The background pictures of Figs. 5(a) and 5(b) are optical microscope images of the sample, while the front color maps are the IR absorbance images of the central portion of the samples at the ENZ position, 8-μm-wavelength, without (Fig. 5(a)) and with (Fig. 5(b)) the ENZ layer. Clearly, the imaging resolution was greatly improved with the SiO2 film. The resolution of the system can be estimated from the distance required for the edge response to rise from 10% to 90% of the maximum [21]. The edge-responses were plotted in terms of transmission at various wavelengths in Figs. 5(c) and 5(d). As expected, the resolution quality decreased as the wavelength increased, and the resolution of ~18 μm at the 8-μm-wavelength was observed with the Si substrate (Fig. 5(c)). On the other hand, with the SiO2 layer, the resolution at the ENZ position was ~12 μm, which was comparable to that at the 4-μm-wavelength and much smaller than that at the 11-μm-wavelength showing ENZ-assisted resolution enhancement (Fig. 5(d)). Figure 5(e) represents normalized resolution (resolution divided by wavelength) plot as a function of wavelength. For Si substrate, the normalized resolutions remained almost constant about 2.2 (black square). On the contrary, in the case of ENZ, strong local minimum was observed at 8 μm with the extracted normalized resolution of 1.5 (red circle). Except for around ENZ position, the normalized resolutions were usually larger than that for Si substrate due to reflection losses at the SiO2 and Si interface and low refractive index of SiO2 compared to Si. Remember that the resolution of our imaging system was 2.7 μm, which was not so much smaller than the ENZ wavelength, 8 μm. Thus, we would like to insist that the resolution at ENZ position might be better than the value proposed in these experiments.
5. Conclusion
In conclusion, we have demonstrated that a thin layer of SiO2 can induce directive emission of highly diffracted near fields into quasi-zeroth order far fields at its ENZ position. This phenomenon is confirmed by resolution enhancement experiments. We believe that the ENZ materials can contribute to obtain high-resolution wide-field imaging of bio tissues, complex chemical mixtures, or various polymers in the mid-IR range. It should be pointed out that the resolution can be enhanced by simply inserting an ENZ layer between the sample and substrate without changing any optics or modifying apparatus. Thus, our method can be directly applicable to conventional microscopy equipment or tools recently developed for high resolution imaging in the mid-IR regime [22, 23]. In addition, we expect that our proposed strategy could be extended to the visible frequency or microwave region with specially designed metamaterials [24–27].
Appendix: FDTD simulation for a dielectric strip
Acknowledgments
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. NRF-2014R1A2A2A01006378).
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