1. Introduction

A Fabry-Pérot (FP) cavity usually exhibits strong resonance with selectivity both on the frequency and the incident angle. However, recent works [1–3] have shown that it is possible to design a FP cavity that is not sensitive to the incident angle at a particular frequency. One approach [1] considers the dispersion of the gap-plasmon [4] or the cavity mode of a dielectric layer sandwiched between two thick metal layers. If the dielectric layer thickness is tuned to create a flat gap-plasmon dispersion, the external light can be resonantly coupled into the cavity at all angles and an omnidirectional emitter has been experimentally demonstrated using this principle [5]. Another approach [2,3] employs an array of metal wires in order to obtain a flat dispersion surface for the eigenmodes in the crystal. It works in the canalization regime and the FP resonance is independent of incident angle with the same propagation constant. This approach has been demonstrated in the microwave regime. In this work, we experimentally demonstrate an all-angle FP cavity lens working in the optical regime that has achieved imaging with high transmittance and high image fidelity. Our system differs from the gap plasmon configuration [1] which has a thick metallic substrate while we have propagating media on both sides of thin metal layers to form an unbounded structure. Our system also employs an entirely different physical mechanism from metal wire array structures which rely on the effective medium approach and thus require deep subwavelength structures while our configuration is a simple layered structure. Our approach can also be useful to obtain super-resolution beyond the diffraction limit [6–9] where high transmittance is usually difficult to achieve due to the impedance mismatch between the lens and the background medium.

2. Theory

The resonant cavity lens in this work consists of a low dielectric sandwiched between two metal slabs of finite thicknesses. As a starting point, we choose to consider the light focusing property of a single slab of metal within a dielectric background first. It has already been known for some time that a single metal slab exhibits a negative Goos-Hänchen (GH) shift [10] for the reflected beam in the TM polarization since the power flow within the metal travels in the opposite direction of the transverse momentum on the metal surface. In fact, the same negative lateral shift also applies to the transmitted beam for the same reason. This phenomenon has the same physical effect as a negative refraction although the transmittance is very small due to the exponential decay within the metal [11]. If we regard the metal slab with the dielectric of certain thickness together as a combined metal-dielectric (MD) layer, the transmitted lateral shift of the beam can be tuned to zero again. In general, the thickness of this dielectric layer required for compensation depends on the angle of incidence. However, after performing a phase analysis detailed in Ref. 12, it can be shown that for particular values of layer thicknesses and material parameters, the combined MD layer has nearly a constant π/2 transmission phase shift independent of angle. The optimal configuration is achieved if the permittivity of the metal is chosen to be:

While a single MD layer structure, with parameters prescribed in Eq. (1) and Eq. (2), already works as a lens, the intensity at the image point is low. Now, if we stack two consecutive combined MD layers together to form a resonant cavity lens, the zero lateral shift can still be maintained and at the same time, the intensity at the image point can be boosted by resonance tunneling. Suppose we denote $t_m/r_m$ as the complex transmission/reflection coefficient of a single metal slab and $\exp \left(i{\varphi }_d\right)$ as the transfer amplitude across the homogeneous region of dielectrics. Then, the total transmission phase shift across the resonant cavity lens is still a constant (independent of angle) given by

To demonstrate the principle of omnidirectional FP resonance, we have chosen Ag as the metal and SiO₂ as the dielectric for the resonant cavity lens so that the two permittivities are nearly matched according to Eq. (1) at a wavelength around 362.2 nm. The permittivity of Ag is taken from the tabulated data in Ref. 13. The thickness of each Ag-SiO₂ layer is 45.8 nm/61.7 nm and the imaginary part of the permittivity of Ag (material loss) is neglected at this moment. Figure 1 shows the transmittance and the transmission phase shift calculated by standard transfer matrix technique. The omnidirectional FP resonance occurs at the same resonating frequency for all incident angles. The transmittance stays as unity with π-phase shift for all angles.

 

Fig. 1 Calculated transmittance and transmission phase shift spectra of the resonant cavity lens for different angles of incidence. The theoretical design neglects material absorption of Ag and each Ag / SiO₂ layers has a thickness of 45.8 nm/61.7 nm.

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Next, we proceed to discuss the imaging property of the resonant cavity lens. Figure 2 shows the transfer amplitude as a function of the transverse wavenumber at the resonating frequency in blue color calculated for the previous design. Since it has unit transmittance from 0 to k₀ (the wavenumber of vacuum) with constant π-phase shift, it effectively behaves as a perfect lens [14] in the propagating wave regime ($k_x<k_0=\omega /c$) apart from a different sign for the constant phase shift. In the regime beyond one k₀ which contributes to subwavelength imaging, the transfer amplitude drops sharply beyond 3 k₀. In the same figure, we have also plotted in dotted line (red color) the transfer amplitude if the imaginary part of the permittivity of Ag (for material absorption) is also included in the calculation. It is useful to compare the results to a multilayer silver lens (three periods of Ag and SiO₂ of equal thickness in this case) of the same total thickness of the resonant cavity lens [15,16]. We see that the transmittance of the resonant cavity lens at the far field stays at a much higher level for the propagating waves, with a compromise of smaller transfer amplitude in the deep subwavelength regime. The multilayer Ag lens (layered “poor man’s superlens”) can achieve a better subwavelength resolution while our resonant design has superior image fidelity by giving a higher far-field transmittance for all incidence angles but with less subwavelength resolution. We have also calculated the image intensity from a line source placed in front of the resonant cavity lens as shown in the inset of Fig. 2. The resolution is around 0.34λ and is calculated with the absorption of Ag. It agrees reasonably well with the transfer amplitude shown in the same figure.

 

Fig. 2 Transfer amplitude as a function of the transverse wavenumber k_x (normalized to k₀, the wavenumber in vacuum) for the design in Fig. 1 without/with absorption in blue/red color. The corresponding case for a multilayer silver lens with the same total thickness is also shown in green color for comparison. Inset: image of a line source with a line width 0.34λ.

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3. Sample fabrication and experiment methods

3.1 Angle resolved transmission

In the experiment, the resonant lens consists of a three layer Ag-SiO₂-Ag FP cavity. Using the theoretical design that ignored material loss as a starting point, we have taken into account of the imaginary part of the permittivity of Ag and performed numerical optimizations on the thicknesses of the metal and dielectric layer to obtain maximum overlap of all the FP resonances for different angles together at the same frequency with high transmittance. Each Ag-SiO₂ layer has a thickness of 30 nm/68 nm in the fabricated device.

To characterize the omnidirectional resonance phenomenon in the resonant cavity lens, the angular-dependence transmittance of propagating waves was measured. The Ag-SiO₂-Ag resonant structure was deposited on a 500 µm thick quartz substrate, the polarized Xenon light source was incident onto this layered lens structure from the silver layer to the quartz substrate with incident angles that varies from 0 to 60 degree. By scanning the wavelength and the incident angles of TM and TE polarizated transmitted light, the transmission property of the resonant cavity lens could be obtained.

3.2 Near field imaging

In addition, we also performed the near-field imaging experiments using the resonant cavity lens illustrated in Fig. 3 . The FP resonant cavity lens was fabricated using the standard photolithography method, which is also used in reported superlens experiments [6,7]. In the photolithography experiment, a 50 nm thick chromium film was deposited on the quartz substrate using radio frequency (RF) sputtering method. A 1D grating mask with 190 nm line width (Line/Space: 190 nm/190 nm) was then fabricated on the chromium film by the focused ion beam (FIB, 201XP, FEI) method. To planarize the rough surface on the grating pattern, the PMMA layer, which is transparent to the UV light, was spun on the grating mask and dry etched to obtain a 10 nm thick spacer. Then, the resonant cavity lens Ag-SiO₂-Ag (30 nm/68 nm/30 nm) was deposited on the quartz substrate using E-Beam evaporator (Edward Auto306) in high vacuum environment. With optimum deposition rate and vacuum pressure, the film could be coated with low surface roughness. The recording medium (photoresist) was fabricated a smooth silicon substrate, as the transmitted UV light can be reflected by the silicon substrate and pass through the exposed the photoresist for the second time to cause blurred image. The anti-reflection layer (200 nm thick BALLI-II) was spun on the silicon substrate first to reduce the amount of reflection from silicon substrate. After that the 350 nm thick positive photoresist Hir1075 (AZ Clariant) was spun on the anti-reflection layer.

 

Fig. 3 Schematic diagram (not drawn to scale) of the resonant cavity lens, standard photolithography method is used to record the image collected by the FP resonant cavity lens.

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The recording medium with silicon substrate was placed on the exposure stage of the optical aligner, then the superlens device fabricated on the quartz substrate was placed in intimate contact with the photoresist layer (Fig. 3) by vacuum suction. When exposed to the filtered UV light (365 nm) from the contact optical aligner (AB-M), the propagating and evanescent waves from the grating mask were collected by the Ag-SiO₂-Ag FP resonant cavity lens. After exposure, the recording medium was carefully separated from the superlens device, the image of the grating transmitted across the lens structure was measured on the developed photoresist with atomic force microscope (DI3100, Veeco). For comparison, the resonant cavity lens was replaced by the 128 nm thick PMMA layer in a control device, in which the image of the grating was recorded on the photoresist without any resonant mechanism.

4. Experiment results

The angle resolved transmission results of propagating waves are shown in Fig. 4 . For TM waves (Fig. 4(a)), the transmission efficiency of the 365 nm wavelength decreases slowly when the incident angles changes from 0 to 60 degree. All the FP resonances are almost independent of the angle of incidence, verifying that the numerical design is successful. On the other hand, the transmittance at 365 nm for the TE waves (Fig. 4(b)) drops sharply with an increasing angle of incidence. Here, we emphasize that our approach is different from the one using a high dielectric as the propagating medium within the cavity to make the resonance less sensitive to the incident angle [17]. The resonant cavity lens reported here actually compensates the propagation phase shift by the reflection phase shift without the need of a high dielectric material, relaxing the stringent material requirement in obtaining a superlens with high transmittance.

 

Fig. 4 (a) The experimental angle resolved transmission of TM modes in the resonant cavity lens; (b) is for TE modes.

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The experimental result of near-field imaging of the resonant cavity lens is shown in Fig. 5(a) . The grating pattern with a line width (190 nm Line/Space) is clearly resolved on developed photoresist with an optimal exposure time of 60 s. Figure 5(d) is the cross-section view of the transferred image of the grating source. The modulation depth of grating is up to 136 nm and the period of ~380.95 nm was measured from its Fourier transform spectrum (Fig. 5(g)). In comparison, the near-field imaging through 3 periods of Ag-SiO₂ (20 nm/22.7 nm) multilayer superlens was also performed. The resonant cavity lens is replaced with the Ag-SiO₂ multilayer structure (layered “poor man’s superlens” configuration). Under optimized exposure time (140 s), the grating pattern (190 nm L/S) is transferred onto photoresist through the multilayer superlens. From the imaging results shown in Fig. 5(b) and Fig. 5(e), it is found that the image of the grating is blurred and the modulation depth is shallower and more irregular. Around the peak signal of grating information (indicated with red arrow) in the Fourier-transformed spectrum (Fig. 5(h)), there is more noise than that in Fig. 5(g). This is mainly because that the multilayer superlens has lower transmission efficiency of propagating waves although it allows stronger resonant enhancement in the regime of evanescent waves (Fig. 2). Therefore, the resonant cavity lens attains a higher image fidelity comparing to the multilayer superlens and also to the single-layer superlens as well.

 

Fig. 5 (a) Atomic force microscope image is recorded by the FP resonant cavity lens from a source grating of 380nm in period; (b) Results from Ag-SiO2 multilayer superlens; (c) In the control experiment, the FP resonant cavity lens is replaced with the 128 nm thick PMMA. (d), (e) and (f) are the corresponding results of cross section analysis. (g), (h) and (i) are the Fourier-transformed spectrum of (d), (e) and (f), red arrows indicate the periods of ~380 nm.

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In a control experiment, the resonant cavity lens was replaced with a 128 nm thick PMMA layer, no focusing mechanism exists. The image of the grating pattern was also recorded on photoresist. Figure 5© shows that the grating cannot be resolved in this PMMA based device. In this case, the diffraction within the medium is not compensated by any focusing mechanisms or amplifications of evanescent waves. From the cross-section analysis of the result (Fig. 5(f)), it shows that the grating pattern cannot be differentiated from the noisy signal, Fourier-transformed spectrum (Fig. 5(i)) shows that the signal of grating is overwhelmed by the noisy background.

A system loss in the current lens configuration exists, such as the resolution of the optical aligner and the surface roughness of the cavity lens structures. However, the grating patterns with period of 190 nm L/S could be resolved with the FP resonant cavity lens and Ag-SiO₂ multilayer structure. In the resonant cavity lens, the image with 190 nm line resolution has much higher imaging fidelity than that in the multilayer structure. This proves that the FP cavity lens has some advantages over multilayer superlens in near-field imaging by efficiently collecting the propagating waves with omnidirectional resonance. In the control experiment, the PMMA device just shows the diffraction phenomenon in the imaging system while the resonant cavity lens (Fig. 5(a)) and the “poor man’s superlens” (Fig. 5(b)) clearly exhibits the functionality of a flat lens.

5. Conclusions

In summary, omnidirectional resonance imaging was experimentally demonstrated in a FP resonant cavity lens. With this kind of FP resonant cavity lens, the image of a grating with sub-wavelength line width was experimentally realized in the near-field. The image fidelity is higher than that the layered “poor man’s superlens” with same total metal thickness. With a high transmittance and high image fidelity, the demonstrated FP resonant cavity lens may have useful applications in bio-imaging, nano-fabrication, nano-lithography and others.