We numerically investigate the optical field enhancement by a metal/dielectric multilayered zone plate. The optical field enhancement at the focal point of a zone plate originates not only from surface plasmon polaritons (SPPs)-assisted diffraction process along the propagation direction of incident light, but also from multiple scattering and coupling of surface plasmons (SPs) along the metal/dielectric multilayer films. By comparing multilayered zone plates to a conventional monolayered zone plate, we present the effects associated with the number of building blocks and different dielectric materials in the building block on the efficiency of the transmission.
© 2009 Optical Society of America
Fresnel zone plate (FZP) is composed of a series of concentric zone rings, alternatively being opaque or transparent zone, with gradually decreasing period. It has been used for focusing and imaging of x rays and extreme-ultraviolet (EUV) radiation, which enables many applications such as nanolithography, spectroscopy, near-field or far-field optical microscopy, and optical antenna. Two major issues associated with FZP are its resolution which is limited to roughly the width of the smallest zone, namely λ/2, and the transmission efficiency which is often low (approximately from a few percent to 40%). Several approaches in the near-field region have been proposed to overcome the limit of resolution.[1, 2] However, the resulted diffraction efficiency of these devices was relatively low (typically less than a few percent), not comparable to far-field devices.
The development of electromagnetic simulation tools, nano-fabrication techniques, and physical analysis tools has enabled manipulation of ‘light’ on nano scale. Since Thomas Ebbessen and co-workers reported the extraordinary optical transmission (EOT) through 2D arrays of subwavelength holes perforated in metallic films in 1998, many renewed attentions have been made to figure out the physical origin of this phenomenon theoretically and experimentally. However, there is still controversy on the enhanced transmission phenomenon. At present, it is widely accepted that the EOT can be explained by diffraction assisted by the enhanced fields associated with surface plasmons (SPs). Moreover, there have been many efforts to further enhance the transmission geometrically. Tang and his co-workers demonstrated that the enhancement of optical transmission in the Ag/SiO2 multilayer with a periodic array of subwavelength holes originates not only from SPs but also from the coupling of SPs with nanostructures which is multiple scatterings and the coupling of electromagnetic waves on the interface of the multilayer.
2. Modeling and simulation methodology
Figure 1 illustrates the schematic diagrams of the proposed structure, where a zone plate, center being opaque, has sandwich structure with building block (N) of silver and silicon dioxide. The dimensions of the zone plate are obtained from the classical equation used in designing conventional FZP. By comparing the transmission efficiency between a multilayered zone plate (Multi-ZP) and a conventional monolayered zone plate (Mono-ZP), the relative enhancement in the field intensity can be evaluated. The thickness of the silver film in the Mono-ZP is comparable to total thickness of Multi-ZP. Each building block of Multi-ZP has identical focal length (f = 1 μm), which makes it easy to fabricate, the thickness of metal layer being tm = 30 nm, and the thickness of dielectric layer td = 30 nm. In addition, we mainly use λ = 405 nm, εAg = -4.01+0.70i, and εsiO2 = 2.16, respectively,  and the light used to excite the surface plasmon polaritons (SPPs) in the zone plate is a circularly polarized wave normally incident from the bottom of the quartz wafer. The focusing properties of the proposed zone plate are simulated and analyzed by TEMPEST, a Maxwell equation solver based on 3D finite-difference time-domain (FDTD) method.
3. Numerical experiments and discussions
Near-field focusing or beaming properties of FZP and plasmonic lens (PL) have been investigated in the visible regime.[7–11] The results have showed the subwavelength focusing or beaming characteristics in the near field are attributed to the interference of diffracted evanescent waves from a large numerical aperture. However, those structures still suffer from lower transmission efficiency (η) even though optical field enhancement by EOT phenomenon is introduced. In this article, by modulating the effective refractive index (neff) of the dielectric layer in building blocks, in which SPPs propagate longitudinally, we demonstrate a metal/dielectric multilayered zone plate with high transmission efficiency.
Figure 2(a) and (b) show the distributions of the transmitted field intensity on the xz-plane for Mono-ZP and Multi-ZP, respectively, with N = 5. In the Mono-ZP, the energy flow in the vicinity of the silver/air interface in the zone rings is remarkably strong, and its intensity attenuates with distance from the interface to both the silver and the air. These are the essential features of the excited surface plasmon on the metal surface. In Fig. 2(c), it is clear that at the focal point, the field enhancement of Multi-ZP is estimated to be about 9.0 times that of Mono-ZP. It is well known that a light wave tends to localize itself mostly in a medium with higher refractive index than its adjacent ones and thereby the light prefers to propagate with low phase velocity. Thus the incident light can propagate along the dielectric layer included in building blocks, generating SPPs in the interface. We can count the dielectric layer in the building blocks as a metal-insulator-metal (MIM) waveguide. Therefore, considering two closely placed parallel metallic plates filled with higher refractive index dielectric layer, the complex propagation constant (β = βr + βii) with slit width can be calculated as[14, 15]
where k0 is the wave vector in free space, εm and εd are the relative dielectric permittivity of the metal and the dielectric, respectively, and w is the width of two metallic plates. The effective refractive index (neff = n′eff + n″eff i) of the dielectric layer is given by neff = β/k0. The inset of Fig. 2(c) plots the effective refractive index as a function of slit width where metal and dielectric films are Ag and SiO2 films, respectively. In obtained effective refractive index, the real part of the effective refractive index increases rapidly with slit width decreasing. The coupling of SPs in the Ag/SiO2 multilayer can be excited even in small slit width due to the tendency of the light to be localized in the higher effective refractive index.
Simulations are also performed to evaluate the effect of the number of building blocks as shown in Fig. 3. It is noted that transmission efficiency is calculated by the maximum intensity at the focal point divided by the integral of incident field intensity given from area within the outmost radius of zone plate. The transmission efficiency is found to be maximized when the number of building block approaches six, but the focal spot size is found to be increased, as shown in Fig. 3(a). Since each building block is designed to have an identical focal length, they contribute differently to the focal spot in the z direction. As a result, the resultant focal spot will be smeared because the focal planes of each building block do not coincide. In the case of Mono-ZP, on the other hand, it is observed that after the metal layer thickness is approximately one order thicker than skin-depth (corresponding to tAg = 120 nm), the transmission efficiency decreases with the thickness increasing. Note that the metal layer thickness in a Mono-ZP corresponds to the total building block in a Multi-ZP. Moreover, its transmission efficiency is much smaller than that of Multi-ZP. As illustrated in Fig. 3(b), when the focal planes of each building block coincide, the transmission efficiency increases and approaches the maximum value (i.e., approximately 40%) with the number of building blocks increasing. Simultaneously, the spot size decreases and approaches the minimum value (i.e., FWHM = 195 nm).
When the incident light impinges on the surface of metal, SPPs can be excited and propagate along the surface. When the SPPs arrive at a slit in the metal, most of them is scattered by slit edge, leaks into the slit and radiates new bulk waves and surface waves. These new bulk waves and surface waves excite new SPPs on the slit walls. The new SPPs propagate along the metal-dielectric building block. It can support another path for incident light to transmit the device. In other words, the SPPs convert the incident light to surface wave. And the surface wave is then injected to the slit and then travel to the exit surface. The field intensity in the slit is higher than at other positions on the metal by orders of magnitude. Although the metal films are absorptive to the 405 nm wavelength, the metal/dielectric multilayer does not absorb the incident light. Most of the light energy is converted to SPP, traveling along the surface to the slit with minimal decay. The zones in the multilayer then provide channels for SPP to exit the ZP. So most of the incident light energy can transmit through the Multi-ZP, even though the multilayer is absorptive. As a result, the transmission of a Multi-ZP can approach the theoretical limit of about 40.5% set by a perfect phase FZP, in which all zones are transparent and have alternating 0/π phase shift.
Figure 4 shows the normalized intensity of different dielectric materials with N = 5. Maximum normalized intensity is achieved at Al2O3 (ε = 3.20) Multi-ZP. The inset of Fig. 4 depicts real and imaginary part of the effective refractive index and the propagation length (Lspp) of SPPs at w = 30 nm as a function of dielectric permittivity (ε d). The complex propagation constant and thereby effective refractive index of SPPs increases until ε d approaches |Re(εm)|. The frequency at which εd = |Re(εm)| is called the resonant surface plasmon frequency. In our simulations, given by |Re(εm)| = 4.01, HfO2 (ε = 3.92) layer is predicted to achieve the closest resonance condition. However, much higher transmittances are achieved at SiO2 and Al2O3 layers than HfO2. Therefore, we also need to take the propagation length of SPPs into account. In general, propagation length of SPPs is provided by the imaginary part of the complex propagation constant, the distance where the intensity falls to 1/e of its initial value is given by Lspp =(2Im(β))-1. Notice that there is a trade-off between the real part and imaginary part of effective refractive index. Although HfO2 layer approaches the closest resonance condition, simultaneously the imaginary part of the complex propagation constant increases rapidly and thereby the propagation length of SPPs decreases. As a result, it is evident that the imaginary part of the complex propagation constant and thereby propagation length of SPPs have an important role to the propagation for the coupled electromagnetic wave on the interface of the multilayer. For ZrO2 layer (εd > |Re(εm)|), both upper and lower interfaces cannot support a SPP mode, which is under cut-off condition.  Hence, its field enhancement is similar to that of Mono-ZP.
In conclusion, a method to obtain high optical field enhancement in the zone plate was proposed. By using metal/dielectric multilayered zone plate, optical field enhancement originates not only from SPPs-assisted diffraction along the propagation direction of incident light, but also from the coupling and multiple scattering of SPs in the multilayer. The imaginary part of the effective refractive index, governing the decay of SP in the multilayer, also has an important role to the propagation of the coupled electromagnetic wave. The proposed Multi-ZP can achieve transmission efficiency close to the theoretical limit of 40.5% set by an ideal alternating phase FZP. Meanwhile it can achieve a FWHM noticeably less than λ/2, the theoretical limit of a conventional far-field FZP. The achieved optical field enhancement, as high as 9 times that of conventional FZP, is expected to offer significant potentials in many applications such as FZP microscopy, optical antennas, optical sensors, and nano-optics devices.
The author was supported from Human Resource Cultivation Program of Samsung Electronics from South Korea.
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