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Article Tunable Plasmofluidic Lens for Subwavelength Imaging Opto-Electronic Article Engineering 2017, Vol 44, Issue 3 Ag d Dielectric liquid Tunable plasmofluidic lens for w Wavefront Wavefront subwavelength imaging Image Source Beibei Zeng* x=0 Center for Integrated Nanotechnologies, Los Alamos National Laboratory, x a b Los Alamos, New Mexico 87545, USA z Abstract: A tunable plasmofluidic lens consisting of nanoslit arrays on a metal film is proposed for subwavelength imaging in far field at different wavelengths. The nanoslit arrays with constant depths but varying widths could gen- erate desired optical phase retardations based on the propagation property of the surface plasmon polaritons (SPPs) through the metal-dielectric-metal (MDM) nanoslit waveguide. We demonstrate the tunability of the plasmofluidic lens for subwavelength imaging by changing the surrounding dielectric fluid. This work provides a novel approach for developing integrative tunable plasmofluidic lens for a variety of lab-on-chip applications. Keywords: surface plasmon polaritons; subwavelength imaging; optofluidics; wavefront modulation DOI: 10.3969/j.issn.1003-501X.2017.03.007 Citation: Opto-Elec Eng, 2017, 44(3): 326−330 phase distribution of the optical field. Each nanoslit in 1 Introduction the metallic slab is designed to transmit light with specif- ic phase retardation, therefore arbitrary phase modula- Recently, the optical diffraction limit has been overcome tion on the wavefront could be realized. However, due to by the perfect lens proposed by Pendry using a slab of the dependence of permittivity of metallic materials on [1] negative refractive index (NRI) media . However, the frequencies, applications would be limited because the difficulty of finding a homogenous NRI media restrains plasmonic lens can only operate at a specific frequency the practical applications of the perfect lens. Considering when the geometries of the nanoslits are fixed. the electrostatic approximation of the perfect lens, the Fluids have unique properties that cannot be found in super-lens could also be used to realize sub-diffraction- solids and these properties can be used to design novel limited imaging, only requiring negative permittivity that devices, such as oil-immersion microscopes [11], liquid is available in natural metals in particular frequency re- mirrors for telescopes [12], liquid-crystal displays [13] and gimes. Therefore, impressive works concerning tunable liquid gradient refractive index lenses [14]. Inte- superlenses have been achieved theoretically and experi- gration and reconfiguration are the two main advantages [2-4] mentally . However, the shortcoming of the superlens of optofluidics. The second advantage of optofluidics is that the object and image should be confined in near means that one can easily change the optical properties of field, usually tens of nanometers away from the superlens the devices by controlling the fluids [15]. Therefore, in this [1, 5] . Therefore, an optical far-field superlens (FSL) has paper, we propose a tunable plasmofluidic lens for been designed for imaging beyond the diffraction limit in subwavelength imaging at different incident wavelengths [6] far field . by varying the surrounding dielectric fluid. On the other hand, as indicated in Ref. [7], a planar metallic slab with arrayed nanoslits of varying widths 2 Working principle could be demonstrated theoretically [8] and experimen- tally [9] to focus light in far field. A planar plasmonic lens Fig. 1 is the schematic drawing of the optical imaging has been proposed to realize subwavelength imaging for process for the tunable plasmonic lens. The plasmonic arbitrary object and image distances [10]. Based on the lens is a silver slab of thickness d with nanoslits located optimum design of nanoslit waveguides in the metallic symmetrically with respect to x=0 plane, represented by slab, the imaging process is achieved by manipulating the the dashed line in Fig. 1. The width of each nanoslit is w. The object (a point light source) is located on the left side of the lens at a distance of a, and the image on the right Received 12 November 2016; accepted 26 December 2016 side at a distance of b. The plasmonic lens is immersed * E-mail: [email protected] inside the dielectric liquid with permittivity d, and each 326 DOI: 10.3969/j.issn.1003-501X.2017.03.007 OEE | Advances nanoslit could be also filled with the dielectric liquid. All (x) 2nπ (0) the components are treated as semi-infinite in y direction. 2πnd 2 2 2 2 The Drude model 2 /[( iV )] is used to a b a x b x , (1) m p c describe the permittivity of silver at different frequencies, 16 where n is an arbitrary integer number, nd is the refrac- where =3.2938, plasma frequency p=1.355210 14 [16] tive index of the surrounding dielectric material, rep- rad/s and collision frequency Vc=1.994410 rad/s . resents the incident wavelength, and x is the position of All the materials are assumed to be nonmagnetic so that each nanoslit. For example, when we choose =730 nm, the magnetic permeability is equal to 1 and only the [22] a=1 m, b=1 m and nd=1.33 (water, H2O) , the re- permittivity has been taken into account. quired phase change at different x positions calculated by Eq. (1) is shown in Fig. 2(a). Ag d Dielectric liquid On the other hand, assuming that the width of each nanoslit w is much smaller than the incident wavelength, it is reasonable for just considering the fundamental w Wavefront Wavefront mode in the nanoslit [5]. The complex propagation con- stant in the slit can be determined by the equation [8, 23]: Image w 2 k 2 2 k 2 Source tanh 0 d d 0 m , (2) 2 2 2 m k0 d x=0 where k0 is the wave vector of free space light, d and m represent the permittivities of the dielectric inside the nanoslit and metal, respectively. It is clearly seen from x a b this equation that the propagation constant changes as the slit width w varies, when k0, d and m are fixed. The z real and imaginary parts of respectively determine the phase velocity and propagation loss of SPPs in the Fig. 1 Schematic of the optical imaging process by the nanoslit. The phase retardation of light transmitting tunable plasmofluidic lens. through the nanoslit can be expressed as: Re(d) , (3) When transverse magnetic (TM) polarized waves im- where d is the thickness of the plasmonic slab, and pinge on the entrance surface of the silver slab, surface originates from the multiple reflections between the en- plasmon polaritons (SPPs) are excited [17]. SPPs propagate trance and exit surfaces of the slab. Both physical analysis through the nanoslit region with specific waveguide and numerical simulations show that the phase retarda- modes until they reach the exit surface where they return tion is dominantly determined by the real part of [8]. into the light mode [17- 18]. It is the diffraction and inter- Therefore, can be approximated as Re(d) , and it ference of the surface plasmon waves that contribute to could be obtained from Eqs. (2) and (3) that the phase the transition from the evanescent waves to the propa- retardation can be tuned by changing the slit width when gating waves in far field [19], which is the coupling mecha- other parameters are fixed [8-10]. According to Eqs. (2) and nism for far field super-resolution imaging [6]. Therefore, 2 (3), if =730 nm, d=1.769( d nd , H2O) and d=200 nm, it is theoretically possible for the plasmonic lens to the width of each nanoslit at position x could be designed achieve subwavelength imaging in far field [10]. For an to meet the requirement of phase distribution depicted in electromagnetic wave incident on such a plasmonic lens, Fig. 2(a), as shown in Fig. 2(b). the phase change of the wave is sensitive to the length [7], However, as the incident wavelength changes while width [8, 20], and material inside the slit as it passes other parameters are fixed, the required phase change [21] through each nanoslit . In the previous works, the in- calculated by Eq. (1) and the permittivity of metal m fluence of the length and width of the nanoslits on the would vary, resulting in the change of propagation con- phase change have been theoretically investigated and stant in each slit according to Eq. (2). Therefore, the widely used for different purposes. In contrast, in this point-to-point subwavelength imaging could not be paper, a tunable plasmonic lens is proposed for achieved again. There are two ways to solve this problem. subwavelength imaging at different wavelengths by vary- Firstly, we could change the positions and widths of the ing the surrounding dielectric material while holding nanoslits to fulfill the requirement of phase change as the nanoslits’ lengths, widths and positions constant. incident wavelength varies. Obviously, this is unpractical According to the equal optical length principle, the because we should use different plasmonic lenses to required phase distribution of light for the point-to-point achieve subwavelength imaging at different wavelengths. imaging of an object localized on the axis x=0 can be ob- Secondly, it is possible for subwavelength imaging at dif- tained by: ferent wavelengths by simply varying the surrounding 327 OEE | Advances 2017, Vol 44, Issue 3 dielectric material. The only requirement for the second Therefore, both the required phase change and phase method is that we should choose different dielectric flu- retardation are invariable at different incident wave- ids ( nd ) to keep the effective wavelength eff / nd lengths, resulting in that the imaging process will be invariable as the incident wave length changes. slightly influenced by the wavelength variability. On the one hand, it is clearly seen in Eq. (1) that if the For example, we choose other two different incident effective wavelength / nd is constant while the inci- wavelengths at 810 nm and 920 nm, with corresponding dent wavelength changes, the required phase change at permittivities of the dielectric fluids at 2.200 (carbon tet- position x for the point-to-point imaging will be invaria- rachloride, CCl4) and 2.846 (phosphorus tribromide, PBr3) ble, as shown in Fig.
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