pubs.acs.org/NanoLett
Plasmonic Lenses Formed by Two-Dimensional Nanometric Cross-Shaped Aperture Arrays for Fresnel-Region Focusing Ling Lin, Xiao M. Goh, Liam P. McGuinness, and Ann Roberts* School of Physics, The University of Melbourne, Vic 3010, Australia ABSTRACT We present the experimental demonstration of what are to our knowledge the first two-dimensional planar plasmonic lenses formed by an array of spatially varying cross-shaped apertures in a metallic film for Fresnel-region focusing. The design utilizes localized surface plasmon resonances occurring inside the apertures, accompanied by an aperture geometry dependent phase shift, to achieve the desired spatial phase modulation in the transmitted field. The performance of lenses with different design configurations was evaluated using a confocal scanning optical microscope, and the effects of diffraction on the optical response of these microscale devices are discussed. KEYWORDS Surface plasmon, planar lenses, far-field focusing
T
ailoring surface plasmon (SP) resonances using patterned metallic nanostructures for optical manipulation has attracted much attention in recent years. As a result of their ability to confine and channel light on a subwavelength scale, a particularly promising application area of SPs lies in developing ultracompact photonic devices.1 Accordingly, a range of nanoscale optical components for controlling SP fields, such as mirrors, waveguides, and lenses, have been demonstrated.2,3 On the other hand, utilizing SP resonances for beam manipulation away from the device surface in the Fresnel region or optical far field have also been suggested4–7 and very recently, miniature plasmonic wave plate8 and conventional plasmonic cylindrical lens (one-dimensional focusing)9 have also been demonstrated. These compact plasmonic devices function in an analogous way to their counterpart elements in conventional refractive optics but with much smaller footprints. Hence, they can be easily integrated into many existing systems for a variety of applications without significant design or functionality impact. In this Letter, we show experimental demonstration of two-dimensional (2-D) focusing with planar plasmonic lenses formed by an array of subwavelength cross-shaped apertures in a thin metal film (Figure 1), where the apertures have dimensions that vary spatially across the device. The focal region lies in the Fresnel region of the device as a whole but in the far field of the individual apertures. The lenses utilize localized surface plasmon (LSP) resonances occurring within the apertures that are accompanied by aperture-geometry dependent phase shifts in the transmitted field to achieve the desired spatial phase modulation for beam manipulation.
To our knowledge, this is the first experimental demonstration of planar plasmonic lenses for 2-D Fresnel-region focusing of this kind. As the basic building block of these lenses is a symmetric cross-shaped aperture formed by simple straight-line elements, the device possesses several advantages in terms of polarization insensitivity, substrate dispensability, and fabrication simplicity. The latter is a particularly attractive feature, as current fabrication capability still imposes a major challenge in the realization of miniaturized devices.7 Therefore, the ability to achieve 2-D focusing (thus 3-D control of light propagation) by these miniature planar lenses presents an important step forward in the practical implementation of plasmonic technology. The important role of LSP resonances in enhanced light transmission through subwavelength apertures in thin metal films has been addressed by several groups10–12 and it has been demonstrated that more complex apertures, for example, coaxial and cross-shaped apertures, generally offer more coupling efficiency of incident light than simple square or rectangular apertures.13,14 Our recent investigation of the optical response of cross-shaped apertures, whether isolated or in periodic arrays, revealed that the characteristics of LSP
FIGURE 1. Schematic of the planar plasmonic lenses formed by variant cross-shaped aperture arrays of periodicity p in thin metal film. The symmetric aperture has a fixed arm-width, w, and a spatially modulated arm length, l.
* To whom correspondence should be addressed,
[email protected]. Received for review: 03/18/2010 Published on Web: 04/19/2010 © 2010 American Chemical Society
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DOI: 10.1021/nl1009712 | Nano Lett. 2010, 10, 1936–1940
FIGURE 3. The transmission efficiency (red solid line) and phase (blue dotted line) of the transmitted field as function of arm length at 850 nm wavelength.
variation, i.e., the phase change also exhibits a rapid modulation in the vicinity where high transmittance appears. A clear view of the relationship between the amplitude and phase of the transmitted waves as function of the arm lengths of the crosses at a specific wavelength (850 nm, the designed operating wavelength of the lenses) is shown in Figure 3. Near the resonant dimension of the cross-shaped apertures, the variation in the amplitude (red solid line) and phase (blue dotted line) of the transmitted field show similar trends as that observed in an electrical RLC resonant circuit, with a total phase modulation of about π. Note that the total available phase modulation can be extended further by changing other parameters of the structure, such as arm width of the aperture and the thickness of the metal films. To construct a far-field lens using aperture arrays in a thin metal film, the phase of light at each lattice position (x, y) of the output interface can be determined from the relation
FIGURE 2. (a) Transmittance and (b) phase variation of light passing through an array of cross-shaped apertures in a silver film as function of wavelength and arm length of the crosses.
resonances occurring within these structures can be tuned by simply altering the arm length of the crosses.15 Extending this study further, we examined the phase change of the transmitted light near the vicinity of LSP resonances using the finite element method (FEM) implemented in COMSOL Multiphysics with the Radio Frequency module.16 Panels a and b of Figure 2, respectively, show 2-D plots of transmission efficiency and phase variation of light passing through a periodic array of cross-shaped apertures as function of wavelength and arm length of the crosses. In these simulations we assume the apertures are in 140 nm thick silver (Ag) films on glass substrate. The crosses are symmetric in the x and y directions with arm lengths, l, that varied between 100 and 300 nm (with a step size of 10 nm), and the arm widths, w, were fixed at 40 nm. A plane wave was incident from the substrate side. The transmission was normalized to that in the absence of the metal film and the phase in the absence of the array was subtracted from the phase of the transmitted field a distance of 1.5 µm below the film. Periodic boundary conditions were used as we intended to use square lattice arrays to construct the planar lenses. The lattice constant p was fixed to 400 nm to separate the spectral locations of surface plasmon polaritons (SPPs) arising from the periodic arrays from those of the LSPs occurring within the nanometric apertures15 and to minimize the perturbation of LSPs by SPPs in the spectral region of interest (700-1000 nm). The optical properties of bulk Ag were taken from ref 17, and the permittivity of the BK7 glass substrate was taken to be 2.31. Figure 2a reveals that the occurrence of high transmittance of these apertures is a dual function of aperture arm length and the wavelength of the incident light, which agrees with the nature of LSP resonances. Furthermore, the phase change of the transmitted waves follows a similar fashion as the transmittance © 2010 American Chemical Society
φxy ) 2π(fd - √x2 + y2 + fd2)/λ + 2nπ + φ00
(1)
where fd is the designed focal length, λ is the wavelength of the incident light, n is an arbitrary integer, and φ00 is the phase at the center of the lenses. Once φxy is determined, the geometry of the aperture at the corresponding lattice position can be retrieved from the results shown in Figure 2b. Since the maximum phase modulation that can be provided by cross-shaped apertures with geometry described above is about π, we impose a second condition when determining the lattice distribution of the apertures in our design, that is
|φxy - φ00 | e π
(2)
Equation 2, together with eq 1, implies that the value of fd will affect the profile (more specifically, number of the apertures) of the resulting 2-D planar lens. For example, we designed two lenses that both operate at 850 nm wavelength using arrays with p ) 400 nm. For fd ) 15 µm and fd ) 25 µm, the longest diagonals of two near-circular lens structures are 7.2 and 8.3 µm, respectively. 1937
DOI: 10.1021/nl1009712 | Nano Lett. 2010, 10, 1936-–1940
FIGURE 5. Measured axial intensity profile (on the y-z plane) of light passing through: (a) a reference structure consisting of apertures with fixed arm lengths (250 nm); (b) a lens with fd ) 15 µm; (c) a lens with fd ) 25 µm. Three structures have identical lattice-site distributions, as shown in panels c and d of Figure 4. (d-h) 2-D intensity profile (on the x-y plane) of (c) at z ) 0 (exit interface of the lens), 7, 14, 21, and 28 µm, respectively.
FIGURE 4. (a) The calculated phase and (b) arm length along one of the symmetric axes (x axis) of the 2-D aperture array lenses operating at 850 nm wavelength: red line, fd ) 15 µm; blue line, fd ) 25 µm. (c) and (d) SEM images of the fabricated devices with fd ) 15 µm and fd ) 25 µm, respectively.
milling technique (FEI Nova Dualbeam FIB and SEM). The performance of the lenses was evaluated using a home-built confocal scanning optical microscope. The sample was illuminated with an 850 nm wavelength unpolarized laser beam from the substrate side. The collimated laser beam has a diameter of approximate 5 mm. The sample was mounted on a closed loop XYZ piezo nanopositioning stage such that the planar lens was situated in the x-y plane with its optical axis orientated along the z direction. The transmitted beam through the lens was collected by a 100× (Nikon, NA 0.95) objective and then focused down to a 62.5 µm multimode fiber that serves as a pinhole in the system. The 3-D spatial intensity profile of the transmitted beam was obtained by taking a sequence of 2-D intensity profiles (on the x-y plane) at different z positions along the propagation direction. The scan in the x-y plane was 15 × 15 µm2 with 100 nm/pixel resolution, and the step size along z direction was 200 nm. The signal-to-noise ratio of the system at the exit interface of the structure was 100:1. Figure 5 shows the axial intensity profile of light passing through three fabricated structures: (a) through a reference structure (no focusing effects) formed by apertures of fixed arm lengths (250 nm); (b) through a structure with a design focal length of fd ) 15 µm; (c) through a structure with fd ) 25 µm, whose 2-D intensity profiles at z ) 0 (exit interface of the lens), 7, 14, 21, and 28 µm are shown in panels d-h, respectively. The lattice distributions of the apertures for the three structures are the same. As displayed in panels b and c of Figure 5, the behaviors of the two lenses with different design focal lengths are rather different. For fd ) 15 µm lens, the transmitted intensity has its maximum at the exit interface of the structures and the intensity of the transmitted beam decreases steadily along the z direction; near the
It must be pointed out that, as is the case with any lens, scattering from the boundary of these compact optical elements introduces additional diffraction effects into the performance of the devices, leading to discrepancies between performance and design specifications based on simple geometric optics. For instance, work presented by Verslegers et al. showed that there existed a considerable mismatch between the theoretically predicted and the measured focal length of lenses based on a nanoslit array. More specifically, they showed that the actual focal length was sensitive to the size of the lenses, even for devices producing the same wavefront curvature at the output interface.9 To facilitate comparison between devices, we truncated the array size of the fd ) 25 µm lens to have the same value as that of fd ) 15 µm lens. Panels a and b of Figure 4, respectively, show the calculated phase and the required arm length along one of the symmetric axes (x axis) of the designed fd ) 15 µm lens (red line) and fd ) 25 µm lens (blue line) whose array-size was truncated to the same as that of fd ) 15 µm lens. Scanning electron microscopy (SEM) images of the fabricated lenses are shown in panels c and d of Figure 4. Fixing the size of the lenses of different focal lengths allows us to obtain a better understanding of behavior of the devices as it regulates the influence of diffraction on the focusing effects of the lenses. Nevertheless, developing methods to ease the diffraction effects existing in these compact optical elements is an ongoing project. The fabrication of the 2-D planar plasmonic lenses involved two main steps. First, a 140 nm thick Ag film was deposited onto a 170 µm thick BK7 glass substrate using electron beam evaporation. The films were then perforated with the desired aperture arrays by a focused ion beam © 2010 American Chemical Society
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maximum intensity along the z axis appears at a distance about 22 µm away from the existing surface of the fd ) 25 µm lens (blue solid line), which matches well with the design value. A plot of the cross section of the transmitted beam at this position (insert of Figure 6) reveals that the beam spot size d at focus is ∼2.3 µm, which is close to the theoretical minimum diffraction limited spot size estimated by the relation d ) 1.22λf/D, where D is the diameter of the lens. It is important to keep in mind that the size of the fd ) 25 µm lens studied here had been specifically truncated to match the size of the fd ) 15 µm lens, which in fact weakened the focusing power of the device. The untruncated planar lens that fully utilized the total π phase shift available by the variant cross-shaped apertures will have a higher power and produce a tighter focal spot, although it will come with the price of altering the focal length of the device. We also noticed that there were some intensity “hot spots” at the output interface of the lens (Figure 5d)san appearance that was consistently observed in different lenses, which mostly occurred near the ends of the diagonal edges of the structures. The cause of this is not yet clear, and we are currently investigating the efficient method to perform 3-D electromagnetic simulations of the optical response of the structures. In conclusion, we have demonstrated 3-D beam manipulation in the optical Fresnel-region using arrays of spatially varying cross-shaped apertures perforated in thin metal films. FEM simulations reveal that near the vicinity of LSP resonances at a specific wavelength, the amplitude and phase of the transmitted field can be tailored by simply varying the arm length of the aperture. This feature allows us to construct compact wavefront control devices using spatially modulated aperture arrays. Although this work has concentrated on the construction of planar plasmonic lenses, the potential of these aperture arrays in developing miniaturized optical devices is not limited to focusing elements. Furthermore, we highlighted the significant influence of diffraction on the performance of the micrometer-scale lenses. This is an important issue that has not been addressed to any great extent by previous research into plasmonic lenses of this kind. The development of methods to accommodate effects due to the finite size of the lens and amplitude transmission variations in compact planar lenses is a project currently under investigation in our group. Further miniaturization of these devices and extending their performance to shorter wavelengths is also a topic of ongoing interest.
FIGURE 6. Intensity distribution along the z axis: blue solid line, output of the fd ) 25 µm lens; red dotted line, output of the reference structure. (insert) the cross section of the beam transmitted through fd ) 25 µm lens at z ) 22 µm.
vicinity of fd the beam intensity is fairly low. In contrast, for the lens with fd ) 25 µm lens the axial intensity maximum of the transmitted beam occurs at around z ) 22 µm, which is close to its designed focal position. The difference in the optical responses of the designed lenses can be understood by considering the diffraction pattern of an aperture of radius a. Along the axis of the beam path, the intensity distribution of the diffracted light at a distance z from the aperture can be estimated using the equation18
I(z) ) 4I0 sin2(πa2 /2λz)
(3)
where I0 is the intensity maximum and z the axial distance from the lens. Equation 3 gives an intensity maximum at z ) 15 µm for 850 nm incident light passing through an aperture of diameter 7.2 µm (the longest diagonal of the fabricated octagonal-shaped structures). Clearly, the position of the axial intensity maximum of the reference structure agrees well with the prediction as shown in Figure 6 (red dotted line). Considering light passing through a micrometerscale lens, without diffraction the output beam would have a spherically converging wavefront as shown in Figure 4a and the transmitted beam will be focused to the designed focal position. However, the existence of the diffraction at the boundary of the devices implies that Huygens’ spherical wavelets centered on these regions carry a divergent wavefront. Consequently, the intensity profile of light transmitted through the fabricated lens is a result of interference between focusing and diffraction effects along the beam path. When the locations of intensity maxima arising from the focusing and the diffraction coincide, the two effects cancel producing a low intensity distribution in the designed focal position of the lens, as illustrated in Figure 5b. Shifting the focal position to the location away from the axial intensity maximum produced by diffraction alone reduces the influence of diffraction on the focusing effect of the device, allowing the behavior of the device to align more closely with the theoretical prediction. As illustrated in Figure 6, the © 2010 American Chemical Society
Acknowledgment. This research was supported under Australian Research Council’s Discovery Projects funding scheme (Project Number DP0878268). The authors thank Dr. David Simpson and Associate Professor Robert Scholten for their help in this experiment. 1939
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