We examined the optical properties such as propagation modes, focal length, side lobes, etc. of metallic subwavelength annular apertures (SAA) and used finite-difference time-domain (FDTD) simulation to compare our experimental findings. Using two different metals, silver and tungsten, we examined the different optical transmission properties of the two metallic SAA structures. The far-field propagation of the silver SAA structure was found to be a type of quasi-Bessel beam when compared with a quasi-Bessel beam generated by a perfect axicon. The propagation characteristics of these two beams were found to match qualitatively. The far-field transmitted light generated by the silver SAA structure was found to possess a 390nm sub-micron focal spot with a 24μm depth of focus, which was much smaller than the focal spot generated by a perfect axicon. We also found that a silver SAA structure can generate a sub-micron quasi-Bessel beam that has a much lower far-field side-lobe when compared to that of non-diffraction beams generated by a tungsten SAA structure.
© 2009 Optical Society of America
The reduction of the focusing spot in an optical system is generally accompanied by a short depth of focus (DOF). Attempting to focus the light beam into a sub-micron or sub-wavelength focal spot while maintaining a long depth of focus, has been a major objective of optical system designers for many years. An ideal non-diffraction beam, termed a Bessel beam, represents one such attempt which was first proposed by Durnin et al. in 1987 . Durnin demonstrated that a non-diffraction beam can be generated by an annular slit with a lens . Several other methods were also proposed to generate quasi-Bessel beams by using axicon  and diffractive elements . However, the smallest spot size achieved remained in the range of several microns. Current research activities on the interaction of light and metallic sub-wavelength structures have increased dramatically, especially on systems associated with the study of surface plasmon polaritons (SPP). A recent works has proposed a new design method which combines plasmonics and diffractive elements. Ebbesen et al. reported the presence of extraordinary optical transmission (EOT) in 1998  and the existence of a directional beaming phenomenon in 2002 . It is known that surface plasmons (SP) can be diffracted by a periodic structure on a metal film to a far-field directional [6–10], and a sub-wavelength aperture can focus the SPP to the center of the exiting metal surface [11–13]. The extraordinary optical transmission (EOT) generated by the cylindrical surface plasmon (CSP) of a metallic sub-wavelength annular aperture (SAA) has also been studied in detail. The role of the CSP has been studied theoretically by examining the transmission red shift of a same SAA structure  and has been experimentally analyzed by Salvi et al. . Haftel et al. further analyzed the CSP dispersion relationship [16,17] of which he attributed the transmission peaks to the resonance of CSP in the channels.
Although much research has been done on near-field and transmission properties, the far-field properties of metallic SAA structures have not been studied widely. In 2008, the sub-micron non-diffraction beam generated by a silver SAA structure was demonstrated . Research showed that a metallic SAA structure offers a new way to generate a sub-micron non-diffraction beam without use of an additional lens, the reason of which is still not clearly understood. In this paper, the optical properties of silver and tungsten SAA structures, which can generate a non-diffraction beam with a sub-micron spot, was performed experimentally and verified using finite-difference time-domain (FDTD) simulation. The transmission intensity distributions in both SAA structures were recorded with a CCD camera using the same exposure time. The transmission mode in the metallic SAA structure was further analyzed using an analyzer, i.e. a different light beam intensity pattern was measured by placing the analyzer at several distinct azimuth angles. We found that the mode in the silver SAA structure was different from the tungsten SAA structure such that the far-field pattern was very different when compared to that of tungsten SAA structure. The far-field pattern of the silver SAA structure was focused into a sub-micron quasi-Bessel beam without possessing the large side lobes like that of tungsten SAA structure. The silver SAA generated quasi-Bessel beam was also compared to the ideal quasi-Bessel Beam. Our new findings can be adopted for such potential applications as plasmonic devices, optical manipulation instruments  and microlithography .
2. Experimental set-up
Figure 1 shows the schematic diagram of our experimental set-up and a SEM image of the SAA structure. The geometric parameter r 1 and r 2 are the inner and outer diameters of the SAA structures, respectively, and θ is the azimuth angle as shown in Fig. 1. Metal was used in regions 1 and 3 while region 2 was composed of a dielectric material. In our set-up, we chose to work with silver and tungsten as the metal materials, and chose air as the adjacent dielectric material. The SAA was prepared by depositing a 250nm thick silver film onto a glass substrate. A 12μm inner diameter ring with a 150nm width slit was then milled by a focused ion beam system (FEI Nova 200). For comparison, another sample was made on tungsten film and prepared under the same set of parameters. A linearly polarized He-Cd laser of 442nm wavelength was used to incident normally onto the backside of the samples. In our experimental set-up, we rotated the analyzer (Olympus U-AN360-3 with polymer polarizing film and extinction ratio of 500 to 1000:1) and placed it between the objective and the CCD camera (Olympus DP70). We then set it to four distinct azimuth angles (0°, 45°, 90°, and 135°) and recorded the corresponding intensities in Fig. 2.
3. Transmission properties of the SAA structures
The first column of Figs. 2(a) and 2(b) shows the images recorded by the CCD camera and which reveal the different intensity distributions. Under the same incident conditions and CCD camera exposure time, the obtained transmission efficiency of the silver SAA structure (Fig. 2(a)) was larger than that of the tungsten SAA structure (Fig. 2(b)). Results show that it was coincident with the EOT phenomenon in the silver SAA structure. For the tungsten SAA structure, the intensity distribution always showed a dual arc shape along the incident polarization, which is similar to a dipole parallel to the incident polarization. The intensity distribution at the annular slit was proportional to cos2 θ, where θ was defined in Fig. 1. However, the intensity distribution in the silver SAA structure was independent of the incident polarization. In order to analyze the distribution in the channel of the silver SAA structure, an analyzer was utilized to examine the performance of our sample. We then further distinguished the output polarization state on the silver SAA structure using linearly polarized laser illumination.
Utilizing the configuration of Fig. 1(a), we obtained the second to fifth columns of Figs. 2(a) and 2(b), and which showed the intensity distribution at the output surface of the silver and tungsten SAA (the colored arrows in each diagram show the direction of the analyzer respectively). The last column of Figs. 2(a) and 2(b) shows the total vector plot in the channel which was derived experimentally from the second to fifth columns of Figs. 2(a) and 2(b). For example, the polarization axis of the analyzer in the second column in Fig. 2 was parallel to the incident polarization. After passing through the analyzer, the direction of the resulting electric field in the recorded intensity distribution was also parallel to the polarization axis. By rotating the polarization axis at several distinct angles, we acquired a series of intensity distributions (the second to fifth columns in Fig. 2) which was related to the direction of the electric fields. Finally, the total vector plot in the channel was obtained. In the case of silver SAA structure, the excited cylindrical surface plasmons (CSP) created a strong field at the silver-air interface. In contrast to tungsten, an electric field can exist inside the silver.
4. Far-field properties of SAA generated non-diffraction beams
Taking our near-field and polarization state investigation as the starting point, we studied the far-field phenomena of silver and tungsten SAA structures. Figure 3 shows our far-field experimental results. The experimental configuration can also be seen in Fig. 1 (without the analyzer). First, a linearly polarized 442nm incident wavelength blue laser was impinged onto the SAA structure. Then, the images of the transmitted light of the tungsten SAA structure and silver SAA structure were taken by moving the focal plane of the objective at different heights above the sample. The output light from the silver and tungsten SAA structures were focused at 12μm above the surface, where a narrow spot size was maintained at 20μm away from the focus.
To verify our experimental data, three dimensional finite-difference time-domain (FDTD) simulations were performed for the silver SAA structure. The incident wave was 442nm and the linear polarization was in the x-direction. The geometric parameters in Fig. 1 were set to r 1 = 6μm, r 2 = 6.15μm, and L = 250nm, respectively. The complex dielectric constant of the silver and tungsten at 442nm wavelength were ε 1 = ε 3 = -5.735+j0.7536 and ε 1 = ε 3 = 4.69+j8.217, respectively . To avoid the fictitious reflection from the perfectly matched layer (PML) boundaries, the total simulation dimension was set at 20μm×20μm×25μm such that the distance between the outer diameter of the SAA structures and PML boundaries was larger than the surface plasmon polariton (SPP) propagation length at the air-silver interface (2.3μm) for the given dielectric constant. The maximum mesh size in the three-dimensional simulation region was set to 10nm.
Figures 4(a) and 5(a) show the far-field pattern along the z-direction of the silver SAA and tungsten SAA structures, respectively. Figures 4(b) and 5(b) show the simulated results at the x-y cross-section where z=12μm of the silver and tungsten SAA. In Fig. 4(a), at the air-silver interface, there exists a strong SPP field. However, at the air-tungsten interface, there was no SPP field from a distance of zero to 400nm in Fig. 5(a). The insets in Figs. 4(b) and 5(b) show the corresponding experimentally obtained far-field patterns. Figures 4(b) and 5(b) show good agreement between the experimental and simulation results. Comparing the results, we found that the silver SAA structure appears to focus the incident light beam into a sub-micron spot without diffracting divergently for several tens of microns, i.e., the beam does not diverge.
In the sixth column of Fig. 2, we obtained the transmission properties of the silver and tungsten SAA structures. Figure 6 shows the intensity distribution in the metallic SAA structures. We used the maximum values to normalize each intensity distribution. The field distribution in the tungsten SAA structure was linearly polarized with a cos2 θ intensity modulation, where θ was defined in Fig. 1. Unlike the tungsten SAA structure, in the silver SAA structure, the field distribution was axially symmetry with an almost uniform intensity distribution (i.e., it was independent of θ).
The non-diffraction beams, also termed Bessel beams, were firstly proposed by Durnin et al. in 1987 . For a theoretical Bessel beam, the intensity distributions at any z positions are related to the zeroth order Bessel function of the first kind. Although the generated beams of silver and tungsten SAA structures have a non-diffraction spot along the z-axis, the intensity distribution of the tungsten SAA structure was accompanied by two large side lobes. Figure 7 shows the normalized intensity distribution of the silver SAA structure versus the x-position at z=20μm and z=25μm. Using curve fitting, the three distributions can be fitted to J 0 2(4.02x). The experimental results shown in Fig. 7 were obtained by utilizing a CCD camera (Olympus DP70). In Fig. 7, the three distributions generated by the silver SAA structure possessed larger side lobes when compared to the Bessel function. However, the peak positions fit almost perfectly together with respect to the Bessel function. The side lobes at z=25μm was smaller than when z=20μm. This is due to the intensity modulation along the z-propagation of the non-ideal quasi-Bessel beam . The inset in Fig. 7 demonstrates the intensity decay along the z-axis. In a Bessel beam generation, the propagating wave must be axially symmetric with respect to the propagation axis and its wave vector must lie on a cone. The quasi-Bessel beam was generated by the interference of refracting beams. In the case of silver, the intensity distribution in the SAA structure was almost uniform, and the diffracting wave provided the condition such that the wave vectors could be found on a cone. Therefore, the generated non-diffraction beam by the silver SAA structure can be considered a type of Bessel beam or a quasi-Bessel beam.
Since the generated non-diffraction beam by the silver SAA structure was a quasi-Bessel beam, we can further compare it with an ideal quasi-Bessel beam. The quasi-Bessel beam can be produced by an annular slit with a lens , an axicon , and diffractive elements . We chose an ideal axicon (i.e., an axicon with sharp tip) to generate an ideal quasi-Bessel beam . The schematic diagram can be seen in Fig. 8 where the ideal axicon was illuminated by a 442nm wavelength plane wave where its beam waist 2w 0 was equal to 12μm. The material of the axicon was BK7 (refractive index of 1.527 at 442nm) and its apex angle τ = 170°. After the axicon, a cone region where the cone angle was equal to 2α 0 was formed by the refracted wave. The cone angle obtained by Snell’s law was as follows:
where n is the refractive index of axicon, n 0 the refractive index of the ambient medium, and τ the apex angle of the axicon. In this particular case, the ambient medium was air (n 0 = 1).
The quasi-Bessel beam was produced in the range from z=0 to z max, where z max=w 0cosα0/sinα0. In this case, the cone angle α 0 was equal to 2.65° and z max=129.5μm. The intensity distribution was thus obtained  by
where P is the incident power and k the wave vector. The intensity distribution along the z-axis of the ideal and silver SAA generated quasi-Bessel beam can be seen in Fig. 9, where shows the DOF of the ideal quasi-Bessel beam at 103μm which was 4 times larger than the silver SAA structure generated Bessel beam. The maximum intensity of the ideal quasi-Bessel beam in Fig. 9 occurred when z=65μm. The relationship between the corresponding intensity distribution versus the x-position at z=65μm can be seen in Fig. 10 (dash dotted green line). Figure 10 also shows the relationship between the intensity distribution of the silver and tungsten SAA structures to the x-position when z =12μm. We found that the far-field pattern of the tungsten SAA structure was accompanied by two large side lobes along the incident polarization. The two large side lobes of the tungsten SAA structure in Fig. 5(b) are the interference of the diffracting waves from the near-field distribution (Fig. 2(b)). On the other hand, Fig. 4(b) shows that the silver SAA structure focuses the incident light beam into a sub-micron spot due to the existence of uniform intensity at the annular slit. The minimum focal spot was 390nm and the energy decay rate along the z-axis was very slow when compared to that of Gaussian beams. From Figs. 4(a) and 9, we can estimate that the depth of focus (DOF) of silver SAA structure generated non-diffraction beams will be close to 24μm (46λ). Therefore, this narrow focal spot and long depth of focus adheres well with the characteristics of a quasi-Bessel beam. The full-width and half-maximum (FWHM) of the ideal quasi-Bessel beam was 3.4μm, which was about 8 times larger than the silver SAA structure generated quasi-Bessel beam. In comparison with the ideal quasi-Bessel beam, the silver SAA structure generated quasi-Bessel beam had a smaller focus spot and a shorter DOF.
We demonstrated experimentally the optical properties such as propagation modes, focal depth, focal spot, etc. of subwavelength annular aperture (SAA) structures. We verified the data using three-dimensional FDTD simulations. We used an analyzer to experimentally determine the intensity distributions and polarization states. The simulation results agreed well with the experimental results. From our analysis, we concluded that a silver SAA structure possesses a more uniform intensity distribution than a tungsten SAA structure. From our far-field measurements, the silver SAA structure appears to focus the sub-micron spot and in turn creates a quasi-Bessel beam without the existence of two significant side lobes. The silver SAA structure generated quasi-Bessel beam was focused to a 390nm sub-micron spot with a 24μm depth of focus. In comparison with an ideal quasi-Bessel beam, the silver SAA structure generated quasi-Bessel had a smaller focus spot and a shorter DOF. Potential applications for near-field and far-field optical fields include plasmonic devices, microlithography and optical tweezers.
This work was financially supported by the Materials and Chemical Research Laboratory of the Industrial Technology Research Institute (ITRI) and by Taiwan’s National Science Council Grant No. NSC 97-2221-E-002-159-MY3.
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