A subwavelength annular aperture (SAA) made on metallic film and deposited on a glass substrate was fabricated by electron-beam lithography (EBL) and which was followed by a metal lift-off process to generate a long propagation range Bessel beam. We propose tuning the focal length and depth of focus (DOF) by changing the diameter of the SAA. We used finite-difference time domain (FDTD) simulations to verify our experimental data. We found that the position of the Bessel Beam focus spot (i.e. focal length) will be farther away from the SAA plane as the diameter of the SAA increases. In addition, the depth of focus (DOF) which is the length of the Bessel beam non-diffracting area, also increases as the diameter of the SAA expands.
©2009 Optical Society of America
Nowadays many semiconductor technologies require elements to be miniaturized in order to integrate as many circuits as possible onto a single chip. Based on Rayleigh’s criteria, we know that the resolution (e.g. focal spot) and DOF (depth of focus) depend on the incident wavelength and numerical aperture (NA) of the imaging system. Two methods can be implemented to decrease the focal spot: by reducing the wavelength of the light source and by increasing the numerical aperture (NA) of the lens. A larger NA will not only reduce the focal spot, but it can also reduce the depth of focus (DOF) simultaneously. With a small DOF, the exposure environment and platform control have stricter demands. In 1987, Durnin et al. [1, 2] showed that Bessel beams can be used to solve free wave equations. They stated that a non-diffracting beam can propagate into infinity without any change in the transverse intensity plane, which satisfies the Helmholtz equation. This means that the narrow beam radius does not suffer from the characteristics of diffractive spreading. The first experimental investigation to establish the diffraction-free beams (also called Bessel beams) was proposed by Durnin et al. They generated the diffraction-free beams by using an annular slit located in the focal plane of a lens and which used a collimated light source to illuminate the slit. Ideally, each point along the slit acts as a point source of light transformed by the lens and which emits a wave plane. A propagating Bessel beam can then be expressed by the superposition of these wave fields with the wave vectors lying on the surface of a cone. In practice, non-diffracting beams have also been generated by using various methodologies such as by axicon [3, 4], Fabry-Perot etalon [5, 6] and holographic elements [7, 8]. It is worth noting that in all the methods, the diffraction pattern can be described by the zeroth-order Bessel function of the first kind (J 0). A recent study [9–11] demonstrated that a subwavelength annular aperture (SAA) structure in metallic films (or plasmonic lenses) excite and focus the electromagnetic energy of surface plasmon polaritons (SPP). It was found that the silver SAA structure can retain the transmission light from diffracting up to tens of micrometers in a far-field region . Although there are many methods to generate non-diffraction beams, previous studies have concentrated little attention on varying the focal length and the depth of focus (DOF) to be within a finite distance.
In this paper, we demonstrate a new technique which uses electron beam lithography (EBL) and which is followed by a metal lift-off process to fabricate a large size SAA structure on metallic film onto a glass substrate. This enlarged structure provides us with the capability to enhance the depth of focus (DOF) of the above-mentioned subwavelength non-diffraction beam. The optical performance, such as the DOF and focal spot of the SAA, was simulated using finite-difference time domain (FDTD) calculations. Results show that by using a SAA structure, it is possible to adjust the depth of focus (DOF) and focal spot size by changing the diameter of the SAA. In addition, we explored the detailed mechanism of Bessel beam formation by analyzing the ratio of the transverse to the longitudinal transmitted intensity of different diameters of the SAA structures. By employing non-diffracting properties (e.g. a large DOF) of Bessel beams, it is possible to adopt this technique to applications such as particle micro-manipulation [13–16], optical microlithography , nanolithography  and laser micro-fabrication processes [19, 20].
2. Experimental set-up
Figure 1 shows the experimental set-up of our Bessel beam generator. We used a linearly polarized He-Cd laser (442nm) as the light source. An attenuator was used to control the intensity of the incident light and a half wave plate was adopted to control the polarization direction. The light source was guided into an inverted microscope (Olympus IX71) by using the reflection mirrors and was normally incident to the back side of the SAA structure.
In order to generate a long propagating range Bessel beam, we created a SAA structure by adopting e-beam lithography (EBL) and incorporating a metal lift-off procedure following the fabrication process. A 100nm thick indium-tin-oxide (ITO) film was first deposited onto a glass wafer to improve the conductivity of the transparent substrate to facilitate the EBL process. In order to strengthen the adhesion between the resist film and substrate, the adhesion enhancer material known as Hexamethyldisilazane (HMDS) was pre-coated below the resist film. HMDS modified the surface of the substrate to offer a better adhesion force, which prevents the patterns from collapsing. A commercially available negative tone resist (ma-N2403, Micro Resist Technology GmbH) was spun coated at 3000 rpm for 50 seconds, followed by soft baking on a 90 deg C hot plate for 90 seconds which resulted in a 300nm thickness resist layer. The electron lithography equipment was based on an ELIONIX ELS-7500EX EBL system with a ZrO/W thermal field emitter (TFE). An accelerating voltage of 50 keV with 100 pA beam current was set to direct the pattern written on the resist layer. A test pattern consisting of an array of blocks with a linear energy dosage increment from 1μC/cm2 to 20μC/cm2 was exposed. The best parameter for writing the aperture in this experiment was found to be at 15μC/cm2. After exposure, the sample was developed with a developer (ma-D532, MRT GmbH) for 60 seconds and rinsed immediately in de-ionized (DI) water for 30 seconds. Using an e-beam evaporator, a 5nm adhesion Cr layer and a 200 nm Ag layer were deposited on top of the sample. Finally, a silver lift-off process was achieved in an ultrasonic bath with a stripper (mr-Rem606, MRT GmbH) at 60 deg C for 20 minutes. Figure 2 shows the fabrication process and a scanning electron micrograph (SEM) of the large SAA structure created. Different diameter rings (e.g. 30μm, 36μm, and 42μm) with the same slit width (200nm) were fabricated using the above-mentioned processes.
3. Experimental results and discussions
In our set-up, we measured the far-field phenomenon of large size SAA structures. The free space propagating beam generated by the large size SAA structure and its intensity profiles are shown in Fig. 3. The photographs of the Bessel beams were taken at different heights by changing the focal plane of the objective. At a propagating distance of about 30μm, a high-quality non-diffracting beam was found. With the assistance of a localized cylindrical surface plasmon (CSP) resonant mode and a guided mode inside the cavity on the cylindrical metal-dielectric interface of the rings, a higher energy was found to be transmitted by the SAA structure [21, 22]. Furthermore, the emitting waves were shown to propagate on the surface of the cone due to the cylindrical symmetry of the aperture. In summary, Bessel beams can be generated by use of SAA structures.
To investigate the results further from an electromagnetic viewpoint, we looked into optical performance such as depth of focus (DOF) and focal length of the SAA structure by performing many numerical simulations to examine the effects of changing the diameter, the slit width of the ring, and thickness of the silver film. In designing our experiments, we utilized the FDTD simulation and the CSP dispersion relationship to calculate the transmission through a SAA structure in a metallic film to find the best parameters. The parameters of SAA structure were found to be a 200nm thick silver film and a 200nm slit width when the dielectric constant of the silver at 442nm wavelength was εm=-5.735+j0.7536 . To guarantee a higher mesh accuracy results, the mesh spacing was set to be less than one-tenth of the wavelength. The incident optical source was a linearly polarized plane wave (λ= 442 nm), incident normally on the backside of the simulation structure. The simulation results of the SAA structures are shown in Figs. 4(a) and 4(b). Figure 4(a) plots the electric field intensity in a y-z plane. It shows that the SAA structure excited CSP waves, which facilitate extraordinary transmission. In addition, the interference of the diffracted waves from the aperture created a long non-diffracting distance of the Bessel beams. The inset of Fig. 4(a) shows the theoretical and the experimental results at the x-y cross-section of z = 30μm above the silver SAA structure. The polarization state of the incident light source was in the x-direction. It showed that there was good agreement between the theoretical and the experimental data. Figure 4(b) presents a y-z cross section of intensity based on the FDTD simulation results at different diameters of the SAA structures. We found that the DOF changed depending on the diameter at a given wavelength. Results show that the DOF can be defined as the interval of half the maximum intensity of the focal spot along the propagation axis. For example, when the diameter of the SAA structure was 15μm, the depth of focus (DOF) is about 16.9μm. As the diameter increased to 30μm, the DOF also increased to about 41.5μm. The results demonstrate that the scale of the focal length and the DOF can be expanded by increasing the diameter of the SAA structure . Moreover, we found that the trend of intensity changed more rapidly for small diameter SAA structures than for larger diameter SAA structures. The reason may be caused by the different radius of the curve at near space where the wavefront acts like spherical wave and at far space where the wavefront acts like a plane wave. All our FDTD simulations were carried out using a PC cluster system (8 PC, 32 CPU and 64GB memory). As the diameter increased to 36μm or 42μm, the total memory requirement was greater than the 64GB limit of the PC cluster system due to the increased simulation region. Therefore, owing to the computational memory limitation, the optical properties of the Bessel beam generated by a larger SAA structure (36μm and 42μm) influenced by the effect of different diameters was investigated only experimentally.
Figure 5 shows the focal length and DOF varying with the three different diameters (30μm, 36μm and 42μm) of the SAA structure. It was observed that the DOF was about 29μm for the SAA structure with a 30μm in diameter. When the diameter of the SAA structure was at 42μm, the DOF increased to 44μm. This result clearly shows that the experimental result was coincident with our simulation value (e.g. 41.5μm). Compared with the simulation results, we note that the focal length and depth of focus (DOF) increased proportionally to the changing diameter of the SAA structure (see Fig. 5). The difference between the experimental and theoretical curves concerning the DOF in the inset of Figure 5 can be explained by the following reasons. First, the electron beam lithography equipment has around 10nm accuracy in defining the geometrical parameters. In addition, the slit edge of SAA structure was not perfectly smooth. The irregular edge was caused by the lift-off process developed using an ultrasonic bath. Therefore, the theoretical model was slightly different from the real SAA structure. Second, since the silver film was developed using a metal deposition process, the real dispersion relationship of silver may be different from the tabulated data published by Johnson and Christy . These reasons influence the agreement between the experimental and the theoretical curves concerning the DOF. From the Bessel beam intensity measurements and numerical investigations, we concluded that a larger diameter SAA structure leads to a longer distance of the Bessel beam. Therefore by adjusting the diameter of the ring, we can fine-tune the focal length and depth of focus (DOF) to fit our application requirements.
We also regarded surface plasmon at each position along the ring as segments of a light source (cylindrical wave diffraction). Due to the symmetric property of the ring, the transmitted light from the ring was always a constructive interference on the propagating central axis. The far field intensity was the supposition of the vector electric field of the SAA structure. In our simulation and experimental work, we found an interesting phenomenon where the maximum intensity of the transmitted light along the propagating axis was independent from the diameter of the SAA structure (under a plane wave incident assumption). In our experimental set-up, the light source was a 1mm Gaussian distribution laser beam that was incident normally to the back side of the SAA structure. The SAA structure (diameter less than 42μm) is put close to the center of the laser spot. Therefore, the intensity uniformity of the incident light source on the SAA structure approached 99.5 % in all our experiments. A possible explanation for the constant focal point intensity is that the emitting light area (2πrΔr) from the annular aperture was multiplied by the intensity decay of the cylindrical wave (1/r) which was a constant value for the different diameters of the SAA structures. Figure 6 illustrates the relationship between the ratio of the longitudinal to the transverse transmitted intensity (Izmax/Irmax) and the half cone angle (θ) of the diffracted light (shown in Fig. 6) in the SAA structure with different diameters. We found that the curves have the same tendency as the rings with different diameters. For the case when the half cone angles θA = θB = 1(rad) for the two different diameters DA and DB (where DA<DB) of the SAA structure, we obtained the same ratio of the longitudinal to the transverse transmitted intensity (Izmax/Irmax ~0.2). This relationship implies that the vector distribution of the electric field on the aperture of the SAA structure possessed a similar mode. Therefore, it appears that we can extend the depth of focus (DOF) and focal length (f) simply by adjusting the diameter of the SAA structure.
We proposed a SAA structure fabrication process based on electron beam lithography followed by a metal lift-off process which can generate Bessel beams. We propose that by changing the diameter of the SAA structure, we can vary the focal length and depth of focus (DOF). The experimental results match the FDTD simulations. We can see that by adopting this technique, we can significantly extend the depth of focus (DOF) by increasing the diameter of the SAA. In addition, the position of focus spot will move away from the structural plane as the ring diameter increases. Therefore, results show that this type of long distance Bessel beam technique can be applied more widely to such fields as photolithography, optical manipulation and fabrication of high aspect ratio structures.
The authors appreciate the financial support from the Material and Chemical Research Laboratory of the Industrial Technology Research Institute (ITRI) and Taiwan’s National Science Council under Grant No. 96-2221-E-002-122.
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