1. Introduction

Interference patterning using multiple beams has been recognized as one of the most important techniques for nano-structuring in the design of functional devices [1–6]. Multi-beam interference lithography has been investigated both theoretically and experimentally for achieving differently shaped photonic crystals [7–10]. Making use of different combinations of laser beams involved in the holographic interference scheme, two- and three-dimensional photonic crystals of dielectric and metallic materials have been produced into differently shaped lattices [11–15]. Flexible interference lithography using fibers to split and deliver the laser beams have been demonstrated to fabricate two-dimensional grating structures [16]. The similar design can also be used to achieve direct writing into metallic nanoparticle films and plasmonic photonic crystals can be produced after annealing processes [17]. The fiber-based system not only enables flexible and compact arrangement of the interference lithography scheme, but also facilitates convenient insertion of optical components to achieve modulation of the interference pattern.

In this letter, we demonstrate polarization control in a three-beam interference lithography scheme using optical fibers to multiply the interference patterns, where a half-wave plate was inserted at different places in the optical paths. Due to the change in the polarization direction of one or all of the interference arms, the interference pattern can be optimized in the contrast and tuned between square lattices and nanoline arrays. The flexibility of such an interference-lithography scheme is thus extended to the versatility of a design of the optical system.

2. Flexible interference lithography using optical fibers

Figure 1(a) shows the design of the flexible interference lithography system using three optical fibers. The fibers (❶, ❷, ❸) were arranged into a rectangular triangle at both the input- and output-coupling ends. Each fiber has a core diameter of 400 μm and a cladding layer of 20 μm. Such a three-fiber scheme can be utilized to produce interference patterns of square lattices, where the generally four-beam interference-lithography system can be thus simplified. As shown in Fig. 1(a), fibers ❷ and ❸ were arranged in a same vertical plane (Y-Z) and fiber ❶ was fixed in a plane (X-Z) perpendicular to that of ❷ and ❸. A half-wave (λ/2) plate for 325 nm was inserted either into the optical path before the light was coupled into the fiber bundle or behind a single fiber of one of the branch arms. Thus, polarization of the laser light may be changed either simultaneously for all of the three laser beams output from the fibers or for only one beam independently. Figure 1(b) shows how the three fibers were arranged at the output coupling ends.

 

Fig. 1 (a) Experimental setup for flexible interference lithography using a three-fiber geometry with a λ/2 plate inserted at different places in the optical path. (b) The geometry for arrangement of the three fibers at the free ends.

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A 325-nm He-Cd laser from Kimmon Koha Co., Ltd. with 30-mW output power was employed as the UV laser source. The diameter of the laser beam at FWHM was about 1.2 mm, which covered the total facet areas of the three fibers at the input. The bundled end for input coupling was mounted on a three-dimensional stage, so that the laser beam can be precisely controlled and coupled equally into the three fibers. Therefore, the fibers function both as a beam splitter and a light-delivering system, replacing the conventional optics. The 325-nm laser beam is vertically polarized at the input. At the free ends, each fiber head is fixed onto a mirror holder before being mounted on a three-dimensional translation stage, so that each fiber end can be positioned and tilted conveniently. The divergent beams coupled out of the fibers were then overlapped onto the film of S3170 photoresist that was spin-coated onto indium-tin-oxide (ITO) glass substrate. The ITO layer has a thickness of about 200 nm and functions as a waveguide when the fabricated structures are used as waveguide grating structures [18]. However, we focus here on a fabrication method of nanograting structures, the ITO layer is important for microscopic characterization using scanning electron microscopy (SEM), where the conductivity of ITO enables better SEM measurements. The glass substrate has an area of 20 × 20 mm² and a thickness of 1 mm. The diameter of the effective area of the grating structures is as large as 10 mm, which is the same as the overlap area of the three laser beams.

A positive photoresist AR-P 3170 purchased from ALLRESIST GmbH was employed, which was spin-coated onto the ITO-glass substrate at a speed of 2000 rpm, so that the thickness of the photoresist layer was measured to be about 200 nm. The sample was then baked at 90 °C for 60 seconds on a hotplate before the exposure process. The output power from each fiber was measured to be 2.4 mW, which was measured about 1 cm behind the fiber end with the output spot smaller than the detector area. The output is nearly the same for all of the three fibers. Therefore, the total exposure dose was 2.4 mW × 3 (three fibers) × 10 seconds (exposure time) = 72 mJ or each fiber contributed 24 mJ to the exposure dose. The exposed sample was then developed in the developer for AR-P 3170 for 8 seconds before being rinsed in pure water.

3. Microscopic and spectroscopic characterization

Theoretical simulations were first performed to understand how polarization control can be used to tune the interference patterns in the three-beam scheme shown in Fig. 1. The modeling is based on the geometry between the wave vectors of the beams from fibers ❶, ❷, and ❸, which are depicted by k₁, k₂, and k₃, respectively, and are oriented at angles of θ₁, θ₂, and θ₃ with respect to Z-axis, as shown in Fig. 2.

 

Fig. 2 Schematic illustration of the interference geometry for the simulations using the same coordinates as shown in Fig. 1. k₁, k₂, k₃ denote the wave vectors of the three beams output from the fibers ❶, ❷, ❸, respectively. The corresponding direction of these three beam are depicted by θ₁, θ₂, θ₃.

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Assuming that the optical electric field of beam $i$ ($i$ = 1, 2, 3) is expressed as:

In the first experimental demonstration, we placed a half-wave plate at the input-coupling or before the bundled end of the fibers. The polarization direction of the initially vertically polarized laser beam at 325 nm was changed from α = 0 to 90 degrees in steps of 10 degrees, where α is the angle of the polarization direction with respect to the vertical axis in the plane perpendicular to the axis of the fiber bundle. Figure 3(a) shows the simulation results of the interference pattern in an area of 2 × 2 μm² and Fig. 3(b) shows the correspondingly experimental results of the fabricated photoresist gratings with an area of 5 × 5 μm², which have been measured using SEM. Square lattices with good contrasts have been achieved at polarization angles of α = 10, 20, and 30 degrees and the interference pattern at α = 30° has the highest contrast among the square-lattice structures, as can be seen in both the simulation and experimental results in Fig. 3. With increasing the value of α, the square lattices become connected into one-dimensional nanolines. Although the structures with higher contrast are observed at α = 40, 50, 60, and 70°, the lattice units become elongated and connected in the direction of X-axis. At α = 80 and 90°, nanolines are observed to constitute the grating structures. However, at α = 0°, no interference patterns are observed in the simulation results and structures with very low contrast can be observed in the fabricated gratings, implying that this is not a correct configuration for photonic nanostructuring. The simulation results in Fig. 3(a) agree very well with the experimental results in Fig. 3(b). Figure 3(c) shows the SEM image of the cross-section of the fabricated structures, which was measured after the sample was cut along the dashed pink line in Fig. 3(a) and corresponds to the simulation and experimental results at α = 40° in Figs. 3(a) and 3(b). Excellent two-dimensional grating structures with a modulation depth of less than 200 nm can be observed, implying successful optimization of the contrast of the fabricated grating structures through tuning the polarization direction of the laser beams.

 

Fig. 3 (a) Simulation results of the interference patterns using the geometry in Fig. 2 with the polarization direction of the input laser beam changed from α = 0 to 90 degrees with respect to the vertical direction. (b) Experimental results of the produced photoresist grating structures. (c) Cross-section demonstration of the fabricated structures with α = 40°, where the sample was cut along the dashed pink line in (a).

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Alternatively, we can also tune the patterned nanostructures by changing the polarization angle (β in Fig. 1(a)) of one of the branch arms of the interference scheme. The upper panels in Figs. 4(a)-(d) show the simulation results and the lower panels show the SEM images of the fabricated grating structures. As shown in Fig. 4(a), the beams from fibers ❷ and ❸ are horizontally polarized, whereas, that from fiber ❶ is polarized with β = 0 (Ф), 45 (∅), and 90° (y). Square lattices were produced for β = 0 and 45° with higher contrast achieved at β = 0, however, nanoline arrays were produced at β = 90°. According to the simulation results in Fig. 4(b), when the output beams from fibers ❷ and ❸ are both vertically polarized, no interference pattern was observed for any polarization directions (β = 0, 45, and 90°) of the light beam from fiber ❶. This is verified by the experimental results in the lower panel of Fig. 4(b), where very low contrast is observed for all of the SEM images.

 

Fig. 4 Interference patterns tuned by changing the polarization direction of one of the three UV laser beams output from the fibers. (a), (b), (c), and (d) correspond to different polarization configurations of the laser beams output from the three fibers ❶, ❷, and ❸. The shapes of Ф, ∅, and y represent polarizations of the light at β = 0, 45, and 90 degrees with respect to the original polarization in a vertical direction. Upper panels: simulation results; lower panels: experimental results with the SEM images of the fabricated photoresist gratings.

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When the beams from fibers ❶ and ❷ are both horizontally polarized, grating structures consisting of horizontally extended nanolines were produced at β = 45 and 90° for beam ❸, whereas, no photonic structures are displayed in the simulation result and the SEM image exhibits very low contrast, as shown in Fig. 4(c). However, when the polarization of the beams from fibers ❶ and ❷ are both changed to vertical directions, grating structures consisting of nanolines extending along 45° with respect to the X (or Y) axis were produced at β = 0 and 45° for beam ❸, according to both the theoretical and experimental results in Fig. 4(d). However, if beam ❸ is changed to vertical polarization (β = 90°), both the theoretical and experimental results again show very poor contrast in the produced grating structures.

In the experiments for the results demonstrated in Fig. 4, the fibers without polarization control by the half-wave plate have been rotated manually at the output ends about their axis to change the polarization directions. The colors denoting the intensity distribution over the interference patterns have been defined using the same scales for all simulation results. Thus, the colors can be used directly to compare the contrast of the nanostructure patterns.

It should be noted that in above simulations it has been assumed that the beams were kept linearly polarized after passing through the fibers. In practice, the polarization of the laser beam generally loses its linearity after passing through a multimode fiber. Such “degradation” of linear polarization results in the reduction of the contrast of the produced nanostructures or leads to some two-dimensional structures, as shown in the SEM images in Fig. 3 and Fig. 4. This explains why the simulation results differ from the measured SEM images, when we compare Fig. 3(a) with Fig. 3(b) for α = 0°, and the simulation results with the SEM images in Fig. 4(b), (c), and (d).

Furthermore, the contrast of the practically fabricated structures is determined not only by the contrast of the interference pattern, but also by the exposure and development processes in interference lithography. This also contributes to the disagreements between simulation and measurement.

Additionally, in demonstrating the simulation results, to compare directly the contrast of the grating structures, we showed the simulation results using a same intensity scale in the vertical axis. Thus, the extremely low-contrast structures cannot be observed in the simulation results, although they may be observable in the SEM images of the fabricated structures.

Nevertheless, excellent agreement between simulation and experimental results at high contrasts ensures validness of the assumptions that the light beams output from the fiber ends basically maintain their linear polarization performance.

4. Conclusions

Fiber-based flexible interference lithography with polarization control using inserted half-wave plate was demonstrated. A rectangular triangle arrangement of three fibers was employed to achieve square lattices of photonic structures. Polarization control not only enabled optimization of the contrast of the photonic structures, but also multiplied the produced interference patterns using one optical design. Such a flexible scheme provides a simple and convenient configuration for inserting polarization adjustment devices and is advantageous in achieving compact nanofabrication systems.