1.

Introduction

Subwavelength periodic structures (SWPS) with periods smaller than light wavelengths can control the intensity, phase, and polarization of light very effectively. They are highly useful for designing a variety of optical components, such as antireflection layers, wave plates, polarization separators, and local electric field enhancers.^1–4 Various lithography methods are available for producing SWPSs: electron beam writing, laser beam writing, laser interference exposure, and nanoimprinting. Each has advantages and disadvantages in terms of patterning accuracy, production throughput, and production cost. In laser writing, which is the subject of the present study, a beam can be scanned in the $x-y$ format^5–7 or in the $r-\theta$ format.^8–10 The most suitable format depends on the symmetries of the structures that need to be produced. The $x-y$ format is typically preferred when square symmetries are sought in the $x$ and $y$ directions; it can be applied to most one- and two-dimensional (2-D) patterns. The $r-\theta$ format is suitable for axial symmetry, and its high rotational speed makes it less time consuming, although it is not necessarily cost effective. A workpiece mounted on a table is rotated at a fixed speed throughout the laser exposure, except for short periods at the start and end.

We have developed an ultraviolet (UV) laser writing system based on a polar scanning strategy, and we have applied it to the fabrication of diffractive optical elements, which typically have micron-scale features. Elements with various beam delivery functions were evaluated for laser machining applications.^11–14 Furthermore, we have explored our system’s potential for use in submicron-scale patterning, and we have examined the effects of pattern errors caused by the polar format. Provided that such errors do not compromise the performance of the SWPSs, this versatile writing system can be extended to the production of subwavelength-scale optical elements.

We report a lithography process by which the polar-format laser writing system forms metal gratings at submicron scales. These gratings can cause surface plasmon resonance (SPR), which appears as a dip in the zeroth-order reflection at the air/grating interface. By observing SPR dips carefully, we can figure out what would happen if there were system-induced fabrication errors. In the next section, the error factors that are pertinent to the polar strategy are described, and sample metal gratings produced with the laser writing system are discussed. In Sec. 3, reflectance spectra obtained from the gratings are presented, and in Sec. 4, the effects of fabrication errors on the far-field responses are discussed. Simple but effective formulas that we have derived explain how SPR characteristics depend on incident polarization and can be applied in general discussions over plasmonic gratings.

2.

Production of Metal Gratings

As schematically depicted in Fig. 1, the laser writing system comprises a rotating table and a slider, and it can write patterns on resist in a polar format by synchronizing the movements of the table and the slider.¹⁵ The system has a ${\mathrm{Kr}}^{+}$ laser source with a wavelength of 413 nm. The exciting beam is focused at 0.5 μm in width ($1/e^2$) by a high-numeric-aperture objective lens, and the resist is exposed to the focused beam. The beam intensity is roughly adjusted by an electro-optic modulator and finely tuned at 266 levels by an acousto-optic modulator (AOM), which is turned on and off at a fixed rate of 2.9 MHz. This rate determines the sampling frequency in the resist patterning in the angular direction. The duty cycle for switching the AOM is set at 25%, 50%, or 75%, taking into account the selected sampling pitch or grating period, and no mechanism for independent beam width adjustment is available in the radial direction. Consequently, the effective writing beam footprint can be skewed in either the radial direction or the scan direction. When a laser linear scale is used, the substrate can be positioned with a 3-nm resolution in the radial direction. The patterning time is determined by the patterns being drawn. We have tested this system by writing linear, tetragonal, and hexagonal patterns with submicron periods.

Fig. 1

Schematic of laser writing system with polar coordinates.

With the polar coordinates employed in the system, as illustrated in Fig. 2, the grating period $P(r)$ in the angular direction is given by

Fig. 2

Polar coordinates and sampling points.

Fig. 3

Grating period deviation versus radius deviation.

By using the laser writing system described above, metal gratings were fabricated as follows. A positive-type photoresist layer was spin-coated to a thickness of 100 nm on a fused silica substrate with a thickness of 1.2 mm and a diameter of 200 mm. The resist-coated substrate mounted on the rotating table was exposed to a focused UV laser beam. The grating patterns were written in a 3-mm wide circular region using a $\sim 0.5\text{-}\mathrm{\mu m}$ wide focused beam at a sampling frequency of 2.9 MHz. With the rotational speed fixed at 225 rpm, the radii for periods of 400, 500, and 600 nm were set at 49, 62, and 74 mm, respectively. The exposed resist was developed in a developer, rinsed in running deionized water, and dried in air to form the resist patterns on the substrate. Then, using the patterned resist as a mask, the fused silica surface was etched by reactive ion etching. When ${\mathrm{C}}_2{\mathrm{F}}_6$, ${\mathrm{CF}}_4$, and ${\mathrm{CHF}}_3$ were used as process gasses, the obtained etch rates were $150\mathrm{nm}/\min$ for resist and $240\mathrm{nm}/\min$ for fused silica, and the etching selectivity was 1.6. Because this was an adequate selectivity, no metal mask was placed between the resist and the substrate. The resist was removed by dry etching with ${\mathrm{O}}_2$ to obtain fused silica gratings. A 3-nm thick adhesive layer of Cr was formed on the fused silica corrugations by vacuum deposition; then, a 100-nm thick plasmonic layer of Au was formed by sputtering. The Au layer was sufficiently thick to prevent incoming light from passing through the gratings. We selected Au for coverage because it remains stable in air, and its dielectric constants enable efficient excitation of surface plasmons at visible wavelengths. Other candidate metals are Ag, Ni, and Al.

Figure 4 shows atomic force microscopy images of subwavelength metallized gratings produced with the polar scanning system. They are tetragonal arrays of (a) holes and (b) pillars, and hexagonal arrays of holes (c) 320-nm wide and (d) 230-nm wide. All these gratings had a common period of 500 nm, and the corrugations were 50 nm or less in depth. The fill factors in Fig. 4(c) and 4(d) were 0.64 and 0.46, respectively. When tetragonal patterns were drawn, the sampling points on the scan lines were aligned in phase, radially, around the rotating center. For hexagonal patterns, the sampling points were aligned out of phase by half a sampling pitch between adjacent scan lines. As a result, the tetragonal gratings had a constant period in the radial direction and a varying period in the angular direction as a function of the radius. The hexagonal gratings had different periods among the three principal directions crossing at 60 deg. Tuning of the exposure beam intensity allowed for the formation of holes and pillars and for the adjustment of fill factors in the range of 0.3 to 0.7. The one-dimensional gratings we fabricated had a fixed period across their grooves, though they are not shown.

Fig. 4

Atomic force microscopy images of metallized gratings: tetragonal arrays of (a) holes and (b) pillars and hexagonal arrays of holes (c) 320-nm wide and (d) 230-nm wide. The scale bar is common to all panels.

3.

Experiment and Results

Reflectance spectra or zeroth-order reflections were obtained by illuminating a metal grating with a collimated white light. The light spot was 2-mm wide and was centered at the radius for a grating period of interest. Within the spot, the grating period varied in the angular direction by at most $\pm 8\mathrm{nm}$. Those spectra were captured using a spectrometer (USB2000, Ocean Optics) against incident polarization orientation $\theta$. The 0-deg orientation was set perpendicular to the polar scanning lines. A 10-μm wide slit was used on the spectrometer. A spectrum from a nonstructured area of the Au layer was used as a reference signal to normalize the spectra from the gratings. We performed computational analyses using the finite-difference time-domain (FDTD) method to compare the theoretically predicted reflectance spectra with the experimental results.

Figure 5 shows the reflectance spectra obtained from a tetragonal grating (hole array) with a 600-nm period at its center for $\theta =0$, 45, and 90 deg. A grating depth of 80 nm was chosen. At that depth, the SPR dip bottomed out, according to the FDTD analysis. SPR dips mediated by the (1, 0) and (0, 1) modes of evanescent waves appeared at around 650 nm. The reflectance minimum (dip depth) varied from 25% to 40%, and the wavelength for the minimum (dip wavelength) shifted by $\sim 5\mathrm{nm}$ over the range of 0 to 180 deg for incident electric vector orientation. The wavelength shift was much smaller than the $\sim 30\text{-}\mathrm{nm}$ FWHM of the dip. In theory, neither the dip depth nor the dip wavelength should change, regardless of the incident polarization orientation, provided the arrays have perfect tetragonal symmetry.

Fig. 5

Reflectance spectra from a 600-nm period tetragonal grating.

Figure 6 shows the reflectance spectra obtained from a hexagonal grating (hole array) with a 600-nm period at its center for $\theta =0$, 60, and 120 deg. A grating depth of 120 nm was selected according to the results of the FDTD analysis. SPR dips, which were caused by the ($1/2$, $3/2$), (1, 0), and ($1/2$, $-3/2$) modes of evanescent waves, emerged at 590 to 610 nm. The reflectance at the dip varied from 17% to 27% over the range of 0 to 180 deg for incident electric vector orientation. The dip wavelength shifted by $\sim 15\mathrm{nm}$, which was smaller than the dip width of $\sim 60\mathrm{nm}$. When the hexagonal structures are identical in the three principal directions, $\theta =30$, 90, and 150 deg, the dip depth and dip wavelength should remain unchanged, regardless of the polarization orientation.

Fig. 6

Reflectance spectra from a 600-nm period hexagonal grating.

Figure 7 shows the SPR dip behavior as a function of the incident polarization orientation, in terms of (a) dip depth and (b) dip wavelength, for the 600-nm period tetragonal grating. These data are taken from Fig. 5. In Fig. 7(a), the reflectance changed in a cycle of $\sim 90\mathrm{deg}$, and the difference between the maximum (weak resonance) and minimum (strong resonance) was $\sim 15\%$. We evaluated several samples and found that the reflectance always had a maximum at around $\theta =90\mathrm{deg}$. The results shown in Fig. 7(a) indicate that the holes could have been somewhat skewed in one of two directions. In Fig. 7(b), the dip wavelength was 651 to 656 nm; thus, the dip shift was $\sim 5\mathrm{nm}$ for the range of 0 to 180 deg for the polarization orientation. We have not yet established any relation between the two curves shown in Fig. 7(a) and 7(b).

Fig. 7

SPR dip behavior as a function of incident polarization orientation for the tetragonal grating whose spectra are shown in Fig. 5: (a) dip depth and (b) dip wavelength.

Figure 8 shows the SPR dip behavior as a function of incident polarization orientation, in terms of (a) dip depth and (b) dip wavelength, for the 600-nm period hexagonal grating. These data are taken from Fig. 6. In Fig. 8(a), the reflectance changed from 17% to 27% in a cycle of $\sim 90\mathrm{deg}$. The reflectance did not necessarily have a maximum at 90 deg, in contrast with the tetragonal gratings. The results shown in Fig. 8(a) indicate that the hole arrays could have been somewhat deformed in three directions: 30, 90, and 150 deg. In Fig. 8(b), the dip wavelengths were 594 to 609 nm, and the wavelength shift was $\sim 15\mathrm{nm}$ for the range of 0 to 180 deg for the polarization orientation. We have found no proof of any significant relation between the two curves shown in Fig. 8(a) and 8(b).

Fig. 8

SPR dip behavior as a function of incident polarization orientation for the hexagonal grating whose spectra are shown in Fig. 6: (a) dip depth and (b) dip wavelength.

4.

Discussion

Because surface plasmons are excited by evanescent waves generated in a metallized grating, the dip depth (reflectance minimum) is undoubtedly associated with the coupling efficiency of incident light into evanescent waves. The reflectance $R$ and coupling efficiency $C$ can be approximately related as $R=1-C$ if bulk absorption in the metal is neglected. Given this assumption, the reflectance for tetragonal gratings, $R_t(\theta )$, can be defined by

Fig. 9

Reflectance as a function of incident polarization orientation for a tetragonal grating (computer simulation).

Likewise, the reflectance for hexagonal gratings, $R_h(\theta )$, can be defined as

Fig. 10

Reflectance as a function of incident polarization orientation for a hexagonal grating (computer simulation).

The coupling efficiencies are related to two factors: the period and surface-relief profile of a grating. They determine an optimal depth at which the efficiency peaks. The period deviation within the spectrum acquisition area was $\sim 8\mathrm{nm}$ (see Sec. 2), which was extremely small to affect the efficiencies. Any possible differences in grating profile between the two directions, which could have been caused by the skewed writing beam, were very likely to cause the efficiency gap. The reflectance formulas described above, though rather simple, explain the observed behaviors of the SPR dips.

Using the plasmonic dispersion relation for a smooth air/metal interface,¹⁸ the resonance wavelength $\lambda$ is given by

Is the behavior of the SPR dips observed in our experiment suitable for practical applications? The answer has much to do with how the metallized gratings are applied. The gratings can be applied as a near-field enhancer to amplify Raman signals. Propagating surface plasmons excited with the gratings are accompanied by enhanced electric fields near their corrugated surfaces, at which Raman signals from target analytes are amplified.^20–22 When 2-D gratings are used in Raman sensing, which is our interest, the use of circular polarization is reasonable, because the optical responses of a spectrometer are usually subject to the polarization of the input signals. In that case, the SPR dips at all orientations would be averaged out, suggesting that using the dip depth or the dip wavelength as a measure of the target molecules would be problematic.

5.

Conclusion

We investigated the potential of using a polar scanning strategy for laser-beam writing of SWPSs. We produced metallized gratings using our laser writing system with polar coordinates, and we measured their SPR characteristics. In our measurements, SPR dips were observed near the theoretically predicted wavelengths, and yet, for 2-D gratings, the dip depth changed by $\sim 2$ times its minimum, whereas the dip wavelength shifted by $\sim 20\mathrm{nm}$ for different orientations of incident linear polarization. The dip shifts occurred because of the skewed writing beam footprint; they were extremely large to be attributed to the polar format. The observed dip shifts can be tolerated when the gratings are used as signal enhancers in Raman sensing applications. We conclude that UV laser lithography based on this polar scanning strategy is a candidate method for surface structuring on submicron scales. Future research work should be aimed at devising a method for realizing an unskewed beam footprint without any dependence on the grating period.