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We demonstrate a novel approach for easy fabrication of 3 dimensional (3D) photonic crystals (PhCs) with adjustable surface orientation by introducing a specially designed matching prism into the previously reported single-beam laser holographic lithography. Large area (over 1 cm2) face-centered cubic (fcc) -type microstructures with (111) and (81¯1¯) surface orientations have been produced to demonstrate the capability and feasibility of this method. The reflection and transmission measurement agrees well with the corresponding band structure calculation. This method will open a new approach to study the surface-orientation related phenomena such as negative refraction in 3D PhCs, which is very difficult to be realized by other fabricating techniques.
©2006 Optical Society of America
1. Introduction
Photonic crystals (PhCs) are periodic dielectric structures whose refractive index is spatially modulated with a period comparable to that of the electromagnetic (EM) wavelength [1, 2], and the resultant photonic dispersion exhibits a band nature that may contain gaps. These gaps may exist over the whole Brillouin zone or only within a limited range of wave vectors. In the last few years, anomalous dispersion properties in PhCs, such as negative refraction [3–6], superprism effect [7–11] and self-collimation [12–17] have been intensely studied. According to the boundary conditions of EM wave, the propagation of the EM wave is sensitive to the surface termination and orientation. By using the finite-difference time-domain method, people had analyzed the influences of the surface termination and orientation to the transmission and the point imaging quality for a slab of PhC with negative refraction [18,19]. By changing the surface orientation, the transmittance of the PhCs slab could decrease from 0.8 to 10-4 [19]. Therefore, termination and orientation of the surface in a PhC play a key role in many optical phenomena [18–23].
With the direct laser write approach, Markus Deubel et. al. had fabricated “Slanted Pore” photonic crystals with controlled surface termination [24]. Different surface orientations in 2D PhCs is easy to be realized by E-beam lithography. To fabricate 3D PhCs, several techniques, such as E-beam lithography, self-assembly, multi-photon polymerization and holographic lithography have been proposed and demonstrated with different levels of success. Among these methods, self-assembly and laser lithographic holography are the two most economical tools. For self-assembly, [111] is the natural crystal growth direction, leading to (111) surface orientation. To obtain other surface orientations, a pre-made template is necessary. This method is depended on the pre-template. Because of the complexity of the pre-template and the high surface energy, surface orientation with complex Miller indices, such as (81¯1¯) , is difficult to fabricate by this method. Until now, only (111), (100), and (110) surface orientations have been realized experimentally [25–28]. As being able to produce defect-free, nanometer-scale structures over large area uniform PhCs in a single step fabrication, laser holographic lithography is a very economical and powerful tool [29–36]. However, most of the previous works have been focused on fabricating (111) direction of fcc-type microstructure.
In this letter, we describe a new approach to fabricate 3D PhCs with adjustable surface orientation by introducing a specially designed matching prism into the laser holographic lithography. The orientation of the PhC surface is tunable by adjusting the cutting angle of the prism. The capability and feasibility of this method have been demonstrated by the fabrication of large area, defect-free fcc-type PhCs with (111) and (81¯1¯) surface orientations (expressed in terms of the lattice vectors). More complex microstructure such as diamond with different surface orientations can be fabricated by this method. To our knowledge, this is the first experimental demonstration of realizing 3D PhCs with tunable surface orientations.
2. Experimental setup and results
Four umbrella-like interference beams are formed by our previously reported experimental setup based on a single-beam and multi-face-prism [36], which was applied to fabricate fcc-type structure with (111) surface orientation. The projection of the beam configuration on the k1 and k4 plane and the sample position is illustrated in Fig. 1(a). Beams k2 and k3 are overlapped in this projection.
Compared to Fig. 1(a), a specially designed matching prism, the critical component in this experiment, is introduced into the optical setup before the sample as shown in Fig. 2(a). This matching prism was used to make the sample’s surface along the desired plane and to solve the refraction problem to preserve the beam configuration inside the photoresist [33]. The cutting angle of the prism is determined by the angle between (111) plane and the desired plane. For example, we chose (81¯1¯) as the target surface orientation here. Then, the cutting angle of the prism was determined as 30°.
The samples used to record the periodic structures were photoresist coated on glass substrates, which contains the resin Epon-SU8 (from Shell) dissolved in γ-butyrolactone (from Aldrich) with 2 wt.-% Irgacure 261 (from Ciba. Co.) acting as cationic photoinitiator. The photoresist solutions were spun onto the glass substrate and the solvent was evaporated by 90°C-95°C hard baking to obtain ~10μm thick photoresist resin films. A Spectral Physics Millennia continuous wave laser at 532nm was used as the irradiation light source. During the exposure process, an angled thick glass window was attached to the substrate to reduce the effects of back-reflected laser light. Silicone oil was applied as the refractive index matching liquid between all the interfaces. After exposing the interference pattern, another soft bake was necessary to complete the cross-linking of the photoresist. Those unlinked regions were washed away first by propyleneglycolmetheylether acetate and then cleaned with acetone, leaving behind a copy of interference pattern permanently embedded in the polymer film.
Fig. 1. (a) Projection of the beam configuration, reproduced on the k1 and k4 plane, to fabricate the (111)-oriented fcc-type PhCs. (b) shows the scanning electron microscopy (SEM) images of PhC structures generated by the beam configuration of Fig. 1(a). The figure inset is the cross section of the sample, where the solid line shows the surface of the sample and the dash dot line shows the [111] direction of the sample. (c) shows the computer simulation of the Fig. 1(b).
Scanning electron microscopy (SEM) images of PhC structures generated by the beam configuration of Fig. 1(a) and Fig. 2(a) are illustrated in Fig. 1(b) and Fig. 2(c) respectively. The figure insets are the cross sections of the samples. Fig. 1(c) and Fig. 2(d) show the computer simulations. It can be seen that the fabrication and simulation results are consistent. In the two insets of Fig. 1(b) and Fig. 2(c), the solid and dash dot lines mark the surface and the [111] direction of the samples separately. From these two figure insets, it is clearly shown that when there is a matching prism with a cutting angle at 30°, the angle between [111] and the surface orientation is 60°, revealing the terminated surface of the sample at (81¯1¯) . When there is no matching prism, [111] direction is perpendicular to the surface, indicating that the surface orientation is (111). These fabricated results correspond well with theoretical predictions. As shown in Fig. 2(b), the fabricated PhC structures exhibit a high degree of order over an area of cm2, depending on the size of the designed prism and the uniform area size of the expanded laser beam. The typical size of the PhCs we fabricated by this technique is shown in the top right inset of Fig. 2(b).
The optical characterization for transmission and reflection of the samples in Fig. 1 and Fig. 2 were performed on a Fourier transform infrared spectrometer (BIO-RAD FTS 6000) combined with an infrared microscope (UMA500). The samples were aligned with their surfaces perpendicular to the optical axis. A square area of 100 μm×100 μm was defined by an aperture in the light path of the microscope. The transmission and reflection were normalized to the bare glass substrate and gold mirror, respectively. The measured reflection for 3D fcc-type periodic structure with (111)-oriented is illustrated in Fig. 3(a), and the sample with (81¯1¯)-oriented is illustrated in Fig. 3(d). We also calculated the band structure by using the plane wave expansion method with the parameters deduced from Fig. 1(b) and Fig. 2(c). In the case of Fig. 1(b), the parameters are as follows: the lattice spacing is 1.19 μm and the photoresist filling factor is 33%. In the case of Fig. 2(c), the parameters are as follows: the lattice spacing is 1.21 μm and the photoresist filling factor is 44.2% (the difference of the lattice spacing is due to the different shrinkage of the two samples when rinsing.). The refractive index for SU-8 was chosen to be 1.6. Two partial photonic band gaps were clearly visible as pronounced peaks in reflections of the two samples. These two reflection peaks are corresponding well with the two pronounced dips in transmission.
Fig. 2. (a) Projection of the beam configuration, reproduced on the k1 and k4 plane, to fabricate the (81¯1¯) -oriented fcc-type PhCs. The cut-off angle of the prism a is 30°. (b) and (c) shows the SEM images of PhC structures generated by the beam configuration of Fig. 2(a). The figure inset is the cross section of the sample, where the solid line shows the surface of the sample and the dash dot line shows the [111] direction of the sample. (d) shows the computer simulation of the Fig. 2(c).
The spectral positions of the two reflection peaks for the two samples are different. The (lll)-oriented sample’s reflection peaks are around 2.54 μm and 1.32 μm, whereas the (8lT)-oriented sample’s reflection peaks are around 2.45 μm and 1.45 μm. These two band structure of the samples with (lll)-oriented and (8l¯1¯) -oriented are shown in the Fig. 3(b) and Fig. 3(c), respectively. From the measured and calculated results shown in Fig. 3, it can be seen that the position of the peak in reflection corresponds well with the partial stop band (outlined by the gray shaded square) expected from the band structure calculation for the measured direction. Where, the Γ-T and Γ-Z direction are [111] and [81¯1¯] direction of the fabricated fcc-type PhCs, respectively. Furthermore, Fig. 3 shows that the difference between the two reflection peaks of the sample with (111)-oriented is 1.22 μm. It is 22% larger than that of the sample with (81¯1¯) -oriented (1.0 μm). Such a large difference in the reflection spectrum is much beyond the slightly difference of the length of lattice vector. It is also much beyond the difference of the photoresist filling factor of the two samples, since the difference between these two peaks is only slightly depended on the photoresist filling factor as shown by our simulation. It is largely due to the difference of the measured directions. The band structure shows that the higher energy reflection peak position is depended on the Γ point while the lower energy reflection peak position is depended on the measured directions (Γ or Z point in our experiment). Because of that, when the measured direction is changing from Γ-T to Γ-Z, the higher energy peak position does not change while the lower energy one is blue shift. So that the difference between the two peaks measured at Γ-T direction is larger than that measured at Γ-Z direction. It is in good agreement with the reflections data.
Fig. 3. (a) Optical intensity reflection spectrum of the (lll)-oriented fcc-type photoresist template in Fig. 1 (b) along the (111) direction (Γ-T), showing two pronounced peaks around 2.54 μm and 1.32 μm. (b) Corresponding band-structure calculation of the (lll)-oriented fcc-type photoresist template in Fig. 1 (b) along the (111) direction (Γ-T). (c) Corresponding band-structure calculation of the (81¯1¯)-oriented fcc-type photoresist template in Fig. 2 (c) along the [81¯1¯] direction (r-Z). The gray shaded area corresponds to the direction measured. (d) Optical intensity reflection spectrum of the (81¯1¯) -oriented fcc-type photoresist template in Fig. 2 (c) along the [81¯1¯] direction (Γ-Z), showing two pronounced peaks around 2.45 μm and 1.45 μm. For comparing the two reflections, (a) and (d) have been shifted to align the higher energy peaks position.
3. Conclusion
In conclusion, we demonstrated a novel approach for the easy fabrication of photonic crystals (PhCs) with tunable surface orientation using the same optical setup of laser holographic lithography by introducing a specially matched prism. We have succeeded in producing large-scale (over 1 cm2), high quality fcc-type PhC structures with (111) and (81¯1¯) surface orientation using this technique. The SEM images are consistent with the simulation results. Furthermore, the reflection/transmission measurements performed on the PhC structures agree well with the corresponding band structure calculation. Unlike self-assembly, this method can be applied to fabricate 3D PhC microstructures with tunable surface orientation without any pre-made templates. Furthermore, more complex micro/nanostructures such as diamond lattice with adjustable surface orientation can be generated. The fabrication of large area 3D PhCs with tunable surface orientations will open a new approach to study the surface-orientation related phenomena such as negative refraction in 3D PhCs, which is very difficult to achieve using other fabricating techniques.
Acknowledgments
This work is partially supported by NSFC-RGC Joint Research Grant (grant no. N_HKUST610/02).
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