1. Introduction

Recently, there has been considerable interest in the fabrication of two- and three-dimensional (2D and 3D) photonic crystals (PCs), which consist of periodic dielectric structures [1,2]. PCs have unique photonic bandgap properties and can be applied in wide range of optical devices. In particular, the introduction of point or line defects into PCs offers various potential applications, e.g. low-loss waveguides [3–7], cavity resonators and microlasers [7–9], etc. Various techniques have been proposed to fabricate templates for PCs such as self-assembly of colloidal particles [10,11], holographic lithography [12–18], and direct laser writing [19–22], etc. However, a critical step towards the incorporation of arbitrary defects, i. e. microcavities or waveguides, in a controllable way, has met some difficulties. Indeed, the pinpoint writing in multi-photon process [23] is not suitable for massive production. The combination of the self-assembly approach with multi-photon polymerization (MPP) microfabrication technique permits obtain photonic crystals with precisely controlled defects [10], but the self-organizing nature of assembly process almost inevitably leads to the formation of unwanted defects and the incorporation of photoresist into assembly process is also not easy. Holographic lithography (HL), however, is a very promising and inexpensive technique to fabricate large area and free-defect PC template [12–18]. Recently, several groups have proposed to combine HL with direct laser writing [24], electron beam lithography [25], focused ion beam [26], or MPP [27] techniques as a promising route to fabricate large-area PCs containing arbitrary defects. However, these techniques need to use high peak power pulsed laser or complicated sources in order to make (ablation or photopolymerization technique) one line defect into the periodic structures, and the defect size is also limited by the scanning range of the microfabrication system (about 100 µm). In order to rapidly and simply introduce arbitrary defects into 2D PCs, we propose, in this paper, to combine HL technique with mask-photolithography technique as an efficient method to produce large-area PC templates with desired long defects. To fabricate periodic structures, we use multiple-exposure of two-beam interference pattern as a simple and efficient method to produce various 2D square or hexagonal structures. Desired defects are introduced in these structures by irradiating the sample with one beam of the same laser through a mask in which the design of defects is patterned.

2. Theoretical study of multiple-exposure of two-beam interference pattern

 

Fig. 1. Schematic of experimental setup: The laser beam is extended by two lenses L₁ and L₂; Three beams, 1, 2, and 3, of the same profile, polarization, and intensity are selected by a triple-iris; Beams 1 and 3 are used to make 2D periodic structures by means of interference, and beam 2 is used to irradiate the sample through a mask.

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Figure 1 shows the experimental setup used to fabricate 2D PC templates with desired defects. 2D periodical structures were fabricated by the interference of two laser beams (1 and 3) emitted from a cw He-Cd laser at 325 nm with multiple-exposure. We chose this method because of its simplicity and capability [12,24] to produce various large-area 2D structures, hexagonal or square, by simply rotating the sample by an angle of 60⁰ or 90⁰ around the symmetrical axis z (Fig. 1). Indeed, it is well known that the interference pattern of two laser beams is a periodic one-dimensional (1D) structure. The double-exposure of two-beam interference pattern at two different directions into a sample therefore generates a double-1D structure, which is equivalent to a 2D structure. Theoretically, the intensity distribution of a two-beam interference pattern is calculated as [13]

where the electric field of each interference beam (called beam 1 and 3 in Fig. 1) can be generally written as

where E ₁₀ and E ₃₀ are the amplitudes of electric field of beams 1 and 3, respectively, ω is the angular frequency, k is the wave number, α is the rotation angle, and θ is the semi-angle of two laser beams which defines the period (Λ) of structures as

where λ is the wavelength of the interference source.

In the case of multiple-exposure of two-beam interference pattern at different angle α, the exposure dose is accumulated: therefore its total intensity distribution is different to that of multiple-beam exposure [13]. It can be expressed as

where i=1, 2, 3, …corresponding to one-exposure, double-exposure, and triple-exposure, etc., at different angle α_i (α ₁=0° for the first exposure).

Note that the polarizations of the interference sources are the same, as illustrated in Fig. 1, and the contrast between the minimal and maximal intensities of two-beam interference is the best comparing with that of the cases of three-beam or four-beam interference [28, 29].

 

Fig. 2. Calculated light intensity distribution of multiple-exposure of two-beam interference pattern. (a) Double-exposure at α=0° and 90°, (b) double-exposure at α=0° and 60°, (c) triple-exposure at α=-60°, 0° and 60°.

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Figure 2 shows the theoretical calculation of intensity distribution of two-beam interference with double-exposure and triple-exposure. In the case of double-exposure at 0⁰ and at 90⁰, perfect periodic square structures (Fig. 2(a)) are obtained as that of one-exposure of four-beam interference [17]. If double-exposure is executed at 0⁰ and at 60⁰, one can fabricate 2D hexagonal structure as that can be obtained by interference of three beams [13], except the structure, i.e. the dot shape, not perfect symmetry (Fig. 2(b)). This imperfection can be improved by employing a symmetrical multiple-exposure. Indeed, applying triple-exposure at 0⁰, -60⁰, and 60⁰, one can get perfect circular dots in the cross section of hexagonal structure as evidently shown in Fig. 2(c). Note that the periodic structures obtained by the triple-exposure depend on the position of one exposure with respect to the other two exposures. Indeed, if the bright lines (high intensity) of the two-beam interference pattern obtained by one exposure coincide with the crossed-points of bright lines obtained by the other two exposures, it forms a hexagonal structure with cylinder rods (Fig. 2(c)). In other word, the cylinder rods are form at the crossed-points of bright lines of three exposures. On contrary, if the bright lines of the two-beam interference pattern obtained by the one exposure are shifted by Λ/2 from crossed-points of bright lines obtained by the other two exposures, it forms a hexagonal structure with air holes. In other cases, the structures obtained by triple-exposure become complicated.

3. Combination of mask-photolithography and HL techniques: results and discussions

The fabrication process is divided in two steps. First, beam 2 is blocked and we made multiple-exposure of two-beam interference pattern, interference of beams 1 and 3 (Fig. 1), to create 2D periodic structures. Second, two beams, numbers 1 and 3, are stopped, and the sample is still fixed in the holder as in the first step, the desired defects were introduced by means of mask-photolithography technique. For the second step, the third beam, beam 2 in Fig. 1, was used as the light source to expose the sample, in the area just exposed by HL technique, through a mask in which various defects such as waveguide and Mach-Zehnder structures are patterned. Note that the order of these two steps can be permuted without changing the final results. The beam profile of three beams, 1, 2, and 3, are the same with the diameter of 1 cm.

The photoresist chosen in this work is a positive photoresist AZ-4620 (Clariant Corp.). This photoresist absorbs the UV light and becomes soluble if the dose is above of its polymerized threshold. When the light is spatially modulated, the photoresist therefore is still insoluble at low light intensity regions (below threshold) and becomes soluble at high light intensity regions (above threshold). We then obtain a periodic insoluble-soluble of AZ materials. When combining with the mask-photolithography technique, the light passes though the defects patterned in the mask and exposes this periodic structure. With high dose of this step, the periodic structure now embeds a soluble-AZ-defect. After developed, we obtain the remaining periodic structure of AZ materials embedding the desired air-defects. This photoresist is very suitable for the combination technique due to its absorption range covering the emission wavelength (325 nm) of the He-Cd laser. Consequently low power of He-Cd laser irradiation is enough to fabricate large area periodical structures (one-photon absorption). The thin film samples with 1 µm thickness were prepared by spin-coating onto glass substrates and baking at 65⁰ C for 2 minutes and then 95⁰ C for 3 minutes to remove the solvent. After exposed by i) two-beam interference (beam 1 and 3) to fabricate 2D structures and ii) one beam (beam 2) through the mask pattern defects, the samples were post-baked at 70⁰ C for 2 minutes and then 120⁰ C for 3 minutes to improve the polymerization. The samples were finally developed for 3 minutes in AZ developer and rinsed by DI water.

 

Fig. 3. AFM images of 2D periodic structures. (a): hexagonal structure obtained with 1s-exposure time. (b) and (c): square structures obtained with 1s- and 2s-exposure time, respectively. The lattice constant, Λ=3 µm (θ=3.1°).

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We first demonstrate that by simply rotating the sample around the z-axis for different exposures, we can obtain square or hexagonal 2D structures. Figure 3 shows the experimental results of such 2D structures with a lattice constant of 3 µm (θ=3.1⁰). The square and hexagonal structures are obtained by double-exposure at α=0⁰ and α=90⁰, and α=0⁰, and α=60⁰, respectively. The periodic structures are uniform for an area of 1cm×1cm. Moreover, by controlling the exposure dose, i.e. the laser power and exposure time, we were able to construct the periodic air-holes or material-cylinders structures. Indeed, Fig. 3(a) and (b) show the periodic air-holes structures obtained with P_2-beam (total power of two beams)=1mW and t_ex (exposure time)=1 second for each exposure. When P_2-beam is fixed and t_ex is increased to two seconds (dose increases), the periodic material-cylinders structures were obtained, as shown in Fig. 3(c) for the case of square structure, for example. The results indicate that the multiple-exposure of two-beam interference pattern technique is an excellent way to fabrication large area 2D PCs. Employing triple-exposure at α=-60⁰, α=0⁰, and α=60⁰, respectively, we has also obtained periodic hexagonal 2D structures with circular dots (not shown), as predicted theoretically in Fig. 3(c), but the results were not repeated due to the difficulty of overlapping of three exposures as discussed above.

Following the multiple-exposure of two-beam interference, we approached the mask to the sample and exposed its by 5 seconds with the laser beam number 3. Our mask contains 3 lines defects (3 cm-length and 3 µm-width) and a Mach-Zehnder structure (1 cm-length, 3 µm-width, and 0.5 mm-separation between 2 branches). Both lines defects and Mach-Zehnder structure are well transferred from the mask to the periodic AZ structures. Figure 4 illustrates AFM pictures of periodical structures with a lattice constant of 3 µm (θ=3.1⁰) embedding well-defined line defects (the size of Mach-Zehnder is too large to be illustrated in the figure). In particular, by using the multiple-exposure of two-beam interference, we were able to control perfectly the orientation of the periodic 2D structures. With well-known orientation of the defects in the mask, we therefore could make the defects into the periodic structures in the desired directions. Indeed, Fig. 4(b) and (c) show the periodic square structures in which the lines defects are made at 0° and at 45° with respect to the orientation of square structures.

 

Fig. 4. AFM images of 2D periodic structures embedding defects. The exposure condition for periodic structures is same as in Fig. 3(a)–(b) and the defects are obtained with 5s-exposure time. In (b) and (c): the line defects are oriented at 0° and at 45° with respect to the direction of square structures, respectively.

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With this combination technique, the position and pattern of defects can be chosen as what we desire (point defect, waveguide, Mach-Zehnder, etc.) with the size varying from several micrometers to several centimeters. The feature size and the types of the periodic structures can be adjusted by changing exposure power or time and the rotation angle α. The lattice constant of the periodic structure can be decreased to a very small value by increasing the angle θ (with laser wavelength of 325 nm, the smallest period was theoretically predicted to be 162.5nm (λ/2)). We have experimentally fabricated the periodic structures with the period as small as 365 nm (θ=30°), as illustrated in Fig. 5. Note that we have also used a negative photoresist SU-8 (Microlithography Chemical Corp.) to make 2D structures embedding defects. Similar results are obtained with this photoresist but the defects are solidified-defects, such as rib waveguide, in place of air-defects as that obtained with AZ. The use of such positive AZ or negative SU-8 photoresists as templates materials depends on what techniques will be used to transfer these templates to high refractive index PCs. Indeed, if the electrodeposition technique [30] is employed to obtain high refractive index PCs waveguide, negative SU-8 photoresist is preferred. In contrast, if dry etching technique [31] is used, it is suitable to use positive AZ photoresist as template material.

 

Fig. 5. AFM images of 2D periodic structures. (a) large scale and (b) zoom in. The period of structure is equal to 365 nm (θ=30⁰).

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4. Conclusion

In conclusion, we have demonstrated both theoretically and experimentally a novel method to fabricate large-area photonic crystals templates with desired defects by use of the combination of multiple-exposure interference and mask-photolithography techniques. Multiple-exposure of two-beam interference pattern at 325 nm into a positive AZ or a negative SU-8 photopolymerizable photoresists has formed large-area (1cm×1cm) square and hexagonal two-dimensional periodic structures. Arbitrary defects were introduced in these structures by irradiating the sample with one beam of the same laser source through a mask. This combination method don’t need complicated pumping source and is very suitable for mass production of large-area periodic structures embedding arbitrary defects.