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Abstract
Custom acrylic multifaced pyramids were machined in-house and used to fabricate, in a single step, photonic crystals and quasicrystals on azobenzene molecular glass thin films with a surface area within the range of cm2. The obtained microcavity patterns have up to 8 -fold rotational symmetry depending on the number of pyramid faces used for laser inscription. The height of the resulting microcavities increases with the number of pyramid faces used and can even grow beyond the initial azobenzene film thickness. Furthermore, anisotropic and Moiré photonic structures were also fabricated upon changing the laser polarization and the number of exposures respectively.
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1. Introduction
Photonic crystals (PC) are interesting periodic dielectric structures that exhibit both rotational and translational symmetries and can have 2, 3, 4 or 6-fold rotational symmetries [1,2]. Any other rotational symmetry (such as 5, 7, 8 and above) lacks translational periodicity and therefore results in photonic quasicrystals (PQC), according to the crystallographic restriction theorem [3,4]. Due to the dependency of their properties to the order of symmetry [4–6], periodic and quasiperiodic photonic crystals have a wide range of applications in thin film coatings [7], plasmonic devices [8,9], sensors [10,11], laser resonators [12,13], SERS applications [14,15], waveguides [16,17] and advanced surfaces for antibacterial, superhydrophobic and cell growth applications [18–22]. To date, many different methods have been employed to create PCs and PQCs on photoresist materials, such as etching [23], multiple exposures with rotation [19,24–26], multiple beam interference lithography [19,25,27–31], direct laser processing [32,33], micro- and nanoimprinting [28,34–36], electron-beam lithography [14,37–39], focused-ion beam lithography [40], diffractive photo-masks and phase masks [41–43], prisms [44–51] and programmable spatial light modulators (SLM) [52,53]. However, on azobenzene materials, both intensity and polarization interference patterns can be used to create nano- and micro-scale surface patterns through a photomechanical trans-cis isomerization mechanism [54–58]. Due to this unique property, the fabrication of PCs and PQCs onto azobenzene films becomes natural since the creation of such complex structures can be achieved using a variety of techniques such as multiple laser exposures through sample rotation, multiple interfering beams or computer-generated holograms [56,59–68]. These techniques, although quite interesting, can be difficult to setup, time consuming to execute, increase the production costs and limit the complexity of the produced PCs and PQCs on azobenzene films. In addition, the fabrication of multiplexed 3D structures, metasurfaces, or Moiré patterns on azobenzene films using the aforementioned techniques requires several time-consuming and precisely well-adjusted steps which makes the fabrication procedure extremely low-throughput due to alignment errors as well as being limited to only small areas [55,56,69,70]. Therefore, there is a need to develop a straightforward all-optical single-step approach for the fabrication of azobenzene-based PCs and PQCs on a large area.
Regarding the photoresist materials, prisms have been used to fabricate PCs and PQCs in order to reduce the number of laser inscription steps [22,46,48–50,71–74]. In these studies, the prisms were used as photomasks in near-field interference lithography techniques which usually require the application of a matching fluid that may stain the film. Also, multi-exposure with prisms were used to generate PQCs on photoresists [22,46,48–50,71–74]. In case of azobenzene, only one report was found on the formation of PCs using a prism-based single-step far-field interference lithography technique [68]. In that paper, Wu et al. [68] used a 3-faced prism to inscribe PC patterns with 3-fold rotational symmetry on azobenzene polymer thin films. No reports were found on the single-step fabrication of PQCs on azobenzene materials. The increased research attention devoted to the development of PCs and PQCs on azobenzene materials requires a technique that can easily and quickly create surface patterns with a high order of symmetry. Therefore, we report for the first time on a universal single-step far-field pyramidal interference lithography (PIL) technique for the fabrication of PCs and PQCs on azobenzene molecular glass thin films. The proposed PIL technique is a high-throughput simple approach enabling the creation of large-area complex structures in the cm2 range within a short period of time in various periodicities ranging from the visible to the IR. Even though azobenzene molecular glass thin films were used in this paper, the presented technique herein can also be applied on any other photosensitive material, such as photoresists. Furthermore, we report for the first time on the inscription of anisotropic photonic crystals and quasicrystals on azobenzene upon changing the inscribing laser polarization. Finally, Moiré photonic crystals and quasicrystals were also fabricated using a double exposure to the laser interference pattern obtained from the multifaced acrylic pyramids.
2. Experimental method
Azobenzene molecular glass (gDR1) thin films were prepared by spin coating a 3 wt% solution of gDR1 in dichloromethane on clean Corning microscope slides followed by annealing at 80 °C; a procedure that is described in detail elsewhere [75]. The films had an average thickness of 300 nm as measured with a Bruker Dektak profilometer. A 532-nm Verdi V6 laser beam was circularly polarized using a quarter-wave plate, then passed through a spatial filter followed by a collimating lens to expand the beam to approximately 10 cm in diameter. The beam size was ultimately controlled with an adjustable iris positioned right before the acrylic pyramids, as illustrated in Fig. 1. Five different pyramids, with 2, 3, 4, 6 and 8 faces, were machined in-house from clear acrylic rods (n = 1.495) using a dividing head in a conventional milling machine and polished using a rotary lap in the same fixture that held it for machining. A 3-µm diamond paste was used for polishing the faces and the base of the pyramids. The angles between the faces and the base of the pyramids were set to be 10 degrees (α=10°) for this work, but they could have been fabricated with any other arbitrary angle, which would have resulted in different periodicity in the resulting photonic structures ranging from about 400 nm up to 31 µm. A typical 8-faced acrylic pyramid with α=10°, specially fabricated for this work, is also shown in Fig. 1.
The laser irradiance was set to 225 mW/cm2 throughout this experiment, unless otherwise noted. Each pyramid was used independently to create a surface pattern onto the azobenzene film. The used pyramid’s vertex was lined up with the center of the collimated beam, and the gDR1 thin film was placed so that the refracted beams from each pyramid face overlapped to create a full interference pattern on it. Various structures were fabricated using the different multifaced pyramids each in a single exposure step lasting 120 s, unless otherwise noted. The surface topography, morphology, modulation depths and pitch values of the resulting surface patterns were measured using a Bruker Dimension Edge atomic force microscope (AFM). A 10-mW He-Ne laser with a wavelength of 632.8 nm was used to produce diffraction patterns from the resulting structures on the azobenzene films and to confirm the resulting pitch values by measuring the angle between the 0 and ±1 diffraction orders (Λ=mλ⁄sinθ).
Normalized pyramidal interference patterns were simulated in Python. The electric field at a certain coordinate was modelled as a simple cosine function (Ex,y = E0cos(kz-ωt)). The physical geometry of the pyramid was used to assign a starting location with coordinates Ax,y on the pyramid for each interfering beam. The electric field was then calculated at every coordinate Bx,y on the gDR1 thin film surface using a translational distance z = d between coordinates Ax,y and Bx,y. The pyramid face dimensions and distance z = d were approximated as the simulations were only used to get an idea of the expected patterns as a function of the number of faces N and the pyramid angle. The total electric field at a certain coordinate Bx,y was determined by summing the electric fields of the N refracted beams on the gDR1 thin film. Then, the total field was squared and time averaged over one period to find the light irradiance at that particular point, which was then plotted as a normalized contour pattern. For Moiré pattern simulations, the coordinates Ax,y were rotated by the desired angle and the resulting irradiance pattern was added to the original simulation. Due to their photomechanical behavior, azobenzene chromophores migrate away from high light irradiance areas, therefore an inverse of the theoretical interference pattern was simulated to mimic the actual pattern that would be created on a gDR1 thin film [76].
3. Results and discussion
Right pyramids with regular bases and number of lateral faces of N = 2, N = 3, N = 4, N = 6 and N = 8 were fabricated for this study using acrylic rods as described above. Except for N = 2 which is similar to a Fresnel biprism, other pyramids have lateral triangular faces connecting at the apex point. A single 532-nm collimated and circularly polarized laser beam (225 mW/cm2) was incident normally on the pyramids with the specified number of faces (N) for 120 s. The laser light passed through the base of the pyramids and was refracted at the lateral faces creating N refracted beams with an angular offset equal to $\varphi = \frac{{360^\circ }}{N}\; $ that overlapped on the gDR1 thin film to create the interference patterns (Fig. 1). Figures 2(a-d) are AFM images of the structures formed in a single-step on different gDR1 thin films for N = 2 (Fig. 2(a)), N = 3 (Fig. 2(b)), N = 4 (Fig. 2(c)) and N = 6 (Fig. 2(d)). The resulting patterns are periodic photonic crystals (PCs) composed of cavity unit cells with both rotational and translational symmetries. The rotational symmetries are defined by the number of faces of the pyramids. For instance, N = 2 created 2-fold symmetry and N = 4 created a photonic crystal with 2 and 4-fold rotational symmetry (Figs. 2(a) and 2(c)). For, N = 3 and N = 6, the rotational symmetries are both 3 and 6-fold however the unit cells in each pattern are different (Figs. 2(b) and 2(d)). For N = 3 (Fig. 2(b)), the pattern is composed of attached hexagonal unit cells, arranged in a 2D honeycomb pattern while for N = 6 (Fig. 2(d)) the unit cells are separated hexagonal volcano shaped microcavities.
Fig. 2. The atomic force microscopy images of the photonic crystals formed using PIL with number of pyramid faces (N) equal to (a) 2, (b) 3, (c) 4 and (d) 6.
When N = 2, a one-dimensional surface relief grating (SRG) was obtained and its pitch value was calculated using Snell’s law and simple trigonometric formulas [46]:
where λ is the wavelength of the inscribing laser beam and n is the refractive index of the pyramid at the inscription wavelength. β is the angle of refraction through the faces of the pyramid, as shown in Fig. 1. To better understand the effect of the variables in Eqs. (1) and (2) on the resulting pitch value of the structures, the pitch value was plotted as a function of the angle between the faces and the base of the pyramids (α), refractive index of the pyramid (n) and the inscribing laser wavelength (λ), as seen in Fig. 3. For simplicity, the angles between the base and the lateral faces (α) of pyramids were chosen to be equal (i.e. right pyramid). However, mismatched α angles could have also been used to create oblique pyramids resulting in the formation of structures with different vectorial periodicities on azobenzene from visible to IR region.Fig. 3. Plots of the pitch values versus the angle between the faces and the base of the pyramid obtained using (Eqs. (1)) and (2).
Using Eqs. (1) and (2), for α=10°, the pitch value of the one-dimensional SRG is calculated to be approximately 3 µm which is confirmed by AFM image (Fig. 2(a)). With α=1°, the resulting one-dimensional SRG pattern had a pitch of approximately 31 µm, which is the highest value ever reported for a diffraction grating on an azobenzene thin film [77] (see Fig. S1(a)). In addition, when the gDR1 thin film is rotated off-normal with respect to the interference pattern created by the pyramid, the grating pitch value became even larger. At an incidence angle of approximately 75 degrees, a one-dimensional SRG was fabricated with a remarkable pitch value of 116 µm (see Fig. S1(b)). For N > 2, off-normal inscription resulted in the PC and PQC patterns with elongated microcavities (see Fig. S1(c)).
For N = 8, a photonic quasicrystal (PQC) forms (Fig. 4(a)) onto the azobenzene thin film which has 8-fold rotational symmetry and no translational symmetry. Note that any number of pyramid faces (such as 5, 7, 10 or above) could have been machined to produce PQC structures using the described single-step process. The simulated structure is shown in Fig. 4(b) matching the pattern obtained by PIL technique. Comparing AFM images in Fig. 2 and Fig. 4 show that by increasing the number of faces of the pyramids (N), the resulting surface patterns became deeper until they went beyond the entire thickness of the gDR1 film (i.e. ∼ 300 nm) for an 8-fold quasicrystal (Fig. 4(a)).
Fig. 4. (a) The atomic force microscopy image of a photonic quasicrystal formed using PIL with number of pyramid faces (N) equal to 8, (b) simulation of the pattern formed by 8-faced pyramid, (c) AFM image of the photonic quasicrystal with 8-fold symmetry transferred onto transparent epoxy thin film, (d) 3D AFM image of the photonic crystal with 4-fold symmetry transferred onto the transparent epoxy thin film.
The PC and PQC structures presented in this work are unique in terms of how they form in a single-step onto azobenzene thin films. For instance, the structures reported previously by multi-step exposures resulted in crossed [78], hexagonal [62] or more complex 3D [67] surface relief undulations. However, the patterns fabricated in this study using a single-step PIL technique are composed of microcavity unit cells instead of surface relief undulations. In other words, they are similar to negative-images of surface relief patterns. This is confirmed by transfer onto a thin transparent epoxy film. The AFM image in Fig. 4(c) shows the transferred 8-fold PQC pattern onto the epoxy film which is similar to the negative-image of Fig. 4(a). The AFM image in Fig. 4(d) is the transferred 4-fold PC pattern onto an epoxy film which is similar to crossed surface relief gratings reported previously fabricated by multi-step lithography techniques [79].
As seen in the AFM images in Figs. 5(a) and 5(b), a hexagonal PC was fabricated onto a gDR1 thin film using a laser irradiance of 165 mW/cm2, an exposure time of 200 s and a 6-faced pyramid. The pattern is composed of hexagonal volcano shaped microcavity unit cells with 6-fold rotational symmetry. When the laser exposure time was increased to 800 s, as seen in Figs. 5(c) and 5(d), the height of the hexagonal microscale unit cells increased from 163 nm to 452 nm, which is almost 1.5 times the initial gDR1 film thickness. Furthermore, the morphology of the unit cells became more distinct as they took the shape of microtubes arranged with a 6-fold symmetry. Similar structures were reported previously through multi-step nanoimprinting lithography and etchings [80]. In this work, however, hexagonally arranged microtubular cavities were made in a single-step procedure in only 800 s, compared to those more time-consuming procedures previously published [80]. Even more interestingly, randomly organized spontaneous nanostructures [81] appeared in-between and inside the microtubular patterns, as seen in Fig. 5(c) and the fast Fourier transform pattern in the inset of Fig. 5(d). Further studies are currently underway to understand the formation of these spontaneous nanostructures alongside with microscale patterns.
Fig. 5. 2D and 3D atomic force microscopy images showing the effect of laser exposure time on the morphology of a typical photonic crystal with 6-fold symmetry on gDR1 thin film. (a, b) after 200 s, (c,d) after 800 s.
Another advantage of using PIL to create PCs and PQCs on azobenzene is that the shape of the obtained unit cells can be manipulated by modifying the inscribing laser polarization. For instance, a PQC with 8-fold symmetry made with an 8-faced pyramid was fabricated at an irradiance of 165 mW/cm2 for 120 s using different light polarizations. Figures 6(a), 6(c) and 6(e) correspond to AFM images from circularly polarized, p-polarized and s-polarized laser beams respectively. The fast Fourier transforms of each PQC is seen in Figs. 6(b), 6(d) and 6(f).
Fig. 6. Atomic force microscopy images and the corresponding fast Fourier transform showing the effect of polarization of the inscription laser beam on morphology of the obtained PQCs using pyramid interference lithography. (a,b) circularly polarized, (c,d) p-polarized, (e,f) s-polarized beams.
It can be seen in Fig. 6 that the orientation and shape of the resulting microcavity unit cells are directly related to the inscription laser polarization. In Fig. 6(a) the morphology of the microcavity unit cells seems to be isotropic, however, in Figs. 6(c) and 6(e), they look perpendicular to the inscription laser polarization, hence forming anisotropic unit cells. As PQCs are already an anisotropic structure [82], this adds an extra order of anisotropy to the entire structure of the obtained PQC. In other words, all PQCs in Fig. 6 have an identical 8-fold rotational symmetry, however, since the shape and orientation of the individual microcavity unit cells change with the polarization of the laser beam, this gives each PQC an extra level of anisotropic characteristic. This effect is related to the photomechanical and polarization-dependent vectorial mass transport of azobenzene molecules as well as the dependence of the contrast of the interference patterns on the polarization of the inscription laser beam [57,83]. Note that for both PCs and PQCs with any degree of rotational symmetry, it is possible to create anisotropic crystallographic subgroups using this PIL technique. This leads to the development of novel optical devices having vectorial anisotropic properties.
So far, it has been shown that isotropic and anisotropic photonic crystals and quasicrystals can be fabricated on gDR1 thin films using a single-step pyramidal interference lithography (PIL) technique. However, multiple exposure of the azobenzene thin films by PIL technique could result in the formation of complex structures such as Moiré photonic crystals (MPC) and Moiré photonic quasicrystals (MPQC). As illustrated in Fig. 7(a), a double inscription of overlapped and tilted PC or PQC patterns creates Moiré structures. One could fabricate many different Moiré patterns by simply changing the angle of rotation or position of the secondary exposure [70]. The structure shown in the AFM image of Fig. 7(b) is formed by overlapping two PCs having 3-fold symmetry and with a sample tilted by θ=10° between the first and second exposures. The structure shown in Fig. 7(c) is the simulation of the obtained Moiré photonic crystal by overlapping two PCs with 3-fold symmetry with a sample tilted by θ=10° which is identical to the obtained pattern in Fig. 7(b). In addition, by overlapping two PQCs having 8-fold symmetry with a sample tilted by θ=10° between the first and second exposures, a MPQC with 8-fold symmetry was created. Figures 7(d) and 7(e) show the AFM image and its corresponding simulation respectively. More interestingly, when the film was tilted at an angle that was half of the angle of symmetry to perform the second exposure ($\theta = \frac{\varphi }{2}$), the rotational symmetry of the initial structure doubled. For instance, by overlapping two exposures from a 6-faced pyramid (i.e. two 6-fold PC) with a sample tilted by θ=30° (half of its rotational angle of symmetry) between the first and second exposures, a quasicrystal with 12-fold rotational symmetry was created (Figs. 7(f) and 7(g)). Note that these novel structures can be made on the centimeter scale in a relatively short period of time (see Fig.S2).
Fig. 7. Moiré photonic crystals and quasicrystals (MPC and MPQC). (a) schematic of the formation of a Moiré pattern with 4-fold symmetry. (b) AFM image of a MPC with 3-fold symmetry (θ=10°), (c) corresponding simulation of the MPC with 3-fold symmetry (θ=10°), (d) AFM image of a MPQC with 8-fold symmetry (θ=10°), (e) corresponding simulation of the MPQC with 8-fold symmetry (θ=10°), (f) AFM image of a MPQC with 12-fold symmetry (θ=30°), and (g) corresponding simulation of the MPQC with 12-fold symmetry (θ=30°).
4. Conclusion
In conclusion, a fast and single-step all-optical pyramidal interference lithography (PIL) technique is proposed for the fabrication of photonic crystals (PC), photonic quasicrystals (PQC), Moiré photonic crystals (MPC) and Moiré photonic quasicrystals (MPQC) onto azobenzene molecular glass thin films in a centimeter scale area and with periodicities ranging from 400 nm to 31 µm. The proposed method is based on using acrylic multifaced pyramids to create far-field laser interference patterns related to the number of pyramid faces. This approach simplifies the fabrication process of complex photonic structures on azobenzene thin films. Also, due to the exceptional photoactivity of azobenzene molecules, this technique was used to create anisotropic photonic structures.
Funding
Defence Research and Development Canada; Natural Sciences and Engineering Research Council of Canada (RGPIN-2020-03881).
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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