- Email: [email protected]
Fabrication of chiral channel in three-dimensional photonic crystal using projection microstereolithography
Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Fabrication of chiral channel in three-dimensional photonic crystal using projection microstereolithography
T
En-Tao Liang, Wei-Xing Zhang, Yi-Gui Chen, Han Shen, Fu-Li Zhao, Wen-Jie Chen, ⁎ Jian-Wen Dong School of Physics & State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou 510275, China
A R T IC LE I N F O
ABS TRA CT
Keywords: 3D printing Photonic crystals Topological photonics Micro-optics
Backscattering-immune propagation is one of the unique characteristics in topological photonic crystals. Such functionality can be realized by constructing a three-dimensional chiral channel in photonic crystals, of which the fabrication process cannot be compatible to complementary metal-oxide-semiconductor lithography. Here, we employed projection microstereolithography to fabricate a three-dimensional chiral channel surrounding in a photonic crystal template with the lattice constant of 462 μm. Both projected band structure and Poynting vector patterns of the three-dimensional chiral channel are numerically calculated. Our work provides a feasible way to fabricate a backscattering-immune waveguide in three-dimensional photonic crystals.
1. Introduction Topological photonics [1], a fascinating field inspired by the mathematics of conserved properties under continuous deformations, has attracted great interest. The edge states between two topologically-distinct media characterized by different topological invariants are guaranteed by bulk-edge correspondence. They suggest unique electromagnetic propagation that are potentially applicable in telecommunication and optical circuits. In the pioneering work, Haldane and Raghu first introduced the concept of topological states into photonic systems [2]. They theoretically proposed a photonic crystal made up of magneto-optic material to realize photonic quantum Hall phase. Soon after that Wang et al. experimentally observed the backscattering-immune transport of the photonic edge mode [3], which allows the electromagnetic (EM) wave to wrap around the scatter without backward reflection. This property helps to increase the fabrication tolerance of photonic devices and enables some exotic application such as cavity with arbitrary shape [4]. However, the realization of magnetic photonic crystal is a challenging work in optical regime because of the weak magneto-optics effect and the intrinsic loss of gyro-materials. Later, researchers have proposed several schemes to realize topological phases in timereversal invariant photonic systems, by employing either pseudo-spin [5] or valley degree of freedom [6]. They achieved the backscattering-immune transport experimentally in bianisotropic metamaterials [7], coupled resonators [8], and dielectric photonic crystals [9]. However, most of these schemes can only guide the electromagnetic wave in 2D plane. Besides, a chiral channel in the three-dimensional all-dielectric photonic crystal has been proposed to realize the backscattering-immune transport in three-dimensional space [10]. Since such kind of chiral channel is a three-dimensional structure with a subwavelength feature size, it is difficult to fabricate using conventional mask-based lithography. Approaches with the ability to produce complicated three-dimensional microstructures
⁎
Corresponding author. E-mail address: [email protected] (J.-W. Dong).
https://doi.org/10.1016/j.ijleo.2019.03.160 Received 22 November 2018; Accepted 31 March 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
E.-T. Liang, et al.
Fig. 1. Schematic illustration of the projection microstereolighography (PμSL) system and the fabricating process. (a) Projection microstereolithography setup. (b) Schematic diagram of the procedure for fabricating a sample with two layers of bars. A substrate is constructed and then the first and the second layer are built on the substrate, which is accomplished by movement of the translation stage.
should be developed to create the chiral channel. During these decades, three-dimensional printing techniques are expected to become revolutionary methods, which is known for building objects in a layer-by-layer way. These manufacturing technologies can be classified into two major categories according to their printing manners: serial and parallel. Among the former techniques, like direct laser writing [11] and fused deposition modeling [12], three-dimensional structures are fabricated in a line-by-line fashion. These processes show high flexibility to construct elaborate features and complex geometries. However, the serial processing scheme makes them time-consuming. The other types of technologies, such as holographic lithography [13], nanoimprint [14] and projection microstereolithography (PμSL) [15,16], work in a parallel way wherein a number of parts are made at the same time. Such procedures are more effective with a relatively few number of steps. PμSL is based on photon-induced polymerization and polymerizes each layer of an object in a single exposure. In such technology, a spatial light modulator is utilized as a dynamic mask for generation of desired optical patterns. Compared to holographic lithography and nanoimprint, PμSL faces fewer restrictions in geometries because of the flexibility of the mask. In 2014, Zheng et al. utilized PμSL to fabricate a kind of mechanical metamaterials with polymers, metals, or ceramics as architected materials [15]. More recently, Kirihara et al. proposed alumina photonic crystals with induced defects produced by such technique [17]. In this paper, we employed PμSL to fabricate a chiral channel in a woodpile photonic crystal of micron scale. The three-dimensional photonic crystal is constructed by stacking 13 layers of bars in the z-direction. A minimum line width of about 90 μm is achieved. Numerical simulations confirm the circular polarization gap, which enables the transport robustness of the channel mode. Besides, the relation between solidified depth and exposure time is experimentally studied as a quantitative guidance for fabrication. Our work suggests a potential way to realize three-dimensional topological photonic crystal in micron-scale.
2. Experimental procedure Fig. 1a depicts the experimental setup. The PμSL technology is based on a photo-polymerization reaction. Here an ultraviolet (UV) LED with wavelength of 405 nm is used as a source (M405L2, Thorlabs). An aspheric lens L1 and two biconvex lens (L2 and L3) are used for collimation. In the system an amplitude-only spatial light modulator (RL-SLM-T1, RealLight, Inc.) is employed as a dynamic mask. After the UV light passes through an aperture, two polarizers P1 and P2 help imaging by modulating the amplitude of the wave. Then the UV beam, loading the messages of a cross-section image of the object, is reflected by a mirror M1 and collected by a biconvex lens L4. Finally, the image of the SLM is projected onto the surface of a photo-curing resin (RP-405-YA01, Prismlab CHINA Ltd), which is the feedstock material of our system. A CCD camera is utilized to monitor the liquid resin surface in real time. When an image is projected, the imaging quality is captured by the CCD so that the imaging plane of L4 can be adjusted to the surface. In order to print a smooth layer of a sample, uniform intensity of a projected image is necessary, by homogenizing the light field before the SLM. As the LED emits an uneven field, we set the aperture behind L2 to realize a simple lowpass filtering, in which only low spatial frequencies are allowed to pass. According to Fourier optics [18], the local fluctuations of intensity distribution will be fuzzed, resulting in a more uniform light pattern. 1046
Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
E.-T. Liang, et al.
Fig. 2. Analysis on horizontal resolution and the relation between exposure energy E and curing depth d. (a) The optical micrograph of a sample with two beams and 8 pillars. A narrowest pillar (the first pillar on the left) shows a width of about 17.6 μm, indicating the horizontal resolution. (b) A relation between the curing thickness d and the exposure energy E. The exposure energy is expressed in a natural logarithmic form. The blue square dots are experimentally measured thicknesses and the red straight line is a linear fit of the data.
During the procedure, an object is constructed in a layer-by-layer fashion. While the UV pattern illuminates on the resin, the liquid-state polymer will solidify in the desired geometry. Then a translation stage (GTS70, Newport), on which the sample rests, is lowered by 90 μm, to be ready for the exposing of the next layer. The translation stage has a minimum step size of 0.1 μm and a travel range of 70 mm. Fig. 1b shows a schematic diagram of the fabricating process, taking a sample with two layers of bar as an example. Before the procedure, the imaging plane is first adjusted to the resin surface by the monitoring setup. Then the stage is totally submerged into the resin, and then raised by 90 μm below the surface of resin. After the disturbed free surface settles (in about 30 s), an image of a rectangle will be projected onto the resin surface. In this step a rectangular substrate is built for the purpose of reinforcing the bottom of the object, just showed in the first step in Fig. 1b. Then the stage moves downward by 90 μm and then the first layer of an object was printed on top of the first layer, as shown in the second step in Fig. 1b. By repeating these processes (the third step in Fig. 1b), the sample can be finally built up. After building an object in the resin, the residual liquid resin can be washed out using alcohol, without any other complicated processes.
3. Processing characterization Before using PμSL to fabricate three-dimensional structure, we need to survey the processing resolution and the exposure time of the system. With these parameters we can quantify the fabrication ability and avoid overexpose. We did a control experiment by fabricating a sample with two beams and several pillars to characterize the resolution. As shown in Fig. 2a, a list of pillars with different widths are made. These pillars are arranged in a horizontal plane and simultaneously fabricated in a single exposure. The widths are measured under an optical microscope and the minimum width is as small as 17.6 μm. Such line width is defined as the horizontal resolution of our system. On the other hand, to investigate the relation between curing depth of the resin and exposure, we measured the thicknesses of solidified layers with different exposure time, when the intensity I is a constant. Here, the averaged intensity is fixed at 0.692 mW/ cm2. The variation of curing depth d as a function of natural logarithm of exposure dosage E (E = I × t ) is depicted in Fig. 2b. To describe the dependence, a semi-empirical equation is used as a numerical model [19], yielding d = Dp ln(E / Ec ) , where Dp (μm) is the penetration depth and Ec (mJ/cm2) is the critical energy, which are both intrinsic parameters of the resin. It shows that d depends linearly on lnE. In our experiments, the curing depths (Fig. 2b, blue dots) with exposure energy from 2.768 mJ/cm2 to 7.612 mJ/cm2 are measured. Each dot is obtained by averaging the results of three different samples, and the red curve is a linear fitting of the dots. These results indicate that the polymerization depth is linearly proportional to the natural logarithm of exposure intensity, which is in good agreement with the numerical model. The relation provides an understanding of the curing process as well as a good quantitative guidance for the control of part thickness and geometries.
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Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
E.-T. Liang, et al.
Fig. 3. A woodpile photonic crystal with a chiral channel. (a) An overview of the woodpile photonic crystal composed of stacking bars with square cross-sections of a × a. The periods in the x–y plane is b. (b) Schematic view of the chiral channel, which is shown as a blue cuboid along the central axis of the woodpile structure, with width of b/2. (c) Top view of the template with a square area of 4 mm × 4 mm. The structure is composed of 10 periods in the x–y plane and 13 layers in the z-direction. (d) Magnified view of the template near the chiral channel.
4. Results Consider a template of three-dimensional woodpile photonic crystal [10], as shown in Fig. 3(a). The unit cell is constructed by four layers of bars (with square cross sections of a × a), stacking along the z direction, while the period in both x- and y- directions is b. Note that the ratio of a to b is equal to 0.3534. The bars on a layer are orthogonal to the ones in the adjacent layers. Fig. 3(b) shows the details of a line defect, where portions of the bars have been removed to construct a chiral channel (blue region). At the frequency regime of polarization gap, only left-handed circularly polarized (LCP) modes are allowed to propagate in such chiral channel, leading to robust transport [10]. The fabrication result is shown in Figs. 3(c) and 3(d), a template with a lateral size of 4 mm is fabricated using PμSL. Along the z-direction 13 layers of bars are stacked, with 10 paralleled bars per layer. The bar width a is 165 μm, and the in-plane periodicity b is 462 μm, leading to a/ b = 0.3571. A chiral channel is embedded in the middle of the structure with a width of 218 μm. We achieve a horizontal feature size of about 90 μm.
5. Discussions In order to achieve the complete photonic band gap and chiral guided mode, the polymer structure should be replaced by a highindex material. Using an inversion process mentioned in Ref.18, the chiral channel structure can be transferred into alumina structure. The dispersion of the chiral channel made of alumina is calculated in Fig. 4a by using a supercell configuration with the lateral size of 10b × 10b. Due to the chirality of the channel, the two LH-polarized bands (blue solid lines) and the two RH-polarized bands (red solid lines) split out and form an LH polarization gap from 235.9 to 245.3 GHz. Within this frequency range, the propagation of the guided mode is robust against isotropic scatterer [10]. Figs. 4b – 4e plot the time-averaged Pz field of an eigen mode in the polarization gap (denoted by red open circle in Fig. 4a). They correspond to four cut-planes at z= −3d/8, −d/8, d/8, 3d/8, respectively. It can be seen that most of the energy flows localize in the defect region, which reveals that this is a guided mode propagating along the channel. Although the sample we made has only 13 layers of bars (˜4 periods) stacked in the z-direction, the polarization gap can manifest itself for the alumina structure with this thickness. To confirm the effect of the polarization gap, we simulate the LH- and RH-transmission spectra for the alumina structure. The results are shown in Fig. 4f. It is found that RHtransmissions remains high while the LH-transmission nearly zero in the frequency regime of the polarization gap (highlighted by the cyan box). And the structure can support robust transport in this regime.
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Fig. 4. Polarization gap of the guided modes in the chiral channel. (a) Dispersion of the electromagnetic modes guided along the chiral line defect. Blue and red lines denote the left-handed (LH) and right-handed (RH) guided modes while the gray regions represent the projected bulk modes of the crystal. The cyan box highlights the LH polarization gap where exists only RH-polarized guided mode. (b–e) Pz components of the timeaveraged Poynting vector of the RH-polarized eigen mode [red open circle in (a)] in the polarization gap with k z = 0.5π / d and the frequency of 239.1 GHz at four different planes of z= −3d/8, − d/8, d/8, 3d/8, respectively. The energy flows of the guided mode localize inside the line defect. (f) Transmission spectra of the chiral channel with 13 layers of bars stacked in the z-direction when illuminated by an LH- or RH-polarized source. Low transmission in the LH spectra from 235.9 to 245.3 GHz is consistent with the predicted polarization gap in (a).
6. Conclusions We build up a projection microstereolithography system to fabricate three-dimensional photonic crystal templates in micronscale, which is difficult to achieve with conventional mask-based lithography. A three-dimensional woodpile photonic crystal is printed with a lateral feature size as small as 90 μm. A chiral channel with a width of 218 μm is constructed inside the photonic crystal. Simulations of the projected band structure and the eigen Poynting vector patterns of the chiral channel are performed. The numerical results prove that the structure supports robust transport when its architected material is replaced by high-index material. Our work provides a feasible way to realize complex three-dimensional photonic crystal templates in micron-scale at low cost, and pave the way for the realization of three-dimensional topological photonic devices. Acknowledgments This work was supported by National Natural Science Foundation of China (No.11761161002), Natural Science Foundation of Guangdong Province (No. 2018B030308005), Science and Technology Program of Guangzhou (No. 201804020029), and Fundamental Research Funds for the Central Universities (No. 16lgjc81). References [1] L. Lu, J.D. Joannopoulos, M. Soljačić, Topological photonics, Nat. Photonics 8 (2014) 821. [2] F.D. Haldane, S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett. 100 (2008) 013904. [3] Z. Wang, Y. Chong, J.D. Joannopoulos, M. Soljacic, Observation of unidirectional backscattering-immune topological electromagnetic states, Nature 461 (2009) 772. [4] Y. Akahane, T. Asano, B.-S. Song, S. Noda, High-Q photonic nanocavity in a two-dimensional photonic crystal, Nature 425 (2003) 944. [5] W.J. Chen, Z.Q. Zhang, J.W. Dong, C.T. Chan, Symmetry-protected transport in a pseudospin-polarized waveguide, Nat. Commun. 6 (2015) 8183. [6] J.W. Dong, X.D. Chen, H. Zhu, Y. Wang, X. Zhang, Valley photonic crystals for control of spin and topology, Nat. Mater. 16 (2017) 298. [7] A.B. Khanikaev, S.H. Mousavi, W.K. Tse, M. Kargarian, A.H. MacDonald, G. Shvets, Photonic topological insulators, Nat. Mater. 12 (2013) 233. [8] K. Fang, Z. Yu, S. Fan, Realizing effective magnetic field for photons by controlling the phase of dynamic modulation, Nat. Photonics 6 (2012) 782. [9] X.T. He, E.T. Liang, J.J. Yuan, H.Y. Qiu, X.D. Chen, F.L. Zhao, J.W. Dong, A Silicon-on-Insulator Slab for Topological Valley Transport, arXiv preprint arXiv:1805.10962 (2018). [10] W.J. Chen, Z.H. Hang, J.W. Dong, X. Xiao, H.Z. Wang, C.T. Chan, Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking, Phys. Rev. Lett. 107 (2011) 023901. [11] M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, C.M. Soukoulis, Direct laser writing of three-dimensional photonic-crystal templates for telecommunications, Nat. Mater. 3 (2004) 444. [12] I. Zein, D.W. Hutmacher, K.C. Tan, S.H. Teoh, Fused deposition modeling of novel scaffold architectures for tissue engineering applications, Biomaterials 23 (2002) 1169. [13] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Fabrication of photonic crystals for the visible spectrum by holographic lithography, Nature 404 (2000) 53. [14] L.J. Guo, Nanoimprint lithography: methods and material requirements, Adv. Mater. 19 (2007) 495. [15] X. Zheng, H. Lee, T.H. Weisgraber, M. Shusteff, J. DeOtte, E.B. Duoss, J.D. Kuntz, M.M. Biener, Q. Ge, J.A. Jackson, S.O. Kucheyev, N.X. Fang, C.M. Spadaccini,
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Ultralight, ultrastiff mechanical metamaterials, Science 344 (2014) 1373. [16] X. Zheng, J. Deotte, M.P. Alonso, G.R. Farquar, T.H. Weisgraber, S. Gemberling, H. Lee, N. Fang, C.M. Spadaccini, Design and optimization of a light-emitting diode projection micro-stereolithography three-dimensional manufacturing system, Rev. Sci. Instrum. 83 (2012) 125001. [17] S. Kirihara, T. Niki, Three-dimensional stereolithography of alumina photonic crystals for terahertz wave localization, Int. J. Appl. Ceram. Technol. 12 (2015) 32. [18] J. Goodman, M. Moeller, Introduction to fourier optics, McGraw-Hill Book Co Ltd (2004) ISBN:0974707724. [19] F.P. Melchels, J. Feijen, D.W. Grijpma, A review on stereolithography and its applications in biomedical engineering, Biomaterials 31 (2010) 6121.
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Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Fabrication of chiral channel in three-dimensional photonic crystal using projection microstereolithography
T
En-Tao Liang, Wei-Xing Zhang, Yi-Gui Chen, Han Shen, Fu-Li Zhao, Wen-Jie Chen, ⁎ Jian-Wen Dong School of Physics & State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou 510275, China
A R T IC LE I N F O
ABS TRA CT
Keywords: 3D printing Photonic crystals Topological photonics Micro-optics
Backscattering-immune propagation is one of the unique characteristics in topological photonic crystals. Such functionality can be realized by constructing a three-dimensional chiral channel in photonic crystals, of which the fabrication process cannot be compatible to complementary metal-oxide-semiconductor lithography. Here, we employed projection microstereolithography to fabricate a three-dimensional chiral channel surrounding in a photonic crystal template with the lattice constant of 462 μm. Both projected band structure and Poynting vector patterns of the three-dimensional chiral channel are numerically calculated. Our work provides a feasible way to fabricate a backscattering-immune waveguide in three-dimensional photonic crystals.
1. Introduction Topological photonics [1], a fascinating field inspired by the mathematics of conserved properties under continuous deformations, has attracted great interest. The edge states between two topologically-distinct media characterized by different topological invariants are guaranteed by bulk-edge correspondence. They suggest unique electromagnetic propagation that are potentially applicable in telecommunication and optical circuits. In the pioneering work, Haldane and Raghu first introduced the concept of topological states into photonic systems [2]. They theoretically proposed a photonic crystal made up of magneto-optic material to realize photonic quantum Hall phase. Soon after that Wang et al. experimentally observed the backscattering-immune transport of the photonic edge mode [3], which allows the electromagnetic (EM) wave to wrap around the scatter without backward reflection. This property helps to increase the fabrication tolerance of photonic devices and enables some exotic application such as cavity with arbitrary shape [4]. However, the realization of magnetic photonic crystal is a challenging work in optical regime because of the weak magneto-optics effect and the intrinsic loss of gyro-materials. Later, researchers have proposed several schemes to realize topological phases in timereversal invariant photonic systems, by employing either pseudo-spin [5] or valley degree of freedom [6]. They achieved the backscattering-immune transport experimentally in bianisotropic metamaterials [7], coupled resonators [8], and dielectric photonic crystals [9]. However, most of these schemes can only guide the electromagnetic wave in 2D plane. Besides, a chiral channel in the three-dimensional all-dielectric photonic crystal has been proposed to realize the backscattering-immune transport in three-dimensional space [10]. Since such kind of chiral channel is a three-dimensional structure with a subwavelength feature size, it is difficult to fabricate using conventional mask-based lithography. Approaches with the ability to produce complicated three-dimensional microstructures
⁎
Corresponding author. E-mail address: [email protected] (J.-W. Dong).
https://doi.org/10.1016/j.ijleo.2019.03.160 Received 22 November 2018; Accepted 31 March 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
E.-T. Liang, et al.
Fig. 1. Schematic illustration of the projection microstereolighography (PμSL) system and the fabricating process. (a) Projection microstereolithography setup. (b) Schematic diagram of the procedure for fabricating a sample with two layers of bars. A substrate is constructed and then the first and the second layer are built on the substrate, which is accomplished by movement of the translation stage.
should be developed to create the chiral channel. During these decades, three-dimensional printing techniques are expected to become revolutionary methods, which is known for building objects in a layer-by-layer way. These manufacturing technologies can be classified into two major categories according to their printing manners: serial and parallel. Among the former techniques, like direct laser writing [11] and fused deposition modeling [12], three-dimensional structures are fabricated in a line-by-line fashion. These processes show high flexibility to construct elaborate features and complex geometries. However, the serial processing scheme makes them time-consuming. The other types of technologies, such as holographic lithography [13], nanoimprint [14] and projection microstereolithography (PμSL) [15,16], work in a parallel way wherein a number of parts are made at the same time. Such procedures are more effective with a relatively few number of steps. PμSL is based on photon-induced polymerization and polymerizes each layer of an object in a single exposure. In such technology, a spatial light modulator is utilized as a dynamic mask for generation of desired optical patterns. Compared to holographic lithography and nanoimprint, PμSL faces fewer restrictions in geometries because of the flexibility of the mask. In 2014, Zheng et al. utilized PμSL to fabricate a kind of mechanical metamaterials with polymers, metals, or ceramics as architected materials [15]. More recently, Kirihara et al. proposed alumina photonic crystals with induced defects produced by such technique [17]. In this paper, we employed PμSL to fabricate a chiral channel in a woodpile photonic crystal of micron scale. The three-dimensional photonic crystal is constructed by stacking 13 layers of bars in the z-direction. A minimum line width of about 90 μm is achieved. Numerical simulations confirm the circular polarization gap, which enables the transport robustness of the channel mode. Besides, the relation between solidified depth and exposure time is experimentally studied as a quantitative guidance for fabrication. Our work suggests a potential way to realize three-dimensional topological photonic crystal in micron-scale.
2. Experimental procedure Fig. 1a depicts the experimental setup. The PμSL technology is based on a photo-polymerization reaction. Here an ultraviolet (UV) LED with wavelength of 405 nm is used as a source (M405L2, Thorlabs). An aspheric lens L1 and two biconvex lens (L2 and L3) are used for collimation. In the system an amplitude-only spatial light modulator (RL-SLM-T1, RealLight, Inc.) is employed as a dynamic mask. After the UV light passes through an aperture, two polarizers P1 and P2 help imaging by modulating the amplitude of the wave. Then the UV beam, loading the messages of a cross-section image of the object, is reflected by a mirror M1 and collected by a biconvex lens L4. Finally, the image of the SLM is projected onto the surface of a photo-curing resin (RP-405-YA01, Prismlab CHINA Ltd), which is the feedstock material of our system. A CCD camera is utilized to monitor the liquid resin surface in real time. When an image is projected, the imaging quality is captured by the CCD so that the imaging plane of L4 can be adjusted to the surface. In order to print a smooth layer of a sample, uniform intensity of a projected image is necessary, by homogenizing the light field before the SLM. As the LED emits an uneven field, we set the aperture behind L2 to realize a simple lowpass filtering, in which only low spatial frequencies are allowed to pass. According to Fourier optics [18], the local fluctuations of intensity distribution will be fuzzed, resulting in a more uniform light pattern. 1046
Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
E.-T. Liang, et al.
Fig. 2. Analysis on horizontal resolution and the relation between exposure energy E and curing depth d. (a) The optical micrograph of a sample with two beams and 8 pillars. A narrowest pillar (the first pillar on the left) shows a width of about 17.6 μm, indicating the horizontal resolution. (b) A relation between the curing thickness d and the exposure energy E. The exposure energy is expressed in a natural logarithmic form. The blue square dots are experimentally measured thicknesses and the red straight line is a linear fit of the data.
During the procedure, an object is constructed in a layer-by-layer fashion. While the UV pattern illuminates on the resin, the liquid-state polymer will solidify in the desired geometry. Then a translation stage (GTS70, Newport), on which the sample rests, is lowered by 90 μm, to be ready for the exposing of the next layer. The translation stage has a minimum step size of 0.1 μm and a travel range of 70 mm. Fig. 1b shows a schematic diagram of the fabricating process, taking a sample with two layers of bar as an example. Before the procedure, the imaging plane is first adjusted to the resin surface by the monitoring setup. Then the stage is totally submerged into the resin, and then raised by 90 μm below the surface of resin. After the disturbed free surface settles (in about 30 s), an image of a rectangle will be projected onto the resin surface. In this step a rectangular substrate is built for the purpose of reinforcing the bottom of the object, just showed in the first step in Fig. 1b. Then the stage moves downward by 90 μm and then the first layer of an object was printed on top of the first layer, as shown in the second step in Fig. 1b. By repeating these processes (the third step in Fig. 1b), the sample can be finally built up. After building an object in the resin, the residual liquid resin can be washed out using alcohol, without any other complicated processes.
3. Processing characterization Before using PμSL to fabricate three-dimensional structure, we need to survey the processing resolution and the exposure time of the system. With these parameters we can quantify the fabrication ability and avoid overexpose. We did a control experiment by fabricating a sample with two beams and several pillars to characterize the resolution. As shown in Fig. 2a, a list of pillars with different widths are made. These pillars are arranged in a horizontal plane and simultaneously fabricated in a single exposure. The widths are measured under an optical microscope and the minimum width is as small as 17.6 μm. Such line width is defined as the horizontal resolution of our system. On the other hand, to investigate the relation between curing depth of the resin and exposure, we measured the thicknesses of solidified layers with different exposure time, when the intensity I is a constant. Here, the averaged intensity is fixed at 0.692 mW/ cm2. The variation of curing depth d as a function of natural logarithm of exposure dosage E (E = I × t ) is depicted in Fig. 2b. To describe the dependence, a semi-empirical equation is used as a numerical model [19], yielding d = Dp ln(E / Ec ) , where Dp (μm) is the penetration depth and Ec (mJ/cm2) is the critical energy, which are both intrinsic parameters of the resin. It shows that d depends linearly on lnE. In our experiments, the curing depths (Fig. 2b, blue dots) with exposure energy from 2.768 mJ/cm2 to 7.612 mJ/cm2 are measured. Each dot is obtained by averaging the results of three different samples, and the red curve is a linear fitting of the dots. These results indicate that the polymerization depth is linearly proportional to the natural logarithm of exposure intensity, which is in good agreement with the numerical model. The relation provides an understanding of the curing process as well as a good quantitative guidance for the control of part thickness and geometries.
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Optik - International Journal for Light and Electron Optics 185 (2019) 1045–1050
E.-T. Liang, et al.
Fig. 3. A woodpile photonic crystal with a chiral channel. (a) An overview of the woodpile photonic crystal composed of stacking bars with square cross-sections of a × a. The periods in the x–y plane is b. (b) Schematic view of the chiral channel, which is shown as a blue cuboid along the central axis of the woodpile structure, with width of b/2. (c) Top view of the template with a square area of 4 mm × 4 mm. The structure is composed of 10 periods in the x–y plane and 13 layers in the z-direction. (d) Magnified view of the template near the chiral channel.
4. Results Consider a template of three-dimensional woodpile photonic crystal [10], as shown in Fig. 3(a). The unit cell is constructed by four layers of bars (with square cross sections of a × a), stacking along the z direction, while the period in both x- and y- directions is b. Note that the ratio of a to b is equal to 0.3534. The bars on a layer are orthogonal to the ones in the adjacent layers. Fig. 3(b) shows the details of a line defect, where portions of the bars have been removed to construct a chiral channel (blue region). At the frequency regime of polarization gap, only left-handed circularly polarized (LCP) modes are allowed to propagate in such chiral channel, leading to robust transport [10]. The fabrication result is shown in Figs. 3(c) and 3(d), a template with a lateral size of 4 mm is fabricated using PμSL. Along the z-direction 13 layers of bars are stacked, with 10 paralleled bars per layer. The bar width a is 165 μm, and the in-plane periodicity b is 462 μm, leading to a/ b = 0.3571. A chiral channel is embedded in the middle of the structure with a width of 218 μm. We achieve a horizontal feature size of about 90 μm.
5. Discussions In order to achieve the complete photonic band gap and chiral guided mode, the polymer structure should be replaced by a highindex material. Using an inversion process mentioned in Ref.18, the chiral channel structure can be transferred into alumina structure. The dispersion of the chiral channel made of alumina is calculated in Fig. 4a by using a supercell configuration with the lateral size of 10b × 10b. Due to the chirality of the channel, the two LH-polarized bands (blue solid lines) and the two RH-polarized bands (red solid lines) split out and form an LH polarization gap from 235.9 to 245.3 GHz. Within this frequency range, the propagation of the guided mode is robust against isotropic scatterer [10]. Figs. 4b – 4e plot the time-averaged Pz field of an eigen mode in the polarization gap (denoted by red open circle in Fig. 4a). They correspond to four cut-planes at z= −3d/8, −d/8, d/8, 3d/8, respectively. It can be seen that most of the energy flows localize in the defect region, which reveals that this is a guided mode propagating along the channel. Although the sample we made has only 13 layers of bars (˜4 periods) stacked in the z-direction, the polarization gap can manifest itself for the alumina structure with this thickness. To confirm the effect of the polarization gap, we simulate the LH- and RH-transmission spectra for the alumina structure. The results are shown in Fig. 4f. It is found that RHtransmissions remains high while the LH-transmission nearly zero in the frequency regime of the polarization gap (highlighted by the cyan box). And the structure can support robust transport in this regime.
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Fig. 4. Polarization gap of the guided modes in the chiral channel. (a) Dispersion of the electromagnetic modes guided along the chiral line defect. Blue and red lines denote the left-handed (LH) and right-handed (RH) guided modes while the gray regions represent the projected bulk modes of the crystal. The cyan box highlights the LH polarization gap where exists only RH-polarized guided mode. (b–e) Pz components of the timeaveraged Poynting vector of the RH-polarized eigen mode [red open circle in (a)] in the polarization gap with k z = 0.5π / d and the frequency of 239.1 GHz at four different planes of z= −3d/8, − d/8, d/8, 3d/8, respectively. The energy flows of the guided mode localize inside the line defect. (f) Transmission spectra of the chiral channel with 13 layers of bars stacked in the z-direction when illuminated by an LH- or RH-polarized source. Low transmission in the LH spectra from 235.9 to 245.3 GHz is consistent with the predicted polarization gap in (a).
6. Conclusions We build up a projection microstereolithography system to fabricate three-dimensional photonic crystal templates in micronscale, which is difficult to achieve with conventional mask-based lithography. A three-dimensional woodpile photonic crystal is printed with a lateral feature size as small as 90 μm. A chiral channel with a width of 218 μm is constructed inside the photonic crystal. Simulations of the projected band structure and the eigen Poynting vector patterns of the chiral channel are performed. The numerical results prove that the structure supports robust transport when its architected material is replaced by high-index material. Our work provides a feasible way to realize complex three-dimensional photonic crystal templates in micron-scale at low cost, and pave the way for the realization of three-dimensional topological photonic devices. Acknowledgments This work was supported by National Natural Science Foundation of China (No.11761161002), Natural Science Foundation of Guangdong Province (No. 2018B030308005), Science and Technology Program of Guangzhou (No. 201804020029), and Fundamental Research Funds for the Central Universities (No. 16lgjc81). References [1] L. Lu, J.D. Joannopoulos, M. Soljačić, Topological photonics, Nat. Photonics 8 (2014) 821. [2] F.D. Haldane, S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett. 100 (2008) 013904. [3] Z. Wang, Y. Chong, J.D. Joannopoulos, M. Soljacic, Observation of unidirectional backscattering-immune topological electromagnetic states, Nature 461 (2009) 772. [4] Y. Akahane, T. Asano, B.-S. Song, S. Noda, High-Q photonic nanocavity in a two-dimensional photonic crystal, Nature 425 (2003) 944. [5] W.J. Chen, Z.Q. Zhang, J.W. Dong, C.T. Chan, Symmetry-protected transport in a pseudospin-polarized waveguide, Nat. Commun. 6 (2015) 8183. [6] J.W. Dong, X.D. Chen, H. Zhu, Y. Wang, X. Zhang, Valley photonic crystals for control of spin and topology, Nat. Mater. 16 (2017) 298. [7] A.B. Khanikaev, S.H. Mousavi, W.K. Tse, M. Kargarian, A.H. MacDonald, G. Shvets, Photonic topological insulators, Nat. Mater. 12 (2013) 233. [8] K. Fang, Z. Yu, S. Fan, Realizing effective magnetic field for photons by controlling the phase of dynamic modulation, Nat. Photonics 6 (2012) 782. [9] X.T. He, E.T. Liang, J.J. Yuan, H.Y. Qiu, X.D. Chen, F.L. Zhao, J.W. Dong, A Silicon-on-Insulator Slab for Topological Valley Transport, arXiv preprint arXiv:1805.10962 (2018). [10] W.J. Chen, Z.H. Hang, J.W. Dong, X. Xiao, H.Z. Wang, C.T. Chan, Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking, Phys. Rev. Lett. 107 (2011) 023901. [11] M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, C.M. Soukoulis, Direct laser writing of three-dimensional photonic-crystal templates for telecommunications, Nat. Mater. 3 (2004) 444. [12] I. Zein, D.W. Hutmacher, K.C. Tan, S.H. Teoh, Fused deposition modeling of novel scaffold architectures for tissue engineering applications, Biomaterials 23 (2002) 1169. [13] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Fabrication of photonic crystals for the visible spectrum by holographic lithography, Nature 404 (2000) 53. [14] L.J. Guo, Nanoimprint lithography: methods and material requirements, Adv. Mater. 19 (2007) 495. [15] X. Zheng, H. Lee, T.H. Weisgraber, M. Shusteff, J. DeOtte, E.B. Duoss, J.D. Kuntz, M.M. Biener, Q. Ge, J.A. Jackson, S.O. Kucheyev, N.X. Fang, C.M. Spadaccini,
1049
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E.-T. Liang, et al.
Ultralight, ultrastiff mechanical metamaterials, Science 344 (2014) 1373. [16] X. Zheng, J. Deotte, M.P. Alonso, G.R. Farquar, T.H. Weisgraber, S. Gemberling, H. Lee, N. Fang, C.M. Spadaccini, Design and optimization of a light-emitting diode projection micro-stereolithography three-dimensional manufacturing system, Rev. Sci. Instrum. 83 (2012) 125001. [17] S. Kirihara, T. Niki, Three-dimensional stereolithography of alumina photonic crystals for terahertz wave localization, Int. J. Appl. Ceram. Technol. 12 (2015) 32. [18] J. Goodman, M. Moeller, Introduction to fourier optics, McGraw-Hill Book Co Ltd (2004) ISBN:0974707724. [19] F.P. Melchels, J. Feijen, D.W. Grijpma, A review on stereolithography and its applications in biomedical engineering, Biomaterials 31 (2010) 6121.
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