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Optically induced three-dimensional Penrose-type photonic quasicrystal lattices in iron-doped lithium niobate crystal
Optics Communications 322 (2014) 205–208
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Optically induced three-dimensional Penrose-type photonic quasicrystal lattices in iron-doped lithium niobate crystal Wentao Jin, Yan Ling Xue n Department of Communication Engineering, School of Information Science & Technology, East China Normal University, Shanghai 200241, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 31 October 2013 Received in revised form 24 February 2014 Accepted 24 February 2014 Available online 4 March 2014
Three-dimensional Penrose-type photonic quasicrystal lattices are optically induced inside an irondoped lithium niobate photorefractive crystal for the first time using a single multi-pinhole plate. The setup of this method is simple and compact dispense with complex optical adjustment system. Induced Penrose-type photonic quasicrystal lattices are analyzed and verified by plane wave guiding and far field diffraction pattern imaging. The quasicrystal microstructures can be maintained for a long time inside the crystal in a dark room. Other more complex three-dimensional photonic quasicrystal structures can be fabricated with this method by designing the multi-pinhole plate flexibly. & 2014 Elsevier B.V. All rights reserved.
Keywords: Quasicrystal structures Photonic lattices Three-dimensional Optically induced Photorefractive Lithium niobate crystal
1. Introduction Photonic crystals have been intensively studied due to the existence of photonic band gaps in the crystal. Their periodically varying refractive indices can prevent the propagation of optical waves with certain wavelengths [1,2]. Quasicrystals, first observed in Al–Mn metallic alloys, exhibit neither translation symmetry nor periodicity but possess a long-range order and orientational symmetry [3]. Exploiting the different properties of quasicrystals in the field of photonic crystals, a new class of material structures called photonic quasicrystals, has attracted a lot of attention in recent several years [4–6]. This new type of photonic crystal with quasiperiodic structure has high flexibility and tunability for defect modes. Similar to periodic photonic crystals, there exist optical band gaps in the photonic quasicrystals [7]. Many interesting photonic band gap properties of photonic quasicrystals have been found, for example, the complete band gaps can be obtained in the photonic quasicrystals with high-order symmetries even if the minimal index contrast is amazingly low [8,9]. Three-dimensional photonic microstructures have been proposed for many applications due to their capability of controlling wave propagation in all dimensions. Nevertheless, it is still a challenge to fabricate three-dimensional micro-scale quasicrystal structures in bulk media. Thus far, several sophisticated techniques n Corresponding author. Department of Communication Engineering, School of Information Science & Technology, East China Normal University, Shanghai 200241, PR China E-mail address: [email protected] (Y.L. Xue).
http://dx.doi.org/10.1016/j.optcom.2014.02.054 0030-4018 & 2014 Elsevier B.V. All rights reserved.
have been proposed to fabricate periodic photonic structures, such as e-beam direct writing, electro-chemical corrosion [10,11]. However, these typical fabrication techniques are not suitable for the fabrication of quasicrystal structures owing to the higher rotation symmetries, especially for three-dimensional photonic quasicrystals. The optical induction technique, a convenient method which adapts multi-beam interference in photorefractive material, has attracted much interest recently in fabricating optical microstructures such as photonic lattices [2,12]. Periodic or quasiperiodic microstructures can be induced optically in the photorefractive media at very low power levels ( micro watts) exploiting the anisotropic electro-optic properties of these materials [13–16]. Although the refractive index modulation in a photorefractive material is low, band gaps appearing in these materials have been demonstrated [2,12,17–19]. Up to now, most of the experimental investigations on optically induced quasiperiodic photonic structures in photorefractive material are reported in strontium barium niobate (SBN) crystal [20–23]. Nevertheless, the generation of nonlinear characteristics in SBN crystals demands a biased electric field externally. And the induced structures in SBN crystals are temporal and disappear after switching off the biased electric field. These limited their application. Iron-doped lithium niobate (LiNbO3:Fe) crystal is a type of photorefractive material different to SBN crystal. A negative refractive index change can be generated up to the order of 10–4–10–3 without the biased electric field [24,25]. The amount of index change is large enough to produce photonic microstructures. Most importantly, LiNbO3:Fe crystal has good characteristics of information storage. So induced photonic microstructures without
206
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any process can be maintained for several weeks in a dark room. Furthermore, after thermally fixing, the induced structures can be fixed in the crystal permanently [26]. However, to the best of our knowledge, there has been no report on the fabrication of threedimensional photonic quasicrystal lattices in lithium niobate crystals. With the increment of the symmetry, more beams are required to fabricate the quasicrystal structures. Conventional multi-beam interference needs a complicated optical setup to accomplish. Multi-beam interference by a single optical element can greatly reduce the complexity of the optics setup. In this paper, we report on experimental fabrication of three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal for the first time using a single multi-pinhole plate. The experimental setup of our method is very simple and stable which avoid antivibration equipment and complicated optical alignment system. Induced Penrose-type quasicrystal structures can exist stably for a long time due to the long dark storage time of LiNbO3:Fe crystals. This method can be flexibly extended to produce diverse complex photonic quasicrystal microstructures by designing the multipinhole plate appropriately. What is more, the experimental method is not limited to photorefractive materials alone. It can be easily well adapted to various photosensitive materials.
2. Experimental methods The schematic representation of the experimental setup to fabricate three-dimensional Penrose-type photonic quasicrystal lattices by a multi-pinhole plate is shown in Fig. 1(a). In beam path a, a continuous-wave (CW) laser is with 532 nm wavelength and 100 mW power. The expanded and collimated laser beam illuminates a multi-pinhole plate. The multi-pinhole plate is placed close to the collimation lens, and both of them are fixed on the same base. This can enhance the mechanical stability of the
optical setup. The pinholes in the multi-pinhole plate can be seen as several coherent point sources. The beams emitted from these pinholes passes through a Fourier-transform lens. Due to twodimensional Fourier transform, these beams interfere in the vicinity of the back focal plane of the Fourier transform lens, as approximate plane waves. The desired interference intensity patterns can be projected into a LiNbO3: Fe crystal (with dimensions of 11 mm 11 mm 4 mm and dopants of 0.03 wt% Fe). So an x-pinhole plate can create the interference of x beams. We can generate diverse quasiperiodic multi-beam interferences using different multi-pinhole plates. Beam path b is used for the plane wave guiding imaging to analyze the three-dimensional Penrosetype photonic quasicrystal lattices. The He–Ne laser is linearly polarized parallel to the c-axis of the crystal (e-polarized), as a probe beam. The e-polarized beam has a striking refractive index contrast due to the higher relevant electro-optical coefficient [12,17]. An imaging lens placed behind the crystal formed an image of the input or output planes on a CCD. Here, we generate the (5 þ1) beams interference by a six-pinhole plate, as shown in Fig. 1(b), and get three-dimensional quasicrystal lattice wave which can induce three-dimensional Penrose-type quasicrystal lattice structures in a LiNbO3:Fe crystal. The diameter of the six pinholes is 0.7 mm. The spacing between adjacent pinholes on the regular pentagon is 14.0 mm. The geometric layout of the (5 þ1) beams is a normally incident central beam surrounded by angularly displaced five side beams [27], as shown in Fig. 1(c). The angles between the central beam and the side beams depend on the spacing of these pinholes and the focal length of Fourier transform lens. The given quasicrystal lattice wave propagates along the direction of þz axis. The computer simulated intensity distribution of interference patterns by (5 þ1) beams for threedimensional Penrose-type quasicrystal lattices are given in Fig. 1 (d) and (e). The photorefractive effect describes the change in the local refractive index of a medium as a result of an optically induced
Fig. 1. (a) Schematic of the experimental setup for the fabrication and analysis of the three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal. λ/2, half-wave plate; LN, LiNbO3:Fe crystal. (b) The six-pinhole plate. (c) The (5 þ1) beams configuration: the central beam (k1) is along the axis of a cone with apex angle; the five side beams (k2–k6) are equally distributed on the cone. (d) Computer simulated interference intensity distribution of (5 þ1) beam interference in the x–y plane. (e) Simulated interference intensity distribution of three-dimensional Penrose-type quasicrystal lattices.
W. Jin, Y.L. Xue / Optics Communications 322 (2014) 205–208
redistribution of charge carriers [2]. Dope iron element into lithium niobate crystal can improve its photorefractive sensitivity markedly. Under illumination with light of appropriate wavelength, the internal charge carriers (holes and electrons) of LiNbO3:Fe crystal are excited into the conduction band via photoionization. The charges in the conduction band then move under the influence of diffusion, drift or the photovoltaic effect and finally are re-captured inside the crystal. This recombination process builds up a static space charge field that produces a refractive-index change via the Pockels effect. Therefore, the photonic structures are formed inside the LiNbO3:Fe crystal. In this process, Fe3 þ provides holes and Fe2 þ provides electrons. The photorefractive process can be seen as the conversion process Fe2 þ 2Fe3 þ þe with the assistance of the photons. Thus, the refractive index modulation in the crystal is caused by the redistributed Fe2 þ and Fe3 þ according to the spatial modulation of light intensity [13].
3. Experimental results Typical experimental results of optically induced threedimensional Penrose-type photonic quasicrystal lattices in a LiNbO3:Fe crystal are shown in Fig. 2. Fig. 2(a) is the intensity pattern of the quasicrystal lattice wave which is captured at the front surface of the crystal initially (in the x–y plane). Induced Penrose-type quasicrystal structures are probed by means of an epolarized plane wave. Fig. 2(b) shows the guided wave intensity images of induced Penrose-type photonic quasicrystal lattices (in the x–y and y–z planes). Three-dimensional Penrose-type quasicrystal lattice structures in the crystal can be viewed clearly, similar to the numerical simulation in Fig. 1(d) and (e). These prove that we have successfully fabricated three-dimensional quasicrystal lattices in the LiNbO3:Fe crystal. Both of the scale
207
bars equal 9 μm. According to measurement, the effective size of induced quasicrystal lattice structures along the direction of the þz axis inside the crystal is 0.8 mm. An important experimental tool for analyzing the induced quasicrystal lattice structures is the far-field diffraction pattern [28]. We let each of the beams produced from pinholes in the sixpinhole plate illuminates the induced quasicrystal lattice structures separately so that the quasicrystal lattice structures are illuminated by some approximate plane waves from the different incidence direction. We then obtain a series of far-field diffraction patterns as shown in Fig. 2(c)–(g). These far field diffraction patterns are exactly alike. Each of these far-field diffraction patterns is formed by the six pronounced diffraction peaks. They are similar to the distribution of pinholes in the six-pinhole plate in Fig. 1(b). According to Fourier transformation, the induced lattice structures have similar spatial frequency components with the quasicrystal lattice wave. In other words, the induced lattice structures also has a three-dimensional Penrose-type quasiperiodic structures. So the far-field diffraction patterns also prove the formation of the three-dimensional Penrose-type quasicrystal lattice structures inside the LiNbO3:Fe crystal. The dark conductivity of LiNbO3:Fe crystal is very low, so the induced quasicrystal structures can be stored in LiNbO3:Fe crystal for a long time in a dark room. We put induced photonic quasicrystal lattices in a dark room and read out again by the plane wave after four weeks. The Penrose-type quasicrystal lattice structures in the crystal are still comparatively clear [in Fig. 2(h)]. After thermally fixing, the induced structures can be fixed in the crystal permanently [26]. Moreover, the induced structure can also be erased by the flush of white light, so that new patterns can be again recorded in the crystal. It is easy to control the quasiperiodic scale of induced threedimensional Penrose-type quasicrystal lattices by changing the focal length of Fourier transform lens or adjusting the spacing of
Fig. 2. The induced three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal. (a) The intensity pattern of the quasicrystal lattice wave which is captured at the front surface of the crystal initially (in the x–y plane). (b) Recorded images of x–y plane of the three-dimensional Penrose-type photonic quasicrystal lattices are induced in the crystal. The recorded images of a portion of the y–z plane of the structures, containing a region near to the propagation axis, are shown in the inset. Both of the scale bars equal 9 μm. (c) Far-field diffraction pattern of the Penrose-type quasicrystal lattices illuminated by the central beam. (d)–(g) Far-field diffraction patterns of induced quasicrystal lattices illuminated by different side beams, respectively. (h) Image of induced Penrose-type quasicrystal lattices structures after storing in a dark room for four weeks.
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the pinholes in the multi-pinhole plate. Moreover, with this method we can freely change the number of pinholes to fabricate much more complex three-dimensional quasicrystal microstructures in the photorefractive crystals. For example, we can generate the interference of (12 þ1) beams by a multi-pinhole plate with thirteen pinholes. In doing so, we can fabricate three-dimensional 12-fold symmetry quasicrystal lattices which are similar to the microstructures in the literature [29].
4. Conclusions In summary, we experimentally demonstrate a convenient approach to fabricate three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal using a multi-pinhole plate. The setup of this method is very stable and flexible. Induced three-dimensional Penrose-type photonic quasicrystal lattices are analyzed and proved by different experimental tools. Induced quasicrystal lattice structures can exist inside the crystal stably for a long time in a dark room. This method can be easily extended to produce more complex three-dimensional quasicrystal microstructures by designing the multi-pinhole plate appropriately. These three-dimensional photonic quasicrystal lattices may serve as a test-bed for studies of band gaps phenomena in threedimensional quasiperiodic lattice systems.
Acknowledgments The authors gratefully acknowledge the support from National Basic Research Program of China (973 Program) under Grant no. 2011CB921604 and the National Natural Science Foundation of China under Grant no. 11234003.
References [1] Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic, San Diego, 2003. [2] B. Terhalle, Controlling Light in Optically Induced Photonic Lattices, Springer, Berlin, 2011. [3] C. Janot, Quasicrystals: A Primer, Clarendon, Oxford, 1994. [4] M.A. Kaliteevski, S. Brand, R.A. Abram, T.F. Krauss, R.D. Rue, P. Millar, Nanotechnology 11 (2000) 274. [5] X. Wang, C.Y. Ng, W.Y. Tam, C.T. Chan, P. Sheng, Adv. Mater. 15 (2003) 1526. [6] M. Peach, Mater. Today 9 (2006) 44. [7] S.S.M. Cheng, L. Li, C.T. Chan, Z.Q. Zhang, Phys. Rev. B 59 (1999) 4091. [8] M.E. Zoorob, M.D.B. Charlton, G.J. Parker, J.J. Baumberg, M.C. Netti, Nature 404 (2000) 740. [9] W. Man, M. Megens, P.J. Steinhardt, P.M. Chaikin, Nature 436 (2005) 993. [10] M.D. Vittorio, M.T. Todaroa, T. Stomeo, R. Cingolani, D. Cojoc, E.D. Fabrizio, Microelectron. Eng. 73–74 (2004) 388. [11] A. Birner, U. Grüning, S. Ottow, A. Schneider, F. Müller, V. Lehmann, H. Föll, U. Gösele, Phys. Status Solidi A 165 (1998) 111. [12] J.W. Fleischer, M. Segev, N.K. Efremidis, D.N. Christodoulides, Nature 422 (2003) 147. [13] W. Jin, Y. Gao, Opt. Mater. 34 (2011) 143. [14] W. Jin, Y. Gao, Opt. Commun. 284 (2011) 5814. [15] W. Jin, Y. Gao, Superlattices Microstruct. 51 (2012) 114. [16] W. Jin, Y. Gao, Appl. Phys. Lett. 101 (2012) 141104. [17] J.W. Fleischer, T. Carmon, M. Segev, N.K. Efremidis, D.N. Christodoulides, Phys. Rev. Lett. 90 (2003) 023902. [18] D.N. Christodoulides, F. Lederer, Y. Silberberg, Nature 424 (2003) 817. [19] H. Martin, E.D. Eugenieva, Z. Chen, D.N. Christodoulides, Phys. Rev. Lett. 92 (2004) 123902. [20] B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D.N. Christodoulides, J.W. Fleischer, Nature 440 (2006) 1166. [21] B. Freedman, R. Lifshitz, J.W. Fleischer, M. Segev, Nat. Mater. 6 (2007) 776. [22] G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, G. Abbate, Opt. Express 16 (2008) 5164. [23] J. Xavier, M. Boguslawski, P. Rose, J. Joseph, C. Denz, Adv. Mater. 22 (2010) 356. [24] F. Chen, M. Stepic, C.E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, M. Segev, Opt. Express 13 (2005) 4314. [25] T. Song, S.M. Liu, R. Guo, Z.H. Liu, N. Zhu, Y.M. Gao, Opt. Express 14 (2006) 1924. [26] J.J. Amodei, D.L. Staebler, Appl. Phys. Lett. 18 (1971) 540. [27] A. Harb, F. Torres, K. Ohlinger, Y.K. Lin, K. Lozano, D. Xu, K.P. Chen, Opt. Express 18 (2010) 20512. [28] X.H. Sun, X.M. Tao, T.J. Ye, P. Xue, Y.-S. Szeto, Appl. Phys. B 87 (2007) 65. [29] N.D. Lai, J.H. Lin, Y.Y. Huang, C.C. Hsu, Opt. Express 14 (2006) 10746.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Optically induced three-dimensional Penrose-type photonic quasicrystal lattices in iron-doped lithium niobate crystal Wentao Jin, Yan Ling Xue n Department of Communication Engineering, School of Information Science & Technology, East China Normal University, Shanghai 200241, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 31 October 2013 Received in revised form 24 February 2014 Accepted 24 February 2014 Available online 4 March 2014
Three-dimensional Penrose-type photonic quasicrystal lattices are optically induced inside an irondoped lithium niobate photorefractive crystal for the first time using a single multi-pinhole plate. The setup of this method is simple and compact dispense with complex optical adjustment system. Induced Penrose-type photonic quasicrystal lattices are analyzed and verified by plane wave guiding and far field diffraction pattern imaging. The quasicrystal microstructures can be maintained for a long time inside the crystal in a dark room. Other more complex three-dimensional photonic quasicrystal structures can be fabricated with this method by designing the multi-pinhole plate flexibly. & 2014 Elsevier B.V. All rights reserved.
Keywords: Quasicrystal structures Photonic lattices Three-dimensional Optically induced Photorefractive Lithium niobate crystal
1. Introduction Photonic crystals have been intensively studied due to the existence of photonic band gaps in the crystal. Their periodically varying refractive indices can prevent the propagation of optical waves with certain wavelengths [1,2]. Quasicrystals, first observed in Al–Mn metallic alloys, exhibit neither translation symmetry nor periodicity but possess a long-range order and orientational symmetry [3]. Exploiting the different properties of quasicrystals in the field of photonic crystals, a new class of material structures called photonic quasicrystals, has attracted a lot of attention in recent several years [4–6]. This new type of photonic crystal with quasiperiodic structure has high flexibility and tunability for defect modes. Similar to periodic photonic crystals, there exist optical band gaps in the photonic quasicrystals [7]. Many interesting photonic band gap properties of photonic quasicrystals have been found, for example, the complete band gaps can be obtained in the photonic quasicrystals with high-order symmetries even if the minimal index contrast is amazingly low [8,9]. Three-dimensional photonic microstructures have been proposed for many applications due to their capability of controlling wave propagation in all dimensions. Nevertheless, it is still a challenge to fabricate three-dimensional micro-scale quasicrystal structures in bulk media. Thus far, several sophisticated techniques n Corresponding author. Department of Communication Engineering, School of Information Science & Technology, East China Normal University, Shanghai 200241, PR China E-mail address: [email protected] (Y.L. Xue).
http://dx.doi.org/10.1016/j.optcom.2014.02.054 0030-4018 & 2014 Elsevier B.V. All rights reserved.
have been proposed to fabricate periodic photonic structures, such as e-beam direct writing, electro-chemical corrosion [10,11]. However, these typical fabrication techniques are not suitable for the fabrication of quasicrystal structures owing to the higher rotation symmetries, especially for three-dimensional photonic quasicrystals. The optical induction technique, a convenient method which adapts multi-beam interference in photorefractive material, has attracted much interest recently in fabricating optical microstructures such as photonic lattices [2,12]. Periodic or quasiperiodic microstructures can be induced optically in the photorefractive media at very low power levels ( micro watts) exploiting the anisotropic electro-optic properties of these materials [13–16]. Although the refractive index modulation in a photorefractive material is low, band gaps appearing in these materials have been demonstrated [2,12,17–19]. Up to now, most of the experimental investigations on optically induced quasiperiodic photonic structures in photorefractive material are reported in strontium barium niobate (SBN) crystal [20–23]. Nevertheless, the generation of nonlinear characteristics in SBN crystals demands a biased electric field externally. And the induced structures in SBN crystals are temporal and disappear after switching off the biased electric field. These limited their application. Iron-doped lithium niobate (LiNbO3:Fe) crystal is a type of photorefractive material different to SBN crystal. A negative refractive index change can be generated up to the order of 10–4–10–3 without the biased electric field [24,25]. The amount of index change is large enough to produce photonic microstructures. Most importantly, LiNbO3:Fe crystal has good characteristics of information storage. So induced photonic microstructures without
206
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any process can be maintained for several weeks in a dark room. Furthermore, after thermally fixing, the induced structures can be fixed in the crystal permanently [26]. However, to the best of our knowledge, there has been no report on the fabrication of threedimensional photonic quasicrystal lattices in lithium niobate crystals. With the increment of the symmetry, more beams are required to fabricate the quasicrystal structures. Conventional multi-beam interference needs a complicated optical setup to accomplish. Multi-beam interference by a single optical element can greatly reduce the complexity of the optics setup. In this paper, we report on experimental fabrication of three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal for the first time using a single multi-pinhole plate. The experimental setup of our method is very simple and stable which avoid antivibration equipment and complicated optical alignment system. Induced Penrose-type quasicrystal structures can exist stably for a long time due to the long dark storage time of LiNbO3:Fe crystals. This method can be flexibly extended to produce diverse complex photonic quasicrystal microstructures by designing the multipinhole plate appropriately. What is more, the experimental method is not limited to photorefractive materials alone. It can be easily well adapted to various photosensitive materials.
2. Experimental methods The schematic representation of the experimental setup to fabricate three-dimensional Penrose-type photonic quasicrystal lattices by a multi-pinhole plate is shown in Fig. 1(a). In beam path a, a continuous-wave (CW) laser is with 532 nm wavelength and 100 mW power. The expanded and collimated laser beam illuminates a multi-pinhole plate. The multi-pinhole plate is placed close to the collimation lens, and both of them are fixed on the same base. This can enhance the mechanical stability of the
optical setup. The pinholes in the multi-pinhole plate can be seen as several coherent point sources. The beams emitted from these pinholes passes through a Fourier-transform lens. Due to twodimensional Fourier transform, these beams interfere in the vicinity of the back focal plane of the Fourier transform lens, as approximate plane waves. The desired interference intensity patterns can be projected into a LiNbO3: Fe crystal (with dimensions of 11 mm 11 mm 4 mm and dopants of 0.03 wt% Fe). So an x-pinhole plate can create the interference of x beams. We can generate diverse quasiperiodic multi-beam interferences using different multi-pinhole plates. Beam path b is used for the plane wave guiding imaging to analyze the three-dimensional Penrosetype photonic quasicrystal lattices. The He–Ne laser is linearly polarized parallel to the c-axis of the crystal (e-polarized), as a probe beam. The e-polarized beam has a striking refractive index contrast due to the higher relevant electro-optical coefficient [12,17]. An imaging lens placed behind the crystal formed an image of the input or output planes on a CCD. Here, we generate the (5 þ1) beams interference by a six-pinhole plate, as shown in Fig. 1(b), and get three-dimensional quasicrystal lattice wave which can induce three-dimensional Penrose-type quasicrystal lattice structures in a LiNbO3:Fe crystal. The diameter of the six pinholes is 0.7 mm. The spacing between adjacent pinholes on the regular pentagon is 14.0 mm. The geometric layout of the (5 þ1) beams is a normally incident central beam surrounded by angularly displaced five side beams [27], as shown in Fig. 1(c). The angles between the central beam and the side beams depend on the spacing of these pinholes and the focal length of Fourier transform lens. The given quasicrystal lattice wave propagates along the direction of þz axis. The computer simulated intensity distribution of interference patterns by (5 þ1) beams for threedimensional Penrose-type quasicrystal lattices are given in Fig. 1 (d) and (e). The photorefractive effect describes the change in the local refractive index of a medium as a result of an optically induced
Fig. 1. (a) Schematic of the experimental setup for the fabrication and analysis of the three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal. λ/2, half-wave plate; LN, LiNbO3:Fe crystal. (b) The six-pinhole plate. (c) The (5 þ1) beams configuration: the central beam (k1) is along the axis of a cone with apex angle; the five side beams (k2–k6) are equally distributed on the cone. (d) Computer simulated interference intensity distribution of (5 þ1) beam interference in the x–y plane. (e) Simulated interference intensity distribution of three-dimensional Penrose-type quasicrystal lattices.
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redistribution of charge carriers [2]. Dope iron element into lithium niobate crystal can improve its photorefractive sensitivity markedly. Under illumination with light of appropriate wavelength, the internal charge carriers (holes and electrons) of LiNbO3:Fe crystal are excited into the conduction band via photoionization. The charges in the conduction band then move under the influence of diffusion, drift or the photovoltaic effect and finally are re-captured inside the crystal. This recombination process builds up a static space charge field that produces a refractive-index change via the Pockels effect. Therefore, the photonic structures are formed inside the LiNbO3:Fe crystal. In this process, Fe3 þ provides holes and Fe2 þ provides electrons. The photorefractive process can be seen as the conversion process Fe2 þ 2Fe3 þ þe with the assistance of the photons. Thus, the refractive index modulation in the crystal is caused by the redistributed Fe2 þ and Fe3 þ according to the spatial modulation of light intensity [13].
3. Experimental results Typical experimental results of optically induced threedimensional Penrose-type photonic quasicrystal lattices in a LiNbO3:Fe crystal are shown in Fig. 2. Fig. 2(a) is the intensity pattern of the quasicrystal lattice wave which is captured at the front surface of the crystal initially (in the x–y plane). Induced Penrose-type quasicrystal structures are probed by means of an epolarized plane wave. Fig. 2(b) shows the guided wave intensity images of induced Penrose-type photonic quasicrystal lattices (in the x–y and y–z planes). Three-dimensional Penrose-type quasicrystal lattice structures in the crystal can be viewed clearly, similar to the numerical simulation in Fig. 1(d) and (e). These prove that we have successfully fabricated three-dimensional quasicrystal lattices in the LiNbO3:Fe crystal. Both of the scale
207
bars equal 9 μm. According to measurement, the effective size of induced quasicrystal lattice structures along the direction of the þz axis inside the crystal is 0.8 mm. An important experimental tool for analyzing the induced quasicrystal lattice structures is the far-field diffraction pattern [28]. We let each of the beams produced from pinholes in the sixpinhole plate illuminates the induced quasicrystal lattice structures separately so that the quasicrystal lattice structures are illuminated by some approximate plane waves from the different incidence direction. We then obtain a series of far-field diffraction patterns as shown in Fig. 2(c)–(g). These far field diffraction patterns are exactly alike. Each of these far-field diffraction patterns is formed by the six pronounced diffraction peaks. They are similar to the distribution of pinholes in the six-pinhole plate in Fig. 1(b). According to Fourier transformation, the induced lattice structures have similar spatial frequency components with the quasicrystal lattice wave. In other words, the induced lattice structures also has a three-dimensional Penrose-type quasiperiodic structures. So the far-field diffraction patterns also prove the formation of the three-dimensional Penrose-type quasicrystal lattice structures inside the LiNbO3:Fe crystal. The dark conductivity of LiNbO3:Fe crystal is very low, so the induced quasicrystal structures can be stored in LiNbO3:Fe crystal for a long time in a dark room. We put induced photonic quasicrystal lattices in a dark room and read out again by the plane wave after four weeks. The Penrose-type quasicrystal lattice structures in the crystal are still comparatively clear [in Fig. 2(h)]. After thermally fixing, the induced structures can be fixed in the crystal permanently [26]. Moreover, the induced structure can also be erased by the flush of white light, so that new patterns can be again recorded in the crystal. It is easy to control the quasiperiodic scale of induced threedimensional Penrose-type quasicrystal lattices by changing the focal length of Fourier transform lens or adjusting the spacing of
Fig. 2. The induced three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal. (a) The intensity pattern of the quasicrystal lattice wave which is captured at the front surface of the crystal initially (in the x–y plane). (b) Recorded images of x–y plane of the three-dimensional Penrose-type photonic quasicrystal lattices are induced in the crystal. The recorded images of a portion of the y–z plane of the structures, containing a region near to the propagation axis, are shown in the inset. Both of the scale bars equal 9 μm. (c) Far-field diffraction pattern of the Penrose-type quasicrystal lattices illuminated by the central beam. (d)–(g) Far-field diffraction patterns of induced quasicrystal lattices illuminated by different side beams, respectively. (h) Image of induced Penrose-type quasicrystal lattices structures after storing in a dark room for four weeks.
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W. Jin, Y.L. Xue / Optics Communications 322 (2014) 205–208
the pinholes in the multi-pinhole plate. Moreover, with this method we can freely change the number of pinholes to fabricate much more complex three-dimensional quasicrystal microstructures in the photorefractive crystals. For example, we can generate the interference of (12 þ1) beams by a multi-pinhole plate with thirteen pinholes. In doing so, we can fabricate three-dimensional 12-fold symmetry quasicrystal lattices which are similar to the microstructures in the literature [29].
4. Conclusions In summary, we experimentally demonstrate a convenient approach to fabricate three-dimensional Penrose-type photonic quasicrystal lattices in LiNbO3:Fe crystal using a multi-pinhole plate. The setup of this method is very stable and flexible. Induced three-dimensional Penrose-type photonic quasicrystal lattices are analyzed and proved by different experimental tools. Induced quasicrystal lattice structures can exist inside the crystal stably for a long time in a dark room. This method can be easily extended to produce more complex three-dimensional quasicrystal microstructures by designing the multi-pinhole plate appropriately. These three-dimensional photonic quasicrystal lattices may serve as a test-bed for studies of band gaps phenomena in threedimensional quasiperiodic lattice systems.
Acknowledgments The authors gratefully acknowledge the support from National Basic Research Program of China (973 Program) under Grant no. 2011CB921604 and the National Natural Science Foundation of China under Grant no. 11234003.
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