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Optical fabrication of wavy lattices and photonic lattices with defects in photorefractive crystal by single step projection method
Superlattices and Microstructures 82 (2015) 136–142
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Optical fabrication of wavy lattices and photonic lattices with defects in photorefractive crystal by single step projection method Wentao Jin, Yan Ling Xue ⇑ Department of Communications Engineering, School of Information Science & Technology, East China Normal University, Shanghai 200241, China
a r t i c l e
i n f o
Article history: Received 29 October 2014 Received in revised form 13 February 2015 Accepted 16 February 2015 Available online 21 February 2015 Keywords: Photonic lattice Wavy microstructures Point defect Line defect Photorefractive
a b s t r a c t We fabricate several different photonic lattice microstructures in iron-doped lithium niobate photorefractive crystal using single step projection method by a spatial light modulator. Wavy photonic lattice and several lattice structures with different defects were one-step induced inside the crystal. This method makes up the weakness of the conventional multiple beams interference method. The experimental setup is very flexible and easy to operate without complicated programming. Induced photonic structures can be fixed or erased and re-recorded in the crystal. The method can be easily extended to fabricate diverse photonic microstructures by drawing different structural patterns on a computer. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Periodic microstructures attracted strong interests in recent years due to many innovative possibilities in manipulating wave propagation and trapping light wave [1,2]. Photonic crystal is a kind of optical nanostructures with periodic arrays of different dielectric materials. Since the introduction of the photonic crystal concept in 1987, the photonic crystals have been under wide researches in theory and experiment, and underwent rapid development in recent years [3–5]. Photonic crystal can form the magic frequency regions named photonic band gaps where the propagation of ⇑ Corresponding author. E-mail address: [email protected] (Y.L. Xue). http://dx.doi.org/10.1016/j.spmi.2015.02.021 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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electromagnetic wave in a certain frequency is forbidden. Because they can control the propagation of light, photonic crystals are suitable for a wide variety of applications, such as surface lasing, optical waveguides, and lasing oscillation nanocavity [3–6]. Photonic crystal also exhibits various new physical phenomena, including the suppression or enhancement of spontaneous emission and low-threshold lasing. Fabricating a variety of micro/nanostructures is always a hot topic of research on photonic crystals. Thus far, some sophisticated fabrication techniques, such as self-assembly, two-photon absorption, colloidal crystallization and electron beam lithography have been proposed and demonstrated with different levels of success [7–10]. Optical induction technique, a convenient method utilizing the photo-induced refractive index change sensitivity in photorefractive materials, has attracted lots of interests recently in fabricating photonic microstructures such as photonic lattices [11–14]. Photonic lattice structures can be induced optically in photorefractive materials at very low light power levels utilizing the photo-induced refractive index change properties of the media. Although the refractive index modulation in a photorefractive material is low (10 4–10 3), spatial band gaps appear in these materials due to the effect of Bragg scattering of eigen waves – Bloch waves – of the induced lattice propagating at small angles [15]. They can be found as solutions of the nonlinear Schrödinger equation describing light propagation in these photonic lattices [16,17]. The existence of one-dimensional as well as two-dimensional photonic spatial band gaps has been demonstrated, enabling to realize a wealth of nonlinear optical phenomena in discrete lattice systems like the formation of discrete optical solitons, tunnelling effects, or quantum effects as Anderson localization [16,17]. Thus photorefractive photonic lattice can be treated as a test-bed for studies of generic spatial band gaps phenomena in photonic periodic structures. The approach of multiple beam interference is a handy and effective method in forming sundry periodic intensity patterns as well as lattice intensity patterns with defects [18–20]. The great majority of optically induced photonic lattices are formed use the multiple beam interference. With this method, the optical intensity pattern with a certain distribution formed by the interference of several monochromatic light beams is irradiated onto photorefractive media and can be developed as a ‘‘record’’ of the interference pattern in the media after exposure. And numerous periodic and quasiperiodic photonic lattice structures have been successfully fabricated in photorefractive crystals [21–25]. However, there exist few limitations with this method. Some arbitrarily intensity distribution patterns, thus the relevant lattice structures, cannot be generated. Wavy lattice structure is an example. Therefore, the researches on overcoming the above shortcoming are meaningful. In this paper, we report on experimental fabrication of several arbitrarily photonic lattices in iron-doped lithium niobate (LiNbO3:Fe) photorefractive crystal by a single step projection method. These photonic lattice structures are hardly formed using the conventional multiple beams interference. The key to our method is the usage of a spatial light modulator (SLM) which can project arbitrarily structural patterns drawn by computer onto a photorefractive crystal to induce the corresponding microstructures. Compared to the previous experiments using SLM, our method is easy to operate without complicated programming, thus reduces the complexity of the experiment [15,26,27]. Wavy lattices and photonic lattice structures with defects are one-step induced inside a LiNbO3:Fe photorefractive crystal. Induced photonic lattice structures have long dark storage time, so they can exist stably for a long time in LiNbO3:Fe crystal. After appropriate process, the induced structures also can be erased and re-recorded in the crystal. Moreover, the method we employed is not limited to this kind of photorefractive material alone. It can be easily well adapted to various photosensitive materials.
2. Experimental methods SLM is a real-time reconfigurable device capable of modifying amplitude (or intensity), phase, or polarization of a light beam. The SLM used in our experiment is a mixed–type reflective SLM. The SLM is with pixel pitch 9.5 lm, resolution 1024 768, and grey scale 256 steps. We only used its amplitude modulation function. For a uniform light beam passing through the SLM, due to the modulation by a grey-scale picture displayed on the SLM, it has an intensity distribution corresponding to the grey scale distribution and is called as writing beam. The grey-scale picture on SLM can be
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drawn by a computer. In order to obtain remarkable amplitude contrast of the projected image, the actual grey-scale picture used in our experiment is a black and white bitmap file. Amplitude reaches maximum while light passes through the white areas, and vice versa. By designing different grey-scale pictures, various intensity distribution patterns become possible, especially those intensity distribution patterns hardly produced by multiple beams interference method. Under the irradiation of coherent light, the modulation instability in photorefractive crystal is easy to appear [28,29]. It will result in the distortion and deformation of induced lattices, which is harmful to the formation of stable lattice structures. However, in the case of partially coherent light, the modulation instability is not so easy to occur due to the presence of a nonlinear threshold. So the partially coherent light makes the appearance of modulation instability harder in photorefractive crystal. This is important in forming stable and clear lattice structures in the crystal [30–32]. We use partially coherent light as the light source in our experiment. The schematic diagram of the experimental setup is shown in Fig. 1. A continuous-wave laser is with 532 nm wavelength and 100 mW power. In beam path a, the linearly polarized laser beam first passes a standard partially coherent light generating system composed with an invert telescope (lenses L1 and L2) and a rotating diffuser near its focal plane [33]. In the invert telescope, the focal length of the lens L1 is 6 mm, and the focal length of the lens L2 is 80 mm. The spot size on the rotating diffuser can be changed by adjusting the distance between the rotating diffuser and its front lens, resulting in the adjustment of the size of the partially coherent light source and the consequent control of the degree of incoherence of the partially coherent light beam. The larger the spot size of light on the rotating diffuser, the lower the degree of spatial coherence of the light beam is. The generated partially coherent light beam is directed onto the SLM. The writing beam outputted from SLM can be compressed by a two lens system (lenses L3 and L4) before irradiating on the crystal. In the two lens system, the focal length of lens L3 is 64 mm, and the focal length of lens L4 is 8 mm. The spacing between the two lenses is equal to the sum of these two focal lengths. The compression ratio of the two lens system is (64 mm/8 mm) = 8. The SLM is located on the front focal plane of lens L3, and the crystal is located on the rear focal plane of lens L4. In this case, a shrunken undistorted image can be projected onto the crystal. In the mutual focal plane of lenses L3 and L4, all undesired stray light components are blocked by appropriate filtering. This can block the stray light from the front portion of the setup. So it is helpful in improving the contrast of bright and shade areas of the projected image on the crystal. The writing beam with the intensity about 40.7–45.2 mW/cm2 illuminates a piece of LiNbO3:Fe crystal (10 mm 10 mm 3 mm, doped with 0.03 wt% iron), and leads to optically induced nonlinear
Fig. 1. Schematic of experimental scheme for fabricating two-dimensional photonic lattice structures in LiNbO3:Fe crystal by single step projection method. k/2: half-wave plate; BS: beam splitter; RD: rotating diffuser; P: polarizer; SLM: spatial light modulator; OA: optical attenuator; M: mirror; SF: spatial filter; L1–L6: lenses; ID: iris diaphragm; F: filter; LN: LiNbO3:Fe crystal.
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index changes inside the crystal. The period scale of the structures displayed on the SLM can be changed by adjusting the scale of grey-scale picture. When the grey-scale picture of a structure is with N pixels in one period, the period of the structures displayed on the SLM is about 9.5N lm in terms of the 9.5 lm pixel pitch of the SLM. The period of shrunken projected image on the crystal is about 9.5N/ 8 lm while the compression ratio resultant from the two lens system is 8 times. Beam path b is used for the plane wave guiding imaging of the induced photonic lattice structures. This probe beam is linearly polarized parallel to the c-axis of the crystal (e-polarized). In doing so, we got a significant refractive index contrast [11,12]. A CCD camera captured images of induced lattice structures when they were probed by the e-polarized plane wave.
3. Experimental results We first produced wavy lattice structures in the crystal, as shown in Fig. 2. It is easy to draw a structural pattern with wavy lattice structures, as shown in Fig. 2a, using computer. Through the modulation of SLM, the partially coherent light beam formed a writing beam with its intensity
Fig. 2. (a) The monochrome black and white bitmap of wavy structures pattern drew by computer. (b) The input intensity pattern of the wavy lattice-forming beam captured at the front surface of the crystal. (c) Image of induced wavy lattice structures in the crystal captured by the CCD. The scale bar is 17 lm.
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distribution corresponding to the drawn wavy structure pattern as shown in Fig. 2b. After an appropriate time exposure, the lattice writing beam induced the analogous structures in the crystal. Fig. 3c is the guided wave intensity pattern of the induced wavy lattice structures, acquired by CCD, when they were probed by a plane wave. The wavy structures in the LiNbO3:Fe crystal can be observed clearly. Because LiNbO3:Fe crystal is a self-defocusing photorefractive material, it can engender a negative refractive index change in the irradiated regions. Therefore, when the induced structures were probed by a plane wave, the guided wave intensity pattern can appear the intensity inversion, as discussed in Ref. [21], compared with lattice-forming wave and the structure pattern drawn by computer. The measurement shows that the period of wavy structures is 17 lm. Similarly, we fabricate several other photonic lattice structures in the crystal, such as photonic lattices with different defects, using this method by drawing different structural patterns. The typical experimental results are shown in Fig. 3. Fig. 3a–c is the structure patterns of periodic lattices with different defects which drew by computer. Fig. 3d–f is relevant guided wave intensity patterns of induced lattice structures with defects corresponding Fig. 3a–c, respectively. Fig. 3d is a two-dimensional square grid lattice microstructures with one point defect. Fig. 3e is a two-dimensional triangle lattice microstructures with line defects and branch structures. There are some high intensity seen in the defect line, it may be caused by the diffraction of periodic pattern in the transmission. Fig. 3f is a two-dimensional lattice microstructures with point defect arrays. These induced lattice microstructures provide possibilities for researches on generic nonlinear optical phenomena in optical microcavity and photonic crystal waveguides in photorefractive crystals. Placing the crystal exactly on the rear focal plane of lens L4 can guarantee the acquirement of distinct and undistorted image on the crystal. Any deviation from the focal plane of lens L4 will cause the image distortion. The more deviation, the more severe distortion the image has and the vaguer the
Fig. 3. (a)–(c) The monochrome black and white bitmaps of lattice structures with different defects, respectively. (d) Image of induced square grid lattice microstructures with one point defect in the crystal. (e) Image of induced triangle lattice microstructures with line defects and branch structures. (f) Image of induced lattice microstructures with point defect arrays. All of the scale bars equal 18 lm.
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projected image is. Finally the corresponding structures in the crystal cannot be induced. Thus, the induced structures in the crystal only exist nearby the focal plane of lens L4. The effective lattice thickness or the defect depth is approximately 0.2 mm in the longitudinal direction. The longer the focal length of lens L4 in the two-lens system, the less obvious the image distortion is. Although the long focal length of lens L4 is helpful in improving the depth of induced structures in the crystal, it will reduce the compression ratio of the two-lens system and is not conducive to inducing the structures with small periods. The dark conductivity of LiNbO3:Fe crystal is very low, so that the induced lattice structures can be stored in the crystal for long time in a dark room. After a thermal fixing process, the induced structures can be fixed in the crystal perpetually. In addition, induced structures can be erased by the flush of white light so that new structures can be induced again in the crystal. This feature considerably widens the applications of these photorefractive photonic lattice structures. 4. Conclusions In conclusion, we have demonstrated a convenient method to fabricate arbitrary photonic lattices in photorefractive crystal using single step projection method by SLM. The experimental method is very flexible and easy to operate without complicated programming. It makes up the deficiency of the multiple beams interference method. Wavy structure and three kinds of photonic lattice structures with different defects are one-step induced inside LiNbO3:Fe crystal. Induced photonic structures can be fixed or erased even re-recorded in the crystal, which implies possible applications in all-optical signal processing and nonlinear photonic devices. 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 Nos. 11234003 and 91436211. References [1] J.D. Joannopoulos, S.G. Johnson, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University, Princeton NJ, 2008. [2] Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic, San Diego, 2003. [3] E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T.J. Kippenberg, I. Robert-Philip, Optomechanical coupling in a twodimensional photonic crystal defect cavity, Phys. Rev. Lett. 106 (2011) 203902. [4] A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, Y. Arakawa, Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap, Nat. Photon. 5 (2011) 91–94. [5] N. Matsuda, H. Takesue, K. Shimizu, Y. Tokura, E. Kuramochi, M. Notomi, Slow light enhanced correlated photon pair generation in photonic crystal coupled-resonator optical waveguides, Opt. Express 21 (2013) 8596–8604. [6] L. Ferrier, O.E. Daif, X. Letartre, P.R. Romeo, C. Seassal, R. Mazurczyk, P. Viktorovitch, Surface emitting microlaser based on 2D photonic crystal rod lattices, Opt. Express 17 (2009) 9780–9788. [7] H.B. Sun, S. Matsuo, H. Misawa, Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin, Appl. Phys. Lett. 74 (1999) 786–788. [8] Y.H. Ye, F. LeBlanc, A. Hache, V.V. Truong, Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality, Appl. Phys. Lett. 78 (2001) 52–54. [9] Z.Y. Zheng, X.Z. Liu, Y.H. Luo, B.Y. Cheng, D.Z. Zhang, Q.B. Meng, Y.R. Wang, Pressure controlled self-assembly of high quality three-dimensional colloidal photonic crystals, Appl. Phys. Lett. 90 (2007) 051910. [10] G. Subramania, S.Y. Lin, Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography, Appl. Phys. Lett. 85 (2004) 5037–5039. [11] J.W. Fleischer, M. Segev, N.K. Efremidis, D.N. Christodoulides, Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, Nature 422 (2003) 147–150. [12] J.W. Fleischer, T. Carmon, M. Segev, N.K. Efremidis, D.N. Christodoulides, Observation of discrete solitons in optically induced real time waveguide arrays, Phys. Rev. Lett. 90 (2003) 023902. [13] P. Rose, M. Boguslawski, C. Denz, Nonlinear lattice structures based on families of complex nondiffracting beams, New J. Phys. 14 (2012) 033018. [14] W. Jin, Y. Gao, M. Liu, Fabrication of large area two-dimensional nonlinear photonic lattices using improved Michelson interferometer, Opt. Commun. 289 (2013) 140–143. [15] J. Xavier, M. Boguslawski, P. Rose, J. Joseph, C. Denz, Reconfigurable optically induced quasicrystallographic threedimensional complex nonlinear photonic lattice structures, Adv. Mater. 22 (2010) 356–360.
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[16] D.N. Neshev, A.A. Sukhorukov, W. Krolikowski, Y.S. Kivshar, Nonlinear optics and light localization in periodic photonic lattices, J. Nonlinear Opt. Phys. Mater. 16 (2007) 1–25. [17] F. Lederer, G.I. Stegeman, D.N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, Discrete solitons in optics, Phys. Rep. 463 (2008) 1–126. [18] L. Wang, B. Terhalle, V.A. Guzenko, A. Farhan, M. Hojeij, Y. Ekinci, Generation of high-resolution kagome lattice structures using extreme ultraviolet interference lithography, Appl. Phys. Lett. 101 (2012) 093104. [19] T.K. Gaylord, M.C.R. Leibovici, G.M. Burrow, Pattern-integrated interference, Appl. Opt. 52 (2013) 61–72. [20] D.E. Sedivy, T.K. Gaylord, Modeling of multiple-optical-axis pattern-integrated interference lithography systems, Appl. Opt. 53 (2014) 12–20. [21] N. Zhu, Z.H. Liu, R. Guo, S.M. Liu, A method of easy fabrication of 2D light-induced nonlinear photonic lattices in selfdefocusing LiNbO3:Fe crystal, Opt. Mater. 30 (2007) 527–531. [22] W. Jin, Y. Gao, A simple method for fabricating two- and three-dimensional photorefractive photonic lattices microstructures, Superlattice Microstruct. 51 (2012) 114–118. [23] W. Jin, Y. Gao, Optically induced two-dimensional photonic quasicrystal lattices in iron-doped lithium niobate crystal with an amplitude mask, Appl. Phys. Lett. 101 (2012) 141104. [24] W. Jin, Y.L. Xue, Optically induced three-dimensional Penrose-type photonic quasicrystal lattices in iron-doped lithium niobate crystal, Opt. Commun. 322 (2014) 205–208. [25] W. Jin, Y.L. Xue, Generation of reconfigurable two-dimensional photorefractive photonic heterostructures with composite periods using multi-lens boards, Opt. Laser Technol. 66 (2015) 106–111. [26] J. Xavier, P. Rose, B. Terhalle, J. Joseph, C. Denz, Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices, Opt. Lett. 34 (2009) 2625–2627. [27] G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, G. Abbate, Two-dimensional photonic quasicrystals by single beam computer-generated holography, Opt. Express 16 (2008) 5164–5170. [28] X. Liu, K. Beckwitt, F. Wise, Transverse instability of optical spatiotemporal solitons in quadratic media, Phys. Rev. Lett. 85 (2000) 1871–1874. [29] N. Zhu, R. Guo, S. Liu, Z. Liu, T. Song, Spatial modulation instability in self-defocusing photorefractive crystal LiNbO3:Fe, J. Opt. A: Pure Appl. Opt. 8 (2006) 149–154. [30] D. Kip, M. Soljacic, M. Segev 1, E. Eugenieva, D.N. Christodoulides, Modulation instability and pattern formation in spatially incoherent light beams, Science 290 (2000) 495–498. [31] M. Soljacic, M. Segev, T. Coskun, D.N. Christodoulides, A. Vishwanath, Modulation instability of incoherent beams in noninstantaneous nonlinear media, Phys. Rev. Lett. 84 (2000) 467–470. [32] H. Martin, E.D. Eugenieva, Z. Chen, Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices, Phys. Rev. Lett. 92 (2004) 123902. [33] M. Mitchell, Z. Chen, M.F. Shin, M. Segev, Self-trapping of partially spatially incoherent light, Phys. Rev. Lett. 77 (1996) 490–493.
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Optical fabrication of wavy lattices and photonic lattices with defects in photorefractive crystal by single step projection method Wentao Jin, Yan Ling Xue ⇑ Department of Communications Engineering, School of Information Science & Technology, East China Normal University, Shanghai 200241, China
a r t i c l e
i n f o
Article history: Received 29 October 2014 Received in revised form 13 February 2015 Accepted 16 February 2015 Available online 21 February 2015 Keywords: Photonic lattice Wavy microstructures Point defect Line defect Photorefractive
a b s t r a c t We fabricate several different photonic lattice microstructures in iron-doped lithium niobate photorefractive crystal using single step projection method by a spatial light modulator. Wavy photonic lattice and several lattice structures with different defects were one-step induced inside the crystal. This method makes up the weakness of the conventional multiple beams interference method. The experimental setup is very flexible and easy to operate without complicated programming. Induced photonic structures can be fixed or erased and re-recorded in the crystal. The method can be easily extended to fabricate diverse photonic microstructures by drawing different structural patterns on a computer. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Periodic microstructures attracted strong interests in recent years due to many innovative possibilities in manipulating wave propagation and trapping light wave [1,2]. Photonic crystal is a kind of optical nanostructures with periodic arrays of different dielectric materials. Since the introduction of the photonic crystal concept in 1987, the photonic crystals have been under wide researches in theory and experiment, and underwent rapid development in recent years [3–5]. Photonic crystal can form the magic frequency regions named photonic band gaps where the propagation of ⇑ Corresponding author. E-mail address: [email protected] (Y.L. Xue). http://dx.doi.org/10.1016/j.spmi.2015.02.021 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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electromagnetic wave in a certain frequency is forbidden. Because they can control the propagation of light, photonic crystals are suitable for a wide variety of applications, such as surface lasing, optical waveguides, and lasing oscillation nanocavity [3–6]. Photonic crystal also exhibits various new physical phenomena, including the suppression or enhancement of spontaneous emission and low-threshold lasing. Fabricating a variety of micro/nanostructures is always a hot topic of research on photonic crystals. Thus far, some sophisticated fabrication techniques, such as self-assembly, two-photon absorption, colloidal crystallization and electron beam lithography have been proposed and demonstrated with different levels of success [7–10]. Optical induction technique, a convenient method utilizing the photo-induced refractive index change sensitivity in photorefractive materials, has attracted lots of interests recently in fabricating photonic microstructures such as photonic lattices [11–14]. Photonic lattice structures can be induced optically in photorefractive materials at very low light power levels utilizing the photo-induced refractive index change properties of the media. Although the refractive index modulation in a photorefractive material is low (10 4–10 3), spatial band gaps appear in these materials due to the effect of Bragg scattering of eigen waves – Bloch waves – of the induced lattice propagating at small angles [15]. They can be found as solutions of the nonlinear Schrödinger equation describing light propagation in these photonic lattices [16,17]. The existence of one-dimensional as well as two-dimensional photonic spatial band gaps has been demonstrated, enabling to realize a wealth of nonlinear optical phenomena in discrete lattice systems like the formation of discrete optical solitons, tunnelling effects, or quantum effects as Anderson localization [16,17]. Thus photorefractive photonic lattice can be treated as a test-bed for studies of generic spatial band gaps phenomena in photonic periodic structures. The approach of multiple beam interference is a handy and effective method in forming sundry periodic intensity patterns as well as lattice intensity patterns with defects [18–20]. The great majority of optically induced photonic lattices are formed use the multiple beam interference. With this method, the optical intensity pattern with a certain distribution formed by the interference of several monochromatic light beams is irradiated onto photorefractive media and can be developed as a ‘‘record’’ of the interference pattern in the media after exposure. And numerous periodic and quasiperiodic photonic lattice structures have been successfully fabricated in photorefractive crystals [21–25]. However, there exist few limitations with this method. Some arbitrarily intensity distribution patterns, thus the relevant lattice structures, cannot be generated. Wavy lattice structure is an example. Therefore, the researches on overcoming the above shortcoming are meaningful. In this paper, we report on experimental fabrication of several arbitrarily photonic lattices in iron-doped lithium niobate (LiNbO3:Fe) photorefractive crystal by a single step projection method. These photonic lattice structures are hardly formed using the conventional multiple beams interference. The key to our method is the usage of a spatial light modulator (SLM) which can project arbitrarily structural patterns drawn by computer onto a photorefractive crystal to induce the corresponding microstructures. Compared to the previous experiments using SLM, our method is easy to operate without complicated programming, thus reduces the complexity of the experiment [15,26,27]. Wavy lattices and photonic lattice structures with defects are one-step induced inside a LiNbO3:Fe photorefractive crystal. Induced photonic lattice structures have long dark storage time, so they can exist stably for a long time in LiNbO3:Fe crystal. After appropriate process, the induced structures also can be erased and re-recorded in the crystal. Moreover, the method we employed is not limited to this kind of photorefractive material alone. It can be easily well adapted to various photosensitive materials.
2. Experimental methods SLM is a real-time reconfigurable device capable of modifying amplitude (or intensity), phase, or polarization of a light beam. The SLM used in our experiment is a mixed–type reflective SLM. The SLM is with pixel pitch 9.5 lm, resolution 1024 768, and grey scale 256 steps. We only used its amplitude modulation function. For a uniform light beam passing through the SLM, due to the modulation by a grey-scale picture displayed on the SLM, it has an intensity distribution corresponding to the grey scale distribution and is called as writing beam. The grey-scale picture on SLM can be
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drawn by a computer. In order to obtain remarkable amplitude contrast of the projected image, the actual grey-scale picture used in our experiment is a black and white bitmap file. Amplitude reaches maximum while light passes through the white areas, and vice versa. By designing different grey-scale pictures, various intensity distribution patterns become possible, especially those intensity distribution patterns hardly produced by multiple beams interference method. Under the irradiation of coherent light, the modulation instability in photorefractive crystal is easy to appear [28,29]. It will result in the distortion and deformation of induced lattices, which is harmful to the formation of stable lattice structures. However, in the case of partially coherent light, the modulation instability is not so easy to occur due to the presence of a nonlinear threshold. So the partially coherent light makes the appearance of modulation instability harder in photorefractive crystal. This is important in forming stable and clear lattice structures in the crystal [30–32]. We use partially coherent light as the light source in our experiment. The schematic diagram of the experimental setup is shown in Fig. 1. A continuous-wave laser is with 532 nm wavelength and 100 mW power. In beam path a, the linearly polarized laser beam first passes a standard partially coherent light generating system composed with an invert telescope (lenses L1 and L2) and a rotating diffuser near its focal plane [33]. In the invert telescope, the focal length of the lens L1 is 6 mm, and the focal length of the lens L2 is 80 mm. The spot size on the rotating diffuser can be changed by adjusting the distance between the rotating diffuser and its front lens, resulting in the adjustment of the size of the partially coherent light source and the consequent control of the degree of incoherence of the partially coherent light beam. The larger the spot size of light on the rotating diffuser, the lower the degree of spatial coherence of the light beam is. The generated partially coherent light beam is directed onto the SLM. The writing beam outputted from SLM can be compressed by a two lens system (lenses L3 and L4) before irradiating on the crystal. In the two lens system, the focal length of lens L3 is 64 mm, and the focal length of lens L4 is 8 mm. The spacing between the two lenses is equal to the sum of these two focal lengths. The compression ratio of the two lens system is (64 mm/8 mm) = 8. The SLM is located on the front focal plane of lens L3, and the crystal is located on the rear focal plane of lens L4. In this case, a shrunken undistorted image can be projected onto the crystal. In the mutual focal plane of lenses L3 and L4, all undesired stray light components are blocked by appropriate filtering. This can block the stray light from the front portion of the setup. So it is helpful in improving the contrast of bright and shade areas of the projected image on the crystal. The writing beam with the intensity about 40.7–45.2 mW/cm2 illuminates a piece of LiNbO3:Fe crystal (10 mm 10 mm 3 mm, doped with 0.03 wt% iron), and leads to optically induced nonlinear
Fig. 1. Schematic of experimental scheme for fabricating two-dimensional photonic lattice structures in LiNbO3:Fe crystal by single step projection method. k/2: half-wave plate; BS: beam splitter; RD: rotating diffuser; P: polarizer; SLM: spatial light modulator; OA: optical attenuator; M: mirror; SF: spatial filter; L1–L6: lenses; ID: iris diaphragm; F: filter; LN: LiNbO3:Fe crystal.
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index changes inside the crystal. The period scale of the structures displayed on the SLM can be changed by adjusting the scale of grey-scale picture. When the grey-scale picture of a structure is with N pixels in one period, the period of the structures displayed on the SLM is about 9.5N lm in terms of the 9.5 lm pixel pitch of the SLM. The period of shrunken projected image on the crystal is about 9.5N/ 8 lm while the compression ratio resultant from the two lens system is 8 times. Beam path b is used for the plane wave guiding imaging of the induced photonic lattice structures. This probe beam is linearly polarized parallel to the c-axis of the crystal (e-polarized). In doing so, we got a significant refractive index contrast [11,12]. A CCD camera captured images of induced lattice structures when they were probed by the e-polarized plane wave.
3. Experimental results We first produced wavy lattice structures in the crystal, as shown in Fig. 2. It is easy to draw a structural pattern with wavy lattice structures, as shown in Fig. 2a, using computer. Through the modulation of SLM, the partially coherent light beam formed a writing beam with its intensity
Fig. 2. (a) The monochrome black and white bitmap of wavy structures pattern drew by computer. (b) The input intensity pattern of the wavy lattice-forming beam captured at the front surface of the crystal. (c) Image of induced wavy lattice structures in the crystal captured by the CCD. The scale bar is 17 lm.
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distribution corresponding to the drawn wavy structure pattern as shown in Fig. 2b. After an appropriate time exposure, the lattice writing beam induced the analogous structures in the crystal. Fig. 3c is the guided wave intensity pattern of the induced wavy lattice structures, acquired by CCD, when they were probed by a plane wave. The wavy structures in the LiNbO3:Fe crystal can be observed clearly. Because LiNbO3:Fe crystal is a self-defocusing photorefractive material, it can engender a negative refractive index change in the irradiated regions. Therefore, when the induced structures were probed by a plane wave, the guided wave intensity pattern can appear the intensity inversion, as discussed in Ref. [21], compared with lattice-forming wave and the structure pattern drawn by computer. The measurement shows that the period of wavy structures is 17 lm. Similarly, we fabricate several other photonic lattice structures in the crystal, such as photonic lattices with different defects, using this method by drawing different structural patterns. The typical experimental results are shown in Fig. 3. Fig. 3a–c is the structure patterns of periodic lattices with different defects which drew by computer. Fig. 3d–f is relevant guided wave intensity patterns of induced lattice structures with defects corresponding Fig. 3a–c, respectively. Fig. 3d is a two-dimensional square grid lattice microstructures with one point defect. Fig. 3e is a two-dimensional triangle lattice microstructures with line defects and branch structures. There are some high intensity seen in the defect line, it may be caused by the diffraction of periodic pattern in the transmission. Fig. 3f is a two-dimensional lattice microstructures with point defect arrays. These induced lattice microstructures provide possibilities for researches on generic nonlinear optical phenomena in optical microcavity and photonic crystal waveguides in photorefractive crystals. Placing the crystal exactly on the rear focal plane of lens L4 can guarantee the acquirement of distinct and undistorted image on the crystal. Any deviation from the focal plane of lens L4 will cause the image distortion. The more deviation, the more severe distortion the image has and the vaguer the
Fig. 3. (a)–(c) The monochrome black and white bitmaps of lattice structures with different defects, respectively. (d) Image of induced square grid lattice microstructures with one point defect in the crystal. (e) Image of induced triangle lattice microstructures with line defects and branch structures. (f) Image of induced lattice microstructures with point defect arrays. All of the scale bars equal 18 lm.
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projected image is. Finally the corresponding structures in the crystal cannot be induced. Thus, the induced structures in the crystal only exist nearby the focal plane of lens L4. The effective lattice thickness or the defect depth is approximately 0.2 mm in the longitudinal direction. The longer the focal length of lens L4 in the two-lens system, the less obvious the image distortion is. Although the long focal length of lens L4 is helpful in improving the depth of induced structures in the crystal, it will reduce the compression ratio of the two-lens system and is not conducive to inducing the structures with small periods. The dark conductivity of LiNbO3:Fe crystal is very low, so that the induced lattice structures can be stored in the crystal for long time in a dark room. After a thermal fixing process, the induced structures can be fixed in the crystal perpetually. In addition, induced structures can be erased by the flush of white light so that new structures can be induced again in the crystal. This feature considerably widens the applications of these photorefractive photonic lattice structures. 4. Conclusions In conclusion, we have demonstrated a convenient method to fabricate arbitrary photonic lattices in photorefractive crystal using single step projection method by SLM. The experimental method is very flexible and easy to operate without complicated programming. It makes up the deficiency of the multiple beams interference method. Wavy structure and three kinds of photonic lattice structures with different defects are one-step induced inside LiNbO3:Fe crystal. Induced photonic structures can be fixed or erased even re-recorded in the crystal, which implies possible applications in all-optical signal processing and nonlinear photonic devices. 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 Nos. 11234003 and 91436211. References [1] J.D. Joannopoulos, S.G. Johnson, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University, Princeton NJ, 2008. [2] Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic, San Diego, 2003. [3] E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T.J. Kippenberg, I. Robert-Philip, Optomechanical coupling in a twodimensional photonic crystal defect cavity, Phys. Rev. Lett. 106 (2011) 203902. [4] A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, Y. Arakawa, Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap, Nat. Photon. 5 (2011) 91–94. [5] N. Matsuda, H. Takesue, K. Shimizu, Y. Tokura, E. Kuramochi, M. Notomi, Slow light enhanced correlated photon pair generation in photonic crystal coupled-resonator optical waveguides, Opt. Express 21 (2013) 8596–8604. [6] L. Ferrier, O.E. Daif, X. Letartre, P.R. Romeo, C. Seassal, R. Mazurczyk, P. Viktorovitch, Surface emitting microlaser based on 2D photonic crystal rod lattices, Opt. Express 17 (2009) 9780–9788. [7] H.B. Sun, S. Matsuo, H. Misawa, Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin, Appl. Phys. Lett. 74 (1999) 786–788. [8] Y.H. Ye, F. LeBlanc, A. Hache, V.V. Truong, Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality, Appl. Phys. Lett. 78 (2001) 52–54. [9] Z.Y. Zheng, X.Z. Liu, Y.H. Luo, B.Y. Cheng, D.Z. Zhang, Q.B. Meng, Y.R. Wang, Pressure controlled self-assembly of high quality three-dimensional colloidal photonic crystals, Appl. Phys. Lett. 90 (2007) 051910. [10] G. Subramania, S.Y. Lin, Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography, Appl. Phys. Lett. 85 (2004) 5037–5039. [11] J.W. Fleischer, M. Segev, N.K. Efremidis, D.N. Christodoulides, Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, Nature 422 (2003) 147–150. [12] J.W. Fleischer, T. Carmon, M. Segev, N.K. Efremidis, D.N. Christodoulides, Observation of discrete solitons in optically induced real time waveguide arrays, Phys. Rev. Lett. 90 (2003) 023902. [13] P. Rose, M. Boguslawski, C. Denz, Nonlinear lattice structures based on families of complex nondiffracting beams, New J. Phys. 14 (2012) 033018. [14] W. Jin, Y. Gao, M. Liu, Fabrication of large area two-dimensional nonlinear photonic lattices using improved Michelson interferometer, Opt. Commun. 289 (2013) 140–143. [15] J. Xavier, M. Boguslawski, P. Rose, J. Joseph, C. Denz, Reconfigurable optically induced quasicrystallographic threedimensional complex nonlinear photonic lattice structures, Adv. Mater. 22 (2010) 356–360.
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