基于Fibonacci序列准周期结构的小角度低通空间滤波器
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摘要
利用常规材料构造了Fibonacci序列准周期结构,运用传输矩阵法研究了该结构的空间传输特性,并基于该结构优良的空间传输特性设计了小角度低通空间滤波器.数值模拟结果表明,该小角度空间滤波器的角域带宽可通过改变序列的结构类型和序列数来调谐,其调谐规律为:随着Fibonacci序列F(m,1)中m值的增加,对应空间滤波器的角域带宽减小;随着序列数的增大,对应角域带宽也减小.在调谐的基础上,还可通过改变构成准周期结构的介质折射率参量来精确调节其角域带宽.相比于基于超材料的小角度空间滤波器而言,基于Fibonacci序列的小角度空间滤波器制备更简单,且有望应用于新一代的高功率激光系统中.
The quasi-periodic structures of Fibonacci sequence composed of conventional materials were proposed,and their spatial transmittance properties were investigated by using the transfer matrix method.The corresponding low-pass spatial filters with a small angle-domain bandwidth were designed based on these good spatial transmittance properties.The numerical simulation results show that,the angle-domain bandwidth can be tuned by changing the structure types and sequence numbers,and the angle-domain bandwidth of the filters becomes smaller and smaller with the increase of the sequence number or m value of Fibonacci sequence F(m,1).On the basis of the above regulation,the accurate adjustment can be made by changing the refractive-index parameter of the quasi-periodic structures.Compared to the former Metamaterial spatial filters with a small angle-domain bandwidth,the spatial filters based on Fibonacci quasi-periodic structures are more simple to be made and more likely to be applied to a new generation of high-power laser system.
The quasi-periodic structures of Fibonacci sequence composed of conventional materials were proposed,and their spatial transmittance properties were investigated by using the transfer matrix method.The corresponding low-pass spatial filters with a small angle-domain bandwidth were designed based on these good spatial transmittance properties.The numerical simulation results show that,the angle-domain bandwidth can be tuned by changing the structure types and sequence numbers,and the angle-domain bandwidth of the filters becomes smaller and smaller with the increase of the sequence number or m value of Fibonacci sequence F(m,1).On the basis of the above regulation,the accurate adjustment can be made by changing the refractive-index parameter of the quasi-periodic structures.Compared to the former Metamaterial spatial filters with a small angle-domain bandwidth,the spatial filters based on Fibonacci quasi-periodic structures are more simple to be made and more likely to be applied to a new generation of high-power laser system.
引文
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[23]ZHANG Jian,ZHENG Jie,ZHANG Yu-Shu.Fibonacci quasi-periodic superstructure fiber Bragg gratings[J].Acta Photonica Sinica,2009,38(8):2050-2054.张健,郑杰,张玉书.菲波纳契准周期超结构光纤光栅[J].光子学报,2009,38(8):2050-2054.
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[26]KE Jie,Zhang Jun-yong.Focusing and imaging properties of fibonacci photon sieve[J].Acta Optica Sinica,2015,35(9):0923001.柯杰,张军勇.斐波那契光子筛的聚焦成像特性[J].光学学报,2015,35(9):0923001.
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[28]TANG Bing-shu.Study on the transmission properties of fibonacci one-dimensional photonic crystal nanometer films in visible region[J].Acta Photonica Sinica,2007,36(8):1426-1430.汤炳书.光学波段菲波纳契序列一维光子晶体纳米膜传输特性研究[J].光子学报,2007,36(8):1426-1430.
[29]CAO Yong-jun,YANG Xu.Transmission properties of the generalized Fibonacci quasi-periodical phononic crystal[J].Acta Physica Sinica,2008,57(6):3620-3624.曹永军,杨旭.广义Fibonacci准周期结构声子晶体透射性质的研究[J].物理学报,2008,57(6):3620-3624.
[30]ZHANG Y,WU Z,CAO Y,et al.Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal[J].Optics Communications,2015,338:168-173.
[31]NING R,LIU S,ZhANG H,et al.Wideband absorption in Fibonacci quasi-periodic graphene-based hyperbolic metamaterials[J].Journal of Optics,2014,16(12):125108.
[32]LIU Xiao.Analysis on the optical properties of one-dimensional generalized Fibonacci photonic crystal[D].Ningbo:Ningbo University,2011:25-27.刘晓.一维广义Fibonacci序列光子晶体结构的光学传输特性研究[D].宁波:宁波大学,2011:25-27.
[33]HAUSMANN B J M,SHIELDS B J,QUAN Q,et al.Coupling of NV centers to photonic crystal nanobeams in diamond[J].Nano Letters,2013,13(12):5791-5796.
[34]LIU Jie,TIE Sheng-nian,LU Hui-dong.Multi-channel drop filter based on two-dimensional photonic crystal[J].Optics and Precision Engineering,2016,24(5):1021-1027.刘杰,铁生年,卢辉东.多信道二维光子晶体滤波器[J].光学精密工程,2016,24(5):1021-1027.
[35]RIEDRICH-MLLER J,KIPFSTUHL L,HEPP C,et al.One-and two-dimensional photonic crystal microcavities in single crystal diamond[J].Nature Nanotechnology,2012,7(1):69-74.
[2]AlMEIDA S P,INDEBETOUW G.Applications of optical Fourier transforms[M].Academic Press,San Diego,1982:41-87.
[3]SCHURING D,SMITH D R.Spatial filtering using media with indefinite permittivityand permeability tensors[J].Applied Physics Letters,2003,82(14):2215-2217.
[4]ZHANG Xin,LIU Hong-jie,ZHAO Jun-pu,et al.Pinhole design of spatial filter in high energy solid-state laser system[J].Laser&Optoelectronics Progress,2010,47(11):111402.张鑫,刘红婕,赵军普,等.高功率固体激光系统空间滤波小孔尺寸设计[J].激光与光电子学进展,2010,47(11):111402.
[5]WANG Gui-ying,ZHAO Jiu-yuan,ZHANG Ming-ke,et al.Basic study on spatial filter used in Nd-glass high power laser system[J].Acta Physica Sinica,1985,34(2):171-181.王桂英,赵九源,张明科,等.钕玻璃高功率激光系统中的空间滤波器的基本研究[J].物理学报,1985,34(2):171-181.
[6]STALIUNAS K,SNCHEZ-MORCILLO V J.Spatial filtering of light by chirped photonic crystals[J].Physical Review A,2009,79(5):053807.
[7]LUO Z,WEN S,TANG Z,et al.Low-pass Rugate spatial filters for beam smoothing[J].Optics Communications,2010,283(13):2665-2668.
[8]MORENO I,ARAIZA J J,AVENDANO-ALEJO M.Thin-film spatial filters[J].Optics Letters,2005,30(8):914-916.
[9]SEREBRYANNIKOV A E,MAGATH T.Transmission through photonic crystals with multiple line defects at oblique incidence[J].Journal of the Optical Society of America B,2008,25(3):286-296.
[10]SEREBRYANNIKOV A E,LALANNE P,PETROV A Y,et al.Wide-angle reflection-mode spatial filtering and splitting with photonic crystal gratings and single-layer rod gratings[J].Optics Letters,2014,39(21):6193-6196.
[11]MAIGYTE L,STALIUNAS K.Spatial filtering with photonic crystals[J].Applied Physics Reviews,2015,2(1):011102.
[12]TANG Z,FAN D,WEN S,et al.Low-pass spatial filtering using a two-dimensional self-collimating photonic crystal[J].Chinese Optics Letters,2007,5(101):S211-S213.
[13]FANG Y T.Direction and frequency filter basing on an ultra-compact structure consisting of dielectric films[J].Optics&Laser Technology,2010,42(5):850-853.
[14]ZHENG G,SHEN B,TAN J,et al.Experimental research on spatial filtering of deformed laser beam by transmitting volume Bragg grating[J].Chinese Optics Letters,2011,9(3):030501.
[15]ZHENG Guang-wei,CHU Xing-chun,ZHENG Qiu-rong.Development of non-focusing low-pass spatial filtering for laser beams[J].Laser&Optoelectronics Progress,2016,53(5):050002.郑光威,楚兴春,郑秋容.非聚焦型光束空间低通滤波技术研究进展[J].激光与光电子学进展,2016,53(5):050002.
[16]LUO Z,TANG Z,XIANG Y,et al.Polarization-independent low-pass spatial filters based on one-dimensional photonic crystals containing negative-index materials[J].Applied Physics B,2009,94(4):641-646.
[17]LUO Z,CHEN M,LIU J,et al.An approach of waveguide mode selection based on the thin-film spatial filters[J].Optics Communications,2016,365:120-124.
[18]LUO Z,CHEN M,DENG J,et al.Low-pass spatial filters with small angle-domain bandwidth based on onedimensional metamaterial photonic crystals[J].Optik-International Journal for Light and Electron Optics,2016,127(1):259-262.
[19]KANG Yong-qiang,GAO Peng,LIU Hong-mei,et al.Reflection band gap in thue-morse quasicrystal containing anisotropic left handed material[J].Acta Photonica Sinica,2015,44(3):0319004.康永强,高鹏,刘红梅,等.含各向异性左手材料的一维Thue-Mores准周期结构的反射带隙[J].光子学报,2015,44(3):0319004.
[20]MAURIZ P W,VASCONCELOS M S,ALBUQUERQUE E L.Optical transmission spectra in symmetrical Fibonacci photonic multilayers[J].Physics Letters A,2009,373(4):496-500.
[21]LIU X,ZHOU J,ZHU B Q,et al.Electro-optical tunable filter with symmetric generalized Fibonacci photonic crystal[J].Acta Photonica Sinica,2011,40(11):1723-1727.
[22]MERLIN R,BAJEMA K,CLARKE R,et al.Quasiperiodic gaas-alas heterostructures[J].Physical Review Letters,1985,55(17):1768-1770.
[23]ZHANG Jian,ZHENG Jie,ZHANG Yu-Shu.Fibonacci quasi-periodic superstructure fiber Bragg gratings[J].Acta Photonica Sinica,2009,38(8):2050-2054.张健,郑杰,张玉书.菲波纳契准周期超结构光纤光栅[J].光子学报,2009,38(8):2050-2054.
[24]PASSIAS V,VALAPPIL N V,SHI Z,et al.Luminescence properties of a Fibonacci photonic quasicrystal[J].Optics Express,2009,17(8):6636-6642.
[25]DONG Ze-dong,LIU You-wen.Optical absorption properties of quasi-periodic microstructures arranged by Fibonacci sequence[J].Acta Optica Sinica,2016 36(6):0605001.董泽东,刘友文.斐波纳契数列准周期微结构光吸收特性[J].光学学报,2016,36(6):0605001.
[26]KE Jie,Zhang Jun-yong.Focusing and imaging properties of fibonacci photon sieve[J].Acta Optica Sinica,2015,35(9):0923001.柯杰,张军勇.斐波那契光子筛的聚焦成像特性[J].光学学报,2015,35(9):0923001.
[27]LUSK D,ABDULHALIM I,PLACIDO F.Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal[J].Optics Communications,2001,198(4):273-279.
[28]TANG Bing-shu.Study on the transmission properties of fibonacci one-dimensional photonic crystal nanometer films in visible region[J].Acta Photonica Sinica,2007,36(8):1426-1430.汤炳书.光学波段菲波纳契序列一维光子晶体纳米膜传输特性研究[J].光子学报,2007,36(8):1426-1430.
[29]CAO Yong-jun,YANG Xu.Transmission properties of the generalized Fibonacci quasi-periodical phononic crystal[J].Acta Physica Sinica,2008,57(6):3620-3624.曹永军,杨旭.广义Fibonacci准周期结构声子晶体透射性质的研究[J].物理学报,2008,57(6):3620-3624.
[30]ZHANG Y,WU Z,CAO Y,et al.Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal[J].Optics Communications,2015,338:168-173.
[31]NING R,LIU S,ZhANG H,et al.Wideband absorption in Fibonacci quasi-periodic graphene-based hyperbolic metamaterials[J].Journal of Optics,2014,16(12):125108.
[32]LIU Xiao.Analysis on the optical properties of one-dimensional generalized Fibonacci photonic crystal[D].Ningbo:Ningbo University,2011:25-27.刘晓.一维广义Fibonacci序列光子晶体结构的光学传输特性研究[D].宁波:宁波大学,2011:25-27.
[33]HAUSMANN B J M,SHIELDS B J,QUAN Q,et al.Coupling of NV centers to photonic crystal nanobeams in diamond[J].Nano Letters,2013,13(12):5791-5796.
[34]LIU Jie,TIE Sheng-nian,LU Hui-dong.Multi-channel drop filter based on two-dimensional photonic crystal[J].Optics and Precision Engineering,2016,24(5):1021-1027.刘杰,铁生年,卢辉东.多信道二维光子晶体滤波器[J].光学精密工程,2016,24(5):1021-1027.
[35]RIEDRICH-MLLER J,KIPFSTUHL L,HEPP C,et al.One-and two-dimensional photonic crystal microcavities in single crystal diamond[J].Nature Nanotechnology,2012,7(1):69-74.