轴棱锥透镜面形偏差对无衍射光束传播特性的影响
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摘要
为了探究轴棱锥透镜面形偏差对无衍射光束传播特性的影响,建立了三种相对理想锥镜母线的偏离模型,即母线向内侧凹陷、外侧凸出、顶点呈双曲线分布的轴棱锥透镜.推导了各偏离锥镜的振幅透过率函数,并基于菲涅耳衍射理论对平面波经三种母线偏离锥镜的出射光场及光强分布进行了理论分析与数值模拟.结果表明:锥镜母线内凹时,光场强度变小,焦深延长,纵截面光场逐渐发散,沿轴向传输时中心光斑直径逐渐变大;锥镜母线外凸时,光场强度激增,焦深变短,纵截面光场逐渐汇聚,沿轴向传输时中心光斑直径逐渐变小;锥镜顶点呈双曲线分布时,光场振荡加剧,场强和焦深几乎不变,纵截面光场发散后逐渐恢复至均匀分布状.研究结果可为分析轴棱锥透镜锥面加工误差对无衍射光束传播特性的影响、进一步完善无衍射光束衍射场理论,以及拓宽其工程应用范围等提供参考.
In order to investigate the influence of the surface deviation axicon on the propagation characteristics of the non-diffracting beam,three deviation models relative to the ideal,which are concave to the inner side,convex to the outer side and hyperbolic distribution of the apex of the axicon were established.The amplitude transmittance function was deduced,and the emergent light field and intensity distribution of plane wave through the three kinds of axicon lens was analyzed and simulated on the basis of Fresnel diffraction theory.The results show that the intensity of the light field decreases,the focal length is prolonged,the light field of the longitudinal section gradually diverges and the diameter of the center spot is gradually increased along the axis when the generatrix concave to the inner side.The intensity of the light field increases,the focal length becomes shorter,the longitudinal section of the light field gradually converges and the diameter of the center spot along the axial becomes smaller when the generatrix convex to the outer side.When the vertex of axicon is distributed in hyperbola,the light field oscillation intensifies,the field intensity and the focal depth are almost constant and the longitudinal section of the light field gradually diverges and then returns to uniform distribution.The study will provide a theoretical basis for analyzing the influence of the machining error of axicon lens on the propagation characteristics of non-diffracting beam,and has a reference significance for further supplementing the diffraction field theory of non-diffracting beam and broadening the range of its engineering application.
In order to investigate the influence of the surface deviation axicon on the propagation characteristics of the non-diffracting beam,three deviation models relative to the ideal,which are concave to the inner side,convex to the outer side and hyperbolic distribution of the apex of the axicon were established.The amplitude transmittance function was deduced,and the emergent light field and intensity distribution of plane wave through the three kinds of axicon lens was analyzed and simulated on the basis of Fresnel diffraction theory.The results show that the intensity of the light field decreases,the focal length is prolonged,the light field of the longitudinal section gradually diverges and the diameter of the center spot is gradually increased along the axis when the generatrix concave to the inner side.The intensity of the light field increases,the focal length becomes shorter,the longitudinal section of the light field gradually converges and the diameter of the center spot along the axial becomes smaller when the generatrix convex to the outer side.When the vertex of axicon is distributed in hyperbola,the light field oscillation intensifies,the field intensity and the focal depth are almost constant and the longitudinal section of the light field gradually diverges and then returns to uniform distribution.The study will provide a theoretical basis for analyzing the influence of the machining error of axicon lens on the propagation characteristics of non-diffracting beam,and has a reference significance for further supplementing the diffraction field theory of non-diffracting beam and broadening the range of its engineering application.
引文
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[9] KIM J,JEONG Y,LEE S,et al.Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping[J].Optics Letters,2012,37(4):623-5.
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[15] MCLEOD J H.The axicon:a new type of optical element[J].Journal of the Optical Society of America,1954,44(8):592-592.
[16] SHI Tu,YANG Yong-ying,ZHANG Lei,et al.Surface testing methods of aspheric optical elements[J].Chinese Optics,2014,7(1):26-46.师途,杨甬英,张磊,等.非球面光学元件的面形检测技术[J].中国光学,2014,7(1):26-46.
[17] YANG Gui-yang,MA Guo-lu,ZENG Guo-ying.Generation theory and experimental study of two stage non-diffracting beam[J].Acta Photonica Sinica,2018,47(7):0708003.杨贵洋,马国鹭,曾国英.双级无衍射光束的生成理论与实验研究[J].光子学报,2018,47(7):0708003.
[18] AHLUWALIA B P,CHEONG W C,YUAN X C,et al.Design and fabrication of a double-axicon for generation of7-2006210tailorable self-imaged three-dimensional intensity voids[J].Optics Letters,2006,31(7):987-989.
[19] BRZOBOHAT Y′O,ZEMNEK P,CˇIMR T.High quality quasi-Bessel beam generated by round-tip axicon[J].Optics Express,2008,16(17):12688-12700.
[20] CHENG Zhi-ming,WU Feng-tie,FANG Xiang,et al.Multi-bottle beam generated by vaulted axicon[J].Acta Physica Sinica,2012,61(21):212-217.程治明,吴逢铁,方翔,范丹丹,朱健强.圆顶轴棱锥产生多个局域空心光束[J].物理学报,2012,61(21):212-217.
[21]WU Feng-tie,JIANG Xin-guang.Modification of vertex manufacture error on an axicon[J].Optics and Precision Engineering,2009,17(10):2506-2511.吴逢铁,江新光.轴棱锥顶点加工误差的修正[J].光学精密工程,2009,17(10):2506-2511.
[22] ZHOU Li-ping,ZHAO Bin,LI Zhu.Influence of manufacture error of an axicon on beam transmission[J].Journal of Huangzhong University of Science and Technology,2001,29(3):61-63.周莉萍,赵斌,李柱.圆锥透镜加工误差对光束传输变换的影响[J].华中科技大学学报:自然科学版,2001,29(3):61-63.
[23] ZHAI Z,ZHAO B.Diffraction intensity distribution of an axicon illuminated by polychromatic light[J].Journal of Optics A:Pure&Applied Optics,2007,9(10):862.
[24]刘式适,刘式达.特殊函数[M].二版.北京:气象出版社,2002.386-426.
[25] ZHOU Lei.Dynamic micro/nano cutting system modeling for prediction and analysis of surface topography[D].Haerbin:School of Mechatronics Engineering,Harbin Institute of Technology,2009.周磊.微纳米动态切削系统建模及表面形貌的预测分析研究[D].哈尔滨:哈尔滨工业大学机电工程学院,2009.
[26] ZHANG S,CHEN H,WU Z,et al.Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression[J].Optics Express,2017,25(22):27104-27118.
[2] DURNIN J.Exact solutions for non-diffracting beams[J].Journal of the Optical Society of American A,1987,4(4):651-654.
[3] AKIMOV D,LEGESSE F B,DELLITH J,et al.Bessel beam coherent anti-Stokes Raman scattering microscopy[J].Journal of the Optical Society of America B,2015,32(9):1773.
[4] MA Guo-lu,LIU Li-xian,YANG Gui-yang,et al.Generating method of non-diffracting beam with long-distance propagation and controllable parameters[J].Chinese Optics,2018,11(1):100-107.马国鹭,刘丽贤,杨贵洋,等.参数可控长距无衍射光束的生成方法研究[J].中国光学,2018,11(1):100-107.
[5] FAHRBACH F O,SIMON P,ROHRBACH A.Microscopy with self-reconstructing beams[J].Nature Photonics,2010,4(11):780-785.
[6] MITRA S,CHANAL M,CLADY R,et al.Millijoule femtosecond micro-Bessel beams for ultra-high aspect ratio machining.[J].Applied Optics,2015,54(24):7358-65.
[7] PLANCHON T A,LIANG G,MILKIE D E,et al.Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination[J].Nature Methods,2011,8(5):417.
[8] MA Guo-lu,ZENG Guo-ying,ZHAO Bin.Measurement of space coordinates in hidden parts by combining nondiffracting attitude probe and total station.[J].Optics and Precision Engineering,2015,23(02):363-370.马国鹭,曾国英,赵斌.基于无衍射姿态探针和全站仪组合测量空间隐藏坐标[J].光学精密工程,2015,23(02):363-370.
[9] KIM J,JEONG Y,LEE S,et al.Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping[J].Optics Letters,2012,37(4):623-5.
[10] FACCIO D,RUBINO E,LOTTI A,et al.Nonlinear light-matter interaction with femtosecond high-angle Bessel beams[J].Physical Review A,2012,85(3):033829.
[11] LU Y,JIANG B.Arrays of Gaussian vortex,Bessel and Airy beams by computer-generated hologram[J].Optics Communication,2016,363:85-90.
[12] MA G,LIU L,ZHAO B.Nondiffracting beam based technology for an attitude measurement system for automatic orientation of shield[J].Optical Engineering,2015,54(11):114106.
[13] HERMAN R M,WIGGINS T A.High-efficiency diffraction less beams of constant size and intensity[J].Applied Optics,1994,33(31):7297.
[14] ZHANG Q,CHENG X M.Diffraction-free,self-reconstructing Bessel beam generation using thermal nonlinear optical effect[J].Applied Physics Letter,2017,111(16):161103.
[15] MCLEOD J H.The axicon:a new type of optical element[J].Journal of the Optical Society of America,1954,44(8):592-592.
[16] SHI Tu,YANG Yong-ying,ZHANG Lei,et al.Surface testing methods of aspheric optical elements[J].Chinese Optics,2014,7(1):26-46.师途,杨甬英,张磊,等.非球面光学元件的面形检测技术[J].中国光学,2014,7(1):26-46.
[17] YANG Gui-yang,MA Guo-lu,ZENG Guo-ying.Generation theory and experimental study of two stage non-diffracting beam[J].Acta Photonica Sinica,2018,47(7):0708003.杨贵洋,马国鹭,曾国英.双级无衍射光束的生成理论与实验研究[J].光子学报,2018,47(7):0708003.
[18] AHLUWALIA B P,CHEONG W C,YUAN X C,et al.Design and fabrication of a double-axicon for generation of7-2006210tailorable self-imaged three-dimensional intensity voids[J].Optics Letters,2006,31(7):987-989.
[19] BRZOBOHAT Y′O,ZEMNEK P,CˇIMR T.High quality quasi-Bessel beam generated by round-tip axicon[J].Optics Express,2008,16(17):12688-12700.
[20] CHENG Zhi-ming,WU Feng-tie,FANG Xiang,et al.Multi-bottle beam generated by vaulted axicon[J].Acta Physica Sinica,2012,61(21):212-217.程治明,吴逢铁,方翔,范丹丹,朱健强.圆顶轴棱锥产生多个局域空心光束[J].物理学报,2012,61(21):212-217.
[21]WU Feng-tie,JIANG Xin-guang.Modification of vertex manufacture error on an axicon[J].Optics and Precision Engineering,2009,17(10):2506-2511.吴逢铁,江新光.轴棱锥顶点加工误差的修正[J].光学精密工程,2009,17(10):2506-2511.
[22] ZHOU Li-ping,ZHAO Bin,LI Zhu.Influence of manufacture error of an axicon on beam transmission[J].Journal of Huangzhong University of Science and Technology,2001,29(3):61-63.周莉萍,赵斌,李柱.圆锥透镜加工误差对光束传输变换的影响[J].华中科技大学学报:自然科学版,2001,29(3):61-63.
[23] ZHAI Z,ZHAO B.Diffraction intensity distribution of an axicon illuminated by polychromatic light[J].Journal of Optics A:Pure&Applied Optics,2007,9(10):862.
[24]刘式适,刘式达.特殊函数[M].二版.北京:气象出版社,2002.386-426.
[25] ZHOU Lei.Dynamic micro/nano cutting system modeling for prediction and analysis of surface topography[D].Haerbin:School of Mechatronics Engineering,Harbin Institute of Technology,2009.周磊.微纳米动态切削系统建模及表面形貌的预测分析研究[D].哈尔滨:哈尔滨工业大学机电工程学院,2009.
[26] ZHANG S,CHEN H,WU Z,et al.Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression[J].Optics Express,2017,25(22):27104-27118.