本征广义琼斯矩阵方法

宋东升; 郑远林; 刘虎; 胡维星; 张志云; 陈险峰

doi:10.3788/CO.2019-0163

本征广义琼斯矩阵方法

宋东升^{1, 2, 3, ,},
郑远林^{2, 3},
刘虎¹,
胡维星¹,
张志云¹,
陈险峰^{2, 3}

1.
中国洛阳电子对抗试验中心，河南洛阳 471000
2.
上海交通大学物理与天文学院先进光通讯网络与系统国家重点实验室，上海 200240
3.
上海交通大学激光等离子体重点实验室 IFSA协作创新中心，上海 200240

详细信息

中图分类号: O436.3
计量
- 文章访问数: 2637
- HTML全文浏览量: 1546
- PDF下载量: 122
- 被引次数: 0
出版历程
- 收稿日期: 2019-08-05
- 修回日期: 2019-09-29
- 刊出日期: 2020-06-01

Eigen generalized Jones matrix method

doi: 10.3788/CO.2019-0163

SONG Dong-sheng^{1, 2, 3
, ,},
ZHENG Yuan-lin^{2, 3},
LIU Hu¹,
HU Wei-xing¹,
ZHANG Zhi-yun¹,
CHEN Xian-feng^{2, 3}

1.
Luoyang Electronic Equipment Test Center of China, Luoyang 471000, China
2.
State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
3.
Key Laboratory for Laser Plasma (Ministry of Education), IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China

Funds: Supported by National Natural Science Foundation of China (No. 11734011); Foundation for Development of Science and Technology of Shanghai (No. 17JC1400402)

More Information

Author Bio:
SONG Dong-sheng (1985—), Male, born in Zhengzhou City, Henan Province. M.Sc., Graduated from Shanghai Jiao Tong University in 2018. Engineer, Luoyang Electronic Equipment Test Center of China. His research interests are on nonlinear optics, frequency conversion and light field regulation. E-mail: sds0754@alumni.sjtu.edu.cn

Corresponding author: sds0754@alumni.sjtu.edu.cn

摘要

摘要: 为了描述完全偏振光在非线性晶体中传播时的偏振态及相位变化，本文基于Ortega-Quijano等人在推导非线性晶体的广义琼斯矩阵时采用的微分广义琼斯矩阵方法，提出了本征广义琼斯矩阵方法。与微分广义琼斯矩阵方法相比，本征广义琼斯矩阵方法使用了更精确的数学技巧，在描述光在非线性晶体中传播的物理过程上更为严谨。解决了微分广义琼斯矩阵不能计算斜入射光或者光轴与实验室坐标不重合时光的偏振变化的问题。首先，根据折射率椭球方程和光的入射方向，计算出非线性晶体中本征光的传播方向和折射率。然后，给出了本征光的本征广义琼斯矩阵。最后，计算了本征光的偏振态和相位变化。本文使用本征广义琼斯矩阵对带有一个奇点的涡旋光在KDP晶体中的传播情况进行模拟计算，计算结果表明，本征广义琼斯矩阵方法能够描述任意入射角度、任意光轴方向的完全偏振光在非线性晶体中的传播过程。
- 本征广义琼斯矩阵方法 /
- 偏振和相位 /
- 非线性晶体 /
- 涡旋光
Abstract: A differential generalized Jones matrix method (dGJM) was recently introduced by Ortega-Quijano and colleagues to derive the GJM for modelling uniaxial and biaxial crystals with arbitrary orientations in laboratory coordinate systems. Later, we propose an eigen generalized Jones matrix method to simulate the phase and polarization of fully polarized light propagating in an anisotropic crystal when the optical axis orientations and light directions are both arbitrary. In our method, we use physics that are equivalent in principle to those of Ortega-Quijano, but we use a modified mathematical technique. We introduce the eigen generalized Jones matrix in the intrinsic coordinate system to precisely calculate the phase and polarization of the light, which overcomes the limitations of the differential generalized Jones matrix method. The simulation results indicate that our method can be used to calculate the polarization distribution, regardless of how the light beam and optical axis positioned, or whether the light beam has a vortex.
- eigen general Jones matrix method /
- phase and polarization /
- anisotropic crystal /
- vortex

HTML全文

Figure 1. Schematic diagram of the three coordinate systems. The black, blue, and red axes represent the laboratory, principal, and eigen coordinates, respectively. z₁ and z₂ are the optical axes.

下载: 全尺寸图片幻灯片

Figure 2. Spatial distributions of the polarization state. (a) Original linear polarization. (b) Left(right) polarization. (c) Circular polarization. (d) Right(left) polarization. (e) Opposite linear polarization.

下载: 全尺寸图片幻灯片

Figure 3. Change in walk-off angle with θ_z.

下载: 全尺寸图片幻灯片

Figure 4. Spatial distributions of the polarization state with a right direction walk-off effect. (a) Original linear polarization. (b) Left (right) polarization. (c) Circular polarization. (d) Right (left) polarization. (e) Opposite linear polarization.

下载: 全尺寸图片幻灯片

Figure 5. Change in walk-off angle with (θ, φ)

下载: 全尺寸图片幻灯片

Figure 6. Spatial distributions of the polarization state with a upward-right direction walk-off effect. (a) Original linear polarization. (b) Left(right) polarization. (c) Circular polarization. (d) Right(left) polarization. (e) Opposite linear polarization.

下载: 全尺寸图片幻灯片

Figure 7. Phase difference and polarization. (a) Phase difference of the refracted light beam in birefringent crystals. (b) Polarization of reflection and refracted light beam at the interface in birefringent crystals.

下载: 全尺寸图片幻灯片

Figure 8. (a) Experimental image and (b) simulation results of proposed method.

下载: 全尺寸图片幻灯片

参考文献(30)

[1]	YU F H, KWOK H S. Comparison of extended Jones matrices for twisted nematic liquid-crystal displays at oblique angles of incidence[J]. Journal of the Optical Society of America A, 1999, 16(11): 2772-2780. doi: 10.1364/JOSAA.16.002772
[2]	LIEN A, CHEN C J. A new 2× 2 matrix representation for twisted nematic liquid crystal displays at oblique incidence[J]. Japanese Journal of Applied Physics, 1996, 35(9B): L1200-L1203.
[3]	AZZAM R M A, BASHARA N M. Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings[J]. Journal of the Optical Society of America, 1972, 62(12): 1521-1523. doi: 10.1364/JOSA.62.001521
[4]	CHEN X F, SHI J H, CHEN Y P, et al. Electro-optic Solc-type wavelength filter in periodically poled lithium niobate[J]. Optics Letters, 2003, 28(21): 2115-2117. doi: 10.1364/OL.28.002115
[5]	CHEN L J, SHI J H, CHEN X F, et al. Photovoltaic effect in a periodically poled lithium niobate Solc-type wavelength filter[J]. Applied Physics Letters, 2006, 88(12): 121118. doi: 10.1063/1.2187944
[6]	SHI J H, WANG J H, CHEN L J, et al. Tunable Šolc-type filter in periodically poled LiNbO3 by UV-light illumination[J]. Optics Express, 2006, 14(13): 6279-6284. doi: 10.1364/OE.14.006279
[7]	LIU X, YANG Y, HAN L, et al. Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials[J]. Optics Express, 2017, 25(7): 7288-7299. doi: 10.1364/OE.25.007288
[8]	PURTSELADZE A L, TARASASHVILI V I, SHAVERDOVA V G, et al. Polarization memory of denisyuk holograms formed in unpolarized light[J]. Journal of Applied Spectroscopy, 2014, 81(1): 63-68. doi: 10.1007/s10812-014-9887-8
[9]	YANG H M, MA C W, WANG J Y, et al. The transmission of polarized light of space attitude in quantum communication[J]. Acta Photonica Sinica, 2015, 44(12): 1227002. (in Chinese) doi: 10.3788/gzxb20154412.1227002
[10]	CAROZZI T D. Simple estimation of all-sky, direction-dependent Jones matrix of primary beams of radio interferometers[J]. Astronomy and Computing, 2016, 16: 185-188. doi: 10.1016/j.ascom.2014.11.002
[11]	CAROZZI T D, WOAN G. A fundamental figure of merit for radio polarimeters[J]. IEEE Transactions on Antennas and Propagation, 2011, 59(6): 2058-2065. doi: 10.1109/TAP.2011.2123862
[12]	BRAAF B. Fiber-based Jones-matrix polarization-sensitive OCT of the human retina[J]. Investigative Ophthalmology &Visual Science, 2016, 57(12).
[13]	MENZEL M, MICHIELSEN K, DE RAEDT H, et al. A Jones matrix formalism for simulating three-dimensional polarized light imaging of brain tissue[J]. Journal of the Royal Society Interface, 2015, 12(111): 20150734. doi: 10.1098/rsif.2015.0734
[14]	YANG T D, PARK K, KANG Y G, et al. Single-shot digital holographic microscopy for quantifying a spatially-resolved Jones matrix of biological specimens[J]. Optics Express, 2016, 24(25): 29302-29311. doi: 10.1364/OE.24.029302
[15]	SHEPPARD C J R. Jones and Stokes parameters for polarization in three dimensions[J]. Physical Review A, 2014, 90(2): 023809. doi: 10.1103/PhysRevA.90.023809
[16]	KANG H, JIA B H, GU M. Polarization characterization in the focal volume of high numerical aperture objectives[J]. Optics Express, 2010, 18(10): 10813-10821. doi: 10.1364/OE.18.010813
[17]	ORLOV S, PESCHEL U, BAUER T, et al. Analytical expansion of highly focused vector beams into vector spherical harmonics and its application to Mie scattering[J]. Physical Review A, 2012, 85(6): 063825. doi: 10.1103/PhysRevA.85.063825
[18]	LI E, MAKITA S, HONG Y J, et al. Three-dimensional multi-contrast imaging of in vivo human skin by Jones matrix optical coherence tomography[J]. Biomedical Optics Express, 2017, 8(3): 1290-1305. doi: 10.1364/BOE.8.001290
[19]	JONES R C. A new calculus for the treatment of optical systems. VII. Properties of the N-matrices[J]. Journal of the Optical Society of America, 1948, 38(8): 671-685. doi: 10.1364/JOSA.38.000671
[20]	HE W J, FU Y G, LIU Z Y, et al. Three-dimensional polarization aberration functions in optical system based on three-dimensional polarization ray-tracing calculus[J]. Optics Communications, 2017, 387: 128-134. doi: 10.1016/j.optcom.2016.11.046
[21]	HE W J, FU Y G, ZHENG Y, et al. Polarization properties of a corner-cube retroreflector with three-dimensional polarization ray-tracing calculus[J]. Applied Optics, 2013, 52(19): 4527-4535. doi: 10.1364/AO.52.004527
[22]	LI Y H, FU Y G, LIU Z Y, et al. Three-dimensional polarization algebra for all polarization sensitive optical systems[J]. Optics Express, 2018, 26(11): 14109-14122. doi: 10.1364/OE.26.014109
[23]	ZHANG H Y, LI Y, YAN CH X, et al. Three-dimensional polarization ray tracing calculus for partially polarized light[J]. Optics Express, 2017, 25(22): 26973-26986. doi: 10.1364/OE.25.026973
[24]	YEH P. Extended Jones matrix method[J]. Journal of the Optical Society of America, 1982, 72(4): 507-513. doi: 10.1364/JOSA.72.000507
[25]	AZZAM R M A. Three-dimensional polarization states of monochromatic light fields[J]. Journal of the Optical Society of America A, 2011, 28(11): 2279-2283. doi: 10.1364/JOSAA.28.002279
[26]	ORTEGA-QUIJANO N, ARCE-DIEGO J L. Generalized Jones matrices for anisotropic media[J]. Optics Express, 2013, 21(6): 6895-6900. doi: 10.1364/OE.21.006895
[27]	ORTEGA-QUIJANO N, FADE J, ALOUINI M. Generalized Jones matrix method for homogeneous biaxial samples[J]. Optics Express, 2015, 23(16): 20428-20438. doi: 10.1364/OE.23.020428
[28]	FLOSSMANN F, SCHWARZ U T, MAIER M, et al. Polarization singularities from unfolding an optical vortex through a birefringent crystal[J]. Physical Review Letters, 2005, 95(25): 253901. doi: 10.1103/PhysRevLett.95.253901
[29]	FLOSSMANN F, SCHWARZ U T, MAIER M, et al. Stokes parameters in the unfolding of an optical vortex through a birefringent crystal[J]. Optics Express, 2006, 14(23): 11402-11411. doi: 10.1364/OE.14.011402
[30]	DMITRIEV V G, GURZADYAN G G, NIKOGOSYAN D N. Handbook of Nonlinear Optical Crystals[M]. 3rd ed. Berlin: Springer, 1999.