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Based on the Richard-Wolf vector diffraction theory and the inverse Faraday effect, a method of generating a high-purity longitudinal needle-shaped magnetization field in the uniaxial crystal is proposed. In this method, the inverse radiation of the electric dipole in the uniaxial crystal is used to construct an optimal entry pupil light field through regulating the multi-parameter of the number of electric dipole pairs N and their array, and then the magnetization field of the desired target is obtained by forward tightly focusing. The simulation results show that when N = 1, the focal length of the magnetic field generated in the uniaxial crystal increases by 1.4 times and the lateral resolution increases by 5% compared with the counterparts in an isotropic medium. It can be further seen that when N = 2 and N = 3, with the increase of the number of electric dipole pairs, the focal length of the needle magnetic field generated in the uniaxial crystal increases by 10%, and the lateral resolution increases by 18%. The purity of the needle magnetic field gradually increases to 1 as the magnetization field profile surface value changes from 0.1 to 1. Especially when N = 2 and the contour surface value is 0.1, the magnetic field purity is as high as 95%. The results provide a feasible scheme for generating a longitudinal magnetization field with higher purity and longer focal length in an anisotropic medium, and also present the theoretical guidance for selecting optimal pupil beams in practical applications such as all-optical magnetic recording, atom capture and lithography.
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Keywords:
- electric dipole /
- inverse Faraday effect /
- tight focus /
- uniaxial crystal
[1] Majors P D, Minard K R, Ackerman E J, Holtom G R, Hopkins D F, Parkinson C I, Weber T J, Wind R A 2002 Rev. Sci. Instrum. 73 4329
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[3] Phelan C F, Hennessy T, Busch T 2013 Opt. Express 21 27093
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[4] Grinolds M S, Warner M, De Greve K, Dovzhenko Y, Thiel L, Walsworth R L, Hong S, Maletinsky P, Yacoby A 2014 Nat. Nanotechnol. 9 279
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[5] van der Ziel J P, Pershan P S, Malmstrom L D 1965 Phys. Rev. Lett. 15 190
Google Scholar
[6] Weller D, Moser A 1999 IEEE Trans. Magn. 35 6
Google Scholar
[7] Albrecht M, Rettner C T, Moser A, Best M E, Terris B D 2002 Appl. Phys. Lett. 81 2875
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[8] Helseth L E 2011 Opt. Lett. 36 987
Google Scholar
[9] Yan W, Nie Z, Liu X, Lan G, Zhang X, Wang Y, Song Y 2018 Opt. Express. 26 16824
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[10] Stanciu C D, Hansteen F, Kimel A V, Kirilyuk A, Tsukamoto A, Itoh A, Rasing T 2007 Phys. Rev. Lett. 99 047601
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[11] Zhang Y, Bai J 2008 Phys. Lett. A 372 6294
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[12] Jiang Y, Li X, Gu M 2013 Opt. Lett. 38 2957
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[13] Wang S, Cao Y, Li X 2017 Opt. Lett. 42 5050
Google Scholar
[14] Luo J, Zhang H, Wang S, Shi L, Zhu Z, Gu B, Wang X, Li X 2019 Opt. Lett. 44 727
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[15] Kimel A V, Kirilyuk A, Usachev P A, Pisarev R V, Balbashov A M, Rasing T 2005 Nature 435 655
Google Scholar
[16] Astakhov G V, Kimel A V, Schott G M, Tsvetkov A A, Kirilyuk A, Yakovlev D R, Karczewski G, Ossau W, Schmidt G, Molenkamp L W, Rasing T 2005 Appl. Phys. Lett. 86 152506
Google Scholar
[17] Iihama S, Xu Y, Deb M, Malinowski G, Hehn M, Gorchon J, Fullerton E E, Mangin S 2018 Adv. Mater. 30 e1804004
Google Scholar
[18] Balanis A 2005 Antenna Theory Analysis and Design (Wiley-Interscience)
[19] Chen W, Zhan Q 2009 Opt. Lett. 34 2444
Google Scholar
[20] Chen W, Zhan Q 2010 J. Opt. 12 045707
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[21] Chen W, Zhan Q 2011 Opt. Commun. 284 52
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[22] Wang J, Chen W, Zhan Q 2012 J. Opt. 14 055004
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[23] 李瑾, 冯晓毅, 王明军 2017 装备环境工程 14 18
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Google Scholar
[25] Volkov P V, Novikov M A 2002 Crystallogr. Rep. 47 824
Google Scholar
[26] Aiello A, Lindlein N, Marquardt C, Leuchs G 2009 Phys. Rev. Lett. 103 100401
Google Scholar
[27] 周志龙, 王朝玉, 兰国强, 柴志军, 聂仲泉, 孔德贵 2021 黑龙江大学自然科学学报 38 109
Google Scholar
Zhou Z L, Wang Z Y, Lan G Q, Chai Z J, Nie Z Q, Kong D G 2021 J. Nat. Sci. Heilongjiang Univ. 38 109
Google Scholar
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图 1 单轴晶体中的电偶极子阵列反向辐射构建入瞳光场示意图
Figure 1. Schematic diagram of the incoming pupil light field constructed by the inverse radiation of electric dipole array in the uniaxial crystal.
图 2 辐射场在分界面处的折射情况示意图
Figure 2. Schematic diagram of the refraction of radiation field at the interface.
图 3 (a1)—(c1) 各向同性介质和(a2)—(c2) 单轴晶体中获得的磁化场强度分布图 (a1), (a2) x-z面; (b1), (b2) y-z面; (c1), (c2) x-y面
Figure 3. The magnetization field intensity distributions obtained in the (a1)–(c1) isotropic medium and (a2)–(c2) uniaxial crystal: (a1), (a2) x-z plane; (b1), (b2) y-z plane; (c1), (c2) x-y plane.
图 4 不同介质中的磁化场沿 (a) x轴和 (b) z轴的归一化强度分布(红实线为各向同性介质, 黑虚线为单轴晶体介质)
Figure 4. Normalized intensity distribution of magnetization field along the (a) x axis and (b) z axis in different media (Red lines refer isotropic media, black dotted lines are uniaxial crystal media).
图 5 针形磁化场强度分布图 (a1) N = 2和(a2) N = 3时所需的入瞳光场; (b1) N = 2和(b2) N = 3时x-z面总磁化强度分布; (c1) N = 2和(c2) N = 3时x-z面纵向磁化场分量强度分布; 针形磁化场沿 (d1) x轴和 (d2) z轴的归一化强度分布(红实线和黑虚线分别为N = 2条件下的总场和纵向磁化场分量, 黑实线和蓝点线分别为N = 3条件下的总场和纵向磁化场分量)
Figure 5. Intensity distributions of the needle magnetic field: required entrance pupil light field when (a1) N = 2 and (a2) N = 3; total magnetization on the x-z plane when (b1) N = 2 and (b2) N = 3; longitudinal magnetization field component strength distribution of the x-z plane when (c1) N = 2 and (c2) N = 3; the normalized intensity distribution of the needle-shaped magnetization field along the (d1) x axis and (d2) z axis (The red solid line and the black dotted line are the total field and longitudinal magnetization field component under the condition of N = 2, respectively; the black solid line and the blue dotted line are the total field and the longitudinal magnetization field component under the condition of N = 3).
图 6 磁化取向纯度对轮廓表面的依赖关系 (a) 轮廓表面值示意图; (b) 取向纯度与轮廓表面值变化曲线图
Figure 6. Dependence of the magnetic orientation purity on the contour surface: (a) Schematic diagram of contour surface values; (b) change curve of orientation purity and contour surface value.
表 1 电偶极子对数N的仿真参数
Table 1. Simulation parameters for electric dipole logarithms N .
电偶极子对数N ${A_n}$ ${d_n}$ ${\beta _n}$ N = 2 ${A_1} = 1.00$ ${d_1} = {\text{3}}{\text{.00}}\lambda $ ${\beta _1} = {\text{5}}{\text{.00\pi }}$ ${A_2} = {\text{1}}{\text{.04}}$ ${d_2} = {\text{4}}{\text{.99}}\lambda $ ${\beta _2} = {\text{5.01\pi } }$ N = 3 ${A_1} = {\text{0}}{\text{.99}}$ ${d_1} = {\text{3}}{\text{.06}}\lambda $ ${\beta _1} = {\text{5}}{\text{.00\pi }}$ ${A_2} = {\text{1}}{\text{.01}}$ ${d_2} = {\text{1}}{\text{.00}}\lambda $ ${\beta _2} = {\text{4}}{\text{.97\pi }}$ ${A_{\text{3}}} = {\text{1}}{\text{.00}}$ ${d_3} = {\text{1}}{\text{.01}}\lambda $ ${\beta _{\text{3}}} = {\text{5}}{\text{.00\pi }}$ 
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[1] Majors P D, Minard K R, Ackerman E J, Holtom G R, Hopkins D F, Parkinson C I, Weber T J, Wind R A 2002 Rev. Sci. Instrum. 73 4329
Google Scholar
[2] Atutov S N, Calabrese R, Guidi V, Mai B, Rudavets A G, Scansani E, Tomassetti L, Biancalana V, Burchianti A, Marinelli C, Mariotti E, Moi L, Veronesi S 2003 Phys. Rev. A 67 053401
Google Scholar
[3] Phelan C F, Hennessy T, Busch T 2013 Opt. Express 21 27093
Google Scholar
[4] Grinolds M S, Warner M, De Greve K, Dovzhenko Y, Thiel L, Walsworth R L, Hong S, Maletinsky P, Yacoby A 2014 Nat. Nanotechnol. 9 279
Google Scholar
[5] van der Ziel J P, Pershan P S, Malmstrom L D 1965 Phys. Rev. Lett. 15 190
Google Scholar
[6] Weller D, Moser A 1999 IEEE Trans. Magn. 35 6
Google Scholar
[7] Albrecht M, Rettner C T, Moser A, Best M E, Terris B D 2002 Appl. Phys. Lett. 81 2875
Google Scholar
[8] Helseth L E 2011 Opt. Lett. 36 987
Google Scholar
[9] Yan W, Nie Z, Liu X, Lan G, Zhang X, Wang Y, Song Y 2018 Opt. Express. 26 16824
Google Scholar
[10] Stanciu C D, Hansteen F, Kimel A V, Kirilyuk A, Tsukamoto A, Itoh A, Rasing T 2007 Phys. Rev. Lett. 99 047601
Google Scholar
[11] Zhang Y, Bai J 2008 Phys. Lett. A 372 6294
Google Scholar
[12] Jiang Y, Li X, Gu M 2013 Opt. Lett. 38 2957
Google Scholar
[13] Wang S, Cao Y, Li X 2017 Opt. Lett. 42 5050
Google Scholar
[14] Luo J, Zhang H, Wang S, Shi L, Zhu Z, Gu B, Wang X, Li X 2019 Opt. Lett. 44 727
Google Scholar
[15] Kimel A V, Kirilyuk A, Usachev P A, Pisarev R V, Balbashov A M, Rasing T 2005 Nature 435 655
Google Scholar
[16] Astakhov G V, Kimel A V, Schott G M, Tsvetkov A A, Kirilyuk A, Yakovlev D R, Karczewski G, Ossau W, Schmidt G, Molenkamp L W, Rasing T 2005 Appl. Phys. Lett. 86 152506
Google Scholar
[17] Iihama S, Xu Y, Deb M, Malinowski G, Hehn M, Gorchon J, Fullerton E E, Mangin S 2018 Adv. Mater. 30 e1804004
Google Scholar
[18] Balanis A 2005 Antenna Theory Analysis and Design (Wiley-Interscience)
[19] Chen W, Zhan Q 2009 Opt. Lett. 34 2444
Google Scholar
[20] Chen W, Zhan Q 2010 J. Opt. 12 045707
Google Scholar
[21] Chen W, Zhan Q 2011 Opt. Commun. 284 52
Google Scholar
[22] Wang J, Chen W, Zhan Q 2012 J. Opt. 14 055004
Google Scholar
[23] 李瑾, 冯晓毅, 王明军 2017 装备环境工程 14 18
Google Scholar
Li J, Feng X Y, Wang M J 2017 Equip. Environ. Eng. 14 18
Google Scholar
[24] Stallinga S 2001 J. Opt. Soc. Am. A 18 2846
Google Scholar
[25] Volkov P V, Novikov M A 2002 Crystallogr. Rep. 47 824
Google Scholar
[26] Aiello A, Lindlein N, Marquardt C, Leuchs G 2009 Phys. Rev. Lett. 103 100401
Google Scholar
[27] 周志龙, 王朝玉, 兰国强, 柴志军, 聂仲泉, 孔德贵 2021 黑龙江大学自然科学学报 38 109
Google Scholar
Zhou Z L, Wang Z Y, Lan G Q, Chai Z J, Nie Z Q, Kong D G 2021 J. Nat. Sci. Heilongjiang Univ. 38 109
Google Scholar
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