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单轴晶体中产生的高纯度纵向针形磁化场

许琳茜 朱榕琪 朱竹青 贡丽萍 顾兵

许琳茜, 朱榕琪, 朱竹青, 贡丽萍, 顾兵. 单轴晶体中产生的高纯度纵向针形磁化场. 物理学报, 2022, 71(14): 147801. doi: 10.7498/aps.71.20220316
引用本文: 许琳茜, 朱榕琪, 朱竹青, 贡丽萍, 顾兵. 单轴晶体中产生的高纯度纵向针形磁化场. 物理学报, 2022, 71(14): 147801. doi: 10.7498/aps.71.20220316
Xu Lin-Xi, Zhu Rong-Qi, Zhu Zhu-Qing, Gong Li-Ping, Gu Bing. High-purity longitudinal needle-shaped magnetization fields produced in uniaxial crystals. Acta Phys. Sin., 2022, 71(14): 147801. doi: 10.7498/aps.71.20220316
Citation: Xu Lin-Xi, Zhu Rong-Qi, Zhu Zhu-Qing, Gong Li-Ping, Gu Bing. High-purity longitudinal needle-shaped magnetization fields produced in uniaxial crystals. Acta Phys. Sin., 2022, 71(14): 147801. doi: 10.7498/aps.71.20220316

单轴晶体中产生的高纯度纵向针形磁化场

许琳茜, 朱榕琪, 朱竹青, 贡丽萍, 顾兵

High-purity longitudinal needle-shaped magnetization fields produced in uniaxial crystals

Xu Lin-Xi, Zhu Rong-Qi, Zhu Zhu-Qing, Gong Li-Ping, Gu Bing
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  • 基于理查德-沃尔夫矢量衍射理论和逆法拉第效应, 提出一种在单轴晶体中产生高纯度纵向针形磁化场的方法. 该方法通过电偶极子对数N及其阵列多参数调控, 利用单轴晶体中的电偶极子反向辐射构建出优化的入瞳光场, 再正向紧聚焦获得所需目标磁化场. 模拟结果表明: 当N = 1时, 单轴晶体中产生的磁化场比在同性介质中焦深长度增加近1.4倍, 横向分辨率提高5%. 当N = 2和N = 3时, 单轴晶体中获得的纵向针形磁化场随着电偶极子对数增加, 轴向焦深增加了10%, 横向分辨率提高了18%. 随着磁化场轮廓表面值从0.1变化到1, 针形磁化场的纯度逐渐增大到1. 尤其当N = 2、轮廓表面值为0.1时, 磁化场纯度高达95%. 研究结果为在各向异性介质中生成更高纯度、针长更长的纵向磁化场提供了可行性方案, 也为全光磁记录、原子捕获和光刻等实际应用中入瞳光场的优化选取提供了理论指导.
    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.
      PACS:
      通信作者: 朱竹青, zhuqingzhu@njnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12174196, 12104288)资助的课题.
      Corresponding author: Zhu Zhu-Qing, zhuqingzhu@njnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174196, 12104288).

    随着超短激光脉冲技术的迅速发展, 激光与磁性材料相互作用引起的特殊效应引起了研究者的广泛关注[1-4]. 其中, 圆偏振光在磁性材料中所引起的逆法拉第效应(inverse Faraday effect, IFE)[5-9]为磁记录提供了更便捷的全光磁记录新方案. 与矢量光焦场调控紧密结合, 该技术将会成为下一代高密度、大容量和高速率的新型存储技术中最有效的途径之一. Stanciu等[10]使用无定形的铁磁合金Gd22Fe74.6Co3.4作为研究对象, 利用40 fs的圆偏振光实验实现了偏振依赖的全光磁反转. 张耀举等[11]对圆偏振光在紧聚焦条件下(数值孔径NA = 0.85)诱导的磁化场分布进行了理论分析, 发现磁化场横纵比约为24%, 纵向磁化场纯度较低, 这将影响全光磁记录的稳定性和磁化反转效率. 顾敏等[12]用一阶角向偏振涡旋光束产生了纯纵向磁化场. 与圆偏振光诱导的磁化场相比, 该磁化场半高全宽(full width at half maximum, FWHM)减少了约15%, 记录密度高达1.4倍. 王思聪等[13]进一步利用二元编码的滤波器来控制紧聚焦场分布, 构造出超长的纯纵向磁针, 该超长磁针可与磁记录充分作用, 能进一步提高磁化反转效率. 本课题组也通过电偶极子阵列反演辐射方法生成了磁化取向任意可控的高纯度磁针阵列[14], 为全光磁记录提供了新的调控自由度. 然而上述研究的磁化场所考虑的记录材料均是各向同性的非磁性光磁材料, 而记录材料的光学各向异性却被忽略, 这将会影响磁化场实际应用中的精准调控.

    近年来, 研究者们在有钙钛矿型结构的各向异性晶体(DyFeO3)[15]、四重磁各向异性的(Ga, Mn)As[16]材料以及[Co/Pt]/Cu/GdFe6Co磁自旋阀结构[17]中相继观察到IFE. 考虑到实际应用中全光磁记录材料的光学各向异性问题, 基于天线理论、理查德-沃尔夫矢量衍射理论和IFE, 本文研究了单轴晶体中电偶极子及阵列辐射理论, 通过调控电偶极子对性能参数, 反向构建优化的入瞳光场, 从而在单轴晶体中产生高纯度纵向针形磁化场. 研究结果将在全光磁记录、磁粒子捕获以及光刻等领域中具有重要的理论意义和应用价值.

    图1所示为单轴晶体中电偶极子阵列反向辐射构建入瞳光场示意图. 为便于分析, 单轴晶体主轴与成像系统光轴(z轴)一致. 2N个相同的电偶极子对沿着z轴对称放置于高数值孔径(numerical aperture, NA)透镜(焦距为f )焦点O(z = 0)处附近, 单轴晶体与空气分界面位于z = –d处, 出瞳面位于z = –f处. 每个电偶极子对由两个正交振荡的电偶极子组成, 电偶极子1(D1)沿着x轴振荡, 电偶极子2(D2)沿着y轴振荡, D1和D2之间具有π/2的相位延迟, 可形成x-y面的圆偏振光. 在入瞳面收集正交电偶极子对的反向辐射场, 从而获得反向构建的入瞳光场. 通过紧聚焦正向运算, 最终在单轴晶体中可以获得目标光诱导磁化场.

    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\r\nFig. 1. Schematic diagram of the incoming pupil light field constructed by the inverse radiation of electric dipole array in the  uniaxial crystal.
    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
    Fig. 1.  Schematic diagram of the incoming pupil light field constructed by the inverse radiation of electric dipole array in the uniaxial crystal.

    单轴晶体的介电张量表示为

    (1)

    其中, $ {\varepsilon _{11}}, {\text{ }}{\varepsilon _{{\text{22}}}}, {\text{ }}{\varepsilon _{33}} $为主相对介电系数, 且${\varepsilon _{11}} = {\varepsilon _{{\text{22}}}} = n_{\text{o}}^2$, ${\varepsilon _{33}} = n_{\text{e}}^2$, ${n_{\text{o}}}$${n_{\text{e}}}$分别表示单轴晶体中寻常光(o光)和非常光(e光)的折射率. 基于天线理论和电场叠加原理[18-22], 忽略偶极子对间相互耦合作用, 球面上A点处收集的辐射场${{\boldsymbol{E}}_A}$可表示为

    (2)

    其中

    (3)

    (2)式中, ${{\boldsymbol{E}}}_{\theta }和{{\boldsymbol{E}}}_{\varphi }$分别表示A点处总辐射电场在仰角$\theta 和方位角\varphi$方向的分量; $C = {\text{j}}{z_{{\text{air}}}}{I_0}{l_0}{{\text{e}}^{ - {\text{j}}{\boldsymbol{k}}f}}$, $ {z_{{\text{air}}}} $为阻抗系数, $ {I_0} $$ {l_0} $分别是标准电流和电偶极子长度, ${\boldsymbol{k}} = 2{\text{π }}/\lambda$为真空中的波矢. $ AU(\theta ) $表示电偶极子阵列调控函数, $ {d_n} $, $ {\beta _n} $$ {A_n} $分别表示第n组电偶极子对的间距、初始相位差和归一化振幅比. ${\boldsymbol{V}}(\theta , \varphi )$是描述单对电偶极子对叠加的总电场.

    假设${{\boldsymbol{E}}_1}$, ${{\boldsymbol{E}}_2}$分别表示D1, D2在A点的辐射电场, 则${\boldsymbol{V}}(\theta , \varphi )$可表示为

    (4)

    根据电偶极子的各向异性辐射特性[23], ${{\boldsymbol{E}}_1}$, ${{\boldsymbol{E}}_2}$可进一步推导并表示为

    (5)

    式中${{\boldsymbol{e}}_\theta }$${{\boldsymbol{e}}_\varphi }$分别是沿仰角$ \theta $方向和沿方位角$ \varphi $方向的单位矢量, 系数$ A(\theta ) $, $ B(\theta ) $, $ C(\theta ) $, $ D(\theta ) $分别为

    (6)
    (7)
    (8)
    (9)

    由于各向同性介质(空气)和单轴晶体之间存在分界面, 电偶极子在分界面处的辐射需要考虑偏振态平行和垂直分量透射系数的差异和相应的像差函数. 辐射场从焦点(z = 0)到出瞳面(z = –f )传播中在分界面(z = –d )处折射情况如图2所示. 其中, k1, k2分别为介质1和介质2中的波矢, p1, p2s1, s2分别表示介质1和介质2中辐射光场平行和垂直的偏振矢量.

    图 2 辐射场在分界面处的折射情况示意图\r\nFig. 2. Schematic diagram of the refraction of radiation field at the interface.
    图 2  辐射场在分界面处的折射情况示意图
    Fig. 2.  Schematic diagram of the refraction of radiation field at the interface.

    根据斯涅耳定律$ {n_1}\sin {\theta _1} = {n_{\text{o}}}\sin \theta $可得透射系数为

    (10)

    其中, ${\theta _{\text{1}}}$表示在介质1中出射光场与z轴的夹角, $\theta $表示在介质2中入射光场与z轴的夹角.

    由于分界面的存在而产生的像差函数表示为[24]

    (11)

    p偏振和s偏振的像差函数表示为[24]

    (12)

    其中, $ \Delta W $表示在介质2中由o光和e光所引起的像差, $ \Delta n = {n_{\text{e}}} - {n_{\text{o}}} $表示介质2中e光和o光的折射率差, 当介质2是各向同性介质时, 则${n_{\text{o}}} = {n_{\text{e}}}$.

    基于(4)式—(12)式以及光的传播特性, 透射后$A'$点处总辐射电场表示为

    (13)

    假设高数值孔径透镜满足正弦条件, 即$r = f\sin {\theta _1}$, 其中$r$表示聚焦系统的径向坐标, 则所获得的入瞳光场表示为

    (14)

    根据单轴晶体中矢量衍射理论[24], 将入瞳光场经高数值孔径紧聚焦后可得到所需的目标焦场${\boldsymbol{E}}$. 考虑晶系具有多样性, 不同的晶系下所诱导磁化场也会发生改变. 文中仅研究输入光垂直入射条件下单轴晶体(例如32, 3m, $\overline 3 $m晶系晶体, 光沿着晶体光轴传播)的情况. 相应的诱导磁化场M表示为[25]

    (15)

    其中, ${{\boldsymbol{E}}^ * }$表示焦场${\boldsymbol{E}}$的共轭, $ {\gamma _1} $$ {\gamma _2} $是单轴晶体的各向异性磁光常数, 与材料的各向异性磁化率成正比. 从(15)式可以看出, 单轴晶体中的诱导磁化场总强度将大于各向同性介质中的情况, 特别是单轴晶体中磁化场纵向分量的强度比在各向同性介质中的强度增加了${\gamma _{\text{2}}}{\text{/}}{\gamma _{\text{1}}}$倍, 这将有助于提高全光磁记录的翻转效率和可靠性.

    为了研究单轴晶体中磁化场分布特性与针形磁化场调控, 本节进行了数值模拟. 如无特别说明, 所选参数为: NA = 0.95, $\lambda $= 633 nm, $ {n_1} $ = 1, $ {n_{\text{o}}} $= 1.5427, $ \Delta n $ = 0.005, $ {\gamma _2}/{\gamma _1} $ = 2, d = ${\text{2}}\lambda $.

    图3为电偶极子对(N = 1)位于焦点处时, 在各向同性介质(第一行)和单轴晶体(第二行)中所获得的磁化场强度分布图. $\lambda $是聚焦光束的波长. 图4为各向同性介质和单轴晶体中沿x轴和沿z轴的归一化强度分布. 相比于各向同性介质, 单轴晶体中磁化场轴向焦深(depth of focus, DOF)从$1.2387\lambda $增加到$2.{\text{8942}}\lambda $, 增长了近1.4倍(这里DOF为磁场强度最大处的50%的轴向全宽), FWHM从$0.4{\text{769}}\lambda $减小到$0.4{\text{570}}\lambda $, 横向分辨率提高了5%, 同时峰值强度产生了因非零横向自旋角动量引起的x轴方向的微小位移[26]. 可见, x-y平面磁斑尺寸非常接近理论衍射极限, 而纵向磁斑尺寸突破了衍射极限, 这是因为单轴晶体介质中的双折射效应使得e光诱导的纯纵向磁化场增强, 将有助于提高全光磁记录的密度. 该结果充分显示出各向异性材料在全光磁记录中的优势, 也直观反映所建模型对磁化场实际应用研究的重要性.

    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\r\nFig. 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 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
    Fig. 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)\r\nFig. 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 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)
    Fig. 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).

    随着N的增加, 所获得的磁化场DOF就越长, 但其轴向强度分布会变得不均匀. 因此, 通过经验直接搜索法[27]可以优化电偶极子对阵列混合辐射场参数. 首先, 设置电偶极子阵列初始值分别为$ {A}_{n}=1, {\beta }_{n}=\text{π} $, 调试${d_n}$的值使得聚焦后的光致磁化场在聚焦区域内具有相对较长的深度; 其次, 调试${A_n}$, 使得在DOF范围内磁化场的最大值能够保持近似相等; 最后, 通过调试${\beta _n}$, 使得磁化场的轴向强度更加均匀. 以电偶极子对数N = 2和N = 3为例, 优化参数如表1所列.

    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 }}$
    下载: 导出CSV 
    | 显示表格

    图5所示为当电偶极子对数N = 2和N = 3时正向计算的针形磁化场分布图. 图5(a1), (a2)为生成针形磁化场所需的入瞳光场, 绿色标记和紫色标记分别表示右旋和左旋椭圆偏振, ${R_{\text{m}}}$表示入射光瞳的最大半径. 从图5(b1), (b2)中可以看出在焦域处形成了沿z方向均匀分布的针形磁化场; N = 2时轴向DOF达$7.799\lambda $, 横向FWHM仅为$0.7688\lambda $, 接近光学衍射极限, 磁针的纵横比可达10; N = 3时轴向DOF达$8.5073\lambda $, 横向FWHM仅为$0.63717\lambda $, 如图5(d1), (d2)所示. 相比于电偶极子对数N = 2的情况, 轴向DOF增加了10%, 横向分辨率提高了18%, 由于电偶极子参数之间会产生相互的制约, 从而导致针形磁化场的轴向强度的均匀性有所降低. 从图5(c1), (c2)中可以发现, 磁化场总场及其纵向分量的轴向DOF完全一致, 径向分量导致磁化场具有较小的旁瓣, 使得总场的FWHM相比于纵向分量增加了$0.{\text{02}}\lambda $, 仅占总场的2%. 这表明磁化场纵向分量${{\boldsymbol{M}}_z}$在总磁化场分布中占主要部分, 针形磁化场磁化取向纯度高.

    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)\r\nFig. 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 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)
    Fig. 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).

    由于聚焦透镜的衍射孔径尺寸有限, 所获得的目标焦场偏振态分布与所设想的圆偏振会有不同, 从而会影响所生成的磁化场取向纯度. 为便于定量评价磁化场取向纯度, 定义

    (16)

    式中${{\boldsymbol{M}}_z}\left( {\theta , \varphi } \right)$表示磁化场的纵向分量.

    图6N = 2和N = 3时生成的纵向针形磁化场的取向纯度P与轮廓表面值的依赖关系, 其中图6(a)为轮廓表面值示意图. 从图6(b)可以看出, 不同N条件下, 随着轮廓表面值从0.1变化到1的过程中, 针形磁化场的纯度逐渐增大. 当N = 2时, 纯度从0.95逐渐增加到1, 即使轮廓表面值低至0.1时, 纯度依然高达0.95. 相比于N = 3情况下的纯度值0.928有所增加, 这可能与N = 3时电偶极子参数优化有关. 该结果表明在各向异性介质中能够生成高纯度纵向针形磁化场, 为提高全光磁记录中磁化翻转有效性提供新的实现方法.

    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\r\nFig. 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.
    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
    Fig. 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.

    研究了单轴晶体中高纯度纵向针形磁化场的生成与调控, 通过收集单轴晶体中电偶极子对及阵列反向辐射场的方法, 理论上推导出了入瞳光场的数学表达式, 再对入瞳光场紧聚焦后获得了纯度大于95%的纵向针形磁化场. 逆向的计算方法解决了正向计算方法所面临的挑战和局限性, 并提供了入射光瞳面电场控制与焦场偏振态控制之间的相关性, 简化了磁化场控制. 相对各向同性介质, 单轴晶体中产生的磁化场磁斑DOF增加了近1.4倍. 在N = 2的情况下, 通过经验直接搜索法优化电偶极子和阵列参数, 在单轴晶体中能够获得横向FWHM达$0.76{\text{88}}\lambda $、轴向DOF达$7.799\lambda $和纯度大于95%的纵向针形磁化场. 增加电偶极子对数(如N = 3), 可获得轴向DOF达$8.5073\lambda $, 横向FWHM仅为$0.63717\lambda $的针形磁化场. 另外, 磁化取向纯度对轮廓表面的依赖关系也充分表明了在各向异性介质中能够生成高纯度纵向针形磁化场. 因此, 本文的研究结果不仅解决了磁化场调控局限于各向同性介质中的实际问题, 同时也为针形磁化场的调控与性能优化提供了可行方法, 这将在自旋电子学和全光磁记录方面具有潜在的实际应用价值.

    [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 4329Google 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 053401Google Scholar

    [3]

    Phelan C F, Hennessy T, Busch T 2013 Opt. Express 21 27093Google 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 279Google Scholar

    [5]

    van der Ziel J P, Pershan P S, Malmstrom L D 1965 Phys. Rev. Lett. 15 190Google Scholar

    [6]

    Weller D, Moser A 1999 IEEE Trans. Magn. 35 6Google Scholar

    [7]

    Albrecht M, Rettner C T, Moser A, Best M E, Terris B D 2002 Appl. Phys. Lett. 81 2875Google Scholar

    [8]

    Helseth L E 2011 Opt. Lett. 36 987Google Scholar

    [9]

    Yan W, Nie Z, Liu X, Lan G, Zhang X, Wang Y, Song Y 2018 Opt. Express. 26 16824Google Scholar

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    Stanciu C D, Hansteen F, Kimel A V, Kirilyuk A, Tsukamoto A, Itoh A, Rasing T 2007 Phys. Rev. Lett. 99 047601Google Scholar

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    Zhang Y, Bai J 2008 Phys. Lett. A 372 6294Google Scholar

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    Jiang Y, Li X, Gu M 2013 Opt. Lett. 38 2957Google Scholar

    [13]

    Wang S, Cao Y, Li X 2017 Opt. Lett. 42 5050Google Scholar

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    Luo J, Zhang H, Wang S, Shi L, Zhu Z, Gu B, Wang X, Li X 2019 Opt. Lett. 44 727Google Scholar

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    Kimel A V, Kirilyuk A, Usachev P A, Pisarev R V, Balbashov A M, Rasing T 2005 Nature 435 655Google 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 152506Google Scholar

    [17]

    Iihama S, Xu Y, Deb M, Malinowski G, Hehn M, Gorchon J, Fullerton E E, Mangin S 2018 Adv. Mater. 30 e1804004Google Scholar

    [18]

    Balanis A 2005 Antenna Theory Analysis and Design (Wiley-Interscience)

    [19]

    Chen W, Zhan Q 2009 Opt. Lett. 34 2444Google Scholar

    [20]

    Chen W, Zhan Q 2010 J. Opt. 12 045707Google Scholar

    [21]

    Chen W, Zhan Q 2011 Opt. Commun. 284 52Google Scholar

    [22]

    Wang J, Chen W, Zhan Q 2012 J. Opt. 14 055004Google Scholar

    [23]

    李瑾, 冯晓毅, 王明军 2017 装备环境工程 14 18Google Scholar

    Li J, Feng X Y, Wang M J 2017 Equip. Environ. Eng. 14 18Google Scholar

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    Stallinga S 2001 J. Opt. Soc. Am. A 18 2846Google Scholar

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    Volkov P V, Novikov M A 2002 Crystallogr. Rep. 47 824Google Scholar

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    Aiello A, Lindlein N, Marquardt C, Leuchs G 2009 Phys. Rev. Lett. 103 100401Google Scholar

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    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 109Google 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 109Google Scholar

    期刊类型引用(1)

    1. 蒋驰,耿滔. 角向偏振涡旋光的紧聚焦特性研究以及超长超分辨光针的实现. 物理学报. 2023(12): 113-120 . 百度学术

    其他类型引用(0)

  • 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

    Fig. 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

    Fig. 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

    Fig. 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)

    Fig. 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)

    Fig. 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

    Fig. 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 }}$
    下载: 导出CSV
  • [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 4329Google 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 053401Google Scholar

    [3]

    Phelan C F, Hennessy T, Busch T 2013 Opt. Express 21 27093Google 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 279Google Scholar

    [5]

    van der Ziel J P, Pershan P S, Malmstrom L D 1965 Phys. Rev. Lett. 15 190Google Scholar

    [6]

    Weller D, Moser A 1999 IEEE Trans. Magn. 35 6Google Scholar

    [7]

    Albrecht M, Rettner C T, Moser A, Best M E, Terris B D 2002 Appl. Phys. Lett. 81 2875Google Scholar

    [8]

    Helseth L E 2011 Opt. Lett. 36 987Google Scholar

    [9]

    Yan W, Nie Z, Liu X, Lan G, Zhang X, Wang Y, Song Y 2018 Opt. Express. 26 16824Google Scholar

    [10]

    Stanciu C D, Hansteen F, Kimel A V, Kirilyuk A, Tsukamoto A, Itoh A, Rasing T 2007 Phys. Rev. Lett. 99 047601Google Scholar

    [11]

    Zhang Y, Bai J 2008 Phys. Lett. A 372 6294Google Scholar

    [12]

    Jiang Y, Li X, Gu M 2013 Opt. Lett. 38 2957Google Scholar

    [13]

    Wang S, Cao Y, Li X 2017 Opt. Lett. 42 5050Google Scholar

    [14]

    Luo J, Zhang H, Wang S, Shi L, Zhu Z, Gu B, Wang X, Li X 2019 Opt. Lett. 44 727Google Scholar

    [15]

    Kimel A V, Kirilyuk A, Usachev P A, Pisarev R V, Balbashov A M, Rasing T 2005 Nature 435 655Google 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 152506Google Scholar

    [17]

    Iihama S, Xu Y, Deb M, Malinowski G, Hehn M, Gorchon J, Fullerton E E, Mangin S 2018 Adv. Mater. 30 e1804004Google Scholar

    [18]

    Balanis A 2005 Antenna Theory Analysis and Design (Wiley-Interscience)

    [19]

    Chen W, Zhan Q 2009 Opt. Lett. 34 2444Google Scholar

    [20]

    Chen W, Zhan Q 2010 J. Opt. 12 045707Google Scholar

    [21]

    Chen W, Zhan Q 2011 Opt. Commun. 284 52Google Scholar

    [22]

    Wang J, Chen W, Zhan Q 2012 J. Opt. 14 055004Google Scholar

    [23]

    李瑾, 冯晓毅, 王明军 2017 装备环境工程 14 18Google Scholar

    Li J, Feng X Y, Wang M J 2017 Equip. Environ. Eng. 14 18Google Scholar

    [24]

    Stallinga S 2001 J. Opt. Soc. Am. A 18 2846Google Scholar

    [25]

    Volkov P V, Novikov M A 2002 Crystallogr. Rep. 47 824Google Scholar

    [26]

    Aiello A, Lindlein N, Marquardt C, Leuchs G 2009 Phys. Rev. Lett. 103 100401Google 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 109Google 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 109Google Scholar

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  • 期刊类型引用(1)

    1. 蒋驰,耿滔. 角向偏振涡旋光的紧聚焦特性研究以及超长超分辨光针的实现. 物理学报. 2023(12): 113-120 . 百度学术

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出版历程
  • 收稿日期:  2022-02-21
  • 修回日期:  2022-03-26
  • 上网日期:  2022-07-05
  • 刊出日期:  2022-07-20

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