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Achieving low frequency electromagnetic wave absorption by gyromagnetic ferrite

Ye Kang-Ping Pei Wen-Jin Xi Xiang Pu Yin Wu Rui-Xin

Achieving low frequency electromagnetic wave absorption by gyromagnetic ferrite

Ye Kang-Ping, Pei Wen-Jin, Xi Xiang, Pu Yin, Wu Rui-Xin
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  • Under the action of static bias magnetic field, the magnetized ferrite has a permeability tensor which can be adjusted by the applied magnetic field. In this paper, the absorption properties of bulk gyromagnetic ferrites under different magnetized conditions are studied and the great potential of gyromagnetic ferrite in achieving low frequency electromagnetic wave absorption is demonstrated. Full wave electromagnetic simulations are performed based on the finite element method (FEM). A floquet port is adopted at the top boundary of the unit cell to simulate a normally incident plane wave. The unit cell boundary conditions are used in the x-y plane to simulate a periodic structure. Orthogonality magnetization in plane is utilized to solve the polarization selectivity in the condition of transverse magnetic field. The influence on absorption capacity of discrete ferrite array structure and the coupling effect of ferrite elements with different sizes are also studied in consideration of the size effect. The simulation results show that a thin bulk gyromagnetic ferrite layer whose thickness is only 4 mm can possess frequency as low as 0.48 GHz and reflectivity below –10 dB. Gyromagnetic ferrite presents different absorption properties under longitudinal magnetization and transversal magnetization, and different polarization directions in transversal magnetization as well. When longitudinal bias magnetic field H0 = 200 Oe, the bandwidth of the reflectivity below –10 dB ranges from 0.48 to 1.84 GHz. The resonant absorption frequency can be regulated by adjusting bias magnetic field and the size of ferrite element. In general, a large bias magnetic field leads to a high resonant frequency due to the ferromagnetic resonance frequency positively associated with the applied magnetic field, but a ferrite array consisting of larger size elements provides a lower resonant frequency for the size resonance negatively associated with the size. By introducing the coupling between elements with different sizes, the reflection bandwidth below –10 dB can be effectively extended to above 80% of the sum of the bandwidth possessed by single unit cell, especially 105.7% under transversal bias magnetic field 700 Oe. And the broadening effect is effective in both longitudinal and transverse magnetized state but it will be weaker when the two absorption peaks are closer. To further understand the absorption mechanism of the two-element absorber, the distribution of the electric field, magnetic field and power loss density are examined. The results prove that the two peaks at the lower frequency exactly originates from $ \Delta R = 0$ and the higher frequency originates from $ \Delta R = 4$, and therefore the widened absorption is contributed by the coupled multiple resonances provided by the elements with different sizes.
      Corresponding author: Wu Rui-Xin, rxwu@nju.edu.cn
    [1]

    Landy N I, Sajuyigbe S, Mock J J, Smith D R, Padilla W J 2008 Phys. Rev. Lett. 100 207402

    [2]

    Ding F, Cui Y X, Ge X C, Jin Y, He S L 2012 Appl. Phys. Lett. 100 103506

    [3]

    Zhang Y, Huang Y, Zhang T F, Chang H C, Xiao P S, Chen H H, Huang Z Y, Chen Y S 2015 Adv. Mater. 27 2049

    [4]

    Wang Y, Du Y C, Xu P, Qiang R, Han X J 2017 Polymers 9 29

    [5]

    Liu Y P, Zhang B Z, Duan J P, Xu Y G 2018 Appl. Opt. 57 10257

    [6]

    Zhang X J, Wang G S, Cao W Q, Wei Y Z, Liang J F, Guo L, Cao M S 2014 ACS Appl. Mater. Interfaces 6 7471

    [7]

    Zhang Y, Huang Y, Chen H H, Huang Z Y, Yang Y, Xiao P S, Zhou Y, Chen Y S 2016 Carbon 105 438

    [8]

    Wang D J, Zhang J Y, He P, Hou Z L 2019 Ceram. Int. 45 23043

    [9]

    周卓辉, 刘晓来, 黄大庆, 康飞宇 2014 物理学报 63 184101

    Zhou Z H, Liu X L, Huang D Q, Kang F Y 2014 Acta Phys. Sin. 63 184101

    [10]

    Zhang K L, Zhang J Y, Hou Z L, Bi S, Zhao Q L 2019 Carbon 141 608

    [11]

    Wang J, Gao C N, Jiang Y N, Charles N A 2017 Chin. Phys. B 26 114102

    [12]

    Wang Y, Du Y C, Qiang R, Tian C H, Xu P, Han X J 2016 Adv. Mater. Interfaces 3 1500684

    [13]

    Alkuh M S, Famili M H N, Shirvan M M M, Moeini M H 2016 Mater. Des. 100 73

    [14]

    Amano M, Kotsuka Y 2003 IEEE Trans. Microwave Theory Tech. 51 238

    [15]

    Kazantsev Y N, Lopatin A V, Kazantseva N E, Shatrov A D, Mal'tsev V P, Vilcakova J, Saha P 2010 IEEE Trans. Antennas Propag. 58 1227

    [16]

    Chen H Y, Zhang H B, Deng L J 2010 IEEE Antennas Wirel. Propag. Lett. 9 899

    [17]

    Rozanov K N, Li Z W, Chen L F, Koledintseva M Y 2005 J. Appl. Phys. 97 013905

    [18]

    Park M J, Choi J H, Kim S S 2000 Intermag Proceedings of International Magnetics Conference Toronto, Canada, April 09−12, 2000 p3272

    [19]

    Jacobo S E, Fano W G, Razzitte A C, Digiovanni N D, Trainotti V 1998 Proceedings of the 67th Annual Conference on Electrical Insulation and Dielectric Phenomena Atlanta, USA, October 25−28, 1998 p273

    [20]

    Bi K, Guo Y S, Liu X M, Zhao Q, Xiao J H, Lei M, Zhou J 2014 Sci. Rep. 4 7001

    [21]

    Yang Y J, Huang Y J, Wen G J, Zhong J P, Sun H B, Oghenemuero G 2012 Chin. Phys. B 21 038501

    [22]

    郭飞, 杜红亮, 屈绍波, 夏颂, 徐卓, 赵建峰, 张红梅 2015 物理学报 64 077801

    Guo F, Du H L, Qu S B, Xia S, Xu Z, Zhao J F, Zhang H M 2015 Acta Phys. Sin. 64 077801

    [23]

    Meena R S, Bhattachrya S, Chatterjee R 2010 J. Magn. Magn. Mater. 322 1923

    [24]

    Liu X S, Hernandez-Gomez P, Huang K, Zhou S Q, Wang Y, Cai X, Sun H J, Ma B 2006 J. Magn. Magn. Mater. 305 524

    [25]

    Bercoff P G, Herme C, Jacobo S E 2009 J. Magn. Magn. Mater. 321 2245

    [26]

    Zuo X, How H, Somu S, Vittoria C 2003 IEEE Trans. Magn. 39 3160

    [27]

    Pozar D M 2004 Microwave Engineering (3rd ed) (New York: Wiely) pp391−395

    [28]

    Yang Y, Yang Y, Wen X, Ding J 2014 J. Appl. Phys. 115 17A521

    [29]

    Zhang K L, Hou Z L, Bi S, Fang H M 2017 Chin. Phys. B 26 127802

  • 图 1  大块铁氧体模型示意图和在不同磁化方式、磁场强度、极化方向下对电磁波的反射率 (a)模型示意图; (b)纵向磁化下不同磁场强度对反射率的影响; (c)横向磁化下不同极化方向的反射率; (d)不同磁化方式对反射率的影响

    Figure 1.  The schematic model and the reflectivity of bulk ferrite under different magnetized methods, magnetic field intensities and polarized directions: (a) The schematic model; (b) the influence of different magnetic field intensities under longitudinal magnetization; (c) different polarized directions under transversal magnetization; (d) the influence of different magnetized methods.

    图 2  基元结构和横向磁化时面内正交磁化作用下铁氧体的反射率 (a)基元结构(A, B分别表示沿y向磁化和x向磁化的铁氧体基元); (b) TE极化; (c) TM极化; (d) TE极化时尺寸效应; (e) TM极化时尺寸效应

    Figure 2.  The unit cell and the reflectivity of transversally orthogonally magnetized ferrite: (a) The unit cell(A and B present the ferrite magnetized along y and x directions, respectively); the reflectivity of (b) TE polarization and (c) TM polarization; the size effect of (d) TE polarization and (e) TM polarization.

    图 3  不同基元大小的铁氧体阵列及其在不同磁化状态下的反射性能 (a)离散的铁氧体阵列; (b)纵向磁化下$\Delta R$的影响; (c)横向磁化TE极化下$\Delta R$的影响; (d)横向磁化TM极化下$\Delta R$的影响

    Figure 3.  Reflection of ferrites array with different element sizes in different magnetized conditions: (a) The discrete array; the influence of $\Delta R$ in (b) longitudinal magnetization; (c) transversal magnetization with TE polarization and (d) transverse magnetization with TM polarization.

    图 4  结构示意图和不同尺寸基元组合的性能 (a)结构示意图(左部分表示超胞1(2)的细节); (b)纵向磁化200 Oe, $\Delta R = 0$$\Delta R = 4$组合; (c)纵向磁化700 Oe, $\Delta R = 0$$\Delta R = 4$组合; (d)纵向磁化700 Oe, $\Delta R = 0$$\Delta R = 2$组合; (e)横向磁化200 Oe, $\Delta R = 0$$\Delta R = 4$组合; (f)横向磁化700 Oe, $\Delta R = 0$$\Delta R = 4$组合; (g)横向磁化700 Oe, $\Delta R = 0$$\Delta R = 2$组合

    Figure 4.  The schematic and the properties of elements combinations with different sizes: (a) Schematic of the array combined by different elements(The left shows the details of supercell1(2)); the combination of $\Delta R = 0$ and $\Delta R = 4$ under longitudinal magnetization (b) 200 Oe and (c) 700 Oe; (d) the combination of $\Delta R = 0$ and $\Delta R = 2$ under longitudinal magnetization 700 Oe; the combination of $\Delta R = 0$ and $\Delta R = 4$ under transversal magnetization (e) 200 Oe and (f) 700 Oe; (g) the combination of $\Delta R = 0$ and $\Delta R = 2$ under transversal magnetization 700 Oe.

    图 5  $\Delta R = 0$$\Delta R = 4$两种阵列组合而成的吸波结构在y = 0平面内的电场, 磁场, 能量损耗密度分布 (a), (b)分别为工作频率1.95和3.05 GHz, 纵向磁化场700 Oe时的情形; (c), (d)分别是工作频率为1.65和2.25 GHz, 横向磁化场700 Oe时的情形

    Figure 5.  Distributions of electric field, magnetic field and power loss density in the y = 0 plane of the absorption structure combined by $\Delta R = 0$ and $\Delta R = 4$ at two absorption peaks: (a) 1.95 GHz and (b) 3.05 GHz of longitudinal magnetization 700 Oe; (c) 1.65 GHz and (d) 2.25 GHz of transversal magnetization 700 Oe.

    图 6  能量损耗密度在x-y截面(正视图)的分布 (a), (b)分别是工作频率为1.95和3.05 GHz, 纵向磁化磁场700 Oe时的情形; (c), (d)分别是工作频率为1.65和2.25 GHz时, 横向磁化场700 Oe时的情形

    Figure 6.  Distributions of power loss density in the x-y cross section (the front view): (a) 1.95 GHz and (b) 3.05 GHz of longitudinal magnetization 700 Oe; (c) 1.65 GHz and (d) 2.25 GHz of transversal magnetization 700 Oe.

  • [1]

    Landy N I, Sajuyigbe S, Mock J J, Smith D R, Padilla W J 2008 Phys. Rev. Lett. 100 207402

    [2]

    Ding F, Cui Y X, Ge X C, Jin Y, He S L 2012 Appl. Phys. Lett. 100 103506

    [3]

    Zhang Y, Huang Y, Zhang T F, Chang H C, Xiao P S, Chen H H, Huang Z Y, Chen Y S 2015 Adv. Mater. 27 2049

    [4]

    Wang Y, Du Y C, Xu P, Qiang R, Han X J 2017 Polymers 9 29

    [5]

    Liu Y P, Zhang B Z, Duan J P, Xu Y G 2018 Appl. Opt. 57 10257

    [6]

    Zhang X J, Wang G S, Cao W Q, Wei Y Z, Liang J F, Guo L, Cao M S 2014 ACS Appl. Mater. Interfaces 6 7471

    [7]

    Zhang Y, Huang Y, Chen H H, Huang Z Y, Yang Y, Xiao P S, Zhou Y, Chen Y S 2016 Carbon 105 438

    [8]

    Wang D J, Zhang J Y, He P, Hou Z L 2019 Ceram. Int. 45 23043

    [9]

    周卓辉, 刘晓来, 黄大庆, 康飞宇 2014 物理学报 63 184101

    Zhou Z H, Liu X L, Huang D Q, Kang F Y 2014 Acta Phys. Sin. 63 184101

    [10]

    Zhang K L, Zhang J Y, Hou Z L, Bi S, Zhao Q L 2019 Carbon 141 608

    [11]

    Wang J, Gao C N, Jiang Y N, Charles N A 2017 Chin. Phys. B 26 114102

    [12]

    Wang Y, Du Y C, Qiang R, Tian C H, Xu P, Han X J 2016 Adv. Mater. Interfaces 3 1500684

    [13]

    Alkuh M S, Famili M H N, Shirvan M M M, Moeini M H 2016 Mater. Des. 100 73

    [14]

    Amano M, Kotsuka Y 2003 IEEE Trans. Microwave Theory Tech. 51 238

    [15]

    Kazantsev Y N, Lopatin A V, Kazantseva N E, Shatrov A D, Mal'tsev V P, Vilcakova J, Saha P 2010 IEEE Trans. Antennas Propag. 58 1227

    [16]

    Chen H Y, Zhang H B, Deng L J 2010 IEEE Antennas Wirel. Propag. Lett. 9 899

    [17]

    Rozanov K N, Li Z W, Chen L F, Koledintseva M Y 2005 J. Appl. Phys. 97 013905

    [18]

    Park M J, Choi J H, Kim S S 2000 Intermag Proceedings of International Magnetics Conference Toronto, Canada, April 09−12, 2000 p3272

    [19]

    Jacobo S E, Fano W G, Razzitte A C, Digiovanni N D, Trainotti V 1998 Proceedings of the 67th Annual Conference on Electrical Insulation and Dielectric Phenomena Atlanta, USA, October 25−28, 1998 p273

    [20]

    Bi K, Guo Y S, Liu X M, Zhao Q, Xiao J H, Lei M, Zhou J 2014 Sci. Rep. 4 7001

    [21]

    Yang Y J, Huang Y J, Wen G J, Zhong J P, Sun H B, Oghenemuero G 2012 Chin. Phys. B 21 038501

    [22]

    郭飞, 杜红亮, 屈绍波, 夏颂, 徐卓, 赵建峰, 张红梅 2015 物理学报 64 077801

    Guo F, Du H L, Qu S B, Xia S, Xu Z, Zhao J F, Zhang H M 2015 Acta Phys. Sin. 64 077801

    [23]

    Meena R S, Bhattachrya S, Chatterjee R 2010 J. Magn. Magn. Mater. 322 1923

    [24]

    Liu X S, Hernandez-Gomez P, Huang K, Zhou S Q, Wang Y, Cai X, Sun H J, Ma B 2006 J. Magn. Magn. Mater. 305 524

    [25]

    Bercoff P G, Herme C, Jacobo S E 2009 J. Magn. Magn. Mater. 321 2245

    [26]

    Zuo X, How H, Somu S, Vittoria C 2003 IEEE Trans. Magn. 39 3160

    [27]

    Pozar D M 2004 Microwave Engineering (3rd ed) (New York: Wiely) pp391−395

    [28]

    Yang Y, Yang Y, Wen X, Ding J 2014 J. Appl. Phys. 115 17A521

    [29]

    Zhang K L, Hou Z L, Bi S, Fang H M 2017 Chin. Phys. B 26 127802

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  • Received Date:  14 August 2019
  • Accepted Date:  31 October 2019
  • Available Online:  07 December 2019
  • Published Online:  01 January 2020

Achieving low frequency electromagnetic wave absorption by gyromagnetic ferrite

    Corresponding author: Wu Rui-Xin, rxwu@nju.edu.cn
  • School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China

Abstract: Under the action of static bias magnetic field, the magnetized ferrite has a permeability tensor which can be adjusted by the applied magnetic field. In this paper, the absorption properties of bulk gyromagnetic ferrites under different magnetized conditions are studied and the great potential of gyromagnetic ferrite in achieving low frequency electromagnetic wave absorption is demonstrated. Full wave electromagnetic simulations are performed based on the finite element method (FEM). A floquet port is adopted at the top boundary of the unit cell to simulate a normally incident plane wave. The unit cell boundary conditions are used in the x-y plane to simulate a periodic structure. Orthogonality magnetization in plane is utilized to solve the polarization selectivity in the condition of transverse magnetic field. The influence on absorption capacity of discrete ferrite array structure and the coupling effect of ferrite elements with different sizes are also studied in consideration of the size effect. The simulation results show that a thin bulk gyromagnetic ferrite layer whose thickness is only 4 mm can possess frequency as low as 0.48 GHz and reflectivity below –10 dB. Gyromagnetic ferrite presents different absorption properties under longitudinal magnetization and transversal magnetization, and different polarization directions in transversal magnetization as well. When longitudinal bias magnetic field H0 = 200 Oe, the bandwidth of the reflectivity below –10 dB ranges from 0.48 to 1.84 GHz. The resonant absorption frequency can be regulated by adjusting bias magnetic field and the size of ferrite element. In general, a large bias magnetic field leads to a high resonant frequency due to the ferromagnetic resonance frequency positively associated with the applied magnetic field, but a ferrite array consisting of larger size elements provides a lower resonant frequency for the size resonance negatively associated with the size. By introducing the coupling between elements with different sizes, the reflection bandwidth below –10 dB can be effectively extended to above 80% of the sum of the bandwidth possessed by single unit cell, especially 105.7% under transversal bias magnetic field 700 Oe. And the broadening effect is effective in both longitudinal and transverse magnetized state but it will be weaker when the two absorption peaks are closer. To further understand the absorption mechanism of the two-element absorber, the distribution of the electric field, magnetic field and power loss density are examined. The results prove that the two peaks at the lower frequency exactly originates from $ \Delta R = 0$ and the higher frequency originates from $ \Delta R = 4$, and therefore the widened absorption is contributed by the coupled multiple resonances provided by the elements with different sizes.

    • 微波吸收材料(microwave absorbing materials, MAMs)因其低反射、高吸收的优点被广泛应用于隐身技术和解决大量通讯设备中电磁辐射带来的电磁干扰(electromagnetic interference, EMI)和电磁兼容(electromagnetic compatibility, EMC)等问题. 近年来, 人们对MAMs进行了大量的研究[1-5]. 一个好的吸波材料应当具有重量轻、厚度薄、吸收性能强和频带宽等特点[6,7]. 目前已经发展了基于铁磁性材料及其氧化物[8,9], 石墨烯及其复合材料[10,11], 碳聚合物[12,13]等不同材料工作在不同波段的吸波结构. 磁性材料因其容易实现与自由空间的阻抗匹配, 从而成为构建薄型宽带吸波体最具有潜力的材料之一[8]. 磁性材料在吸波材料的设计中常常被当作吸波涂层来应用, 由于磁性材料同时存在介电损耗和磁损耗两种作用, 因此仅需很薄的材料层就能够有很好的吸收效果[14-19]. 铁氧体是一种常用的磁性介质材料, 在吸波设计得到了广泛的应用, 例如最常使用的片状铁氧体[20-22]. 铁氧体在低频电磁波的吸收方面也有学者做过研究, 为了调节共振吸收频率需要调整各种元素的掺杂、离子取代[23-25]来改变铁氧体的磁晶各项异性场、饱和磁化强度和居里温度. 这种方法过程繁琐, 且吸收带宽很窄, 样品成型就不能再改变其吸收特性.

      本文重点研究旋磁性铁氧体在不同磁化状态下的低频电磁波吸收特性. 通过改变外加偏置磁场可以调节铁氧体材料的磁导率从而实现共振吸收频率的调节. 我们研究了在两种不同的磁化方式下, 大块铁氧体和铁氧体阵列的结构参数对吸波能力的调节作用. 模拟计算结果显示: 不同磁化状态下4 mm大块旋磁铁氧体在低频段对电磁波都有着显著的吸收作用且其反射率–10 dB频率能低至0.48 GHz, 共振吸收频率可由磁场和铁氧体基元大小调节, 而且吸收带宽可以通过不同尺寸基元各自的磁共振形成的多谐振峰及其耦合加以展宽.

    2.   旋磁铁氧体的吸波特性
    • 首先考虑大块铁氧体材料和金属背板组成的吸波结构, 铁氧体厚度$h = 4 \;{\rm{mm}}$, 如图1(a)所示. 本文选用的锶铁氧体的电磁参数如下: 相对介电常数${\varepsilon _{\rm{r}}} = {\rm{22 }}$(在研究频段基本保持不变), 损耗角正切$\tan \delta = {\rm{0}}.{\rm{01}}$, 饱和磁化强度$4{\text{π}}{M_{\rm{s}}} = 4000 \;{\rm{G}}$, 谐振线宽$\Delta H = 2000 \;{\rm Oe}$ (1 Oe = 79.6 A/m)[26]. 当外加偏置磁场为H0时, 根据Landau-Lifshitz模型, 旋磁铁氧体的相对磁导率为[27]:

      Figure 1.  The schematic model and the reflectivity of bulk ferrite under different magnetized methods, magnetic field intensities and polarized directions: (a) The schematic model; (b) the influence of different magnetic field intensities under longitudinal magnetization; (c) different polarized directions under transversal magnetization; (d) the influence of different magnetized methods.

      式中${\omega _0} = \gamma {H_0}$是铁磁共振频率, γ为旋磁比, ${\omega _{\rm{m}}} = \gamma 4{\text{π}}{M_{\rm{s}}}$是铁氧体的特征频率, $\alpha = \dfrac{{{\mu _0}\gamma \Delta H}}{{2\omega }}$为铁氧体的损耗系数.

      根据传输线模型, 当磁性材料厚度固定时, 在电磁波垂直入射的情况下, 单层吸波材料的反射率R随频率的变化为[28]

      式中, Zin为大块铁氧体表面的输入阻抗:

      其中f为电磁波频率, h是铁氧体厚度, c为自由空间的光速, ${\mu _{\rm{e}}}$为等效磁导率.

    • 当给铁氧体施加偏置磁场时, 存在两种不同的磁化状态, 分别是纵向磁化(偏置磁场和电磁波的传播方向相同, 都平行于z轴)和横向磁化(偏置磁场和电磁波的传播方向垂直, 偏置磁场沿y(x)轴, 本节考虑沿y轴的情况). 考虑线性极化的电磁波垂直入射到图1(a)所示的吸波结构上, 我们比较了两种磁化方式以及不同大小的偏置磁场下材料吸收性能的变化.

      在纵向磁化时, 进入旋磁铁氧体的电磁波会被分解成左旋圆极化波(LHCP)和右旋圆极化波(RHCP). 对于这两种电磁波, 铁氧体材料呈现出不同的等效磁导率, 分别是$\mu - \kappa $$\mu + \kappa $, 从而导致入射电磁波的极化方向发生旋转, 此即法拉第旋转效应[27]. 在铁磁谐振频率附近, LHCP分量会被完全衰减, 由于损耗的存在, RHCP分量也会部分衰减. 由于偏置磁场垂直于波振面, 电磁波的吸收效果与电场的极化方式无关. 纵向磁化时铁氧体表面反射率的计算结果如图1(b)所示. 当H0 = 200 Oe时, 在0.48—1.84 GHz存在–10 dB以下的反射. 改变偏置磁场的大小可以灵活地调节铁磁共振吸收的频率, 磁场增大会导致吸收峰向高频移动, 带宽略有缩小, 所以为了获得较好的低频吸收性能, 偏置磁场不能过大.

      在横向磁化时, 电磁波的吸收效果与电场的极化方式有关. 对TE极化波(电场平行y轴, 与偏置磁场平行), 其具有等效磁导率${\mu _{\rm{e}}} = ({{{\mu ^2} - {\kappa ^2}}})/{\mu }$, 它受到铁氧体磁化的影响; 对TM极化波(电场平行x轴, 垂直于偏置磁场), 由于波的传播常数与H0无关, 并未受到铁氧体磁化的影响, 因此也被称为寻常波[27]. 横向磁化铁氧体表面反射率的计算结果如图1(c)所示, 对于TE极化的电磁波, 铁氧体在1 GHz附近表现出对电磁波强烈的吸收作用; 但是, 对于TM极化的电磁波, 铁氧体没有吸收作用. 可见横向磁化铁氧体的吸收作用具有极化选择性.

      图1(d)比较了相同大小磁场下, 不同磁化方式铁氧体的电磁吸收效果. 可以看到相比于横向磁化, 纵向磁化时吸收峰较深, 同时吸收带宽相对较宽. 对比该图中无偏置磁场的结果, 可以看出磁化明显改善了低频的吸收效果, 所以低偏置磁场下的旋磁性材料可以有效加强低频电磁波的吸收.

    • 横向磁化存在极化选择性的问题, 可以考虑采用面内磁化方向正交的方式来解决. 将图1(a)中的大块铁氧体变成由图2(a)所示的六边形基元平铺而成, 基元边长R = 20 mm. 平铺的基元以六角点阵结构排列, 晶格常数${a_0} = \sqrt 3 R$. 图中A, B区域分别表示沿y方向磁化和沿x方向磁化的铁氧体基元.

      Figure 2.  The unit cell and the reflectivity of transversally orthogonally magnetized ferrite: (a) The unit cell(A and B present the ferrite magnetized along y and x directions, respectively); the reflectivity of (b) TE polarization and (c) TM polarization; the size effect of (d) TE polarization and (e) TM polarization.

      图2(b)图2(c)计算了横向磁化时面内正交磁化在不同偏置磁场大小的情况下对电磁波的反射率. 与图1(c)对比明显的是, 图2(c)铁氧体对TM极化的电磁波同样具有强烈的吸收作用. 图2(b)表示的TE极化和图2(c)表示的TM极化均表现出两个吸收峰, 位于低频处的吸收峰可以被偏置磁场调节, 它是由铁磁共振导致的, 其共振吸收频率随偏置磁场的变化与图1(b)相符, 但是吸收性能会下降, 这是因为此时有效吸收面积减小; 位于高频处的吸收峰, 即使偏置磁场改变其频率仍保持在4 GHz, 其与偏置磁场、极化方向无关的特性表明这是由尺寸效应产生的, 当R改变时, 该处的吸收峰则会发生频偏. 图2(d)图2(e)研究了偏置磁场为200 Oe时增大R对电磁波反射性能的影响, 点阵结构保持六角点阵不变. 可以看到, 随着基元尺寸变大, 图2(d)图2(e)所示的高频处的尺寸共振峰会逐渐向低频移动. 我们的计算结果表明, 面内正交磁化可以有效地解决横向磁化的极化选择性问题, 并且由于尺寸效应的引入会形成一个高频处的吸收峰.

    3.   旋磁铁氧体阵列对吸波性能的影响
    • 将铁氧体变成离散阵列的形式, 该离散化将会导致额外的共振出现, 即阵列基元的尺寸共振. 尺寸共振与磁共振的共同作用会导致吸收峰的偏移和吸收性能的改变. 我们研究在保持晶格常数a0一定的条件下, 铁氧体基元大小会如何影响吸收性能.

    • 研究结构如图3(a)所示, 铁氧体基元边长比周期单元边长R = 20 mm缩小$\Delta R$, 铁氧体材料的占空比会相应减小, 材料的颜色索引同图1, 厚度固定在4 mm. 我们计算了$\Delta R = 2$$\Delta R = 4$的情况, 晶格常数${a_0} = 20\sqrt 3 \;{\rm{ mm}}$.

      Figure 3.  Reflection of ferrites array with different element sizes in different magnetized conditions: (a) The discrete array; the influence of $\Delta R$ in (b) longitudinal magnetization; (c) transversal magnetization with TE polarization and (d) transverse magnetization with TM polarization.

      电磁仿真结果表明, 对于磁场为纵向偏置(图3(b))和横向偏置的TE极化情况(图3(c)), 随着基元变小(占空比减小), 铁氧体阵列的吸收频率会向高频移动, 说明尺寸共振频率与基元大小有一定的逆相关, 不同的是纵向磁化时吸收峰强度会随着占空比减小而递减, 但是横向磁化时吸收强度却在$\Delta R = 2$时最大, 在这种情况下阵列与自由空间的阻抗匹配最佳, 反射最小. 因此对TE极化的电磁波可以选择横向磁化下适当占空比的铁氧体基元大小以加强对电磁波的吸收效果.

      图3(d)所示, 当磁场横向偏置, 电磁波为TM极化时, 与黑色实线所代表的大块材料无吸收作用相比, 离散的阵列在高频端出现明显的电磁吸收. 虽然和图3(b)以及图3(c)的离散程度一样, 但是由于此时电磁波不受铁氧体磁化的影响, 铁氧体材料内部电磁波波长比受磁化影响时要长, 所以尺寸共振效应会发生在高频. 总之, 不仅能够通过偏置磁场来调节共振吸收频率, 调整基元大小同样可以起到调节吸收频率的作用.

    • 拓展吸收带宽的有效方法是采用多谐振. 之前有工作研究了用不同厚度的阵列基底来产生$(2 n + 1)\lambda /4$多谐振峰, 从而达到吸收带宽的拓展[29]. 图3的计算结果表明: 随着基元尺寸的变化(改变$\Delta R$), 旋磁铁氧体共振吸收频率会有所变化. 因此我们可以通过将两种不同尺寸的基元组合, 产生多谐振峰并利用它们之间的耦合作用来拓展带宽. 结构设计如图4(a)所示, 依旧采用六角点阵, 材料的颜色索引同图1. 为了保证每种基元原本的吸收性能, 我们采取一个正六角形超胞(该超胞由七个同种基元构成, 见图4(a)左)以保护同种基元之间的相互作用. 由于七个正六边形基元无法镶嵌满一个超胞, 为了保证吸收强度, 将六个空角处填满了铁氧体材料. 当应用偏置磁场时, 有限尺寸的铁氧体材料会产生退磁效应, 退磁系数与铁氧体基元的长径比R/h相关. 考虑到这一点, 当基元尺寸R变化时, 基元的高度h会相应变化以使R/h保持不变从而保证阵列中不同尺寸的铁氧体基元内部的磁场相等. 并且由(4)式可知h的变化也会带来吸收频率的变化, 图4单种基元的反射率曲线是基于相应的h计算的. 同前文一致($R/h = 20/4$, $\Delta R = 0$R = 20 mm), 长径比固定为5. 数字1, 2用以区分构成超胞使用的基元不同($\Delta R$不同).

      Figure 4.  The schematic and the properties of elements combinations with different sizes: (a) Schematic of the array combined by different elements(The left shows the details of supercell1(2)); the combination of $\Delta R = 0$ and $\Delta R = 4$ under longitudinal magnetization (b) 200 Oe and (c) 700 Oe; (d) the combination of $\Delta R = 0$ and $\Delta R = 2$ under longitudinal magnetization 700 Oe; the combination of $\Delta R = 0$ and $\Delta R = 4$ under transversal magnetization (e) 200 Oe and (f) 700 Oe; (g) the combination of $\Delta R = 0$ and $\Delta R = 2$ under transversal magnetization 700 Oe.

      图4(b)给出了纵向磁化下$\Delta R = 0$$\Delta R = 4$两者组合的计算结果, 偏置磁场大小为200 Oe. 由于$\Delta R = 4$时, 反射率勉强能低于–10 dB(见图4(b)蓝色虚线), 因此当两种基元组合后(图4(b)黑色实线), 虽能明显地看到两个吸收峰的共同作用, 但是当频率靠近$\Delta R = 4$的吸收峰时, 反射率会略高于–10 dB. 为了使其降低到–10 dB以下, 可以加大磁场, 见图4(c). 当偏置磁场为700 Oe时, 其–10 dB带宽为1.77 GHz (1.59—3.36 GHz, 图4(c)黑色实线)远大于任一基元单独作用的带宽, 是单种基元作用带宽之和的83.5% ($\Delta R = 0$带宽为1.11 GHz, $\Delta R = 4$带宽为1.01 GHz, 两者之和为2.12 GHz, 见图4(c)红色虚线和蓝色虚线). 图4(d)研究了纵向磁化700 Oe时$\Delta R = 0$$\Delta R = 2$的组合, 对比图4(c), 此时两者之间的共振吸收峰相距较近, 因此扩展带宽的效果要弱于$\Delta R = 0$$\Delta R = 4$的组合. 图4(e)图4(g)给出的是横向磁化的情况, 当应用弱偏置场200 Oe的时候, –10 dB带宽为1.69 GHz (0.81—2.50 GHz, 图4(e)黑色实线)是单种基元作用带宽之和的87.6% ($\Delta R = 0$带宽为0.91 GHz, $\Delta R = 4$带宽为1.02 GHz, 两者之和为1.93 GHz, 见图4(e)红色虚线和蓝色虚线). 当应用强偏置场700 Oe时, –10 dB带宽为1.67 GHz (1.41—3.08 GHz, 图4(f)黑色实线)是单种基元作用带宽之和的105.7% ($\Delta R = 0$带宽为0.63 GHz, $\Delta R = 4$带宽为0.95 GHz, 两者之和为1.58 GHz, 见图4(f)红色虚线和蓝色虚线). 如图4(g)所示, 同纵向磁化时一样, 由于两吸收峰靠得太近, 耦合作用很微弱, 横向磁化时$\Delta R = 0$$\Delta R = 2$的组合对吸收带宽的扩展也会弱于$\Delta R = 0$$\Delta R = 4$的组合.

      为了探究两种基元组合后吸波结构的吸收机理, 我们研究了吸波结构在共振吸收频率处的电磁场分布与能量损耗密度分布状态. 图5给出了最具代表性的$\Delta R = 0$$\Delta R = 4$组合阵列在y = 0平面内的计算结果. 图5(a)图5(b)对应于图4(c)的纵向磁化状态. 图5(a)绘制了低频吸收峰f = 1.95 GHz的场图, 磁场集中分布在$\Delta R = 0$超胞的铁氧体基元的中下部位, 对比分析电场、磁场和能量损耗密度可以发现能量损耗密度和磁场分布具有高度一致性, 说明在低频吸收峰的能量损耗主要来自于$\Delta R = 0$的铁氧体基元的磁共振. 图5(b)在高频吸收峰f = 3.05 GHz时, 磁场和能量损耗密度主要集中在$\Delta R = 4$超胞内离散的铁氧体. 图5(c)图5(d)对应于图4(f)的横向磁化状态, 同纵向磁化一样, 横向磁化低频吸收峰f = 1.65 GHz的能量损耗密度主要分布在$\Delta R = 0$区域, 高频f = 2.25 GHz的能量损耗密度主要分布在$\Delta R = 4$区域. 略不同于纵向磁化的是, 集中分布的磁场会更多地耦合到另一种基元, 例如图5(d)集中分布在$\Delta R = 4$的磁场, 在邻近它的$\Delta R = 0$的两端区域也有较强的值. 能量损耗密度在x-y截面(正视图)的分布情况也在图6中给出(图6(a)图6(b)对应纵向磁化, 图6(c)图6(d)对应横向磁化). 结果显示不论是纵向磁化还是横向磁化, 低频吸收峰的能量损耗主要来源于$\Delta R = 0$的铁氧体基元, 高频吸收峰的能量损耗主要来源于$\Delta R = 4$的离散铁氧体基元. 可见, 两种不同尺寸的基元组合后, 保留了原先单种基元各自的磁共振, 因此形成了两个吸收峰, 两个相距较近的吸收峰之间相互耦合(见图4(b)图4(g))从而实现了吸收带宽的拓展.

      Figure 5.  Distributions of electric field, magnetic field and power loss density in the y = 0 plane of the absorption structure combined by $\Delta R = 0$ and $\Delta R = 4$ at two absorption peaks: (a) 1.95 GHz and (b) 3.05 GHz of longitudinal magnetization 700 Oe; (c) 1.65 GHz and (d) 2.25 GHz of transversal magnetization 700 Oe.

      Figure 6.  Distributions of power loss density in the x-y cross section (the front view): (a) 1.95 GHz and (b) 3.05 GHz of longitudinal magnetization 700 Oe; (c) 1.65 GHz and (d) 2.25 GHz of transversal magnetization 700 Oe.

    4.   结 论
    • 本文研究了旋磁铁氧体在各种磁化状态下对电磁波的吸收性能. 计算结果表明, 4 mm薄层旋磁铁氧体反射率的–10 dB频率低至0.48 GHz, 且可由偏置磁场灵活调节, 通过面内正交磁化可以有效地解决横向磁化时的极化选择性问题. 控制铁氧体基元的填充比也可以起到调节吸收频率的作用, 同时还能起到调节吸收强度的作用. 通过不同尺寸铁氧体基元组合, 形成多谐振峰可以将吸收带宽拓展, 这种展宽作用在纵向磁化和横向磁化状态都是有效的, 它可将–10 dB吸收带宽拓展至单种基元吸波材料吸收带宽之和的80%以上. 特别是采用横向偏置场700 Oe时, 带宽可拓展至单种基元带宽和的105.7%. 对吸波结构在共振吸收频率处电磁场和能量损耗的分析, 证实了不同尺寸的基元组合后保留了原先单种基元各自的磁共振, 从而说明了吸收带宽的拓展来源于不同尺寸基元耦合后形成的多谐振.

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