An absorbing material based on the non-reciprocity of magnetic surface plasmon state of ferrites

Abstract

Under external biased magnetic field conditions, magnetic surface plasmon state (MSPs) can be excited on the surfaces of ferrites, endowing them with unidirectional propagation characteristics of surface waves within a certain frequency bandgap. This paper presents an absorbing material based on the non-reciprocity of MSPs of ferrites. Firstly, by utilizing the unidirectional properties of MSPs and the rational design of metal components on the surfaces of ferrites, a unidirectional transmission structure is realized, exhibiting forward transmission and backward cutoff in the non-reciprocal bandgap. Then, by adding a metal plane being added at the bottom of the structure, the entire material exhibits high-efficiency electromagnetic wave absorption within the unidirectional bandgap of the MSPs. Furthermore, by adjusting the bias magnetic field and utilizing ferrites with varying saturation magnetizations, absorptions in different frequency bands, including the P-band, can be realized. To demonstrate the presented design, a prototype is fabricated and tested. The experiment results agree well with the simulation, confirming excellent wave absorption performance. Our study offers a new approach for designing absorbing materials, with potential applications in radar stealth and electromagnetic interference reduction.

Graphical abstract

Keywords

radar absorbing material / non-reciprocity / ferrites / magnetic surface plasmon state

1 Introduction

Radar absorbing material (RAM) plays a crucial role in electromagnetic applications. There are various methods to realize RAMs, such as high-loss media, circuit analog absorber and metamaterials [1-9]. However, these traditional RAMs exhibit symmetric effects on incident and reflected waves, meaning that incident electromagnetic (EM) waves can not only propagate through them with loss, but also propagate in the opposite direction after being reflected by the cloaked objects. The natural property of tradition RAMs makes achieving the ideal non-reflection impossible.

Ferrites are widely applied in the construction of traditional reciprocal RAM due to their high permeability, low cost and accessibility [10-16]. Due to the unique off-diagonal terms of their permeability tensors, ferrites under a biased magnetic field (BMF) exhibit interesting characteristics, such as the Faraday effect and MSPs [17-22]. Research on surface plasmons has drawn great interest in the past decade years [23-25]. As a unique surface wave state of ferrites, MSPs exhibits unidirectional propagation characteristics of EM waves in certain frequency bands under BMFs, which offers a possible approach to realize RAMs with asymmetric effects and achieve the ideal non-reflection [26-31].

In this paper, the characteristics of MSPs are first analyzed. Then, a unidirectional transmission structure based on MSPs is proposed. The structure is composed of periodically arranged cuboid-shaped ferrites with copper strips asymmetrically attached to their surfaces. By utilizing the characteristics of MSPs and the asymmetric structural design, the presented structure exhibits unidirectional transmission of forward-propagating waves and cutoff of the backward waves. After placing a metal plane at the bottom of the structure, an absorbing material is achieved. The proposed material exhibits efficient absorption of incident waves while blocking backward reflections. A prototype of the absorbing material is fabricated and tested. The consistency between experimental and simulation results indicates that the absorbing material proposed in this paper achieves excellent absorbing performance. In addition, simulations reveal that efficient wave absorption in different frequency bands can be achieved by adjusting the BMF and the saturation magnetizations of ferrites.

2 Design and realization of the absorbing material

2.1 Transmission characteristics of MSPs

Considering the material composed of periodic structures of ferrite cuboids and packing mediums, EM waves can propagate in arbitrary directions in the material without an applied BMF. Due to the influence of high permeability materials on EM wave propagation, when EM waves are incident on structures composed of materials with different permeabilities, electromagnetic energy concentrates from low-permeability regions to high-permeability regions [32, 33].

Fig.1(a) visualizes the concentration of EM energy toward ferrites when the y-polarized EM waves are incident on the presented material from the +z and –z directions, which indicates that the incident electromagnetic waves propagate mainly in the ferrite regions of the material.

When a +y direction BMF is applied to the material, MSPs is activated on the surfaces of ferrites and the permeability tensor of the y-direction magnetized ferrites is

(1)\left({\mu }_f\right)=\left(\begin{array}{ccc}\mu & 0& \mathrm{j}\kappa \\ 0& {\mu }_0& 0\\ -\mathrm{j}\kappa & 0& \mu \end{array}\right),

where \mu ={\mu }_0\left(1+\frac{{\omega }_0{\omega }_m}{{{\omega }_0}^2-{\omega }^2}\right),\kappa ={\mu }_0\frac{\omega {\omega }_m}{{{\omega }_0}^2-{\omega }^2}. {\omega }_0=\gamma H is the Lamor frequency, H is the applied y-direction BMF, {\omega }_{\mathrm{m}}= 4\pi \gamma M_{\mathrm{s}} is the saturation magnetization frequency, \gamma is the gyromagnetic ratio, and M_{\mathrm{s}} is the saturation magnetization.

By combining the permeability tensor with Maxwell’s equations and the boundary condition between ferrites and mediums, the surface dispersion relation on the interface between ferrites and mediums can be derived. The wave propagation of MSPs is proved to possess unidirectional property in the frequency bandgap of {\omega }_0+\frac{{\omega }_m}{2} to {\omega }_0+{\omega }_m [34, 35]. EM waves within this unidirectional bandgap can only transfer in one direction {\hat{k}}_0 on the surface of the ferrite, determined by the following relation of

(2){\hat{k}}_0=\hat{n}\times \hat{H},

where \hat{n} is the outward normal unit vector of the surface of the ferrite and \hat{H} is the unit vector of the BMF. Since the outward normal unit vectors of left and right surfaces of the ferrites are opposite, the propagation directions of surface waves on these two surfaces are also opposite.

Therefore, EM waves on the surfaces of ferrites are only able to propagate in certain directions according to Eq. (2). In addition, the magnetic loss of ferrites under BMF increases significantly due to the permeability tensor in form of Eq. (1), which causes substantial attenuation of EM waves in the interior regions of the ferrites. Based on this analysis, the primary propagation of EM energy in the presented material under BMF is in the form of surface waves along the interface between ferrites and mediums, as shown in Fig.1(b).

2.2 Unidirectional transmission structure

Fig.1 reveals that the above materials support the transmission of EM energy in the form of unidirectional surface waves. However, the total transmission of EM energy remains reciprocal in the entire structure since both forward and backward incident energy can propagate through it. To achieve total unidirectional transmission, copper strips are introduced on the left surfaces of ferrites, as shown in Fig.2(a). The copper strips are equivalent to the terminal inductances and play the roles of terminal short circuit, causing total reflection of surface waves along the left surfaces [36, 37]. Thus, a structure with unidirectional propagation characteristics is obtained. EM waves incident in the - z direction concentrate mostly to the right surfaces of ferrites and propagate through the structure, while the EM waves incident in the +z direction concentrate to the left surfaces but are blocked by the copper strips and finally absorbed by the ferrites.

A unidirectional transmission structure is designed as an example, using cuboid ferrites made of yttrium iron garnet (YIG) with a saturation magnetization of 4\pi M_{\mathrm{s}}=1800\mathrm{G}\mathrm{a}\mathrm{u} \mathrm{s}\mathrm{s}, a dielectric loss tangent of 0.0001 and a relative permittivity of {ϵ}_r= 15. The permittivity of the packing medium is 3.3 and a +y direction static BMF of 1200 Oe is applied. The permeability tensor of the ferrites is calculated using Eq. (1). The theoretical non-reciprocal bandgap is 6−8.4 GHz. The detail dimensions of the structure are given in Tab.1.

Taking the -z direction as forward and +z direction as backward, the structure is simulated when the incident wave is in the -z and +z directions, respectively. The normalized electric field distribution is shown as Fig.2(c). The results indicate that the forward incident wave concentrates on the right surface of the ferrite, while the backward incident wave concentrates only in the area below the copper strip on the left surface. Compared to that of the forward incident wave, the electric field intensity of the outgoing wave for the backward incident wave is much smaller, indicating that most forward incident energy propagates through the structure, while backward energy is nearly totally blocked. The above phenomenon is quantified in the transmission characteristic curves shown in Fig.2(d). The significant differences between the forward and the backward curves in the non-reciprocal bandgap indicate the unidirectional transmission of waves in the structure. Here, the attenuation of the forward incident wave is attributed to surface waves creeping back to the left surfaces along the bottom surfaces and the loss of ferrites.

In order to validate the influence of the position of copper strips on transmission characteristics, structures with different d_3 are simulated, as shown in Fig.3. By comparing the transmission characteristics of forward and backward waves, it can be found that the best unidirectional performance is achieved when the copper strip is centered on the left surface, corresponding to a d_3 of 4.5 mm.

2.3 The absorbing material

Building upon the unidirectional transmission structure, we propose an absorbing material with asymmetric effect to incident and reflected waves by introducing a metal ground plane at bottom of the structure, as shown in Fig.4(a). The function of the metal plane is to block the creeping propagation of surface waves along the bottom surfaces of the ferrites while simultaneously shielding the cloaked object from incident wave irradiation. Our analysis reveals that most forward incident EM waves transform into surface waves concentrated on the right surface. After being reflected by the metal plane, a portion of the reflected EM energy shifts to the left surfaces through the medium region and propagates backward in surface mode, while the remainder is exhausted by the high-loss ferrites. Ultimately, the backward propagating waves accumulating on the left surfaces of ferrites are blocked by the copper strips, which is shown in Fig.4(c). From the simulation results of blue curve in Fig.4(d), it can be observed that the material shows excellent absorption performance in the non-reciprocal frequency band of 6−8.4 GHz.

To thoroughly investigate the influence of structural design on absorption characteristics, we examine reflection coefficients of modified versions of the materials, as shown in Fig.4(d). The black curve represents the reflection of the structure in which the ferrites are replaced by reciprocal mediums. The incident wave is nearly totally reflected. The red curve represents the reflection of the structure in which the copper strips are removed. The absorption characteristics shown by the red curve are mainly attributed to the loss of the ferrite body mode. The blue curve represents the complete structure of the presented absorbing material. It can be observed that the blue and red curves are nearly the same outside the non-reciprocal band of 6−8.4 GHz, but there are obvious differences within the non-reciprocal band, which highlights the crucial role of the asymmetric transmission in enhancing absorption of the presented materials.

We further explore the effect of periodic distances of ferrites on EM energy concentration and absorption performance, as shown in Fig.5. The blue line in Fig.5(a) reveals the concentration of EM energy, which is quantified through the 3 dB attenuation distance along -x direction from the surfaces of ferrites in the medium regions. It can be found that the 3 dB attenuation distances increase with the increase of periodic distances. Meanwhile, the red line in Fig.5(a) shows that the ratios between 3 dB attenuation distances and periodic distances remain consistent. Fig.5(b) shows the reflection of the presented material with different periodic distances, which illustrates that the optimal absorption occurs at a periodic length of 16 mm, establishing this as the ideal configuration.

To demonstrate the above design and analysis, a prototype of the absorbing material is fabricated, as shown in Fig.6(a)−(d). The prototype contains three layers of foam boards, which are the top, the bottom and the middle main layer. Ferrite cuboids are periodically inserted in the main layer of the foam board. Magnets are arranged periodically perpendicular to the ferrites to provide approximately uniform BMFs. Together with screws, the top and bottom layer of foam boards fills the remaining blank space of the structure and fixes the whole assembly. A copper plane is placed under the bottom layer. Fig.6(e) shows the experimental results and the simulation results. The experimental results show excellent agreement with simulation results, confirming the material’s outstanding absorption performance in the frequency band of 6−8.4 GHz. The minor frequency discrepancies observed are attributed to practical limitations in achieving perfectly uniform BMFs compared to idealized simulation conditions.

3 Discussion of the designable absorption frequency band

The material’s absorption bands are demonstrated to be flexibly designable due to the characteristics of MSPs. The non-reciprocal band of {\omega }_0+ {\omega }_m/2 to {\omega }_0+ {\omega }_m is determined by the BMF and saturation magnetization of ferrites. Thus, the absorption frequency of the material can be adjusted through varying the ferrites and magnets. To validate this, the reflection of absorbing material under various conditions is simulated. Firstly, the saturation magnetization of ferrites is fixed at 1800 Gauss while the BMF is varied from 400 to 2000 Oe. Since the BMF is only proportional to {\omega }_0, this tuning shifts only the starting frequency of the non-reciprocal band without altering the bandwidth. It can be observed from Fig.7(a) that the absorption bands below −10 dB shift towards higher frequencies with increasing BMF, while the bandwidth remains around 2.4 GHz. Secondly, the saturation magnetizations of ferrites are varied from 1500 to 2100 Gauss while the BMF remains 1200 Oe. Since saturation magnetization is proportional to {\omega }_m, the changes will affect both the starting frequency and the bandwidth. As shown in Fig.7(b), the starting frequencies of absorption bands of the three curves are approximately 5.5, 5.9, and 6.3 GHz, with corresponding bandwidths of 2, 2.4, and 2.8 GHz, respectively. These results align with the theory that the starting frequency and bandwidth of non-reciprocal band of {\omega }_0+{\omega }_m/2 and {\omega }_m/2 vary linearly with saturation magnetization, which is confirmed by the simulation results.

Based on the above analysis, a P-band absorbing material is realized with ferrites of 250 Gauss and BMF of 100 Oe. The reflection is shown in Fig.7(c) and dimensions of the structure in material are given in Tab.2. The absorption band is 0.65−0.9 GHz while the thickness of the material is 34 mm which is less than 1/10 of the wavelength in the lowest operating frequency.

4 Conclusion

In conclusion, this work successfully demonstrates a novel unidirectional transmission structure leveraging the non-reciprocal transmission characteristics of MSPs of ferrites. The innovative combination of the unidirectional properties of MSP with strategically placed copper components enables unprecedented control over wave propagation, permitting forward transmission while completely blocking backward waves within the non-reciprocal bandgap of 6−8.4 GHz. By incorporating a metal ground plane at bottom of the structure, an absorbing material is constructed, showing exceptional performance by efficiently absorbing incident waves while suppressing reflections. The design offers flexible designability with simulations confirming tunable absorption bands through either BMF adjustment or ferrite material selection. Practical implementation potential is further enhanced by the possibility of realizing a real-time controllable absorption band without changing the structure by using electromagnets to provide the BMF. Experimental validation via prototype fabrication and testing demonstrates excellent agreement with simulations, confirming high-efficiency wave absorption within the non-reciprocal band of 6−8.4 GHz. The demonstrated P-band absorber highlights the scalability of technology across different frequency ranges. This research establishes a new approach to RAM design, with potential applications in advanced radar stealth systems and electromagnetic interference reduction. The unique non-reciprocal absorption mechanism opens new possibilities for next-generation electromagnetic wave control technologies.

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