Introduction

Negative refractive index (NRI) metamaterials with simultaneously negative permittivity and negative permeability have been recently stimulated tremendous fundamental and practical interests due to their unique electromagnetic properties such as the reversals of both Doppler shift and Cherenkov radiation, enhancement of evanescent wave and subwavelength resolution imaging, etc1,2,3,4,5. Metamaterials are a class of materials in which subwavelength features, rather than the constituent materials, control the macroscopic electromagnetic properties. Most of the reports demonstrated the metamaterials realized by periodic artificial metallic structures6,7,8,9,10,11,12,13. For instance, using periodic continuous wires to produce effective negative permittivity and using periodic split-ring resonators (SRRs) to provide effective negative permeability14. The unusual electromagnetic properties of metamaterials originate from the structure rather than being inherited directly from the materials15, which sets great challenges for realizing the tunable and two-dimensional negative refractive properties16,17.

Ferrite-based metamaterials have been reported in which negative magnetic permeability is achieved by substituting SRR elements with ferrites18,19,20,21,22,23. The negative permeability appears when the ferromagnetic resonance (FMR) of the ferrite taking place. By combining the ferrites and metallic wires, the NRI properties can be realized. In previous studies, our group designed a magnetically tunable and two-dimensional NRI metamaterial consisting of an array of yttrium iron garnet (YIG) rods and copper wires24,25. As the ferrites used in these metamaterials are soft magnetic materials, in order to realize the FMR and negative permeability, an external magnetic field must be applied around the ferrites, which makes the ferrite-based metamaterials difficult for practical application20,26,27. Recently, Harris et al.28 outlined the advances in ferrite-based metamaterials and discussed the application of permanent magnetic ferrite in microwave devices. Gu et al.29 designed a photonic crystal composed of self-biased strontium ferrite rods and experimentally proved that this photonic crystal can realize the negative refraction without applied magnetic field.

Here, we report a metamaterial composed of permanent magnetic ferrite rods and metallic wires, which exhibits not only negative refraction but also near zero refraction. Since no external magnetic field is needed, the near-field scanning maps can be measured with the wedge-shaped and slab-shaped samples to prove the negative and near zero refractive properties.

Results

Theoretical calculations

The permanent magnetic ferrite-based metamaterial studied here consists of permanent magnetic ferrite rods and metallic wires. Figure 1a shows the schematic diagram of the unit cell of one permanent magnetic ferrite rod and one metallic wire. The permanent magnetic ferrite rods are used to produce effective negative permeability while the metallic wires are used to provide effective negative permittivity. With the rectangular sample of the ferrite-based metamaterials inserted into the rectangular waveguide, the scattering parameters are measured by the vector network analyzer (Agilent ENA5071C). The measured scattering parameters are used to retrieve the effective material parameters. The retrieval method is described in detail elsewhere30. The retrieved effective permeability μeff and effective permittivity εeff are shown in Fig. 1b. Firstly, there is one remarkable frequency dispersion in the range of 8–14 GHz and the negative μeff appears at 9.8–12.5 GHz. As the frequency increases from 9.8 GHz, one observes a decrease in μeff to a minimum. With further increase in frequency, μeff increases to a near-zero value. Secondly, it can be seen that the negative εeff appears at 8–14 GHz. The value of the εeff increases as the frequency increases. Hence, we can predict that the value of the refractive index is negative and increases to 0 as the frequency increases from 9.8 GHz to 12.5 GHz. The measured transmission spectra for permanent magnetic ferrite-based metamaterial is shown in Fig. 1c. One can see that there is a broad passband in the transmission spectra. It has been proved that the passband emerges just in the region where both permeability and permittivity are negative, which means that the metamaterials have negative refractive index. The passband appears at the frequency range from 10 to 12.2 GHz, which is in good agreement with the results shown in Fig. 1b. Due to using the different permanent magnetic ferrite to prepare metamaterials, the losses in the passband for the permanent magnetic ferrite-based metamaterials are higher than that for the photonic crystal in Ref. 29. In addition, the transmission property along y direction is the same as that along the x direction. In Ref. 29, the passband of the photonic crystal in Γ-M direction is different from that in Γ-K direction. In comparison with the photonic crystal, the permanent magnetic ferrite-based metamaterial shows a better consistency in transmission property.

Figure 1
figure 1

Sample characterization.

(a) Schematic diagram of the unit cell of one permanent magnetic ferrite rod and one metallic wire. The length directions of the permanent magnetic ferrite rod and metallic wire are parallel to the z axis. The propagation of the incident electromagnetic wave is along the y axis and the electric field and magnetic field are along z and x directions, respectively. (b) Effective permeability and permittivity retrieved from measured scattering parameters. (c) Measured transmission spectra for permanent magnetic ferrite-based metamaterial.

Performance simulation for wedge-shaped structure

To corroborate the theoretical design, we have simulated the propagation of TE wave through a wedge using the retrieved effective material parameters at the working frequency f = 10.85 GHz. The magnitude of the incident power is 1 W. The wedge angle is 26.6° and the side lengths are 110 mm, 55 mm and 120 mm, respectively. The distribution of electric field is shown in Fig. 2. The arrows represent the propagation direction of the wave. There is no refraction at the first surface due to the source wave of 10.85 GHz normally incident on the vertical surface of the wedge. The wave passes through the wedge and undergoes an obvious negative refraction at the second surface.

Figure 2
figure 2

Simulation of distribution of electric field for wedge-shaped sample.

The incident wave is coming from the right, shooting normally onto the vertical surface of the wedge. The dots represent the wedge-shaped sample. The wedge angle is 26.6° and the side lengths are 110 mm, 55 mm and 120 mm, respectively. Arrows represent the propagation direction of the wave.

Near-field scanning system

To confirm the simulated results of the negative refractive behavior of the permanent magnetic ferrite-based metamaterial, we have utilized the near-field scanning system (microwave planar waveguide)31 to measure the propagation of an electromagnetic wave through the wedge composed of permanent magnetic ferrite rods and metallic wires. The photograph of the near-field scanning system is shown in Fig. 3a. The upper and lower metal plates form the planar waveguide, which restrict the polarization of the electric field to lie uniformly along the z direction and further restrict propagation to the x-y plane. A rectangular waveguide is utilized in the lower plate as the waveguide adapter to excite a plane wave (8–18 GHz). Only the electromagnetic wave with TE10 mode can propagate in this waveguide. The incident wave is formed by the creation of a channel in absorbing material and the wedge sample is placed directly at the end of the channel. A detecting probe is installed in the upper plate to measure the amplitude and phase of the local electric field. The feeding and detecting probes are connected to the output and input ports of the vector network analyzer (Agilent ENA5071C), respectively. The lower metal plate is carried by the 2D moving stage, which can be controlled by a computer to move in x and y directions with a scanning step of 4 mm so that we can measure electromagnetic field distributions within a certain area. A wedge-shaped sample was placed in the near-field scanning system. The wedge angle is 26.6° and the side lengths are 110 mm, 55 mm and 120 mm, respectively. Besides, a slab-shaped sample has also been prepared, as shown in Fig. 3b. The slab is 150 mm long and 20 mm wide, with a point source placed 5 mm from the longer side of the slab.

Figure 3
figure 3

Near-field scanning setup.

(a) Photograph of the near-field scanning system. The inset shows the optical image of the as-prepared wedge sample composed of permanent magnetic ferrite rods and metallic wires. The wedge angle is 26.6° and the side lengths are 110 mm, 55 mm and 120 mm, respectively. (b) Optical images of the as-prepared slab sample placed next to the point source in the near-field scanning system. The slab is 150 mm long and 20 mm wide, with a point source placed 5 mm from the longer side of the slab.

Near-field scanning maps for wedge-shaped structure

The measured electric fields (real part and phase) for an incident wave at a series of frequencies refracting from a wedge are shown in Fig. 4. The wedge boundaries are shown by the dashed lines and the normal of the wedge surface is shown by the dotted line. The incident wave is coming from the right, shooting normally onto the vertical surface of the wedge. Arrows represent the propagation direction of the wave. In order to demonstrate the negative refractive properties, we chose three frequencies of the wave, which is respectively 9.85 GHz (strong absorption), 10.85 GHz (negative refractive index), 15.8 GHz (far away from FMR). The electric field (real part) for the source wave at 9.85 GHz propagating into the wedge is shown in Fig. 4a. There is no wave appeared in the left area of the wedge. From Fig. 1b, the permeability of the permanent magnetic ferrite is negative at 9.85 GHz, but it is well known that there are large losses around the FMR frequency. In addition, the wedge-shaped sample has a large number of ferrite rods. Hence, the strong absorption leads to the above phenomenon. The waves at the upper and lower of the map are coming from the same source with no obstruction. Figure 4b shows the phase mapping for the source wave at 9.85 GHz propagating into the wedge, exhibiting the same result as that in Fig. 4a. When the source wave of 10.85 GHz is incident upon the wedge, the measured spatial maps of real part and phase of electric field are demonstrated in Fig. 4c and 4d. Due to the wave normally incident on the vertical surface of the wedge, there is no refraction at the first surface. The wave passes through the wedge and undergoes an obvious negative refraction at the second surface. The negative refractive behavior observed in the experimental results is in good agreement with that observed in simulated ones. When the frequency of the wave increases to 15.8 GHz which is far away from the FMR, the coupling between the ferrite and the electromagnetic field is weak. The wave does not interact with the ferrite strongly and the refractive index of the ferrite is close to 126. Therefore, the wave passes through the wedge with the positive refraction, as shown in Fig. 4e and 4f.

Figure 4
figure 4

Measured near-field scanning maps demonstrating the refractive properties.

The measured spatial maps of (a) real part and (b) phase of electric field for an incident wave at 9.85 GHz (strong absorption), (c) real part and (d) phase of electric field for an incident wave at 10.85 GHz (negative refractive index), (e) real part and (f) phase of electric field for an incident wave at 15.8 GHz (far away from FMR) refracting from a wedge. The wedge boundaries are shown by the dashed lines and normal of the wedge surface is shown by the dotted line. The incident wave is coming from the right, shooting normally onto the vertical surface of the wedge. Arrows represent the propagation direction of the wave.

Compared with the real part mapping of the electric field, the phase mapping can exhibit the refractive behavior more obviously. The measured spatial maps of the phase of electric field for an incident wave at a series of frequencies refracting from a wedge are shown in Fig. 5. In all cases, the propagation direction of the refracted wave lies on the same side of the surface normal as the incident wave. In Fig. 5a, one observes that the incident wave at 10.4 GHz has a certain refraction angle (about 18°) from the normal of the second surface. The phase mapping of the electric field for the source wave at 11.5 GHz propagating into the wedge is shown in Fig. 5b. In contrast to the incident wave at 10.4 GHz, the incident wave at 11.5 GHz has a relatively small refraction angle (about 10°) from the normal of the second surface. In Fig. 5c, when the frequency of the wave increases to 12.2 GHz, the wave has a near zero refraction angle from the normal, which exhibits a near zero refractive behavior. Based on the FMR behavior of the gyromagnetic ferrites, the effective permeability of the permanent magnetic ferrite rod is changing from negative to zero as the frequency of the wave increases. Since the index of refraction is directly related to the permeability via , the permanent magnetic ferrite-based metamaterials could exhibit near zero refractive index, which results in the near zero refractive behavior as shown in Fig. 5c.

Figure 5
figure 5

Measured near-field scanning maps demonstrating the transition of the refractive behavior.

The measured spatial maps of the phase of electric field for an incident wave at (a) 10.4 GHz (negative refractive index), (b) 11.5 GHz (negative refractive index) and (c) 12.2 GHz (near-zero refractive index) refracting from a wedge.

Negative refractive behavior in slab-shaped structure

To further prove the negative refractive behavior of the permanent magnetic ferrite-based metamaterial, the simulated map of distribution of electric field at a frequency of 10.55 GHz for a slab placed next to a point source is shown in Fig. 6a. The material parameters used in this simulation are chosen to be consistent with the measured ones. The wave emanating from the point source located at the lower side of the slab is refocused to a point at the upper side of the slab. It looks like a point source existed at the upper side of the slab and the electromagnetic wave continues emanating from this point. This behavior indicates the slab has a negative refractive index and the refractive index n approximately equal to −1. Besides simulation, a slab-shaped sample composed of permanent magnetic ferrite rods and metallic wires has also been prepared. The measured spatial map of the real part of electric field for a slab placed next to a point source at a frequency of 10.55 GHz is shown in Fig. 6b. The slab boundaries are shown by the dashed lines. The black dot represents the point source which is below the slab. It can be seen that the refractive behavior observed in experimental results is in good agreement with that observed in simulated ones. When the wave emanating from the point source passes through the slab, it is refocused to a point at the other side of the slab. The focusing behavior observed in simulation and experiment confirms the negative refractive properties of the permanent magnetic ferrite-based metamaterials.

Figure 6
figure 6

Focusing maps demonstrating the negative refractive behavior.

(a) Simulation of distribution of electric field and (b) measured spatial maps of the real part of electric field for a slab placed next to a point source at a frequency of 10.55 GHz. The slab boundaries are shown by the dashed lines. The black dot represents the point source which is below the slab.

Discussion

We fabricated a metamaterial composed of permanent magnetic ferrite rods and metallic wires. Due to high effective internal magnetic anisotropy, the permanent magnetic ferrite can provide effective negative permeability without external magnetic field when the nature resonance takes place. We prepared the wedge-shaped and slab-shaped structures of permanent magnetic ferrite-based metamaterials to investigate the refractive properties. Our design has been corroborated by the numerical calculation and measured near-field scanning electric field maps demonstrating that this metamaterial exhibits both negative refraction and near zero refraction. We believe that our results will pave the way for a new class of ferrite-based metamaterials without resorting to an external magnetic field bias. In contrast to the previous ferrite-based metamaterials, such a metamaterial has greater potential for practical applications such as waveguiding and imaging.

Methods

Theoretical description

The negative permeability of the ferrite can be obtained when the FMR takes place. The equation of the effective permeability for the soft magnetic ferrite under an applied magnetic field is well known from the ferromagnetic resonance (FMR) studies and can be expressed by24

with

where α is damping coefficient of ferromagnetic precession, γ is the gyromagnetic ratio, F = ωmr, ωm and ωr are characteristic frequency and FMR frequency of the ferrite, Ms is the saturation magnetization caused by the applied magnetic field, H0 is the applied magnetic field, Ha is the magnetocrystalline anisotropy field, Nx, Ny and Nz are the demagnetization factor for x, y and z directions, respectively.

As is well known, the permanent magnetic ferrite possesses a giant magnetocrystalline anisotropy field. Hence, the permanent magnetic ferrite has a large remanent magnetization Mr at the easy magnetization direction after the magnetization process. By interacting with the magnetic field of an electromagnetic wave, the FMR can take place in the permanent magnetic ferrite without external magnetic field, which is called nature resonance. The characteristic frequency ωm and FMR frequency ωr of the permanent magnetic ferrite can be expressed as32

From Eq. (7), one can see that the FMR frequency of the permanent magnetic ferrite is determined by the anisotropy field and demagnetising field. Eqs. (1), (2), (3), (6) and (7) provide an insight into the physics about the effective permeability of the permanent magnetic ferrite. The negative permeability of the ferrite appears at an upper frequency region above the FMR frequency. Periodic continuous metallic wires can produce effective negative permittivity and ferrites provide effective negative permeability. By combining the ferrites and metallic wires, the negative refractive properties can be realized.

Sample fabrication

As a typical M-type hexagonal ferrites, BaFe12O19 presents permanent magnetic bias due to its high effective internal magnetic anisotropy. The commercial BaFe12O19 rods were sliced with dimensions of 1 ×1 × 10 (l × w × h) mm3. The height direction is along the easy magnetization direction. The saturation magnetization Ms, remanent magnetization Mr, linewidth ΔH and relative permittivity εr of the BaFe12O19 rods are 2800 Oe, 2000 Oe, 1200 Oe and 16.4, respectively. The size of the copper wires is 0.5 × 0.03 × 10 (l × w × h) mm3. The permanent magnetic ferrite-based metamaterial is composed of BaFe12O19 rods and Cu wires. The optical image of the as-prepared wedge sample composed of BaFe12O19 rods and Cu wires is shown as an inset in Fig. 3a and the slab sample is shown in Fig. 3b. Using a shadow mask/etching technique, we prepared 0.4 mm thick FR-4 dielectric substrates (εr = 4.4 and tanδ = 0.014) with copper wires spacing of 5 mm on one side. The BaFe12O19 rods were pasted back-to-back with copper wires on the other side of the substrates. The permanent magnetic ferrite-based metamaterials were obtained by assembled the rod-wire units into a wedge-shaped structure or a slab-shaped structure. In order to measure the scattering parameters, a rectangular sample was also prepared, which has the same structure as shown in Ref. 24.