Terahertz isolator based on nonreciprocal magneto-metasurface

Sai Chen; Fei Fan; Xianghui Wang; Pengfei Wu; Hui Zhang; Shengjiang Chang

doi:10.1364/OE.23.001015

1. Introduction

Recent progress in terahertz (THz) sources and detectors is turning the “THz gap” into one of the most rapidly growing technological fields. To develop THz communication and imaging systems, high-performance active devices to control and manipulate THz waves are in high demand, such as waveguide [1], switch [2], modulator [3–5], filter [6, 7], polarizer [8, 9], and isolator [10, 11]. Recently, artificial electromagnetic (EM) material, such as photonic crystals [12], metamaterial [13, 14], metasurface [15, 16], and plasmonics [17] has drawn many attentions for its unusual EM properties and has been broadly introduced into the THz regime. Metasurface, defined as two dimensional micro-nano structures, has been a research focus for its exceptional abilities for controlling the flow of light beyond that offered by conventional, planar interfaces between two natural materials [15, 18].Moreover, they are compatible with on-chip nano-photonic devices, which is of critical importance for future applications in optoelectronics, ultrafast information technologies, microscopy, imaging and sensing. Recently, metasurface has been proved an effective way to transmit as well as control THz waves [7, 19, 20].

The magneto-optical (MO) microstructure, such as magnetic photonic crystals or magneto-plasmonics [21, 22], has become a research hotspot in recent years. Through the reasonable design of device structure, MO effect can be significantly enhanced by plasmonic resonance or bandgap effect [23, 24]; conversely, MO effect will lead to the splitting of plasmonic resonance, nonreciprocal transmission, giant Faraday rotation effect and other new physical mechanism and phenomena [25–27]. Moreover, the properties of MO devices can be controlled by external magnetic field. The unique nonreciprocal effect and magnetic tunability of MO device makes it irreplaceable in the high performance isolators, phase shifters, MO modulators and magnetic field sensors. However, the improvement of THz MO devices is still challenging.

Isolator is a nonreciprocal one-way transmission device, in which the time reversal symmetry of transmission system is broken. The forward EM wave propagates with low insertion losses, but the backward wave cannot transmit due to a large attenuation. In the communication and radar systems, isolator plays great important roles in the source protection, impedance matching, noise-cancelling and decoupling. However, due to lack of feasible broadband low-loss one-way transmission devices in the THz regime, such as isolator and circulator, THz echoes of the reflection and scattering for system components bring some noise severely limiting the performance of these THz systems. In recent years, a number of nonreciprocal photonic devices have been investigated in the microwave and near-infrared regime based on enhanced Faraday rotation or oblique incidence in the MO devices [28–31]. However, because the MO materials responding at THz frequencies are very rare, the nonreciprocal THz transmission mechanism is still unclear. M. Shalaby et.al. presented the first THz isolator based on the traditional Faraday effect in a bulk permanent magnet, of which performance is limited by the large loss of magnet [11]. Until recently, THz MO micro-structure devices provide new opportunities for the development of THz isolator. Some preliminary works for THz isolators have been reported by Fan et.al [10, 17] and Hu et.al [21]. Those devices are hardly fabricated and difficult in coupling THz waves in the device, which leads a large insertion loss for the forward transmission.

In this work, we introduce THz MO material into an asymmetric metasurface structure to realize a strong MO nonreciprocal THz transmission for the first time, forming a THz magneto-metasurface isolator. The numerical simulations show a maximum isolation of 43 dB and a 10 dB operating bandwidth of 20 GHz under an external magnetic field of 0.3 T, and the insertion loss is smaller than 1.79 dB. Importantly, we discuss the necessary conditions to realize THz nonreciprocal transmission in this magneto-metasurface, which highly depend on the relations of the structure asymmetry, wave polarization direction and external magnetic field direction, and prove the asymmetry metasurface structure leads to the magnetoplasmon mode splitting and nonreciprocal resonance enhancement. Moreover, the isolation dependences and tunability on the external magnetic field, temperature and device structure parameters are also investigated, which show that the best operating state with very high isolation can be well designed for this device.

2. Material and structure

2.1 Device structure

The schematic of the metasurface is shown in Fig. 1. A periodically patterned InSb layer with the thickness D = 100 μm is coated on the silica substrate layer with the thickness (along the z axis) of T = 40 μm. The unit cell of the patterned InSb is axial symmetry for the y axis and asymmetry for the x axis and the detailed geometry is labeled in Fig. 1(b), and the unit cell period P = 100 μm with the square lattice. The width of the vertical stick in InSb layer is d = 10 μm and the length of the vertical stick is h₂ = 50 μm. The length of the horizontal stick L = 70 μm and the width of this stick h₁ = 21 μm. The gap between the two horizontal sticks (along the y axis) g = 30 μm. As shown in Fig. 1(a), THz waves are perpendicularly incident into the periodic plane along the x axis, the polarization direction of the THz waves is along the y axis, and an external magnetic field is applied along the x axis. In this case, the vectors of K, E and B are orthogonal to each other, and along the E direction the geometry of the device is asymmetric.

Fig. 1 Schematic structure of the proposed isolator. (a) The 3D view of the device including the directions of the wave polarization and external magnetic field and the coordinate system in this work; (b) The geometry of the unit cell structure, D = 100 μm, T = 40 μm, L = 70 μm, P = 100 μm, h₁ = 21 μm, h₂ = 50 μm, d = 10 μm, and g = 30 μm.

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2.2Magneto-optical property of InSb in the THz regime

In the THz regime, the permittivity of silica is 3.61. When the external magnetic field along the x direction is applied, the semiconductor InSb shows a strong gyrotropy near the cyclotron frequency ω_c, The ω_c is proportional to the external magnetic field through $ω_{c} = e B / m^{*}$ , where B is the magnetic flux density, m* is the effective mass of the carrier and m* = 0.015m_e for the InSb, m_e is the mass of electron; e is the electron charge. In the configuration of E and B shown in Fig. 1(a), the dielectric function of InSb becomes a nonreciprocal tensor expressed as [17]:

[\begin{matrix} ε_{x} & 0 & 0 \\ 0 & ε_{y} & - ε_{y z} \\ 0 & ε_{y z} & ε_{z} \end{matrix}]

where three different tensor elements in Eq. (1) can be written as:

\begin{array}{l} ε_{x} = ε_{\infty} - ε_{\infty} \frac{ω_{p}^{2}}{ω (ω + γ i)}, \\ ε_{y} = ε_{z} = ε_{\infty} - ε_{\infty} \frac{ω_{p}^{2} (ω + γ i)}{ω [{(ω + γ i)}^{2} - ω_{c}^{2}]}, \\ ε_{y z} = ε_{\infty} \frac{i ω_{p}^{2} ω_{c}}{ω [{(ω + γ i)}^{2} - ω_{c}^{2}]}, \end{array}

where ε_∞ is the high-frequency limit permittivity, ε_∞ = 15.68; ω is the circular frequency of the incident THz wave; γ is the collision frequency of carriers, γ = e/ (μm*) = 0.1π THz; ω_p is plasma frequency written as ω_p = (Ne²/ε₀m*) ^1/2, N is intrinsic carrier density, ε₀ is the free-space permittivity.

Furthermore, we can derive that Re (ε_y) = −Im (ε_yz) and Re (ε_yz) = Im (ε_y), where Re () represents the real part and Im () represents imaginary part. Moreover, the dielectric property of the InSb greatly depends on the N, and the N strongly depends on the temperature T, which follows [32],

N ({cm}^{-3}) = 5.76 \times 10^{14} T^{1.5} \exp [- 0.26 / (2 \times 8.625 \times 10^{- 5} \times T)] .

The dielectric tensor of the InSb shows a strong dispersion and gyrotropy properties, and it is strongly dependent on the external magnetic field and temperature in the THz regime.

We calculated the dielectric tensor elements of the InSb by Eqs. (1)–(3) with the different external magnetic field and temperature as shown in Fig. 2. The calculation results will be used in the following investigation. The permittivity dramatic changes are near the ω_c leading to a very strong dispersion. With the increase of the external magnetic field, the resonance of permittivity proportionally moves to a higher frequency and the value of permittivity becomes smaller. The permittivity also strongly depends on the temperature. The temperature does not influence the location of the ω_c, but the intensity of the cyclotron resonance increases with the temperature. Therefore, when the device is in the temperature range of 160-205 K, the external magnetic field of 0-0.5 T can induce a strong gyrotropy of InSb in the THz regime, and thus the optical and MO properties of the device can be controlled by the external magnetic field and temperature.

Fig. 2 (a) The real part of ε_x, ε_y and ε_yz and the imaginary part of ε_x of InSb in the THz regime with the dependence on the external magnetic field at 195K and (b) with the dependence on the temperature at 0.3 T.

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If a THz wave propagates along the z direction in this MO medium, the K, E and B are orthogonal to each other forming a Voigt MO configuration, the wave equation $k^{2} E - k (k \cdot E) - ω^{2} ε μ \cdot E = 0$ can be written from as [33]:

- β^{2} [\begin{matrix} E_{x} \\ E_{y} \\ E_{z} \end{matrix}] + [\begin{matrix} 0 \\ 0 \\ β^{2} E_{z} \end{matrix}] + ω^{2} μ_{0} [\begin{matrix} ε_{x} & 0 & 0 \\ 0 & ε_{y} & - ε_{y z} \\ 0 & ε_{y z} & ε_{y} \end{matrix}] [\begin{matrix} E_{x} \\ E_{y} \\ E_{z} \end{matrix}] = 0.

Two eigensolutions can be obtained by Eq. (4):

E_{x} \neq 0, E_{y} = 0, E_{z} = 0, β_{1}^{2} = ω^{2} μ_{0} ε_{x},

E_{x} = 0, E_{y} = - i \frac{ε_{y z}}{ε_{y}} E_{z}, β_{2}^{2} = ω^{2} μ_{0} \frac{ε_{y}^{2} - ε_{y z}^{2}}{ε_{y}} .

The first solution in Eq. (5) corresponds to a linearly polarized eigenwave. The electric field vector E is perpendicular to the direction of wave propagation K and is parallel to the direction of external magnetic field (B), which is not affected by the external magnetic field according to ε_x in Eq. (2). The second solution in Eq. (6) is an elliptically polarized eigenwave. The electric field vector lies in the y-z plane and is perpendicular to the direction of external magnetic field (B), which interacts with the external magnetic field according to ε_y and ε_yz in Eq. (2). In the bulk medium, these two solutions lead to a Voigt MO birefringence effect. In the ensuing discussions, we will see the nonreciprocal THz transmission due to the asymmetry of patterned MO structure based on these solutions. In this work, we do not discuss the Faraday configuration (K∥B).

3. Device property

3.1 Nonreciprocal transmission

The performance of the isolator mainly depends on two aspects: one is the transmittance of the forward propagation, which identifies the insertion loss of the isolator; the other is the isolation between the backward transmission and forward transmission. Here, we simulate the transmission spectra of forward wave |S₂₁|² and backward wave |S₁₂|² in dB by the commercial software CST Microwave Studio shown in Fig. 3(a), where the K, E and Bare set as shown in Fig. 1(a). The corresponding isolation spectrum expressed by Iso = |S₂₁|²-|S₁₂|² is shown in the inset of Fig. 3(a). In Fig. 3(a), both the forward and backward waves have a resonance valley that cannot transmit light within this frequency band. The resonance of backward wave is always located at a lower frequency than that of the forward wave, so when the backward wave cannot transmit through this metasurface, the forward wave at the same frequency can transmit through this metasurface. When T = 195 K, B = 0.3 T, the backward wave |S₁₂|² = −44.79 dB at 0.68 THz, and the forward wave |S₂₁|² = −1.79 dB at this frequency, so the isolation peak Iso = 43 dB with a 10 dB bandwidth of 20 GHz as shown in Fig. 3(a). Fig. 3(b) shows the steady magnetic field of the metasurface with nonreciprocal transmission property: the wave of 0.68 THz can transmit from Port 1 to Port 2, but it cannot transmit from Port 2 to Port 1, thus the isolation function of this device is well performed.

Fig. 3 (a) The transmission spectrum of the forward waves |S₂₁|² and backward waves |S₁₂|², when T = 195 K, B = 0.3 T, the inset picture is the isolation spectra of the isolator. (b) Steady magnetic field of the isolator at 0.68 THz when T = 195 K, B = 0.3 T in the x-z cut plane.

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3.2 Discussions on polarization and asymmetry

Now, we analyze which factors lead to the above nonreciprocal transmission in this magneto-metasurface. The transmission spectra of the forward and backward waves with different directions of the incident wave polarization and external magnetic field are simulated as shown in Fig. 4. There are two resonances V₁ and V₂ in Fig. 4. One is located at near 0.7 THz and the other is at 0.94 THz. The resonance V₂ appears in the E_x-B_x and E_x-B_y case both with E_x component and the V₁ appears in E_x-B_y and E_y-B_x case where the polarization direction is orthogonal to the external magnetic field. Only in the case of E_y-B_x, the resonance V₁ splits as $V_{1}^{-}$ and $V_{1}^{+}$ for the backward and forward THz waves, which realize nonreciprocal transmission and isolation function. In other cases, the forward and backward spectra are overlapped with reciprocal transmission.

Fig. 4 Transmission spectrums of the forward waves |S₂₁|² and backward waves |S₁₂|² in the different direction of the polarization and external magnetic field when T = 195 K, B = 0.3 T. The label such as ‘Ey-Bx’ means the polarization direction of THz waves is along the positive direction of y axis and the external magnetic field direction is along the positive direction of x axis.

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As the eigensolutions shown in Eq. (6), the E_y-B_x case has the elliptically polarized component E_y and E_z in the y-z plane, and the E_x-B_y case has E_x and E_z in the x-z plane. The resonance V₁ appears in these two cases, which indicate they are both induced by the elliptically polarized modes in the different plane. A magnetic dipole resonance will be induced by the rotationally changing electric field of this elliptically polarized magneto mode. Therefore, as the magnetic field shown in Fig. 3 (b), it is a typical magnetic dipole resonance excited in the InSb sticks at 0.68 THz. The energy of the backward transmission waves is strongly localized in the metasurface by this resonance. The resonance frequency and intensity are mainly determined by the width of InSb stick orthogonal to the polarization direction of incident waves when material parameters are fixed. Of course, this resonance is also strongly related to the structure symmetry. We can notice that the magnetic dipole resonances in E_y-B_x and E_x-B_y case are quite different, which originates from the asymmetry of the metasurface. If a circularly polarized light is left-handed rotation in the x-z plane for the forward transmission, it is right-handed rotation for the backward transmission as shown in Fig. 3(b). According to Eq. (6), if the device structure is symmetric along the x direction as shown in Fig. 4(c), the forward and backward waves (left and right rotating waves) are totally equivalent, so it is a reciprocal transmission in the E_x-B_y case. But when the structure is asymmetric along the polarization direction of incident wave in the rotating plane as shown in Fig. 4(b) (just the E_y-B_z case, the asymmetric geometry along the y direction), the forward and backward waves are no longer equivalent. The effective refractive indexes of the left and right rotating magnetoplasmon modes become different, so the resonance frequencies of the forward and backward waves move to a higher and lower frequency respectively, splitting as the $V_{1}^{-}$ and $V_{1}^{+}$ . This is a pair of the nonreciprocal resonance modes in the asymmetry magneto-metasurface, which lead to high isolation in the THz transmission. Therefore, the interactions of three factors, that is the asymmetry of metasurface structure, wave polarization direction and the external magnetic field direction, determine the resonance and nonreciprocal transmission in this metasurface.

In addition, both in the E_x-B_x and E_x-B_y case the THz waves have the component E_x in the MO structure, so the resonance V₂ is induced by the E_x polarization in the metasurface structure, which is a traditional metasurface resonance result. In E_y-B_y case, the THz wave is linearly E_y polarized in the MO structure, so there is neither the V₂ resonance associated with E_x nor the V₁ resonance associated with elliptical polarization.

The discussions above can be concluded as follows: (1) the generation and frequency of the resonances are related to the unit structure and polarization state in the metasurface, indirectly related to the external magnetic field; (2) The first condition for the nonreciprocal transmission is the MO interaction between the incident waves and external magnetic field, so the metasurface should have MO material in the THz regime and the THz waves polarization direction should be orthogonal to the external magnetic field in the Voigt configuration; (3)The second condition is the metasurface structure is asymmetric along the polarization direction of normal incident wave which satisfies the first condition. We use the structural asymmetry in our work, but in the previous reports, other methods can also break the symmetry of the transmission system, and realize nonreciprocal transmission in the MO systems. For examples, symmetric gratings covered on a MO material substrate can realize the nonreciprocal transmission by an oblique incidence at the optical frequency [30, 31]. Their maximum isolation only reaches 17dB and the nonreciprocal performance is highly sensitive to the incidence angle. Therefore, this nonreciprocal device based on oblique incidence is not appropriate for an isolator. Instead of oblique incidence, asymmetric geometry in the magneto-metasurface is a new way to realize the nonreciprocity, which is more suitable for THz isolator, due to its normal incidence and a high isolation over 40dB. Therefore, a more general conclusion for the second condition is that the transmission system is asymmetric for forward and backward waves. “Asymmetry” here can be one of the conditions as follows: structural asymmetry, oblique incidence, or asymmetric magnetization of MO material.

3.3 Dependence and tunability of the device

According to Eq. (2) and Fig. 2, the MO property of InSb is strongly dependent with the external magnetic field and temperature, and this leads to the tunability of this isolator by the different external magnetic field and temperature. Frist, we simulate the transmission spectra of backward waves and isolation spectra with the different external magnetic field at T = 195 K shown in Fig. 5(a) and 5(b). With the increase of the external magnetic field, the resonance and the isolation peak move to a higher frequency. Moreover, the isolation initially increases up to the maximum value at 0.3 T and then decreases when the external magnetic field continues to increase. Up to 0.4 T, the isolation is too low to well perform the one-way transmission function. Therefore, the central operating frequency of this magneto-metasurface can be tuned from 0.55 to 0.8 THz by the external magnetic field and its best isolation state is under an external magnetic field of 0.3 T at T = 195 K.

Fig. 5 (a) Transmission spectra of the backward waves and (b) isolation spectra under the different external magnetic field when T = 195K; (c) (d) under the different temperature when B = 0.3T; (e) (f) under the different thickness of InSb layer when B = 0.3T, T = 195K.

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Second, the transmission and isolation dependence on the temperature for this metasurface is also simulated at B = 0.3 T as shown in Figs. 5(c) and 5(d). The results show that the resonance and isolation peak move to a higher frequency as the temperature increases and its strength increases to the maximum value at 195 K and then decrease when temperature continues to increase. Therefore, like changing the external magnetic field, the central operating frequency of this device can be tuned from 0.6 to 0.75 THz by the temperature from 165 K to 205 K.

Finally, we discuss the isolation dependence on geometry parameters of the device. We simulate the transmission and isolation under the different thickness(from 80 μm to 120 μm) of InSb layer as an example, and the results are shown in Figs. 5(e) and 5(f) when B = 0.3 T,T = 195 K. The resonance and isolation peak move to a lower frequency as the thickness increases. The intensity of the forward transmission resonance increases higher and higher as the thickness increase, and the isolation is much higher than other cases when the thickness is 100 μm. In this case, the MO effect well matches to the resonance from device structure at a specified frequency, which makes the divided left or right rotating resonance mode enhanced by the magneto-plasmons in the InSb, so the maximum nonreciprocal transmission is obtained. Additionally, the robustness of the geometric parameters is considered. According to our numerical simulations, we find that the results (i.e. isolation, bandwidth, and insertion loss) can be accepted when the geometric parameters of L, d, h₁, h₂ and g have a deviation within ± 1.5 μm. For example, when the sharp corners of metasurface structure changes rounded corners with a radius of 1.5μm, the isolation slightly descends but is still over 35dB. Therefore, this device with micrometer precision can be well fabricated by the deep reactive ion etching of MEMs technology.

From the discussions above, we can see that there is a best isolation state with the certain external magnetic field and temperature (just corresponding to the specified dielectric and MO parameters of InSb) for a certain designed geometry parameters of the device. Through reasonable structure design and parameter selection, an optimal state that has a maximum nonreciprocal transmission and MO enhanced resonance can be designed in this magneto-metasurface.

4. Conclusion

In conclusion, we have investigated the nonreciprocal transmission and tunability of a THz isolator based on the magneto-metasurface. The numerical simulation shows a maximum isolation of 43 dB and a 10 dB operating bandwidth of 20 GHz under an external magnetic field of 0.3 T, and the insertion loss is smaller than 1.79 dB. Importantly, we find the physical principles to form THz nonreciprocal transmission in the magneto-metasurface, which strongly depend on the relations of the structure asymmetry, wave polarization direction and external magnetic field direction. Moreover, the isolation dependences and tunability on the external magnetic field, temperature, and device structure are also investigated, which show that the best operating state with very high isolation can be well designed for the device. This low-loss, high isolation, easy coupling THz magneto-metasurface isolator has broadly potentials for THz application systems.

Acknowledgments

This work is supported by the National Basic Research Program of China (Grant No.2014CB339800), the National High Technology Research and Development Program of China (Grant No. 2011AA010205), the National Natural Science Foundation of China (Grant No. 61171027; Grant No. 61378005), and the Science and Technology Program of Tianjin (Grant No. 13RCGFGX01127) and the Fundamental Research Funds for the Central University (Grant No. 14CX02020A).

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Terahertz isolator based on nonreciprocal magneto-metasurface

Abstract

1. Introduction

2. Material and structure

2.1 Device structure

2.2Magneto-optical property of InSb in the THz regime

3. Device property

3.1 Nonreciprocal transmission

3.2 Discussions on polarization and asymmetry

3.3 Dependence and tunability of the device

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (6)

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