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Abstract
Active beam steering and energy distribution have important applications for terahertz (THz) communication, radar, and imaging. However, the spin-conjugated mirror symmetry of a passive Pancharatnam–Berry (PB) metasurface limits the active energy distribution. Here, we prepared a low dispersion, low loss, and high magneto-optical coefficient La:YIG single crystal, $\pm {45}^\circ$ Faraday rotation angle that can be actively tuned by a weak magnetic field in broadband THz range at room temperature. Based on this functional material, a THz magneto-optical (MO) spin-modulated metadevice has been demonstrated, which is integrated with a La:YIG, an anisotropic metasurface, and a PB metasurface layer. The spin-conjugated mirror symmetry is broken by the MO chirality effect and photonic spin Hall effect in this metadevice so that spin-selective beam steering within the range of $\pm {27}^\circ - {\rm \pm 41}^\circ$ is dynamically manipulated by external magnetic fields and power distribution can be tuned with the max modulation depth of 91.6%. More importantly, the MO crystal introduces nonreciprocal phase shift between two spin states so that the device not only achieves active THz beam steering but also provides isolation for reflected waves with the max isolation of 23 dB. This mechanism of THz nonreciprocal spin beam steering provides multiple functions for THz point-to-point networking communication, anti-shielding, anti-interference, and power distribution.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
In the face of increasing information transmission and processing capacity, the active and multifunctional wavefront manipulation of terahertz (THz, ${1}\;{\rm THz} = {{10}^{12}}\;{\rm Hz}$) waves becomes more urgent [1–5]. In the last decades, metasurfaces have gained much attention due to their powerful ability to manipulate the amplitude, phase, and polarization of THz waves [6–9]. By properly arranging the geometric size and spatial orientation of the meta-cell, well-designed spatial phase and polarization distributions can be obtained. Among them, the Pancharatnam–Berry (PB) metasurface is composed of spatially rotated anisotropic meta-atoms to achieve spin conversion and gradient phase distribution for a pair of photonic spin states with left and right-handed rotating (i.e., $L$ state and $R$ state), which has been applied in special beam generators [10–12], beam splitters [13,14], spin-multiplexing holograms [15,16], and metalenses [17–19]. However, the behaviors of the $L$ and $R$ spin state are always mirrored symmetric and correlatively spin-locked in a typical PB metasurface. Moreover, due to the lack of an active control mechanism, the outgoing wavefront is fixed. Therefore, the realization of active spin-locked breaking is significant for the manipulation of THz beams.
To achieve dynamical wavefront manipulation, it is necessary to apply functional materials that are sensitive to external excitations (e.g., optical [20], electrical [21–23], magnetic [24], and thermal field [25]). Moreover, the chirality of the device (i.e., spatial mirror symmetry breaking) is the fundamental condition for the spin-locked release. Fortunately, the magneto-optical (MO) materials have not only magneto-tunability but also optical chirality, including the Faraday rotation (FR) effect due to the different phase shifts between the $L$ and $R$ spin state and the magneto-optical circular dichroism (MCD) originated from the intensity difference between them [26–32]. Moreover, when the external magnetic field (EMF) is inverted, the chirality of MO materials will be reversed, which indicates the nonreciprocal transmission (i.e., time-reversal symmetry breaking). The nonreciprocal one-way transmission is vital for protecting THz core components, eliminating echo noise, and realizing multi-channel isolation and duplex communication.
Fig. 1. (a) Geometry of the metadevice. Inset, diagrams and SEM photos of the meta-atom. (b) Schematic diagram of the AR-THz-TDPS system experiment setup.
In the THz region, some MO materials exhibit significant magneto-optical effects. Strong FR and MCD effects have been observed in some narrow gap semiconductors (e.g., InSb [33,34], InAs [35,36], HgTe [37,38]) and can be tuned with temperature and EMF, but they work at low temperatures. Recently, MO spectrum and topological photonic band characteristics of Dirac and Weyl semi-metals in the THz band have been studied, showing enhanced magneto-optical activity (MOA) and photonic spin Hall effect (PSHE) [39,40]. However, even if these 2D materials have strong magneto-optical coefficients, it is difficult to achieve large FR angles due to their nanoscale thickness, while operating conditions of low temperature (4 K) and strong magnetic field (7 T) also limit their application [41,42]. By contrast, ferrites have the advantage of operating at room temperature. In 2013, Shalaby et al. experimentally demonstrated the THz Faraday isolator by using ${{\rm SrFe}_{12}}{{\rm O}_{19}}$ permanent magnet material, but high insertion loss limited the practical application of the device [43]. In 2021, Grebenchukov et al. reported that hexagon ferrites achieve THz FR of 20°/mm and an absorption coefficient of ${5}\;{{\rm cm}^{- 1}}$ [44]. More recently, rare-Earth-doped large-area yttrium iron garnet (YIG) single-crystal films such as La:YIG and Bi:YIG have achieved a lower insertion loss, higher FR effect, and magnetic tunability, compared with permanent magnet materials [45,46].
Therefore, by combining the MO chirality in YIG materials, artificial spin conversion, and wavefront distribution of the metasurface, more exotic transmission effects are expected, and new manipulation techniques will be developed. However, the dynamic photonic spin chirality and wavefront manipulation by the magnetic field have been rarely reported yet in the THz band. In this work, an active MO spin-modulated metadevice is proposed, which consists of the YIG crystal, an anisotropic metasurface layer, and a PB metasurface layer. This MO metadevice achieves the dynamic spin conversion, resulting in active energy distribution in the different deflection angles for the $L$ and $R$ state. More importantly, due to the nonreciprocal phase shift between the $L$ and $R$ state, the device achieves active THz beam steering with an echo isolation function.
2. FUNCTIONAL MATERIAL AND STRUCTURE DESIGN
A. Device Structure
The structure diagram of the MO metadevice is shown in Fig. 1(a). The first layer is the YIG layer with a thickness of $d = {2.4}\;{\rm mm}$. La: yttrium iron garnet single-crystal film (La:YIG) with the thickness of 300 µm was grown from a supersaturated melt based on the ${\rm PbO} {\text -} {{\rm B}_2}{{\rm O}_3}$ flux by the standard liquid phase epitaxy method on a three-inch (111)-orientated gadolinium gallium garnet (GGG) substrate. After the growth is completed, the substrate is ground off. The Si metasurface was fabricated by photolithography and reactive ion beam etching on a high-resistance (${\gt}{10}\;{\rm K}\Omega \;{\rm cm}$) Si wafer with a height of $H = {1}\;{\rm mm}$. Both layers have the etching depth of ${h_1} = {h_2} = {200}\;{\unicode{x00B5}{\rm m}}$ and the meta-atom period of $P = {200}\;{\unicode{x00B5}{\rm m}}$. The front layer is an anisotropic metasurface layer composed of long rectangular elements with a length of ${l_1} = {160}\;{\unicode{x00B5}{\rm m}}$ and a width of ${W_1} = {80}\;{\unicode{x00B5}{\rm m}}$. The back is a PB metasurface layer composed of the axis-orientated meta-atoms with a length of ${l_2} = {160}\;{\unicode{x00B5}{\rm m}}$ and a width of ${W_2} = {80}\;{\unicode{x00B5}{\rm m}}$. And four meta-atoms form a supercell along the $x$ axis, and they have the same shape and size and are rotated sequentially with a rotation step of $\theta = {45}^\circ$. The Si metasurface was tightly bonded to the YIG crystal using the ultraviolet adhesive.
B. MO Properties of La:YIG
First, the MO characteristics of La:YIG crystal are measured at room temperature by an angle-resolved THz time-domain polarization spectroscopy (THz-TDPS) system shown in Fig. 1(b) at the deflection angle $\alpha = {0}^\circ$. The YIG sample is placed in the center of the magnets (i.e., the EMF is along the direction of wave propagation, which can be adjusted from ${-}{0.26}\;{\rm T}$ to ${+}{0.26}\;{\rm T}$. “+” denotes along the propagation direction, and “−” denotes opposite to the propagation direction). The detailed experimental system and data processing methods are provided in Section S1 in Supplement 1. The schematic diagram of the FR effect of YIG under the EMF is shown in Fig. 2(a), which originates from the nonreciprocal phase shift of the conjugated spin states in the YIG. The results are shown in Fig. 2(b), which shows that the FR angle increases gradually with the increase of EMF, and the rotation direction is exactly opposite for the forward and backward EMF. The maximum rotation angle reaches up to ±44º at $B = \pm {0.26}\;{\rm T}$ in a broadband THz range from 0.2 to 1.1 THz. The polarization ellipses of the output light at 0.3 THz are obtained to illustrate the FR effect as shown in Fig. 2(c) by the THz-TDPS system, and the polarization of the output light remains in the LP state but rotates an angle. Furthermore, the intensity polar-distribution map by rotating the THz polarizer in a 0.3 THz single-frequency transmission system also confirms the same conclusion as shown in Fig. 2(d). The FR angle $\varphi$ is determined by the following expression [47]:
where $V$ is the Verdet coefficient, and $d$ is the thickness of the YIG crystal. According to Eq. (1) and the experimental data above, we can obtain $V = {70.5}^\circ { /}({\rm T \cdot mm})$ in the THz band. More detailed THz optical and MO properties of this La:YIG single crystal can be found in Section S2 in Supplement 1. Overall, La:YIG single crystal has low dispersion ($n = {4}$ and $\Delta n \lt {0.05}$), a lower THz absorption coefficient (${\lt}{5}\;{{\rm cm}^{- 1}}$), and a higher MO coefficient than the previously reported THz MO materials in the broadband THz spectrum, which make it an ideal candidate functional material for the development of high-performance THz MO devices working at room temperature under a relatively low magnetic field.Fig. 2. (a) Schematic diagram of the Faraday rotation. (b) Experimental Faraday rotation angle in the broadband THz range and (c) the polarization ellipses of the electric vector at 0.3 THz with the EMF varying from ${-}{0.26} \sim + {0.26}\;{\rm T}$. (d) Intensity polar-distribution map at 0.3 THz when $B = {0}\;{\rm T}$, ${-}{0.26}\;{\rm T}$, and ${+}{0.26}\;{\rm T}$.
C. Metasurface Design
Then, the transmission characteristics of the anisotropic layer and PB layer are explored. The anisotropic phase shifts of both layers are simulated by the finite-difference time-domain (FDTD) method. The simulation methods can be found in Section S3 in Supplement 1. As shown in Fig. 3(a), the anisotropic phase shift between the long and short axis is about 90° in the range of 0.4–1 THz. As shown in Fig. 3(b), when an LP wave with a polarization angle of ${+}{45}^\circ$ incidents the anisotropic metasurface, the $L$ state is always much larger than the $R$ state, indicating that the incident LP wave is converted into an $L$ spin wave. Moreover, the corresponding experimental results are shown in Section S4 in Supplement 1. So, the anisotropic metasurface layer acts as a broadband THz quarter-wave plate (QWP).
Fig. 3. (a) Simulated phase difference of the anisotropic layer and PB metasurface layer in the $x$ and $y$ axis orthogonal directions. (b) Output spin transmittance of the anisotropic layer when the ${+}{45}^\circ$ LP wave inputs. (c) Spin conversion of PB meta-atoms. (d) Diffraction efficiency of the output spin states.
In addition, the anisotropic phase shift of the PB meta-atoms is about 180° at 0.5–0.9 THz in the orthogonal directions as shown in Fig. 3(a). The photonic spin conversion of the PB meta-atom is shown in Fig. 3(c). In the range of 0.5–0.9 THz, the cross-spin states of $LR$ and $RL$ are always much higher than the co-spin components $LL$ and $RR$. Thus, the meta-atoms realize the spin conversion between the $L$ and $R$ state, which plays the role of a broadband THz HWP. Moreover, the diffraction efficiency of the PB supercell for the ${+}{1}$st order is more than 60%, while it is almost 0 for the 0 order, so the output wave can be deflected to the ${+}{1}$st order with a high extinction ratio, as shown in Fig. 3(d). Since the FR effect of the YIG layer works in a frequency-independent ultra-wide THz band, the metadevice can work efficiently when the operating frequency band of the anisotropic metasurface layer as QWP is overlapped with that of the PB metasurface layer as HWP. Therefore, the working band of the whole metadevice can be predicted in the region of 0.55–0.9 THz.
3. RESULTS AND DISCUSSION
A. Active Beam Steering and Energy Distribution
Based on the above characteristics of the YIG crystal, the anisotropic metasurface, and the PB metasurface, when a $y$-LP wave is incident, the output Jones matrix of the whole metadevice can be written as [48,49]
Then, the output spin components can be solved according to Eq. (2) as follows:
Fig. 4. Schematic diagram of MO spin-modulated metadevice under (a) $B = - {0.26}\;{\rm T}$, (b) 0 T, and (c) ${+}{0.26}\;{\rm T}$. (d) CD map with the different EMFs and frequencies of one metadevice supercell. The normalized far-field diffraction efficiency distribution under the different EMF and deflection angles at (e) 0.65 THz and (f) 1.05 THz.
Figure 4(d) shows the CD map (with EMF and frequency variation) of one supercell (including four different meta-atoms) in the MO metadevice. Because of the mirror symmetry of the whole structure, the device is achiral when there is no EMF. When the EMF is applied, YIG has MO nonreciprocal phase shift to the $L$ and $R$ spin state. After passing through the anisotropic metasurface, the mirror symmetry of the system is broken, converting this MOA into an MCD effect as shown in Fig. 4(d). Due to the PSHE of PB metasurface layer, a pair of chiral spin states are separated in space so that this tunable MCD effect is ultimately manifested as a different energy distribution in the two deflection sides in the frequency band of 0.55–0.9 THz. The far-field deflection distributions of the MO metadevice at 0.65 THz and 1.05 THz are simulated as shown in Figs. 4(e) and 4(f), respectively. At 0.65 THz, the diffraction efficiency of $L$ state gradually increases as the forward EMF increases at the negative deflection angle and decreases when the EMF is reversed. The corresponding change of the $R$ state is exactly the opposite. Meanwhile, the function of active beam steering disappears at 1.05 THz since it is out of the working band of HWP and QWP.
Next, the steering of the $L$ state was measured under the different EMFs in the experiment. According to the PSHE in the $K$ space, the relationship between the frequency $f$ and the deflection angle $\alpha$ is as follows: ${K_x} = {\sin}\alpha = c/(P \times f)$ [50], where $P = {4}p = {800}\;{\unicode{x00B5}{\rm m}}$ is the period of one supercell and $c$ is the speed of light in vacuum. Thus, the broadband frequency range of 0.55–0.9 THz is dispersed to a wide deflection angle range of $\pm {43}^\circ - {\pm 25}^\circ$. The transmission spectra at different deflection angles $\alpha$ of 27°–41° are detected by the angle-resolved THz-TDPS under different EMFs from ${-}{0.26}\;{\rm T}$ to ${+}{0.26}\;{\rm T}$, as shown in Fig. 5(a). It is obvious that the diffraction efficiency of $L$ state gradually decreases with the EMF changing from ${+}{0.26}\;{\rm T}$ to ${-}{0.26}\;{\rm T}$. As shown in Fig. 5(b), the ellipsoidal polarizations of output light at 35° are drawn, which indicates the steering beams are converted to a pure $L$ state and the amplitude decreases gradually. Moreover, taking $\alpha = {35}^\circ$ as an example, the diffraction efficiency of the $R$ state is exactly opposite to the that of $L$ state with the variation of EMF as shown in Fig. 5(c). Therefore, a MO spin-conjugated modulation effect has been observed in the deflection angle range of $\pm {25}^\circ - {\pm 43}^\circ$. The modulation depths are shown in Fig. 5(d), and the max modulation depths are 91.6% and 90.7% for the $L$ and $R$ state at $\alpha = {35}^\circ$, respectively. The modulation process of the two conjugated spin states is not independent, in which energy is distributed dynamically between them, and as one decreases, the other increases. Therefore, the MO metadevice realizes the active beam steering and energy distribution.
Fig. 5. (a) Transmission spectra at different angles of 27°, 29°, 32°, 35°, 38°, and 41° under different EMFs of ${-}{0.26}\;{\rm T - + 0.26}\;{\rm T}$. (b) Ellipsoidal polarization of output light at the angle of 35°. (c) Diffraction efficiency of $R$ and $L$ state at 35° varies with different EMFs. (d) Modulation depth of $R$ and $L$ state.
B. Nonreciprocal One-Way Steering
Next, we are concerned with whether the reflected echo of the deflected spin states can pass through the transmission system composed of MO metadevice and a $y$ direction THz polarizer again, as illustrated in Fig. 6(a). For the reflective spin waves ${| R\rangle ^\prime}$ and ${| L \rangle ^\prime}$, the Jones matrix can be written as [48,49]
The detailed matrix is shown in Section S6 in Supplement 1. It can be seen that, although the metadevice realizes the multifunctions of the LP to spin state conversion, beam separation, and steering, the reflected spin beams returning along the original path still have the same nonreciprocal one-way transmission function as the common Faraday optical isolator. When the rotation angle is close to $\pm {45}^\circ$, the system obtains the highest isolation degree.
Fig. 6. (a) Schematic diagram of the nonreciprocal one-way transmission. Simulated electric field distributions of (b) forward and (c) backward transmission.
The nonreciprocal one-way deflection of this MO metadevice has been stimulated by the electric field distributions of the forward and backward transmission at $f = {0.67}\;{\rm THz}$ and $B = + {0.26}\;{\rm T}$. As shown in Fig. 6(b), when the $y$-LP wave incidents the metallic wire polarizer and MO metadevice, most of the output light is converted into the $L$ spin state and deflected to the direction of ${+}{35}^\circ$. As shown in Fig. 6(c), the reflected $L$ spin wave with ${+}{35}^\circ$ incident angle is converted to $x$-LP waves after passing through the metadevice again, but it cannot pass through the $y$ direction polarizer. As a result, the backward wave is forbidden to pass through the whole transmission system, achieving a nonreciprocal one-way deflection.
Then, the one-way transmission function of the metadevice is verified by experiment. Because of the nonreciprocal MO property of YIG, the forward and backward transmission can equalize to the forward and backward EMF. The experimental deflection efficiency of the $L$ and $R$ state at the deflection angle of 27°–41° under $B = \pm {0.26}\;{\rm T}$ has been observed as shown in Figs. 7(a) and 7(b). When a forward EMF is applied, the $L$ spin state can be detected at the forward deflection angle, but the $R$ spin state is isolated (no signal can be detected at any positive or negative deflection angle). When the EMF is reversed, the $L$ spin state is forbidden, while the $R$ spin state is allowed to pass through, and the signal is detected at the forward deflection angle. Therefore, the MO metadevice obtains the function of nonreciprocal one-way deflection, and the isolation rate for the $L$ and $R$ state can be calculated from the experimental data as follows: ${R_{{is\!o}}}({\rm dB}) = - 10\log (I_L^ + /I_L^ -)$ and ${R_{{is\!o}}}({\rm dB}) = - 10\log (I_R^ + /I_R^ -)$. As shown in Fig. 7(c), for the deflection angle from 27° to 41°, the isolation rates are all over 10 dB and reach the maximum value of 23 dB at the deflection angle of 35°. This function can effectively reduce the reflected signal to protect sources and depress echo noise in THz steering systems.
Fig. 7. Experimental deflection efficiency of $L$ and $R$ state at the deflection angle $\alpha = {27}^\circ - {41}^\circ$: (a) $B = + {0.26}\;{\rm T}$ and (b) ${-}{0.26}\;{\rm T}$. (c) Isolation rate of $L$ and $R$ state.
4. CONCLUSION
To sum up, a THz MO metadevice achieves MO spin-modulation with active THz beam steering and nonreciprocal one-way transmission. This device mainly benefits from our preparation of La:YIG single crystal, of which room temperature operating, magnetic tunability, low dispersion, low loss, and high MO coefficient in a wide THz band provide an excellent functional material for the development of various THz MO tunable and nonreciprocal devices. By the combination of the FR effect in YIG crystal, artificial anisotropy, and PSHE of the two metasurface layers, the functions of dynamical steering and power distribution for the $L$ and $R$ spin states are achieved, and the corresponding max modulation is up to 91.6% and 90.7% at the deflection angle of 35°. More importantly, as the nonreciprocal phase shifts between $L$ and $R$ spin states introduced by YIG crystal, the device can not only achieve active beam steering but also provide one-way isolation with the max isolation of 23 dB. Its working frequency region is 0.55–0.9 THz with the defection angle of $\pm {25}^\circ - {\rm \pm 43}^\circ$. Therefore, the active manipulation mechanism and metadevice of both spin asymmetry and time-reversal asymmetry transmission provide applications in multi-channel multiplexing, steering, and energy distributors in the THz point-to-point networking communication with anti-shielding and anti-echo fuctions at room temperature.
Funding
National Natural Science Foundation of China (61831012, 61971242, 62235004, 62335012, 62371258); National Key Research and Development Program of China (2017YFA0701000).
Disclosures
The authors declare no conflict of interest.
Data availability
All relevant data are presented in the paper and Supplement 1. Additional data related to this paper may be requested from the authors.
Supplemental document
See Supplement 1 for supporting content.
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