On-chip terahertz isolator with ultrahigh isolation ratios

Terahertz isolators, one of the typical nonreciprocal devices that can break Lorentz reciprocity, are indispensable building blocks in terahertz systems for their critical functionality of manipulating the terahertz flow. Here, we report an integrated terahertz isolator based on the magneto-optical effect of a nonreciprocal resonator. By optimizing the magneto-optical property and the loss of the resonator, we experimentally observe unidirectional propagation with an ultrahigh isolation ratio reaching up to 52 dB and an insertion loss around 7.5 dB at ~0.47 THz. With a thermal tuning method and periodic resonances, the isolator can operate at different central frequencies in the range of 0.405–0.495 THz. This on-chip terahertz isolator will not only inspire more solutions for integrated terahertz nonreciprocal devices, but also have the feasibility for practical applications such as terahertz sensing and reducing unnecessary reflections in terahertz systems.

these components strongly depend on the temperature and external magnetic field. 23 Specifically, the anti-angle elements are proportional to the magnetic field. The 24 dielectric permittivity of InSb can be described by the following Supplementary   25 Equations (1)~(5), where the magnetic field is along the z-direction. 1 In these equations, ωp=ne 2 /(m * ε0) represents the plasma frequency, which depends on 33 the carrier concentration n and the equivalent mass m * . We note that the n could be 34 expressed by Supplementary Equation (6), which corresponds to temperature T. kb is 35 the Boltzmann constant and n0 is the intrinsic doping carrier density. 2 γ refers to the 36 carrier scattering rate, and ε∞=15.6 is the background high-frequency dielectric constant. 37 ωc=eB/m * denotes the electron cyclotron frequency determined by the magnetic field. 38 The contribution of phonons to the function can be expressed in the Supplementary 39 Equation (5). ωt and ωl describe horizontal and vertical optical phonon frequency, 40 respectively, and γph represents the phonon damping rate. 1,2 41 According to the model, when the applied magnetic field is B=0 T, we have ωc=0, 42 and therefore εxy=-εyx=0. In this case, the matrix in Supplementary Equation (1) 43 becomes a symmetric matrix, which indicates that the InSb is a reciprocal material. 44 When the applied magnetic field B>0 T is considered, εxy and εyx are not 0. We have an 45 asymmetric dielectric constant matrix, and therefore the nonreciprocity is introduced.
In the calculation, the mode conversion loss in the resonator, coupling loss between

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In the calculations, we use the finite element method to simulate the effective refractive 88 indices. Firstly, a waveguide is designed with a width of 300 μm, a ridge height and a 89 substrate height of 60 μm, as shown in Fig. 1b, which can support linear TE mode. As 90 to InSb, we utilize a 500 μm-thick wafer in the experiment, therefore the same 91 parameter is considered in the simulations. Moreover, the temperature is set to T=300 K 92 in all simulations. To obtain a better performance, we selected L=4 mm, R=4 mm, and 93 a waveguide gap of around 35 μm as the resonator parameters.

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According to the transmission model, we can calculate the transmission spectra of 95 the device. When r=a, the resonator is in a critical coupling state, and the mismatch 96 between r and a will leads to an obvious decrease of the extinction ratio. As shown in  It should be noted that the InSb has a smooth edge after cleaving, as shown in the 141 inset, the largest fluctuation is 5.2 μm. In the experiment, we observe the smallest gap 142 between InSb and the silicon waveguide to discuss the state of the device.       Supplementary Fig. 6c (gap=7.7 µm) and 6d (gap=15.67 µm). When the gap is 7.7 µm, 236 the resonant frequencies in CW and CCW directions shift in two directions and the extinction ratio of CW direction possesses a larger decrease, which is similar to 238 measurements in the main text. When the gap is 15 µm, the resonances in both CW and 239 CCW directions move towards the higher frequencies, which is consistent with the 240 simulation in Supplementary Fig. 6a. In Fig. 4a of the main text, we observe the tuning of nonreciprocal state when B=0.76 T.

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While the chip is in a reciprocal state for the case of B=0 T, and the tuning process is 258 also observed in the experiment, as shown in Supplementary Fig. 7. In this case, CW  Meanwhile, the chip temperature varied with the introduction of the applied 272 current. During this process, the frequency detuning mainly comes from the thermal-273 optical effect of the silicon ring. In this case, the temperature-dependent frequency 274 detuning can be described by the Supplementary Equation (12). 6,7 With measured 275 frequency detuning, we can obtain the temperature around the ring structure.
In the equation, ΔF refers to the frequency detuning, and ΔT represents the variation of First of all, the decreasing trend is the result of the decreasing frequency detuning.

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With the applied magnetic field, it can be observed that the frequency detuning 337 decreases, as shown in Fig. 4a  analyzed, as shown in Supplementary Fig. 11. When the temperature changes from 341 300 K to 500 K, we can find that the real part differences of the effective refractive  Fig. 12a and 12b, the frequency detuning is the origin of the isolation 356 ratio reduction.
Secondly, the increase of isolation ratios is the result of high extinction ratios at 358 several conditions. For different temperatures, the coupling strengths (self-coupling 359 coefficient (r)) and the loss of the resonator (the round-trip transmission coefficient (a)) 360 will change. When the parameter a changes towards the condition a=r, the extinction 361 ratio of the resonator increases. Considering that the parameter a in CW and CCW 362 directions are different, when a high extinction ratio is realized in a single direction, we 363 can obtain high isolation ratios.

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A typical example is illustrated in Supplementary Fig. 13. Without applied 365 currents, the extinction ratio of CCW mode is 27 dB, and the related isolation ratio is 366 19.6 dB. While the applied current is set to 319.2 mA, the extinction ratio of CCW 367 mode is 39.2 dB, and the related isolation ratio is 25.2 dB. Considering that we can 368 observe a significant decrease of frequency detuning, the extinction ratio is the origin 369 of the isolation ratio increasing.