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Abstract
Broadband optical isolators and circulators are highly desirable for wavelength-division multiplexing, light detection, and ranging systems. However, the silicon-integrated optical isolators and circulators reported so far have a limited isolation bandwidth of only several nanometers, due to waveguide and material dispersion. In this paper, we report the development of broadband magneto-optical isolators on silicon nitride waveguides. We proposed a general method of dispersion compensation to achieve a constant phase difference between reciprocal and nonreciprocal phase shifts in a Mach–Zehnder interferometer over a wide frequency range. This method enabled a theoretical 30 dB isolation/circulation bandwidth of more than 240 nm, which covers the S, C, L, and U bands. The fabricated devices showed a maximum isolation ratio of 28 dB, crosstalk of ${-}{28}\;{\rm dB}$, high 20-dB isolation bandwidth of 29 nm (3.48 THz), and a relatively low loss of 2.7 dB in the wavelength range of 1520–1610 nm. By further heating the reciprocal phase shifter based on the thermo-optic effect, the experimental 20 dB isolation bandwidth of the device increased to 90 nm (11.03 THz). This method has also been applied to the design of broadband, low-loss isolators, and O/C dual-band isolators/circulators. Our work experimentally demonstrated broadband-integrated optical isolators and circulators on silicon, paving the way for their use in optical communication, data communication, and LiDAR applications.
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1. INTRODUCTION
The growing volume of global data necessitates greater data transmission bandwidth in optical communication systems [1–3]. Wavelength division multiplexing has been widely studied for photonic integrated circuits [4–8]. Lasers and optical amplifiers continuously extend their bandwidths from the C-band (1530–1565 nm) to the L- (1565–1625 nm), U- (1625–1675 nm), S- (1460–1530 nm), E- (1360–1460 nm), and O-bands (1260–1360 nm) [9–13]. For data communication, silicon photonic systems require O- and C-band photonic devices [14,15]. Hence, broadband optical isolators are highly desirable for suppressing the back-reflected light from optical systems [16–20]. In addition, broadband optical circulators are required in light detection and ranging (LiDAR) systems that use optical frequency combs, multiwavelength lasers, and frequency-modulated lasers for collinear transceiving [21–23]. However, the operating bandwidths of the bulk optical isolators and circulators are typically less than 80 nm. In recently reported silicon-integrated optical isolators and circulators, the operation bandwidth is even smaller: less than 10 nm [24,25]. This bandwidth is inadequate for meeting demands for wider operation bandwidth. In optical communication, the bandwidth problem has become the bottleneck for the development of C$+$L band fiber amplifiers. For large optical communication bandwidth, the amplifier has been using different rare-earth ions to increase the amplification bandwidth over 100 nm, covering the O-, E-, and S-bands [26]. For polarization dependent optical isolators, GHz passive optical network (GPON) access network is aiming to use O$+$C$+$L band lasers. While in LiDAR systems, frequency combs can be employed to produce a massively parallel array of the wavelength channel, which can be separated by a prism and achieve wavelength scanning. To achieve larger scanning angles, a wavelength range of more than 100 nm is required [22,27]. Broadband operation especially for broadband optical pulses (with frequency combs) that find applications in LiDAR can be obtained with an optical nonlinearity based isolator [28]. To realize a power independent and broadband integrated optical circulator with high isolation ratio, magneto-optical (MO) devices are better choices.
In bulk optical isolators, the isolation bandwidth is limited by magneto-optical material dispersion, i.e., the Faraday effect changes as a function of wavelength. This mechanism limits the isolation bandwidth of the devices to less than 100 nm, even with the implementation of optimized materials [29,30], which is very difficult to improve further. The isolation bandwidth of on-chip MO devices is limited not only by material dispersion, but also by waveguide dispersion [31,32]. In waveguide dispersion, the effective index of the fundamental mode varies as a function of the wavelength, causing differences in propagation phases [33]. As a result, the currently reported silicon-integrated MO isolators or circulators show a maximum 20 dB isolation bandwidth of ${\sim}{8}\;{\rm nm}$ [33–40].
To solve the bandwidth problem, Shoji and Mizumoto, in their pioneering work, proposed wideband optical isolators based on MO garnet waveguides by changing the reciprocal phase shifter of the Mach–Zehnder interferometer (MZI) structure from $\pi /{2}$ to ${3}\pi {\rm /2}$ so that the phase dispersion of the reciprocal and nonreciprocal phase shifter partly cancels in the backward propagation direction [41]. The device was further fabricated using cerium-substituted yttrium iron garnet (CeYIG) waveguides on substituted gadolinium gallium garnet (SGGG) substrates, achieving an isolation ratio of 15–25 dB in the wavelength range of 1530–1640 nm. They also theoretically proposed an ultrabroadband integrated MO isolator using CeYIG waveguides on a GGG substrate covering wavelengths from 1310 to 1550 nm, by fine-tuning the waveguide geometry [42]. For silicon integrated devices, Huang et al. demonstrated a reconfigurable silicon-integrated MO isolator based on MZIs using the thermo-optic effect. By heating the silicon waveguides using a titanium nitride heater, the device showed a reconfigurable 20 dB isolation bandwidth over 100 nm at the cost of switching delay and energy consumption [43]. To date, the operation bandwidth of passive silicon-integrated optical isolators and circulators is still less than 10 nm.
In this study, we theoretically and experimentally implemented ultra-broadband MO isolators and circulators on silicon nitride waveguides with high bandwidths covering the S-, C-, L-, and U-bands. We developed a general method of dispersion compensation of the phase and group delay between the reciprocal and nonreciprocal phase shifters. This method has been applied to the development of broadband achromatic metalenses [40,44]. Using this method, the material dispersion of MO thin films can be precisely compensated by SiN waveguides in broadband or at multiple wavelengths. Theoretical results showed that the designed integrated MO isolators achieved 30 dB isolation bandwidth of over 240 nm, covering the S-, C-, L-, and U-bands. The experimentally fabricated device based on foundry-fabricated SiN devices achieved maximum 28 dB isolation ratio, ${-}{28}\;{\rm dB}$ cross talk, high 29 nm (3.48 THz) 20-dB isolation bandwidth, and relatively low loss of 2.7 dB across the wavelength range of 1520–1610 nm. By heating the reciprocal phase shifter based on the thermo-optic effect, the experimental 20 dB isolation bandwidth of the device had been increased to 90 nm (11.03 THz). We further demonstrate that this method can generally be applied to design low-loss and dual-band nonreciprocal photonic devices, which hold promise for various applications in broadband optical communication, data communication, and LiDAR systems.
2. RESULTS
A. Device Design
Figure 1(a) shows the sketch of the proposed MZI-type optical isolator/circulator. Two broadband 3 dB directional couplers (DCs) were designed on SiN for light beam splitting and combination [45,46] (see details in Supplement 1). MO/SiN waveguides show nonreciprocal phase shift (NRPS) for the transverse magnetic (TM) mode [39]. The cross section of the fabricated MO/SiN waveguide is shown in the inset of Fig. 1(a). The dispersion compensation structure consists of a pair of SiN waveguides with different widths and lengths in both arms of the MZI.
Fig. 1. Device structure and operation principles. (a) Schematics of an ultra-broadband MO isolator on SiN. (b) Operation principle of the proposed ultra-broadband MO isolator. (c) Desired phase shift difference $\Delta \varphi$ and group delay difference $\Delta {\rm GD}$ of the proposed MO isolator.
Fig. 2. Design of the dispersion compensation structure. (a) Cross-sectional profile and simulated ${{E}_y}$ field distribution of the fundamental TM mode of the MO/SiN waveguide. (b) Cross-sectional profile and simulated ${{E}_y}$ field distribution of the ${{\rm TM}_0}$ mode of the SiN waveguide. (c) Measured nonreciprocal phase shift $\Delta \beta$ of ${{\rm Ce}_{1.4}}{{\rm Y}_{1.6}}{{\rm Fe}_5}{{\rm O}_{12}}$ films as a function of wavelength. (d) Simulated effective index of the ${{\rm TM}_0}$ mode as a function of SiN waveguide widths. (e) Fitted effective refractive index ${{n}_{{\rm eff}}}$ of the ${{\rm TM}_0}$ mode in SiN waveguides changing with waveguide width, at ${\omega _0} = {193.548}\;{\rm THz}$. (f) Fitted $\partial {{ n}_{{\rm eff}}}/\partial \omega$ of ${{\rm TM}_0}$ mode in SiN waveguides changing with waveguide width, at ${\omega _0} = {193.548}\;{\rm TH}$. The insets show the structure and the measurement transmission spectra of the ring isolator.
The transmission phases ${\varphi _1}$ and ${\varphi _2}$ and group delays ${{\rm GD}_1}$ and ${{\rm GD}_2}$ of the fundamental TM (${{\rm TM}_0}$) mode can be calculated in these two waveguides. The phase shift introduced by these two waveguides can be expressed as a Taylor series near the center frequency ${\omega _0}$ [44]:
Subsequently, material and device dispersions were analyzed. We first simulated the dispersion of $\Delta \varphi ({\rm NRPS})$ of the MO/SiN waveguide. The structure of the MO/SiN waveguide cross-section and the corresponding simulated ${{ E}_y}$ field distribution of the fundamental TM (${{\rm TM}_0}$) mode are plotted in Fig. 2(a). The NRPS changes with the wavelength owing to the Faraday rotation dispersion of the CeYIG material [48]. We then characterized the NRPS at different wavelengths using a SiN-integrated MO racetrack ring isolator [25,39]. This is the first measurement of the MO material dispersion using an MO ring isolator on SiN. The NRPS $\Delta \beta$ at different wavelengths can be obtained by measuring the forward and backward transmission spectra of the device under an in-plane applied magnetic field (1000 Gs) [49] through
where $\Delta \lambda$ is the splitting wavelength difference of the same set of resonance peaks in the forward and backward transmission spectra, and ${{L}_{{\rm MO}}}$ refers to the length of the MO/SiN waveguide in the micro-ring isolator. $\Delta \beta$ means nonreciprocal phase shift obtained from the transmission spectra of the micro-ring isolator in Fig. 2(c). FSR means the free spectral range of the micro-ring isolator whose transmission spectra were shown in the inset of Fig. 2(c). The measured NRPS $\Delta \beta$ is shown as a function of wavelength in Fig. 2(c). The results can be fitted linearly in the wavelength range of 1520–1600 nm [28], resulting in a group delay $\partial (\Delta \varphi ({\rm NRPS}))/\partial \omega$ of 3.181 fs at 1550 nm wavelength when the length of the MO/SiN waveguide is designed to be 891.8 µm. This result indicates that good dispersion compensation can be achieved in this wavelength range, even when considering only the first two terms of Eq. (1). By applying the refractive indices of silicon nitride, MO materials, and silicon dioxide (${{\rm SiO}_2}$) as functions of wavelength [42], the corresponding Faraday rotation of CeYIG as a function of wavelength was calculated using COMSOL (see details in Supplement 1). The linear fitting of the Faraday rotation as a function of wavelength can be expressed as ${\rm FR} = {15.549}\lambda - {29181.217}\;({\rm deg/cm})$, where the Faraday rotation at 1550 nm wavelength was then calculated to be ${-}{5080.267}\;{\rm deg/cm}$. This result is comparable to the Faraday rotation measurement results of ${{\rm Ce}_{1.4}}{{\rm Y}_{1.6}}{{\rm Fe}_5}{{\rm O}_{12}}$ thin films [48].Fig. 3. Simulated phase shift and transmission spectrum of the device. (a) Schematic of the designed dispersion compensation structure. (b) Simulated reciprocal and nonreciprocal phase shift as a function of the wavelength of the SiN isolator. (c) Simulated phase shift for the forward ($\Delta \varphi ({\rm RPS}) + \Delta \varphi ({\rm NRPS})$) and backward ($\Delta \varphi ({\rm RPS}) - \Delta \varphi ({\rm NRPS})$) transmission directions. (d) Simulated transmission spectra of the proposed ultra-broadband MO isolator on SiN.
We further simulated the effective index (${{n}_{{\rm eff}}}$) of the fundamental TM (${{\rm TM}_0}$) mode of the SiN waveguides as a function of the waveguide width. Figure 2(b) shows the structure of the SiN waveguide cross section and ${{E}_y}$ field distribution of the ${{\rm TM}_0}$ mode. Figure 2(d) shows the ${{ n}_{{\rm eff}}}$ of the ${{\rm TM}_0}$ mode as a function of the wavelength and SiN waveguide width. Based on the simulation results, ${{ n}_{{\rm eff}}}$ and $\partial {{ n}_{{\rm eff}}}/\partial \omega$ at ${\omega _0} = {193.548}\;{\rm THz}$ (1550 nm) were plotted as functions of the SiN waveguide width and fitted, as shown in Figs. 2(e) and 2(f). Therefore $\Delta \varphi ({\rm RPS})$ and $\partial (\Delta \varphi ({\rm RPS}))/\partial \omega$ at ${\omega _0}$ can be expressed analytically as
For the isolation port to allow broadband isolation, the propagation phase and group delay must satisfy the following conditions:
The width and length of the dispersion-compensated SiN waveguide can be calculated based on Eqs. (5)–(8). As we have only two independent variables, we can set one of the SiN waveguide widths (${{ W}_2}$) to a fixed value of 1 µm. Additionally, we set the length of both SiN waveguides to be ${L}$. Then, the width ${{W}_1}$ and the length ${L}$ of the SiN waveguide is calculated to be 0.5 and 5.53 µm for ${\rm RPS} = \pi /{2}$ and 0.9 and 115.62 µm for ${\rm RPS} = {3}\pi {\rm /2}$, respectively, using Eqs. (7) and (8). To reduce the mode-mismatch-induced scattering loss, identical taper structures were introduced in both arms of the MZI, as shown in Fig. 3(a).
Based on the above results, we simulated $\Delta \varphi ({\rm NRPS})$ and $\Delta \varphi ({\rm RPS})$ of the proposed device, as shown in Fig. 3(b), where the NRPS outside the measurement wavelength in Fig. 2(c) is extrapolated from the linear fitting results of the Faraday rotation. Both curves show almost the same slope in the wavelength range of 1480–1700 nm, as indicated by the gray-shaded region in the figure. Figure 3(c) shows $|\Delta \varphi ({\rm RPS})\;{\pm}\;\Delta \varphi ({\rm NRPS})|$ as a function of the wavelength for both forward ($+$) and backward (−) propagation. The backward propagation phase difference between the two arms always approaches $\pi$ in the wavelength range of 1480–1700 nm. However, the forward phase difference deviates from 0. Fortunately, the forward propagation loss is less sensitive to phase errors. The simulated forward and backward transmission spectra of the device are presented in Fig. 3(d). The device demonstrated a theoretical 30-dB isolation bandwidth over the 240 nm wavelength range of 1440–1680 nm. In the same wavelength range of 1440–1680 nm, the maximum forward propagation loss caused by the non-zero phase difference was 0.8 dB. While a 5% size change of the dispersion compensation SiN waveguide may cause the isolation ratio to decrease from ${\gt}{30}\;{\rm dB}$ to about 19 dB, the footprint of the SiN integrated magneto-optical isolator is about ${1.3}\;{\rm mm} \times {0.3}\;{\rm mm}$, which can be further optimized by increasing the Faraday rotation of the MO materials.
B. Device Fabrication and Characterization
The proposed device was fabricated based on 400 nm SiN platform in a silicon photonics foundry, followed by MO film deposition [39]. 50 nm YIG and 130 nm CeYIG thin films with Faraday rotation of ${-}{5000}\;{\rm deg/cm}$ at 1550 nm wavelength were deposited on SiN waveguides. The optical absorption loss of the CeYIG films was tested to be around 120 dB/cm. As a result, the figure of merit of the CeYIG reached 41.67 deg/dB, which has potential for further improvement for the loss and footprint optimization of the integrated MO devices. The device was characterized on a polarization maintaining, fiber-butt-coupled system, as detailed in [39]. An in-plane magnetic field of 1000 Gs was applied perpendicular to the light propagation direction. The magnet can be further integrated on silicon by deposition of soft magnetic materials such as NiFe films. Figure 4(a) shows the transmission spectra of the ultra-broadband SiN integrated MO isolator and circulator, together with the transmission spectra of a reference SiN straight waveguide on the same chip. At 1588 nm, the measured maximum isolation ratio and crosstalk reached 28 dB. The insertion loss was 2.7 dB. The 20-dB isolation bandwidth of this device was 29 nm, ranging from 1565 to 1594 nm wavelength. The 10-dB isolation bandwidth of the device covered the entire C-band and extended to the S- and L-bands and was restricted by the limited tunable wavelength range (1520–1610 nm) of the laser source. Across the entire 10-dB isolation bandwidth, the device showed insertion loss of ${2.7}\;{\pm}\;{0.1}\;{\rm dB}$. In theoretical design, the output powers from the two ports of the MZI should be equal to each other at the center wavelength of 1550 nm before the growth of MO thin films, with reciprocal phase shift designed to be $\pi /{2}$. However, due to the fabrication error of the SiN waveguides in two arms, a difference of about 2 dB has been generated between the output powers of the two ports at the center wavelength. The simulation results show that the widths of the pair of SiN waveguides providing reciprocal phase shift change from 500 and 1000 nm to about 450 and 980 nm due to the fabrication error, respectively. We further calculated the reciprocal phase shift corresponding to the transmission spectra. The reciprocal phase shift of the fabricated device deviated by about 0.22 rad from the designed value. As a result, after deposition of 50 nm YIG and 130 nm CeYIG thin films on the MZI structure analyzed above, the corresponding theoretical transmission spectra of the device can be simulated considering the limitation of the beam splitting ratio of about 0.48:0.52. Obviously, when the discussed fabrication error occurs, the proposed MO isolator showed smaller bandwidth. The theoretical 20 dB isolation bandwidth was now less than 40 nm (1540–1580 nm wavelength), consistent with the experimental result, as shown in Fig. 4(a). There is about 10 nm drift between the minima of the theoretical and experimental transmission curves. The drift of the wavelength corresponding to the minimum transmittance is mainly caused by the phase deviation of the device due to the fabrication error of the waveguide size and CeYIG film thickness.
Fig. 4. Experiment results of the device. (a) Measured transmission spectra of the ultra-broadband SiN MO isolators compared with the theoretical one. (b) Measured transmission spectra of the ultra-broadband SiN MO isolator and circulator under reciprocal phase shifter heating based on the thermo-optic effect. The inset shows the isolation ratio of the device within wavelength from 1520 to 1610 nm.
Table 1. Comparison of MO Isolator Device Performances near the C-Band in Terms of the Isolation Bandwidth
To fabricate TE mode silicon integrated nonreciprocal MO devices, we have demonstrated in previous work that the TM mode devices could work under the TE polarization by adding polarization rotators at both ends of the devices [39]. In this case, RPS and NRPS in the MZI structure can still be designed under the TM polarization, which is consistent with the structure proposed in this work. The insertion loss of the polarization rotator is below 0.1 dB in the design and was measured to be 0.35 dB in the experiment. We carried out theoretical simulation on applying these rotators to the isolator device in this work, and the device shows ${\gt}{35}\;{\rm dB}$ theoretical isolation and 0.15 dB insertion loss in the wavelength range from 1500 to 1600 nm.
3. DISCUSSION
A key advantage of the proposed method is that the device dimensions can be determined analytically using Eqs. (5) and (6). Furthermore, low-insertion loss and multiband nonreciprocal photonic devices can be designed using this method. For instance, to mitigate the forward transmission loss, in Fig. 3(d), caused by phase deviation from 0 rad, we can decrease the group delay of $\Delta \varphi ({\rm RPS})$ to slow down the change of $\Delta \varphi ({\rm RPS}) + \Delta \varphi ({\rm NRPS})$ with wavelength. Specifically, we reduce the group delay of $\Delta \varphi ({\rm RPS})$ to 2.5 fs from 3.181 fs so that the forward phase difference is close to 0 rad (see Supplement 1, Section 4). Figure 5(a) depicts the designed phase difference between the two arms of the device for the forward ($+$) and backward (−) propagation directions as a function of wavelength. Figure 5(b) shows the corresponding transmission spectra. The phase error-induced loss of the device is significantly reduced from 0.8 dB [Fig. 3(d)] to less than 0.3 dB over a wavelength range from 1440 to 1680 nm. Furthermore, the device can maintain a broadband optical isolation of over 20 dB in this wavelength range.
Fig. 5. Device optimization employing the proposed dispersion compensation method. Simulated phase shift of the forward ($\Delta \varphi ({\rm RPS}) + \Delta \varphi ({\rm NRPS})$) and backward ($\Delta \varphi ({\rm RPS}) - \Delta \varphi ({\rm NRPS})$) transmission directions for the (a) loss optimization design and (c) dual isolation band design. Corresponding transmission spectra of the (b) loss optimized device and (d) dual-isolation band device.
The device can also be designed as a dual-isolation-band optical isolator by employing the proposed dispersion compensation method. Designing a multiwavelength MZI device presents a formidable challenge owing to the almost linear variation in the transmission phase of the waveguide changing with the waveguide size and wavelength. Nevertheless, our method allows the introduction of additional parameters into the dispersion compensation structure to concurrently optimize the device characteristics at various wavelengths. To design a dual band optical isolator operating at 1310 and 1550 nm, we first reduced the length of the MO/SiN waveguide by setting $\Delta \varphi ({\rm NRPS})$ to be $\pi /{2}$ at 1310 nm. We then introduced four parameters, ${{W}_1}$, ${{W}_2}$, ${{L}_1}$, and ${{L}_2}$, to the phase-compensation structure shown in Fig. 3(a) to allow phase difference and dispersion compensation at multiple wavelengths (see details in Supplement 1, Section 5). Figure 5(c) presents the designed phase difference between the two arms in the forward and backward directions, and Fig. 5(d) displays the corresponding transmission spectra. The isolation bandwidth of the device was adjusted to cover both the O- and C-bands. The theoretical 20-dB isolation bandwidth covers the wavelength range of 1260–1680 nm. Nonetheless, owing to the large forward transmission phase mismatch around the 1550 nm wavelength, the corresponding forward transmission loss reaches nearly 2 dB, necessitating unconventional phase shifter structures with nonlinear changes of transmission phase with structure parameters for further optimizations.
As for the generation of the on-chip magnetic field, we proposed an on-chip electromagnet structure. In the structure shown in Fig. 6(a), two gold wire electrodes are placed on both sides of the MO/SiN waveguide. Soft magnetic materials such as NiFe can be patterned on Au. When introducing electric current into the gold wires, the generated magnetic field magnetizes the patterned NiFe films, as shown in Fig. 6(b). The magnetic field generated by NiFe can provide a local magnetic field to saturate the garnet films, as shown in Fig. 6(c), realizing an on-chip electromagnet. Considering the saturation magnetization of 10,000 Gs in the NiFe films [51], the simulated horizontal magnetic field in the Ce:YIG films reaches 240 Oe, which is enough to saturate the polycrystalline Ce:YIG films. Further study of the electromagnet is under investigation.
Fig. 6. (a) Top view of the proposed SiN integrated electromagnet. (b) Cross-sectional structure of the SiN integrated electromagnet and the schematic diagram of the magnetic field generated by applying electric current in the gold wires. (c) Schematic diagram of the magnetic field generated by magnetized NiFe films.
The reflection and scattering loss of the MO/SiN waveguide junction can be theoretically minimized by tapering structures. In our device, we introduced a linear taper structure to the device. We opened the silicon dioxide window into the taper structure so that after the deposition of MO films, the effective refractive index contrast varies linearly with the light transmission distance. In this way, the theoretical loss and reflections caused by the interface could be optimized to ${\lt}{0.01}\;{\rm dB}$ and ${\lt}-\! {40}\;{\rm dB}$, respectively. Indeed, the realistic optical reflection of the adiabatic taper may be up to ${-}{20}\;{\rm dB}$ or higher due to fabrication errors as discussed in [52], thus disrupting the stable operation of the laser [53–55]. To solve this problem, a longer adiabatic taper of 100 µm may result in lower optical reflection. Besides, vertical taper structures fabricated by grayscale lithography or vertical directional couplers can also effectively reduce the optical reflections. For instance, a vertical taper structure fabricated by grayscale lithography resulted in a measured ${-}{34}\;{\rm dB}$ refection at high index contract waveguide junctions [56–58].
In summary, we report ultra-broadband SiN integrated MO isolators and circulators based on dispersion compensation. The dispersion-compensation waveguide geometries can be calculated analytically by designing the propagation phase and group delay of the MO and SiN waveguides. High performance, ultra-broadband isolators with 27 dB maximum isolation ratio, 2.9 dB insertion loss, and 90 nm (11.03 THz) 20-dB isolation bandwidth are experimentally demonstrated based on 400 nm SiN devices, surpassing the bandwidth of previously reported devices by one order of magnitude. Our study provides a general method for designing broadband MO devices on silicon, paving the way for applications in broadband optical communication, data communication, and LiDAR systems.
4. MATERIALS AND METHODS
A. Device Fabrication
The devices under study were initially fabricated in a silicon photonics foundry. To fabricate the SiN waveguide, a layer of 400 nm SiN films was first deposited on an ${{\rm SiO}_2}$ bottom cladding using low-pressure chemical vapor deposition (LPCVD) technique, followed by reactive ion etching (RIE). After an ${{\rm SiO}_2}$ upper cladding was deposited, chemical mechanical polishing (CMP) was employed to planarize the top ${{\rm SiO}_2}$ cladding. This was followed by RIE to expose the SiN waveguide core in the MO waveguide section. At this point, the fabrication of SiN waveguides has been done. The next step involved the deposition of YIG and CeYIG thin films of 50 and 150 nm, respectively, by pulsed laser deposition [39].
B. Device Characterization
The devices were characterized using a polarization-maintaining fiber-butt-coupled system. An external in-plane magnetic field of 1000 Oe was applied perpendicular to the propagation light in the MO/SiN waveguides to saturate the garnet films. A Keysight 81960A tunable laser was employed to provide a continuous wave spectrum with wavelengths ranging from 1520 to 1610 nm. The input optical power was 8 dBm. The light was coupled into the device under test by means of butt coupling through a lens-tipped polarization-maintaining fiber. The output signal was then coupled into another fiber connected to an optical power sensor (Agilent 81636 B). The wavelength detection interval was set to 2 pm. A free-space polarization control bench was used to obtain TM-polarized light. During the backward transmission test, the direction of the applied magnetic field remained unchanged, and the connection status of the input and output fibers with the laser and sensor was switched.
C. Broadband Optical Beam Splitter
Broadband optical beam splitting was achieved using a SiN broadband 3 dB directional coupler for TM polarization, employing the mode evolution principle [50]. The thickness of the SiN waveguide was fixed at 400 nm, and the space between the two coupled SiN waveguides was maintained at 450 nm. Within a 500 µm long adiabatic taper, the width of one SiN waveguide slowly changed from 1300 to 1000 nm, while the width of another SiN waveguide slowly changed from 700 to 1000 nm. The structure was simulated using a finite-difference time-domain (FDTD) method.
D. Characterization of the Faraday Rotation
COMSOL software was employed to simulate the wavelength dependence of the Faraday rotation of CeYIG. We first obtained the off-diagonal component $\gamma$ of the permittivity tensor of CeYIG by simulation according to the measured NRPS, based on the perturbation theory [39]. Using the obtained $\gamma$, we calculated the Faraday rotation ${\theta _F}$ of CeYIG at each wavelength [33]. The Faraday rotation of the CeYIG thin films as a function of the wavelength was determined by repeating the aforementioned simulations and calculations.
Funding
Ministry of Science and Technology of the People’s Republic of China (2021YFB2801600); National Natural Science Foundation of China (51972044, 52021001, 52102357, U22A20148); Science and Technology Department of Sichuan Province (23ZYZYTS0043, 99203070).
Acknowledgment
W. Y. and Z. W. contributed equally to this work by jointly searching the data, performing simulations and experiments, and writing the manuscript. Y. Y., D. W., Z. Z., and X. S. contributed to the discussion. J. Q. and L. B. conceived the study and supervised the project. All the authors contributed to the final version of this manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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