Driven by the rapid development of data communication and optical communication, multi-port photonic devices such as arrayed waveguide gratings, optical switch matrices, and photonic neural networks have been developed [1–5]. As a key component in photonic systems, nonreciprocal photonic devices introduce key functionalities to block the reflected light, or re-route backward transmission signal to a different channel compared to the input [6,7]. However, most reported silicon integrated nonreciprocal photonic devices to date were unit devices. Typical device structures include Mach–Zehnder interferometers (MZIs) [7–10], multi-mode interferometers (MMIs) [11,12], and micro-ring resonators [13–15] with a maximum of only four ports, limiting the device functionality to only optical isolation and circulation.

Multi-port silicon integrated nonreciprocal optical devices allow different scattering matrices between forward and backward propagation directions, which may add another degree of freedom for optical data transmission. For bidirectional optical communication or sensing between multi-ports, nonreciprocal optical routing is usually achieved by adding bulk optical circulators in each port, which leads to bulky and complex systems [1–5,10–18]. Therefore, achieving nonreciprocal optical transmission between multi-ports on-chip can greatly simplify the system and introduce design flexibility. So far, the only reported multi-port magneto-optical device on silicon was based on cascaded magneto-optical (MO) micro-ring resonators [13], demonstrating optical circulation functionality between six ports. However, the device showed a limited operation bandwidth and similar functionality as an optical circulator. Multi-port nonreciprocal optical devices with larger bandwidths and alternative functionalities are yet to be explored.

In this paper, we report the development of a multi-port nonreciprocal optical router via a magneto-optical phased array (OPA) on silicon (Si) [19]. We experimentally demonstrated silicon integrated multi-port nonreciprocal optical transmission in an optical phased array structure based on the nonreciprocal phase shift (NRPS) effect [20–25]. On-demand nonreciprocal scattering matrices between forward and backward propagation light are achieved by deposition of magneto-optical thin films on silicon waveguide arrays, introducing nonreciprocal phase profiles between forward and backward propagation light. We demonstrated functionalities such as optical circulation and nonreciprocal optical routing between different ports. Experimentally, we demonstrate optical isolation ratio up to 16 dB and minimum crosstalk of −18dB at 1551 nm wavelength in a 5×5 nonreciprocal optical router based on an MO phased array.

Figure 1(a) shows the sketch of the nonreciprocal magneto-optical phased array on 220 nm silicon on insulator (SOI) platforms. The device consists of several input and output ports, two slab Si waveguides connecting to the input and output ports, a phase element array based on Si waveguides providing reciprocal phase shift (RPS), and an MO/Si waveguide array providing nonreciprocal phase shift. The operation of this nonreciprocal optical routing device fundamentally relies on beam deflection modulation via an optical phased array structure [19]. Transverse magnetic (TM) polarized light enters the phase element array after passing through the input Si slab waveguide. It then propagates through the phase element array and the MO/Si waveguide array. After accumulating phase shifts consisting of RPS and NRPS in each waveguide in the array, the input light forms a phase gradient at the output of the waveguide array, so that it can be refocused into the corresponding output port [22,24]. However, when light is reversely incident at the output port, the NRPS accumulated in the MO/Si waveguide array is different from that of the forward direction, so that the backward transmission light can be focused to different ports from the original input port. This mechanism makes it possible to implement on-chip nonreciprocal optical routing via an MO phased array.

Let us consider the accumulated phase shift when light propagates from the input port Ij to the output port Ok through the ith waveguide in the waveguide array, as shown in Fig. 1(a). The total phase shift can be written as φi(fwd)=φS(j,i)+φSOI(i)+φMO,i++φS(k,i),(1)where φS(j,i) is the phase shift when propagating from input port Ij to the ith waveguide in the slab waveguide WG1, φSOI(i) is the reciprocal phase shift when propagating through the ith silicon waveguide, φMO,i+ is the nonreciprocal phase shift when propagating through the ith MO/Si waveguide, and φS(k,i) is the phase shift when propagating from the ith waveguide to the output port Ok in the slab waveguide WG2. Constructive interference and high transmittance will be observed at the Ok port when φi between adjacent waveguides satisfies 2mπ (m=0,1,2…) phase difference at the designed wavelength [22]. For backward propagation, due to the nonreciprocal nature of the MO/Si waveguide, the phase shift is φi(bwd)=φS(j,i)+φSOI(i)+φMO,i−+φS(k,i),(2)where φMO,i− is the backward propagation phase shift of the MO waveguide, which differs from φMO,i+ due to the nonreciprocal phase shift. In this case, different phase profiles can be obtained by designing different lengths of the MO/Si arrayed waveguides. Therefore, on-demand nonreciprocal transmission between forward and backward propagation can be achieved.

We can further express each of the phase terms as follows. φS(j,i) and φS(k,i) can be expressed as φS(j,i)=ωcneffSlab(yi−yIj)2+f12,(3)φS(k,i)=ωcneffSlab(yi−yOk)2+f22,(4)where ω is the frequency, c is the speed of light in vacuum, and neffSlab is the effective index of the TM mode in the slab Si waveguides. yi−yIj and yi−yOk refer to the difference in the distance from the jth input port and kth output port to the ith arrayed waveguide along the y direction. f1 and f2 are the lengths of the input and output slab waveguides. Figure 1(b) shows the zoom-in sketch of the phase element array, which is used to provide the required reciprocal phase shift difference between waveguides in the array. The phase element consists of a wider waveguide (w1) with length L1,i and effective index neff1 for the fundamental TM mode. The rest of the silicon waveguides consist of a narrower waveguide (w2) with length L2,i and effective index neff2 for the fundamental TM mode. Thus, adjusting the wider Si waveguide’s length within a fixed total length introduces different reciprocal phase shifts. To avoid misalignment issues when connecting Si waveguides with different lengths to the same slab Si waveguide, we adopt the phase design with uniform waveguide lengths. The transmission phase of the ith silicon waveguide φSOI(i) and nonreciprocal phase shift Δβ can be expressed as φSOI(i)=ωcneff1L1,i+ωcneff2L2,i,(5)Δβ=2βωε0N∬γn04Hy∂zHydxdy,(6)where Δβ and β are the NRPS and propagation constant of the fundamental TM mode in the MO/Si waveguide, respectively. ω is the angular frequency, γ is the off diagonal component of the permittivity tensor of the MO material, ε0 is the vacuum dielectric constant, N is the power flux along x direction, n0 is the refractive index of the magneto-optical material, and Hy is the magnetic field along y direction. The wider waveguide within the phase element is placed directly adjacent to the edge of the slab Si waveguide primarily to minimize the junction loss during light transmission from the slab waveguide to the waveguide array. Figure 1(d) shows the cross section of the MO/Si waveguide. The silicon dioxide (SiO2) upper cladding in the MO/Si waveguide region was etched to expose the upper surface of the Si waveguide. This structure allowed Ce:YIG/YIG thin films to be directly deposited on top of Si waveguides, providing NRPS for the TM polarized light [26]. The thickness of the MO films is selected considering the figure of merit (FoM) of the MO/Si waveguide, as mentioned in our previous work [8]. We control the Ce:YIG film thickness at 150 nm in the experiments. The transmission phase of MO/Si waveguides φMO,i± can be expressed as φMO,i±=±ΔβLMO,i+ωcneff(MO)LMO,i,(7)where neff(MO) is the TM0 mode effective index of the MO/Si waveguide under zero applied magnetic field. LMO,i is the length of the ith MO/Si waveguide. The length of the MO/Si waveguide LMO,i can be calculated by considering forward and backward transmission phase difference φMO,i+−φMO,i− allowing forward and backward propagation light to be focused at different ports. The length of each MO/Si waveguide can be expressed as LMO,i=φMO,i+−φMO,i−Δβ.(8)

We simulated the transmission field profile of the device based on the above equations, as shown in Figs. 1(e) and 1(f). On-demand nonreciprocal optical routing can be achieved between different ports. For instance, an optical circulator can be realized as shown in Fig. 1(e). In this case, a phase gradient is introduced by the NRPS in the MO/Si waveguides for the backward incidence. The device operates as an optical circulator between the designed ports. It is possible to design different phase profiles of the waveguides so that more than one focusing point for forward and backward directions can be achieved. In this case, we can obtain multi-port nonreciprocal optical routing as shown in Fig. 1(f). The forward transmission light is focused to three ports, whereas the backward propagating light from one of the forward output ports is focused to two different ports. Therefore, nonreciprocal routing is achieved.

The device was designed at 1550 nm wavelength. We first designed the slab waveguide regions, as shown in the simplified device structure in Fig. 2(a). The slab waveguide lengths f1, f2, the number of waveguides, and the port spacing D influence the insertion loss and isolation ratio of the device. The forward and backward theoretical transmission phase gradients for the structure analysis are depicted in Fig. 2(b), corresponding to the case of Fig. 1(e) when the focal lengths f1 and f2 are initially set to be 200 μm. The forward (backward) transmission phase gradients indicate the phase distribution before focusing in the slab waveguide WG2 (WG1), consisting of the transmission phase accumulated in the WG1 (WG2) and the arrayed waveguides.

The focusing design requires that each of the arrayed waveguide transmission paths shares the same phase shift from the input to the output [22], which determines the desired forward phase gradients. Before the employment of NRPS, the phase gradients of the device in the backward transmission direction, which is shown as the initial backward phase gradients in Fig. 2(b), can be derived utilizing the Lorentz reciprocity theorem [27]. The relative distribution of the initial backward phase gradients is the same as the forward one, while it is increased uniformly in terms of the absolute value for the following uniform NRPS distribution design (NRPS=0 in the center waveguide), which does not affect the light focusing and transmission states. Then the desired backward phase gradients for output focusing, which are calculated using Eqs. (3) and (4), can be realized by introducing NRPS to the initial backward phase gradients. The introduced NRPS φMO,i+−φMO,i− in each arrayed waveguide is also shown in Fig. 2(b), by computing the disparity between the desired backward transmission phase gradients and the initial backward transmission phase gradients. The length of each MO/Si waveguide can be calculated accordingly using Eq. (8). As shown in Fig. 2(b), the closer to the edge of the waveguide array, the larger the required NRPS. The largest required NRPS in the waveguide array is 3.26 rad, corresponding to the MO/Si waveguide length of 745.1 μm. Figure 2(c) shows the forward focusing efficiency, defined as the transmission efficiency of light traveling from the slab waveguide WG2 to the target output port, as a function of the number of the arrayed waveguides N and the slab waveguide length f2. With increasing N from 6 to 17, the focusing efficiency monotonously increases from 60% to 85%. The focusing efficiency also changes with the length of the output slab Si waveguide f2. A larger f2 requires more waveguides to cover the phase gradient range of 2π, while a smaller f2 leads to a sparser sampling of the phases with fixed waveguide spacing. The optimal f2 is in the range of 50–100 μm, leading to the focusing efficiency of 85%. We fixed f2=50μm in our device design.

For backward propagation, the waveguide spacing D and Si slab waveguide length f1 influence the isolation ratio and insertion loss. The isolation ratio is defined as the maximum transmission power difference between the two ports in the forward and backward transmission directions. Figures 3(a) and 3(c) show the simulated isolation ratio and insertion loss as a function of D and number of arrayed waveguides N for the case of Fig. 1(e). When the length of the input Si slab waveguide f1 is fixed at 200 μm, the isolation ratio increases with the number of arrayed waveguides and spacing D between the backward output ports, as plotted in Fig. 3(a). As the focusing efficiency increases with the number of waveguides, larger waveguide spacing D leads to weaker crosstalk from adjacent waveguides. However, larger D requires a larger nonreciprocal phase gradient to allow efficient backward light focusing, which leads to longer MO/Si waveguides and larger insertion loss, as shown in Fig. 3(c). The theoretical insertion loss was obtained by calculating the focusing efficiency and total transmission loss in each arrayed waveguide including the Si and MO/Si waveguides. Under the same D=6μm as shown in Figs. 3(b) and 3(d), smaller f1 also requires a larger transmission phase difference between the forward and backward transmission directions, which results in a sharp increase in MO/Si waveguide loss. At the same time, the limited number of arrayed waveguides could provide a larger phase gradient range for smaller f1 in the backward transmission direction, which improves the isolation ratio to a certain extent. Considering the trade-off between the isolation ratio and insertion loss, we chose D=6μm, f1=200μm, N=13, which leads to an isolation ratio of 21 dB and insertion loss of 3 dB. The insertion loss includes the focusing loss, junction loss, and waveguide loss, where the waveguide loss consists of the transmission loss in the Si and MO/Si waveguides.

Next, we designed the waveguide arrays. The lengths of Si and MO/Si waveguides are determined by the forward and backward propagation phase profiles. For example, the case of Fig. 1(e) requires forward and backward phase profiles as shown in Fig. 2(b), including the transmission phase accumulated in the input slab waveguide and the arrayed waveguides. For the Si phase element arrays, we fixed the waveguide width at 1 μm and 500 nm. The 1 μm wide Si waveguide introduces reciprocal phase shift of 8.538 rad/μm. For MO/Si waveguides, the waveguide width is fixed at 500 nm, which introduces nonreciprocal phase shift Δβ of 4.375 rad/mm. In this case, the length of each arrayed phase element was fixed to be 6 μm, consisting of 500 nm and 1 μm Si waveguide sections. The length of the 1 μm wide Si waveguide can be adjusted from 0 to 6 μm. Phase shifts ranging from 0 to 2π can be achieved by changing the length ratio of wide and narrow waveguides in the phase element. The waveguide gap was designed at 1.5 μm to avoid strong mode coupling between Si waveguides. After passing through the 6-μm-long phase elements, the spacing between the Si waveguides was rapidly expanded to 5 μm to eliminate inter-waveguide crosstalk. The MO/Si waveguide array consists of MO/Si waveguides with different lengths, providing NRPS for the TM polarized light with MO thin films deposited on the top of Si channel waveguides. The lengths of slab Si waveguides f1 and f2 are independently determined, resulting in asymmetric input and output slab waveguides. It is the optimized design for all the following devices, with balanced factors being essential to achieve the desired optical performance.

Figure 4 shows the illustration of nonreciprocal optical routing based on a 5×5 nonreciprocal router. In Fig. 4(a), the device is designed to allow the forward transmission as I1 to O2, whereas the backward transmission as O2 to I3, i.e., similar to a three-port circulator. Figure 4(b) shows the simulated transmission spectra during the process of light beam focusing. A theoretical isolation ratio of 21 dB and a crosstalk of −21dB were observed at 1550 nm wavelength, with total insertion loss of 3 dB, among which the focusing loss was 0.7 dB as shown in the simulation results in Fig. 4(b). The theoretical isolation ratio was mainly limited by the small distance D between the backward output ports. The backward focusing loss was slightly larger than the forward one because the phase gradient is no longer symmetrical compared to forward propagation, as shown in Fig. 3(b). When the wavelength deviated from the center wavelength 1550 nm, changes of the propagation constant in the Si and MO/Si waveguides led to the offset of the phase gradient, which resulted in the deterioration of the focusing efficiency and the isolation ratio. The connections between other gray ports in the 5×5 device are not designed, resulting in inefficiency. If an electrode is used to magnetize the MO materials, and heat the Si waveguide in the future, reconfigurable nonreciprocal optical transmission can be achieved [28,29].

More complex nonreciprocal optical routing can be realized by dividing the waveguide array into different regions to focus the incident light to different ports. Figure 4(c) shows an example. Light entering from I1 is transmitted through both O2 and O3 for the forward, whereas the backward incident light from O3 exits at I4. This is realized by splitting the arrayed waveguides into two parts for two-port focusing in the forward transmission direction, whereas for backward propagation, the phase gradients are changed through NRPS for another port focusing, as shown in Fig. 4(d). The phase gradients in the forward transmission direction exhibit a symmetrical design aimed at focusing the transmission light to two distinct outputs, separately. The backward phase gradients are tailored for single-port focusing, mirroring the configuration depicted in Fig. 2(b). The largest required NRPS in the waveguide array reaches 3.54 rad, corresponding to the MO/Si waveguide length of 810.9 μm. Theoretical transmission spectra of the device are shown in Fig. 4(e). We observed a theoretical isolation ratio of 18 dB between I1 and O3, and crosstalk of −21dB between I1 and O4 at 1550 nm wavelength, with focusing loss of 0.9 dB and 1.2 dB for light transmission from O3 to I4 and from I1 to O2/O3, respectively. The relatively higher focusing loss for forward transmission (I1→O2/O3) was attributed to the reduction in the number of arrayed waveguides corresponding to each focusing point after the arrayed waveguide splitting. The theoretical insertion loss of the device could be then obtained as 3.5 dB.

More complicated nonreciprocal transmission can be realized as shown in Fig. 5(a). When the forward propagating light is incident from I3, it transmits to O1, O3, and O5. When the light is backward incident from O3, it transmits to I2 and I4. The phase gradients of the waveguide array for the forward and backward transmission directions for the case of Fig. 1(f) are shown in Fig. 5(b). In the corresponding transmission direction, the arrayed waveguides are divided into several parts according to the number of target ports to be focused. Then the forward and backward transmission phases in each part of the arrayed waveguides can be separately calculated as shown in Fig. 5(b). Theoretical transmission spectra of the device with the incident light from I3 and O3 are shown in Figs. 5(c) and 5(d). A minimum crosstalk of −21dB between O3 and O4 could be achieved. The theoretical isolation ratio reached 21 dB between I3 and O3 at 1550 nm wavelength. The focusing loss from I3 to O3 was about 1.5 dB because only half of the arrayed waveguides were designed for the light transmitting to O3. The focusing loss from O3 to I2/I4 was about 1.2 dB, which was similar to the situation shown in Fig. 4(d). Considering the corresponding focusing loss, the theoretical insertion loss of the device was 3.8 dB. It is worth noting that the focusing performance shows minimal degradation from the loss difference in the arrayed waveguides. The extra focusing loss from waveguide loss inhomogeneity is under 0.1 dB in the simulation when the number of arrayed waveguides N>9.

The proposed devices were fabricated in a silicon photonics foundry followed by MO thin film deposition. The Si waveguide was fabricated on a 220 nm silicon on insulator (SOI) wafer by reactive ion etching (RIE). The SiO2 top cladding was then etched to expose the silicon waveguide core. Yttrium iron garnet (YIG) and cerium substituted yttrium iron garnet (Ce:YIG) thin films were deposited to form the MO/Si waveguides. Details of the fabrication process can be found in our previous publication [8]. The transmission spectra were then measured under a 1000 Oe in-plane magnetic field applied on a polarization maintaining, fiber-butt-coupled system as detailed in Ref. [8].

An optical microscope image of the fabricated three-port optical circulator is shown in Fig. 6(a). The inset shows the scanning electron microscope (SEM) image of the cross-sectional structure of the MO/Si waveguide, which is consistent with Fig. 1(d). Figure 6(b) shows the measured transmission spectra of the three-port optical circulator. The device achieved 19 dB isolation ratio between port 1 and port 2 with −19dB crosstalk between port 1 and port 3 at 1552.3 nm wavelength. The device insertion loss was 12 dB, which was mainly attributed to the junction loss between the Si and MO/Si waveguides (3.5 dB), Si and MO/Si waveguide loss (2.5 dB), and focusing loss (6 dB) due to the fabrication causing non-ideal phase gradients. Figure 6(c) shows the optical microscope image of the fabricated four-port nonreciprocal optical router for the case of Fig. 4(c). The corresponding measured transmission spectra of the device are shown in Fig. 6(d). The forward optical transmission power from port 1 to ports 2 and 3 was equally divided at 1552.7 nm. At 1549.9 nm wavelength, the device showed a maximum isolation ratio of 12 dB between port 1 and port 3 with a minimum crosstalk of about −16dB between port 4 and port 1. The minimum insertion loss of the device at 1552.5 nm was 15 dB, mainly attributed to the junction loss between the Si and MO/Si waveguides (3.5 dB), Si and MO/Si waveguide loss (3 dB), and focusing loss (8.5 dB) due to the fabrication causing non-ideal phase gradients. The insertion loss of the device could be further optimized through the taper designs at the junctions between slab Si waveguides and arrayed Si waveguides as well as precise phase control based on the thermo-optic effects.

Finally, the optical microscope image of a 5×5 nonreciprocal optical router for the case of Fig. 1(f) is shown in Fig. 7(a). The measured transmission spectra of the device are shown in Figs. 7(b) and 7(c). An isolation ratio up to 16 dB between I3 and O3 with a minimum crosstalk of −18dB between I1 and I2 was achieved at 1551 nm wavelength.

The high insertion loss of fabricated devices mainly includes the junction loss, MO/Si waveguide loss, and focusing loss due to phase error. The junction loss and MO/Si waveguide loss can be further minimized by employing tapered structures and optimized MO thin films [14]. In addition, the growth quality of the YIG seed layer can be improved by systematically optimizing the growth substrate temperature and oxygen partial pressure [30]. This allows for a thinner YIG layer, enabling a thicker Ce:YIG layer. Consequently, the MO/Si waveguide FoM is boosted, and the device loss is further lowered. The phase offset due to fabrication error also seriously affects the focusing efficiency in experiments because of the long transmission length of the phased waveguide array in the device. When the fabricated width of the silicon waveguide changed 5% from the designed value of 500 nm to 475 nm in the case of Fig. 6(a), the phase shift offset due to the fabrication error reached nearly 12 rad. Compared with the theoretical ideal focusing efficiency of 85%, the focusing efficiency considering the fabrication error drops to about 25%. The high focusing loss can be mitigated by shortening the silicon waveguide length with push-pull magnetic field application [10] and using thermo-optic heating to compensate for the phase errors [26]. The three nonreciprocal optical routing examples in the manuscript are independent, each realized through individually designed phase gradients. While currently operating in fixed states, reconfiguring nonreciprocal transmission states within the same device structure is feasible via phase modulation on Si and MO/Si waveguides [31,32].

In summary, we experimentally demonstrated a silicon integrated magneto-optical phased array at near infrared optical communication wavelengths. On-demand multi-port nonreciprocal optical routing has been demonstrated in a 5×5 magneto-optical nonreciprocal router based on SOI waveguides. The fabricated device showed −18dB crosstalk and 16 dB isolation ratio at 1551 nm wavelength. Such magneto-optical phased array demonstrated in this work allows different scattering matrices for forward and backward incidence, adding a new degree of freedom for optical communication and data communication applications.

The nonreciprocal phase shift of MO/Si waveguides is simulated via the finite element method (FEM). The silicon waveguide’s cross section is 500nm×220nm. The thicknesses of the YIG seed layer and Ce:YIG films are 50 nm and 150 nm, respectively. At 1550 nm wavelength, the refractive indices of silicon, silicon oxide, and MO materials are set as 3.48, 1.45, and 2.25. The optical transmission simulation of the device uses the finite difference time domain (FDTD) method. Focusing efficiency in forward and backward transmission directions is obtained by setting the corresponding input light intensity and phase shift for each arrayed waveguide.