1. Introduction

Optical nonreciprocity enables isolation and circulation, which prevent undesired light routing to mitigate back-reflections and interference between components. However, Lorentz reciprocity cannot be broken in linear waveguides [1], which accommodate a bidirectional flow of light. This presents a crucial limitation for Silicon Photonic (SiP) circuits, which leverage the commercially available CMOS process flow to enable low-cost, large-scale deployment. Nevertheless, integrated optical isolators have been demonstrated by inducing non-reciprocal (NR) behaviour via magneto-optic or acousto-optic [2] interactions. Acousto-optic interactions have employed silicon nitride (SiN) [3] or lithium niobate (LN) [4] racetrack resonators. However, these designs have a narrow bandwidth [5] and require CMOS-incompatible fabrication processes. Alternatively, magneto-optic (MO) interactions evoke NR behaviour via either polarization mode conversion (PMC) [6] or a NR phase shift (NRPS) [7]. Relative to the direction of propagation, a perpendicular magnetic field induces NRPS between counter-propagating modes in a racetrack whereas a parallel magnetic field induces Faraday rotation of the modes in a waveguide which manifests as PMC. Faraday rotation has been the most commonly used approach because of its low insertion loss (IL), high isolation ratio, and broad optical bandwidth. It is limited by birefringence due to the asymmetry of the waveguide cross-section, which can be mitigated by quasi-phase matching (QPM) the modes [8,9]. The strength of the MO interaction depends on the Verdet constant, V, of the host material. For reference, V is 12-17°/(T-cm) for single crystalline Si [10] or up to 103°/(T-cm) for n-type Si [11] at a wavelength of 1550 nm. Hence, achieving an appreciable rotation would require either a long interaction length [12,13] or a strong applied magnetic field for it to be comparable to -1263°/cm for Ce-doped yttrium iron garnet (Ce:YIG), 100°/cm for YIG on Si [14], or -5900°/cm for Ce:YIG on SiN [15] at saturation magnetization. These options utilize a garnet layer deposited on the waveguide which induces an MO interaction with the evanescent field of the optical mode [16]. As a result, operation is limited to the transverse magnetic (TM) mode even though photonic circuits typically use the transverse electric (TE) mode [17]. It is possible to switch between modes by using a reciprocal PMC [17,18] albeit with additional complexity and loss. Additionally, garnets offer high yield and throughput but compatibility is restricted due to mismatched lattice constants and thermal expansion coefficients [5] as well as contamination from introducing garnets to the CMOS process. Hence, although standalone, integrated isolators have been demonstrated using a vertical-axis electromagnet above garnet on a waveguide [19–21], these solutions still require post-processing steps in addition to those available to the CMOS fabrication process flow. The main limitation of utilizing garnets is therefore their requirement of post-processing and magnetic biasing [5]. Alternatively, all-passive NR transmission was demonstrated in SiP [22] but required high intensity optical pulses which are not used in optical communication systems. In this context, previously demonstrated on-chip isolators required customized post-processing steps which are incompatible with the process flow of integrated photonics foundries. They essentially face a trade-off between performance and feasibility. This introduces a need to quantify the limitations of CMOS fabrication processes in meeting the requirements for on-chip optical isolator designs and achieving MO interactions using SiP. Addressing it would help determine whether modern fabrication techniques may enable isolator designs which were previously considered infeasible [23]. We therefore demonstrate a standalone device which generates a magnetic field inside Si waveguides using an input electrical current. To our knowledge, this is the first demonstration of an on-chip, horizontal-axis electromagnet which was fabricated using exclusively the CMOS process flow for the purpose of standalone NR PMC in Si waveguides. In this sense, the key advantages of this design are that it required no post-processing and was capable of standalone operation. It is therefore highly feasible to both manufacture and deploy, respectively, which are crucial to its commercial viability.

2. Device design

A Si waveguide was surrounded by an electromagnetic coil to emulate a tunnel of electrical current. The coil was situated above the waveguide and surrounded it on three sides rather than being wound around it. This is because the Si crystal was grown directly on the buried oxide (BOX) layer prior to the deposition of additional materials, which implied that the fabrication process did not accommodate metallization below the Si layer. The coil was separated from the waveguide by a gap of 1 µm on the sides and 600 nm above. Its axis was parallel to the waveguide to align the direction the magnetic field with the optical path. The pitch was minimized to 9.3 µm and height was fixed at 2.95 µm within the constraints of the fabrication process [24]. Electrical connections consisted of a phosphorus-doped Si (n-Si) layer, and two aluminium (Al) metallization layers along with their tantalum nitride (TaN) vias. To compensate for the diamagnetic expulsion of the magnetic field by Si and SiO₂, two longitudinal strips each of Al and titanium nitride (TiN) were deposited co-axially inside the coil to emulate a paramagnetic solenoid core. This design was the basis for 15 device variations, which were fabricated on a SiP chip as shown in Supplementary Figure S2. These variations reflected the common use cases in SiP circuitry and were characterized in the Supplementary Information. The primary design spanned a length of 1097.4 µm (corresponding to 118 windings) around a Si strip waveguide of 500 nm width and 220 nm thickness. The model of the device was scaled-down to only 5 windings, as shown in Fig. 1, to minimize the computational demand of the 3D simulation. The total length of this model was 51.5 µm, which consisted of the coil length and an electrical connection shown in Fig. 1(c). It hosted an interaction length of 47.17 µm, which was 0.667 µm longer than the coil length due to the overlap between windings.

 

Fig. 1. Design of an electromagnetic coil surrounding a strip waveguide on 3 sides. The Si waveguide (red) is surrounded by the coil made of Al (grey), n-Si (maroon) and TaN (blue) with a core made of Al and TiN (green). The SiO₂ cladding is not shown. (a) Schematic of the front view of a single winding. An input electric current (white arrows) enters from behind and circulates clockwise through the layers: Al→TaN→Al→TaN→Al→TaN→n-Si→TaN→Al→TaN→n-Si. It then exits the front of the winding from the n-Si layer and enters the next winding through a TaN via (not shown). (b) Side, (c) bottom, and (d) perspective views of the simulated coil with 5 windings and a ${w_{\textrm{gap}}}$ of 1 µm. Axes units are in µm.

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The coil was designed to maximize the $B$-field in the waveguide while minimizing its size and response time. To ensure a fast response, the inductance also needed to be minimized. This could be accomplished in three ways based on Supplementary Equation (S10): (i) by minimizing the inner cross-sectional area ${A_{\textrm{coil}}}$, (ii) by increasing the length, l, or (iii) by reducing the number of windings, n. However, increasing l for a constant n or vice versa would increase the pitch and thereby reduce the B field. For the area, the width of the gap between the doped-Si edges of the coil and the sidewalls of the Si waveguide, ${w_{\textrm{gap}}}$, was set at either 0.5 µm or 1 µm to characterize the trade-off between inductance and applied B field. A ${w_{\textrm{gap}}}$ of 1 µm resulted in an area ${A_{\textrm{coil}}}$ of 37.19 µm² which resulted in a transient time of 210 fs based on Supplementary Equation (S11).

3. Device response

3.1 Electro-thermal response

An applied DC voltage difference generated an input current up to 14.28 mA with a current density distribution shown in Fig. 2(a). The average resistance per unit length was measured to be 12.8294 Ω/µm at room temperature, which is the vertical intercept of Fig. 2(b). Resistance was proportional to input current due to the corresponding rise in temperature from resistive heating as simulated in Fig. 2(c). This asymptotic rise imposed an upper limit on the current. It also increased the temperature in the waveguide as seen in Fig. 2(d).

 

Fig. 2. Electrical response of the coil. (a) Simulation of current density through the model coil at an input current of 14 mA. (b) Experimentally measured resistance per unit coil length of 11 device variations (dots) fitted to the simulation result (solid, black line). The labelling convention uses the device number and coil length, as given in Supplementary Table S2. The variations include both coil widths and all 3 coil lengths. Axes units are in µm for the device model. (c) Simulation of temperature distribution in the coil at an input current of 14 mA. (d) Temperature in the waveguide across the device length caused by resistive heating in the coil.

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The current density in the upper Al layer was much higher than that in the lower layers due to the difference in resistivity between Al and n-Si. The contribution of Al and TaN to resistive heating was also negligible. Hence, only the dominant, temperature-dependent resistivity of n-Si was evaluated. Based on the measurements in Fig. 2, the electrical response of n-Si followed Supplementary Equation (S8). Its coefficient of resistivity at room temperature, ${\rho _0}$, and temperature coefficient of resistivity, $\alpha $, were fitted at 1.5152 × 10⁻⁵ Ω-m and 0.0019 K^-1, respectively. The initial decline in resistance at low currents was assumed to be caused by either the semiconductor-metal junctions between the n-Si and TaN layers which acted as Schottky barriers, or a loading effect of the measurement equipment. At an input current of 14 mA, the maximum temperature in the waveguide was 600 K. Although this was lower than the melting point of the materials, it may affect dispersion [25] and consequently the Verdet constant of the modes. It could be compensated by externally regulating the temperature of the chip. Additionally, considering its fast response time, larger currents could be admissible by driving the coil with a pulsed signal so that the maximum B field could be increased at a relatively reduced average power. Resistive overheating would therefore be mitigated by balancing the duty cycle of the pulse with the time required to sufficiently cool the device. However, stabilizing the temperature fluctuations could prove challenging.

The operating voltage reached a maximum of 145 V before breakdown. This limit did not depend on the input current even though the power drawn, $P = {V^2}/R$ was different for each tested coil length. Hence, it is likely that the breakdown did not occur in the coil itself. Damage was only noticeable at the ends of the coil as seen in Supplementary Figure S2(c), which indicated a possible breakdown in its connection. This could be caused by a high voltage difference between two layers. For example, the electrical [26] and thermal [27] conductivity of TaN are both approximately 100 times smaller than Al. Additionally, the dielectric strength of non-conductive layers is also weakened at higher temperatures. Since the Si substrate acts as a floating ground, a breakdown pathway could have been thermally activated in the SiO₂ layer between the metals and the substrate.

3.2 Electro-magnetic response

The magnetic flux density around the device is shown in Fig. 3(a)-(g) for an input current of 14 mA. The serpentine architecture of the coil generated an alternating $B$-field [28] as shown by the distribution of the ${B_\textrm{Y}}$ component in Fig. 3(e)-(g). Figure 3(e) shows how the positive phase of the ${B_Y}$ oscillation, ${B_Y}$ (+), was focused by the current tunnel. In between tunnels, as shown in the inset of Fig. 3(d), the waveguide was exposed to the core which caused a leakage of the internal $B$-field. It effectively reversed the direction of ${B_\textrm{Y}}$ in the waveguide to produce oscillations between -0.58 mT and 1.16 mT. This field reversal could be used to support QPM in the waveguide as indicated in Supplementary Figure S4. The MO interaction could therefore be enhanced by shaping the applied $B$-field oscillations for a suitably dispersion engineered [29] waveguide mode.

 

Fig. 3. Simulated B field around the coil. (a) Front view, (b) side view, and (c) top view for the coil with a gap width of 1 µm. (e) Front view, (f) side view, and (g) bottom view of the ${B_Y}$ component of the same design. In each plot, the positions of its orthogonal cross-sections are visible. Axes units are µm. (d) Both B and ${B_Y}$ magnitudes along the waveguide centerline for increasing input currents and a ${w_{\textrm{gap}}}$ of 1 µm. The interaction length is marked by vertical, black, dashed lines. The black, solid line in the center indicates the location of the image in (a) and (e). Inset: Distribution of ${B_Y}$ at the negative peak at a propagation length of 30 µm (indicated by the black, dotted line) with the same colour scale as (e). Axes units are in µm for the device model. (h) $\smallint {B_Y}\textrm{d}y$ integrated over the propagation length for both gap widths of 0.5 µm and 1 µm, as well as for 160 nm above the coil (equivalent to the distance between the Al strip and the waveguide centerline). Inset: Difference in $\smallint {B_Y}\textrm{d}y$ between ${w_{\textrm{gap}}}$ for the positive and negative phases of the integrated ${B_Y}$ field.

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In Fig. 3(h), the ${B_Y}$-field was integrated along the interaction length, $\smallint {B_Y}\textrm{d}y$ inside the waveguide for both gap widths. For comparison with the upper half of the coil, it was also evaluated above the top Al layer (at the same distance as the waveguide centerline from the bottom Al layer). The field above the coil was found to be equivalent to that in the current tunnel due to the higher current density in the upper region. Counter-intuitively, a larger ${w_{\textrm{gap}}}$ of 1 µm supported a stronger overall ${B_Y}$-field in the waveguide despite the oscillation amplitude being smaller. This was because the walls and upper layer of the coil acted as a secondary current tunnel which focused the ${B_Y}(- )$ field along whichever segments of the waveguide were not shielded by the lower windings of the coil. The effect is shown in the inset of Fig. 3(d). Additionally, since a wider ${w_{\textrm{gap}}}$ was accommodated by a wider coil (as described in the Supplementary Information), ${B_Y}(- )$ was less focused. This effect is shown in the inset of Fig. 3(h) in which the two lines represent $\smallint {B_{Y,{w_{gap}} = 0.5\mu m}}\textrm{d}y - \smallint {B_{Y,{w_{gap}} = 1\mu m}}\textrm{d}y$ for the negative and positive phases of B_Y separately. The larger offset of the negative phase indicates that the contribution of ${B_Y}(+ )$ from the tunnel was less dependent on ${w_{\textrm{gap}}}$ than ${B_Y}(- )$ from the coil. The negative phase also exhibited a steeper rate of change because the current density was higher in the upper parts of the coil. As a result, the overall ${B_Y}$-field was stronger for a ${w_{\textrm{gap}}}$ of 1 µm. The ${B_Y}$ strength could therefore be increased by redesigning the coil to supply a higher current density in the lower region and mitigate any leakage. For example, removing the n-Si layer would reduce the resistance by two orders of magnitude.

3.3 Magneto-optic response

Each single-mode waveguide was evaluated for both TE₀ and TM₀ modes at center wavelengths of 1310 nm and 1550 nm corresponding to the lowest dispersion and loss wavelengths, respectively, in optical communication systems. The Verdet constant, V, of the modes in each waveguide was determined by their frequency-dependent effective index as shown in Supplementary Figure S4. Its dependence on the chromatic dispersion of the modes was found to be strongly related to the waveguide geometry. This relationship explains the difference in V between these waveguides and bulk Si [10]. Modal dispersion also affected the PMC efficiency because of the resulting phase mismatch between modes as seen in Fig. 4. Propagation loss was neglected since its main source was sidewall roughness, which was assumed negligible at micrometer length scales. A low loss allows the device to be cascaded or incorporated in a racetrack so that rotation could be accumulated by multiple passes through the interaction region. This could be amplified by dispersion engineering the waveguide to increase the optical path length [29] and enhance the interaction [30].

 

Fig. 4. Faraday rotation in the device. (a) Rotation of the TM₀ mode at a wavelength of 1310 nm in a strip waveguide along the propagation length for increasing input currents. The beginning and end of the interaction region are marked as black, dashed lines for reference. (b) Spectral dependence of the total accumulated rotation of each mode and each waveguide type for the longest device length of 1097.4 µm at an input current of 14 mA.

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The rotation of the TM₀ mode at a wavelength of 1310 nm is shown in Fig. 4(a) for increasing input currents. Since the angle of rotation was too low to be measured, the effect of mode beating was ignored. This implied the assumption of perfect phase matching between the TE₀ and TM₀ modes. The oscillatory behaviour of the rotation along the interaction length was therefore caused by the alternating ${B_Y}$-field in the waveguide. The accumulated rotation of each mode was extrapolated for the fabricated device lengths and are listed in Supplementary Table S3. The rotation at the longest interaction length of 1097.4 µm is shown in Fig. 4(b) for both gap widths and strip and slot waveguide types. These curves resemble V in Supplementary Figure S4 since the rotation depended on V when the applied B field and interaction length were fixed. Hence the spectral dependence of rotation was determined by V. The TM₀ mode of the strip waveguide underwent the most rotation of 50.71×10⁻¹² ° at a wavelength of 1352 nm.

4. Discussion

This standalone device acts as a building block on the roadmap toward utilizing magnetic fields on-chip in commercial applications, which to our knowledge, has not been demonstrated by state-of-the-art integrated MO isolators. The target rotation was 45° since it could be connected in series with a 45° reciprocal PMC [8,9] to achieve full 90° rotation for NR PMC. The output polarization could be filtered by a polarization beam splitter [31] to measure an intensity and phase modulation in the output polarizations. A change of the input current could then be mapped to a change in the output polarization state using the Poincaré sphere [8]. If the change in intensity is small, it could be detected by a lock-in amplifier, which would require the coil to be driven by an AC signal with a pulse duration larger than its transient time. Forward and backward propagation could be measured by reversing the direction of electric current in the coil, which is equivalent to reversing the propagation direction [17] due to the device symmetry.

In this design, the angle of rotation mainly depended on the input current, interaction length, and dispersion of the fundamental modes. It could be improved by optimizing ${w_{\textrm{gap}}}$, removing n-Si from the coil, co-designing the coil and waveguide to ensure QPM, and enhancing the MO interaction. It is possible that resistive heating could be circumvented to some extent by driving the coil for a shorter duration of time than that required to reach a temperature corresponding to its damage threshold. Essentially, the time required for heating or cooling could be regulated by an alternating current (AC) with an appropriate frequency and duty cycle. An AC driving signal could also be connected to a lock-in amplifier to detect small changes in the optical response. The interaction region could be increased by either cascading the devices, incorporating an optical cavity, or dispersion engineering the waveguide. In an optical cavity such as a racetrack, the optical pulse would undergo multiple passes as determined by its quality ($Q$) factor and accumulate a rotation of $\theta \times Q$. Alternatively, a spiral waveguide could also facilitate a predefined number of passes through the interaction region [12,13]. It is also worth considering inducing NRPS instead of NR PMC, since this would lift the degeneracy of counter-propagating resonant modes [14], thereby inducing isolation. The disadvantage would be a narrower optical bandwidth [5] in comparison to interferometer-based designs [32]. Additionally, the resonance would not increase rotation since the MO interaction is independent of the amplitude of the optical pulse.

Additional materials may also be considered to improve the performance. Doping the waveguides could enable their refractive index to be dynamically modulated using the free-carrier plasma dispersion effect. This would allow for the spatiotemporal modulation of MO coupling for slow light, which could improve the interaction or enable explorations in combining the Zeeman and Stark effects [33]. Additionally, combining the coil design with garnet deposition would enable a standalone, MO isolator for commercial applications. Specifically garnet deposited in a slot waveguide [8,34] could provide a significantly enhanced MO interaction. The lower index of garnet would also amplify the field concentrated in the slot. It could be complemented by CMOS-compatible materials such as SiN, Ge [35], or complementary materials such as graphene [36]. Along with overcoming the limitations described previously, these upgrades are expected to increase the angle of rotation by multiple orders of magnitude. We believe that a combination of these techniques would enable mass manufacturable, integrated optical isolators.

5. Conclusion

We have demonstrated a standalone, CMOS-based Faraday rotator consisting of a waveguide surrounded by a coil. The electrical response of the coil was demonstrated, and the performance of the device was simulated. The design was characterized over 15 design variations including 4 waveguide types, 2 gap widths, and 3 coil lengths. In this evaluation, the TM₀ mode of the strip waveguide at a wavelength of 1352 °nm underwent the most rotation of 50.71×10⁻¹² °. Having been fabricated in the CMOS process flow and capable of standalone operation, it surpasses two key limitations of current on-chip isolator designs regarding manufacturability and deployment, respectively. In this context, the signifiance of this design is in the commercial viability of the device. Additionally, our investigation provided the basis for a set of clearly identifiable upgrades which will improve the feasibility of inducing NR PMC in the SiP platform before requiring any post-processing, additional materials, or external magnetic biasing. This approach therefore provides a strong, alternative pathway to improve the commercial viability of future isolator designs. Even beyond optical isolation, the realization of a MO interaction using CMOS-compatible fabrication processes can enable a variety of novel design opportunities in SiP.