Expanding the quantum photonic toolbox in AlGaAsOI

All of the components were fabricated using an AlGaAs photonic layer grown via molecular-beam epitaxy (MBE). The full fabrication procedure has been detailed previously.23,2423. L. Chang, W. Xie, H. Shu, Q. F. Yang, B. Shen, A. Boes, J. D. Peters, W. Jin, C. Xiang, S. Liu, G. Moille, S. P. Yu, X. Wang, K. Srinivasan, S. B. Papp, K. Vahala, and J. E. Bowers, “Ultra-efficient frequency comb generation in AlGaAs-on-insulator microresonators,” Nat. Commun. 11, 1331 (2020). https://doi.org/10.1038/s41467-020-15005-524. T. J. Steiner, J. E. Castro, L. Chang, Q. Dang, W. Xie, J. Norman, J. E. Bowers, and G. Moody, “Ultrabright entangled-photon-pair generation from an AlGaAs-on-insulator microring resonator,” PRX Quantum 2, 010337 (2021). https://doi.org/10.1103/prxquantum.2.010337 Briefly, a GaAs chip with a 400-nm-thick AlGaAs photonic layer is bonded onto a 3-μm-thick thermal SiO2 buffer layer on a Si substrate. After removing the substrate through selective wet etching, the AlGaAs surface is passivated using an 8 nm film of Al2O3 grown via atomic layer deposition (ALD). Deep ultraviolet photolithography is used to pattern photoresist, which is used to etch a SiO2 hardmask and then the AlGaAs photonic layer to define the components. Another ALD deposition of Al2O3 passivates the surface before a 1.0 μm thick SiO2 cladding layer is deposited. Finally, 10 nm of titanium and 100 nm of platinum are deposited as resistive heaters for thermo-optic tuning.

A. Edge couplers

Before a fully integrated QPIC is fabricated, it is necessary to utilize either fiber-based or free-space optical testing instruments. Thus, one of the first components to design is an efficient structure to couple light into and out of the photonic chip. Various strategies have been explored for efficient coupling,3232. R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7, 201 (2019). https://doi.org/10.1364/prj.7.000201 but many of the methods that achieve ultra-high efficiency require additional fabrication steps—electron-beam lithography, anti-reflection coatings, or a full redesign of the input/output facet structure. For high throughput testing of individual components, much simpler structures can be used; as long as the fiber-to-chip coupling efficiency can be adequately characterized, any undesirable effects due to the input/output coupling can be isolated from the component performance.There are two main categories of fiber-to-chip couplers: vertical couplers and edge couplers (also called “in-plane” and “butt” couplers, respectively). As the name suggests, vertical couplers accept incoming light from the top of the chip (out of plane), while edge couplers couple light impinging from one of the facets of the photonic chip (in plane). Depending on the desired application or testing design, there may be a benefit for utilizing either type of coupler. Vertical couplers are useful for more compact designs as they do not require waveguides to be routed completely to the edge of the photonic chip.3333. L. Cheng, S. Mao, Z. Li, Y. Han, and H. Y. Fu, “Grating couplers on silicon photonics: Design principles, emerging trends and practical issues,” Micromachines 11, 666 (2020). https://doi.org/10.3390/mi11070666 Generally, vertical couplers utilize periodic gratings that satisfy the Bragg condition in the waveguide to couple light into an optical fiber oriented almost perpendicular to the surface.33,3433. L. Cheng, S. Mao, Z. Li, Y. Han, and H. Y. Fu, “Grating couplers on silicon photonics: Design principles, emerging trends and practical issues,” Micromachines 11, 666 (2020). https://doi.org/10.3390/mi1107066634. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006). https://doi.org/10.1143/jjap.45.6071 Edge couplers, on the other hand, can be much simpler to design and less sensitive to fabrication variation. Instead of relying on grating-based structures, edge couplers manipulate the waveguide dimensions to expand the waveguide mode to be closer matched with the mode in the fiber.3535. X. Mu, S. Wu, L. Cheng, and H. Y. Fu, “Edge couplers in silicon photonic integrated circuits: A review,” Appl. Sci. 10, 1538 (2020). https://doi.org/10.3390/app10041538 The easiest way to achieve this conversion is to taper the waveguide to a narrow tip (called an “inverse taper”) where the mode becomes weakly confined and expands closer to the mode size of the fiber. A standard taper, where the waveguide width is expanded at the facets, can also serve as an edge coupler. However, in high-index contrast platforms, the design typically has lower efficiencies since the strongly confined mode will remain smaller than the fiber mode. The waveguide becomes capable of supporting multiple modes, and the high-index contrast produces large backreflections.3535. X. Mu, S. Wu, L. Cheng, and H. Y. Fu, “Edge couplers in silicon photonic integrated circuits: A review,” Appl. Sci. 10, 1538 (2020). https://doi.org/10.3390/app10041538 Other edge coupling strategies include utilizing multiple inverse tapers in a trident or dual-tip design,3636. Y. Liu and J. Yu, “Low-loss coupler between fiber and waveguide based on silicon-on-insulator slot waveguides,” Appl. Opt. 46, 7858–7861 (2007). https://doi.org/10.1364/ao.46.007858 polymer-based spot size converters,3737. G. Roelkens, P. Dumon, W. Bogaerts, D. van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photonics Technol. Lett. 17, 2613–2615 (2005). https://doi.org/10.1109/lpt.2005.859132 or multi-layer spot size converters.3838. Q. Fang, T.-Y. Liow, J. F. Song, C. W. Tan, M. B. Yu, G. Q. Lo, and D.-L. Kwong, “Suspended optical fiber-to-waveguide mode size converter for silicon photonics,” Opt. Express 18, 7763 (2010). https://doi.org/10.1364/oe.18.007763 Due to the much simpler design, here we report only on inverse taper AlGaAsOI edge couplers. A scanning electron microscope (SEM) image of several inverse tapers is shown in Fig. 2(a). The facet is on the right side of the image, and the waveguides taper from 600 nm width (on the left) down to 200 nm at the facet. For a more in-depth study of the various types of coupling strategies, readers are referred to Ref. 3232. R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7, 201 (2019). https://doi.org/10.1364/prj.7.000201, which highlights various vertical and edge coupling strategies on the silicon-on-insulator (SOI) platform.

The inverse taper design reduces the confinement of the waveguide mode, increasing its effective modal area and decreasing its effective index of refraction. This allows for moderately high simulated coupling efficiencies (losses <3 dB) to a (typically) lensed fiber aligned with the waveguide facet. The overall coupling loss is determined by effects such as reflection at the chip facet (due to refractive index mismatch), fiber-to-waveguide mode mismatch, and mode-conversion within the waveguide taper.

To determine the optimal design for an inverse taper edge coupler, the dimensions of the waveguide taper were varied and simulated using Lumerical MODE software. Here, we show only the results for inverse tapers designed for the fundamental transverse electric (TE) mode because the components shown in the rest of this article are designed to operate with TE polarized light. Similar calculations can be made for the transverse magnetic (TM) mode. For a given Gaussian beam and waveguide geometry, the power overlap between the waveguide mode and fiber mode is calculated to estimate an upper bound on coupling efficiency and determine the optimum waveguide dimensions. This calculation does not include loss due to mode conversion or reflection at the interface. Figure 2(b) illustrates the simulated mode overlap between a Gaussian beam with a mode field diameter of 2.5 µm (which matches the mode field diameter of commercially available lensed fibers) and a 400 nm thick AlGaAsOI waveguide with various taper widths. Narrow taper widths enlarge the waveguide mode to be nearly mode-matched with the incoming fiber mode, but the weak confinement of these narrow waveguides typically comes with additional loss as light propagates through the narrow taper back to a waveguide width of ≥400 nm for the components. The fabrication of sub-200-nm features is challenging using the standard photolithography process; so, we limit our taper designs to 200 nm or larger. Along with the simulated data, Fig. 2(b) also shows a measured value for the coupling loss for a 200 nm edge coupler at a wavelength of 1550 nm. The measured value was collected by sending 6.95 dBm (∼5 mW) of light into a straight waveguide with 200 nm tapers on the input and output facet. The collected power through the waveguide was 1.16 ± 0.23 dBm, indicating an approximate loss of 2.9 dB/facet (the waveguide propagation loss is <1 dB/cm and the waveguide is less than 2 mm; so, the contributions of propagation loss are ignored in this measurement). The measured loss is larger than the simulated mode overlap, which is expected because the measurements also include reflections and mode conversion loss in the taper. The simulated mode overlap acts as an upper bound for the efficiency of the inverse taper. The 2.9 dB/facet of coupling loss in the AlGaAsOI platform is similar to the sub-3 dB coupling loss expected from standard SOI inverse taper edge coupler designs.3535. X. Mu, S. Wu, L. Cheng, and H. Y. Fu, “Edge couplers in silicon photonic integrated circuits: A review,” Appl. Sci. 10, 1538 (2020). https://doi.org/10.3390/app10041538 The use of narrower taper widths [as shown in Fig. 2(b)] or an anti-reflection coating will improve the coupling efficiency further, but ease of fabrication and reliability are prioritized; so, for our initial devices, 200 nm inverse tapers are utilized.

B. Waveguide crossings

Several methods have been explored for creating low-loss waveguide crossings including vertical coupling into polymer strip waveguides,3939. A. V. Tsarev, “Efficient silicon wire waveguide crossing with negligible loss and crosstalk,” Opt. Express 19, 13732 (2011). https://doi.org/10.1364/oe.19.013732 multi-planar crossings,4040. J. Chiles, S. Buckley, N. Nader, S. W. Nam, R. P. Mirin, and J. M. Shainline, “Multi-planar amorphous silicon photonics with compact interplanar couplers, cross talk mitigation, and low crossing loss,” APL Photonics 2, 116101 (2017). https://doi.org/10.1063/1.5000384 multimode interference-based crossings,41–4341. W. Chang and M. Zhang, “Silicon-based multimode waveguide crossings,” J. Phys.: Photonics 2, 022002 (2020). https://doi.org/10.1088/2515-7647/ab869842. W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 32, 2801 (2007). https://doi.org/10.1364/ol.32.00280143. S. Wu, X. Mu, L. Cheng, S. Mao, and H. Y. Fu, “State-of-the-art and perspectives on silicon waveguide crossings: A review,” Micromachines 11, 326 (2020). https://doi.org/10.3390/mi11030326 and subwavelength gratings.4444. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express 18, 16146 (2010). https://doi.org/10.1364/oe.18.016146 Many of these methods involve additional fabrication steps that can introduce excess loss and system design and fabrication challenges. A basic approach for waveguide crossing relies on tapering an input single-mode waveguide section into a larger waveguide cross section that can support higher-order modes and relies on the beating between the fundamental mode and the higher-order mode to create an electric field maximum that is centered in the waveguide at the crossing location. By focusing the mode into the center of the wide waveguide, evanescent coupling to the perpendicular waveguide is minimized. This design can be completed with a basic linear taper (which will be referred to as a “simple crossing”) or a more complex structure. Here, we consider simulations of both simple and inverse-design crossings and report results from an inverse design approach (which will be referred to as a “13-width crossing”) that utilizes 13 different widths in a parabolic taper that requires no additional fabrication steps and maintains low-loss, high-isolation transmission. The second design utilizes a swarm optimization protocol such that the optical mode is transmitted with minimal coupling to the crossed waveguide.The simple crossing design is illustrated in Fig. 3(a) and uses the beating between the fundamental and higher-order mode to create a confined optical mode centered at the location of the crossing. The beat length, Lπ, is defined as Lπ = π/(β0 − β1), where β(0,1) is the propagation constant of the fundamental waveguide mode and first-order waveguide mode, respectively. For a 1.5 μm multimode waveguide width (wm), the fundamental and first-order TE modes have effective indices of ∼3.00 and 2.87, respectively, at a wavelength of 1550 nm. Using these effective indices, the beat length is calculated as 5.95 μm. Finite difference time domain (FDTD) simulations were utilized to account for the transition region between the single-mode waveguide and the wider, multimode waveguide as well as allow for a larger bandwidth crossing to be designed where the average loss across a 100 nm bandwidth is utilized instead of maximizing at a single wavelength. The simulated mode profile for the simple crossing design and the simulated transmission through the device is shown in Figs. 3(b) and 3(c), respectively. From the mode profile simulation, it is clear that the beating between the fundamental and higher order mode creates a local maximum at the location of the crossing that minimizes the optical mode scattered into the perpendicularly oriented waveguide. The simulated loss through this structure is 0.15 dB at a wavelength of 1550 nm.Figure 3(d) shows the 13-width waveguide crossing with critical dimensions depicted. This design utilizes a swarm optimization protocol in an FDTD solver to optimize the transmission through the crossing by allowing the width to vary at 13 equally spaced sections along the taper. A parabolic interpolation between the 13 widths ensures a smooth transition between the various widths. The 13-width crossing design was also optimized for a bandwidth of 100 nm to maintain a low-loss performance of the crossing across a broad bandwidth, which will be compatible with broadband entangled photon pair generation in quantum photonic circuits. Lower loss structures can be made when optimizing for a smaller bandwidth. Starting with an input waveguide width of 400 nm and total crossing length (L) of 9 μm, the optimizer was allowed to vary the widths w2-w13 between 200 and 2000 nm. Figure 3(e) shows the electric field profile for the optimal crossing design at a wavelength of 1550 nm, and Fig. 3(f) plots the simulated transmission through the waveguide crossing as a function of the input wavelength. This crossing design has a simulated loss of ∼0.1 dB at a wavelength of 1550 nm. Since the loss of the 13-width crossing design is smaller than the simple crossing design, the 13-width crossing was fabricated and tested initially.With the simulated waveguide crossing loss of the order of 0.1 dB, the cutback method4242. W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 32, 2801 (2007). https://doi.org/10.1364/ol.32.002801 is used to measure the loss per crossing to remove the coupling-dependent loss and reduce detector sensitivity limitations. For the 13-width crossing, waveguides between 10 and 50 crossings were fabricated, and the loss through each line of crossing was measured across eight trials with complete re-alignment of the input and output fibers for each trial to remove any systematic variations due to coupling loss. Figure 4(a) shows a microscope image of few of the waveguide crossings in one of the lines. The vertical waveguide channels are terminated with tapered waveguides in spiral geometry to prevent backreflections into the crossing. The horizontal spacing of the crossings is varied randomly between 25 and 35 μm to avoid photonic cavity effects. Using the cutback method, the transmission through the crossings was measured at a wavelength of 1550 nm, and the results are shown in Fig. 4(b). The dashed line indicates a linear fit of the loss as a function of the number of crossings, providing an estimated loss of 0.23 dB/crossing. The error bars on the data points indicate the standard deviation of the eight independent measurement trials.These results for the 13-width waveguide crossing [Fig. 3(b)] indicate that the fabricated crossings have slightly higher loss than the simulated loss at a wavelength of 1550 nm. This additional loss is likely due to fabrication variations in the widths along the device; the inverse design is more sensitive to fabrication variation than the use of a simple waveguide crossing. The measured 0.23 dB of loss for the AlGaAsOI 13-width crossing is comparable to the 0.2 dB of insertion loss reported from a genetic algorithm-designed SOI waveguide crossing4545. P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760 (2009). https://doi.org/10.1364/ol.34.002760 and less than the loss of 0.3 dB from silicon nitride waveguide crossings.4646. H. Yang, P. Zheng, G. Hu, R. Zhang, B. Yun, and Y. Cui, “A broadband, low-crosstalk and low polarization dependent silicon nitride waveguide crossing based on the multimode-interference,” Opt. Commun. 450, 28–33 (2019). https://doi.org/10.1016/j.optcom.2019.05.052 Other manuscripts report ≤0.1 dB of insertion loss for elliptical tapers4747. T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, 646–647 (2004). https://doi.org/10.1143/jjap.43.646 and even of the order of 0.02 dB for sub-wavelength grating-based structures.4848. Y. Zhang, A. Hosseini, X. Xu, D. Kwong, and R. T. Chen, “Ultralow-loss silicon waveguide crossing using Bloch modes in index-engineered cascaded multimode-interference couplers,” Opt. Lett. 38, 3608 (2013). https://doi.org/10.1364/ol.38.003608 Reference 4343. S. Wu, X. Mu, L. Cheng, S. Mao, and H. Y. Fu, “State-of-the-art and perspectives on silicon waveguide crossings: A review,” Micromachines 11, 326 (2020). https://doi.org/10.3390/mi11030326 compares various results of waveguide crossing on the SOI platform.

C. 3 dB couplers multimode interferometers and directional couplers

A standard building block in both classical and quantum PICs is the 3 dB coupler. In QPICs, 3 dB couplers are utilized as their classical counterparts to distribute light evenly between two waveguides, to interfere single photons, and to serve as a component for tunable Mach–Zehnder interferometers (MZIs) for programmable PICs. This places strict requirements on the devices, such as low loss for potential scalability, a large bandwidth to support broadband quantum light generation, and precise splitting ratios to maximize the extinction ratio (ER) and minimize cross-talk in MZIs. We explore two designs for creating on-chip 3 dB couplers: multimode interferometers (MMIs) and directional couplers (DCs). MMIs are based on the self-imaging principle, similar to the aforementioned simple waveguide crossings; however, unlike in the waveguide crossing design, the beat length between the two modes, Lπ, is used to calculate the core length necessary to achieve a splitting ratio as close to 3 dB as possible. The second coupler design based on DCs uses the overlap of evanescent modes between two neighboring waveguides, allowing the mode to fully couple into the adjacent waveguide. The full crossover length relies on the difference in refractive index between the even and odd supermodes created when two waveguides are in close proximity. DCs are straightforward couplers to design and are capable of any splitting ratio by adjusting the coupling length, but they are also more susceptible to fabrication imprecision and errors compared to MMIs.

Figure 5 depicts two MMI and DC designs and results from FDTD simulations. For the MMIs, a core width of 2.1 μm was selected. Because the self-imaging length scales with the MMI core width, a narrow width was chosen to reduce the component footprint. Symmetric input and output tapers expand the mode from a waveguide width of 0.4 μm to 0.9 μm nearest to the core. A 0.3 μm separation leaves no excess core width beyond the dimensions of the tapers in an effort to reduce Fabry–Pérot effects due to reflections. The core length design began by first calculating the beat length and multiplying it by a factor of 1.5, resulting in Lπ = 18.75 μm. The full device was then simulated using FDTD, and the electric field profile is shown in Fig. 5(b). With a combination of the calculated beat length and FDTD simulations, a core length of 17.2 μm was chosen. The 1.55 μm difference between both methods is due to the input taper expanding the mode prior to reaching the MMI core not being considered during the beat-length calculation.Unlike the MMIs, the DC design utilizes the same waveguide width, 0.4 μm, across the entire device. Symmetric sine bend waveguides on the input and outputs with transverse displacements of 1.0 and 8.0 μm enable light to propagate near the coupling region. The minimum radius of these sine bends is kept to 20 μm to reduce bending loss. The separation between the waveguides in the coupling region where the evanescent modal overlap occurs is 0.3 μm. The coupling length for the full transfer of light from one waveguide to the other was first calculated with L=λ2(n0−n1) to give an estimate of the full crossover length of the mode, where n(0,1) is the effective index of the even supermode and odd supermode, respectively, that exists when the two waveguides are brought in close proximity. The finite difference eigenmode (FDE) result for the full crossover length is 48.47 μm. Thus, for a 3 dB coupler, L = 24.23 μm. A sweep of the coupling region using FDTD simulations of the full DC structure is depicted in Fig. 5(d). The results of this simulation suggest an optimal 3 dB coupling length of 17.0 μm. The difference between the two values is due to extra coupling effects in the sine bends. From the MZI measurements discussed in Sec. , we can extract the performance of the couplers.

D. Mach–Zehnder interferometers (MMI and DC)

Tunable MZIs are a key component in QPICs, playing an important role for numerous functions, including as reconfigurable postselected entangling gates (R-PEGs),4949. J. C. Adcock, S. Morley-Short, J. W. Silverstone, and M. G. Thompson, “Hard limits on the postselectability of optical graph states,” Quantum Sci. Technol. 4, 015010 (2018). https://doi.org/10.1088/2058-9565/aae950 demultiplexers,5050. F. Horst, W. M. J. Green, S. Assefa, S. M. Shank, Y. A. Vlasov, and B. J. Offrein, “Cascaded Mach-Zehnder wavelength filters in silicon photonics for low loss and flat pass-band WDM (de-)multiplexing,” Opt. Express 21, 11652–11658 (2013). https://doi.org/10.1364/oe.21.011652 variable beam splitters,5151. C. M. Wilkes, X. Qiang, J. Wang, R. Santagati, S. Paesani, X. Zhou, D. A. B. Miller, G. D. Marshall, M. G. Thompson, and J. L. O’Brien, “60 dB high-extinction auto-configured Mach–Zehnder interferometer,” Opt. Lett. 41, 5318–5321 (2016). https://doi.org/10.1364/ol.41.005318 filters,5252. M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Passive high-extinction integrated photonic filters for silicon quantum photonics,” in Conference on Lasers and Electro-Optics (Optica Publishing Group, 2016), paper FM1N.6. and single photon quantum logic gates.5353. J. C. Adcock, C. Vigliar, R. Santagati, J. W. Silverstone, and M. G. Thompson, “Programmable four-photon graph states on a silicon chip,” Nat. Commun. 10(1), 3528 (2019). https://doi.org/10.1038/s41467-019-11489-y In an MZI, a 3 dB coupler splits light evenly into two different paths that may be equal (balanced MZI) or unequal (unbalanced MZI) in length, which then recombine with another coupler. Here, we focus on two variations of thermo-optically tunable unbalanced MZIs employing both DCs and MMIs. These devices were designed using the transfer matrix method,5454. M. A. Tran, T. Komljenovic, J. C. Hulme, M. L. Davenport, and J. E. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28, 1517–1520 (2016). https://doi.org/10.1109/lpt.2016.2556713 where each component of the MZI can be represented by a matrix, two equivalent matrices for the 3 dB couplers, and a standalone matrix representing the path imbalance. Since many MZIs are required for a complete QPIC, the loss across each device must be minimized. Each coupler also should exhibit as close to a 3 dB splitting ratio as possible to achieve a maximum extinction ratio (ER), defined here as the power ratio of neighboring MZI fringes in the transmission spectrum.Figure 6(a) shows an optical image of an MZI utilizing DCs as couplers with a 45 μm path imbalance on the top arm with the metal thermal tuner above the 1 μm thick cladding to sweep and control the MZI phase. One advantage of thermo-optic tuning with AlGaAs is its inherent large thermo-optic coefficient, which, for an MZI with a 60 μm path imbalance and a 10.28 nm free spectral range (FSR), allows for a full 2π phase sweep with 20 mW/π efficiency, which is 10 (0.6) times more efficient than silicon nitride5555. J.-M. Lee, W.-J. Lee, M.-S. Kim, S. Cho, J. J. Ju, G. Navickaite, and J. Fernandez, “Controlled-NOT operation of SiN-photonic circuit using photon pairs from silicon-photonic circuit,” Opt. Commun. 509, 127863 (2022). https://doi.org/10.1016/j.optcom.2021.127863 (silicon5656. J.-M. Lee, M.-S. Kim, J. T. Ahn, L. Adelmini, D. Fowler, C. Kopp, C. J. Oton, and F. Testa, “Demonstration and fabrication tolerance study of temperature-insensitive silicon-photonic MZI tunable by a metal heater,” J. Lightwave Technol. 35, 4903–4909 (2017). https://doi.org/10.1109/jlt.2017.2763244). The transmission spectrum of MZIs with MMIs and DCs are shown in Figs. 6(b) and 6(c), respectively, for two different input/output configurations. We observe an ER above 10 dB across ≥100 nm bandwidth for through ports and ≥200 nm for cross ports, comparable to silicon MZIs.52,5752. M. Piekarek, D. Bonneau, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Passive high-extinction integrated photonic filters for silicon quantum photonics,” in Conference on Lasers and Electro-Optics (Optica Publishing Group, 2016), paper FM1N.6.57. J.-M. Lee, W.-J. Lee, M.-S. Kim, and J. J. Ju, “Noise filtering for highly correlated photon pairs from silicon waveguides,” J. Lightwave Technol. 37, 5428–5434 (2019). https://doi.org/10.1109/jlt.2019.2942436 With the wavelength-dependent ER measurements, the true coupling coefficient κ of each coupler can be extracted,5454. M. A. Tran, T. Komljenovic, J. C. Hulme, M. L. Davenport, and J. E. Bowers, “A robust method for characterization of optical waveguides and couplers,” IEEE Photonics Technol. Lett. 28, 1517–1520 (2016). https://doi.org/10.1109/lpt.2016.2556713 as shown in Fig. 6(d). The DC (MMI) couplers exhibit an average coupling coefficient of 0.501 ± 0.03 (0.52 ± 0.11) across a 100 (200) nm bandwidth centered at 1570 (1550) nm, respectively.

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