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Abstract
High-density silicon waveguide arrays manufactured on a complementary metal-oxide-semiconductor (CMOS)-foundry platform hold great promise for optical information processing and photonic integration. However, evanescent waves arising from nanoscale confinement would cause significant optical crosstalk in waveguide arrays, which remains a vital issue in various applications. Here, by utilizing silicon photonic nanohole metamaterials, we propose a scheme to greatly suppress the crosstalk in the devices and then demonstrate ultra-compact low-crosstalk waveguide arrays. For a 100-µm-long waveguide array at a half-wavelength pitch, low crosstalk of −19 dB can be obtained in a wide range of wavelengths (1500 nm–1580 nm). In the experimental demonstrations, our approach exhibits the ability to suppress the crosstalk over a broad bandwidth without substantially increasing the propagation loss as well as the promising design flexibility, which shall pave the way for metamaterials enabled high-density waveguide arrays.
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1. Introduction
Silicon photonics provides an excellent platform for low-cost large-scale photonic integration and next-generation communication systems [1–7]. In such systems, silicon waveguide arrays are among the cornerstones, which can be used in many fields, including optical phased arrays [2,8–12], optical interconnection [13,14], wavelength-division multiplexing [15,16] and space-division multiplexing [17]. Moreover, to obtain large-scale integration and thus a densely integrated photonic circuit, compact waveguide arrays are needed. However, miniaturization of waveguide arrays is usually hampered by the wave nature of light, i.e. the evanescent wave in the cladding causes the waveguide crosstalk [18]. Then, in silicon waveguide arrays, to avoid the optical crosstalk, adjacent waveguides are required to be separated large enough [19,20], which limits the integration density of photonic chips.
To overcome this limit, various schemes have been proposed to reduce crosstalk between the waveguides [1,8,21–25]. To suppress the crosstalk, Jacob et al. proposed an extreme skin-depth (e-skid) waveguide by using all-dielectric metamaterial cladding [22]. Compared with conventional on-chip waveguides, the coupling length of that device is improved more than one order of magnitude. However, the pitch of the device is 1 um, which is larger than half wavelength. To reduce the pitch size to be half wavelength, Song et al. demonstrated a waveguide array by varying the widths of waveguides from 450 nm to 330 nm [1]. The propagation constant difference as well as the phase mismatch condition can be obtained. Thus, the crosstalk can be suppressed to -20 dB. Meanwhile, Wang et al. designed and demonstrated a low-crosstalk nano-structured silicon waveguide array [21,24]. By placing two thin silicon strips (width = 40 nm) between adjacent waveguides, the geometric symmetry of the array can be destroyed and the crosstalk is below about −20 dB. Moreover, Yi et al. demonstrated a compact sinusoidal silicon waveguide array. By introducing the sinusoidal waveguide with the appropriate period and amplitude, the coupling dispersion can be controlled and the modal crosstalk can be reduced to ∼ −25 dB [8].
In this study, to achieve the excellent device performance, we propose a scheme to suppress the crosstalk and then demonstrate metamaterial enabled high-density waveguide arrays. In the devices, by using nanohole metamaterials, we introduce phase mismatch in waveguide arrays and thus significantly suppress the optical coupling. For a 100-µm-long waveguide array, our experimental results show that an IL of 1 dB and crosstalk of −21 dB can be obtained at 1550 nm. Moreover, for the array, crosstalk remains below −19 dB in 1500 nm-1580 nm. With such low crosstalk and large bandwidth, our device can not only enable high-density integration of waveguide components with the potential significant reduction in on-chip space and cost, but also help to improve the performance of important devices such as optical phased arrays with a wider beam-steering range [1]. Furthermore, in the experimental demonstrations, our approach exhibits the ability to suppress the crosstalk over a broad bandwidth without substantially increasing the propagation loss as well as the promising design flexibility, which shall pave the way for metamaterials enabled dense integration.
2. Theoretical analysis and design
2.1 Physics and principles for low crosstalk waveguide arrays
The structure of such a typical silicon photonic nanohole metamaterials enabled waveguide array is illustrated in Fig. 1, which is built by periodically repeated supercells with a waveguide pitch of G. In the device, each supercell consists of a silicon straight waveguide without air holes and several silicon nanohole metamaterial enabled waveguides. Here, widths and heights of all the waveguides are set to 500 nm and 220 nm, respectively, in order to effectively confine the optical energy in the waveguide core. And, in each nanohole metamaterial waveguide, subwavelength air holes with a constant diameter are periodically distributed along the silicon waveguide while the period of nanoholes is set to P [26,27]. Note that, in each supercell, holes in different nanohole metamaterial waveguides would have different diameters, as shown in Fig. 1. Moreover, all the waveguide modes propagate along the z direction.
Fig. 1. (a) Schematic view of the waveguide array. (b) Calculated effective propagation constants of a straight waveguide without air holes and nanohole metamaterial enabled waveguides with different hole diameters (d). The period of nanoholes is set to 200 nm. Inset: Top view of such a waveguide in the calculation. Here, for straight waveguide without nanoholes, d is set to 0.
Here, we develop a general theoretical analysis based on coupled mode theory (CMT) to illustrate the device principle. In this one-dimensional (1D) model, each waveguide supports a waveguide mode with a constant propagation constant β, since all the waveguide has the same width. Meanwhile, the amplitude of the waveguide mode for the m-th waveguide is denoted to be am, which has the time dependence (ejwt). In the dense array, waveguides are brought into close proximity. Then, the waveguide modes would be coupled due to the interaction of evanescent fields. If the coupling is weak, the coupled equation can be expressed as [28–31]:
To suppress the crosstalk between the waveguides, we should enlarge the effective propagation constant differences between adjacent waveguides (βm-βm ± 1) and thus create the phase mismatch condition [1]. As shown in Eq. (1), this could be achieved by changing the self-coupling coefficients (Kmm) and then the effective propagation constant (βm) of waveguides in the array. Meanwhile, for silicon waveguides, the electrical intensity of the waveguide mode peaks at the center of the waveguide. Thus, we introduce subwavelength air holes with a constant diameter in the waveguide center and then utilize such nanohole metamaterial enabled waveguide structure. Note that, with nanoholes in the waveguide center, the overlap between the dielectric perturbation and optical mode volume can be increased. Then, as shown in Eq. (3), both the self-coupling coefficients (Kmm) and the effective propagation constant of waveguides (βm) can be effectively controlled. Furthermore, with such large overlap, we can also shrink the nanohole size. Then, low loss nanohole metamaterial enabled waveguides can still be obtained, which would be beneficial for on-chip applications. Moreover, for each nanohole metamaterial enabled waveguide in the array, its self-coupling coefficient is determined by the dielectric perturbation induced by its nanoholes. Based on the Eq. (3), we then calculated the effective waveguide propagation constant of nanohole metamaterial enabled waveguides using the dielectric perturbation. Figure 1(b) shows the calculated waveguide effective propagation constants of straight waveguide and nanohole metamaterial waveguides with different nanohole diameters. For the straight waveguide without air holes, the effective propagation index is a constant β=$9.526 \times {10^6}{m^{ - 1}}$.Meanwhile, for nanohole metamaterial enabled waveguides, the effective propagation index strongly changes around the nanoholes. And, the variation of the effective waveguide propagation index increases when the nanohole diameter increases. Note that, here the calculations are performed at 1550 nm, while similar optical behavior of the waveguides can also be overserved at other wavelengths. Thus, to create the effective waveguide propagation constant differences in the array, the diameters of nanoholes in different waveguides are set to be different, which can then be used to vary the self-coupling coefficients and then introduce the effective propagation constant differences between adjacent waveguides. In this way, the phase mismatch can be obtained and the optical crosstalk can be effectively suppressed.
2.2 Design and simulations
To verify the above analysis and choose proper parameters, we first choose a two-waveguide system to simulate the optical crosstalk between two adjacent waveguides. As shown in Fig. 2(a), the two-waveguide system consists of a straight waveguide without holes and a nanohole metamaterial enabled waveguide with a hole diameter of D. Meanwhile, the two waveguides have identical dimensions with a width of 500 nm and a thickness of 220 nm. And, the period of nanoholes is set to P = 200 nm, while the length of waveguide is set to 100 µm. We then perform the device simulation with varied nanohole diameters and waveguide pitches, as shown in Fig. 2(c). With a constant pitch size, we can find that the maximum crosstalk of the two-waveguide system decreases if the nanohole diameter increases. Based on the above analysis, this is due to the fact that the self-coupling coefficient as well as the effective propagation constant difference could be enlarged if the nanohole diameter increases, which could thus effectively suppress the crosstalk. Moreover, the optical crosstalk can also be reduced by enlarging the waveguide pitch, since the increased waveguide pitch can decrease the mutual coupling coefficient, as shown in Eq. (2). Note that, the waveguide pitch should be no larger than half wavelength (775 nm) in many applications. Thus, to obtain a crosstalk below −20 dB, the nanohole diameter should be larger than 40 nm. Moreover, to validate the analysis and evaluate the low-crosstalk performance, here we simulated a typical two-waveguide system with a nanohole diameter of 80 nm and a pitch size of 775 nm. As shown in Fig. 2(b), One can find that the power launched into the two-waveguide system is tightly concentrated in the input waveguide while the crosstalk is barely observable.
Fig. 2. Designed structure and simulated optical crosstalk. (a) Schematic configuration of the two-waveguide system. (b) Numerically simulated power distribution of the system. (c) Maximum crosstalk of the system (nanohole diameter and pitch vary) at 1550 nm. (d) Schematic configuration of the SC3 waveguide array. (e) Simulated transmission spectra of the array. For each input waveguide i, only Ti,i ± 1 plus the worst are shown to avoid a cluttered view. (f) Transmission statistics of all simulated transmission spectra at 1550 nm. When light is injected into a given waveguide i, transmission of all nine waveguides, j = 1, 2, . . ., 9, are simulated (9 × 9 = 81 transmission statistics in total for different i).
We then build a high-density silicon array as shown in Fig. 2(d), which consists of three identical supercells. In each supercell, there are three different waveguides (called ‘SC3’), including a straight waveguide, a nanohole metamaterial waveguide with a hole diameter of d1, and a nanohole metamaterial waveguide with a hole diameter of d2. Considering the fabrication limitation for nanoholes, d1 and d2 are set to 80 nm and 120 nm, respectively. Here, in this device, we choose three different waveguides to break the coupling symmetry and then introduce strong propagation constant differences between adjacent waveguides. In this way, the optical crosstalk can be effectively suppressed. Meanwhile, the waveguide pitch and the period of nanoholes are set to 775 nm and 200 nm, respectively. And, the length of the array is set to 100 µm.
The simulated transmission spectra of the high-density array are shown in Fig. 2(e). When light is injected into a given waveguide i, transmission spectra of all nine waveguides Tij(λ), j = 1, 2,…,9, are simulated (9 × 9 = 81 transmission spectra in total for different i). Meanwhile, for each waveguide i, only the two nearest neighbors (Ti,i ± 1) plus the worst crosstalk channel are plotted, in order to avoid a heavily cluttered presentation. We can note that the ILs of all input waveguides are lower than 0.15 dB, and the peaks of all crosstalk channels are below −22.4 dB from 1500 nm to 1580 nm. Evidently, the ILs and the crosstalk are fairly low. Moreover, the statistics of each transmission spectrum at 1550 nm are shown in Fig. 2(f), which shows that the waveguide array has an IL of 0.15 dB and crosstalk of −22.43 dB.
In addition, fabrication tolerance of the silicon waveguide array is studied through simulation. By introducing deviations in waveguide width (ΔW), hole diameter (ΔD), and pitch (ΔP), we examine their impact on the transmission spectrum and the max crosstalk, as shown in Fig. 3. One can find that the proposed waveguide array works well at 1550 nm, when the fabrication error is about ±20 nm. These findings highlight the design's considerable tolerance to manufacturing variations, presenting a viable solution for integrating photonic devices in environments where precise fabrication is challenging.
Fig. 3. Fabrication tolerance of the designed waveguide array, (a) waveguide width variation, (b) hole diameter variation, (c) pitch variation.
3. Experiments
We then fabricated the SC3 waveguide array to experimentally verify the transmission characteristics. Fabrication was carried out on a silicon-on-insulator (SOI) wafer, which consists of a 220 nm-thick top silicon layer on a 3 µm-thick silicon dioxide layer. The device patterns were first defined by the electron beam lithography, followed by a single-step inductively coupled plasma dry etching process. Then, the patterns were fully transferred onto the top silicon layer. Note that, the etching was performed under carefully controlled conditions to ensure high precision and uniformity of the fabricated structures. Figure 4(a) shows the microscope image of the fabricated device, including the waveguide array and grating couplers (GCs). The scanning electron microscope image of the SC3 waveguide array is shown in Fig. 4(b). Here, the waveguide pitch is 775 nm.
Fig. 4. Characterization of fabricated SC3 waveguide array. (a) Microscope image. (b) SEM image. (c) Normalized measured transmission spectra. For each input waveguide i, only Ti,i ± 1 plus the worst are shown to avoid a cluttered view. (d) Transmission statistics of all measured transmission spectra.
In the experiment, we used a tunable continuous wave laser (Keysight 81960A) and a power meter to characterize the device’s optical performance. Before being injected onto the chip from the selected waveguide input port (Ii), light from the laser source was firstly adjusted to be TE-polarized by a polarization controller. Then, after passing through the device, the output light power from output ports (i.e., O1–O9) was recorded by a power meter. The spectral responses of the devices are normalized to that of the reference GCs which is fabricated on the same chip. And, GCs were utilized to couple light in to and out of the chip while the coupling loss is ∼6.5 dB/facet.
Figure 4(c) shows the measured transmission spectra of the fabricated device, which are normalized according to the reference grating coupler (GC). When the light was injected into the input port for one of waveguides I1, I2, . . ., I9, the transmissions of the TE0 mode were measured at all output ports. From these figures, one can find that the IL of the waveguide array is low and the crosstalk remains below about −19 dB from 1500 nm to 1580 nm. The statistics of each transmission spectrum at 1550 nm are shown in Fig. 4(d). Based on these measured results, it can be found that the device has an IL of 1 dB and crosstalk of −21 dB at 1550 nm. Note that, the experimental results quantitatively agree with the simulations. Meanwhile, compared with the simulated ILs and crosstalk, the measured results might be a little larger. This could be attributed to additional losses from fabrication processes and the noise floor of our experimental setup.
4. Advanced concept for flexible design
Our concept could also be used to obtain other types of low-crosstalk nanohole metamaterial enabled waveguide arrays, if we properly control the effective propagation constant difference between adjacent waveguides and then create the phase mismatch condition. To demonstrate the design flexibility, we have designed a 100-µm long waveguide array, which consists of two SC4 supercells. As shown in Fig. 5(a), each SC4 supercell is composed of four different waveguides, including a straight waveguide, a nanohole metamaterial waveguide with a diameter of d1, a nanohole metamaterial waveguide with d2, and a nanohole metamaterial waveguide with d3. Here, d1, d2, and d3 are set to 90 nm, 120 nm and 60 nm, respectively. Meanwhile, the waveguide pitch is set to 775 nm. Figures 5(b) and (c) display the simulated results, revealing that the ILs of all input waveguides are as low as 0.3 dB and the crosstalk is lower than −21 dB from 1500 nm to 1580 nm.
Fig. 5. Design and characterization of a SC4 waveguide array. (a) Schematic configuration. (b) Simulated transmission spectra. (c) Transmission statistics of all simulated transmission spectra. (d) SEM picture of the fabricated device. (e) Measured transmission spectra. (f) Transmission statistics of all measured transmission spectra at 1550 nm. Note that, for each input waveguide i, only Ti,i ± 1 plus the worst are shown to avoid a cluttered view in (b) and (e). Meanwhile, for clear illustration, transmissions of some channels are not shown in (f), when they are lower than −80 dBm (the noise floor of our measurement setup).
We then fabricated and characterized the SC4 high-density waveguide array. Figure 5(d) shows the SEM image of the device while Fig. 5(e) and 5(f) show the measured transmission spectra and transmission statistics of the fabricated waveguide array. It can be observed that the IL of the array is 0.5 dB and the crosstalk is −20.8 dB at 1550 nm. Meanwhile, the crosstalk remains below approximately −15.2 dB from 1500 nm to 1580 nm. Based on the results, one can find that the low-crosstalk silicon photonic metamaterial enabled waveguide array shows promising design flexibility.
5. Discussion
We have proposed a concept to suppress the crosstalk between adjacent waveguides and then demonstrated silicon photonic metamaterial enabled high-density waveguide arrays. In the experiment, the 100-µm-long SC3 device we designed and tested had a low IL of 1 dB and crosstalk of −21 dB at 1550 nm. Meanwhile, the crosstalk is lower than −19 dB across a wide range of wavelengths from 1500 nm to 1580 nm. With a half wavelength pitch and very low crosstalk, our experiment results have demonstrated the potential for significantly improving waveguide density limits and associated performance limits.
Moreover, the potential benefits of our metamaterial enabled waveguide array extend beyond its low crosstalk and high density. The favorable design flexibility of our proposed waveguide array suggests that it may also be a robust solution for practical applications. In our experiment, the waveguide array demonstrated (SC4 waveguide array) provides such an example of the versatility of our design approach. By including multiple waveguide types in a single waveguide array, we have shown that our metamaterial waveguide array has the potential to enhance the functionality of Si photonic devices and systems.
Overall, we believe that our work presents a significant advancement in the field of Si photonic devices and systems. The potential benefits of our metamaterials enabled high-density waveguide array make it a promising candidate for future applications in integrated photonics, optical communication systems, and other related areas.
Funding
National Natural Science Foundation of China (62275149, U23A20356); Shanghai Education Development Foundation; Shanghai Municipal Education Commission.
Acknowledgments
We acknowledge funding from National Natural Science Foundation of China (62275149, U23A20356) and “Shuguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission. We thank the support of device fabrication by the Center for Advanced Electronic Materials and Devices of Shanghai Jiao Tong University.
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.
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