1. Introduction

In recent years, the demands for the transmission capacity of communication systems have increased significantly due to the exponential growth of cloud services and data centers. The optical interconnect technology has attracted intensive attention due to its potential to enable ultra-high-capacity data transmission. Particularly, transmission capacity can be further increased by utilizing several multiplexing technologies, such as wavelength division multiplexing (WDM) [1,2], mode division multiplexing (MDM) [3], and polarization division multiplexing (PDM) [4]. Among them, WDM is one of the most successful technologies, which greatly increases the link capacity by utilizing multiple wavelength channels, and has been widely applied in communication systems [5]. However, the number of wavelength channels is difficult to increase infinitely in a limited bandwidth due to the limitations of the laser linewidth and crosstalk between adjacent channels. Moreover, in WDM systems, each wavelength channel requires an independent laser source, which increases the system cost and complexity with the increase of wavelength channels. A promising method is utilizing other properties of light to further increase the transmission capacity, and the emergence of MDM and PDM provides new dimensions for multiplexing technology. Therefore, it’s valuable to combine multi-wavelengths, multi-modes, and dual-polarizations to realize hybrid (de)multiplexing systems. In this way, the data transmission capacity of optical interconnect systems can be further increased [6,7].

Silicon photonics is one of the most attractive implementations to achieve a high-performance on-chip hybrid (de)multiplexer because of its complementary metal-oxide semiconductor (CMOS) compatibility, high-volume production, and high manufacturing accuracy [8–12]. In addition, the high-index contrast of silicon waveguides provides high confinement of the optical field within a small core which enables a small bending radius to achieve high integration densities for various functions compared with other materials such as lithium niobate [13–15] and silicon nitride [16–19]. The development of silicon-based hybrid (de)multiplexers has made considerable progress. For example, in [20] and [21], a silicon-based 64-channel hybrid MDM-WDM (de)multiplexer was demonstrated by integrating a 4-mode-channel (de)multiplexer based on asymmetric directional couplers (ADCs) and 16-wavelength-channel (de)multiplexers based on arrayed-waveguide-grating (AWG) with a wavelength spacing $\Delta {\lambda }_{ch}$ = 3.2 nm. The crosstalk of the adjacent wavelength channel is about −10 dB$\sim$−15 dB. In [4], an 18-channel hybrid PDM-WDM (de)multiplexer was realized by combining two 9-wavelength-channel bi-directional AWG with a polarization diversity circuit based on a polarization rotator (PR) and a polarization-beam splitter (PBS). The wavelength spacing ($\Delta {\lambda }_{ch}$) is 3.2 nm and the crosstalk between adjacent wavelength channels is about −13 dB. However, the performance of AWG is seriously sensitive to phase errors. Several silicon-based wavelength division multiplexers were realized with compact microring resonators (MRRs) [22–26]. As demonstrated in [23], a 64-channel hybrid MDM and WDM multiplexer consisting of a 4-channel mode (de)multiplexer and two 16-wavelength-channel (de)multiplexers based on bi-directional MRRs. A thermal tuning electrode was added to calibrate the deviation to eliminate the influence of fabrication errors and temperature on resonance wavelength. In [26], a 96-channel hybrid PDM-MDM-WDM (de)multiplexer was achieved by monolithically integrating a 6-channel mode/polarization (de)multiplexer and six 16-wavelength-channel (de)multiplexers.

In this paper, we proposed a 128-channel hybrid MDM-PDM-WDM (de)multiplexer by monolithically integrating an 8-channel hybrid MDM-PDM multiplexer and four 16-wavelength-channel (de)multiplexers based on bi-directional MRRs arrays. The 8-channel MDM-PDM (de)multiplexer was realized by a polarization beam splitter (PBS) and cascaded six asymmetric directional couplers (ADCs) for TE and TM modes. The advantages of this type mainly include low loss, low crosstalk, and compact footprints. The WDM configuration presented in this study utilizes bi-directional MRR arrays, resulting in a smaller footprint in comparison to alternative filter structures, such as AWGs [27,28], Bragg gratings [29–31], and cascaded Mach-Zehnder interferometers (MZIs) [32–35]. In addition, in order to eliminate the influence of fabrication errors and environmental temperature on the resonance wavelength of the MRR, a multi-wire TiN thermal tuning electrode is added to calibrate the deviation of the wavelength. For the fabricated 128-channel hybrid MDM-PDM-WDM (de)multiplexer, the insertion loss is 3$\sim$8.5 dB, the inter-mode crosstalk is −7$\sim$−23 dB, and the inter-wavelength crosstalk is −8$\sim$−20 dB. The resonance wavelength of MRRs is calibrated by thermal tuning with a tuning efficiency of 0.45nm/mW, and the wavelength spacing ($\Delta {\lambda }_{ch}$) is approximately controlled to 1.4 nm. The demonstrated hybrid (de)multiplexer can be further extended by increasing mode and wavelength channels.

2. Device design and principle

As shown in Fig. 1, the hybrid (de)multiplexer is realized by monolithically integrating an 8-channel hybrid MDM-PDM (de)multiplexer and four 16-wavelength-channel bi-directional MRR arrays. The hybrid MDM-PDM (de)multiplexer on the left side of Fig. 1 is for measurement. The hybrid MDM-PDM (de)multiplexer operates with four transverse electric (TE) modes ($\textrm{TE}_{0}$, $\textrm{TE}_{1}$, $\textrm{TE}_{2}$, and $\textrm{TE}_{3}$) and four transverse magnetic (TM) modes ($\textrm{TM}_{0}$, $\textrm{TM}_{1}$, $\textrm{TM}_{2}$, and $\textrm{TM}_{3}$). The WDM (de)multiplexer configuration entails the utilization of sixteen MRRs within each MRR array, effectively separating the signals into sixteen distinct wavelengths. To further reduce the footprints of the hybrid (de)multiplexer, a bi-directional operation scheme is employed for the MRR arrays. It connects two adjacent output ports of the MDM-PDM demultiplexer, resulting in a reduction of the number of MRRs by half. The wavelength spacing between adjacent channels ($\Delta {\lambda }_{ch}$) is 1.4 nm. In addition, a thermal tuning electrode was added to eliminate the influence of fabrication errors and environmental temperature on resonance wavelength. It can be found that the electrodes are cascaded between adjacent MRRs. The purpose of utilizing this structure is to reduce the number of metal pads and thereby reduce the size of the device. Compared with the non-cascaded electrode structure, the flexibility of the thermal tuning may be reduced. Still, it also can achieve thermal tuning for each MRR by simultaneously adjusting the voltage on all pads. For the hybrid MDM-PDM-WDM (de)multiplexer, there are eight input ports for the signals, including $\textrm{TE}_{0}$ modes ($\textrm{I}_{11}{\sim }\textrm{I}_{14}$) and $\textrm{TM}_{0}$ modes ($\textrm{I}_{21}{\sim }\textrm{I}_{24}$). When the optical signal is coupled into the $\textrm{I}_{11}$ port and $\textrm{I}_{21}$ port, the input fundamental modes will remain unchanged. For light coupled into $\textrm{I}_{12}{\sim }\textrm{I}_{14}$ ports and $\textrm{I}_{22}{\sim }\textrm{I}_{24}$ ports, the fundamental modes will convert into $\textrm{TE}_{1}{\sim }\textrm{TE}_{3}$ and $\textrm{TE}_{1}{\sim }\textrm{TE}_{3}$ modes, respectively. When signals arrive at the output port of the bus waveguide, they are all demultiplexed into $\textrm{TE}_{0}$ modes ($\textrm{O}_{11}{\sim }\textrm{O}_{14}$) and $\textrm{TM}_{0}$ modes ($\textrm{O}_{21}{\sim }\textrm{O}_{24}$), and then two adjacent modes are transferred into the same MRR array. Each MRR array can operate bi-directionally and has two drop ports, and thus signals with identical wavelengths and different modes can be separated.

 

Fig. 1. Schematic diagram of the proposed MDM-PDM-WDM (de)multiplexer.

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2.1 Mode and polarization (de)multiplexer

The hybrid MDM-PDM (de)multiplexer is realized by combining two four-channel modes (de)multiplexers for TE polarization and TM polarization, as shown in Fig.2 (a). The splitting and combining of two fundamental modes ($\textrm{TE}_{0}$ and $\textrm{TM}_{0}$) are accomplished using a PBS, while the (de)multiplexing of the high order modes ($\textrm{TE}_{1}$, $\textrm{TE}_{2}$, $\textrm{TE}_{3}$, $\textrm{TM}_{1}$, $\textrm{TM}_{2}$, and $\textrm{TM}_{3}$) is achieved through the cascaded ADCs. The optical signal of $\textrm{TE}_{0}$ mode is input from $\textrm{I}_{11}{\sim }\textrm{I}_{14}$, and the optical signal of $\textrm{TM}_{0}$ mode is input from $\textrm{I}_{21}{\sim }\textrm{I}_{24}$. When the optical signal is coupled into the $\textrm{I}_{11}$ port and $\textrm{I}_{21}$ port, the light will remain in the $\textrm{TE}_{0}$ mode and $\textrm{TM}_{0}$ mode, respectively. The optical signals that are coupled into the bus waveguide from other ports will be converted into corresponding high-order modes. After propagating through the bus waveguide, the optical signals will be de-multiplexed and grouped into the MRR arrays.

The PBS is achieved by using a three-waveguide coupler, as shown in Fig. 2(b). The overall structure of the PBS can be interpreted as a wide waveguide in the middle and two narrow waveguides on the sides. The input $\textrm{TM}_{0}$ mode undergoes two consecutive mode conversion processes. Initially, the $\textrm{TM}_{0}$ mode in the narrow waveguide is coupled into the wide waveguide, where it undergoes mode conversion and is transformed into the $\textrm{TM}_{1}$ mode. Subsequently, the $\textrm{TM}_{1}$ mode is coupled to another narrow waveguide, where it undergoes another mode conversion process and is converted back to the original $\textrm{TM}_{0}$ mode. To achieve a high-efficiency mode conversion, the widths of the narrow waveguides and the wide waveguide should be optimized to satisfy the phase-match condition between the $\textrm{TM}_{0}$ mode in the narrow waveguide and the $\textrm{TM}_{1}$ mode in the wide waveguide. The coupling length and the gap between the narrow waveguide and the wide waveguide also should be optimized to enable high coupling efficiency. The width of the narrow waveguide ($w_{a1}$, $w_{a2}$) is 400 nm to keep single mode, and the gap between the narrow waveguide and the wide waveguide ($w_{gap1}$, $w_{gap2}$) is 300 nm. The three coupling lengths $L_{1}$, $L_{2}$, and $L_{3}$ of the PBS are 8 $\mu$m, 3 $\mu$m, and 9 $\mu$m, respectively. On the other hand, the input $\textrm{TE}_{0}$ mode will not be coupled into the wide waveguide in the middle because of the unsatisfied phase-matching condition, and it will propagate along the bus waveguide without extra loss. Figure 3(a) and (b) show the simulated light propagation for the $\textrm{TE}_{0}$ mode and $\textrm{TM}_{0}$ mode in the designed PBS. We conducted simulations to analyze the spectral characteristics of the PBS by using the bus waveguide as the input, as shown in Fig. 3(c) and (d). It can be seen that when the $\textrm{TM}_{0}$ mode inputs, the PBS has a poor extinction ratio of about 8 dB. But in the entire hybrid MDM-PDM-WDM (de)multiplexer, the poor polarization extinction ratio has little impact on overall performance. The main reason is that although about 10 % of the power of the light will be output from the through port, the optical signal remains in $\textrm{TM}_{0}$ mode and will not be coupled into the subsequent MRR arrays.

 

Fig. 2. (a) Schematic diagram of the hybrid MDM-PDM (de)multiplexer; Zoomed-in view of the PBS (b) and ADC (c).

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Fig. 3. Light propagation of the $\textrm{TE}_{0}$ mode (a), and $\textrm{TM}_{0}$ mode (b) in PBS. Calculated transmission spectra of the launched $\textrm{TE}_{0}$ mode (c), and $\textrm{TE}_{1}$ mode (d).

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The couplings of high-order modes are realized by using six cascaded ADCs, as shown in Fig. 2(a). The input optical signal is coupled into the bus waveguide and converted to the corresponding high-order mode. To satisfy the phase-matching, the width of the access waveguide is 400 nm, and the corresponding width of the bus waveguide for $\textrm{TE}_{1}$, $\textrm{TE}_{2}$, $\textrm{TE}_{3}$, $\textrm{TM}_{1}$, $\textrm{TM}_{2}$, and $\textrm{TM}_{3}$ modes are 0.83 $\mu$m, 1.29 $\mu$m, 1.63 $\mu$m, 1.03 $\mu$m, 1.69 $\mu$m, and 2.36 $\mu$m, respectively. Figure 4 shows the simulated light propagation of the six high-order modes in the designed ADCs. Figure 5 shows the simulated transmission spectra of the launched high-order modes in the corresponding coupler in the wavelength range of 1480-1520 nm. It can be seen that light is efficiently coupled into the bus waveguide and converted to the desired high-order mode, and the simulated crosstalks of ADCs are less than −20 dB.

 

Fig. 4. Light propagation of $\textrm{TE}_{1}$ (a), $\textrm{TE}_{2}$ (b), $\textrm{TE}_{3}$ (c), $\textrm{TM}_{1}$ (d), $\textrm{TM}_{2}$ (e), and $\textrm{TM}_{3}$ (f) modes in cascaded ADCs.

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Fig. 5. Simulated transmission spectra of the launched $\textrm{TE}_{1}$ (a), $\textrm{TE}_{2}$ (b), $\textrm{TE}_{3}$ (c), $\textrm{TM}_{1}$ (d), $\textrm{TM}_{2}$ (e), and $\textrm{TM}_{3}$ (f) modes in the corresponding ADC.

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2.2 Wavelength (de)multiplexer

Figure 6(a) shows the schematic diagram of the MRR and TiN thermal tuning electrode. The wavelength (de)multiplexer consists of four MRR arrays with sixteen wavelength channels. Each MRR operates bi-directionally and has two drop ports, which separate the signals carried by the same wavelength and adjacent modes. In this way, the number of MRRs can be reduced by half, and thus the footprint of the device can be effectively reduced. For example, the light input from $\textrm{I}_{13}$ and $\textrm{I}_{14}$ will excite $\textrm{TE}_{2}$ mode and $\textrm{TE}_{3}$ mode, and the group of optical signals including sixteen wavelength-channels are de-multiplexed and dropped from ports $\textrm{O}_{13}$ and $\textrm{O}_{14}$, and then go through MRR${\#}$A. The optical signals dropped from ports $\textrm{O}_{13}$ and $\textrm{O}_{14}$ propagate in opposite directions in MRR${\#}$A, and optical signals with the same wavelength are output from the two drop ports of the MRR.

 

Fig. 6. Schematic diagram of the MRR and thermal tuning electrode (a). The cross-section of the MRR waveguide(b). Simulated transmission spectra of the MRR arrays of $\textrm{TE}_{0}$ mode (a) and $\textrm{TM}_{0}$ mode (b).

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Since different polarizations correspond to different effective refractive indices, the structural parameters of the MRR for $\textrm{TE}_{0}$ mode and $\textrm{TM}_{0}$ mode are also different. The design of the MRR needs to consider two aspects. First, the FSR should be large enough to cover all multiplexed wavelengths. To avoid different wavelength channels at the same resonance wavelength, the FSR should meet the following equation:

Here N is the number of wavelength channels, and $\Delta {\lambda }_{ch}$ is the channel spacing between adjacent channels. Second, the bending loss should be small to increase the Q factor of the MRR to reduce the crosstalk between adjacent channels. The former requires a smaller radius while the latter is the opposite. Therefore, we should optimize the size of the MRR to make a trade-off between the FSR and the bending loss.

According to the simulation, the requirement is easy to achieve for the $\textrm{TE}_{0}$ mode. When we adopt the single-mode waveguide size ($500 nm \times 220 nm$) and the radius of $\textrm{TE}_{0}$ mode MRR is 3 $\mu$m, the FSR is about 30.01 nm, and the simulated bending loss is lower than 1 dB/cm, which can be negligible. Compared with the $\textrm{TE}_{0}$ mode, the bending loss of the $\textrm{TM}_{0}$ mode is more sensitive to the bending radius. If we adopt the same waveguide size with the $\textrm{TE}_{0}$ MRR, the bending loss can be negligible when the radius is larger than 15 $\mu$m, and the corresponding FSR is only 6.76 nm. To enlarge the FSR and maintain a low bending loss, we made an optimization by increasing the width of the waveguide to 850 nm and reducing the radius to 4 $\mu$m. The optimization achieves a suitable FSR of 23.52 nm while maintaining an acceptable bending loss of 42 dB/cm. The determination of the channel spacing ($\Delta {\lambda }_{ch}$) is predominantly influenced by two factors: the number of channels contained within an FSR and the level of crosstalk between adjacent channels. The channel spacing of dual polarizations is chosen to be 1.4 nm and the number of wavelength channels is 16. Here the parameters are determined by making a trade-off between the two factors to increase the number of channels while maintaining low crosstalk. Figure 6(c) and (d) show the simulated transmission spectra of TE-type and TM-type MRR arrays, respectively. The simulated inter-wavelength crosstalks between the adjacent channels of $\textrm{TE}_{0}$ mode and $\textrm{TM}_{0}$ mode are < −23 dB and < −11 dB, respectively. It must be admitted that the inter-wavelength crosstalk characteristic of $\textrm{TM}_{0}$ mode is not as good as $\textrm{TE}_{0}$ mode due to the influence of the bending loss. In addition, the gap between the microring and the bus waveguide should be optimized to approach critical coupling conditions to achieve a high extinction ratio (ER), and it is preferably within fabrication tolerances. According to the simulation results, the gap between the microring and the bus waveguide of dual polarizations are 200 nm and 250 nm, respectively.

The resonance wavelength of the MRR is seriously sensitive to environmental temperature and fabrication deviation. Therefore, we added a TiN thermal tuning electrode to each MRR to calibrate the resonance wavelength. As shown in Fig. 6(a), a multi-wire thermal tuning electrode is designed to increase the tuning efficiency and fusing current while ensuring no additional optical loss. The multi-wire structure electrode makes the heat injection surface approximate a 1D heat flow in the direction perpendicular to the MRR. The width of the electrode was 1 $\mu$m, the total length is 90 $\mu$m, and the corresponding resistance is 1000 $\Omega$. Figure 6(b) shows the cross-section of the MRR waveguide, the gap between the waveguide layer and the thermal tuning electrode layer is 850 nm, without additional optical loss.

3. Fabrication and results

The proposed 128-channel hybrid MDM-PDM-WDM (de)multiplexer is fabricated on the silicon-on-insulator (SOI) platform with a 220-nm-thick top-silicon layer and a 2-$\mu$m-thick BOX layer. Figure 7(a) shows the microscope image of the fabricated MDM-PDM-WDM (de)multiplexer. An MDM-PDM multiplexer and an MDM-PDM de-multiplexer are connected to both sides of the bus waveguide, respectively. The $\textrm{TE}_{0}$ mode ($\textrm{I}_{11}{\sim }\textrm{I}_{14}$) and $\textrm{TM}_{0}$ mode ($\textrm{I}_{21}{\sim }\textrm{I}_{24}$) grating couplers are utilized to couple optical signals in/out of the chip. The enlarged view of the PBS and ADC is shown in Fig. 7(b), and the enlarged view of the MRR with thermal tuning electrode is shown in Fig. 7(c). The (de)multiplexer has a total of 68 thermal tuning pads.

 

Fig. 7. Microscope image of the fabricated MDM-PDM-WDM (de)multiplexer (a), the enlarged view of the PBS and ADC (b), and the enlarged view of the MRR with thermal tuning electrode (c).

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The optical characterizations of the fabricated (de)multiplexer were measured. A broadband tunable laser was used as the source, and an optical spectrum analyzer (OSA) was used to record the optical power and scan the spectrum. The polarization of the injected light is adjusted by using a polarization controller (PC).

We first characterized the performance of the hybrid MDM-PDM (de)multiplexer. We set a cascaded hybrid MDM-PDM multiplexer and de-multiplexer structure on the chip to measure the transmission performance from $\textrm{I}_{\textrm{ij}}$ to $\textrm{O}_{\textrm{ij}}$. The optical signal is injected into one of the input ports, and the transmission spectra are measured at all output ports. Figures 8(a-h) show the measured transmission spectra of eight channels. Considering the actual operating wavelength range of the device, the measured wavelength range is 1480 nm-1520 nm, and it can be seen that the inter-mode crosstalks are < −25 dB, < −22 dB, < −16 dB, < −18 dB, < −20 dB, < −20 dB, < −21 dB, and < −22 dB for the launched $\textrm{TE}_{0}$, $\textrm{TE}_{1}$, $\textrm{TE}_{2}$, $\textrm{TE}_{3}$, $\textrm{TM}_{0}$, $\textrm{TM}_{1}$, $\textrm{TM}_{2}$, and $\textrm{TM}_{3}$ mode, respectively.

 

Fig. 8. Measured transmission spectra at the eight ports when an optical signal is launched at (a) $\textrm{I}_{11}$, (b) $\textrm{I}_{12}$, (c) $\textrm{I}_{13}$, (d) $\textrm{I}_{14}$, (e) $\textrm{I}_{21}$, (f) $\textrm{I}_{22}$, (g) $\textrm{I}_{23}$, (h) $\textrm{I}_{24}$.

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We then measured the transmission spectra of the fabricated hybrid MDM-PDM-WDM (de)multiplexer. To eliminate the influence of random manufacturing errors and environmental temperature on MRR, we used thermal tuning electrodes to calibrate the resonance wavelength, and the measured tuning efficiency is 0.45 nm/mW. Figures 9(a-h) show the transmission spectra of the hybrid (de)multiplexer after thermal tuning, it can be seen that the channel spacing is approximately controlled at $\Delta {\lambda }_{ch}$ = 1.4 nm. Note that the spectra of $\textrm{TM}_{1}$ and $\textrm{TM}_{2}$ mode are distorted. The distortion is mainly caused by the measurement method. We used a direct current (DC) probe to apply voltage for thermal tuning, and the resonance wavelength after the redshift overlaps with the resonance wavelength of the subsequent MRRs, resulting in spectral distortion. The distortion can be eliminated by tuning sixteen MRRs simultaneously. The on-chip insertion loss is about 3$\sim$8.5 dB for dual polarizations. The fluctuations in insertion loss are mainly caused by the dispersion of directional couplers and waveguide-to-MRR coupling coefficients, fabrication errors, and measurement errors. On the other hand, there are some deviations in the insertion loss between the hybrid MDM-PDM-WDM (de)multiplexer and the hybrid MDM-PDM (de)multiplexer mentioned above, and the insertion loss of some channels is smaller than the hybrid MDM-PDM (de)multiplexer. The deviations are mainly caused by measurement and fabrication errors, especially the fluctuations between different reference grating couplers. The hybrid MDM-PDM (de)multiplexer has 16 grating couplers, and the hybrid MDM-PDM-WDM has a total of 136 grating couplers. There are slight deviations between different grating couplers, which lead to calibration errors in the process of calculating the insertion loss. The variations of insertion loss are partly caused by measurement, including the alignment between the fiber and grating couplers, and the vibration of the test platform. The inter-wavelength crosstalks for the TE and TM polarizations are < −20 dB and < −8 dB, respectively. As shown in Fig. 9, the measured transmission spectra are in agreement with the simulation. It can be clearly seen that the Q factor of the TM-type MRR is lower than the TE-type, resulting in high inter-wavelength crosstalk. The main reason is that the TM-type MRR has a higher bending loss. Reducing the bending loss of the TM-type MRR while increasing the FSR is the key to improving the performance. The inter-mode crosstalks for the output ports are < −12 dB, < −7 dB, < −12 dB, < −14 dB, < −23 dB, < −22 dB, < −20 dB, and < −19 dB for the launched $\textrm{TE}_{0}$, $\textrm{TE}_{1}$, $\textrm{TE}_{2}$, $\textrm{TE}_{3}$, $\textrm{TM}_{0}$, $\textrm{TM}_{1}$, $\textrm{TM}_{2}$, and $\textrm{TM}_{3}$ mode, respectively. The principal factor contributing to the elevated inter-mode crosstalk levels observed in the hybrid MDM-PDM-WDM (de)multiplexer, in contrast to the mode (de)multiplexer, stems from the alteration of the optical signal’s propagation direction caused by the reflection at the end of the de-multiplexer. Consequently, the optical signal emerges from the drop port of the adjacent mode. The crosstalk can be reduced by adding a taper as an antenna at the end of the ADCs.

 

Fig. 9. Measured transmission spectra at output port $\textrm{O}_{11}$ (a), $\textrm{O}_{12}$ (b), $\textrm{O}_{13}$ (c), $\textrm{O}_{14}$ (d), $\textrm{O}_{21}$ (e), $\textrm{O}_{22}$ (f), $\textrm{O}_{23}$ (g), $\textrm{O}_{24}$ (h).

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4. Discussion and conclusion

In Table 1, we have summarized the performances of some reported hybrid (de)multiplexers. Our proposed hybrid MDM-PDM-WDM (de)multiplexer simultaneously utilized four modes, dual polarizations, and sixteen wavelengths to enhance the transmission capacity. Compared to other works, this work utilized more dimensions to realize more channels and reduced the channel spacing to increase the number of wavelength channels within a fixed wavelength range. In terms of the device footprint, compared with the AWG structure, the MRR structure has a natural advantage in footprint, and the use of the bi-directional MRR structure makes the device more compact. Moreover, we used a high-efficiency thermal tuning electrode for each MRR to calibrate the resonance wavelength. But it must be admitted that this work still has some aspects that need to be optimized. For example, the inter-wavelength crosstalk decreased due to the reduction of the wavelength spacing, and we can optimize the Q factor of the MRR to decrease the inter-wavelength crosstalk. If the bending loss of the $\textrm{TM}_{0}$ mode is hard to reduce, we can set a polarization rotator (PR) at the output of each high-order TM mode coupler to convert $\textrm{TM}_{0}$ mode to $\textrm{TE}_{0}$ mode, and ultimately perform WDM in the TE-type MRR arrays. In this way, the inter-wavelength crosstalk of the $\textrm{TM}_{0}$ mode can be reduced. The inter-mode crosstalk can be further decreased by reducing the reflection at the end of the mode de-multiplexer. Furthermore, there exists additional potential for optimization with regard to the optical bandwidth and fabrication tolerance. The PBS based on the bent directional coupler, and mode (de)multiplexer based on adiabatic directional coupler have significant advantages in these areas. In our subsequent work, we will focus on optimizing the structure of the device to improve its performance.

Table 1. Summary of the reported silicon hybrid (de)multiplexer.

View Table

In summary, we proposed and demonstrated a silicon-based 128-channel hybrid MDM-PDM-WDM (de)multiplexer, which utilized simultaneously dual polarizations, four modes, and sixteen wavelengths to enhance the transmission capacity. The device consists of an 8-channel MDM-PDM multiplexer and four bi-directional MRR arrays with sixteen wavelength channels. The measurement results show the insertion loss is 3$\sim$8.5 dB, the inter-mode crosstalk is −7$\sim$−23 dB, and the inter-wavelength crosstalk is −8$\sim$−20 dB. We used thermal tuning electrodes with a tuning efficiency of 0.45 nm/mW to calibrate resonance wavelengths, and the channel spacing is approximately controlled to 1.4 nm. It is believed that the demonstrated device has great potential for next-generation low-cost and high-speed optical communication networks.