In recent years, data traffic has grown explosively due to global digitalization, and high-capacity optical interconnects have received much attention with the increasing massive data [1,2]. As the backbone of modern communication networks, the single-mode fiber (SMF) communication system has been extensively studied. Unfortunately, the SMF system utilizing wavelength-division multiplexing (WDM) and advanced optical modulation technologies is now hitting its theoretical capacity ceiling [3–5]. Mode-division multiplexing (MDM), which utilizes multiple orthogonal modes as an independent signal carrier, is capable of further increasing the transmission capacity of the optical waveguide, and thus is regarded as a promising option for next-generation high-capacity data transmissions. Currently, the MDM technology has been widely investigated in not only optical fiber transmission systems utilizing few-mode fibers (FMFs) [6,7] but also on-chip optical networks for shot-reach optical interconnection [8–10]. However, these two systems are not connected yet conveniently due to the huge difference of mode properties. A multimode coupler for efficient coupling between silicon photonic chips and FMFs becomes extremely important for optical networks to transmit massive data in low-loss FMFs and process data on large-scale photonic chips.

In principle, the most formidable challenge to design a multimode fiber-chip coupler is the huge mode mismatch between an FMF and a silicon photonic waveguide, which induces high coupling loss and intermode crosstalk. Great efforts have been made to address this problem by using grating couplers [11–20] and edge couplers [21–30]. Basically, grating coupling features the advantages of compact footprints, large misalignment tolerances, and wafer-scale testing convenience [11]. By utilizing the directionality of two-dimensional gratings, a four-channel multimode coupler for the LP01 and LP11 modes is proposed and demonstrated with peak coupling losses of 4.9 dB and 6.1 dB in a 3-dB bandwidth of 20 nm [17]. For the 2D multimode grating coupler (incorporated with phase shifters) reported very recently [31], only four mode-channels can be coupled selectively from the set of eight modes. Nevertheless, the inherent narrow bandwidth and polarization sensitivity of grating couplers hinder the further performance improvement, and it is still difficult to be scaled for more mode-channels.

In contrast, the edge coupling method potentially presents the advantages of low losses and large bandwidths if the mode mismatching can be minimized. In Refs. [22–24], multimode couplers based on multi-tip waveguides are proposed, and it is possible to achieve coupling losses of ∼7dB for the LP01 and LP11a modes in a broad bandwidth of ∼100nm [23]. It should be mentioned that these schemes can only work for lateral higher-order modes (e.g., the LP11a mode) due to the core height restriction of silicon photonic waveguides. A potential solution is introducing a dual-core waveguide by depositing an additional SiN or polymer outer-core upon the silicon core to accommodate the LP11b modes [27,28]. Theoretically, the six TE or TM modes in a silicon photonic waveguide can evolve to the linearly polarized (LP) modes in the outer-core waveguide adiabatically. However, the fabrication of these dual-core waveguides needs special processes and is incompatible with standard fabrication processes. Alternative approaches are to use specially processed fibers to reduce the mode mismatch, such as a tapered FMF or a rectangular FMF [29,30,32]. More recently, a multimode coupler is proposed to realize the coupling of the LP01/LP11a modes by inserting a metasurface structure between the fiber and the chip [33]. Besides, a femtosecond-inscribed photonic lantern incorporated with three fiber-based polarization beam splitters (PBSs) was proposed for FMF-chip coupling [34]. However, these mentioned methods are either difficult for massive fabrication or packaging. It is still very challenging to realize on-chip high-efficiency multimode couplers enabling the simultaneous launching of six LP01-x/y, LP11a-x/y, and LP11b−x/y mode-channels in an FMF, which has not been reported yet.

In this paper, we propose a novel scheme for efficient multimode coupling between a silicon photonic chip and an FMF by introducing silica planar lightwave circuits (PLCs) as an intermediate for the first time. Despite that the PLCs have been used as the interposer to be connected with the dense optical I/Os on silicon for single-mode coupling previously [35–37], the situation becomes totally different for the case of multimode coupling. Here the multimode PLC chip with a polarization-insensitive mode (de)multiplexer serves as an indispensable element for mode (de)multiplexing and mode conversion. With the present scheme, each mode-channel in the FMF is efficiently coupled/demultiplexed into the corresponding TE0 or TM0 mode in silicon photonic waveguides, which can be connected with any other photonic devices on the chip, such as wavelength filters, optical modulators, or photodetectors for realizing optical transmitters/receivers. As a proof of concept, a six-channel multimode FMF-chip coupler/(de)multiplexer is designed and demonstrated, showcasing excellent performances with low overall excess losses of 0.77–1.39 dB and low intermode crosstalk of <−27.2dB for the six mode-channels over a broad wavelength range of 150 nm in theory. Experiment results show that the minimum coupling loss of 1.36–2.48 dB and low intermode crosstalk of <−14.2dB for all six modes can be realized. The 1-dB bandwidths are ∼80nm, 60 nm, and 55 nm for LP01-x/y, LP11a-x/y, and LP11b-x/y modes, respectively. The proposed concept of multimode coupling holds great promise for the development of next-generation MDM systems.

Considering the scenario of connecting an FMF and a silicon photonic chip, the major obstacle for efficient multimode coupling lies in the huge mode mismatch between the FMF and the sub-micron silicon photonic waveguides, especially for the higher-order modes with more than one peak in the vertical direction. As it is well known, FMFs are mainly used for data transmissions and photonic chips are often used for data transmitting/receiving/routing in MDM systems. Therefore, it is preferred to (de)multiplex and finally couple the fundamental/higher-order mode-channels in an FMF to the fundamental modes in silicon photonic waveguides.

Figure 1 shows the proposed novel scheme of photonic chips enabling the mode (de)multiplexing and multimode coupling for the FMF-chip connections. As a representative example, here we consider the case with the LP01-x/y, LP11a-x/y, and LP11b-x/y mode-channels supported in the FMF. The proposed coupling scheme consists of a multimode edge coupler using multimode waveguide segments (MWSs), a three-channel dual-polarization PLC mode (de)multiplexer, bi-level multicore dual-polarization spot-size converters (SSCs), and PBSs on a silicon photonic chip. The LP01-x/y, LP11a-x/y, and LP11b-x/y modes launched from the FMF are efficiently butt-coupled to the multimode silica optical waveguide via the MWSs. Then the PLC-based polarization-insensitive mode (de)multiplexer is used to demultiplex these three guided-modes into the LP01-x/y modes supported in the three single-mode silica optical waveguides. These LP01-x/y modes are then butt-coupled to the TE0/TM0 modes in the corresponding silicon photonic waveguides via the SSCs. Finally, the TE0/TM0 modes are separated with three PBSs on the silicon chip. The silicon PBSs are realized by using three cascaded directional couplers; the illustration is also shown in Fig. 1. The first bent directional coupler is used to separate the TE/TM polarization based on the phase-matching condition, and the other two directional couplers act as a key role for filtering out the undesired weak cross-coupled power, thus achieving a high extinction ratio. The PBS used here features advantages of broad bandwidths, low losses, and high extinction ratios, as demonstrated in our previous work [38].

The cross-sections of the silica optical waveguides and silicon photonic waveguides are shown in the inset of Fig. 1. In this paper, a step-index FMF with a core-diameter of 14 μm and a refractive-index difference of Δn=0.3% is considered. Accordingly, the silica optical waveguides used here have a refractive-index difference of Δn=1.5%, and the Ge-doped SiO2 core regions are designed with different heights (hSiO2−1 and hSiO2−2). The core height hSiO2−1 is chosen as 6.5 μm to support the LP01, LP11a, and LP11b modes, while the singlemode silica optical waveguides are designed with a core height of hSiO2−2=4μm according to the singlemode condition. The core height of the silicon photonic chip hSi is chosen as 220 nm, which is popularly used for silicon photonics.

Figure 2(a) shows the schematic configuration of the proposed PLC chip, which consists of the mentioned MWS-based multimode edge coupler and a three-channel polarization-insensitive mode (de)multiplexer. The design of each section is described in detail below.

Since the cross-section of the FMF used in this work is much larger than that of the multimode silica optical waveguide, we introduce an MWS-based multimode edge coupler to improve the coupling efficiency, as shown in Fig. 2(b). Previously, a segment waveguide formed with interleaved low- and high-index regions of silica, which can expand the spot size of the optical field in the silica optical waveguide, has been used to improve the coupling efficiency between the fundamental modes of a single-mode fiber and a single-mode silica optical waveguide [39]. Here we develop an MWS to expand the mode fields of not only the fundamental modes but also the higher-order modes (i.e., the LP01-x/y, LP11a-x/y, and LP11b-x/y modes) for better mode matching with the FMF. In particular, the present MWS-based multimode edge coupler can be fabricated easily with a single-step etching process, which is much simpler than those 3D inverse taper couplers reported previously [28]. The mode confinement ability of the MWS as well as the corresponding optical-field spot sizes can be optimized by modifying its duty cycle f=a/Λ, where a is the length of the segment and Λ is the period. In this way, one can achieve excellent mode matching between the MWS and the FMF when appropriately choosing the duty cycle f1 at the facet. On the other hand, the duty cycle f1 is varied gradually along the MWS to be f2 at the other end, where f2 should be maximized to decrease the index abruption and minimize the transmission loss. Here, we choose f2=0.8, and correspondingly the minimum gap is 1.08 μm, according to the minimal feature size allowed by the lithography process available in our lab.

For the MWS-based multimode edge coupler, the total coupling loss includes two parts, i.e., the mode mismatch loss and the mode transmission loss. The former one is often evaluated by the overlap coupling efficiency between the modal fields of the FMF and the silica optical waveguide, which is mainly determined by the duty-cycle f1 and the waveguide width wm. The MWS is roughly equivalent to a channel waveguide with the same width and a lowered refractive-index-contrast Δn′=Δn·f1. Figures 3(a)–3(c) show the calculated mode mismatch loss between the LP01, LP11a, and LP11b modes in the FMF and the corresponding modes in the silica optical waveguide as a function of f1 when choosing different core widths wm. The solid and dashed curves respectively refer to the x-polarization and the y-polarization. Notably, the coupling is polarization insensitive due to the low-index-contrast of silica optical waveguides. Besides, it should also be pointed out that the core width wm has a remarkable influence on the mode mismatch loss for both LP01 and LP11a modes (which are sensitive to the width variation). In contrast, the core width wm has a slight influence on the mode mismatch loss for the LP11b mode, because the LP11b mode is mainly determined by the waveguide thickness. The design with wm=12μm is chosen to minimize the mode mismatch losses for both LP01 and LP11a modes. Moreover, the LP01, LP11a, and LP11b modes achieve their lowest mode mismatch loss when f1=0.2, 0.22, 0.35, respectively, and here we choose f1=0.35 as a trade-off. Accordingly, the mode mismatch losses are as low as 0.39 dB, 0.28 dB, and 0.40 dB for the LP01, LP11a, and LP11b modes in theory, respectively.

The mode transmission loss is mainly caused by the radiation due to the index-abruption of the segments. The segment period Λ should be short enough to make sure that light is well confined in the MWS, while the period number N should also be chosen appropriately to make the segments varied gradually from f1=0.35 to f2=0.8. Figures 3(d)–3(f) show the calculated overall coupling loss as the segment period Λ varies at the wavelength of 1550 nm. The period number N is chosen as 60. The coupling loss increases greatly when increasing the segment period Λ, and low transmission losses are achieved for all the LP01, LP11a, and LP11b modes when Λ<10μm.

Figures 3(g)–3(i) give a comparison of the overall coupling loss between the FMF and the PLC chip when using the present MWS structure and the ordinary channel waveguide without the MWS structure, respectively. The parameters of the MWS are given as Λ=5.4μm, f1=0.35, f2=0.8, wm=12μm, and N=60, while the channel waveguide is chosen optimally as wm=12μm and h=6.5μm. The simulated overall coupling losses between the FMF and the channel waveguide are 1.28 dB, 1.82 dB, and 3.16 dB for the LP01, LP11a, and LP11b modes, respectively. In contrast, when using the MWS structure, the coupling losses are significantly decreased to 0.46 dB, 0.51 dB, and 0.57 dB for LP01, LP11a, and LP11b modes, respectively. The simulated light propagation from the silica multimode waveguide to the FMF is also shown in the insets, showing successful optical-field expansion with the assistance of MWSs.

The PLC-based mode (de)multiplexer is the vital building block for the present scheme. Previously, there have been several types of structures proposed [40,41], while none of them are developed with high compatibility for coupling with silicon photonic chips. Here a three-channel PLC-based polarization-insensitive mode (de)multiplexer is proposed as an example, as illustrated in Fig. 2(a). The present PLC-based mode (de)multiplexer consists of coupler #a, a mode rotator, and coupler #b. At the input end, the multimode silica optical waveguide with a core height of hSiO2−1 (which is the same as that for the MWS) supports the LP01, LP11a, and LP11b modes. For the single-mode silica optical waveguide at the output end, the core height is chosen as hSiO2−2 to support the LP01 mode only, and a square-like core region is designed to be suitable for efficient coupling with a polarization-insensitive SSC on the silicon photonic chip.

The launched LP01 mode goes through the bus waveguide directly and is output from port O1, while the launched LP11a mode is demultiplexed to the LP01 mode in the access waveguide connected to port O2 by the coupler #a. Meanwhile, the launched LP11b mode goes through coupler #a with low loss and low crosstalk, because the coupling coefficient between the LP11b mode and the LP01 mode of the access waveguide modes is very weak due to their opposite mode field symmetry [42]. After that, the LP11b mode is rotated to the LP11a mode by using the mode rotator formed on the bus waveguide, and is finally demultiplexed to the LP01 mode in the access waveguide connected to port O3 by coupler #b.

Figure 2(c) shows the schematic configuration of the mode (de)multiplexer based on an adiabatic directional coupler for couplers #a and #b (which are designed with different heights). Here the widths of the bus waveguide wb and the access waveguide wa are both tapered with a length of Lc to realize an adiabatic mode evolution, and therefore the couplers have broad bandwidth and large fabrication tolerances. The gap between these two waveguides is set as wg. Figures 4(a) and 4(b) show the calculated effective indices of the guided-modes in silica optical waveguides with different core heights of 6.5 and 4 μm as the core width w varies. The core widths are carefully chosen according to the design rule given in Refs. [8,43]. Here (wa1, wa2, wb1, wb2, wg, Lc) are both chosen as (1.3, 2.5, 7.0, 4.5, 2.5, 3000) μm for couplers #a and #b. Figures 4(c)–4(j) show the simulated transmissions of the designed couplers (#a and #b) when the LP01 and LP11a modes are launched, respectively. The simulated light propagation in them is also given in the insets when operating at the wavelength of 1550 nm. It can be seen that the LP11a mode is efficiently coupled to the LP01 mode in the access waveguide while the launched LP01 mode stays in the bus waveguide. The designed PLC mode (de)multiplexers have a low excess loss of <0.08dB and low intermode crosstalk of <−36.4dB over a broad wavelength range of 1480–1630 nm.

The coupling of the LP11b modes is not easy due to its vertical anti-symmetry mode field. Therefore, we introduce a mode rotator based on a bi-level taper with vertical asymmetry, as shown in Fig. 5(a). With such a two-layer axis-twist waveguide, the LP11 mode can be rotated efficiently, which is similar to the twist waveguide [44,45]. In principle, the waveguide at the input end should have a small aspect ratio for supporting the LP11b mode but prohibiting the LP11a mode. In contrast, the waveguide at the output end is twisted to have a large aspect ratio for supporting the LP11a mode but prohibiting the LP11b mode. The tiny tip on the upper layer can be formed by using a mask with an appropriate angle with respect to the waveguide. Here the core width wr1 at the input end is chosen as 4 μm to filter out the residual power of the LP11a mode in the bus waveguide of coupler #a. The core width wr2 at the output end is chosen as 7 μm, which is identical to the core width wa1 of coupler #b to support the LP11a mode. The length of the mode rotator Lr is chosen optimally so that the LP11b mode can be completely converted to the LP11a mode. Figure 5(b) shows the calculated power transmission as the length Lr varies. As it can be seen, when Lr is chosen to be longer than 1500 μm, the rotation can be realized with a sufficiently low loss of <0.02dB. Figures 5(c) and 5(d) show the simulated light propagation and the transmission loss for the launched LP11b mode. The mode conversion is realized with a low excess loss of <0.04dB and low crosstalk of <−22.6dB over the wavelength range of ∼150nm. In addition, the transmission of the rotator with the launched LP01 mode is also shown in Figs. 5(e) and 5(f), showing that the LP01 mode passes through the mode rotator with an ultra-low insertion loss of almost zero, and low LP01−LP11b intermode crosstalk of <−47.2dB.

Figures 6(a)–6(c) show the simulated light propagation of the mode (de)multiplexer consisting of coupler #a, the mode rotator, and coupler #b when the LP01, LP11a, and LP11b modes are launched when operating at 1550 nm, respectively. It can be seen clearly that the launched LP01-x/y mode goes through the bus waveguide directly and the LP11a-x/y mode is demultiplexed by coupler #a, while the LP11b-x/y mode is rotated to LP11a-x/y mode by the mode rotator and then demultiplexed by coupler #b. All the mode-channels are efficiently demultiplexed into the fundamental modes in the single-mode silica optical waveguide as desired. Figures 6(d)–6(f) show the corresponding transmissions at ports O1, O2, and O3 of the mode (de)multiplexer when the LP01-x/y, LP11a-x/y, and LP11b-x/y modes are launched, respectively. The mode (de)multiplexer works well with low losses of <0.1dB and low intermode crosstalk less than −30.3/−27.2dB, −31.6/−33.8dB, and −30.5/−27.2dB for the LP01-x/y, LP11a-x/y, and LP11b-x/y modes in the wavelength range of 1480–1630 nm, respectively.

The analysis for the fabrication tolerance was also carried out by assuming that the core width has a variation from −0.5 to +0.5μm, as shown in Figs. 6(g)–6(i). It shows that the core width deviation affects the performance of the mode (de)multiplexer gently, and the mode (de)multiplexer exhibits the excellence with large fabrication tolerances. One might notice that the crosstalk increases slightly to ∼−21.6dB as the core width increases, which is still acceptable. In summary, the simulation results indicate that the designed PLC-based mode (de)multiplexer possesses advantages of low loss, low intermode crosstalk, and large fabrication tolerance, which is helpful as a vital building block for the FMF-chip coupler.

To achieve efficient coupling between the guided-modes in a silica optical waveguide and the TE0/TM0 modes in a silicon photonic waveguide, a bi-level multicore polarization-insensitive SSC is proposed, as shown in Figs. 7(a) and 7(b). The strip silicon photonic waveguide evolves to a tri-core waveguide with an adiabatic taper first, and then the three cores of the trident-waveguide are separated gradually to achieve the maximum spatial overlap with the modes in the silica optical waveguide. In particular, the angle-etched bi-level tapers are introduced at the end of each core of the SSC, which efficiently weakens the mode confinement in the vertical direction. As a result, the coupling efficiency of both TE0 and TM0 modes can be improved greatly. Even though there is a very sharp waveguide tip for the SSC, the structure can be fabricated easily with an overlay process provided by a standard silicon photonics foundry.

For the design of the SSC, the mode mismatch loss of the SSC and the singlemode silica optical waveguide with a 4μm×4μm core is estimated first by calculating the mode field overlap as a function of the tip width w and gap g, as shown in Figs. 7(c) and 7(d). Here the core height at the end of the SSC is chosen as 150 nm to be compatible with the standard foundry processes. The overlap coupling efficiency is insensitive to the deviation of the tip width w when the gap g is chosen to be around 1.0 μm for TE-polarization. Notably, the TM-polarization mode even has a larger fabrication tolerance than the TE-polarization mode. Table 1 shows the parameters of the designed SSC. Figures 7(e) and 7(f) calculate the total coupling loss of the SSC when choosing different buffer layer thicknesses (hBOX). The light is likely to leak into the substrate with a thin cladding, resulting in a higher coupling loss. When the layer thickness is larger than 3 μm, the coupling loss becomes stable. Thus, a thicker cladding would be preferable. The total coupling losses of the SSC are 0.29–0.32 dB and 0.68–0.79 dB for TE- and TM-polarizations in the wavelength range of 1480–1630 nm, respectively. The light propagation of the designed SSC is also given in Figs. 7(g) and 7(h). The TE0/TM0 modal fields at the output port of the SSC are shown in the insets, respectively. According to the tolerance analysis shown in Figs. 7(i) and 7(j), an additional loss of 1.0 dB is introduced when there is a horizontal misalignment of ∼±1.5μm or a vertical misalignment of ±1.1μm. Compared with the conventional single-tip SSCs, the present bi-level multicore SSC has great performance improvements in coupling efficiency, polarization sensitivity, and bandwidth. In conclusion, the total coupling losses (i.e., from the FMF to the silicon singlemode waveguide) are ∼0.77/1.20dB, 0.86/1.29 dB, and 0.96/1.39 dB for LP01-x/y, LP11a-x/y, and LP11b-x/y modes, respectively.Table 1.

Structure Parameters of the SSC (in μm)

Figures 8(a) and 8(b) show the scanning electron microscope (SEM) images of the MWS and mode rotator on the fabricated PLC chip. Figure 8(c) shows the polished facet at the output-end of the mode demultiplexer, where three single-mode silica optical waveguides can be seen clearly. Figure 8(d) shows the microscope image of the silicon photonic chip integrating three pairs of PBSs and SSCs, and the input ports are separated with a distance of 127 μm so that the chip can be connected with a fiber array (FA). Figure 8(e) shows the butt-coupled FA, the silicon photonic chip, the PLC chip, and the FMF for the measurement.

The performance of the MWS fabricated on the PLC chip was characterized first. Figure 9(a) shows the measured normalized coupling loss between the MWS and the FMF for the LP01-x/y, LP11a-x/y, and LP11b-x/y modes. The minimum coupling losses for the three modes are ∼0.49/0.53dB, 0.91/1.05 dB, and 1.11/1.95 dB, which occur at the wavelengths of ∼1549nm, 1566 nm, and 1548 nm, respectively. The coupling loss ranges are 0.49–1.13 dB, 0.91–1.75 dB, and 1.11–2.59 dB over a broad wavelength range of 80 nm. One might notice that the device shows slight polarization dependence, which is supposed to be caused by thermal-stress-induced material birefringence that occurs in the fabrication [46]. The coupling loss between the bi-level multicore SSC on silicon and the single-mode silica optical waveguide was also characterized, as shown in Fig. 9(b). The measured coupling loss is about 0.67 dB and 1.02 dB at 1550 nm with 1-dB bandwidth exceeding 85 nm and 60 nm for TE- and TM-polarizations.

The overall coupling loss from the silicon photonic chip to the FMF is further measured by using the experimental setup in Fig. 8(e), which includes the coupling loss between the FMF and the PLC chip (i.e., the coupling loss of the MWS), the on-chip transmission loss of the PLC chip, and the coupling loss between the PLC chip and the silicon photonic chip (i.e., the coupling loss of the SSC). Figure 9(c) shows the normalized overall coupling loss for six mode-channels. The minimum coupling losses are ∼1.49/1.36dB, 1.43/1.40 dB, and 2.48/1.87 dB for the LP01-x/y, LP11a-x/y, and LP11b-x/y modes, while the 1-dB bandwidths are ∼80nm, 60 nm, and 55 nm, respectively. The coupling loss becomes higher at the longer wavelength, which is possibly due to the substrate leakage. This can be improved by thickening the buffer layer for the silicon photonic chip. From the experiment results mentioned above, the on-chip mode transmission loss M of the PLC chip can be derived using Eq. (1) given as Mon-chip=Mall−MMWS−MSSC.(1)

As a result, the calculated on-chip transmission loss is less than ∼0.8dB in the wavelength range of 1520–1625 nm. The difference between the simulation and experiment results is mainly due to the fabrication errors because of the dimensional variation of the waveguide cores.

The near-field images of the optical fields emitted from the FMF were also observed, as shown in Fig. 10(a). The clear images of the LP01-x/y, LP11a-x/y, and LP11b-x/y mode intensity distributions are successfully observed at the output port of the FMF, indicating that the proposed FMF-chip coupler worked well with all the mode-channels. The MDM transmission experiment was also carried out to characterize the crosstalk performance. The light is selectively launched at one of the input ports, and the powers of six output ports are monitored simultaneously. Figure 10(b) shows the measured intermode crosstalk at each output port when the LP01-x/y, LP11a-x/y, and LP11b-x/y modes are excited at the corresponding input ports. From the experiment result, it can be seen that the intermode crosstalk is lower than −14.26dB. The system performance can be further improved to minimize the crosstalk limitation by using advanced techniques such as the multiple-input multiple-output (MIMO) digital signal processing (DSP) method [47].

Table 2 gives a comparison of the FMF-chip coupler reported in recent years. Among them, the multimode grating coupler usually has a compact footprint, while the performance is still quite limited with low coupling efficiency and narrow bandwidths [12,13,16–18]. Furthermore, it is difficult to be scaled up to handle more mode-channels. For the edge couplers based on planar multicore structures, it is possible to achieve broadband operation and high coupling efficiency. However, they can work for the lateral higher-order LP modes only, and it is also difficult to handle more mode-channels [22–24]. For the edge coupling scheme with the assistance of dual-core designs such as additional SiN or polymer waveguides, thick core and cladding layers are required to achieve efficient coupling for all the desired mode-channels; the fabrication is usually quite complicated [28,30]. Notably, there are several designs of photonic lanterns based on fibers/photonic integrated circuits developed to serve as the FMF demultiplexer, while most of them are not designed yet to be compatible for coupling with silicon photonic chips and these 3D structures are still difficult for massive fabrication [34,48,49]. As a summary, most multimode coupling schemes reported previously mainly utilize the mode demultiplexing on silicon, which is not friendly to realize high-efficiency coupling with an FMF due to the huge mode mismatch.Table 2.

Comparison for the FMF-Chip Couplers Reported Previously

In contrast, the present scheme of multimode coupling provides a promising option for achieving efficient mode coupling/(de)multiplexing to connect an FMF and a silicon photonic chip. Here the introduction of a PLC-based dual-polarization mode (de)multiplexer integrated with a segment waveguide coupler is one of the keys for low-loss and low-crosstalk multimode coupling. Silica waveguides are attractive due to the low propagation loss and nearly perfect vertical sidewalls, making it an ideal candidate for low-loss multimode coupling. The overall coupling efficiency can also be enhanced by improving the fabrication processes in the lab. Compared with the free-space couplers that require bulk elements and delicate high precision alignment showing coupling loss of 8–13 dB [49], this interconnect configuration enables high coupling efficiency and exhibits less package difficulty. To be further employed in MDM systems, MIMO DSP methods can be introduced to lower the negative influences due to the intermode crosstalk in the transmission. To the best of our knowledge, the present on-chip configuration for connecting an FMF and a silicon photonic chip is so far the first one to demonstrate experimentally the operation with six mode-channels simultaneously, which particularly exhibits excellent performances of high coupling efficiency and low intermode crosstalk in a broad bandwidth. Furthermore, considering that a silica waveguide with only ∼410nm size is able to handle power up to ∼13W corresponding to a maximum power density of ∼23W/μm2 [50], the proposed silica chip is available for high-power operation (similar to optical fibers). Besides, light is divided into three parts by the PLC chip before entering the silicon photonic waveguides, and optical damage can be effectively avoided in the coupling. This is promising for the applications requiring high-power operation. The proposed scheme incorporates the superiorities of silica optical waveguides for manipulating the LP modes and a silicon photonic waveguide for polarization-handling, which thus provides an effective fiber-chip coupling solution even for multiple mode-channels of dual polarizations. The mode-channel number is possible to be scaled up by introducing a PLC mode (de)multiplexer with more mode-channels [51]. Therefore, the proposed photonic chip with mode (de)multiplexing/coupling provides a promising option for the chip-FMF connections as desired for MDM systems. It is also expected to be extended to the photonic chips based on other materials such as lithium niobate, silicon nitride, and chalcogenide.

In summary, we proposed a novel scheme for efficient multimode coupling by merging a PLC chip and a silicon photonic chip. The mode (de)multiplexer based on a low-Δ silica optical waveguide is introduced as an indispensable intermediate, so that the demultiplexing of LP modes in the FMF can be done on the silica PLC chip by tailoring the mode conversion related to mode symmetric properties. Particularly, a novel multimode waveguide segment structure is proposed to expand the mode fields of the silica multimode bus waveguide, thus achieving the high-efficiency butt-coupling with the FMF. Moreover, an elaborate bi-level multicore polarization-insensitive spot-size converter is designed to achieve high-efficiency coupling between the silicon photonic waveguide and the single-mode silica optical waveguide. Theoretically, the six-channel FMF-chip coupler for the LP01-x/y, LP11a-x/y, and LP11b-x/y modes can work with low coupling losses of 0.77–1.39 dB and low intermode crosstalk of <−27.2dB in a broad bandwidth (>150nm). Minimum coupling losses of 1.36–2.48 dB are experimentally demonstrated, enabling the simultaneous coupling between FMF and the silicon photonic chips. This is promising for realizing energy-efficient and low-cost short-reach optical interconnects with full MDM fiber-chip communication links in the future.

The 3D finite-difference beam propagation method is used to simulate the MWS and the PLC mode (de)multiplexer. The calculation of the overlap coupling loss of the MWS-FMF and the SSC-PLC is carried out in the ANSYS Lumerical FDE solver. The 3D finite-difference time-domain (3D-FDTD) method is utilized to calculate the overall coupling loss between the SSC and the silica single-mode waveguide.

The designed PLC chip was fabricated based on the silica-on-insulator platform, which has a 6.5-μm-thick doped silica core layer, a 10-μm-thick buried oxide layer, and a silicon substrate. The silica core layer was etched with an inductively coupled plasma (ICP) dry-etching process by using a chromium hard mask. An overlay process was utilized to form the dual-layer silica cores of different heights. Finally, a 15-μm-thick silica upper-cladding was developed by using the flame hydrolysis deposition (FHD) process. The refractive-index-contrast of the silica optical waveguide is Δ=1.5%.

The silicon photonic chip was fabricated on a silicon-on-insulator (SOI) wafer, which has a 220-nm-thick top-silicon layer and a 3-μm-thick buried oxide layer. The electron beam lithography (EBL) and the ICP process were used to form the bi-layer silicon waveguide. A 2.3-μm-thick SiO2 thin film was deposited above the Si core layer as the upper-cladding by utilizing the plasma enhanced chemical vapor deposition (PECVD) process.

The coupling losses were measured by using a tunable laser (Keysight 81940A), an in-line polarization controller (PC), and an optical power-meter (Keysight 81633A). The characterization was carried out by launching the x-/y-polarization modes from the SOI chip. The LP01-x/y, LP11a-x/y, and LP11b-x/y modes are launched from ports O1, O2, and O3 of the PLC chip, respectively. The launched light is coupled finally from the PLC chip to the FMF. The FMF used here has a total length of 1 m. The output spectrum from the FMF is recorded by the power meter. The mode field patterns after the FMF were measured by a 40× objective, a polarizer, and a charge coupled device (CCD) camera. Here the polarizer is introduced before the CCD to verify the polarization state of the mode field to be measured. The MDM transmission experiment was carried out by using another identically fabricated PLC chip as the FMF demultiplexer, and fiber PBSs were used after the PLC chip to separate the two polarizations. Since the mode field rotation may occur in the twisted FMF, which possibly results in increased crosstalk (e.g., LP11a and LP11b modes) during the MDM transmission, here an FMF PC was used to adjust the rotation of the mode field manually before demultiplexing. The experimental setup is shown in Fig. 11.