1 Introduction

Mode-division multiplexing (MDM) techniques have been extensively explored to meet the rapidly growing demands of communication bandwidth [1], [2]. Different from wavelength-division multiplexing techniques [3], MDM techniques increase data transmission density by utilizing monochromatic lasers [4], [5], which do not suffer from high costs, thermal management complexity, and large system footprints. It, therefore, attracts significant attention for MDM applications based on photonic integrated circuits (PICs) [6], [7]. Moreover, silicon photonics provides a promising platform for developing on-chip optical interconnects and optical communications combined with MDM techniques [8] with the advantages of negligible optical loss at 2–2.5?μm wavelengths and intrinsic compatibility with the complementary metal oxide semiconductor (CMOS) technology for high-volume and cost-efficient device fabrication [9], [10], [11], [12], [13], [14]. Nowadays, diverse studies of on-chip MDM silicon waveguide devices have been proposed and demonstrated, namely, spatial mode multiplexers/demultiplexers [15], bend waveguides [16], and waveguide crossings [17], [18].

On the other hand, low-dimensional material-based heterogeneous silicon photonics has been widely studied in the past decade, ranging from the telecommunication band to mid-infrared wavelengths [19], [20], [21]. Compared with bulk semiconductors, low-dimensional materials have the merits of tailorable electronic bandgaps, neglectable lattice mismatch with silicon-on-insulator (SOI) wafers, and excellent stability. To date, many great efforts have been made to demonstrate waveguide-integrated light sources [22], modulators [23], [24], [25], and photodetectors [26], [27], [28] based on graphene [29], [30], [31], [32], black phosphorus [33], [34], and transition metal dichalcogenides [35], [36], [37]. However, the study of waveguide components integrated with low-dimensional materials for MDM applications has seldom been experimentally explored.

In this paper, we demonstrated waveguide-integrated spatial mode filters with PtSe₂ nanoribbons to eliminate modal crosstalk at 2-μm wavelengths for on-chip MDM applications. Due to the strong interaction between light in an ultrathin silicon waveguide with a deep-subwavelength thickness and subtly designed PtSe₂ nanoribbons, optical modes with different orders can be intensely and selectively absorbed. To be specific, we experimentally achieved a TE₁-to-TE₀ modal extinction ratio (ER) of 12?dB and a TE₂-to-TE₀ modal ER of 14.5?dB in PtSe₂-on-silicon waveguides at 2200-nm wavelengths. Our study offers a new approach to developing on-chip spatial mode filters for MDM applications.

2 Device structure and theoretical analysis

Figure 1(a) shows schematics of the on-chip spatial mode filters. Asymmetric directional couplers can be used for energy conversion between the fundamental and high-order modes. Detailed designs of the asymmetric directional couplers can be found in the Appendices. Meanwhile, PtSe₂-on-silicon waveguide devices were designed to develop TE₁ and TE₂-mode filters. As shown in Figure 1(b) and (c), the filters consist of ten-layer thick PtSe₂ nanoribbons and multi-mode silicon waveguides that were designed on an SOI wafer with a 70-nm thick top silicon layer and a 2-μm thick buried oxide. We then theoretically optimized the proposed spatial mode filters by using finite-element method software (COMSL Multiphysics). Figure 1(d) shows the effective refractive indices (RIs) as a function of the silicon waveguide width (W_WG) at a wavelength of 2,200?nm. As the W_WG increases, more eigenmodes could be supported by the silicon waveguide. It is well known that, when W_WG is fixed, the higher the mode order, the higher the optical loss. On the other hand, when the mode order is fixed, the wider the waveguide, the lower the optical loss. Here, we chose W_WG−1 = 3?μm for supporting the TE₀ and TE₁ modes and W_WG−2 = 4.2?μm for supporting the TE₀ and TE₂ modes as a trade-off. Normalized electric-field intensity profiles across the silicon waveguide and simulated electric-field distributions of the TE₀, TE₁, and TE₂ modes are presented in Figure 1(e). As for the TE₁-mode filter, one PtSe₂ nanoribbon was designed to be placed on the surface center of the TE₁ mode waveguide, providing a large overlap with the electric field of the TE₀ mode. Therefore, the energy of the TE₀ mode can be filtered from the device. As for the TE₂-mode filter, two PtSe₂ nanoribbons were designed to be placed ±0.77?μm from the center of the TE₂-mode waveguide surface, resulting in a significant absorption to the TE₀ mode. Figure 1(f) and (g) present simulated optical losses of different modes in the TE₁-mode and TE₂-mode filters as a function of the PtSe₂ nanoribbon width (W), where the parameters of PtSe₂ used in the theoretical modal are obtained by fitting [38]. With the W₁ and W₂ increase, the optical losses of the waveguide modes increase. Especially the TE₀ mode shows the most significant increase in optical loss, rising from 0.00337?dB/μm and 0.00273?dB/μm to 0.16526?dB/μm and 0.13939?dB/μm in TE₁-mode and TE₂-mode filters. Meanwhile, the optical losses of TE₁ and TE₂ modes vary moderately. We used the modal ER, defined as the ratio of transmittance of the pass mode and the filtered mode, as a figure of merit (FOM) of the proposed device. When there is no PtSe₂ nanoribbon on the waveguide, the optical losses only depend on their propagation losses in the silicon waveguide. According to simulations, the TE₀-to-TE₁ and TE₀-to-TE₂ modal ERs without the PtSe₂ can be calculated as 0.00988?dB/μm and 0.01796?dB/μm at 2,200?nm wavelengths. Theoretical results also show that when W₁ = 1,200?nm and W₂ = 1,500?nm, we can obtain a maximum TE₁-to-TE₀ modal ER of 0.07438?dB/μm and a maximum TE₂-to-TE₀ modal ER of 0.05659?dB/μm, as indicated in the insets of Figure 1(f) and (g). It is worthwhile to note that the ultrathin silicon waveguide with the deep subwavelength thickness not only increases the optical absorption which helps reduce the device footprints but also improves the fabrication tolerance due to low-index waveguide devices, benefitting MDM applications based on the PtSe₂-on-silicon waveguide devices at 2-μm wavelengths and beyond, i.e. 3-μm wavelengths by using a suspended membrane waveguide [11].

Figure 1:

Schematics and theoretical results of the spatial mode filters. (a) Schematics of the devices, including the input single-mode waveguides, asymmetric directional couplers, and multi-mode waveguides integrated with the PtSe₂ nanoribbons. 3D and cross-section views of the (b) TE₁-mode filter and (c) TE₂-mode filter. (d) Simulated effective RIs of the eigenmodes in the ultrathin silicon waveguides with different widths. (e) Normalized electric-field intensity profiles across the pure silicon waveguide and simulated electric-field distributions of the TE₀, TE₁, and TE₂ modes. Arrow symbols indicate the positions of the PtSe₂ nanoribbons in the following fabrication process. (f) Calculated optical losses of the TE₀ and TE₁ modes in the TE₁-mode filter. The inset shows the calculated modal ER of the TE₁-mode filter with different widths of the PtSe₂ nanoribbons. (g) Calculated optical losses of the TE₀ and TE₂ modes in the TE₂-mode filter. The inset shows the calculated modal ERs of the TE₂-mode filters with different widths of the PtSe₂ nanoribbons.

3 Device fabrication and characterization

Based on the theoretical analysis, we fabricated the designed spatial mode filters. The silicon waveguide devices were first fabricated by using electron-beam lithography (EBL) and reactive-ion etching (RIE) processes, as shown in Figure 2(a). In the second step, we transferred a PtSe₂ film onto the fabricated silicon chip by using a modified wet transferring recipe, as shown in Figure 2(b). As for the recipe, a polymethyl methacrylate (PMMA) layer was spinning coated on top of a ten-layer chemical vapor deposition (CVD)-growth PtSe₂ film on a silica substrate (SixCarbon Technology). Then, the PtSe₂ film was separated from the silica substrate with the help of hydrofluoric acid wet etching and cleaned in deionized (DI) water. After that, the PtSe₂ film was transferred onto the fabricated silicon chip. The PMMA was removed using an acetone solution, followed by cleaning it with anhydrous ethanol and DI water. Finally, the proposed devices were developed with the PtSe₂ film patterning by using photolithography and argon plasma etching processes, as shown in Figure 2(c). More details of the PtSe₂-on-silicon waveguide fabrication can be found in our previous study [38].

Figure 2:

Fabrication of the proposed spatial mode filters. (a) Silicon waveguide device fabrication processes. (b) PtSe₂ film wet transferring processes. (c) PtSe₂ nanoribbon patterning processes.

We characterized the fabricated spatial mode filters by using scanning electron microscopy (SEM), atomic force microscopy (AFM), and Raman spectroscopy. Figure 3(a) and (b) illustrate the SEM images of the TE₁ and TE₂-mode filters. We utilized grating couplers to couple the TE₀-mode light into and out of the ultrathin silicon waveguides. 50-μm-long tapers on both sides of the multi-mode waveguide were used to adiabatically connect the multi-mode waveguide and single-mode waveguide without changing the mode order. The insets are the zoom-in images of the spatial mode filters. The cross-section view of the silicon waveguide is shown in Figure A.3. Moreover, the AFM measurement shows that the thickness of the ten-layer PtSe₂ nanoribbon was ∼6?nm, as shown in Figure 3(c). In addition, the quality of the PtSe₂ film was characterized by measuring the Raman spectra of the PtSe₂ film before and after its transfer, as shown in Figure 3(d). Three characteristic peaks can be observed around 179?cm⁻¹, 208?cm⁻¹, and 235?cm⁻¹, representing the E_g peak, A_1g peak, and longitudinal optical (LO) peak, respectively. The E_g peak has moderate variation, while three measurements from different positions show similar profiles, revealing the excellent quality of the PtSe₂ film with good homogeneity and few defects after the wet transferring process [39].

Figure 3:

Characterization of the proposed spatial mode filters. (a) SEM image of the TE₁-mode filter. (b) SEM image of TE₂-mode filter. (c) AFM measurement of the PtSe₂ film. The inset shows the height distribution of the PtSe₂ film surface. (d) Raman spectra of the PtSe₂ film before and after its transfer.

4 Measurement and discussion

Finally, we verified the experimental performance of the spatial mode filters. Figure 4(a) shows the transmission spectra of the silicon devices before integrating the PtSe₂ nanoribbons process. When the light travels from Port 01 to Port 02 and from Port 11 to Port 12, the transmittance is much higher than that from Port 01 to Port 12 or Port 11 to Port 02, where optical losses are more than 45?dB. The TE₂-mode filter without PtSe₂ nanoribbons is also consistent with the description above, as shown in Figure 4(b). Here, due to the compact device footprints, the optical losses of the waveguide and taper can be neglected. The maximum coupling efficiency of the grating coupler was measured as −8?dB at the center wavelength of 2,200?nm, while the coupling losses of the TE₁-to-TE₀ and TE₂-to-TE₀ asymmetric directional couplers were ∼2?dB and ∼4?dB. After integrating the PtSe₂ nanoribbons on the waveguides, the measured normalized transmittance around 2,200?nm wavelengths of the TE₁ and TE₂-mode filters, which are deducted the noises to avoid the interferences, are shown in Figure 4(c) and (d). Figure 4(e) and (f) display the modal ERs of the TE₁ and TE₂-mode filters. Here, considering the fabrication process and simulated results, we obtained four filters with the sizes of the PtSe₂ nanoribbons set as W₁ = 1,100?nm and 1,200?nm, L₁ = 100?μm for the TE₁-mode filters, and W₂ = 800?nm and 900?nm, L₂ = 75?μm for the TE₂-mode filters. Due to the significant overlap of the PtSe₂ nanoribbons with the evanescent fields of the ultrathin waveguides, the optical losses of the TE₀ mode are more than 15?dB in the TE₁ and TE₂-mode filters. Besides, benefiting from the subtly designed sizes and positions of the PtSe₂ nanoribbons, the maximum modal ERs are up to 12?dB for the TE₁-mode filter and 14.5?dB for the TE₂-mode filter. It can also be seen that there is less variation in optical losses as the width increases, which agrees well with the simulation. The results indicate that the spatial mode filters have the advantages of high filtering efficiency, high selectivity, generous tolerances, and low limitations in the fabrication process, being suited for use in on-chip photonic integration systems.

Figure 4:

Experimental results of the fabricated spatial mode filters. Transmittance of the (a) TE₁ and (b) TE₂-mode filters before integrating the PtSe₂ nanoribbons process. Transmittance of the (c) TE₁ and (d) TE₂-mode filters after the PtSe₂ transfer and patterning. Measured modal ERs of the (e) TE₁-mode and (f) TE₂-mode filters.

5 Conclusions

In summary, we demonstrated the on-chip spatial mode filters with PtSe₂ nanoribbons to eliminate modal crosstalk at 2-μm wavelengths. Ten-layer PtSe₂ nanoribbons were subtly designed and fabricated on 70-nm thick silicon waveguide devices to provide selective giant absorption to undesirable optical modes in silicon waveguides. Our experimental results show that the TE₁-to-TE₀ and TE₂-to-TE₀ modal ERs of more than 12?dB and 14.5?dB can be achieved in the PtSe₂-on-silicon waveguides at 2200-nm wavelengths. Our study is expected to open an avenue toward developing high-performance spatial mode filters with optoelectronic materials with suitable bandgaps for on-chip MDM applications.