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Abstract
The mode-division-multiplexing (MDM) technology has become an alternative solution to further increase the link capacity in optical communication systems. Ultralow loss waveguide crossings for multimode waveguides are requisite in on-chip MDM systems. We propose and demonstrate an ultralow loss silicon multimode waveguide crossing using a combination of fully etched and shallowly etched waveguides in the multimode-interference coupler region to reduce the imbalance for two transverse electric polarized (TE) modes. By engineering the geometries and the proportion of the two waveguides, the self-imaging positions for different modes can coincide exactly. Simulated results show that the insertion losses are 0.043 and 0.084 dB for the fundamental TE (TE0) mode and the first-order TE (TE1) mode at 1550 nm, while the experimental values are 0.1 and 0.12 dB, respectively. The measured crosstalk is less than -30 dB for both modes within a 75 nm wavelength span.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The on-chip photonic circuits provide an alternative solution for optical interconnections with advantages of high energy efficiency, large bandwidth, and high integration density. The wavelength-division-multiplexing (WDM) and mode-division-multiplexing (MDM) technologies have been proposed to further increase the link capacity in the communications [1–4]. In contrast with WDM system employed multiple wavelengths from several laser sources, the MDM system using multiple eigenmodes to simultaneously carry independent signals can significantly save the power consumption. The multimode waveguide crossings are essential building blocks for the on-chip complex MDM routing.
Over the past years, numerous investigations on improving the performance of single-mode waveguide crossings were reported [5–12]. The typical schemes were based on the multimode interference (MMI) coupler using self-imaging effect [5–7]. Other configurations were subsequently proposed for ultralow loss or multifunctional purposes [8–12]. However, single-mode waveguide crossings were not compatible with high-order modes, and the waveguide crossings should be redesigned to accommodate the MDM systems. The reported multimode waveguide crossings are mainly based on different schemes: MMI couplers [13], Y-junctions [14], two-dimensional nanostructures [15,16], and Maxwell’s fisheye lens [17,18]. A waveguide crossing for two transverse magnetic polarized (TM) modes was demonstrated based on MMI couplers [13], though the self-imaging positions and the performance for different modes did not coincide perfectly. Another multimode waveguide crossing, consisting of Y-junctions cascaded with a 2×2 MMI crossing matrix, was proposed for two transverse electric polarized (TE) modes [14]. The imperfect fabrication of the Y-junction resulted in a larger loss of the fundamental TE (TE0) mode, compared to the first-order TE (TE1) mode. The two-dimensional nanostructure, optimized by the inverse design, was subsequently proposed, whereas the performances were limited by the fabrication accuracy [15,16]. Recently, the star-topological multimode waveguide crossings were proposed by using the metasurface and gray-scale electron-beam lithography to form on-chip Maxwell’s fisheye lens, respectively [17,18]. However, the feature size of the metasurface was small, and the gray-scale lithography required complicated and critical fabrication. The existing solutions were either incompatible with complementary metal-oxide-semiconductor (CMOS) technique or unable to achieve consistent and high performance for both modes.
In previous work, we theoretically proposed a CMOS compatible multimode waveguide crossing based on silicon-on-insulator (SOI) platform [19]. A combination of fully etched and shallowly etched waveguides was implemented in the MMI coupler region to compensate the offset of self-imaging positions between TE0 and TE1 modes, achieving ultralow loss and imbalance. Here, the comprehensive analysis and experimental results are investigated and provided. The simulations show the insertion losses (ILs) are 0.043/0.084 dB for TE0/TE1 modes at 1550 nm. Experimentally, the values are 0.1/0.12 dB. To our best knowledge, this is the lowest loss silicon waveguide crossing for both TE0 and TE1 modes. Within a 75 nm wavelength, the crosstalk at cross port is less than -30 dB for both modes.
2. Principle
The device is designed on the SOI platform with a 220 nm silicon layer surrounded by silica cladding. The fully etched and 70 nm shallowly etched waveguides are utilized. Figure 1(a) shows the schematic in an aerial view. It consists of fully etched nonadiabatic tapered waveguides (region “I”), fully etched waveguides (region “II”), adiabatic tapered mode-size converters (region “III”), and 70 nm shallowly etched waveguides (region “IV”). When the TE0 and TE1 modes are injected into region I, as shown in Fig. 1(b), the TE0 mode partially evolves to the second-order TE (TE2) mode, while the TE1 mode partially evolves to the third-order TE (TE3) mode. The regions II and IV are MMI regions with different etching depths and waveguide widths, and region II is a connecting part between them for mode conversion. The launched TE0 and the excited TE2 modes interfere in regions II, III and IV, while the launched TE1 and the excited TE3 modes interfere. The intersection is placed at the self-imaging positions of both modes, and it can achieve low ILs and crosstalk for both modes.
Fig. 1. (a) Schematic of the proposed waveguide crossing. (b) Schematic of the nonadiabatic tapered waveguide. (c) Fully etched waveguide. (d) Shallowly etched waveguide.
There are two main loss sources for a waveguide crossing. The first is the mode mismatch at the interface of a waveguide and the broad crossing section perpendicular to it, shown as the red dashed line in Fig. 1(a). In conventional fully etched waveguides with limited width, only quasi-TE modes that contain fractional TM components are supported, while the crossing section can be considered as a slab waveguide with infinite width supporting pure TE modes. The amount of TM component should be reduced since it will be dissipated at the interface inevitably. Introducing shallowly etched waveguides is an effective way to lower the TM components and thus reduce the mismatch at the intersection. The waveguides with shallower etching depth containing less TM components are beneficial to reduce ILs. The other source is the mismatch of self-imaging positions between two modes. To explore the self-imaging positions, the beat lengths of TE0 and TE1 modes in the multimode waveguide are discussed, and they can be expressed as [20],
where LB, j is the beat length of TEj mode (j = 0, 1), ${\beta _{T{E_j}}}$ is the propagation constant of TEj mode. ${\beta _{T{E_j}}} = ({2\pi \cdot {n_{T{E_j}}}} )/\lambda$, λ is the operation wavelength, and ${n_{T{E_j}}}$ is the effective refractive index of TEj mode. Accordingly, the beat length in Eq. (1) can be rewritten as,Fig. 2. Calculated ratios of dn1 and dn0 with different waveguide width and waveguide etching depth. The inset is the cross section of the multimode waveguide.
Equation (3) can be satisfied by choosing either the waveguides on the red curve or the combination of two waveguides on different side of the curve. Instead of choosing the geometries on the curve, 70 nm etching depth for the crossing section and 220 nm etching depth for the input/output waveguide are chosen, considering a shallower etching is beneficial to reduce the IL. The widths of the multimode waveguides are determined by the values of dn1/dn0 and the number of guided modes. The waveguide geometries of the proposed scheme are marked by the blue stars in Fig. 2. By adopting a combination of the two waveguides with optimized lengths, the overall beat length can satisfy Eq. (3), and the self-imaging positions of both modes can coincide at the intersection in the MMI coupler.
As shown in Fig. 1(b), the input waveguide width W0 is set to be 0.9 µm to support TE0 and TE1 modes. The width of the fully etched multimode waveguide W1 is set to be 1.8 µm to support TE0 to TE3 modes, as shown in Fig. 1(c). Similarly, the shallowly etched waveguide width W2 is 2.3 µm, and the slab width W3 is 4 µm, as shown in Fig. 1(d). The nonadiabatic tapered waveguide length Lt1 is set to be 1.1 µm to optimize the proportion of two modes, targeting a high transmittance. The adiabatic tapered mode-size converter is utilized to connect the fully etched and shallowly etched parts, and the length Lt2 is set to be 8 µm to avoid excess losses. The values of the fully etched waveguide length L1 and the shallowly etched waveguide length L2 are optimized to be 3.55 and 4.2 µm, respectively. The footprint of the whole structure is 33.7 µm × 33.7 µm.
3. Simulated and experimental results
Figures 3(a) and 3(b) show the simulated electric field for TE0 and TE1 modes at 1550 nm, respectively. Clearly, TE0 and TE1 modes both propagate through the waveguide crossing with barely scattering to cross ports, since the self-imaging positions for both modes coincide exactly. Figures 3(c) and 3(d) denote the simulated transmission spectra at bar ports with wavelength ranging from 1500 to 1600 nm. The ILs are less than 0.87 and 0.54 dB for TE0 and TE1 modes in the whole range, and the values are only 0.043 and 0.084 dB at 1550 nm. Figures 3(e) and 3(f) show the simulated transmission spectra at cross ports, indicating that the crosstalk for both modes is less than -56 dB within the 100 nm wavelength span. The TE0 and TE1 modes, which are even and odd modes, cannot excite each other in the symmetric structure. Therefore, the crosstalk at bar ports can be ignored.
Fig. 3. Simulated electric field of (a) TE0 and (b) TE1 modes. Simulated transmission spectra of (c) TE0 and (d) TE1 modes at bar port, and (e) TE0 and (f) TE1 modes at cross port.
The device is fabricated by using the 284 nm deep ultraviolet lithography and inductively coupled plasma etching. Figure 4 shows the microscope image of the device, consisting of two input grating couplers (GCs), four output GCs, one mode multiplexer (MUX), two mode de-multiplexers (DEMUXs), and the multimode waveguide crossings. Ten crossings are cascaded to mitigate the measurement errors. The MUX is utilized to generate TE0 and TE1 modes at the input port, and the DEMUXs at tenth bar port and cross port of the first crossing are utilized to de-multiplex the TE0 and TE1 modes. Two input GCs are labelled as “TE0” and “TE1”, denoting the input of TE0 and TE1 links, respectively. The four output GCs at bar and cross ports are labelled as “TE0B”, “TE1B”, “TE0C” and “TE1C”, denoting the output at bar and cross ports of TE0 and TE1 links, respectively. The MUX and DEMUX are composed of counter-tapered couplers [21]. The referenced MUX and DEMUX are fabricated on the same chip, and the measured spectra are shown in Fig. 5. The transmission spectra are normalized by subtracting the losses of the GCs. The average excess losses of the referenced mode MUX and DEMUX are 0.05 dB for TE0 mode and 0.43 dB for TE1 mode with the wavelength ranging from 1525 to 1600 nm. The crosstalk is less than -24 dB for both modes at 1550 nm.
Figures 6(a) and 6(b) show the normalized measured transmission spectra of the fabricated device by subtracting the losses of the GCs. Limited by the bandwidth of light source and GCs, the measured spectra range from 1525 to 1600 nm. By deducting the excess losses of the mode MUX and DEMUX, the ILs of ten crossings are 1 dB for TE0 and 1.16 dB for TE1 at 1550 nm. Accordingly, the ILs of a single crossing are 0.1 and 0.12 dB for TE0 and TE1 modes, respectively. The values over the whole wavelength span are less than 0.81 and 0.69 dB. The effective refractive index and dn0 are both wavelength-dependent. The dn0 is larger at the longer wavelength, and the resulting beat length is shorter. The beat length mismatch leads to larger IL at the longer wavelength for TE0 mode, as shown in Fig. 6(a). The crosstalk at bar port is -25 dB for TE0 link and -32 dB for TE1 link, while the crosstalk at cross port is -49 dB for TE0 link and -47 dB for TE1 link at 1550 nm. By comparing the spectra in Fig. 5, the crosstalk at bar port is almost introduced by the mode MUX and DEMUX. The crosstalk at cross port is less than -30 dB for both modes within 75 nm span. Finally, a comparison of the reported silicon multimode waveguide crossings with experimental results is summarized in Table 1.
Table 1. A summary of silicon multimode waveguide crossings.
4. Conclusion
We demonstrated an ultralow loss dual-mode waveguide crossing for MDM systems. A combination of fully etched and shallowly etched waveguides in the MMI region is utilized to reduce the offset of the self-imaging positions between two different modes. The measured results show that the ILs of a single crossing at 1550 nm are 0.1 and 0.12 dB for TE0 and TE1 modes, respectively. The crosstalk at cross port is less than -30 dB for both TE0 and TE1 links within the measured 75 nm wavelength span.
Funding
National Natural Science Foundation of China (61911530161, 61922034); Program for HUST Academic Frontier Youth Team (2018QYTD08).
Disclosures
The authors declare no conflicts of interest.
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