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Abstract
A mode splitter is a key device to eliminate undesired modes but allow desired modes go through for an on-chip mode-division multiplexing (MDM) system. Here, we propose a silicon high-order mode (HOM) pass filter based on the cascaded plasmonic bridged subwavelength gratings (BSWGs). A metal bridge is introduced to generate a plasmonic hybrid mode, which has a significant influence on the fundamental mode but a neglected impact on the first-order mode. A silicon HOM-pass filter for handling the TM0 and TM1 modes is optimized by using the 3D full-vectorial finite difference time domain (3D-FV-FDTD) method. The numerically simulated results indicate that the optimized mode filter is with a low loss of 0.63 dB and a mode extinction ratio (ER) of 26.4 dB based on 4-cascaded plasmonic BSWGs. The 3 dB bandwidth is over 493 nm from 1222 nm to 1715 nm. With the mode ER > 15.0 dB, a broad bandwidth of 150 nm can be achieved. The performance of the proposed mode filter is tolerant to the width error of ± 50 nm. The proposed silicon HOM-pass filter can be utilized in on-chip MDM systems for mode controlling.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, mode-division multiplexing (MDM) has attracted significant attention as a promising approach to counter the capacity limit of optical transmission systems [1]. The implementation of the MDM technology can achieve a dramatically increased capacity for both the optical communication systems and optical interconnects by employing individual eigen-modes as independent signal-channels [2,3]. Silicon photonics based on-chip MDM systems have gained research attention to build a highly integrated optical interconnect system [4], because silicon photonics can provide the compact footprint, complementary-metal-oxide-semiconductor (CMOS) compatible fabrication-process, high performance, and low cost [5]. Various passive devices have been reported based on silicon-on-insulator (SOI) for on-chip MDM systems, including the mode multiplexer (MUX)/demultiplexer (DeMUX) [6], multimode crossing [7], multimode bent waveguide [8], mode splitter [9], mode converter [10], and mode filter [11].
A mode filter is an essential element of an on-chip MDM system, similar to the fundamental wavelength filter in a wavelength-division multiplexing (WDM) system [11]. A mode filter can be utilized to eliminate undesired modes but allow desired modes go through. Generally, a high-order mode with a weaker confinement is easier to be filtered by using an adiabatic taper or a bent waveguide, compared with a fundamental mode with a stronger confinement. However, it is challenging to filter a fundamental mode while keeping high-order modes unaffected. In order to achieve a high-order mode (HOM) pass filter, several approaches have been reported based on the mode converters incorporated with Mach-Zehnder interferometers (MZIs) [12,13], multimode interference (MMI) [14], gratings [15–17], metamaterials [18], inverse designed structure [19], and phase-change materials [20–23].
One approach could be the use of the mode converters incorporated with MZIs to build a HOM pass filter. Both the passive and tunable mode filters have been proposed and demonstrated by using two mode converters composed of two MZIs and an adiabatic taper [12,13]. For this approach, a HOM is firstly converted to a fundamental mode via the first mode converter and then propagates through the central adiabatic taper, and finally converted back to the original HOM via the second mode converter. On the contrary, the fundamental mode is converted to a HOM via the first mode converter and then filtered via the central adiabatic taper. Although a low loss of 0.52 dB and a high mode extinction ratio (ER) of 37 dB can be achieved based on this approach [12], a π phase shifter is needed for the concurrent input two-modes, which would induce the phase-sensitive spectral fluctuation of the transmitted HOM. In order to achieve a phase-insensitive HOM-pass filter, an MMI architecture incorporated with a Y-junction has been reported [14]. For this approach, two in-phase and anti-phase TE0 pairs were obtained by deploying a Y-junction and then input into the MMI for generating a central TE1 channel and two outer TE0 channels. An insertion loss < 1.2 dB and a mode ER > 15 dB over 100 nm bandwidth can be obtained based on this MMI structure.
Another approach could be the use of the grating based structures to construct a HOM pass filter, including the 1D photonic crystal grating waveguide [15], subwavelength grating (SWG) based contra-directional coupler [16], and phase-shifted long-period grating (LPG) [17]. Guan et al. have proposed a HOM pass filter based on a 1D photonic crystal silicon grating waveguide [15]. This grating waveguide was optimally designed as a Bragg grating and an SWG for the TE0 and TE1 modes, respectively, thereby the fundamental mode can be reflected and meanwhile the HOM can propagate through the SWG as a Bloch mode. A compact length of only 15 µm can be achieved for this HOM filter with an ultra-high ER of 59.4 dB but a relatively high insertion-loss of 1.3 dB [15]. He et al. demonstrated a two-mode blocking filter by using an SWG based contra-directional coupler [16]. For this HOM filter, an insertion loss < 1.4 dB and a mode crosstalk (CT) < -21.0 dB were measured over a 35 nm bandwidth. As the Bragg condition and phase-matching condition of the contra-directional coupler must be met for these two kinds of gratings [15,16], the operating bandwidths are relatively limited. To further extend the bandwidth, Huang et al. reported a HOM pass filter to reject the fundamental mode of a three-mode waveguide based on a phase-shifted LPG [17]. A broad bandwidth > 140 nm can be obtained for this mode filter fabricated with polymer material. However, a relatively high insertion loss > 1.5 dB was also induced for the HOMs. We can see that the grating based HOM pass filters suffer from a relatively high insertion loss and a limited bandwidth due to the required phase-conditions.
Recently, a TM-polarized HOM-pass filter was proposed and numerically studied by using the hyperbolic metamaterial [18]. However, there is no natural hyperbolic material around 1550 nm wavelength. An ultra-compact and broadband HOM-pass filter was proposed based on the inverse designed structure [19], which can achieve a compact footprint of 1.56 × 2.4 µm2, a low insertion loss < 0.26 dB, and a high mode ER > 24.5 dB over a 100 nm bandwidth. Nevertheless, a fully etched hole with a radius of 45 nm is used in this structure, which is nontrivial to be fabricated. Recently, optical phase change materials have emerged and been implemented for the design of many photonics devices, including the graphene, vanadium dioxide (VO2), indium tin oxide (ITO) and so on [24]. Graphene has been used to achieve a HOM-pass filter with high mode ERs. Chang et al. demonstrated a broadband mode filter over the C + L band by embedding a graphene layer in a polymer waveguide [20]. Xing et al. proposed and studied a broadband mode filter by depositing graphene layers on the top of the waveguide for both the TE0 and TE1 modes filtering [21]. For the TE1 mode pass filter, a broad 3 dB bandwidth of around 450 nm can be obtained and an insertion loss of 2.0 dB is induced due to the graphene absorption-loss. Similarly, the TE1 and TE2 mode-pass filters have been proposed and numerically designed based on the graphene integrated waveguides [22]. For this TE1 mode pass filter, a mode ER of 9.9 dB and a relatively large loss of 9.9 dB were obtained for a 200 µm-long waveguide. Huang et al. proposed a reconfigurable mode filter based on the VO2 material, which can achieve a mode ER of 13.9 dB and an insertion loss of 3.5 dB for the TE1 mode pass [23]. We can see that although a broadband mode filter can be realized by integrating the optical phase change materials, the tradeoff between the HOM filtering efficiency and the loss of the fundamental mode should be considered. At present, these reported HOM-pass filters are limited by the relatively high loss of the fundamental mode and the low efficiency of the HOM filtering. Therefore, the design of a low-loss and broadband mode filter is still challenging for on-chip MDM systems.
In this paper, we propose a low-loss and broadband silicon HOM-pass filter based on the cascaded plasmonic bridged SWGs (BSWGs) for on-chip MDM systems. As we know, an SWG can be generally considered as a homogenous medium [25], thereby both the fundamental and high-order modes can propagate through this SWG with ultra-low losses, and their equivalent indices can be engineered by varying the duty cycle and pitch of the SWG. In addition, a broad bandwidth can be achieved as the dispersion effect in an SWG can be suppressed due to its small pitch [26]. By introducing a central bridge into an SWG waveguide, a BSWG can be yielded to provide a new dimension for the design of new photonic devices [27]. In this case, different with a conventional BSWG with a silicon bridge, a metal bridge is inserted at the center of the proposed plasmonic BSWG along the propagation direction, which has a significant influence on the fundamental mode but a neglected impact on the first-order mode. Consequently, the first-order mode propagates through the plasmonic BSWG waveguide with an ultra-low loss, whereas the fundamental mode will suffer from a large loss due to the mode-mismatch, radiation loss, and plasmonic absorption-loss. A low-loss and broadband silicon HOM-pass filter with a high mode ER can be achieved by cascading several plasmonic BSWG waveguides. In this case, a HOM-pass filter for handling the TM0 and TM1 modes is optimized based on a plasmonic BSWG with an aluminum (Al) bridge as an example. The proposed mode filter is studied by using the 3D full-vectorial finite difference time domain (3D-FV-FDTD) method for both the band-diagram and propagation characteristics.
2. Structure and principle
The schematic diagram of the proposed silicon HOM-pass filter is shown in Fig. 1(a) based on the cascaded plasmonic BSWG waveguides. The proposed HOM-pass filter is comprised of N-cascaded mode filters, shown as mode filter 1, mode filter 2, …, and mode filter N in Fig. 1(a). Each mode filter consists of a plasmonic BSWG in between two adiabatic tapers. These two tapers are with an identical length of Lt and they are similar to the tapers used for a conventional BSWG [28], which can convert the modes of a silicon nanowire to the Bloch modes of a BSWG and vice versa. According to the Bloch’s theorem, an SWG with a short period behaves as a periodic segmented waveguide, which can support localized Bloch-Floquet modes without propagating loss [25]. The Bloch-Floquet mode can be expressed by an electric field along the propagation direction [26]: E(x, z +Λ) = EB(x, z) exp(-γBΛ), where EB(x, z) is the field distribution of the Bloch mode within a single period and γB is its complex propagation constant. Generally, γB = αB + jkB = αB + j(2π/λ)nB, where αB and kB are the attenuation and propagations constants and nB is the effective index of the Bloch mode. It can be observed from Fig. 1(a) that the width of input taper is linearly narrowed from the BSWG width, W to the bridge width, Wb, and that of the output taper is from Wb to W. For the middle BSWG, an Al bridge with the length of Lb is introduced at the center of the plasmonic BSWG along the propagation direction instead of a silicon bridge for a conventional BSWG. The cross-sections of the plasmonic BSWG in a Si-Al-Si block and an Al block are shown in Figs. 1(b) and 1(c), respectively. The thicknesses of the silicon core layer and Al bridge are same and denoted by h. The schematic diagram of the proposed plasmonic BSWG is shown in Fig. 1(d) and the pitch and duty cycle are represented by Λ and f, respectively. The proposed mode filter is based on the SOI platform, which can be fabricated by using the following steps: (i) the silicon section of the plasmonic BSWG is fabricated based on the plasma enhanced chemical vapour deposition (PECVD) and reactive ion etching (RIE). (ii) After step (i), the “bridge cavity” where the Al bridge would be fabricated was obtained. For the plasmonic structure, the Al layer is deposited by a lift-off process using e-beam lithography, thermal evaporation of Al and lift-off [29]. (iii) Finally, the plasmonic BSWG is cladded with a PECVD SiO2 cladding.
Fig. 1. (a) Schematic of the proposed silicon HOM-pass filter based on cascaded plasmonic BSWG waveguides. Cross-sections of the plasmonic BSWG in (b) a Si-Al-Si block and (c) an Al block. (d) Schematic diagram of the plasmonic BSWG.
The operation principle of the proposed HOM-pass filter is given as: the fundamental mode of the plasmonic BSWG cannot be supported due to the central Al bridge, while a plasmonic hybrid mode can be generated and supported in this plasmonic BSWG. A plasmonic hybrid waveguide can provide subwavelength confinement in two dimensions with a relatively low propagation-loss. The plasmonic hybrid mode can be strongly confined in a 2D nano-region, which is a hundred times smaller than a diffraction limited spot [30]. Different with the surface plasmon polaritons (SPPs) of a plasmonic waveguide, the plasmonic hybrid mode is with a lower propagation-loss than that of the SPPs, as the optical energy of the SPPs is within dissipative metallic regions only confined in one dimension. Although an adiabatic taper is implemented at the input port, the input fundamental mode of a silicon nanowire will suffer from a relatively large loss due to the mode mismatch. Moreover, the radiation loss would also be induced at the junction between the taper and plasmonic BSWG. There may be a small amount of power of the input fundamental mode coupled to the plasmonic hybrid mode in the BSWG, but this mode is a lossy mode. In order to absorb this unnecessary mode, an Al material with a high extinction-coefficient > 15 is used as the central bridge in this case [31]. Finally, the input fundamental mode can be eliminated owing to the coupling loss, radiation loss, and absorption loss. For the input first-order mode, it will not be affected by the Al bridge, because there are two symmetric field-lobes with respect to the central Al bridge but no field in the central region of the plasmonic BSWG. Therefore, the first-order mode can propagate through the plasmonic BSWG with an ultra-low loss. Furthermore, the mode ER can be improved by cascading several plasmonic-BSWGs based mode filters. As the phase-matching condition is not required for the proposed HOM-pass filter, the operating bandwidth is expected to be wide benefitting from the BSWG structure. The proposed schematic can be extended to design any HOM-pass filter. As a TMn mode has n + 1 lobes along the x direction, n metal-bridges can be inserted in between n + 1 lobes, thereby yielding a TMn pass mode filter. For this TMn pass mode filter, the operating modes with the mode order lower than n can be filtered out.
3. Characterization of mode properties
The mode properties of the plasmonic BSWG are studied by using the 3D-FV-FDTD based band-diagram calculation [32]. The thickness of the silicon core layer is chosen to be a typical value of h = 220 nm. The refractive indices of the silicon, silica, and Al materials are based on the values in the Ref. [31] and the material dispersion is included. To achieve a subwavelength structure, the pitch and duty cycle of the plasmonic BSWG are set as Λ = 250 nm and f = 0.5, respectively [26]. The band-diagrams of both the conventional and plasmonic BSWGs are calculated with respect to both the wavelength and wave-vector. Sequentially, the effective indices of the fundamental and first-order Bloch-modes can be obtained and shown in Fig. 2 for different BSWG waveguide-widths, W. In the calculations, the bridge width was set to be Wb = 100 nm and the operating wavelength was chosen as λ = 1550 nm. It can be noted from Fig. 2 that for the conventional BSWG with a silicon bridge, the effective indices of the TM0 and TM1 Bloch-modes are denoted by the black and red lines, respectively. If an Al bridge is introduced instead of the silicon bridge, the TM0 mode will transform to a plasmonic hybrid mode while the TM1 mode will keep its field shape. In this case, the TM1 Bloch-mode of the plasmonic BSWG is named as TM1 mode, whereas the plasmonic hybrid mode is named as TM0 mode, and their mode profiles are shown in Fig. 3. It can be noted from Fig. 2 that although with the same parameters, the effective index of the TM0 mode in the plasmonic BSWG is significantly different with that of the TM0 mode in a silicon BSWG. On the contrary, the effective index of the TM1 mode is only slightly different with that of the TM1 mode in a silicon BSWG. Hence, a huge mode-mismatch would be induced between the input fundamental mode and the TM0 mode of the plasmonic BSWG. In this case, the width of the BSWG waveguide is chosen as W = 2 µm and an effective-index >1.5 can be achieved for the first-order mode, TM1. The mode fields of the Poynting vector, Pz of the TM1 and TM0 modes are shown in Fig. 3. It can be observed that the mode fields of the first-order mode at both the wide and bridge segments are same to those for a silicon BSWG, thereby this mode can propagate through the plasmonic BSWG and can be converted by the adiabatic tapers with a low loss. However, for the TM0 mode, the mode fields are not only confined in the silicon segments, but also distributed at the upper and bottom interfaces of the Al bridge. This TM0 mode can be considered as a plasmonic hybrid mode with a relatively high propagation-loss.
Fig. 2. Variations of the effective indices of fundamental and first-order TM modes with the waveguide width of BSWG for both silicon and aluminum bridges. Here, the BSWG pitch, Λ = 250 nm; duty cycle, f = 0.5; bridge width, Wb = 100 nm and operating wavelength, λ = 1550 nm.
Fig. 3. Mode fields of Poynting vector, Pz of both (a)(b) TM1 and (c)(d) TM0 Bloch-modes at (a)(c) wide (Si-Al-Si) and (b)(d) bridge (Al) segments of the plasmonic BSWG with W = 2 µm and Wb = 100 nm.
For the proposed plasmonic BSWG, the bridge width should be optimized to avoid the impact on the first-order Bloch-mode, TM1. Variations of the effective indices of both the TM1 and TM0 Bloch-modes are calculated with respect to the bridge width, as shown in Fig. 4. It can be noted that the effective indices of both Bloch-modes are decreased with the increase of the bridge width, while the descending slope of the TM1 Bloch-mode is more flat. It can also be noted from Fig. 4 that the effective index of the TM1 Bloch-mode is almost constant with the bridge-width changing from Wb = 50 nm to 100 nm. In order to eliminate the effect of the Al bridge on the TM1 Bloch-mode, the bridge width is chosen as Wb = 100 nm in this case. Although a narrower bridge-width can also be selected, the fabrication process would also be more demanding.
Fig. 4. Variations of the effective indices of both TM1 and TM0 Bloch-modes with the bridge width, Wb of the plasmonic BSWG. Here, the BSWG pitch, Λ = 250 nm; duty cycle, f = 0.5 and BSWG width, W = 2 µm.
4. Operation, bandwidth, and fabrication tolerance
The propagation characteristics of the proposed silicon HOM-pass filter are investigated by using the 3D-FV-FDTD method. As shown in Fig. 1(a), two adiabatic tapers are implemented at both the input and output ports for each mode filter. As the widths of the BSWG and bridge have been determined as W = 2 µm and Wb = 100 nm, respectively in Section 3, the taper length, Lt will be optimized in this Section. To obtain the necessary length of two tapers, the mode-filter 1 shown in Fig. 1(a) is picked as a calculated model. Variation of the power transfer efficiency with the pitch number of the taper is shown in Fig. 5 for the input TM1 mode through the mode-filter 1. In the numerical simulations, the length of the middle plasmonic BSWG is set as Lb = 12.5 µm. As these two tapers are surrounded by the subwavelength gratings, the pitch number, N of these gratings can represent the taper length, Lt = N × Λ. It can be noted from Fig. 5 that the power transfer efficiency is increased with the increase of the pitch number of the taper and that is larger than 95.5% for the pitch number, N ≥ 100. For the pitch number, N = 100 (Lt = 25 µm), the insertion loss of the input TM1 mode through the mode-filter 1 is calculated to be 0.19 dB. Meanwhile, the insertion loss of the input TM0 mode through the mode-filter 1 is calculated to be 3.4 dB, shown as a horizontally dash-dotted line in Fig. 5. The propagation fields of both the TM0 and TM1 modes are shown as two insets in Fig. 5. It can be observed that the input TM1 mode is converted to the TM1 Bloch-mode of the plasmonic BSWG and then reconverted to the output TM1 mode with a low loss by using two adiabatic tapers. Although more than half amount of power of the input TM0 mode can be cut down via the mode-filter 1, the mode ER is too small for a practical on-chip MDM system. As stated in Section 2, the input TM0 mode can be converted to the TM0 plasmonic-hybrid mode and absorbed by the central Al bridge. Although the propagation loss of this generated plasmonic-hybrid mode is relatively larger than that of a conventional Bloch-mode of a silicon BSWG, this plasmonic-hybrid mode is confined in two dimensions with a relatively low propagation-loss compared with SPPs of a plasmonic waveguide. Generally, there are two approaches to achieve a high mode ER by lengthening the plasmonic BSWG or cascading multiple HOM-pass filters. Although a larger loss of the input TM0 mode can be achieved via a longer BSWG length, a total length > 1000 µm is required for a mode ER > 15 dB, which is an unacceptable length for a compact on-chip system. Alternatively, the silicon HOM-pass filter based on the cascaded plasmonic BSWGs can be considered to enhance the mode ER and a compact device length < 260 µm can be achieved, as shown in Fig. 7. Hence, we adopted cascaded multiple HOM-pass filters to achieve a high mode ER in this case.
Fig. 5. Variation of the power transfer efficiency of the input TM1 mode with the pitch number for the adiabatic taper. The horizontally dash-dotted line represents the power transfer efficiency of the TM0 mode for the taper with the pitch number, N = 100. The Poynting vector, Pz propagation fields of both the TM0 and TM1 modes are shown as two insets for N = 100. Here, the BSWG pitch, Λ = 250 nm; duty cycle, f = 0.5; BSWG width, W = 2 µm; bridge width, Wb = 100 nm and BSWG length, Lb = 12.5 µm.
Next, the number of the cascaded mode filters is studied by using the 3D-FV-FDTD method. Variations of the power transmittances of the input TM0 and TM1 modes with the number of the cascaded mode filters are shown in Fig. 6. In the numerical simulations, the lengths of the adiabatic taper and the middle plasmonic BSWG are set as Lt = 25 µm and Lb = 12.5 µm for each mode filter. It can be noted from Fig. 6 that the power transmittance of the input TM0 mode is decreased dramatically with the number of the cascaded mode filters from 1 to 4, whereas that of the input TM1 mode is slightly reduced from 0.19 dB to only 0.63 dB. To achieve a mode ER > 20 dB, the number of the cascaded mode filters is chosen to be 4 in this case. In addition, any higher mode ER can also be obtained by cascading more mode-filters, but this would increase the device length. In this case, the insertion loss of the input TM1 mode is 0.63 dB and the mode ER is calculated to 26.4 dB. The propagation fields for the input TM0 and TM1 modes along 4-cascaded mode filters are shown in Figs. 7(a) and 7(b), respectively. It can be observed that the input TM0 mode can be completely eliminated via the optimized 4-cascaded mode-filters, while the input TM1 mode can propagate through the cascaded mode filters smoothly. Hence, a high-performance HOM-pass filter can be achieved based on the cascaded plasmonic-BSWG waveguides. It should be noted that the proposed mode filter is designed only for the TM polarization. For the TE polarization, the dominant Ex component is strongly enhanced in the low-index metal-section because of the large discontinuity for the electric field at Si-Al-Si interfaces. The insertion losses of the TE0 and TE1 modes were calculated to be 41.6 and 51.5 dB, respectively. Hence, both the TE0 and TE1 modes would be filtered out for the proposed mode filter.
Fig. 6. Variations of the power transmittance with the number of cascaded filters for both the TM0 and TM1 modes. Here, the BSWG pitch, Λ = 250 nm; duty cycle, f = 0.5; BSWG width; W = 2 µm and bridge width, Wb = 100 nm.
Fig. 7. (a) Poynting vector, Pz field of TM0 mode and (b) Hx field of TM1 mode along the propagation direction for the mode filter based on 4-cascaded mode filters.
Next, the operation bandwidth of the HOM-pass filters based on both the 4-cascaded mode filters and one mode filter are calculated by using the 3D-FV-FDTD method. Variations of the power transmittance of 4-cascaded mode filters and one mode filter with the operating wavelength are shown in Figs. 8(a) and 8(b), respectively. It can be noted from Fig. 8(a) that the 3 dB bandwidth is calculated to be 493 nm from 1222 nm to 1715 nm. The 1 dB bandwidth of 4-cascaded mode filters based HOM-pass filter is over 100 nm from 1518 nm to 1618 nm. It can also be noted from Fig. 8(b) that for the one mode filter based HOM-pass filter, the 3 dB bandwidth is larger than 600 nm and the 1 dB bandwidth is calculated to be 512 nm from 1240 nm to 1752 nm. We can see that the operation bandwidth is significantly decreased with the increase of the number of the cascaded mode filters from one to four. Although this one mode-filter can provide a wider bandwidth, the mode ER is substantially lower than that of the 4-cascaded mode filters. It can be noted from Fig. 8(a) that for the 4-cascaded mode filters based HOM-pass filter, the operating bandwidth is over 150 nm from 1433 nm to 1588 nm for the mode ER > 15.0 dB. However, it can be noted from Fig. 8(b) that for the one mode filter, the mode ER is lower than 3.4 dB for the simulated 600 nm bandwidth. Hence, there is a compromise between the mode ER and operation bandwidth. These results also confirm that our proposed HOM-pass filter is with a broad bandwidth benefitting from the BSWG structure.
Fig. 8. Variations of the power transmittance of (a) 4-cascaded mode filters and (b) one mode filter with the operating wavelength for both the TM0 and TM1 modes.
For the fabrication tolerance, variations of the power transmittance with the change of the width of the plasmonic BSWG are calculated by using the 3D-FV-FDTD method and shown in Fig. 9(a). For the CMOS process of most foundries, a fabrication error of ± 20 nm may be generated for the lithography process. Here, we extend the fabrication error of the BSWG width to ± 50 nm. It can be noted from Fig. 9(a) that with the width error of ΔW = ± 50 nm, the deterioration of the insertion loss of the TM1 mode is less than only 0.5 dB and the mode ER is larger than 24.0 dB. Variations of the power transmittance with the offset between the Al bridge and adiabatic taper are also calculated and shown in Fig. 9(b). It can be noted that even when the offset is changed by ± 20 nm, the resulting transmission deterioration of the TM1 mode is less than 0.11 dB. A high mode ER > 23.1 dB can be retained over a wide variation of offset by ± 20 nm. We can see that our proposed HOM-pass filter via cascaded plasmonic BSWG-waveguides is tolerant to both the width error of the BSWG waveguides and the variation of offset between the Al bridge and adiabatic taper.
Fig. 9. Variations of the power transmittance with (a) width error of the plasmonic BSWG and (b) offset between the Al bridge and adiabatic taper for the optimized mode filter.
The performances of the reported and our proposed HOM-pass filters are summarized in Table 1. Compared with the mode converter and MZI based mode filters, our proposed structure is with a broader bandwidth, because the MZI based structures are limited by the phase condition. Both the lower loss and wider bandwidth can be achieved for our proposed mode filter compared with the MMI and Y-junction based structure. Compared with the 1D photonic crystal grating, SWG, and LPG based structures, the loss of the HOM can be significantly reduced from >1.3 dB to only 0.63 dB and the 3 dB bandwidth is also dramatically increased from < 170 nm to 493 nm. Although the inverse designed structure based mode filter is with a low loss of < 0.26 dB, the bandwidth is limited to 100 nm and the fabrication of the nano-sized circle is difficult. For the graphene integrated mode filters, a broad bandwidth can be obtained, but the loss of the HOM is relatively high. Similarly, the VO2 based mode filter also suffers from a large loss of the HOM. Our proposed cascaded plasmonic-BSWGs could provide an efficient approach to yield a low-loss and broadband HOM-pass filter for on-chip MDM systems.
Table 1. Comparison of reported HOM-pass filters and our proposed structure
5. Conclusion
In conclusion, we have proposed and optimized a silicon HOM-pass filter by using the cascaded plasmonic BSWG-waveguides. By introducing a metal bridge at the center of the BSWG, a plasmonic hybrid mode can be generated in the BSWG waveguide. The input fundamental mode was converted to the TM0 plasmonic hybrid mode with a large loss due to the mode mismatch. Moreover, this mode suffers from both the absorption and radiation losses. The input first-order mode was not affected by the metal bridge. The mode and propagation characteristics of the plasmonic BSWG were studied by using the 3D-FV-FDTD based band-diagram and propagation calculations. A TM1 mode-pass filter was optimized based on 4-cascaded plasmonic BSWGs. The results show that the optimized mode filter is with a low loss of 0.63 dB and a broad 3 dB-bandwidth of 493 nm. A high mode ER of 26.4 dB can be achieved by using 4-cascaded plasmonic BSWGs. In addition, any higher mode-ER can also be obtained by cascading more plasmonic BSWGs. The proposed structure can enable low-loss and broadband mode filtering for on-chip MDM systems.
Funding
National Natural Science Foundation of China (11904178); Natural Science Foundation of Jiangsu Province (BK20180743); NUPTSF (NY218108, NY219048); Research Center of Optical Communications Engineering & Technology, Jiangsu Province (ZXF201801).
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