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Abstract
Mode filters are fundamental elements in a mode-division multiplexing (MDM) system for reducing modal cross-talk or realizing modal routing. However, the previously reported silicon mode filters can only filter one specific mode at a time and multiple modes filtering usually needs a cascade of several filters, which is adverse to highly integrated MDM systems. Here, we propose a unique concept to realize compact, scalable and flexible mode filters based on backward mode conversion gratings elaborately embedded in a multimode waveguide. Our proposed method is highly scalable for realizing a higher-order-mode-pass or band-mode-pass filter of any order and capable of flexibly filtering one or multiple modes simultaneously. We have demonstrated the concept through the design of four filters for different order of mode(s) and one mode demultiplexer based on such a filter, and the measurement of two fabricated 11μm length filters (TE1-pass/TE2-pass) show that an excellent performance of insertion loss <1.0dB/1.5dB and extinction ratio >29dB/28.5dB is achieved over a bandwidth of 51.2nm/48.3nm, which are competitive with the state-of-the-art.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode-division multiplexing (MDM) has drawn extensive attention as a promising solution to counter the dramatically increasing capacity demand of optical transmission systems [1,2]. In a MDM system, each eigen-mode is taken as an independent transmission channel that transmits signal individually. Therefore, the capacity of an MDM system can be dramatically increased by increasing the number of supported eigen-modes. Recently, silicon-on-insulator (SOI) platform has become very popular for building highly integrated on-chip MDM systems, owning to its compact waveguide footprint and matured complementary-metal-oxide-semiconductor compatible fabrication-process [3,4]. So far, various fundamental devices for on-chip MDM systems have been reported including the mode (de)multiplexer [5–8], mode switching [9], multimode crossing [10], multimode bending [11,12], mode splitter [13,14], mode converter [15–17] and mode filter [18].
A mode filter, which rejects the unwanted modes while letting the desired modes pass through, is an essential element in the MDM system for reducing modal cross-talk or realizing modal routing. It is well known that high-order modes can be easily stripped out from a multimode waveguide by using a tapered transition to match their cut-off conditions or an appropriately designed waveguide bending [18]. However, it is still challenging to realize a high-order-mode (HOM) pass filter that filters low-order modes while reserving high-order modes. So far, several HOM pass filters have been reported numerically or experimentally based on different approaches [19–27]. Some of the HOM pass filters are based on phase change materials or special metamaterials, such as graphene [20], vanadium oxide [21] and hyperbolic materials [22]. However, these devices usually suffer from more complicated fabrication processes or additional material absorption-loss of the desired HOM. Another approach is based on a mode conversion architecture enabled by two Mach-Zehnder interferometers and an adiabatic taper [24,25]. Although flexible mode filtering can be realized by turning the phase shifter, the cascaded scheme usually leads to a relatively large footprint. Compact all-silicon filters have recently been demonstrated using 1D photonic crystal grating waveguide [19] and subwavelength grating based contra-directional coupler [26]. In Ref. [19], a TE1-pass filter of 15-μm in length with a measured ultra-high extinction ratio (ER) of ∼50dB and insertion loss (IL) of 1.8 dB was achieved, whereas it can only be used for filtering one specific HOM. Although the mode filter proposed in Ref. [26] can be extended to block arbitrary mode, the operating bandwidths are limited, e.g., for TE0-mode blocking case, the bandwidth is 35nm (IL < 1.4 and ER > 21dB). Moreover, the cascading of various mode blocking filters are required for multiple-mode blocking. Recently, a scalable and selective HOM pass filter architecture based on asymmetric directional couplers (ADCs) has been proposed and experimentally demonstrated using polymer material [27]. Although underling principle is supposed to be compatible with silicon platform, the actual device performance is to be verified. Therefore, for building highly integrated SOI based on-chip MDM systems, a compact, flexible, and scalable HOM pass filter which can be easily fabricated by standard silicon process with high performance is desirable.
In this paper, we propose a unique concept to realize scalable and flexible HOM pass filter based on backward mode conversion gratings elaborately embedded in a multimode waveguide. Different from previously reported SOI based HOM pass filters [19,20,23] focusing on filtering only one specific HOM, our proposed method can implement a filter of any order. By utilizing different configuration of gratings, flexibly filtering of multiple lower-order modes in a multimode waveguide can be realized. To the best of our knowledge, no such a scalable and flexible mode filter on SOI has been reported yet. Based on the proposed concept, compact two-mode (TE1-pass), three-mode (TE2-pass) and four-mode (TE3-pass/TE2,3-pass) filters with low insertion loss (IL) < 1.0dB and high extinction ratio (ER) > 20dB are proposed. Additionally, a compact MDM scheme based on a TE2-pass filter and a bidirectional ADC is realized with a theoretical bandwidth of ∼100nm for IL < 1.0dB and channel crosstalk (CT) > 21dB. The fabricated two-mode (three-mode) filters are demonstrated experimentally with a high performance of IL < 1.0dB (1.5dB) and ER > 29.0dB (28.5dB) over bandwidths of 51.2nm (48.3nm), which proves the effectiveness of our concept. Moreover, the compact footprint and the simple waveguide structure of the proposed device may make it very suitable for highly integrated MDM systems.
2. Device structure and principle
Figures 1(a) and (b) show the schematic configurations of the proposed two-mode (TE1-pass) and three-mode (TE2-pass) filters. For the TE1-pass filter illustrated in Fig. 1(a), a proper waveguide width (w11) is selected so that TE0 and TE1 modes are supported in the waveguide. A row of periodic rectangular holes with a width of w12 are fully etched at the center of the waveguide, which forms a Bragg reflector for the TE0 mode. The length, period and duty cycle of the Bragg reflector are set to be a1, Λ1, and a1/Λ1, respectively. Similarly, for the TE2-pass filter as shown in Fig. 1(b), the waveguide width (w21) is determined to ensure three guided modes (TE0, TE1 and TE2) in the waveguide. To simultaneously filter two lower order modes, two rows of periodically distributed rectangular holes with a width of w22 are etched alternately in this waveguide. Here, it is noted that TE1 mode is antisymmetric, which cannot be converted from the symmetric TE0 mode by a symmetric waveguide structure [28]. The spacing between the two periodic rows is w23, which is determined through the modal characteristics as will be studied in the following analysis. The period and duty cycle of these rectangular holes are Λ2 and a2/Λ2, respectively. The filters are all designed on a standard SOI wafer with a 220nm-thick top silicon layer (i.e., h = 220nm) covered by SiO2 as shown Fig. 1(c).
Fig. 1. Top view of the proposed TE1–pass filter (a) and TE2- pass filter (b); cross-sectional view of the multimode waveguide(c).
The working principle of the designed filters is based on the backward mode conversion mechanism in a multimode waveguide engineered by gratings as illustrated in Fig. 1. When different modes are injected into the corresponding multi-mode waveguide, by elaborately embedding gratings with proper parameters, the unwanted low-order modes (TE0 in TE1-pass filter; TE1 and TE0 in TE2-pass filter) are backward reflected, while the desired high-order modes pass through the waveguide with very low loss. For the TE2-pass filter, it should be noted that the power of TE0 and TE1 modes are interconverted during the reflection. According to the coupled mode theory [29], to achieve efficient backward coupling between different order modes, the following phase-match condition should be approximately satisfied
where ${\beta _{\textrm{forward}}}$ and ${\beta _{\textrm{backward}}}$ are the propagation constants of the specific forward and backward lower-order modes, respectively. Here, by substituting $\beta ={\pm} {{2\pi n} / \lambda }$ into Eq. (1), the pitch of the grating is determined as where λ0 is operating wavelength, nforward and nbackward are the effective indices of the forward and backward lower-order modes, respectively. On the other hand, to let the desired higher-order modes pass through the device with low loss, the subwavelength-guided wave propagation condition must be satisfied [30] where npass is the effective index of the desired high-order mode(s). Since the mode effective indices of HOMs are lower than lower-order modes, the conditions defined in Eqs. (2) and (3) are easily fulfilled. The principle is well-suited for SOI waveguides owing to the relatively large modal birefringence. It is noted that the principle can be extended to design an HOM pass filter of any order as well as TM mode filters. Moreover, flexibly and simultaneously filtering of multiple lower-order modes can also be realized by combining different configuration of gratings that fulfill the above conditions. A design concept or method with these characteristics is usually described as scalable and flexible [16,17,27].3. Design and optimization
To validate the design principle, we first calculated the TE modal characteristics of a standard SOI waveguide (as shown in Fig. 1(c)) in terms of the waveguide width using a mode solver based on the finite difference frequency-domain method [31] as shown in Fig. 2. Here, the operation wavelength is set to be 1550nm and the effective indices of Si and SiO2 are 3.476 and 1.444, respectively. From Fig. 2(a), one sees that the mode indices generally increases with the increase of the waveguide width and great modal birefringence between different orders of modes is observed, which are very beneficial to meet the above conditions. Here, the widths of the TE1- and TE2-pass filters are respectively selected as w11 = 700nm and w21 = 1000nm, which ensures sufficient space from the cut-off points to make the desired higher-order modes being well supported.
Fig. 2. (a) Simulated effective refractive indices of TE eigenmodes at 1550nm wavelength for 220nm thick silicon waveguides with different widths; field distributions of TE0 mode (b), TE1 mode (c) and TE2 mode (d) for a multimode waveguide with a width of 1000 nm.
For the present design, the loss of the desired high-order modes mainly comes from the abrupt discontinuities generated by the grating interfaces. Therefore, the width and position of the gratings (w12, w22 and w23) are key parameters that determinate the ILs of the two filters. Here, a simple but effective approach [29] is taken by properly choosing the above three parameters through the power distribution of waveguide modes. As an example, Fig. 2(b) shows the electric field patterns of three TE modes (TE0, TE1 TE2) supported in a standard multimode waveguide (as shown in Fig. 1(c)) with a width of w21 = 1000nm. From the figures, one sees that the power of TE0 mode mainly concentrates near the center of the waveguide and gradually decays toward the core sides, while that of TE1 (TE2) mode have two (three) peaks in the waveguide core with one (two) zero point(s) as marked by red dashed circle in Figs. 2(c) and (d). Therefore, for the TE1-pass filter, to make the TE0 mode strongly reflected while simultaneously reducing the influence on the TE1 mode, the grating is preferred to be placed at the center of the core (TE1 zero point). Similarly, for the TE2-pass filter, the gratings are better to be placed near the zero points of the TE2 mode. Moreover, to minimize the influence of the gratings on the desired modes, a narrow grating width is recommended. Making a balance between device performance and fabrication difficulty, we set w12 = 80nm, w22 = 60nm and w23 = 340nm as a primary design and the variation of these parameters will be further studied in the following analysis.
The period Λ is a critical parameter to determine the operating wavelength of the devices. After initially determining the widths and position of the gratings, we can roughly calculate the grating period using Eq. (2). Here, for the sake of simplicity, the effective indices in Fig. 2(a) were utilized to perform the calculation. The grating period Λ1 that satisfies the strong reflection of the TE0 mode in a 700nm multimode waveguide is estimated to be ∼320nm. Similarly, the grating period Λ2 that satisfies the reverse coupling condition between TE0 and TE1 in a 1000nm multimode waveguide is ∼325.5nm. To verify the effectiveness of parameters determined above, we further calculated the band diagrams of the two filters using the 3D finite difference frequency-domain (FDTD) method [32] as shown in Figs. 3(a) and (b). In this simulation, the duty cycle is set to be 0.5. From the two figures, a large bandgap around 1550 nm for the unwanted lower-order mode(s) for both the two filters is observed, while the desired higher Bloch mode is supported in a wide wavelength range across the bandgap. Moreover, the phenomenon of anti-crossing of the TE0 and TE1 modes due to the antisymmetric multimode Bragg waveguide gratings [33] is also illustrated in Fig. 3(b).
Usually, the rejection of the undesired mode(s) can be improved by increasing the period number N (equal to the number of holes in the waveguide along the longitudinal direction) via enhancing the reflection. Figures 4(a) and (b) show the normalized transmission for different input modes through the two filters with respect to the period number of the gratings at the wavelength of 1550 nm. Here, the calculated eigenmodes are utilized as the mode sources which directly injected into the input port of the filter. A numerical monitor placed at the output port of the filter is used to detect the field data for transmission calculation. It can be clearly seen that the transmission of lower-order mode(s) generally decreases with the increase of grating periods and the variation become slower when N tends to lager, while that of the desired higher-order mode remains at a high level (∼0.3 dB and ∼0.4 dB for TE1- and TE2-pass filters, respectively) without noticeable changes. It is also noted that very small changes for the TE1 mode of the TE2-pass filter is observed when the period number is higher than 30, and the corresponding transmission is below 30 dB for both TE0 and TE1 modes. The reason that TE1 extinction does not increase after N = 35 may due to its relatively lower reflection coefficient decided by the grating structure. It is also noted that the results show an oscillatory length dependence, which is caused by reflection and scattering sites present in the device (eg. abrupt discontinuities at two ports) leading to Fabry–Perot modes and standing waves. Making a balance between the compactness and the performance of the devices, the grating period is selected to be N = 35, which corresponding to a device length L of ∼11 um, where L = N×Λ.
Fig. 4. Simulated normalized transmission for different input modes through the two filters with respect to the grating period number at the wavelength of 1550nm: (a) TE1-pass and (b) TE2-pass.
4. Numerical characterization
Using the parameters determined above, the 3D FDTD method is further utilized to give a comprehensive assessment of the performance and fabrication tolerances of the filters. The ER and IL are two crucial figures of merit to characterize the performance of the device, which are defined as
To further evaluate the performance of the devices, the fabrication tolerances of the key structural parameters are analyzed. Figures 6(a-c) show the ER and IL of the two filters with respect to the variations of the grating widths (w12, w22) and separation (w23) at the wavelength of 1550 nm. From Fig. 6(a), we can clearly observe that with the increase of the grating width, the ER increases, while the IL decreases. Therefore, for TE1-pass filter, we may need to make a trade-off between the ER and IL to choose a proper grating width. If we consider a high performance of ER > ∼40 dB and IL < ∼0.3 dB, the fabrication error should be less than ±20 nm from the initialized width of w12 = 80 nm. From Figs. 6(b) and (c), one sees that the IL is insensitive to the variations of both the grating width w22 and separation w23, while the ER for TE0 mode always decreases with the increase of w22 and w23. In addition, the ER for the TE1 mode first increases and then decreases with the increase of w22 and w23, and the maximum ER is seen at w22 = 60nm and w23 = 340nm. The fabrication tolerances are 40nm (Δw22, ± 20nm) and 60nm (Δw23, ± 30nm) for ensuring ER > 29dB (both TE0 and TE1) and IL < 0.5dB.
Fig. 5. Simulated normalized transmission spectra of each order mode of the above filters in a wavelength range from 1450 nm to 1650nm: (a) TE1-pass and (b) TE2-pass; Field evolution of the electric field components along the devices for different input modes of the two filters at the wavelength of 1550 nm: (c) TE1-pass and (d) TE2-pass.
Fig. 6. Simulated ER and IL of the two filters with respect to the variations of the grating widths (a) w11, (b) w22 and the separation (c) w23 at the wavelength of 1550 nm.
Figures 7(a-d) show the ER and IL for the two devices with respect to the pitch width and the grating period. For this calculation, the optimal periods Λ1 = 320 nm and Λ2 = 325.5 nm are chosen when the variation of the pitch width is considered; while a fixed duty cycle a/Λ=0.5 is selected when exploring the deviation of the grating period. From Figs. 7(a) and (c), one sees that the deviation of the pitch widths has little influence on the performance of the two devices. In a range of ±20 nm, the IL can always keep below 0.3 dB and the ER shows slight variations around a very high level (ER∼40 dB for TE1-pass filter; ER∼40 dB/30 dB (TE0/TE1) for the TE2-pass filter). From Figs. 7(b) and (d), little change is observed for the IL of both the two filters with the variation of the grating period, while the ER is very sensitive to the grating period deviations. For the TE1-pass filter, an ER > 25 dB can be guaranteed in a periodic deviation range about 35 nm (305nm∼340 nm). For the TE2-pass filter, the grating period deviation should be ∼40 nm (310∼350 nm) for maintaining ER > 25 dB. Therefore, if the optimal periods determined above are taken, the period error should be controlled within ±15 nm.
Fig. 7. Simulated ER and IL of the two filters with respect to the variations of the pitch widths and the grating periods: (a) a1 and (b) Λ1 for TE1-pass filter; (c) a1 and (d) Λ1 for TE2-pass filter.
5. Fabrication and measurement
To validate the design principle and the simulation results, the filters are fabricated on a standard SOI wafer with a 220 nm thick top silicon layer and 2μm buried oxide layer. An electron beam lithography process is utilized for the photoresist-patterning, followed by an inductively coupled plasma etching process to etch the Si waveguide structure, and finally a plasma-enhanced chemical vapor deposition to deposit a 2.2um SiO2 upper-cladding layer. With the state-of-the-art semiconductor fabrication process, waveguides with feature size of hundreds of nanometers can be easily fabricated with high accuracy [34]. The cost in the device fabrication is mainly decided by the number of processes and the device size (area). For such a simple waveguide structure with one-step etching, the cost will not be expensive. Alternatively, there are many open access fabs providing multi-project wafer service [35], which can greatly reduce the fabrication cost through shared identical processes, but with a longer fabrication cycle. Figures 8(a-d) show the microscope images of waveguide configurations for the measurements and the corresponding scanning electron microscope (SEM) images of the fabricated filters. To accomplish the measurements, a (de)multiplexing scheme based on adiabatic tapers and ADCs [8] is used to add/drop TE0, TE1 and TE2 modes in multimode waveguides from TE0 mode in single-mode waveguides. Grating couplers are utilized to couple light between fibers and silicon waveguides. Meanwhile, identical waveguide configurations without the central filters are adopted for measurement normalization. The light output from a broadband source is first connected to a polarization controller and then coupled to the mode input port (marked in microscope images, left-hand side) on the chip via a fiber probe. An optical spectrum analyzer with fiber probe is connected to the corresponding mode output port (marked in microscope images, right-hand side). By adjusting the polarization controller to search the maximal output in the spectrum analyzer, we can detect the corresponding mode transmission spectra.
Fig. 8. Microscopic images (a) and SEM images (b) of fabricated TE1-pass filter and microscopic images (c) and SEM images (d) of TE2-pass filters.
Figures 9(a) and (b) show the measured transmission spectra for different input modes of the two filters, respectively. For comparison, we also plotted the theoretical results in the same figure using dotted lines. Here, the theoretical results are obtained by scanning the optimal period length within in a fabrication error less than 10 nm based on the design parameters. A broadband source (NKT Photonics, SuperK FD6) and an optical spectrum analyzer (YOKOGAWA, AQ6375B) were utilized for the measurement. From Fig. 9(a), one can observe that the ER for the TE1-pass filter is larger than 20 dB in the wavelength range from 1500 to 1580 nm, and the measured IL is lower than 2.0 dB. Here, limited by the working bandwidth of all the auxiliary test components such as the grating couplers and the mode (de)multiplexers, the measurement bandwidth of the devices are usually about 80nm [8,19]. If a critical performance of IL < 1.0dB and ER > 29dB is considered, the operating bandwidth is ∼ 51.2nm (1518.3nm to 1569.5nm), which covers the whole C band. As for the TE2-pass filter shown in Fig. 9(b), in a bandwidth of 48.3nm (1518.5nm to 1566.8nm), TE2 mode passes through the filter with an IL lower than 1.5dB, and both TE0 and TE1 are filtered out with an ER higher than 28.5dB. In general, the experimental results agree well with the simulation, which proves the effectiveness of the proposed concept.
Fig. 9. Measured transmission spectra for different input modes of the two filters: (a) TE1-pass and (b) TE2-pass.
6. Extension and discussion
6.1 Flexible HOM pass filter scheme
It is worth noting that the proposed HOM pass filter scheme is highly flexible and scalable. Here, if a multimode waveguide that supports four modes (TE0, TE1, TE2 and TE3) or more is considered, we can flexibly let one or several highest order mode(s) pass by properly engineering the gratings. As an example, we designed a TE3-pass filter and a two-mode pass (TE2, 3-pass) filter based on a multimode waveguide supporting four guiding TE modes as shown in Figs. 10(a) and (b). For simplicity, we simply give the waveguide parameters in the figure caption and these parameters may not be necessarily the optimal ones since we only intend to prove the flexibility and scalability of the principle. It is also noted that a flexible and arbitrary mode filter scheme (like a bandpass filter in the WDM system) can be constructed by simply combine the present HOM(s) pass filter and a tapered based lower-order pass filter as shown in Fig. 10(c). As far as we know, such a filter has not been reported previously.
Fig. 10. Top view of the proposed TE3-pass filter (a) and TE2,3-pass filter (b); schematic diagram of a flexible mode filter scheme (c). The waveguide parameters are: a3 = 167nm, Λ3 = 334nm, w31 = 1300nm, w32 = 65nm, w33 = 290nm, a4 = 152.5nm, Λ4 = 305nm, w42 = 80nm, and w43 = 460nm.
Figures 11(a) and (b) show the transmission spectra of the TE3-pass filter and the TE2, 3-pass filter, respectively. For the TE3-pass filter, the IL is calculated to be 1.0 dB at the wavelength of 1550nm and the corresponding ER of TE3-TE0, TE3-TE1, TE3-TE2 are 50.0dB, 26.7dB and 40.3dB, respectively. An operating bandwidth of ∼95nm (1488nm to 1583nm) can be achieved for ER > 21dB and IL < 2dB. For the TE2,3-pass filter, the calculated ILs of TE2 and TE3 are respectively 0.14dB and 0.44dB at 1550nm, and the corresponding ERs relative to the undesired TE0 and TE1 modes are both higher than 20dB. The operating bandwidth for ER > 15dB and IL < 1.5dB is ∼85nm (1505nm-1590nm). Figures 11(c) and (d) show the field evolution of the main electric field components along the propagation distance for different input modes of the two filters at the wavelength of 1550 nm, respectively. From Fig. 11(c), one sees that the TE3 mode directly passes through the device almost without loss, while the TE0, TE1 and TE2 are reflected (TE0 and TE2 are interconverted; TE1 without change). From Fig. 11(d), the desired TE2 and TE3 mode directly pass through filter, while TE0 and TE1 are reflected and interconverted.
Fig. 11. Simulated normalized transmission spectra of each order mode of the above filters in a wavelength range from 1450nm to 1650nm: (a) TE3-pass and (b) TE2,3-pass; Field evolution of the electric field components along the devices for different input modes of the two filters at the wavelength of 1550 nm: (c) TE3-pass and (d) TE2,3-pass.
6.2 Mode (de)multiplexer scheme
The above filters can also be used to construct a compact mode (de)multiplexer scheme. Here, as an example, a three mode (de)multiplexer was designed based on a TE2-pass filter and an ADC as shown in Fig. 12. The ADC is realized by simply selecting a proper width of the single-mode waveguide to satisfy the phase matching of the TE1 mode in the multimode waveguide. Comparing with the widely used cascaded-ADC (de)multiplexer, the present design is more compact since only one ADC is used and no tapered design is required for adiabatic mode conversion.
Fig. 12. Top view of the three mode (de)multiplexer with the waveguide parameters: L = 20μm and g = 95nm.
Figure 13(a) shows the field evolution of the main electric field components along the (de)multiplexer for different input modes at the wavelength of 1550 nm. From the figures, one sees that the TE0, TE1 and TE2 modes injected to the multimode waveguide propagate along different optical paths and finally output at different channels. Figures 13(b-d) show the transmission responses detected at different output ports (O1, O2, and O3) when the TE0, TE1, and TE2 modes are inputted, respectively. From the figures, one can observe that all the three modes can efficiently output at the corresponding output channel with a low loss (IL <1.0 dB) in a wide wavelength range of 100nm and the CT with respect to the remaining two channels are generally higher than ∼21dB. The device has a simple structure and a compact footprint, which may be a promising candidate for on-chip mode (de)multiplexing.
Fig. 13. Simulated field evolution of the electric field components along the devices for different input modes at the wavelength of 1550 nm; Normalized transmission responses detected at different output ports (O1, O2, and O3) when the TE0 (b), TE1 (c), and TE2 (d) modes are inputted, respectively.
7. Conclusion
In summary, we have proposed a concept to realize scalable and flexible on-chip silicon mode filters based on backward mode conversion gratings elaborately embedded in a multimode waveguide. By utilizing different configuration of gratings, flexibly filtering of multiple lower-order modes in a multimode waveguide is realized. The scalability of the proposed concept is demonstrated by the design of four different devices including two-mode (TE1-pass), three-mode (TE2-pass) and four-mode (TE3-pass/TE2,3-pass) filters. Simulated results show that low IL < 1.0dB and high ER > 20dB can be achieved for all the four devices with very compact length ∼11μm. Additionally, a compact MDM scheme based on a TE2-pass filter and a bidirectional ADC is realized with a theoretical operating bandwidth of ∼100nm for IL < 1.0dB and channel CT > 21dB. The fabricated two-mode/three-mode filters are demonstrated experimentally with a high performance of IL < 1.0dB/1.5dB and ER > 29dB/28.5dB over bandwidths of 51.2nm and 48.3nm, which proves the effectiveness of our concept. Moreover, the waveguide structure is simple and can be fabricated on standard SOI platform with one-step etching process. This work offers an effective approach for designing compact, flexible and scalable mode filters on SOI platform, which has excellent potential to be used in highly integrated SOI based on-chip MDM systems.
Funding
National Natural Science Foundation of China (12004092); Natural Science Foundation of Hebei Province (H2019201170); Science and Technology Project of Hebei Education Department (QN2020259); Advanced Talents Program of Hebei University (521000981203).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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