Scalable selective high order mode pass filter architecture with asymmetric directional couplers

: We propose a novel design architecture to realize scalable selective mode ﬁlter based on the asymmetric directional coupler structure. In this structure, any arbitrary high-order mode can pass, whereas other unwanted modes are blocked. Furthermore, multiple optical modes can be blocked by only adjusting the structural parameters. As a proof of concept, we experimentally demonstrated a three-mode device and the scalability of the proposed structure is demonstrated by another design of four-mode ﬁlter. The proposed architecture oﬀers scalability and high-design ﬂexibility, and it has excellent potential to be used in advanced mode division multiplexing optical networks.


Introduction
Mode division multiplexing (MDM) technology has enticed significant attention as a feasible solution to the future capacity demand of optical networks [1][2][3][4][5][6][7][8][9][10][11] to support the future 5G wireless networks, Internet of Things, massive cloud infrastructure deployment and machine-to-machine communications.In the MDM system, each optical mode is regarded as an independent data channel that carries information signal.The transmission capacity of a fibre optic system can be increased by increasing the number of allowed modes in the MDM system.In this context, several important aspects [2], namely, compatibility, integration and crosstalk, must be considered when discussing the requirement for MDM system.A smooth transition to the MDM system must address the component and connectivity challenges to scale up the capacities beyond those of existing WDM systems [12].
Mode filters are essential devices in MDM systems, and they are vital in filtering undesired modes after demultiplexing different optical modes.Mode filters can significantly reduce modal cross-talk and improve system performance.Moreover, for the construction of mode-controlling devices, mode pass and mode block filters are needed.However, high-order modes have weak optical confinement and can be stripped out easily by using a tapered structure with a favorable mode cut-off width.Meanwhile, with the conventional structure, low-order modes are difficult to filter out because of their strong optical confinement in the core.Despite the importance of these devices, to date, very little research has been published [13][14][15][16][17][18][19][20] on high-order mode pass filters in the planar lightwave circuit (PLC) platform.Some of the reported works used special materials, such as graphene [13][14], hyperbolic materials [15] and vanadium oxide (VO 2 ) [16], to realize low-order mode filter operation.The operation of some of these devices is confined to either transverse magnetic (TM) or transverse electric (TE) modes.Recent studies demonstrated low-order mode filtering based on mode conversion [17][18] and optically resonant devices, such as subwavelength grating [19] and the 1D photonic crystal silicon waveguide [20].However, these structures [16,[19][20] are focused on blocking only one specific high-order mode, and multiple-mode filtering by these structures requires the cascading of various mode blocking filters.Therefore, for continuous improvement and full design flexibility, a mode filter device capable of filtering multiple optical modes is desirable.Furthermore, designing a selective mode filter which can pass an arbitrary high-order mode and filter out all unwanted modes is also highly desirable.
In this work, we propose a novel design structure for a selective mode filter based on the asymmetric directional couplers (ADC) in the PLC platform.Here, any arbitrary high-order mode (TE K ) is allowed to propagate, and all the remaining unwanted modes, including the fundamental mode (TE 0 ), are blocked.A conceptual diagram is presented in Fig. 1.The design architecture has the unique advantage of scalability, and the same structure can be extended to realize mode filtering with an increased number of optical modes.Here, we use three ADCs to form our unique structure, and this device does not require cascaded structures for filtering multiple optical modes.Moreover, by merely adjusting the structural parameters and without using any material of special optical properties (such as graphene, hyperbolic material and VO 2 ) particular high-order mode pass filter operation can be achieved, thereby offering high design flexibility.As a proof of concept, we experimentally demonstrated a three-mode device.In this device, the fundamental (TE 0 ) and first-order modes (TE 1 ) are blocked, and only the second-order mode (TE 2 ) can pass.In addition, the scalability of the proposed structure is demonstrated by another design of four-mode filter.In this structure, the third-order (TE 3 ) mode is allowed to pass, and other remaining modes are filtered out.We fabricate the devices using polymer material and characterize in the C-Band.Both the devices have negligible polarization dependence.The measured TE 2 -to-TE 0 extinction ratio is 20.57dB, and TE 2 -to-TE 1 extinction ratio is 21.59 dB at 1.550 µm wavelength for the three-mode filter.For the four-mode filter, the measured TE 3 -to-TE 0 extinction ratio is 20.81 dB, TE 3 -to-TE 1 extinction ratio is 17.17 dB, and TE 3 -to-TE 2 extinction is 20.79 dB at 1.550 µm wavelength.The experimental performance agrees reasonably well with the simulation.The operation principle of the device holds for TE and TM polarization and the design idea is compatible with other PLC platforms also, such as silicon photonics.

General architecture of the mode filter
The general architecture of the selective high-order mode pass filter is presented in Fig. 2. At two ends, PortA and PortB are used as the device's multi-mode light input and output ports, respectively.The device consists of one central waveguide core and two side cores.The structure of the proposed design is bi-directional, and to facilitate discussion, we consider light propagation to be from PortA to PortB unless otherwise stated.In the central core, a single-mode filter waveguide (SMFW) is sandwiched between the two multi-mode waveguides (MMW) at the two ends of the device.The function of the SMFW is to allow only the fundamental mode from PortA and block the high-order modes.The connections are done by using two linear tapers.Taper1 connects MMW at PortA to SMFW, and Taper2 connects SMFW to Taper2 at PortB.Taper2 is only used as the adiabatic transition medium from SMFW to MMW in PortB and does not have any active function in the mode filter operation.However, for light propagation from PortB to PortA, the functions of Taper1 and Taper2 will be swapped.The side core is used as the coupling waveguide (CW) for the central core to facilitate evanescent coupling between the two cores.The width of the MMW is selected as W N to support the maximum number of modes N in a multimode waveguide.If K (K = 1, 2,..L,. . .N) represents any arbitrary high-order mode, then the width W 0 of the CW must be designed such that it satisfies the phase's matching condition, i.e. the effective index of the Kth-order mode (TE K ) of the MMW (neff K ) being equal to the effective index of the fundamental mode (TE 0 ) of the CW (neff 0 ).According to coupled mode theory, when neff K = neff 0 , efficient mode conversion occurs between the TE K mode of the MMW and the TE 0 mode of the CW.Similarly, by the reciprocity principle of linear optics, the TE 0 mode of the CW will be coupled to the TE K mode of the MMW.As shown in the Fig. 2, two ADCs are associated between the two cores.ADC1 at PortA couples the TE K mode of the MMW to the TE 0 mode of the CW, whereas ADC2 couples the TE 0 mode of the CW to the TE K mode at PortB.Furthermore, the other side core is a multi-mode filter waveguide (MMFW) connected with an adiabatic taper (Taper3), which is tapered into a single-mode waveguide.The function of this side core is to couple the TE 0 mode of the SMFW to any high-order mode (TE L ) of the MMFW, and then, Taper3 is used to filter out that specific high-order mode.ADC3 performs this coupling function by satisfying the phase-matching condition neff 0 = neff L .The width W L of the MMFW can be designed to support any high-order mode from the 1st to the Nth order as long the phase-matching condition is satisfied.The function of Taper3 is to filter out that high-order mode (TE L ).For light propagation from PortB to PortA, Taper4 will perform this task of Taper3.
The TE 0 mode launched at PortA propagates through Taper1 to the SMFW region, where ADC3 is activated.The TE 0 mode from SMFW is coupled to the TE L mode of the MMFW.Taper3 blocks the TE L mode and radiates out to the cladding because it supports only the TE 0 mode.Consequently, no light comes out of PortB.Thus, the TE 0 mode launched at PortA is filtered out.Then, the TE K mode launched at PortA is coupled to the TE 0 mode of the CW by ADC1 and then coupled back to the TE K mode by ADC2 after propagation through CW and light exits from PortB.Hence, the arbitrary high-order TE K mode is allowed by the device to propagate.By contrast, all the other high-order modes (except the TE K ) mode launched at PortA cannot propagate through SMFW and be filtered out as cladding modes.They also cannot be coupled to CW due to phase mismatch.Thus, all the high-order modes except the TE K mode are filtered out, and no light comes out of PortB.Again, for light launched into PortB, the device function will be exactly similar, where Taper2 and Taper4 will perform these same tasks of Taper1 and Taper3, respectively.In summary, our proposed device works as a selective mode filter which passes only the arbitrary TE K (TM K ) mode and blocks all the remaining modes.

Three-mode filter device
For proof of concept, we experimentally demonstrate a three-mode device using the polymer material.The refractive index of the core is set as 1.569, and the cladding is 1.559 with an index difference of 0.01 at 1.550 µm wavelength.These refractive indices represent the polymer material we use to fabricate the device.The mode filter device is designed, and its performance is simulated using the commercially available Rsoft CAD, BPM environment.The ADCs are designed based on the phase-matching conditions.Given additional fabrication issues, the design of the waveguide has an embedded channel structure, and the core height is set to H = 4.50 µm.With our proposed structure, many dimensions are possible for satisfying the phase-matching conditions.Figure 3(a) shows the waveguide width dependence of effective indices for three different modes in a rectangular waveguide for TE polarization.To create the design example, we fix the width W 2 = 14.25 µm of the MMW to support the TE 0 , TE 1 and TE 2 modes only.In Fig. 3(a), the horizontal line 'a' represents the phase-matching condition for the TE 2 and TE 0 modes, whose effective indices are equal to 1.56008.In this case, the width of the CW should be W 0 = 2.30 µm to satisfy the phase-matching condition between the TE 2 mode of the MMW and the TE 0 mode of the CW.Here, ADC1 will couple the TE 2 mode from PortA of MMW to the TE 0 mode of the CW, and ADC2 will couple back the TE 0 mode to the TE 2 mode of the MMW at PortB.Thus, the device will work as the TE 2 mode pass filter for this design condition and block the TE 0 and TE 1 modes.
With the width of the MMW fixed, i.e.W 2 = 14.25 µm, the horizontal line 'b' in Fig. 3(a) represents the phase-matching condition for the TE 1 and TE 0 modes, whose effective indices are equal to 1.56305.In this case, the width of the CW should be W 0 ´= 5.56 µm to satisfy the phase-matching condition between the TE 1 mode of the MMW and the TE 0 mode of the CW.Here, ADC1 will couple the TE 1 mode of MMW to the TE 0 mode of the CW, and ADC2 will couple back this TE 0 mode to the TE 1 mode of the MMW at PortB.For this design condition, the device will work as the TE 1 mode pass filter.Hence, the device can either work as the TE 2 mode pass filter or the TE 1 mode pass filter by simply adjusting the width of the CW, thereby offering high design flexibility.
To verify the design concept, we experimentally demonstrate the device function as a TE 2 mode pass filter, and Fig. 3(b) shows the structure of the three-mode filter device.The width of the MMW is selected as W 2 =14.25 µm to support three modes only, and a width of CW is selected as 2.30 µm to satisfy the phase-matching condition between the TE 2 and TE 0 modes.To simplify our design, we set the width of the MMFW as W 2 =14.25 µm; thus, ADC1, ADC2 and ADC3 will be identical in dimension, as shown in Fig. 3  The operation of the three-mode filter is illustrated in Fig. 4(a) with the evolution of the launched modes at different propagation lengths of the device.The figure clearly indicates that the TE 0 and TE 1 modes are blocked and only the TE 2 mode is allowed to propagate by the mode filter.In Fig. 4(a, i), when the TE 0 mode is launched into PortA, it propagates through Taper1 to the SMFW region (at Z 2 ), and here, ADC3 is used.The TE 0 mode from SMFW is coupled to the TE 2 mode of the MMFW at Z 3 .Taper3 blocks the TE 2 mode and radiates out to the cladding at Z 4 , given that it supports the TE 0 mode only.Consequently, no light exits PortB; thus, the TE 0 mode launched at PortA is filtered out.In Fig. 4(a,ii), when the TE 1 mode is launched into PortA, it cannot propagate through the SMFW at Z 2 .Given that, this section allows only the TE 0 mode, and the TE 1 mode is blocked.Therefore, no light exits PortB for the launch of the TE 1 mode at PortA.However, as shown in Fig. 4(a,iii), when the TE 2 mode is launched at PortA, ADC1 is activated.The TE 2 mode is coupled to the TE 0 mode of the CW by ADC1.After propagation through CW (at Z 3 ), the TE 0 mode is coupled back to the TE 2 mode by ADC2, and light exits PortB.Hence, only the TE 2 mode is allowed by the device to propagate.Therefore, the device functions as a selective mode filter.
We evaluate the performance of the three-mode filter by computing the transmission characteristics of each optical mode in the C-band.The material loss is not considered for the simulation.determine the different design parameters, which are summarised in Table 1.The total length of the device is 9.71 mm.

Scaling to a four-mode filter device
To demonstrate the scalability of our proposed design, we present the structure of a four-mode filter.The refractive indices of the core and the cladding material are the same as those of the three-mode device, and the performance of the device is simulated using the Rsoft.Three ADCs are designed based on the phase-matching conditions.Figure 5(a) shows the waveguide width dependence of the effective indices of the four modes in a rectangular waveguide for TE polarization.To show a design example of our proposed method, we fix the width W 3 = 22.00 µm of the MMW to support the TE 0 , TE 1 , TE 2 and TE 3 modes only.In Fig. 5(a), the horizontal line 'a' represents the phase-matching condition for the TE 3 and TE 0 modes, whose effective indices are equal to 1.56081.In this case, the width of the CW should be W 0 = 2.83 µm to satisfy the phase-matching condition between the TE 3 mode of the MMW and the TE 0 mode of the CW.Here, ADC1 will couple the TE 3 mode from PortA of MMW to the TE 0 mode of the CW, and ADC2 will couple back the TE 0 mode to the TE 2 mode of the MMW at PortB.Hence, the device will work as the 3 mode pass filter for this design condition.With a fixed width of the MMW, i.e.W 3 = 22.00 µm, the horizontal line 'b' in Fig. 5(a) represents the phase-matching condition for the TE 2 and TE 0 modes, whose effective indices are equal to 1.56285.In this case, the width of the CW should be W 0 ´= 5.02 µm to satisfy the phase-matching condition between the TE 2 mode of the MMW and TE 0 mode of the CW.Here, ADC1 will couple the TE 2 mode of MMW to the TE 0 mode of the CW, and ADC2 will couple back the TE 0 mode to the TE 2 mode of the MMW at PortB.In this design condition, the device will work as the TE 2 mode pass filter.Similarly, finding the phase-matching condition for the TE 1 mode and estimating the suitable width of the CW are easy, and the device will operate as the TE 1 mode pass filter.Hence, by only adjusting the width of the CW, the four-mode device can work as any arbitrary high-order mode pass filter, thereby offering high design flexibility.
To verify the design concept and scalability of the proposed structure, we demonstrate the device function as the TE 3 mode pass filter.Figure 5(b) shows the structure of the four-mode filter device.As stated, the width of the MMW is selected as W 3 =22.00µm to support the four modes only, and the width of CW is selected as W 0 = 2.83 µm to satisfy the phase-matching condition between the TE 3 and TE 0 modes.To simplify our design, we also set the width of the MMFW as W 3 = 22.00 µm.Thus, ADC1, ADC2 and ADC3 will be identical in dimension, as shown in Fig. 5(b).As in the three-mode device, we ignore Taper4 and use MOST in Rsoft CAD to determine the different design parameters, which are summarised in Table 1.The total length of the device is 9.95 mm.
The operation of the four-mode filter is illustrated in Fig. 6(a) with the evolution of the launched modes at different propagation lengths of the device.The figure clearly indicates that the mode filter blocks the TE 0 , TE 1 and TE 2 modes and allows only the TE 3 mode to propagate.In Fig. 6(a,i), when the TE 0 mode is launched into PortA, it propagates through Taper1 to the SMFW region at Z 2 , and here, ADC3 is activated.The TE 0 mode from SMFW is coupled to the TE 3 mode of the MMFW at Z 3 .Taper3 blocks the TE 3 mode and radiates out to the cladding at Z 4 , given that it supports the TE 0 mode only.Consequently, no light exits PortB, which means that the TE 0 mode launched at PortA is filtered out.When the TE 1 and TE 2 modes in Fig. 6(a,ii) and 6(a,iii), respectively, are launched into PortA, these high-order modes cannot propagate through the SMFW.Given that, this section allows only the TE 0 mode through, and the TE 1 and TE 2 modes are blocked at Z 2 .Thus, no light exits PortB for the launch of the TE 1 and TE 2 modes at PortA.However, as shown in Fig. 6(a,iv), when the TE 3 mode is launched at PortA, ADC1 is activated.The TE 3 mode is coupled to the TE 0 mode of the CW by ADC1 and is then coupled back to the TE 3 mode by ADC2 at Z 4 after propagation through CW (at Z 2 ).Consequently, light exits PortB.Thus, only the TE 3 mode is allowed by the device to propagate.Therefore, the device design is scalable to other high-order mode pass filters.We evaluate the performance of the four-mode filter by computing the transmission characteristics of each optical mode in the C-band.The material loss is not considered for the simulation.Figures 6(b) and 6(c) show the simulated transmission spectra of the mode filter for the TE and TM polarization, respectively.The device has excess losses of 0.47 and 0.37 dB for the TE 3 mode and the TM 3 mode transmission, respectively, for the centre wavelength of 1.550 µm.Like the three-mode filter, the device has negligible polarization dependence because of the small index contrast between the core and the cladding material.As shown in Fig. 6(b), the device offers overall TE 0 , TE 1 and TE 2 mode rejection of less than -19.61 dB, less than -20.10 dB and less than -25.12 dB, respectively, in the C-band.The TM 0 , TM 1 and TM 2 mode rejection is less than -19.25, -19.99 and -24.93 dB, respectively, in the C-band, as shown in Fig. 6(c).

Fabrication
The three-mode and four-mode filters were fabricated with polymer materials EpoClad and EpoCore (micro resist technology GmbH) using the standard micro-fabrication process.The measured refractive indices of the EpoClad and EpoCore were 1.559 and 1.569, respectively, at 1.536 µm wavelength, with negligible material birefringence.The fabrication steps of waveguide devices using EpoCore and EpoClad is illustrated in Fig. 7.The devices were fabricated on Si wafer, and after cleaning the wafer, O 2 surface treatment was necessary to increase the adhesion between the substrate and polymer material.To form the lower cladding, EpoClad was spin coated on top of the wafer by the spinner (Laurell WS650B-6NPP LITE) and kept for 15 minutes for relaxation.After soft baking step, the EpoClad was then exposed to ultraviolet (wavelength, λ = 365 nm) system for 2 minutes at a power intensity of 350-500 MJ/cm 2 .The sample then went through multiple steps of hard baking and cooling and finally post-cured at 130°C for 45 minutes.The next part was to form the core layer and before spin coating, the EpoCore on top of the EpoClad film, 30 seconds oxygen plasma treatment was again necessary to improve the adhesion.We then spin coat the EpoCore and kept for 15 minutes in room temperature for relaxation.The wafer was prebaked and cooled down to room temperature to start the photolithography process.The device pattern was transferred from the designed glass mask to the EpoCore film after UV exposure using high-performance contact mask aligner (Karl Suss MJB-4).The structure was patterned after development and hard baking.
To achieve the desired core height of 4.50 µm, the unwanted EpoCore was removed by dry etching using reactive ion etching (Vision 320 RIE) system at the specific plasma condition.We measured the thickness of the polymer material using step profiler (Ambios XP-2), and the thickness of EpoClad and EpoCore were measured 5.65 µm and 4.53 µm respectively.The next step was to form the upper cladding, and EpoClad was again spin coated, UV cured and baked to form the upper cladding of 5.50 µm .As shown in Fig. 8, we tested the samples for further characterization and measurements after cleaving.
In the practical application, the mode filter devices would directly handle the optical modes on a chip.However, for our experimental demonstration, we need to excite each supported mode at the input (PortA) of the device.The conventional approach is to tune the offset launch position of the fibre to waveguide alignment using micro-positioner and excite the symmetric and asymmetric modes at the waveguide.The main problem of this approach is to selectively excite the pure symmetric and asymmetric mode at the multi-mode waveguide.To overcome this issue, a three-mode multiplexer [21] based on an unbalanced Mach-Zehnder interferometer with three input ports, namely, Port1, Port2 and Port 3, was used to selectively launch a specific mode at PortA of the device.The output of the multiplexer was connected to the input of the three-mode device at PortA as shown in Fig. 8(a,ii) to form a multimode channel altogether in the same substrate.Which implies that the input of the combined test device was single mode waveguide branch of the multiplexer (Port1, Port2, and Port3) and output was the multimode end of the device (PortB).The cross-section of the input and output end facet of the fabricated device are shown at Figs. 8(a,iii) and 8(a,iv)) respectively.In addition, we fabricated a three-mode multiplexer, a test device on the same substrate to characterise the performance of the mode filter.Similar arrangements had been followed for the four-mode filter device where a four-mode  multiplexer [22] based on cascaded asymmetrical directional coupler was used to selectively launch the specific mode at PortA of the device as shown in Fig. 8(b).

Three-mode filter device
A tunable laser (81940A, Keysight Technology) was used to characterize the performance of the three-mode filter in the C-band.Light from the tunable laser was launched into Port1, Port2 and Port3 of the multiplexer by using a lensed fibre.We controlled the polarization (TE or TM) of the light by using a polarization controller (PC) and linear polarizer placed at the input and output of the device, respectively.A near-field output image of the device was captured using an InGaAs CCD camera (C10633, Hamamatsu Photonics).A reference device consisting only the three-mode multiplexer with identical parameters was fabricated and characterized on the same substrate to accurately evaluate the performance of the mode filter.The output mode field patterns of the multiplexer are shown in Fig. 9(a).At 1.550 µm wavelength and for the TE 0 mode launched at Port1, Port2 and Port3, the device excites the TE 0 , TE 1 and TE 2 modes at the output, respectively.However, as shown in the Fig. 9(a), for the mode filter, only a clear TE 2 mode pattern is visible, and the TE 0 and TE 1 modes are blocked by the three-mode filter.Thus, the device functions as the TE 2 mode pass filter and confirms the functionality of our proposed design.The near-field images were similar for the TM polarization also.To characterize the device further, we measured the wavelength dependence of the device in the C-band.The transmission characteristics were obtained by launching the fundamental mode at the three input ports (Port1, Port2 and Port3) of the multiplexer, and the output power was measured from the output of the mode filter at PortB.The output power was measured using a power meter (Newport 2832-C).The light was transmitted through a 10X objective lens, a linear polarizer and an optical aperture before it reached the power meter.Figures 9(b) and 9(c) shows the transmission spectra of the fabricated three-mode filter device for the TE and the TM polarization respectively.
As shown in Fig. 9(b), the TE 2 -to-TE 0 extinction ratio is 20.57dB, and the TE 2 -to-TE 1 extinction ratio is 21.59 dB at 1.550 µm wavelength.The TM 2 -to-TM 0 extinction ratio is 18.91 dB, and the TM 2 -to-TM 1 extinction ratio is 18.06 dB at 1.550 µm wavelength, as shown in Fig. 9(c).The output power was normalized to the input power launched into the lensed fibre, and the losses (∼4.28 dB) caused by the three-mode multiplexer were deducted for our measurement.Also, the extinction ratio of the multiplexer was measured to be greater than 21 dB over C band ensuring that the modal crosstalk of the multiplexer would not significantly affect the mode filter's overall extinction ratio.The measured insertion loss of the mode filter was 6.70 dB (6.91 dB) for the TE 2 (TM 2 ) mode transmission at 1.550 µm wavelength.The insertion loss included the fibre-to-waveguide coupling loss at the input (2.65 dB), material loss (2.75 dB/cm) and excess loss (∼1.30dB).The insertion loss of the device can be significantly reduced by using a material with very low optical loss at the C-band.As shown in Fig. 9(b), the TE 2 -to-TE 0 and TE 2 -to-TE 1 extinction ratios are greater than 17.05 and 20.87 dB, respectively, in the Cband.The TM 2 -to-TM 0 and TM 2 -to-TM 1 extinction ratios are greater than 16.34 and 17.52 dB, respectively, in the C-band, as shown in Fig. 9(c).The device is very weakly polarization sensitive, and the experimental results agree well with the simulation and confirm the device function as a TE 2 (TM 2 ) mode pass filter.

Four-mode filter device
As in the three-mode filter, we used the same procedure to characterize the performance of the four-mode filter in the C-band.Light from the tunable laser was launched separately into Port1, Port2, Port3 and Port4 of the four-mode multiplexer by using a lensed fibre.The output mode field patterns of the reference four-mode multiplexer, which was fabricated on the same substrate, are shown in Fig. 10(a) .For the TE 0 mode launched at Port1, Port2, Port3 and Port4, the device excites the TE 0 , TE 1 , TE 2 and TE 3 modes at the output, respectively.However, as shown in Fig. 10(a), for the four-mode filter, only a clear TE 3 mode pattern is visible, and all the remaining modes are blocked by the mode filter.Hence, the device functions as the TE 3 mode pass filter and confirms the scalability of our proposed design.To characterize the device further, we measured the wavelength dependence of the device in the C-band.As with the three-mode filter, the transmission characteristics were obtained by launching the fundamental mode separately at the four input ports (Port1, Port2, Port3 and Port4) of the multiplexer, and the output power was measured from the output of the mode filter at PortB.The output power was measured using a power meter (Newport 2832-C), and the mode field pattern was cross-checked during each measurement, as shown in Fig. 10(a).Figures 10(b 10(c).The output power was normalized to the input power launched into the lensed fibre, and the losses (∼3.45 dB) caused by the four-mode multiplexer were deducted for our measurement.Also, the extinction ratio of the multiplexer was measured to be greater than 20 dB over C band ensuring that the modal crosstalk of the multiplexer would not significantly limit the overall extinction ratio of the mode filter.The measured insertion loss of the mode filter was 7.32 dB (7.25 dB) for the TE 3 (TM 3 ) mode transmission at 1.550 µm wavelength.The insertion loss included the fibre-to-waveguide coupling loss at the input (2.90 dB), material loss (2.95 dB/cm) and excess loss (∼1.35 dB).The insertion loss of the device can be significantly reduced by using a material of very low optical loss at the C-band.As presented in Fig. 10(b), the TE 3 -to-TE 0 , TE 3 -to-TE 1 and TE 3 -to-TE 2 extinction ratios are greater than 17.15, 16.12 and 19.20 dB, respectively, in the C-band.The TM 3 -to-TM 0 , TM 3 -to-TM 1 and TM 3 -to-TM 2 extinction ratios are greater than 16.98, 17.03 and 19.63 dB, respectively in the C-band, as shown in Fig. 10(c).The device has negligible polarization dependence, and the experimental results agree well with the simulation and confirm the device functionality as the TE 3 (TM 3 ) mode pass filter.Hence, the scalability of our proposed design is validated by experimental demonstration.

Conclusion
We proposed a novel architecture for realising selective mode filtering using ADCs.This architecture can block multiple optical modes and allow any arbitrary high-order mode (TE K ).As proof of concept, we experimentally demonstrated a three-mode device.In this device, the TE 0 and TE 1 modes were blocked, and only the TE 2 mode could pass.Also, the scalability of the proposed structure was demonstrated by another design of the four-mode filter.In this structure, the third-order (TE 3 ) mode could pass, and other remaining modes were filtered out.The performance of both of the devices was demonstrated successfully by simulation and experiment.We fabricated the devices using standard polymer microfabrication process and characterised in the C-band.For the three-mode device, the TE 2 -to-TE 0 and TE 2 -to-TE 1 extinction ratios were higher than 17.05 and 20.87 dB, respectively, in the C-band.Again, for the four-mode device the TE 3 -to-TE 0 , TE 3 -to-TE 1 and TE 3 -to-TE 2 extinction ratios were higher than 17.15, 16.12 and 19.20 dB, respectively, in the C-band.Both the devices had negligible polarization dependencies for the TE and TM polarization.The design architecture has the unique advantage of scalability, and the same structure had been extended to realize mode filtering with an increased number of optical modes.Moreover, these devices do not require cascaded structures for filtering multiple optical modes.Also, by merely adjusting the structural parameters and without using any material of special optical properties, particular high-order mode pass filter operation can be achieved, thereby offering high design flexibility.The proposed structure is expected to be used in future MDM optical networks due to its scalability and high design flexibility.The design idea is compatible with other PIC platforms also, such as silicon photonics.

Fig. 1 .
Fig. 1.Conceptual diagram of the proposed mode filter.In this diagram, the arbitrary high-order mode TE X is allowed to propagate (here, TE K = TE 2 ), and other remaining modes are blocked.

Fig. 2 .
Fig. 2. General architecture of the proposed mode-selective high-order mode pass filter.The structure of the device is bi-directional, and the schematic shows the operation of the device given light propagation from PortA to PortB.
(b).For fabrication and experimental demonstration of the proposed design, we ignore Taper4 from Fig.2because it does not have any function for light propagation from PortA to PortB.

Fig. 3 .
Fig. 3. (a) Variation of effective index with waveguide width at a thickness of H = 4.50 µm for the TE 0 , TE 1 and TE 2 modes of a channel waveguide.The horizontal lines 'a' and 'b' shows the phase-matching condition for the TE 2 to the TE 0 mode and the TE 1 to the TE 0 mode, respectively, for a fixed MMW width of W 2 = 14.25 µm; (b) Diagram of three-mode TE2 mode pass filter.For experimental demonstration, the structure is designed based on light propagation from PortA to PortB only.
Figures 4(b) and 4(c) show the simulated transmission spectra of the mode filter for the TE and the TM polarization, respectively.The device has excess losses of 0.42 and 0.33 dB for the TE 2 mode and the TM 2 mode transmission, respectively, for the centre wavelength of 1.550 µm.The device has negligible polarization dependence due to the small index contrast between the core and the cladding material.As shown in Fig. 4(b), the device offers an overall TE 0 mode rejection of less than -19.82 dB and TE 1 mode rejection of less than -31.68 dB in the C-band.The TM 0 and TM 1 mode rejection is less than -19.44 and -27.21 dB, respectively, in the C-band, as shown in Fig. 4(c).We employ the multi-variable optimiser and scanner (MOST) tool in Rsoft CAD to

Fig. 4 .
Fig. 4. (a) Beam propagation simulation of the three-mode filter device when (i) the TE 0 mode, (ii) the TE 1 mode and (iii) the TE 2 mode, respectively, are launched at PortA.The evolution of the launched modes is shown at Z 1 = 0.50 mm, Z 2 = 3.40 mm, Z 3 = 5.50 mm and Z 4 = 7.00 mm; Computed transmission spectra in the C-band for (b) the TE and (c) the TM polarization respectively.The output power is normalised to the input mode power, and the material loss is not considered in the simulation.

Fig. 5 .
Fig. 5. (a) Variation of effective index with waveguide width at a thickness of H = 4.50 µm for the TE 0 , TE 1 , TE 2 and TE 3 modes of a channel waveguide.The horizontal lines 'a' and 'b' show the phase-matching condition for the TE 3 to the TE 0 mode and the TE 2 to the TE 0 mode, respectively, for a fixed MMW width of W 3 = 22.00 µm; (b) Schematic of four-mode TE 3 mode pass filter.For experimental demonstration, the structure is designed based on light propagation from PortA to PortB only.

Fig. 6 .
Fig. 6.(a) Beam propagation simulation of the four-mode filter device when (i) the TE 0 mode, (ii) the TE 1 mode, (iii) the TE 2 mode and (iv) the TE 3 mode are launched at PortA.The evolutions of the launched modes are shown at Z 1 = 0.50 mm, Z 2 = 3.60 mm, Z 3 = 5.80 mm and Z 4 = 8.00 mm; Computed transmission spectra in the C-band for (b) the TE and (c) the TM polarization respectively.The output power is normalised to the input mode power, and the material loss is not considered in the simulation.

Fig. 8 .
Fig. 8. (a) Three mode device: (i) Microscopic image of ADC1 near PortA, (ii) Schematic structure for characterizing the device where a three-mode multiplexer was connected to the input of the mode filter, (iii) cross section of the three input ports and (iv) cross section at output PortB; (b) Four mode device: (i) Microscopic image of ADC3 and CW section, (ii) Schematic structure for characterizing the device where a four-mode multiplexer was connected to the input of the mode filter, (iii) cross section of the four input ports and (iv) cross section at output PortB.

Fig. 9 .
Fig. 9. (a) Near-field images were captured from the output of the three-mode multiplexer and three-mode filter when the TE 0 mode was excited into Port1, Port2 and Port3 respectively at 1.550 µm wavelength.; Experimentally measured transmission spectra of the three-mode filter in the C-band for (b) the TE and (c) the TM polarization, respectively.

Fig. 10 .
Fig. 10.(a) Near-field images were captured from the output of the four-mode multiplexer and four-mode filter when the TE 0 mode was excited into Port1, Port2, Port3 and Port4 respectively at 1.550 µm wavelength.; Experimentally measured transmission spectra of the four-mode filter in the C-band for (b) the TE and (c) the TM polarization, respectively.
) and 10(c) shows the measured transmission spectra of the fabricated four-mode filter device for the TE and the TM polarization respectively.As shown in Fig. 10(b), the TE 3 -to-TE 0 , TE 3 -to-TE 1 and TE 3 -to-TE 2 extinction ratios are 20.81,17.17 and 20.79 dB, respectively, at 1.550 µm wavelength.The TM 3 -to-TM 0 , TM 3 -to-TM 1 and TM 3 -to-TM 2 extinction ratios are 18.89, 17.40 and 20.11 dB, respectively, at 1.550 µm wavelength, as presented in Fig.