Three-mode multiplexer and demultiplexer based on the Mach-Zehnder interferometer

: Mode division multiplexing (MDM) is a groundbreaking technology that meets future optical network capacity demand in conjunction with the wavelength multiplexing division (WDM). In our work, we propose a three-mode mux/demux device that comprises a three-arm unbalanced Mach-Zehnder interferometer (MZI) inserted between three Y-junctions. The device is compact and offers a high extinction ratio. Moreover, it has a simple structure. The maximum simulated excess loss is 0.37 dB with a minimum extinction ratio of 25.71 dB in the 1.550 µm wavelength, in different multiplexing and demultiplexing conditions. The device will find application in expanding the fiber transmission capacities in future MDM systems.


Introduction
The demand for higher capacity requires the worldwide deployment of high-speed optical networks to manage the progression of non-stop internet networks.Over the last few decades, optical communication systems have found innovative approaches to compensate for the exponential growth of the internet-compelled traffic by using various multiplexing technologies.Time division multiplexing, wavelength division multiplexing and polarisation division multiplexing are well established in optical communication networks.However, the maximum capacity per fiber is limited to 100 Tb/s due to fiber nonlinearity characteristics.Thus, Pb/s or even Eb/s capacity fiber transmission systems are required to compensate for the exponential growth of the internet-compelled traffic.As a realistic solution for the potential capacity requirement of optical networks, MDM technology has received considerable attention [1][2][3][4][5][6][7][8][9][10][11] in combination with WDM.In an MDM transmission system, mode mux/demux is the primary device to combine or isolate different optical mode channels spatially.To meet the requirement for a smooth transition from the existing single-mode WDM system to the MDM system, all MDMspecific system upgrades must be performed with a strict view to the reuse of the deployed fiber infrastructure [2,12].Therefore, the mode mux/demux is a useful device that can effectively interface between WDM and MDM system integration.The platforms available to implement mode mux/demux devices are bulk optical platform [13][14][15], fiber optic platform [16][17][18][19][20][21] and photonic integrated circuit (PIC) platform.PIC-based mux/demux devices  generally achieve high packing density and compatibility with other waveguide-based devices.In recent years, several structures, such as asymmetrical Y-junctions [22][23][24][25][26][27][28], microring resonators [29,30], Mach-Zehnder interferometers [31][32][33], multimode interference couplers [34][35][36], tapered directional couplers [37][38][39][40][41], asymmetric directional couplers [42][43][44][45][46] and vertical directional couplers [47][48][49][50][51], have been proposed for PIC-based mux/demux device implementation.
In this paper, we propose a PIC-based three-mode mux/demux device that can multiplex and demultiplex signal carried by the fundamental (TE 0 ), first-order (TE 1 ) and second-order (TE 2 ) mode.The three-mode mux/demux is fabricated using the standard polymer waveguide microfabrication process and experimentally characterized in the C-band (1.530-1.565µm wavelength).This device is compact and offers a high extinction ratio compared to the other mux/demux devices in the polymer waveguide platforms [47,48,51].

Device design and simulation
The 3-mode mux/demux schematics are shown in Fig. 1.The device can be considered as four parts, that is, an unbalanced three-arm MZI sandwiched by three Y-junctions.The dimension of the waveguide is selected, such that the stem of the Y-junctions functions as a three-mode multimode waveguide and supports only the TE 0 , TE 1   The optical signal launched into PortA splits in the three arms of the first Y-junction.After propagation on different optical path lengths in the three unbalanced arms of the MZI, the second Y-junction recombines them.Because of the phase difference contributed by the three MZI arms and the interactive length of the THMI, light can be retrieved from an output port and constitutes an efficient mode transition between the input and output ports.On this basis, when the TE 0 mode is launched at PortA, the light comes out from Port1 after propagating through different sections of the three-mode device.Similarly, the input light is retrieved from Ports 2 and 3 when TE 1 and TE 2 modes are launched at PortA, respectively.This occurrence exhibits the demultiplexing function of the device.The device functions in reciprocal and launching the TE 0 mode separately at Port1, Port2 and Port3 excites the TE 0 , the TE 1 and the TE 2 mode at PortA respectively and perform the multiplexing property as shown in Fig. 1.
We use the commercially available software tool 3D-RSoft BPM to simulate the device performance as mode mux/demux.The simulations are performed with 1.539 (core refractive index) and 1.512 (cladding refractive index) at 1.550 µm wavelength.The commercially available BCB (Dow Chemical Co.) and Epoxy OPTOCAST 3505 (Electronic Material Inc.) polymer were used as the core and cladding material, respectively, for the fabrication work.The waveguide dimensions are selected such that the three-mode region supports only the TE 0 , TE 1 and TE 2 modes.In contrast, the single-mode region supports only the fundamental TE 0 mode.Given the core refractive index of 1.539 and cladding refractive index of 1.512 with a fixed thickness of 3.00 µm, the cut-off width for four (m = 0, 1, 2, 3) guided modes in an embedded channel waveguide is shown in Fig. 2. The waveguide thickness is set to 3.00 µm, the width of the single-mode region is set to W 1 = 3.00 µm and the width of the three-mode region is W 2 = 9.00 µm.To implement the three-mode mux/demux device, we design and optimize each section of the device by the MOST tool (multivariable optimizer and scanner) in the RSoft CAD.The material loss of the device is disregarded in the simulation.We design the half branching angle of the outer two arms of the three Y-junctions as 1°to minimize the radiation losses in the transition regions.The length of each Y-junction arm (L Y1 , L Y2 and L Y3 ) is 900 µm as shown in Fig. 3.The maximum simulated loss in the transition region is less than 0.05 dB for TE 0 mode transmission.The separations of the three unbalanced arms of the MZI (from the center of the middle arm of the Y-junctions, as marked by the dashed line in Fig. 3) are D 1 = 18.71 µm, D 2 = 17.30µm and D 3 = 28.10 µm.The interactive length (L TMI ) is set at 324 µm for the best operation in the transverse electric (TE) polarization at the 1.550 µm wavelength.However, to achieve optimal performance in transverse magnetic (TM) polarization, fine adjustment of the device parameters is required.The total length of the simulated device is 0.55 cm, which can be significantly reduced by the use of platforms with high-index contrast materials, such as silicon-on-insulators.To assess the performance of the mode mux/demux, we perform the numerical investigation using RSoft BeamPROP.For multiplexing operation, the figure of merit mode extinction ratio (ER) is defined as where P Mode is the output mode power from PortA when the TE 0 mode is launched into Ports 1-3; and i = j = 0, 1, 2. Again, for the TE 0 mode launched into Port1: i = 0, j ≠ 0; For example, for the TE 0 mode launched at Port1, the light comes out from PortA as the TE 0 mode.Hence, the mode extinction ratio between TE 0 (i = 0) and TE 1 (j = 1) is defined as ER(M 01 ).Meanwhile, the extinction ratio between TE 0 (i = 0) and TE 2 (j = 2) mode is defined as ER(M 02 ).Hence, as shown in Eq. ( 1), the mode extinction ratio, in this case, is defined as Similarly, for the TE 0 mode launched at Port2, the mode extinction ratios are defined as ER(M 10 ) and ER(M 12 ).
For the launch at Port3, the extinction ratios are ER(M 20 ) and ER(M 21 ).The wavelength dependence of the device in the multiplexing configuration is presented in Fig. 6  The maximum simulated excess loss of the device under various demultiplexing and multiplexing conditions is 0.37 dB at the 1.550 µm wavelength without considering the material loss in the simulation.The radiation loss at the Y-junctions primarily contributes to the excess loss.The device shows an overall good performance in the C-band.Nonetheless, the parameters are optimized for the best performance in the TE polarization at the 1.550 µm wavelength.The performance of the device is polarization-dependent.The extinction ratio decreases by approximately 4-12 dB in the C-band for the TM polarization.However, the device parameters need to be finely adjusted to achieve optimal performance in the TM polarization.

Device fabrication
To demonstrate our design experimentally, the device was realized in polymer materials with numerous advantages: easy processing and reproduction, low-cost fabrication, index compatibility to conventional fiber and easy coupling.Moreover, polymer materials exhibit a good thermo-and electro-optic property; thus, they are preferred in realizing tunable waveguide devices.Hence, the device was fabricated using commercially available polymer BCB as core and epoxy as a cladding material.However, the device design is compatible with other waveguide platforms also such as SOI.The detailed process of device fabrication is shown in Fig. 7.After the oxygen plasma cleaning of the silicon wafer substrate, we spin-coated the epoxy on top of the substrate to form the lower cladding for our device fabrication.The epoxy was then exposed to the radiation of a UV spot curing system (Novacure 2100) at a power intensity of 5000 mW/cm 2 for 5 min and post cured at 130 °C for 60 min.We then spin-coated the BCB on top of the epoxy and cured it in nitrogen gas at 270 °C for 45 min.In this manner, the BCB layer in nitrogen gas was prevented from being oxidized by the atmosphere.An oxidized BCB has a larger refractive index and introduces high material loss.The thickness of the BCB ultimately decides the overall thickness of the waveguide.The thickness of the polymer films was measured using the Ambios XP-2 step profiler.The thickness of the epoxy and BCB was 5.40 µm and 3.05 µm, respectively.
We removed the unwanted BCB from the layer by dry etching to achieve the desired device structure.Meanwhile, a thin chromium (Cr) metal layer of 100 nm was deposited on top of the film by the Denton Vacuum, LLC RF sputter coating system to protect the required pattern of the BCB.Cr was used as a metal mask due to its excellent adhesive and inert properties to other materials.Photolithography was used to transfer the device pattern from a mask to a thin film.Positive PR resin (SPR 61112B) was spin-coated on top of the metal layer and soft baked.A Karl Suss MJB-3 high-performance mask aligner was used to align the PR layer with the designed mask, and UV light was exposed to the uncovered PR.The pattern of the glass mask was conveyed to the PR after development and hard baking and we tested the device for further characterization after cleaving.The refractive index of the epoxy and BCB was measured with the Metricon 2010 prism coupler system at 1536 nm.The refractive indices of the epoxy and BCB were 1.5122 and 1.5388 for TE polarisation, respectively.A microscopic image of the key sections of the fabricated device is shown in Fig. 8.The fabricated device's total length was 7.50 mm, which included 2.00 mm of straight waveguide leads at the two ends of the mode mux/demux.When designing our photomask, we had another test device in which two mux/demux were connected back to back at the multiplexing end to form a three-input and three-output device.This structure was used to characterize the device's performance.

Observation of the mode field
An 81940A Keysight Technology tunable laser was used to characterize the device performance in the C-band.Light from the tunable laser was launched separately into the demultiplexing end (Ports 1-3) of the device and excites the TE 0 mode using a lensed fibre.The polarization state of the device was adjusted by using a polarization controller placed at the input end of the lensed fiber.A polariser was placed at the output of the device to obtain the TE polarization.The output mode near-field image was captured using a C10633, Hamamatsu Photonics InGaAs CCD camera shown in Fig. 9.The output mode field pattern of the device at the multiplexing end (PortA) at the 1.550 µm wavelength is shown in Fig. 10.Clear-mode field patterns of the TE 0 , the TE 1 and the TE 2 mode are observed at PortA for the launch of the TE 0 mode at Ports 1-3, respectively, thereby confirming the device function as a multiplexer.

Measurement of the mode extinction ratio
To further characterize the device, we need to calculate different mode extinction ratios, as defined by Eq. ( 1).However, measuring the mode extinction ratio experimentally is difficult because the individual power of the TE 0 , TE 1 and TE 2 mode must be measured separately.With our existing measurement setup and due to the unavailability of the direct measurement tools to separate the power of the TE 0 , TE 1 and TE 2 modes, we fabricated another test device in the same substrate to measure the mode extinction ratio of the device.
The test device was designed by connecting two mux/demux back-to-back at PortA (multiplexing end) to form a three-input (Ports P-R) and a three-output (Ports X-Z) device, as shown in Fig. 11(a).In this case, we could measure the mode extinction ratio by allowing each excited mode at PortA to demultiplex at the three single-mode output ports.Moreover, the measured mode extinction ratio would be the ratio among each output port power.For this measurement, the multiplexer (Fig. 10) was used as the calibrator device to confirm the excitation of the TE 0 , the TE 1 and the TE 2 mode at PortA.The measurement would be considered successful if the three separately excited modes were demultiplexed as the fundamental mode at the three output ports.Figures 11(b), 11(c) and 11(d) show the near-field image of the test structure at output Ports X-Z for the launch of the fundamental mode at the input ports by using the lensed fiber.Figure 13 shows the simulated crosstalk variation due to the MZI path separation D 2 and D 3 for the demultiplexing function when the TE 0 mode is launched into Port A. To measure the port extinction ratio when the device functions as a demultiplexer, each supported mode at the input (PortA) of the device must be excited.The conventional approach is to tune the offset launch position of the fiber-to-waveguide alignment and excite the symmetric and asymmetric modes at the waveguide.The main problem of this approach is selectively exciting the pure symmetric and asymmetric modes at the multimode waveguide.To overcome this issue, we can use our calibrated device to excite the fundamental and first-and second-order modes at the output of the multiplexer selectively.The measured port extinction ratio will be the extinction ratios among each output port power.Therefore, the procedure is similar to measuring the mode extinction ratios ER(M ij ), as discussed in the prior sections.The measurement results will provide similar outcomes to the measured mode extinction ratios provided that the mode extinction ratio is measured by the power of each port in Eqs. ( 4)-( 6).Moreover, these results further support the reciprocal function of the mode mux/demux.We had measured the insertion loss of the three-mode mux/demux by using this test structure.Half of the test structure's total excess and material losses were the excess and material losses of the three-mode mux/demux.Given the similar fiber-to-waveguide coupling loss in both devices, the maximum measured insertion loss of the device was 8.51 dB at the 1.550 µm wavelength.The various mode-dependent insertion loss was 8.51 ± 3 dB in the C band, including the fiber-to-waveguide coupling loss (2.50 dB/facet) at both ends, material loss (2.00 dB/cm) and the excess loss (∼2 dB).Table 2 gives comparisons of the different three-mode mux/demux based on polymer waveguide platform.

Conclusion
In summary, we proposed a PIC-based three-mode mux/demux device that can multiplex and demultiplex signals carried by the fundamental and first-and second-order modes.The measured performance of the device agreed with the simulated performance.The device has a simple structure, and we have successfully measured the mode extinction ratio by allowing each excited mode at the multiplexer end to demultiplex at the three single-mode output ports.Moreover, the device is compact and offers a high extinction ratio compared to the other mux/demux devices on the same platforms.In particular, at a wavelength of 1.550µm, for various multiplexing conditions, all measured mode extinction ratios were higher than 20 dB for the TE polarization.
Our simulation shows that the mux/demux device has high fabrication tolerance in width, height and Y-junction's separation.However, the device performance is sensitive to the separation of the MZI unbalanced arms.To extend the work on mode mux/demux, researchers should demonstrate multiplexing and demultiplexing properties for higher-order modes, such as TE 3 , TE 4 and TE 5 .The most powerful mode-controlling function could be achieved by integrating the mode mux/demux with other MDM devices.
Along with downscaling of chip dimensions, integration and interconnection aspects are becoming more important for MDM technologies.The issues of their inter-compatibility, scalability and performance, in particular, are far from being resolved.The on-chip integration of various mode processing devices into a complete optical link would be of particular interest in the next step.The three-mode mux/demux has the potential to be a useful device that would interface effectively in WDM and MDM system integration and extend the fiber transmission capacity.

Disclosures.
The authors declare no conflicts of interest.
and TE 2 modes.Each Y-junction has three arms, and each branch is designed to carry the TE 0 mode only.The three arms of the MZI are also intended to support the TE 0 mode.The first Y-junction acts as a mode splitter.Light is then split into the three arms of the Y-junction depending on the specific mode launched at PortA.The three unbalanced arms of the MZI connected to the Y-Junction contribute to an additional phase shift to the individual arms of the Y-junctions.The Three-mode interferometer (THMI) is formed by connecting the multimode stem of the second and third Y-junctions back to back.Light is retrieved from the three single-mode branches of the third Y-junction, and three outputs are designated as Port1, Port2 and Port3.

Fig. 1 .
Fig. 1.Schematic configuration of the three-mode mux/demux with a three-mode multiplexing end (PortA) and a single-mode three port (Ports 1-3) demultiplexing end.The cross-section of the three-mode region and the single-mode waveguide is shown in the inset.

Fig. 2 .
Fig. 2. Waveguide width dependence of effective index in a rectangular waveguide with a core refractive index of 1.539 and cladding refractive index of 1.512 at the center wavelength of 1.550 µm.The thickness of the waveguide is 3.00 µm.

Fig. 3 .
Fig. 3. Top view (X-Z plane) of the three-mode mux/demux showing different lengths and dimensions (not to scale).

Figure 4
demonstrates the operation of the device as a multiplexer.When the fundamental TE 0 mode is launched from Port1, the TE 0 mode is excited at PortA [Fig.4(a)].Meanwhile, when the TE 0 mode is launched from Port2 and Port3, the TE 1 mode and the TE 2 mode are excited at PortA [Figs.4(b) and 4(c)], respectively.Our simulation result also confirms that the demultiplexing function is reciprocal to the light path.When the fundamental TE 0 mode is launched at PortA, the light comes out of Port1 [ Fig. 5(a)].Meanwhile, when TE 1 and TE 2 modes are launched at PortA, the light comes out of Port2 and Port3 [Figs.5(b) and 5(c)], respectively.

Fig. 5 .
Fig. 5. BPM simulation of the demultiplexing function at the 1.550 µm wavelength when (a) the TE 0 mode, (b) TE 1 mode and (c) TE 2 mode are launched at PortA.

Fig. 8 .
Fig. 8. Microscopic image of the key sections of the mux/demux device: (a) Y-junction 1, (b) three arms of the unbalanced MZI and (c) Y-junction 3.

Fig. 9 .
Fig. 9. Experimental setup for obtaining the output near-field images from the fabricated device.The output mode field images were obtained using a CCD.
For example, for the light launched into Port P, the mode extinction ratio ER(M 01 ) and ER(M 02 ) are calculated as ER(M 01 ) = 10log 10 ( single-mode step-index fiber to detect the total power separately at Port X, Port Y, and Port Z by launching light at Port P, Port Q and Port R, respectively.We measured the output power of each port by using a Newport 2832-C optical power meter.The wavelength dependence of the experimentally measured extinction ratio is shown in Fig. 12.For the TE 0 mode launched at Port P, the device had a mode extinction ratio of ER(M 01 ) = 23.05dB and ER(M 02 ) = 22.61 dB at the 1.550 µm wavelength [Fig.12(a)].Meanwhile, ER(M 10 ) = 23.70 dB and ER(M 12 ) = 23.21dB at the 1.550 µm wavelength when the TE 0 mode was launched into Port Q [Fig.12(b)].For the TE 0 mode launched at Port R, ER(M 20 ) = 20.19dB and ER(M 21 ) = 21.77dB at the 1.550 µm wavelength [Fig.12(c)].The minimum mode extinction ratio for all launching ports was greater than 17.40 dB (ER(M 10 )) in the C-Band for the TE 0 mode launched at Port Y.The measured performance of the device agreed with the simulated performance.However, the mode extinction ratio near the center wavelength was lower than the simulation primarily due to the rough sidewall and slight variation in the unbalanced MZI arm distance introduced in the fabrication process.

Fig. 12 .
Fig. 12. Experimentally measured mode extinction ratio (ER(M ij )) in the C-band for the multiplexing function when the TE 0 mode was launched at (a) Port P, (b) Port Q and (c) Port R.

Fig. 13 .
Fig. 13.Variation of Crosstalk due to the MZI path separation D 2 and D 3 at (a) Port2 and (b) Port3 for the demultiplexing function when the TE 0 mode is launched into PortA.