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Abstract
In this paper, we present an efficient polymer two-mode (de)multiplexer with two cascaded horizontal waveguide asymmetric directional couplers (ADCs). Through extensive simulations, the optimized waveguide core dimensions were determined, and the distance L from the starting position of the first ADC to the cascaded position was 35300 µm. With the cascaded ADCs, the $E_{21}^x\; $ mode of the wider waveguide was coupled into the $E_{11}^x\; $ mode of the narrower waveguide with a coupling ratio of 96.73% at 1550 nm when the separation between the waveguide cores was 5 µm. The coupling ratio and extinction ratio of the fabricated (de)multiplexer reached a maximum of 96.12% and 14.21 dB at 1540 nm, respectively. The coupling ratios were greater than 90% in the wavelength range 1533–1565 nm with a minimum insertion loss of 9.75 dB. The influence of different cascaded positions on the mode coupling ratio, mainly caused by the large phase difference between the modes owing to the slowly varying envelope approximation, is analyzed theoretically and verified experimentally. The proposed cascaded two-mode (de)multiplexer can reduce the preparation process requirements and increase the channel capacity of optical communication systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode division multiplexing (MDM) technology, which allows each mode in a few-mode fiber (FMF) to carry its own channel, has garnered considerable attention for increasing the capacity of communication systems [1,2]. In an MDM system, a mode (de)multiplexer is a key component for launching (separating) different mode channels into (from) an FMF. In addition, by combining a multicore fiber (MCF) and various types of MDM technologies, the communication capacity can exceed the order of Pbit/s, and there is great potential for MDM devices to be utilized in the field of long-distance optical information transport over 100 km [3,4].
Mode (de)multiplexers based on silicon [5–10] and polymer waveguides [11–21] have been widely investigated because they are more suitable than fiber-based mode (de)multiplexers [22–25] for achieving compact, highly compatible, and integrated optical devices. Polymer waveguides offer remarkable advantages over silicon waveguides owing to their lower propagation loss, simple fabrication process, and lower cost in the field of board-level optical interconnection. At present, there are various waveguide structures available for mode (de)multiplexing, including waveguide gratings [7,10,14,17,19], multimode interferometers (MMIs) [6,8,26], asymmetric Y-junctions [18,27,28], and waveguide asymmetric directional couplers (ADCs) [5,9,11–13,15,16,20,21,29,30]. Among these, horizontal ADCs have been broadly researched for their extensible structure design, relatively simple fabrication process, and high mode conversion efficiency of above 95% experimentally [9,13,21,29].
Recently, ADCs with three-dimensional (3D) structures have been proposed to implement multiplexing of high-order modes (for example, the $E_{12}^x\textrm{ }$ mode) in the vertical direction [11,13,16]. In addition, the number of multiplexing modes can be expanded by adding more waveguides to the different core layers in the vertical direction. However, this requires several applications of spin-coating and lithography, and the waveguide cores located in different layers must be precisely aligned, which significantly complicates their fabrication. Moreover, the separation between the upper and lower output waveguide ports is extremely small; therefore, a tilted transition waveguide structure is necessary, which would influence the mode coupling and fabrication tolerance. Alternatively, several non-planar ADCs with different waveguide core heights have also been proposed to support the multiplexing of multiple modes [20,29]. However, indispensable reactive ion etching (RIE) techniques are introduced into their fabrication, which significantly increases the complexity of the process. As a result, the required preparation accuracy significantly increases, and the losses of the waveguide cores deteriorate significantly. In general, the mode coupling ratio decreases with an increase in the separation between the waveguide cores in the ADC [12,21,29]. Therefore, the separation is set to a smaller value. In our previous study, a three-mode (de)multiplexer based on horizontal ADCs was fabricated with a separation of 3 µm and a coupling ratio as high as 98% [21]. Such tight separation requires an extremely high preparation accuracy; otherwise, the performance of the fabricated mode (de)multiplexer may seriously deteriorate owing to the inherent properties of the polymer material and limitations of the fabrication process [31,32]. Certain lithography equipment with extremely high precision can be considered; however, this increases the fabrication cost significantly. If a cascaded structure is adopted in a horizontal ADC-based mode (de)multiplexer, the power obtained from multiple-mode coupling can be superimposed at a relatively large separation between the waveguide cores, which not only reduces the process difficulties but also ensures a high coupling ratio. This design scheme for mode (de)multiplexers has not yet been investigated.
In this paper, a two-mode (de)multiplexer based on two cascaded horizontal polymer waveguide ADCs is proposed. The proposed design superimposes the power obtained from the mode coupling of two ADCs at a large waveguide core separation, which can reduce fabrication difficulties and improve the mode coupling ratio. First, the optimal dimensional parameters of the waveguide cores were determined according to the phase-matching condition. Furthermore, the variations in the mode coupling characteristics with deviations of the waveguide core widths, wavelengths, and cascaded position were explored in detail. Subsequently, using ultraviolet (UV) lithography, a cascaded two-mode (de)multiplexer based on polymer waveguides was fabricated. The dimensions and contours of the device were measured using a 3D optical profiler. Finally, an experimental setup for mode multiplexing was constructed to verify the functionality of the fabricated (de)multiplexer, and the near-field images and mode coupling ratios of the device were obtained.
2. Design and simulation
Figure 1 illustrates a structural schematic of the cascaded two-mode (de)multiplexer. Three rectangular waveguide cores, denoted as Core1, Core2, and Core3, form two identical horizontal ADCs, which are located on the same plane. The optical power of Core2 and Core3 are superimposed at the cascaded position and eventually output together. The addition of Core3 distinguishes the cascaded structure from the conventional ADC structure. The proposed cascaded structure can superimpose the power of the $E_{11}^x$ mode obtained from the mode coupling of the two ADCs; thus, the coupling ratio is ultimately improved. The widths of the three waveguide cores are w1, w2, and w3 (= w2), and the height is uniformly h. d represents the separation between the waveguide cores of each ADC in the coupling region, and nc and ncl are the refractive indices of the waveguide core and cladding, respectively. Points A and B in Fig. 1 are the starting position of Core2 and the cascaded position, respectively. The distance between points A and B along the z-direction is defined as L. When the coupling ratio reaches a maximum, the two waveguide cores of the ADC should be separated to stop coupling between the two modes. Therefore, a cosine-type S-bend was introduced into each ADC, the longitudinal and transversal lengths of which are denoted as T1 and T2, respectively. As a few-mode waveguide (FMW), Core1 supports at least the $E_{11}^x\textrm{ }$ and $\textrm{ }E_{21}^x\textrm{ }$ modes. Core2 and Core3 support the $E_{11}^x$ mode only, indicating that they are both single-mode waveguides (SMWs). When excited in Core1, the $E_{21}^x$ mode is coupled into the $E_{11}^x$ mode of Core2 and Core3, and then the mode power is superimposed at the cascaded position. Consequently, the mode coupling ratio can be improved.
Fig. 1. Structure schematic of the proposed cascaded two-mode (de)multiplexer. The inset shows the structure of the S-bend and the cross section of the coupling regions.
From mode coupling theory [33,34], the power of the $E_{11}^x$ and $E_{21}^x\; $ mode in an ADC can be expressed as:
where A11(z) and A21(z) denote the field amplitudes of the $E_{11}^x$ mode of the SMWs and the $E_{21}^x$ mode of the FMW, respectively. z is the distance of light wave propagation along the z-direction, and $D = C/\sqrt K $, where C denotes the coupling coefficient between the $E_{11}^x$ and $E_{21}^x$ modes. K represents the power transfer coefficient, which is expressed as: where β11 and β21 are the propagation constants of the $E_{11}^x$ and $E_{21}^x$ modes, respectively. When β11 = β21, the power of the $E_{21}^x$ mode can be highly coupled to that of the $E_{11}^x$ mode. As shown in Fig. 2(a), to achieve the best coupling effect at a specific waveguide core separation d, the phase-matching condition must be satisfied. In other words, the effective refractive index (ERI) of the $E_{21}^x$ mode of Core1 must be equal to those of the $E_{11}^x$ modes of Core2 and Core3. At an operating wavelength of 1550 nm, nc and ncl are 1.575 and 1.563, respectively, which are based on the properties of the chosen polymer material. The variation in the ERIs of the modes with increasing waveguide core width is illustrated in Fig. 2(b) when h = 6 µm. The ERIs of the $E_{11}^x$, $E_{21}^x$, and $E_{31}^x$ modes increased with waveguide core width. To meet the phase-matching condition, the waveguide core widths w1 and w2 (= w3) were calculated as 12.9 and 5 µm, respectively. Therefore, the ERIs of the $E_{21{\; }}^x$ mode of Core1 and the $\textrm{ }E_{11\textrm{ }}^x$ modes of Core2 and Core3 were all 1.5702. In addition, the ERI of the $E_{11\textrm{ }}^x$ mode of Core1 was 1.5725, which indicated that coupling could not be implemented between the $\textrm{ }E_{11\textrm{ }}^x$ mode of Core1 and the $\textrm{ }E_{11\textrm{ }}^x$ modes of Core2 and Core3.Fig. 2. (a) ERI of the $\textrm{ }E_{21\textrm{ }}^x$ mode of Core1 matches that of the $E_{11\textrm{ }}^x$ mode of Core2/Core3. (b) Variation in the ERIs of the $E_{11}^x$, $E_{21}^x$, and $E_{31}^x\textrm{ }$ modes with increasing waveguide core width when the wavelength and height are 1550 nm and 6 µm, respectively.
The coupling ratio [11,16] between the $E_{21\textrm{ }}^x$ mode of Core1 and the $\textrm{ }E_{11\textrm{ }}^x$ modes of Core2 and Core3 can be obtained from:
where P1 represents the output power of the $E_{21\textrm{ }}^x$ mode of Core1, and P23 represents the output power of the superimposed $E_{11\textrm{ }}^x$ modes of Core2 and Core3.The coupling length [33] is the propagation distance of light when the mode coupling ratio is at its maximum, which is denoted as CL. According to the 3D finite-difference beam propagation method (3D FD-BPM) (Beam-PROP, RSoft), the coupling length increases sharply with increasing separation d; however, the coupling ratio first increases and then decreases rapidly, as illustrated in Fig. 3(a). Figure 3(b) depicts that the normalized power of the $E_{21\textrm{ }}^x$ and $\textrm{ }E_{11\textrm{ }}^x$ modes varies periodically with the propagation distance of light. When the separation is 3 µm and 5 µm, and the corresponding coupling lengths CL21 are 2075 µm and 6185 µm, respectively. It is important to note that when d is less than 1 µm, the ADC can be regarded as a new waveguide structure with an impure mode field distribution, which will worsen the coupling between the two waveguide modes [21]. Therefore, d should be set as an appropriate value. Although an excellent coupling effect can be obtained when d is 2–3 µm, extremely high preparation accuracy is required. When d is larger than 4 µm, the preparation process is simple; however, the performance of conventionally-structured mode (de)multiplexers degrade significantly. Therefore, the cascaded structure of an optical waveguide is expected to improve the mode coupling ratio. Considering the above factors, d was set to 5 µm. Under these conditions, the mode coupling ratio and coupling length were 82.3% and 6185 µm, respectively. To ensure that as much power as possible from Core1 is coupled to Core2 and Core3, the coupling lengths CL1 and CL2 of the two ADCs should be set to their optimal values. In addition, the extinction ratio is also an important performance of a (de)multiplexer, which is expressed as [30]:
where Pn and Pi are the power coupled to the desired and undesired modes, respectively.Fig. 3. (a) Variation in coupling lengths and coupling ratios with the separation between waveguide cores at 1550 nm. Variation in normalized power of the $E_{21\textrm{ }}^x$ and $\textrm{ }E_{11\textrm{ }}^x$ modes with the propagation distance of light when the separation between waveguide cores is (b) 3 µm, and (c) 5 µm, respectively.
The superposition of the power of the modes can be considered as the interference of two columns of light waves in Core2 and Core3. Coherent light waves can be expressed as:
where Ea0 and Eb0 represent the peak values of the amplitudes of the two columns of light waves, and φa and φb are their respective light phases. ω is the angular frequency. According to the principle of light wave interference [35,36], the superimposed light wave can be expressed as:The amplitude E0 can be obtained from the following equation:
The amplitude of the superimposed light wave depends on the phase difference between the two columns of the light waves at the superimposed positions. When φa – φb = 0, amplitude E0 reaches its maximum value. However, the phase of the light wave varies with the propagation path; thus, a suitable cascaded position must be determined to improve the mode coupling ratio. Furthermore, E0 also depends on the amplitudes Ea0 and Eb0, the scalar electric field of which is expressed as:
where $\bar{k}$ is a constant chosen to represent the average phase variation of the field. The so-called “slowly varying field” u with z is introduced to factor the rapid phase variation out of typical guide-wave problems, which is known as the slowly varying envelope approximation (SVEA) [37,38].In the simulation, the coupling lengths CL1 and CL2 were both set to 6185 µm, and T1 and T2 were fixed at 2000µm and 65 µm, respectively. When the $E_{21\textrm{ }}^x$ mode was excited in Core1, the coupling ratio of the (de)multiplexer and the normalized output power (NOP) of Core3 varied periodically with increasing L, as shown in Fig. 4(a). The NOP reached a maximum value of 0.837 when L = 35300 µm and decreased to a minimum value of 0.176 when L = 18800 µm. Accordingly, the coupling ratios of these two cases were calculated as 96.73% and 85.26%, which correspond to phase differences of 0 and π, respectively. Because of the SVEA, the period of the phase of the $E_{11}^x$ mode of Core2 and Core3 was approximately 675 µm. Furthermore, because the initial phases of the $E_{11}^x$ mode of Core2 and Core3 were different, the period of the coupling ratio and NOP was approximately 33000 µm. Figure 4(b), (c), and (d) show the propagation of light waves with L set to 18800, 23200, and 35300 µm, respectively. From the output near-field images, it is clear that a portion of the $E_{21\textrm{ }}^x$ mode always remained in Core1, and the intensity of the output of the $E_{11\textrm{ }}^x$ mode with L = 35300 µm was greater than that with L = 18800 and 23200 µm. This is because the phase difference between the two $E_{11\textrm{ }}^x$ modes was small at the cascaded position. Moreover, when L = 35300 µm in Fig. 4(d), the optical path difference between the two $E_{11}^x$ modes was an integer multiple of the wavelength, and the amplitudes of the $E_{11}^x$ mode superimposed by constructive interference and reached a maximum. However, in Fig. 4(b) and (c), this condition was not satisfied when L was 18800 and 23200 µm, respectively, and thus destructive interference occurred, resulting in a larger energy loss of the $E_{11}^x$ mode. Accordingly, the intensity of the output $E_{11}^x$ mode was largest, as shown in Fig. 4(d). Considering that the total length of the device should be as small as possible for fabrication, L was finally set to 35300 µm. Similarly, a cascaded two-mode multiplexer was simply simulated by exchanging the waveguide core widths of Core1 and Core2 (Core3). However, the NOP of the superimposed $E_{21\textrm{ }}^x$ mode was extremely small and the field distribution of the $E_{21\textrm{ }}^x$ mode was no longer pure after its superposition. This is mainly because the changed waveguide structure at the cascaded position severely affects the field distribution of higher-order modes. Therefore, this type of cascaded structure based on the superposition of higher-order modes can be subsequently optimized, but is not investigated in this work.
Fig. 4. (a) Variation in the coupling ratio of the cascaded two-mode (de)multiplexer and the NOP of Core3 with L. Simulated propagation results at 1550 nm when the $E_{21\; }^x$ mode was excited in Core1 with L set to (b) 18800 µm, (c) 23200 µm, and (d) 35300 µm.
Several factors may contribute to the deviation between the measurement and design sizes. Therefore, the impact of deviations on the mode-coupling characteristics should be determined. As shown in Fig. 5(a), the mode coupling ratio fluctuated considerably owing to waveguide core width deviations. In the simulation, the center distance between Core1 and Core2 (Core3) in Fig. 1 was fixed at 13.95 µm. Simultaneous widening or narrowing of the Core1 widths w1 and Core2 (Core3) widths w2 (w3) resulted in a decrease in the coupling ratio CR21. For instance, when w1 and w2 were reduced by 0.1 µm from the design value, CR21 decreased from 96.73% to 85.21%. Furthermore, Fig. 5(b) indicates the variation in the mode coupling ratio with waveguide core height deviations. The fluctuation of the coupling rate was less than 1% when h was varied by ±0.3 µm, which indicated that the mode-coupling characteristics were slightly influenced by the height deviations. Therefore, to ensure that the deviation is as small as possible, controllable factors in the process should be sufficiently managed.
Fig. 5. Variation in the couplings of the cascaded two-mode (de)multiplexer with deviations in the (a) waveguide core widths, and (b) waveguide core heights at 1550 nm.
Figure 6 (a) illustrates the variation in the coupling ratios with increasing wavelength for the conventional and cascaded ADC structures, where the coupling lengths CL1 and CL2 were both set to the optimum value of 6185 µm. The coupling ratio of the conventional ADC structure increases linearly with the wavelength. However, the coupling ratio of the cascaded ADC structure first increased and then decreased with increasing wavelength, with a maximum value of 96.73% at 1550 nm and a minimum value of 83.71% at 1530 nm. The cascaded two-mode (de)multiplexer had an operating bandwidth (OBW) of approximately 1533–1570 nm, with coupling ratios higher than 90%. It is clear that the coupling ratio of the cascaded ADC structure was always greater than that of the conventional ADC structure when the wavelength was less than 1568 nm. As depicted in Fig. 6(b), the extinction ratio first increased and then decreased with increasing wavelength. It was higher than 12 dB over 1530–1570 nm, and reached a maximum of 14.46 dB at 1549 nm. The simulation results show that the proposed cascaded design functions well as a two-mode (de)multiplexer, which can improve the coupling ratio by superimposing the power of the modes. Moreover, the coupling ratios of the $E_{11}^y$ and $E_{21}^y$ modes were simulated further, as shown in Fig. 7. The simulation results indicated that the coupling ratio of the $E_{21}^y$ mode also increased first and then decreased with increasing wavelength, and was higher than 90% over 1530–1570 nm, reaching a maximum value of 94.37% at 1549 nm. The proposed (de)multiplexer is very slightly affected by polarization.
Fig. 6. (a) Variation in the coupling ratio of different ADC structures when the wavelength varies from 1530 to 1570 nm. (b) Variation in the extinction ratio of the cascaded ADC structure when the wavelength varies from 1530 to 1570 nm.
Fig. 7. Variation in the coupling ratio of the cascaded ADC structure for the $E_{mn}^x$ and $E_{mn}^y$ modes when the wavelength varies from 1530 to 1570 nm.
3. Fabrication and measurement
Based on the UV photolithography technology [39,40], a cascaded two-mode (de)multiplexer was fabricated for the experiment. The polymer materials EpoClad_10 and EpoCore_10 (Micro Resist Technology GmbH) were used for waveguide cladding and core, respectively, because of our refractive index design. The main fabrication processes of the cascaded two-mode (de)multiplexer are shown in Figs. 8: (a) the under-cladding layer with a thickness of ∼20 µm was fabricated by spin-coating EpoClad_10 for 30 s at 2000 rpm, (b) the core layer with a thickness of 6 µm was fabricated by spin-coating EpoCore_10 for 180 s at 5000 rpm, (c) the core layer was exposed by UV light (365 nm), (d) the core layer was developed for 20 s, (e) the upper-cladding layer was fabricated using the same procedure as (a). To verify the effect of the cascaded position on the coupling ratio, L was set to 18800 and 35300 µm, respectively.
Fig. 8. Major steps in fabricating the (de)multiplexer: (a) spin-coating the under-cladding layer, (b) spin-coating the core layer, (c) UV exposure, (d) developing, (e) spin-coating the upper-cladding layer.
The dimensions of the fabricated cascaded two-mode (de)multiplexer were measured using a 3D optical profiler (S neox, Sensofar-Tech), as shown in Fig. 9(a) and (b). The waveguide core widths w1, w2, and w3 were measured as 12.90, 5.03, and 5.10 µm, respectively. The measured height h was 6.06 µm, and the waveguide core separation d for the two ADCs was 4.97 and 5.03 µm. It is evident that the dimensional data obtained were in good agreement with the design. Figures 9(c), (d), and (e) display the images of the two coupling regions and the cascaded location of the fabricated (de)multiplexer, respectively, which were observed using scanning electron microscopy (SEM) (JSM-7500F, JEOL). The waveguide cores of the coupling regions were completely separated and no sticking was observed. Figure 9(f) shows the end-face profile of the (de)multiplexer, indicating the good through-light performance of the device.
Fig. 9. Measured waveguide core dimensions of (a) Core1 and Core2 and (b) Core2 and Core3 in the coupling region under the 3D profilometer. SEM images of (c) coupling region1, (d) coupling region2, and (e) the cascaded position. (f) A photograph of the end face of the fabricated (de)multiplexer when the waveguide cores are injected with light.
The measurement setup for the cascaded two-mode (de)multiplexer is illustrated in Fig. 10(a). The optical signal emitted by the tunable laser (TSL-710, Santec) was transmitted to a single-mode fiber (SMF) (SMF28-e, Corning). x-polarization was obtained using a polarization controller (FPC562, Thorlabs). Subsequently, the light propagated into an all-fiber mode converter based on CO2-laser-inscribed long-period fiber gratings (LPFG) in an FMF (Four-Mode Step-Index Fiber, YOFC) to excite the LP11 mode [22]. A six-dimensional adjustment frame (M-562F-XYZ, Newport) was used to realize precise alignment between the FMF and waveguide. To capture the output near-field images, an infrared charge-coupled device (CCD) camera (IK1112, EHD Imaging) was used with a 40× optical objective at the output end of the cascaded two-mode (de)multiplexer. Figure 10(b) shows photographs of the experimental setup and the fabricated cascaded two-mode (de)multiplexer on an FR-4 substrate. As shown in Fig. 10(c), the total length of the fabricated device was 40 mm, with good optical transmission performance.
Fig. 10. (a) Schematic of the two-mode (de)multiplexer test system. Photographs of (b) the measurement system and the device on the FR-4 substrate under test and (c) verification of the total length and optical transmission performance of the device.
When the $E_{21}^x$ mode was launched into Core1, output near-field images were captured by the infrared CCD camera over a wavelength range of 1530–1560 nm, as shown in Fig. 11. Pure near-field images of the superimposed $E_{11}^x$ mode of Core2 and Core3 were obtained. The light intensity of the $E_{11}^x$ mode from Core 3 with L = 18800 µm was smaller than that with L = 35300 µm, which is in accordance with the simulation results shown in Fig. 4(a). The power of the $E_{21}^x$ mode of Core1 was highly coupled to that of the $E_{11}^x\; $ mode of Core2 and Core3 at 1540 nm when L = 35300 µm, and a small portion of the power of the $E_{21}^x$ mode remained in Core1. In summary, the cascaded waveguide structure functioned well as an effective two-mode (de)multiplexer with the $E_{21\; }^x$ mode of Core1 coupled to the $E_{11\; }^x$ modes of Core2 and Core3 when L = 35300 µm.
Fig. 11. Output near-field images captured by infrared CCD camera when the $E_{21\; }^x$ mode was launched into Core1.
Furthermore, L was adjusted by ±1000 µm to reduce the influence of the dimensional deviation of the waveguide cores on coupling. The measured input power of Core1, the measured output power of Core1 and Core3 and the calculated coupling ratio CR21 are summarized in Table 1. The optimal coupling ratio was 96.12% when L = 34300 µm. However, it was the highest at only 75.03% when L = 18800 µm. The maximum coupling ratio at a design L of 35300 µm was not achieved owing to dimensional errors in the manufacturing process. Moreover, the variations in the coupling ratios and extinction ratios with increasing wavelength were obtained, as depicted in Fig. 12(a) and (b), respectively. Similar to the simulation results in Fig. 6(a) and (b), the coupling ratio and extinction ratio first increased and then decreased with increasing wavelength. When L was 34300 µm and the wavelength was 1540 nm, the maximum coupling ratio and extinction ratio were 96.12% and 14.21 dB, respectively. In conclusion, the experimental results were in agreement with the simulated values.
Table 1. Output power and coupling ratios of the device with different cascaded position L
Fig. 12. Variation in measured (a) coupling ratios CR21 and (b) extinction ratios ER21 with increasing wavelength.
The insertion and propagation losses were measured when the ${\boldsymbol E}_{21}^{\boldsymbol x}$ mode was launched into Core1. The total insertion loss (TIL) of the ${\boldsymbol E}_{21}^{\boldsymbol x}\; $ mode of Core1, with one end of the device connected to an FMF and another end connected to an MMF, was measured as 9.75 dB. Samples with the same dimensions and material as Core1 and Core2 (Core3) were fabricated to evaluate the propagation losses of the waveguide. The propagation losses of the ${\boldsymbol E}_{21}^{\boldsymbol x}$ mode of Core1 and the ${\boldsymbol E}_{11}^{\boldsymbol x}$ modes of Core1 and Core2 (Core3), measured using the cutback method, were 2.1, 1.8, and 3.1 dB/cm, respectively, at 1550 nm. The larger losses of Core1, Core2 (Core3) were attributed to their smaller core sizes and high surface roughness.
To better demonstrate the experimental performance of the fabricated (de)multiplexer, parameters such as coupling ratios and insertion losses were compared with the design presented in [11,13,15], as shown in Table 2. The proposed cascaded structure can also achieve a high coupling ratio and relatively low losses.
Table 2. Comparisons of reported and our proposed polymer waveguide (de)multiplexer
In future research, additional cascaded structures can be added to further improve the coupling ratio, and the deviation tolerance can be improved by designing tapered waveguide structures. Additionally, thermal reflow technology [41,42] can be utilized in the preparation process to reduce the sidewall roughness of the waveguide cores, which can improve the performance of the proposed (de)multiplexer. Moreover, the proposed (de)multiplexer can support more waveguide modes by adopting a multilayer waveguide structure [11,13,16] or cascading more ADC structures in the horizontal direction [12,21,29]. However, multilayer waveguide structures require extremely high alignment accuracy, and the added ADC structures in the horizontal direction require a more sophisticated design.
4. Conclusion
In this study, an efficient polymer two-mode (de)multiplexer consisting of two cascaded horizontal ADCs was investigated in detail. Based on mode coupling theory, the variation law of the coupling ratio with the separation between the waveguide cores and cascaded position was analyzed. The cascaded ADC structure increased the coupling ratio from 82.3% to 96.73% at 1550 nm when the separation between waveguide cores was 5 µm, with an optimal cascaded position of L = 35300 µm. At other cascaded positions, the coupling ratios were small because of the large mode phase difference caused by the SVEA. Experimentally, the coupling ratio and extinction ratio of the fabricated (de)multiplexer reached a maximum value of 96.12% and 14.21 dB at 1540 nm, respectively, when L = 34300 µm, and the difference between the experimental and theoretical results was attributed to the dimensional deviations of the fabricated device. Further experiments showed that the coupling ratios of the (de)multiplexer were higher than 90% over the wavelength range 1533–1565 nm. The minimum value of the total insertion loss of the device with the FMF and MMF connected at both ends was 9.75 dB. The propagation losses measured using the back-cut method for the $E_{21}^x$ mode of Core1 and the $E_{11}^x$ modes of Core1 and Core2 (Core3) were 2.1, 1.8, and 3.1 dB/cm at 1550 nm, respectively. In addition, the influence of different cascaded positions on the mode-coupling characteristics was verified, which agreed with the simulation results. The proposed cascaded horizontal ADC structure enhances the performance of the (de)multiplexer and reduces the accuracy requirements of the fabrication process; therefore, it can be used in the MDM systems of integrated photonic circuits.
Funding
Science and Technology Commission of Shanghai Municipality (16511104300); National Natural Science Foundation of China (61735009, 62027818); National Key Research and Development Program of China (2020YFB1805800).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from authors upon reasonable request.
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