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Abstract
A compact and efficient polymer three-mode (de)multiplexer with two cascaded waveguide directional couplers fabricated on the same substrate along the horizontal direction is proposed. Three waveguides formed two couplers, where two narrower waveguides were placed on either side of the central waveguide. By optimizing the core height and width, the two couplers can ensure that the $E_{11}^x$ mode of the two narrower waveguides are highly coupled into the $E_{21}^x$ and $E_{31}^x$ modes of the central waveguide at a wavelength of 1310 nm. The structural size of the fabricated three-mode (de)multiplexer using ultraviolet (UV) lithography technology is in agreement with the designed value. The fabricated device, which is 35 mm long, exhibits coupling ratios of 98.07% and 95.43% for the two couplers, respectively. The insertion losses of the three waveguides are 5.23 dB, 8.58 dB, and 14.39 dB, respectively. The device can achieve the multiplexing of three modes in two dimensions, which can increase the channel capacity of optical communication.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With rapid development in the fields of communications, supercomputers, and big data centers, traditional electrical interconnect technologies can no longer meet modern data processing speed and bandwidth requirements. The on-chip optical interconnect, with its high speed, broadband, low power consumption, and easy optoelectronic integration, can effectively solve this problem [1–3]. Various signal modulation methods have been proposed to realize high-speed transmission of optical signals, such as wavelength division multiplexing [4], time division multiplexing [5], code division multiplexing [6], and mode division multiplexing (MDM) [7,8]. Among the aforementioned technologies, mode division multiplexing has garnered considerable attention in the field of optical interconnection technology. MDM is a multiplexing technology that increases the channel capacity of optical communication systems by using the spatial freedom of light waves [9]. In an MDM system, several spatial modes in one channel can be separated, with each one carrying an independent channel. Communication capacity levels in excess of Pbit/s can be achieved using a combination of multicore fiber (MCF) and various types of MDM, and MDM has been proven to have great potential for long-haul transmission over 100 km [10–12].
To achieve more compact, compatible, and highly integrated optical devices, mode division (de)multiplexers based on silicon waveguides [13–21] and polymer waveguides [22, 23] have attracted much attention. Compared to silicon waveguides, polymer waveguides have significant advantages in terms of simplicity of fabrication process, error tolerance and fabrication cost. Polymer mode (de)multiplexers are more compatible with fiber MDM systems because the refractive indices and dimensions of the polymer waveguides are close to those of silicon fibers. Currently, numerous technologies are available for mode division multiplexing, including waveguide grating technology [13,23], multimode interference technology [15,16], asymmetric Y-junction waveguide coupling technology [17–19], and waveguide directional coupling technology [14, 20–22]. Among these technologies, waveguide directional couplers are widely studied owing to their advantages of flexible and scalable design, relatively simple fabrication process, and high coupling ratios. Polymer materials can be used to obtain a high-precision and low-loss structure to ensure high coupling ratios and excellent mode selectivity [24,25]. On-board optical interconnect technology based on polymer waveguides has become the preferred solution for short-haul and high-speed computing communication designs [26–28]. Generally, a horizontal directional coupler based on a polymer optical waveguide is widely used for coupling between the fundamental mode and a type of high-order mode, such as the $E_{21}^x$ mode, with an experimental coupling ratio higher than 95% [29]. The tapered structure of an optical waveguide can be used to relax the fabrication tolerance, which can ensure high mode-conversion efficiency [30–32]. In addition, different waveguide core heights can be designed to implement high coupling between the fundamental mode and another type of high-order mode, such as the $E_{12}^x$ mode. However, this increases the complexity of the fabrication process and is not easy to control [33]. To further increase the data capacity, (de)multiplexers that support more than two modes have been developed. Among them, different core heights and core tapered structures have been proposed, but they are limited to simulated designs without experimental validation [34]. Some have adopted multilayer structures with strict alignment accuracy requirements, which increased the manufacturing difficulty [22,35]. In addition, when the number of multiplexed modes is too large, the crosstalk between different modes will be difficult to control, which in turn will affect device performance.
In this report, a three-mode (de)multiplexer based on two horizontal polymer waveguide directional couplers is presented. First, the optimal waveguide core structural parameters of the (de)multiplexer were determined through a simulation of the mode coupling characteristics based on the mode coupling theory. Furthermore, the changes in coupling lengths and coupling ratios with deviations of waveguide core widths and wavelengths were discussed in detail. Subsequently, a three-mode (de)multiplexer was fabricated based on UV lithography technology, the profile and size of which were measured using a 3D optical profiler. Finally, an experimental setup for mode multiplexing was established. The near-field images and mode coupling ratios of the fabricated three-mode (de)multiplexer were obtained experimentally.
2. Design and simulation
The structural model of the three-mode (de)multiplexer is shown in Fig. 1. The two horizontal directional couplers are composed of three rectangular waveguide cores, namely Core1, Core2, and Core3, which are located on the same layer. The three parallel waveguide cores have a uniform height h and widths w1, w2, and w3. The separations of the waveguide cores of each directional coupler in the coupling region are d1 and d2, respectively, and the distances between the centers of Core1 and Core2 and those of Core2 and Core3 are s1 and s2, respectively. The refractive indices of the waveguide core and cladding are denoted as ncore and ncladding, respectively. Core1, Core2, and Core3 are all few-mode waveguides (FMWs), where Core1 supports the $E_{11}^x$ and $E_{21}^x$ modes and Core2 and Core3 both support the $E_{11}^x$, $E_{21}^x$, and $E_{31}^x$ modes. In addition, S-bends are applied at the two side waveguide cores for mode separation when the coupling length reaches the optimal value [36,37]. Specifically, the $E_{11}^x$ mode can be completely coupled into the $E_{31}^x$ mode or $E_{21}^x$ mode of Core2 when excited in Core1 or Core3, respectively, and the $E_{11}^x$ mode still remains in Core2 when excited in Core2.
Fig. 1. Schematic diagram of the proposed three-mode (de)multiplexer with the inset showing the cross section of the coupling region.
According to the coupled-mode theory [38], the power of the fundamental and high-order modes in a directional coupler can be defined as
where A(z) and B(z) represent the slowly varying field amplitudes of the fundamental mode in one waveguide core and the high-order mode in the other waveguide core, respectively, and z is the distance that the light wave travels along the z-direction. D is expressed as $D = C/\sqrt k $, where C is the coupling coefficient between the two modes. The power transfer coefficient, k, is defined as When the propagation constants of the two modes are equal (βA = βB), the power of the fundamental mode can be efficiently coupled to that of the high-order mode. The function of the proposed (de)multiplexer is to realize the coupling of the three modes of $E_{11}^x$, $E_{21}^x$, and $E_{31}^x$. To implement the maximum coupling ratios between the three modes, the effective refractive index (ERI) of the $E_{31}^x$ mode of Core2 must be equal to that of the $E_{11}^x$ mode of Core1, and the ERI of the $E_{21}^x$ mode of Core2 must be equal to that of the $E_{11}^x$ mode of Core3, as shown in Fig. 2(a). In our design, ncore = 1.576 and ncladding = 1.564 at a wavelength of 1310 nm, which were determined according to the data sheets of the polymer materials EpoCore_10 and EpoClad_10 (Micro Resist Technology GmbH). The relationship between the ERIs of the modes and the widths of each core is depicted in Fig. 2(b), with a fixed height of 8 µm for the three waveguide cores. The ERIs of all three modes increase with the width of the waveguide core and eventually tend to a constant value. When the widths of Core1, Core2, and Core3 are 5.2 µm, 20 µm, and 8.9 µm, respectively, the ERIs of the $E_{11}^x$ mode of Core1 and $E_{31}^x$ mode of Core2 are both 1.5722, and the ERIs of the $E_{11}^x$ mode of Core3 and $E_{21}^x$ mode of Core2 are both 1.5736. In this case, the phase-matching condition was satisfied. In addition, the ERI of the $E_{11}^x$ mode of Core2 is 1.5744; therefore, the phase-matching condition cannot be fulfilled. The $E_{11}^x$ mode of Core2 cannot be coupled to the other modes of Core1 or Core3.Fig. 2. (a) The ERIs of the $E_{31}^x$ and $E_{21}^x$ modes in Core2 match those of the $E_{11}^x$ mode of Core1 and Core3, respectively. (b) Variation of the ERIs of the $E_{11}^x$, $E_{21}^x$, and $E_{31}^x$ modes with the width of the waveguide core at a wavelength of 1310 nm and the height fixed at 8 µm.
The performance of the (de)multiplexer can be characterized by the coupling ratios between the fundamental mode and the high-order mode [33,34]. The coupling ratio between the $E_{31}^x$ mode of Core2 and the $E_{11}^x$ mode of Core3 is given by
and the coupling ratio between the $E_{21}^x$ mode of Core2 and the $E_{11}^x$ mode of Core3 is given by where P1 and P2 are the output powers from Core1 and Core2, respectively, when only the $E_{11}^x$ mode is excited in Core1. P′2 and P3 are the output powers from Core2 and Core3, respectively, when only the $E_{11}^x$ mode is excited in Core3. The coupling length between the $E_{11}^x$ mode of Core1 and the $E_{31}^x$ mode of Core2 is denoted as L31, and the coupling length between the $E_{21}^x$ mode of Core2 and the $E_{11}^x$ mode of Core3 is denoted as L21.To ensure the maximum conversion of mode power, the light propagation distance required for the maximum coupling ratio, that is, the coupling length, must be determined. In our study, the 3D finite-difference beam propagation method (3D FD-BPM) (Beam-PROP, RSoft) was employed to build a structural model of the waveguide directional coupler. In the simulation, the coupling lengths were set to optimum in order to enable maximum power of Core1 or Core3 to be coupled into Core2. The dependence of the optimal coupling lengths and coupling ratios on the separation between waveguide cores was obtained, as shown in Fig. 3. As the separation increased, the coupling length increased steadily, whereas the coupling ratios first increased and then decreased. Specifically, when the separation is below 1 µm, it can be regarded as a combinatorial waveguide structure, where the mode field distributions are impure, and therefore the coupling effect between the two waveguide modes will be weakened. Therefore, the separation should be determined to a suitable value to ensure optimal performance of the three-mode (de)multiplexer. Considering that the separation should be larger to reduce the crosstalk and be easy to implement by UV lithography, the separation of waveguide cores is chosen as 3.0 µm, that is, d1 = d2 = 3.0 µm. Under these conditions, CR31 and L31 were 98.21% and 5040 µm, respectively. Similarly, CR21 and L21 were 99.72% and 15450 µm, respectively.
Fig. 3. Variation of coupling lengths and coupling ratios with the separation of waveguide cores at a wavelength of 1310 nm.
Some factors in the fabrication process may cause deviations between the actual device dimensions and the design dimensions. Therefore, it is necessary to determine the influence of the waveguide core width deviation on the mode coupling characteristics. Figure 4(a) illustrates that the mode coupling characteristics are significantly affected by the width of the waveguide cores. It is assumed that the center spacings s1 and s2 of the waveguide cores in Fig. 1 are fixed. Regardless of whether w1, w2, and w3 become wider or narrower at the same time, the coupling ratios CR21, CR31, and coupling length L31 always decrease, whereas the coupling length L21 increases when the widths of the three cores become narrower. For example, when w1, w2, and w3 are all increased by 0.1 µm from the design value, CR31 decreases from 98.21% to 80.18% and L31 decreases from 5040 µm to 4364 µm. Therefore, various factors should be controlled during fabrication to ensure that the actual waveguide core size is as close to the design as possible. Furthermore, the wavelength dependence of the mode coupling characteristics over the wavelength range of 1260–1360 nm is shown in Fig. 4(b), where the central wavelength (CW) is 1310 nm. It is clear that the coupling characteristics of the $E_{21}^x$ and $E_{31}^x$ modes are affected by the wavelength. The coupling ratio CR31 was 99.66% at 1290 nm and decreased to 92.30% at 1260 nm and 86.36% at 1360 nm, whereas the coupling ratio CR21 was always greater than 92%, with a maximum of 99.89% at 1320 nm. As for the coupling length, both the coupling lengths decreased monotonically with increasing wavelength, where L31 decreased from 5774 µm to 4140 µm and L21 decreased from 17224 µm to 13100 µm. Furthermore, Fig. 4(c) illustrates the variation of coupling ratios with wavelength when the coupling lengths L31 and L21 were set to the optimal values of 5040 µm and 15450 µm, respectively. It is indicated that the operating bandwidth of the three-mode (de) multiplexer is approximately 1270–1330 nm with coupling ratios higher than 92% theoretically.
Fig. 4. (a) Variation of coupling lengths and coupling ratios with deviations of waveguide core widths at a wavelength of 1310 nm. (b) Variation of coupling lengths and coupling ratios when the wavelength varies from 1260–1360 nm. (c) Variation of coupling ratios with wavelength when the coupling lengths L31 and L21 are set to the optimal values of 5040 µm and 15450 µm, respectively.
In the design, cosine-type S-bends were introduced into Core1 and Core3. When the coupling ratio reached a maximum, the waveguide cores were separated by the S-bends to stop the coupling between modes. In Fig. 5(a), the two parameters X1 and X2 represent the longitudinal and lateral lengths of the cosine-type S-bend, respectively. To determine appropriate parameters, the value of X1 was fixed at 5000 µm and the value of X2 was gradually changed from 10 µm to 65 µm. The relationship between the normalized output power and X2 is shown in Fig. 5(b). From the figure, the normalized power gradually decreases with an increase in X2. Therefore, the value of X2 was finally chosen as 22 µm, considering the actual preparation and testing factors. Under these conditions, the normalized output power was 0.9959 and 0.9781, respectively, when w1 = 5.2 µm and w3 = 8.9 µm.
Fig. 5. (a) The structure of the S-bend for mode separation with parameter X1 for longitudinal length and parameter X2 for lateral length. (b) Variation of normalized output power with X2 when X1 is fixed at 5000 µm.
Figure 6(a) shows the top view of the final structure design by 3D FD-BPM simulation. The longitudinal length of each S-bend was 5000 µm, and the final separation between Core1 and Core2 and between Core2 and Core3 is 25 µm considering d1 = d2 = 3 µm. Due to the influences of the S-bends, the lengths of the coupling regions for the two directional couplers were finally set to 4500 µm and 15000 µm respectively. In Figs. 6(b) and (d), almost all the power of Core1 or Core3 can be coupled into Core2, with coupling ratios higher than 98% and 99% respectively, when the $E_{11}^x$ mode was excited in Core1 or Core3. Conversely, the $E_{11}^x$ mode of Core2 always transmits steadily forward, as shown in Fig. 6(c). From the simulation, the proposed design works well as a three-mode (de)multiplexer.
Fig. 6. (a) Top view of the designed structure by BPM simulation. Simulated propagation results at 1310 nm for the $E_{11}^x$ mode excited in (b) Core1, (c) Core2, and (d) Core3.
It is important to note that the simulation results of proposed three-mode (de)multiplexer were based on 1310 nm, mainly because 1310 nm is an important wavelength as 1550 nm in optical communications. In addition, the simulation results showed that the coupling ratios at 1310 nm were larger than those at 1550 nm.
3. Fabrication and measurement
The three-mode (de)multiplexer was fabricated using UV photolithography technology [39,40]. Therefore, in the experiment, the polymer materials EpoClad_10 and EpoCore_10 (Micro Resist Technology GmbH) were used for the waveguide cladding and core, respectively. The process of fabricating the mode division (de)multiplexer was composed of five steps, which is described in Fig. 7(a) the EpoClad_10 film was spin-coated and cured onto a cleaned FR-4 substrate as the under-cladding layer with a thickness of ∼15 µm, (b) a layer of EpoCore_10 for three cores was spin-coated onto the under-cladding layer with a thickness of 8 µm, (c) the core layer was photoetched by a mask-less UV lithography machine (Heidelberg, MLA100), (d) the designed pattern was obtained by a standard development process using developer mr-Dev 600 (Micro Resist Technology GmbH), and (e) the upper-cladding layer with a thickness of ∼15 µm was fabricated using the EpoClad_10 film. Some factors in the fabrication process may influence the characteristics of the actual device, which slightly deviate from the simulation. Thus, the lengths of the coupling regions of L31 and L21 were changed by ±20 µm, that is, L′31 = L31 ± 20 µm and L′21 = L21 ± 20 µm.
Fig. 7. Major steps in the fabrication of the (de)multiplexer: (a) spin-coating and curing the under-cladding layer; (b) spin-coating the core layer; (c) photoetching by mask-less UV lithography machine; (d) developing and forming the core structure of the (de)multiplexer; (e) spin-coating the upper-cladding layer, curing it, and completing the process.
The fabricated three-mode (de)multiplexer, measured by a 3D optical profiler (S neox, Sensofar-Tech), is shown in Fig. 8. The waveguide core widths w1, w2, and w3 were measured to be 5.1922, 19.9950, and 8.9010 µm, respectively, and d1, d2, and h were measured as 3.0315, 3.0960, and 7.9135 µm, respectively, as shown in Figs. 8(a) and (b). It is clear that the measurement results conform well to the design (w1 = 5.2 µm, w2 = 20 µm, w3 = 8.9 µm, d1 = d2 = 3.0 µm, and h = 8.0 µm). From Figs. 8(c) and (d), there is no residual in the 3D images of the coupling regions, showing a good separation morphology. The end-face profile of the (de)multiplexer in Fig. 8(e) indicates that the device has good light permeability.
Fig. 8. Measured waveguide dimensions of (a) Core1 and Core2 and (b) Core2 and Core3 in the coupling region under the 3D profilometer. 3D images of the coupling regions between (c) Core1 and Core2 and (d) Core2 and Core3. (e) Photograph of the end face of the fabricated device when the waveguides are injected with light.
A sketch map of the three-mode (de)multiplexer measurement setup is shown in Fig. 9(a). An optical signal with a wavelength of 1310 nm propagated from a light source (S4FC1310, Thorlabs) and was coupled into a single-mode fiber SMF (SMF28-e, Corning). Then, the light passed through a polarization controller to obtain the x-polarization. Moreover, a small core diameter SMF with a mode diameter of ∼6 µm was used to achieve better mode field matching between the fiber and the waveguide. Precise alignment between the small core diameter SMF and the three cores was realized with the help of a six-dimensional adjustment frame (M-562F-XYZ, Newport). At the output end of the (de)multiplexer, the output near-field images were captured using an infrared charge-coupled device (CCD) camera (C10633, Hamamatsu) after passing through a 40× optical objective lens. Figure 9(b) shows photographs of the measurement setup and the device on the FR-4 substrate under test, where the length of the fabricated device was measured to be 35 mm.
Fig. 9. (a) Three-mode (de)multiplexer test system. (b) Photographs of the measurement setup and the device on the FR-4 substrate under test.
In the measurement, the output mode from the small-diameter SMF can be regarded as a Gaussian distribution, which is similar to the $E_{11}^x$ mode. Hence, when launched into Core2, almost all of the power is coupled to the $E_{11}^x$ mode, as shown by the output near-field images in Fig. 10(b) captured by the infrared CCD camera. However, from the output near-field images in Figs. 10(a) and (c), we can conclude that it is not the best coupling effect for the device according to the design, which is derived from the dimensional error in the fabrication process. When L′31 = L31 - 20 µm and L′21 = L21 + 20 µm, the power of the $E_{11}^x$ mode in Core1 and Core3 was almost coupled to the $E_{31}^x$ mode and $E_{21}^x$ mode of Core2. As expected, the device functioned well as an effective three-mode (de)multiplexer with the $E_{11}^x$ mode of Core1 and Core3 coupled into the $E_{31}^x$ and $E_{21}^x$ modes of Core2, respectively.
Fig. 10. Output near-field images captured by infrared CCD camera when the $E_{11}^x$ mode was launched into (a) Core1, (b) Core2, and (c) Core3.
Further, the coupling ratios and losses of the fabricated three-mode (de)multiplexer were measured at a wavelength of 1310 nm, as shown in Table 1. According to Eq. (4) and Eq. (5), the coupling ratios CR31 and CR21 were calculated as 95.43% and 98.07%, respectively, when L′31 = L31 - 20 µm and L′21 = L21 + 20 µm. This means that the fabricated (de)multiplexer has the effect of mode-division multiplexing. The total insertion losses (TILs) for the $E_{31}^x$, $E_{11}^x$, and $E_{21}^x$ modes are denoted as TIL31, TIL11, and TIL21, respectively, which main include the propagation losses of waveguides and the coupling losses between the waveguide cores and the fiber. This can be tested by the method in which the power from the device excited by the small core diameter SMF is received by the multi-mode fiber (MMF) with a core diameter of 50 µm. To further decrease the coupling loss, an index-matching liquid was applied to the connection between the small core diameter SMF and waveguide and between the MMF and waveguide. The large insertion losses were mainly derived from the sidewall roughness induced by preparation process limitations and the mode filed mismatch between the waveguide cores and the fiber. Thanks to its larger end-face size, the coupling efficiency of Core2 was larger than that of Core1 and Core3, and thus TIL11 was much smaller than TIL21 and TIL31. The propagation losses for the $E_{11}^x$ mode of Core1, Core2, and Core3 were measured to be 3.5, 1.5, and 2.2 dB/cm, respectively, by applying the back-cut method to isolated reference waveguide cores of the same size.
Table 1. Coupling ratios and insertion losses of the device
Compared with the (de)multiplexers proposed in Refs. [22,33,35], the proposed three-mode (de)multiplexer has good experimental performances in terms of coupling ratios and insertion losses, as illustrated in Table 2. From the above, the obtained coupling ratios measured were smaller than the simulated results. This is mainly because there are differences in the structure of the fabricated three-mode (de)multiplexer. There are deviations between the simulation and measurement values of parameters w1, w2, w3, d1, d2 and h. Moreover, the sidewall roughness on the waveguide core is also a non-negligible factor, which not only significantly increases the transmission loss but also greatly reduces the performance of the device. In future studies, a tapered waveguide core structure can be introduced to increase the deviation tolerance. In addition, the sidewall roughness of the waveguide cores can be further reduced after the thermal reflow process [41], and a tapered fiber can be utilized to further reduce the coupling losses between the fiber and the waveguide cores.
Table 2. Comparisons of reported and our proposed polymer waveguide (de)multiplexer
4. Conclusion
In this study, based on UV lithography technology, a compact and efficient polymer three-mode (de)multiplexer with two cascaded horizontal waveguide directional couplers was fabricated. The optimal structures of the (de)multiplexer were obtained through a mode coupling simulation, as well as the mode coupling ratios and coupling lengths. The (de)multiplexer allows the fundamental mode (i.e., the $E_{11}^x$ mode) of two FMWs to be coupled into the high-order mode (i.e., the $E_{21}^x$ and $E_{31}^x$ modes) of another FMW. The experimental device, which had a length of 35 mm, was measured for its function, insertion losses, and mode coupling ratios at a wavelength of 1310 nm. The maximum values of the coupling ratios for the $E_{21}^x$ and $E_{31}^x$ modes were 98.07% and 95.43%, respectively. The minimum values of the total insertion losses of Core1, Core2, and Core3 with fibers connected at both ends were 14.39 dB, 5.23 dB, and 8.58 dB, respectively. The number of modes can be increased by adding more directional couplers. Based on horizontal directional couplers only, the (de)multiplexer is relatively simple to manufacture and requires relatively low accuracy. Our proposed three-mode (de)multiplexer can be widely used in MDM systems to increase the channel capacity.
Funding
National Key Research and Development Program of China (2020YFB1805800); National Natural Science Foundation of China (61735009, 62027818); Science and Technology Commission of Shanghai Municipality (16511104300).
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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