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Abstract
In this paper, Y-branched circular core single-mode/few-mode polymer optical waveguides are designed and fabricated using the Mosquito method we have developed. They comprise a low loss multiplexing (MUX) device for mode division multiplexing. In the Mosquito method, since a liquid core monomer is dispensed into another liquid cladding monomer while the needle scans along the path of the wiring patterns, it was difficult to form in-plane core crossings and core branches. In this paper, to form single-mode/few-mode Y-branched cores, we apply a unicursal needle-scan path for the Y-branch structure with the Mosquito method. For MUX device applications, cores satisfying the single-mode condition are successfully formed on the two-port side while the one-port side has a few-mode core.
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1. Introduction
Due to the rapid spread of cloud computing technologies over the last couple of years, the transmission capacity of optical networks installed inside and outside datacenters is increasing dramatically, and much greater bandwidth has been required. In long-distance optical links, the transmission capacity has been extended by wavelength-division multiplexing (WDM) technology, in which different light signals at multiple wavelengths are transmitted through a single core in a single-mode fiber (SMF). However, using WDM technology, the increasing quantity of wavelengths to be multiplexed and the use of optical amplifiers significantly increase the optical power density in an SMF core. Thus, there is a concern that “fiber fuse” might occur, and nonlinear optical effects such as four-wave mixing cannot be ignored. In order to realize much larger transmission capacity, space division multiplexing (SDM) technology including mode division multiplexing (MDM) has attracted much attention since it could decrease the power density in a core in one fiber. Using MDM technology, a signal is multiplexed over different propagation modes in few-mode fibers (FMFs). In order to realize the MDM optical links, a mode multiplexer (MUX) is required to connect several different signal light sources to an FMF. Some MDM-MUXs have already been proposed to couple the light to the lowest and higher order modes in FMFs, separately [1–3], and have shown remarkable advantages in loss and crosstalk. However, these MUX devices present some difficulties in their fabrication processes, device complexities, and packaging.
In this paper, in order to address the above issues, we focus on polymer optical waveguide MUX devices with single-mode and few-mode cores fabricated using the Mosquito method. As the propagating modes in circular-core FMFs are expressed as linearly-polarized (LP) modes, the core cross-sectional shapes in waveguides should be circular to exhibit wide overlap in the mode field profiles, resulting in efficient light coupling even for the high-order modes. Our previous publications [4–6] have shown that single-mode circular core polymer optical waveguides can be fabricated with a simple fabrication process named the Mosquito method. Using the Mosquito method, branch structures even with 3-dimensional (3-D) patterns of a circular cross-sectional core are expected to be formed. Applying the 3-D structure, multiplexing of orthogonal modes (LP11a and LP11b modes) with LP01 mode could be achieved. Although 3-D structures can be fabricated using the laser direct writing (LDW) [7], the refractive index difference between the core and cladding cannot be freely varied, as far as we know, since the base material for the core and cladding in the LDW method is identical. Meanwhile, different monomers can be used for the waveguides by the Mosquito method, which enables to vary the core cladding index contrast. Therefore, in this paper, the Mosquito method is utilized to fabricate the waveguide-based MDM-MUX.
Waveguide MDM-MUXs were already fabricated as part of the Mach-Zehnder interferometer (MZI) waveguide structure [8] using the Mosquito method. Although the MZI MDM-MUX devices realize light power transition between two single-mode and few-mode cores aligned in parallel, precise control over the core diameter and core monomer dispensing positions is required for efficient light coupling. In addition, the coupling efficiency is sensitive to the signal wavelength. In this paper, for an MDM MUX device, we focus on Y-branched structures, which are widely investigated as MDM MUX devices [9–11]. The precise core alignment (with well controlled narrow pitch) that is required for the MZI waveguides is not necessarily required for Y-branched waveguides. Moreover, insertion loss is expected to be reduced since there is no space between the two cores, in contrast to the MZI waveguide devices. We already succeeded in fabricating multimode Y-branched core waveguides using the Mosquito method [12] without structural disruption by employing a unicursal needle-scan path. However, single-mode/few-mode Y-branched waveguides need to control the core diameter whereas maintaining the Y-branched structure. In this paper, first, the optimum Y-branched waveguide allowing low-loss MDM MUX is designed using the beam propagation method (BPM). Then, the designed waveguides are experimentally fabricated using the Mosquito method. Next, the functionality of the fabricated Y-branched waveguide MDM-MUX is demonstrated. Finally, we redesign the waveguide for lower-loss MDM-MUX with a more compact Y-branched structure.
2. Design of Y-branched waveguides
2.1 Asymmetric single-step bending structure
In this paper, we focus on asymmetric Y-branched waveguides to use as an MDM MUX device. As a multimode MDM MUX device, an output beam with a high numerical aperture (NA) or large beam size is necessary to launch the higher-order modes in graded-index multimode fibers (GI-MMFs), as shown in our previous publication [13].
Hence, in this section, structures for low-loss asymmetric Y-branched waveguide are investigated using BPM simulation. The insertion loss is calculated using the structure shown in Fig. 1(a). Here, we assume that the LP01 mode with a mode-field diameter (MFD) of 7.2 μm at 1310-nm wavelength is coupled to cores (A) and (B) on the two-port side. We refer to well-known definition of MFD that is a diameter at which the optical intensity equals to 1/e2 of the highest intensity. The insertion loss is calculated at the output from core (C) on the one-port side whereas varying the branch angle θ. In the calculation, combinations of folded lines are assumed to compose the Y-branched structure, as shown in Fig. 1(a), where the length of the core merge region L is defined as 250 μm / tan θ.
Fig. 1. (a) Model structure of asymmetric Y-branched waveguide, and (b) calculated insertion loss of the asymmetric Y-branched waveguide.
The calculated results are shown in Fig. 1(b), which include a coupling loss of 1.0-dB at the input end. From Fig. 1(b), when the light is coupled to core (B), the insertion loss almost monotonically decreases as the branch angle increases, since less optical power tends to leak at the two-core merging (tapered) region (the crotch of the Y-branch). Hence, the maximum insertion loss of 5.5 dB is observed at θ = 1.7° (L = 8.4 mm), whereas the minimum loss is 1.3 dB at θ = 10° (L = 1.4 mm). Contrastingly, when the light is coupled to core (A) on the two-port side, the loss almost monotonically increases with increasing the branch angle. The minimum insertion loss of (A) → (C) is 3.2 dB at θ = 0.1° (L = 143 mm), at which the loss of (B) → (C) is almost the same value (3.3 dB). In addition, when θ > 2° (L < 8.4 mm), the insertion loss increases significantly. As the broken curve indicates, the sum of the two losses, (A) → (C) and (B) → (C) monotonically increases with respect to the branch angle, because the loss of (A) → (C) contributes more to the total loss. Therefore, to reduce the total insertion loss, the branch angle should be as small as possible. On the other hand, the lower branch angle leads to longer L, resulting in a large waveguide device. For example, a branch angle of 0.1° corresponds to L = 71.6 mm (91.6 mm in total).
2.2 Asymmetric multi-step bending structures
In order to achieve low insertion loss with shorter L, an asymmetric Y-branched waveguide with a multi-step bending structure is designed, as shown in Fig. 2(a). In the design, the branch angle (angle at the core merge point) and the core merge length L are fixed to 0.1°, and 30 mm, respectively, and the bending angle between the two arms is varied. The other calculation conditions are the same as those in Section 2.1.
Fig. 2. (a) Asymmetric Y-branched structure model with multi-step bending, and (b) calculated bending angle dependence of the insertion losses of the waveguide.
The results are shown in Fig. 2(b). At smaller bending angles, the insertion loss is close to a minimum value of 3.3 dB, which corresponds to the loss value when θ = 0.1° in the simple Y-branched structure shown in Fig. 1(a). If we allow that the design can afford an insertion loss of 4.3 dB, which is 1.0 dB greater than this minimum value, the bending angle can be as high as 1.2° while still meeting the design requirements. This loss criterion is just arbitrary in this paper. Therefore, introducing the multi-step bending structure, the insertion loss can be kept low with a core merge length L as short as 30 mm. In the next section, Y-branched polymer waveguides with multi-step bending are fabricated.
3. Fabrication of single-mode waveguides using the Mosquito method
3.1 Single-mode condition
The fabrication steps for polymer optical waveguides using the Mosquito method are shown in Fig. 3. First, a liquid-state cladding monomer is coated in an area surrounded by a 0.5-mm thick silicone rubber frame on a glass substrate as shown in Fig. 3(a). Next, the tip of a syringe needle connected to a microdispenser is inserted into the cladding, and the needle scans while dispensing the core monomer to form the waveguide structure, as shown in Fig. 3(b). Finally, both the core and cladding monomers are cured under UV light exposure to obtain a polymer waveguide in Fig. 3(c). Here, the Reynolds number is calculated to be an order of 10−3, which is small enough for the monomer flow to be laminar flow, and by applying the Navier-Stokes equation, the core monomer flow rate (Q) during the core monomer dispensing under a steady state condition is expressed as Eq. (1) [4,14]. As shown in Fig. 4, (p), (d), (L), and η represent the core monomer dispensing pressure, the needle inner diameter (I.D.), the needle length, and the core monomer viscosity, respectively. Assuming the core cross-sectional shape to be a perfect circle, the core diameter (2a) is calculated as Eq. (2), where U represents the needle scan velocity.
To fabricate single-mode and few-mode waveguides, it is well known that the core radius a needs to be controlled according to the V number, which is expressed by Eq. (3).
Here, λ represents the free-space wavelength. When waveguides have step-index (SI) circular cores, it is well known that the waveguides support only the lowest-order mode (LP01 mode) when V is less than 2.405. In the waveguides fabricated using the Mosquito method, the waveguide cores have graded refractive index profiles, since mutual diffusion of the core and cladding monomers occurs during the interim time. We define the interim time as the time after the core monomer is dispensed (Fig. 3(b)) to the moment that the UV curing begins (Fig. 3(c)).
In this paper, UV curable acrylic resins supplied by Kyoritsu Chemical & Co. Ltd., XS-CA02k2.2 (nd = 1.514) and X-CL01k2 (nd = 1.501) are used for the core and cladding materials, respectively. The fabrication conditions are shown in Table 1. First, six straight cores (not Y-branched) are formed in one cladding under different dispensing pressures and needle-scan velocities shown in Table 1. Although all p and U are different in Table 1, the core diameters right after being dispensed derived from Eq. (2) are fixed to an identical value of 4 μm. The near-field pattern (NFP) images of the fabricated waveguides are measured using the setup shown in Fig. 5. Here, a laser diode (LD) at a wavelength of 1310 nm (TSL-550 from Santec Corporation) is used as the light source. In addition, an SMF with an MFD of 8.2 μm at 1310 nm (PA-A2 from Sumitomo Electric Industries, Ltd.) is used as the fiber probe to couple the light into the waveguide cores.
Table 1. Fabrication conditions for straight waveguides
Cross-sectional photos and measured NFP images are shown in Fig. 6. As expected by Eq. (2), the core diameters and MFDs are almost identical in all the channels. The average core diameter measured in the horizontal and vertical directions is 4.5 μm and 4.0 μm, respectively. From the NFP images, we confirm that all the cores satisfy the single-mode condition to show an average MFD of 5.5 μm. This uniform core diameter, and thus a uniform MFD, can be achieved by the material combination selected: the inter-diffusion between the core and cladding monomers is not significantly high due to their moderate miscibility, so that the cores formed could have index profiles close to an SI.
3.2 Single-mode Y-branched waveguide
In this section, the fabrication conditions of single-mode Y-branched waveguides are investigated. Previously, we reported that multimode Y-branched waveguides were successfully fabricated by scanning a needle on a unicursal path as shown in Fig. 7 [12]. In the needle-scan path program, there is no separate single core on the one-port side but instead just a turn-around point, as shown in Fig. 7(a). However, when the needle scans and dispenses the core monomer, the turn-around point, which is on the second arm of the two-port side, is dragged from the far right edge towards the middle of the structure. Then, a crotch and separate core are formed as shown in Fig. 7(b). In addition, although the needle scan path design does not explicitly contain a gradual core curve, the actually formed cores do gradually curve, as shown in Fig. 7(c), because the dispensed core monomer shifts slightly from the originally dispensed pattern due to monomer flow caused by the needle scan. It is important to keep the core diameter small enough to satisfy the single-mode condition without disruption of the Y-branched structure.
Fig. 7. (a) Needle scan path for Y-branched multimode waveguide in the Mosquito method, (b) schematic top-view of the actually fabricated waveguide, and (c) top-view photo of multimode Y-branched waveguide.
In this section, the core diameter needs to be reduced by increasing the needle scan velocity, as investigated in Table 1 in Section 3.1. As with those straight waveguides, X-CL01k2 is used for the cladding. On the other hand, X-CA02k2, which is almost the same UV curable acrylic resin as XS-CA02k2.2, but has a different refractive index of nd = 1.528, is used for the core. Other fabrication conditions are summarized in Table 2. Top-view photos of fabricated Y-branched waveguides are shown in Fig. 8, where the needle-scan velocities are varied to 15 mm/s, 30 mm/s, and 45 mm/s for Figs. 8(a), (b) and (c), respectively. As shown in Fig. 8, the one-port (right hand) side tends to split forming a X-branched structure when the needle-scan velocity increases. Meanwhile, the designed Y-branched structure is successfully formed with a needle scan velocity as low as 15 mm/s, as shown in Fig. 8(a). This is because the low scan velocity can reduce the variation in the core monomer position due to the cladding monomer flow caused by the needle scan.
Fig. 8. Top-view photos of Y-branched waveguides fabricated at different needle scan velocities: Scan velocity (a) 15 mm/s (b) 30 mm/s (c) 45 mm/s.
Table 2. Fabrication conditions of reduced core Y-branched waveguides
Next, the branch angle is varied. In Section 2.1, we find low-loss Y-branched waveguides are formed when the branch angle is low. In this section, Y-branched waveguides with four different branch angles are fabricated. The fabrication conditions are summarized in Table 3, and their top-view photos with branch angles of 4°, 3°, 2°, and 1° are shown in Figs. 9(a), (b), (c), and (d), respectively. From Fig. 9, we confirm that needle scan paths with a lower branch angle can form a Y-branched structure without structural deformation. Meanwhile, when the branch angle is larger than 1°, since the fraction of cladding monomer flow in the direction perpendicular to the core axis increases, no separate core on the one-port side could be formed successfully. From Fig. 9(d), the branch angle actually formed is estimated to be 1.0°, which agrees well with the needle scan path.
Fig. 9. Top-view photos of Y-branched waveguides fabricated varying the branch angle:
Branch angle (a) 4°, (b) 3°, (c) 2°, and (d) 1°.
Table 3. Fabrication conditions of waveguides with different branch angles
Finally, a small-core Y-branched waveguide that satisfies the single-mode condition is fabricated. Although a low branch angle is desired to reliably form a Y-branched structure, as mentioned above, a longer waveguide is required to preserve a sufficient intercore pitch (250 μm) on the two-port side, and the resulting propagation loss of such a long waveguide might be high. Therefore, in order to keep the waveguides short, a multi-step bending structure shown in Fig. 10 is used in the needle scan path. When X-CA02k2 is used for the core, the core diameter should be less than 3.5 μm to satisfy the single-mode condition assuming an SI circular core. All of this makes the fabrication process very sensitive to mistakes, and the alignment of those cores with other optical devices requires very high position accuracy. Hence, an alternative material, XS-CA02k2.2 is used for the core. We already used XS-CA02k2.2 in Section 3.1 to accommodate the core diameter requirement. The other fabrication conditions are summarized in Table 4. Top views of the core branched and bending structure regions are shown in Figs. 11(a) and 11(b), respectively, whereas cross-sectional views of the fabricated Y-branched waveguide are shown in Fig. 11(c). The bending and branch angles actually formed are estimated from Figs. 11(a) and 11(b) to be 2.0° and 0.3°, respectively, which slightly larger than the scan path settings shown in Fig. 10, probably due to the multi-step bending scan path. Meanwhile, the cross-sectional views show that cores with circular cross-sections are formed with a high reproducibility. In order to verify that all the cores in the waveguide satisfy the single-mode condition, the NFPs from those cores are measured by coupling a beam at 1310-nm wavelength via an SMF (P84644-06 from Furukawa Electric Co., Ltd.) with an MFD of 5.5 μm. The beam is coupled from the two-port side ((A)→(C), (B)→(C)), and from the one-port side ((C)→(A), (C)→(B)). When the single-mode condition is satisfied, the output field intensity should have a Gaussian profile regardless of the launch condition. From Fig. 12, we verify that all the NFP images show Gaussian field patterns of LP01 mode. Thus, single-mode Y-branched waveguides are successfully fabricated using the Mosquito method. We also find from Fig. 12 that the MFD of core (C) at 1-port side is slightly larger than those of cores (A) and (B) at 2-port side. This MFD difference is attributed to the core size difference among them as shown in Fig. 11. When fabricating the waveguide, the needle-scan path shown in Fig. 10 is applied, in which a separate core in the 1-port side is formed by a merger of two cores due to the monomer flow by the same mechanism shown in Fig. 7(b) the scan end region of the upper core (core (A)) and the scan start region of the lower core (core (B)). Therefore, the core diameter at 1-port side could be larger than those at 2-port side. Since the MFD is determined by the combination of the core diameter and the index contrast of the core and cladding, the MFD differs only slightly compared to the core diameter difference shown in Fig. 11. When applying this needle-scan path, we need to decrease the 1-port side core diameter by adjusting the dispensing conditions at the crotch region.
Fig. 11. Top-view photos of (a) branched structure region, (b) bending structure region, and (c) cross-sectional photos of the fabricated single-mode Y-branched waveguide.
Table 4. Fabrication conditions of single-mode Y-branched waveguide
3.3 Fabrication of single-mode/few-mode Y-branched waveguides
In this section, Y-branched waveguides that can be used in MDM MUX devices are fabricated applying the conditions for the single-mode Y-branched waveguide described in Section 3.2. The principle of an MDM using a Y-branched waveguide is shown in Fig. 13. The effective refractive indices (neff) of the modes in the two-port side cores are a key [15]. Figure 13(b) shows an example of the relationship between neff and the core diameter, calculated using the BPM, assuming SI circular core waveguides. When neff of the lowest order (LP01) modes on the two-port side and the LP11a mode on the one-port side have the same value, the power of the LP01 mode transfers to the LP11a mode very efficiently. On the other hand, less power transfers when neff of those modes differ significantly.
Fig. 13. (a) Schematic view of the principle of MUX using an asymmetric Y-branch waveguide and (b) power transition mechanism from single-mode core to few-mode core.
Such neff control is possible by adjusting the diameters of the two cores on the two-port side, as shown in Fig. 13(b). Hence, we fabricate asymmetric Y-branched waveguides, whose cores on the two-port side support the lowest order mode (LP01 mode) only, while the core on the one-port side supports two modes: the lowest and second lowest modes (LP01 and LP11 modes). Here, the Y-branched structure is defined by the needle scan path shown in Fig. 10, in which the core diameter w1 (larger one) on the two-port side should be close to the core diameter w3 on the one-port side, being different from the core diameter w2 (smaller one) on the two-port side. In order to form the cores with different diameters on the two-port side, the needle scan velocities are set to 12 mm/s for (A) → (C) but 16 mm/s for (C) → (B) in Fig. 10. From Eq. (2), diameters of cores (A), (B), and (C) are calculated to be 5 μm, 4 μm, and 6 μm, respectively. The other fabrication conditions are the same as those in Table 4. Top view photos of the branched and core bending structures actually formed are shown in Figs. 14(a) and 14(b), respectively, whereas cross-sectional views of the fabricated waveguide is shown in Fig. 14(c). From Fig. 14, an asymmetric Y-branched single-mode/few-mode core waveguide with no structural deformation is successfully obtained. From Figs. 14(a) and 14(b), the bending and branch angles are estimated to be 0.6° and 0.2°, respectively, which deviate slightly from those in the scan path settings.
Fig. 14. Top view photos of (a) branched structure and (b) bending structure in the fabricated asymmetric Y-branched waveguide, and (c) cross-sectional photos of the same waveguide.
The NFP image and the insertion loss of the fabricated waveguide are measured. The same measurement setup as Fig. 5 is used for NFP. Meanwhile, the setup for the insertion loss measurement is shown in Fig. 15, where the LP01 mode in the cores on the two-port side is launched by butt-coupling an SMF (P84644-06, MFD = 5.5 μm at 1310 nm). From the measured NFP images in Fig. 16, we confirm that the single-mode condition is satisfied in cores (A) and (B) on the two-port side, whereas two-mode patterns are clearly observed in core (C) on the one-port side. Furthermore, an intensity profile featuring the LP01 mode is observed when the light is coupled at the larger core (A), whereas a profile of the LP11 mode is observed when the light is coupled to the smaller core (B). Therefore, we experimentally confirm that the LP01 mode in core (B) is converted to the LP11 mode in core (C), whereas the LP01 mode in core (A) is maintained in core (C). On the other hand, intensity profiles featuring the LP01 mode is observed when the light is coupled to core (C), which means the cores on the two-port side of the Y-branched waveguide support only the LP01 mode. In other words, the fabricated asymmetric Y-branched waveguide exhibits the functionality of an MDM MUX device.
Fig. 16. (a) Measured NFPs from the fabricated asymmetric Y-branched waveguide, and (b) calculated NFPs using BPM.
The insertion losses at a wavelength of 1310 nm are 3.9 dB and 4.1 dB in the propagation directions of (A)→(C) and (B)→(C), respectively. Applying the needle-scan shown in Fig. 10, the insertion losses are calculated by BPM simulation. Here, the diameters of cores (A), (B), and (C) in Fig. 10 are set to 5 μm, 4 μm, and 6 μm, respectively. The LP01 mode with an MFD of 7.2 μm is coupled to cores (A) and (B), whereas the LP01 mode or LP11 mode in core (C) is launched to simulate propagation in the opposite direction. The other calculation conditions are the same as those in Section 2.2. The calculated NFP images are shown in Fig. 16(b). Output fields featuring the LP01 mode are observed at core (C) when the light is coupled to core (A) as well as at cores (A) and (B) when coupled to core (C), whereas the field featuring the LP11a mode is observed at core (C) when the light is coupled to core (B). The MFDs estimated from the simulated NFPs are analyzed and listed in Fig. 16(b). These NFPs and even MFDs agree well with those measured experimentally, as shown in Fig. 16(a). Since the height of core (A) is slightly lower than that of core (B), a tilted intensity profile of the LP11a mode could be observed in the propagation direction of (B)→(C) in Fig. 16(a). Thus, we theoretically verify that the designed Y-branched waveguide can function as an MDM MUX device. However, the insertion losses are calculated to be 0.35 dB and 2.31 dB in the propagation directions of (A)→(C) and (B)→(C), respectively. The difference between the calculated and the experimentally measured losses could be attributed to the material inherent loss which is estimated to be 0.2–0.3 dB/cm (0.5–0.75 dB for a 2.5-cm long waveguide). This material inherent loss is not included in the loss calculation. The monomer flow (described in Fig. 7(b)) could also be another cause of the loss difference since the actually fabricated structure could not accurately reproduce the designed one. On the contrary, when the light is coupled to (C), the propagation losses are 0.66 dB and 2.23 dB in the propagation direction of (C) → (A) and (C) → (B), respectively. Therefore, we redesign the Y-branched waveguides to be used as MDM MUX devices in the next section.
4. Redesign for low-loss Y-branched waveguide
In this section, we theoretically investigate a lower loss design for asymmetric Y-branched structures by introducing a cosine-curve as an alternative to the folded-line structure.
The insertion loss is calculated using the same simulation conditions as those in Section 2. Here, the core merge region is approximated by a cosine curve structure to gradually bend the core compared to the previous folded-line structure. The curve is defined as follows: the origin of the x- and z-axes (0, 0) is located on the connecting point of straight and curved cores of core (A) on the two-port side. Then the trace of the core center with respect to the z-axis for the curved structure to the connecting point with straight core (C) is expressed by Eq. (4).
Core (B) is just straight. Figure 17(a) shows the calculated propagation view by the BPM in the waveguide with L = 3.6 mm exhibiting the minimum total loss compared to L = 1.4 mm. The light is coupled to core (A). From Fig. 17 (a) the defined cosine curve structures with the x-z coordinates are confirmed visually, and we observe where the light leaks from the core. Figure 17(b) shows the calculated insertion loss with respect to L, which includes a 1.0-dB coupling loss at the input on the two-port side. The insertion loss when the light is coupled to core (B) decreases for short L, as indicated by the orange marks, since the light power is less likely to leak at the core merge region. Contrastingly, when the light is coupled to core (A), the loss increases with reducing L due to an increase in the bending loss. Particularly in a range of L < 4 mm, the loss increases exponentially with decreasing L. In Fig. 17(a), low power leakage could be confirmed visually in the waveguide with L = 3.6 mm, compared to that with L = 1.4 mm. Therefore, to reduce the total insertion loss, an optimum L exists, as indicated by the total loss curve in Fig. 17(b). In order to keep the insertion losses in both couplings from core (A) and (B) to no greater than 4.3 dB (1.0-dB excess loss compared to that with sufficiently long L (ex. L = 143 mm)), the optimum L is determined to be 3.6 mm, which is almost one eighth of L (=30 mm) in the folded-line model. This results in a more compact MUX device.
Fig. 17. (a) Propagation views of asymmetric Y-branched waveguide with a cosine-curve bend structure, and (b) insertion loss comparison of asymmetric Y-branched waveguides with respect to the core merge length.
5. Conclusion
In this paper, single-mode and single-/few-mode Y-branched circular core waveguides are designed and fabricated using the Mosquito method in order to produce MUX devices for MDM.
In the simulation, by introducing asymmetric Y-branched structures, a branch angle as low as 0.1° is required for a low-loss structure. However, such a low branch angle could result in a large device size. Hence, in this paper, we employ a multi-step bending structure, from which the insertion loss remains low as 3.3 dB with a total device length of 5 cm.
Then, we successfully fabricated single-mode Y-branched waveguides using the Mosquito method. We employ the multi-step bending structure in the needle-scan path and succeeded in fabricating a low-loss single-mode Y-branched waveguide with a short waveguide length. Applying these fabrication conditions, finally a single-mode/few-mode Y-branched waveguide is fabricated, in which the cores on the two-port side satisfy the single-mode condition, while that on one-port arm supports two modes. We both experimentally and theoretically confirmed that the fabricated single-mode/few-mode Y-branched waveguide can function as a low-loss MDM MUX.
Finally, we redesigned the waveguides by introducing a cosine-curve bending structure to realize more compact and lower loss MDM MUX devices. Then, we confirm that the optimum core merge length as small as 3.6 mm, almost one eighth of folded-lines model, is possible with the newly designed asymmetric Y-branched waveguides.
Funding
Japan Science and Technology Agency (JPMJSP2123); Japan Society for the Promotion of Science (JP18H05238).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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