We design graded-index (GI) circular-core waveguides to realize low-loss light coupling via 45-degree mirrors using a ray-trace simulator. The waveguide’s structural parameters, which determine the insertion loss of the waveguides with 45-degree mirrors, are the cladding thickness, the core size, the refractive index of materials, and the mirror angle. The optimum waveguide structural parameters are determined, and the GI circular-core waveguide with the appropriate structural parameters which is actually fabricated exhibits much lower total link loss than step-index (SI) core waveguides. The tight optical confinement of the GI-core contributes to the reduction of loss increment due to the mirror structure.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The arithmetic capacity of high performance computers (HPCs) has grown dramatically in recent years. The growth of HPC performance would be supported by optical interconnect technologies, which are expected to realize high-bandwidth data transmission and high-density wiring as well as low-power consumption. Actually, several top-ranked HPCs in TOP500  have already deployed multimode optical fiber (MMF) links in their rack-to-rack and board-to-board interconnects . The next issue is how to realize on-board optical interconnects in which the signal conversions from electronic to optical and vice versa are as close to LSI chips as possible. Thus, optical printed circuit boards (O-PCBs) have been drawing much attention.
The performance improvement of transmitters (light sources), transmission media, and detectors (photodiodes) is significant in order to realize high-bandwidth data transmission for MMF optical links. Vertical cavity surface emitting lasers (VCSELs, multimode) emitting at 850-nm wavelength are used as a light source on the O-PCB since VCSELs are widely deployed in the MMF links. Actually, VCSEL-based on-board optical engines have been developed, and as high as >1-Tb/s (28 Gb/s × 24 ch) data transmission was attained . On the other hand, polymer optical waveguides have been a candidate for on-board optical transmission media. Accordingly, intensive efforts have been made to develop step-index (SI) polymer optical waveguides [4–7] applying conventional lithography methods. However, the waveguides integrated on board should connect with graded-index MMF (GI-MMF) at the board edge. Here, it is a concern that mode field and profile mismatches between the SI square and GI circular cores would cause a high coupling loss.
Hence, we developed a unique fabrication method for polymer optical waveguides, named the Mosquito method . One of the features of the Mosquito method is the capability to fabricate GI circular-core waveguides . The GI circular cores allow the high coupling efficiency with GI-MMF [10,11], because the mode field and profile mismatches with GI-MMF are small enough. Hence, we have focused on the application of GI circular-core waveguides as a promising component for the O-PCB.
Here, since VCSELs and photodiodes are supposed to be mounted on the board surface to emit and couple the light perpendicularly to the board, respectively, it has been a common design of the O-PCBs that the signal light is coupled to and from the polymer waveguides integrated on the board via 45-degree mirrors formed on the waveguide ends . In , we investigated the optical properties of GI square core waveguides with 45-degree mirrors and reported the superiorities of GI waveguides in the perpendicular optical coupling via the mirrors compared to the conventional SI square-core waveguides. However, the coupling properties of GI “circular” core waveguides that are fabricated using the Mosquito method are still unclear, so the GI circular-core waveguides have not been optimally designed in order to realize low-loss light coupling via 45-degree mirror.
In this paper, we focus on the GI circular-core waveguides with a 45-degree mirror, and design the optimum waveguide structure for realizing low-loss light coupling via 45-degree mirrors.
2. Fabrication for a 45-degree mirror on the waveguide fabricated using the Mosquito method without designing the structural parameters
In this paper, we focus on the inter- and intra-board optical links as shown in Fig. 1(a). For the optical link design, the link power budget is important. The link power budget defined as the difference between the output power from the light source and the minimum sensitivity of the photodiode is shown schematically in Fig. 1(b). As illustrated in Fig. 1(b), the total optical link loss must be lower than the link power budget. Figure 1(c) shows the breakdown of the link loss: the link loss can be classified into the propagation loss (of fibers and waveguides) and the coupling loss mainly. The propagation loss of waveguides is determined by the waveguide materials, which is, in general, approximately 0.04 dB/cm at 850-nm wavelength in the case of well-applied optically transparent organic polymers. Hence, in 50-cm waveguide links, the total propagation loss is estimated to be about 4.0 dB as illustrated in Fig. 1(c). On the other hand, the coupling loss occurs at all the connection points regardless of the waveguide length. In many cases, an approximately 2.0-dB coupling loss is allotted to each connection point. In the link composed of two polymer optical waveguides as shown in Fig. 1, since there are four connection points between the waveguides and other optical components, an 8.0-dB coupling loss is added in total. Thus, in relatively short reach links such as on O-PCBs, the coupling loss contributes significantly to the link budget. Therefore, the reduction of the coupling loss is indispensable for the high-bandwidth optical links on O-PCB.
In this section, we investigate the excess loss when mirrors are formed on a waveguide fabricated using the Mosquito method.
2.1 Waveguide fabrication
In this paper, we apply the Mosquito method, which is the fabrication method for polymer optical waveguides with circular cores we had previously developed. The fabrication procedure of the Mosquito method is described in  in detail. The most unique point of the Mosquito method is the ability to easily form a circular core with a GI profile. Here, UV curable silicone-based resins (FX-W712 for core, FX-W715 for cladding supplied by ADEKA Corporation) are applied. The refractive indices of the core and cladding materials are 1.526 and 1.484, respectively. After the waveguide fabrication, we form the mirror on one end by manually polishing the edge using abrasive papers.
A cross-section of the fabricated waveguide and the side view of the formed mirror are shown in Fig. 2. Here, we adopt the several fabrication parameters that we already confirmed to be appropriate for a straight waveguide (without mirror). The fabricated waveguide accordingly has a 134-μm thick cladding (as depicted by the arrow in Fig. 2(a)), and 48-μm diameter core. Meanwhile, the mirror angle measured on the photo in Fig. 2(b) is 46.93° which deviates slightly from the ideal angle of 45° due to the manual polishing process.
2.2 Loss increment due to the mirror fabrication
Figure 3 shows the experimental setup for the insertion loss measurement of the waveguide with a mirror. We use two types of setup shown in Figs. 3(a) and (b), for before and after the mirror fabrication, respectively in order to measure the loss increment due to the mirror fabrication. These setups assume intra- and inter-board optical links: two waveguides are connected with an MMF as shown in Fig. 1(a). The two waveguides are named “the waveguide on the Tx side”, and “the waveguide on the Rx side” as shown in Fig. 3(b). We use a 50-µmø GI-MMF(50GI-MMF) for a launch probe with a VCSEL source at an 850-nm wavelength. The output light from the 50GI-MMF is coupled to a waveguide core on the Tx side via a 45-degree mirror. This launch condition mimics a VCSEL chip with an NA of approximately 0.20. The other end of the waveguide on the Tx side is connected to a 50GI-MMF in order to guide the output light to an optical power meter, and the coupling loss between the waveguide on the Tx side and MMF is also included in the insertion loss. The waveguide on the Rx side is also launched using a 50GI-MMF with the same VCSEL source. The light propagating through the waveguide is reflected at the mirror to be coupled to a 50-µmø SI-MMF to mimic a 50-µmø photodiode (PD).
The insertion losses of the waveguide before and after the mirror formation are shown in Table 1. The insertion loss is increased by forming a mirror, which is independent of whether the mirror is on the Tx or Rx side, and thus the link of the waveguide with a mirror exhibits total loss as high as 6.79 dB. It is a critical problem that the total link loss is doubled due to the mirror formation. Thus, the design for the optimum waveguide structure must realize low-loss light coupling via a 45-degree mirror.
3. Optical link loss estimation using ray-trace simulation
3.1 Simulation model and waveguide structural parameters
To design the optimum waveguide structure, the optical loss in the waveguide-based link is theoretically calculated by means of a ray-trace simulator. The optical link model for the simulation is shown in Fig. 4. This simulation model refers to an intra- and inter-board optical link composed of two waveguides (as they would be integrated on PCBs) connected with an MMF. The light from a light source (mimicking a VCSEL chip: spot size = 10 μm, NA = 0.20) is coupled to the first waveguide (the waveguide on the Tx side) via the mirror. The waveguide is connected to a 50-μmø GI-MMF (mimicking an MT connector). After propagating through the GI-MMF, the light is coupled to another waveguide (the waveguide on the Rx side) with an MT connector, and finally reflected at the mirror at the end on the second waveguide to enter into a 50-μmø photodetector (PD). We focus on four different types of waveguide: a GI circular-core waveguide (index exponent g in a power-law approximation of the index profile is set to 2 or 4 ), a GI square-core waveguide (index exponent g is set to 3 ), an SI circular-core waveguide, and an SI square-core waveguide for comparison. Here, for simplicity, the waveguides are assumed to have no propagation loss (0 dB/cm). As any coatings are not applied on the mirror surface, the mirror reflection is caused just by the difference of refractive indices between the core material and the air.
In this paper, we determine the optimum waveguide structural parameters for low link loss. The parameters we study are the cladding thickness, the core size, the refractive indices of the core and cladding materials (ncore and nclad), and the mirror angle, as shown in Fig. 5. The cladding thickness is defined as the distance between the top of the cladding and the top of the core. The core size means the core diameter in the case of circular-core waveguides, while the core height (width) in the case of square-core. ncore is defined as the highest value of the core index in the case of GI core.
3.2 Optical link loss
As mentioned above, since the waveguides are assumed to have no propagation loss, we can simulate the optical coupling loss at desired points in the waveguide-based links by calculating the optical power difference. At first, some parameters are fixed as follows: the cladding thickness = 25 μm, the core size = 50 μm, ncore / nclad = 1.526 / 1.511, respectively, and the mirror angle = 45°, and then, the coupling losses at four important points, connection 1 to 4 in Fig. 4 are calculated.
The accumulated optical loss at each connection point is shown in Fig. 6. It is noted that the optical loss in the GI circular core waveguide-based link is the lowest among the four waveguides studied in this paper. At connection point 4, a 2.47-dB loss advantage is observed in GI circular core compared to the SI-square core, and even a 0.71-dB advantage is observed compared to the SI-circular core. Therefore, only the core shape difference between square and circle reduces the loss by 1.76 dB. Moreover, by forming a GI-profile in a circular core, further loss reduction of 0.71 dB is attained. On the other hand, there is only 0.06-dB loss difference between GI circular- and GI square-core waveguide links, which are as low as 0.781-dB and 0.838-dB link losses, respectively.
The low loss in the GI waveguide links is attributed to the high coupling efficiency with the MMF and the PD. In Fig. 6, the GI waveguide shows remarkably low coupling loss at connection points 2 and 4, compared to the other SI core counterparts. This high coupling efficiency stems from the optical confinement effect of GI core regardless of core outer shape. We now shift our focus to only a GI-circular core as the GI polymer optical waveguides.
3.3 Optical loss caused at the 45-degree mirror
Here, the optical loss at the mirror is investigated in more detail. We analyze the optical loss caused at the mirror, and categorize the loss into three different factors: cladding loss, mirror loss, and waveguide loss. The cladding loss is caused when the light rays penetrate into the cladding and they are no longer confined in the core. The mirror loss is caused when the light is reflected at the mirror. The light rays which inject to the mirror with an angle that does not satisfy the total reflection condition leak out, which results in the mirror loss. After mirror reflection at the Tx side, some light rays cannot be coupled to the core because the divergence angle of the light is larger than the acceptance angle of the waveguide, which is named the waveguide loss.
Figure 7 shows the calculated optical losses at the mirror. On the Tx side, while the mirror loss is almost the same among all the waveguides, the waveguide loss of the GI circular-core waveguide is slightly higher than the SI counterparts. This is caused by the local NA in the GI cores. At the mirror on the Tx side, the light rays with relatively large divergence angles reach the periphery of the core due to diffraction, so they could not be confined in GI core because of a low local NA at the core periphery. However, this higher waveguide loss is not serious because only a 0.183-dB difference is observed between GI circular- and SI square-core waveguides. On the other hand, on the Rx side, the refractive index profile exhibits a large influence on both the mirror and the cladding losses. In the case of the GI circular-core waveguide, the mirror and the cladding losses are quite low: an improvement in the loss by 1.46-dB lower loss is realized compared to the SI square-core waveguide.
This superiority of the GI waveguides, particularly on the Rx side, also stems from the tight optical confinement effect of GI core. In the case of the SI waveguides, since the output NFP largely extended to whole core while the NA is uniform at any points in the core, some rays reaching at the mirror on the Rx side do not satisfy the total reflection condition. Furthermore, even if the rays that satisfy the total reflection condition are appropriately reflected at the mirror, the spot size and divergence angle of the output beam at the detector tend to be larger than the detection area of the photodiode, resulting in high coupling loss at the photodetector. On the other hand, because the GI core waveguides maintain a small beam spot size before and after the mirror reflection, the beam spot size when it reaches the photodetector might be small even if the output beam from the mirror on the Rx side has diverged. In addition, because of the local NA as mentioned above, the rays injected to the mirror at the core periphery propagate parallel to the core axis, so those rays are reflected perpendicular to the core axis, and fall directly on the photodetector. Because of these characteristics, the low mirror loss and high coupling efficiency with the photodetector (low cladding loss) are attained.
Thus, it is confirmed that the tight optical confinement effect of GI waveguides realizes the low-loss light coupling via 45-degree mirrors.
4. Low-loss light coupling design
In this section, the waveguide structural parameters of cladding thickness, core size, refractive index, and mirror angle are varied. We investigate the effect of these parameters on the optical loss, and determine the optimum waveguide structure for realizing low-loss light coupling via 45-degree mirrors.
4.1 Cladding thickness
The dependence of the loss on the cladding thickness is calculated as shown in Fig. 8. Here, the other parameters are fixed as follows: the core size = 50 μm, ncore / nclad = 1.526 / 1.511, respectively, and the mirror angle = 45°. The index values of the polymer materials (FX-W712 for core, FX-W713 for cladding supplied by ADEKA Corporation) actually used for waveguide fabrication are applied.
As shown in Fig. 8, the cladding thickness is an important parameter to obtain a low-loss light coupling. The SI square-core waveguide could show a loss higher than 3 dB even if the cladding thickness is extrapolated to 0 μm. This is because the SI square core waveguide shows 1.23-dB coupling loss at connection 2 as well as connections 1 and 4 shown in Fig. 6. On the other hand, it is noted that the optical loss of the GI waveguide depends significantly on the cladding thickness. The optical loss of the GI circular-core waveguide decreases more sharply with decreasing the cladding thickness compared to the SI counterparts. When the cladding thickness is smaller than 150 μm, the GI-circular core waveguide exhibits the lowest optical loss among the three waveguides, and with a 25-μm cladding thickness, the GI waveguide shows a 2.61-dB advantage over the SI square core waveguide.
When the cladding thickness is large, the light from the light source diverges during the propagation through the thick cladding, which leads to the high coupling loss at the mirror on the Tx side. In particular, GI waveguides show relatively high coupling loss because of the local NA of the waveguide: the diverged light cannot be coupled completely to the core. However, with the small cladding thickness, since the beam spot size of the light from the light source still remains small even when it reaches to the mirror on the Tx side, the GI core maintains this small beam spot size during the propagation, resulting in the highly efficient optical coupling with the MMF and the photodetector.
4.2 Core size
The dependence of the loss on the core size is calculated as shown in Fig. 9(a). Here, the other parameters are fixed as follows: the cladding thickness = 25 μm, ncore / nclad = 1.526 / 1.511 (the same values as those in 4.1), respectively, and the mirror angle = 45°.
Figure 9(a) shows that the optical loss (both the Tx and Rx sides) of the GI waveguide link decreases with increasing the core size, and reaches the lowest value of approximately 1 dB when the core size is larger than 45 μm. When the core size is larger than 35 μm, the GI waveguide shows the lowest optical loss among the three waveguides. In the case of 40-μm (relatively small) core size, the GI waveguide exhibits a 0.56-dB advantage compared to the SI square-core waveguide. On the other hand, when the waveguides have a 60-μm (relatively large) core size, the optical loss advantage in the GI waveguide increases to 4.47 dB compared to the SI square core waveguide.
On O-PCBs, photodiodes which have relatively small detector size such as 35 μmø are necessary for a bit rate higher than 25 Gbps. Hence, the calculated results when a 35-μm PD is used at the Rx side is shown in Fig. 9(b) for comparison. Figure 9(b) shows that the superiority of the GI waveguide to the SI counterparts is more remarkable than as shown in Fig. 9(a). The GI waveguides exhibits a low optical loss even when the core size is in a range from 35 to 65 μm, and even at 35-μm core size, as high as 1.32-dB advantage of the GI waveguide is observed over the SI square-core waveguide.
These superiorities of the GI waveguides stem from the tight optical confinement effect of the GI core. In the case of SI waveguides, the core size affects their coupling efficiency with both the transmitter and the receiver more directly than for GI waveguides. For the high coupling efficiency at the Tx side, the core size of both the GI and SI core waveguides should be large enough to receive the diverged input beam at the mirror. However, since the output NFP from SI-core waveguides is uniformly extended to the entire core, the coupling efficiency at the Rx side (with a small sized PD) decreases significantly with increasing core size. Because of the trade-off between the core size and coupling efficiencies to light source and PD, the SI core waveguide shows the obvious optimum core size that minimizes the total link loss, as shown in Fig. 9. On the other hand, in the case of the GI-core waveguide, as the output NFP size could be smaller than the core size particularly under a restricted modal launch (RML) condition, a larger core size affects the coupling efficiency less at the Rx side, even for a PD with a small effective area. Larger core sizes effectively contribute to the high coupling efficiency at the Tx side, resulting in the wide core size range to exhibit a total link loss as low as 1 dB.
4.3 Refractive index
We investigate the dependence of the loss on the refractive indices of the core and cladding materials (ncore and nclad) in this section. Here, the other parameters are fixed as follows: the cladding thickness = 25 μm, the core size = 50 μm, and the mirror angle = 45°. ncore is varied from 1.525 to 1.80, while the waveguide NA is fixed to 0.20, 0.25, and 0.30. Hence, the corresponding nclad is calculated in order to satisfy the specific waveguide NA with each ncore.
As mentioned above, the calculated link loss includes the coupling loss only, which means the optical losses inherent to the waveguide itself and the Fresnel reflection loss are excluded. The effect of the Fresnel reflection loss must be taken into consideration for investigating the dependence of the optical loss on the refractive index. Therefore, we calculate the Fresnel reflection loss using the same method as , and sum up the results to calculate the coupling loss.
The total calculated optical loss (sum of the coupling loss and the Fresnel reflection loss) with respect to ncore is shown in Fig. 10. It is noted that the dependence of the optical loss on ncore is almost independent of the waveguide NA in both the GI circular and SI square core waveguides. Therefore, only ncore is the most important parameter when selecting the refractive index of the waveguide materials.
At relatively low refractive index (ncore < 1.575), the optical loss increases with decreasing ncore. The main cause of this high optical loss is the mirror loss (mentioned in Section 3.3). In the case of low ncore, it is difficult to satisfy the total reflection condition on the mirror surface with some rays having relatively large incident angle, which could leak out at the mirror. In the case of relatively high refractive index (ncore > 1.65), the mirror loss is negligible, but the Fresnel reflection loss at the boundary between the waveguide core and the air (n = 1.0) both at the Tx and Rx sides gradually increases with increasing ncore. This trade-off in ncore brings out the lowest optical loss point ncore to be approximately 1.60 as shown in Fig. 10.
As mentioned above, the mirror loss is more influential when ncore is low. Metal coating on the mirror surface which can reflect all the light is a typical method to reduce the mirror loss and is commonly applied . Therefore, we assume a metal coating on the mirror surface in the simulation model, by which all the light rays are reflected. Figure 11 shows the calculated loss reduction by applying the mirror coating with respect to ncore of the GI circular core waveguide. It is apparent that, in the case of ncore as low as 1.525, approximately 0.4-dB loss reduction is observed. However, loss reduction decreases with increasing ncore, and when ncore is higher than 1.60, further reductions are insignificant. The metal coating on the mirror surface can be expensive, and thus it is more desirable to select a material whose ncore is close to 1.60, which allows the lowest loss in Fig. 10.
4.4 Mirror angle
We investigate the dependence of the loss on the mirror angle in this section. Here, in order to calculate the optical loss of the waveguides on the Tx and Rx sides individually, the simulation model is divided into two waveguides as shown in Fig. 12. The other parameters are fixed as follows: the cladding thickness = 125 μm, the core size = 50 μm, and ncore / nclad = 1.525 / 1.512 and 1.650 / 1.638 (the waveguide NA is fixed to be 0.20).
Figures 13 and 14 show the calculated mirror angle tolerance curves. As shown in Fig. 13, it is found that the mirror tolerance curves are asymmetric when ncore is as low as 1.525, and the optimum mirror angle which allows the lowest optical loss is approximately 44 o at the Tx side compared to approximately 46 o at the Rx side in both SI and GI core waveguides. On the other hand, ncore as high as 1.650 realizes symmetric mirror angle tolerance curves as shown in Fig. 14, and the optimum mirror angles at both the Tx and Rx sides are estimated to be approximately 45°.
The difference of the optimum mirror angle between the Tx and Rx sides shown in Fig. 13 stems from the effect of the mirror loss (mentioned in Section 3.3). In the case of lower ncore, the mirror loss is a large part of the total loss (as illustrated in Fig. 11), which suggests that the optimum mirror angle could shift from 45° in order for as many rays as possible to satisfy the total reflection condition. At the Tx side, the optimum mirror angle shifts to be smaller because a small mirror angle allows a large angle of incidence between the rays from the light source and the mirror surface. In contrast, at the mirror on the Rx side, the light rays inject into the mirror with a larger angle of incidence in order to satisfy the total reflection condition, when the mirror angle is large. Therefore, the mirror angles allowing the minimum coupling loss are different between the Tx and Rx sides. However, such a mirror-angle dependent loss makes it difficult to fix the mirror angle to a common value for both the Tx and Rx sides.
Accordingly, we investigate the optimum mirror angle dependence on ncore as shown in Fig. 15. Here, the waveguide NA is fixed to be 0.20 following to all the investigations mentioned above. Figure 15 shows that with increasing ncore, the optimum mirror angles at the Tx and Rx sides converge to the same angle, which is near 45°. It is remarkable that the convergence rate of the GI circular-core waveguide is higher than that of the SI waveguide. By selecting a core material whose refractive index is higher than 1.625, the optimum mirror angle at the Tx and Rx sides matches at approximately 45. 04°. Meanwhile, in the SI core waveguide, the optimum mirror angle common to both sides is obtained only when the core has an index higher than 1.7. Thus, GI waveguides allow a wider range of material selection to obtain the low optical loss with using the same waveguide (with mirror) at both the Tx and Rx sides.
4.5 Design for efficient light coupling
We demonstrate a benefit of GI circular-core waveguides: low-loss light coupling via a 45-degree mirror if the waveguides are designed to have the optimum structural parameters. Table 2 summarizes the optimum waveguide structural parameters for GI circular-core waveguides.
To reduce the coupling loss, it is best to make the cladding thickness as small as possible, but this could be difficult, and in some cases could be dependent on the fabrication process and the specification of O-PCBs. However, under less than 150-μm cladding thickness, GI circular-core waveguides exhibit lower coupling loss than the SI core waveguides.
Another advantage of GI waveguides is the wider range of the core sizes which allow a low optical loss. Based on the investigation in this paper, the core size range to maintain low optical loss even for smaller photodetector size is from 45 to 60 μm.
In terms of the refractive indices of the waveguide materials, we can focus only on the refractive index of the core material since the optical loss is independent of the waveguide NA. Using the core material with an index close to 1.60, we can simultaneously realize two advantages: one is the low-loss light coupling and the other is unnecessity for metal coating on the mirror.
The dependence of the loss on the mirror angle is correlated with the refractive index of the core materials. In the case when ncore > 1.625, agreement of the optimum mirror angle at both the Tx and Rx sides is attained: the optimum mirror angle is calculated to be 45.04° in the GI circular core waveguide. However, only an angle deviation of approximately 0.5 o from the optimum value is allowed to suppress the loss increment.
5. Fabrication for a 45-degree mirror on the waveguide fabricated using the Mosquito method with the optimized structural parameters
In this section, we experimentally fabricate a polymer optical waveguide using the Mosquito method so that it has the optimum structural parameters which are theoretically confirmed above (Section 4), in order to realize low-loss light coupling via a 45-degree mirror.
5.1 Waveguide fabrication
Here, UV curable organic-inorganic hybrid resins (NP-003 for core, NP-210 for cladding supplied by Nissan Chemical Ltd.) are applied. The refractive indices of the core and cladding materials are 1.600 and 1.580, respectively. A cross-section of the fabricated waveguide and the side view of the formed mirror are shown in Fig. 16. The fabricated waveguide has a 90-μm thick cladding (as depicted by the arrow in Fig. 16(a)), and a 50-μm diameter core. Meanwhile, the mirror angle measured on the photo in Fig. 16(b) is 45.98°. These waveguide structural parameters well agree with the optimum structural parameters shown in Table 2.
5.2 Loss increment due to the mirror fabrication
Table 3 summarizes the insertion losses of the waveguide before and after the mirror formation under the same measurement setup utilized in Section 2.2 (Fig. 3). Since the loss increment due to the mirror formation is reduced dramatically, the insertion losses at both the Tx and Rx sides after the mirror formation are approximately 1 dB, and thus a total link loss of less than 2.00 dB is attained. Figure 17 shows the insertion loss comparison between the waveguide without the optimum structure fabricated in Section 2.2 (named “unoptimized waveguide”) and the waveguide with the optimum structure fabricated in this section (named “optimized waveguide”). The optimized waveguide exhibits 4.79 dB less total link loss than the unoptimized waveguide.
The high optical loss observed in the unoptimized waveguide is attributed not only to its inappropriate structure but also to its refractive index profile in the core. In Section 2.2, since we use a pair of core and cladding materials which have a low compatibility, the unoptimized waveguide is assumed to have SI-circular cores, which leads to the high insertion loss even in the straight waveguide before the mirror formation. Furthermore, as mentioned in Fig. 9 (Section 4.2), in the case of SI circular core waveguides, the optical loss is affected substantially by the change of the core size, so the core diameter deviation causes the loss increase after the mirror formation. In addition, since the refractive index of the core material is relatively low (ncore = 1.526), the mirror loss (mentioned in Section 3.3) is caused at both the Tx and Rx sides, resulting in the high optical loss in total. The relatively low core index also leads to the asymmetrical mirror angle dependence curves where the optimum mirror angle on the Tx and Rx sides are different as described in Fig. 13, so 46.93-degree mirror angle of the unoptimized waveguide causes the excess loss at the Tx side.
On the other hand, the optimized waveguide is fabricated utilizing a pair of the materials with high compatibility to form a GI circular core, hence the core-cladding boundary is blurry in the cross-section shown in Fig. 16(a). The low-loss light coupling via 45-degree mirrors is attained by forming the optimum structure in GI circular-core waveguides.
We theoretically investigated the optical loss at 45-degree mirror on the edge of GI circular-core multimode polymer waveguides assumed to be fabricated using the Mosquito method, and compared to SI core counterparts. We unveiled the guideline of the optimum structural design for GI circular-core waveguides in order to realize the low-loss light coupling via 45-degree mirrors. We experimentally fabricated a GI circular-core waveguide using the Mosquito method with the optimum waveguide structure parameters that were derived from the theoretical simulation, and then, efficient light coupling via 45-degree mirrors was successfully realized compared to an SI circular-core waveguide without the optimum design.
Japan Society for the Promotion of Science (18J21804)
2. A. Benner, “Optical interconnect opportunities in super computers and high end computing,” in Optical Fiber Communication Conference and Exposition 2012, Paper Otu2B4 (2012).
3. H. Nasu, K. Nagashima, T. Uemura, A. Izawa, and Y. Ishikawa, “>1-Tb/s on-board optical engine for high-density optical interconnects,” in Proceedings of Optical Fiber Communication Conference 2017, Paper W1A.4 (2017).
4. M. Hikita, S. Tomaru, K. Enbutsu, N. Ooba, R. Yoshida, M. Usai, T. Yoshida, and S. Imamura, “Polymeric optical waveguide films for short-distance optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 5(5), 1237–1242 (1999). [CrossRef]
5. R. Dangel, C. Berger, R. Beyeler, L. Dellmann, M. Gmür, R. Hamelin, F. Horst, T. Lamprecht, T. Morf, S. Oggioni, M. Spreafico, and B. J. Offrein, “Polymer-waveguide-based board-level optical interconnect technology for Datacom application,” IEEE Trans. Adv. Packag. 31(4), 759–767 (2008). [CrossRef]
6. N. Bamiedakis, J. Beals, R. V. Penty, L. H. White, J. V. Degroot, and T. V. Clapp, “Cost-effective multimode polymer waveguides for high-speed on-board optical interconnects,” IEEE J. Quantum Electron. 45(4), 415–424 (2009). [CrossRef]
7. R. C. A. Pitwon, K. Wang, J. Graham-Jones, I. Papakonstantinou, H. Baghsiahi, B. J. Offrein, R. Dangel, D. Milward, and D. R. Selviah, “FirstLight: Pluggable optical interconnect technologies for polymeric electro-optical printed circuit boards in data centers,” J. Lightwave Technol. 30(21), 3316–3329 (2012). [CrossRef]
8. K. Soma and T. Ishigure, “Fabrication of a graded-Index circular-core polymer parallel optical waveguide using a microdispenser for a high-density optical printed circuit board,” IEEE J. Sel. Top. Quantum Electron. 19(2), 3600310 (2013). [CrossRef]
10. Y. Koike, Y. Takezawa, and Y. Ohtsuka, “New interfacial-gel copolymerization technique for steric GRIN polymer optical waveguides and lens arrays,” Appl. Opt. 27(3), 486–491 (1988).
11. R. Kinoshita, K. Moriya, K. Choki, and T. Ishigure, “Polymer optical waveguides with GI and W-shaped cores for high bandwidth density on-board interconnects,” J. Lightwave Technol. 31(24), 4004–4015 (2013). [CrossRef]
12. M. Immonen, M. Karppinen, and J. K. Kivilahti, “Fabrication and characterization of polymer optical waveguides with integrated micromirrors for three-dimensional board-level optical interconnects,” IEEE Trans. Electron. Packag. Manuf. 28(4), 304–311 (2005). [CrossRef]
15. H. Numata, S. Nakagawa, and Y. Taira, “High-density optical interconnect based on TIR and metal coated precise mirror attached waveguide,” in Proceedings of Conference on Lasers and Elctro-Optics 2009, Paper JWA40 (2009). [CrossRef]