We fabricate multimode polymer optical waveguides with circular graded-index (GI) cores which are aligned in parallel at desired positions using the Mosquito method. In the Mosquito method, three-dimensional wiring patterns can be formed with a simple process. However, the core position is likely to deviate from the designed position because of multiple fabrication factors. Hence, in this paper, the dominant parameters to influence on the core height in the cladding are investigated both theoretically and experimentally. In particular, a linear relationship between the core height and the needle-tip height is confirmed with theoretical fluid analysis. Using this relationship, we succeeded in fabricating a waveguide in which the maximum variation of the core height from the designed value is controlled to be less than 10 µm.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The processing speed in high-performance computers (HPCs) has been increasing in order to meet the demand for a large-scale analysis in various fields . If the conventional electric wiring remains, there are many technical issues for sustaining the growth of HPC performance, such as the data rate, link distance, and power consumption. Hence, optical interconnect technologies have received much attention to address these issues. In particular, in rack-to-rack interconnections, optical data links using multimode optical fibers (MMFs) with a 50-µm diameter graded-index (GI) core have already been deployed , in which the link distance is 100 m or less. In MMF links, optical-electrical signal conversions are carried out at the edge of the board, and on-board wiring is still dominated by conventional copper electrical circuits. However, to further advance HPC systems, even such a short-reach on-board data links should be replaced by optical links. Because of the high connectivity with the MMF links, multimode polymer optical waveguides are expected to be applied to on-board wiring [2, 3].
In on-board circuits, much higher density wiring should be required in addition to shorter wiring length. Multilayered structures have been proposed as a high-density wiring component . When multilayered waveguides are fabricated using a conventional fabrication process, photolithography [4–6], the fabrication steps such as exposure and development are required to be repeated several times.
Meanwhile, we have proposed a simple fabrication method for polymer optical waveguides named the Mosquito method. By means of the Mosquito method, not only two-dimensional but also three-dimensional waveguide patterns can be formed without photomasks and multiple steps . We have demonstrated that polymer optical waveguides with GI circular cores  are successfully fabricated using the Mosquito method. Here, the control of the core position in both horizontal and vertical directions has been an important issue, particularly for three-dimensional optical wiring. It was already confirmed that the core position in parallel direction (horizontal intercore pitch) was improved . However, the core position in the vertical direction is likely to deviate from the designed, affecting the core height, namely, the distance from the substrate surface to a core. Therefore, in this paper, we theoretically investigate several factors to determine the core height using a fluid mechanics simulation, and then the simulated optimum fabrication condition is applied to the core height control in the experimentally fabricated waveguides.
2. The Mosquito method
2.1. Fabrication procedure of the Mosquito method
The procedure of the Mosquito method consists of just three steps as shown in Fig. 1. At first, a liquid state cladding monomer is coated on a glass substrate. Next, another liquid state core monomer is dispensed from the tip of a syringe needle. The wiring patterns are formed by scanning the needle with dispensing the core monomer. Here, the tip of the needle remains inserted in the cladding monomer during the needle scan. The syringe is connected to a microdispenser system by which viscous monomers are able to be dispensed by applying appropriate pressure in the syringe. Finally, both the core and cladding monomers are cured under UV exposure.
In this paper, ML-808GX and SHOT MASTER 300DS-S from Musashi Engineering, Inc. are used as the microdispenser and the desktop robot, respectively. We select UV curable resins for fabricating the waveguides: an organic-inorganic hybrid resin, NP-210 (9,000 cP) from Nissan Chemical Ind., Ltd. is applied to the cladding, while four types of monomers with various viscosities are used for the core (A) X-CA02 (acrylate resin, 650 cP) from Kyoritsu Chemical & Co., Ltd. (B) LU30P (vinyl acrylate resin, 2,530 cP) (C) NP-832MF (organic-inorganic hybrid resin, 6,620 cP) from Nissan Chemical Ind., Ltd. (D) X-CA01 (acrylate resin, 11,000 cP) from Kyoritsu Chemical & Co., Ltd. (E) NP-003 (organic-inorganic hybrid resin, 51,300 cPs) from Nissan Chemical Ind., Ltd.
2.2. Factors to influence on the core height and related parameters
In the Mosquito method, as explained in the previous section, the wiring patterns are formed while both core and cladding monomers are uncured in a liquid state. Therefore, the core position is likely to deviate from the designed position. The possible fabrication parameters to influence on the core height from the surface of the substrate are listed in Table 1. Here, the instances when the core position can shift are divided into the following three steps: dispensing the core monomer, dispensing neighboring cores, and the curing process. It was already confirmed in  that the core height tended to be smaller than the designed height after dispensing the core monomer. After dispensing the first core, multiple neighboring cores are also dispensed, so an interim time is applied until completing the UV curing for all the cores. During the interim time, the cores dispensed prior might ascend or descend depending on the monomer density difference between the core and cladding. Moreover, when multichannel wiring patterns are formed, the core positions could be influenced by the cladding monomer flow caused by the needle scan to form the neighboring channels. During the UV curing process, the core height could vary due to the volume shrinkage after the conversion from monomer to polymer, particularly in the vertical direction (from top to bottom).
3. Theoretical analysis using fluid mechanics simulation
In order to theoretically investigate the core height dependence on various fabrication parameters shown in Table 1, we perform a flow simulation using COMSOL Multiphysics. In this simulation, the real complex core monomer flow is simplified to a steady incompressible laminar viscous flow. We focus on the height difference between the dispensed core and the needle-tip right after dispensing the core monomer, where the amount of monomer wetting and the needle scan velocity are taken into account. Here, the definitions of the core height, the needle-tip height, and the height difference between the core height and the needle-tip height are schematically shown in Fig. 2: the core height is the distance from the bottom of the cladding (top of the substrate) to the center of the core, while the needle-tip height is the distance from the bottom of the cladding to the needle tip.
3.1. Core height dependence on monomer wetting on the needle outer wall
We focus on the effect of the monomer wetting on the needle outer wall, which is caused by surface tension. First, we investigate monomer wetting during the dispensing procedure. A side-view photo when the needle scans for dispensing the core is shown in Figs. 3(a) and 3(b). Here, two important parameters, the length of the base and the vertical height, are defined as shown in the enlarged image in Fig. 3(b). Then, these two parameters are experimentally measured using the side-view photo under a needle scan velocity of 15 mm/s, and the dependence of these parameters on the needle-tip height is shown in Fig. 4. It is found from Fig. 4 that the length of the base increases with decreasing the needle-tip height. This is because the needle length inserted in the cladding monomer is longer such that amount of displaced fluid increases.
The side-views of the simulated monomer flow to investigate the influence of the monomer wetting are shown in Fig. 5. Figure 5(a) is the result when the effect of the monomer wetting is neglected under a 500-µm thick waveguide for comparison. Here, the thickness of the waveguide is defined as the length between the top and bottom surfaces of the cladding monomer. Meanwhile, in Fig. 5(b), we suppose a curve slope (approximated by an exponential curve) for the boundary between the monomer wetted on the needle outer surface and the air, and a 1000-µm thick waveguide with a different effect of monomer wetting (corresponding to a monomer wetting with a 500-µm vertical height) in Fig. 5(c). The size of the monomer wetting in Fig. 5(b) is set to be the same as the one observed in Fig. 3. In Fig. 5, the core monomer flow is indicated by the white lines, while the pressure distribution in the cladding monomer is shown by the color variation: the higher pressure is indicated by red while lower by blue.
It is found from Fig. 5 that two factors mainly determine the height of the formed core : One is how low the pressure is at the area behind the needle (left-hand side of the needle), as shown by blue color in Figs. 5(a)-5(c). Because of the lower pressure, the core monomer ascends just after dispensed in all the cases in Fig. 5. The other one is how wide the low-pressure area which is formed at the area behind the needle (left-hand side of the needle), by which the core monomer once ascended does not descend but maintains its height. When the monomer wetting is taken into consideration, as shown in Figs. 5(b) and 5(c), the lower pressure areas are wider than that in Fig. 5(a) without monomer wetting. Actually, the calculated core heights under each condition in Figs. 5(a)-5(c) when the needle-tip height is 300 µm are 251.6 µm, 262.5 µm, and 274.9 µm, respectively. We already confirmed in  that the lower pressure area behind the needle is wider with increasing monomer wetting size. The simulated core height under the conditions in Fig. 5 shows the same tendency as the experimentally observed result in Fig. 6. Although the cores tend to be formed at higher positions with the existence of the monomer wetting, the core heights calculated and actually formed were lower than the needle-tip height due to the relaxation of the pressure distribution at the far end from the needle, as shown in Figs. 5(b), 5(c) and 6, which was already confirmed in [10, 11]. The difference between the conditions (b) and (c) is the length of the base (the size) of the wetted monomer on the left-hand side of the needle. From Figs. 3 and 6, since we find the boundary shape could be close to the curved line shown in Fig. 5(b), the boundary shape is set to be the curved line in the simulation hereafter.
3.2. Core height dependence on the scan velocity
In the above section, we find that the monomer wetting on the needle wall affects the core height. In this section, another fabrication parameter, the needle-scan velocity is considered. The transverse cross-sectional view of the simulated monomer flow under an 80-mm/s scan velocity is shown in Fig. 7. The size of the monomer wetting under an 80-mm/s scan velocity is also experimentally measured and taken into consideration. It is confirmed from the observation that the size of the monomer wetting is larger with increasing the scan velocity. Figures 5(a)-5(c) in the above section show the simulated monomer flow under 15 mm/s. The height difference between the core and the needle-tip is calculated under different needle-tip heights, and the results are shown in Fig. 8. Again, the core height and the height difference between the core and the needle-tip are defined as shown in Fig. 2. Figure 8 shows that the core could be formed at a higher position under an 80-mm/s scan velocity. Hence, it is found that the height difference is smaller under high scan velocity (the height of the formed core is larger), as shown in Fig. 8. This could be because the monomers ascend abruptly due to wider area of low pressure region behind the needle, since the scan velocity is higher.
4. Experimental analysis
We focused on the dependence of the height difference between the dispensed core monomer and the needle-tip on the monomer wetting and on the needle scan velocity in the above section. It was confirmed from the simulation results that the monomer wetting influenced the core height, and the calculated core height increased with increasing the needle scan velocity. However, in these simulations, the real core and cladding monomer flows are simplified to a single-phase flow and therefore the viscosity of the core monomer is not part of the simulation. Therefore, in this section, the core height dependence on the core monomer viscosity is experimentally investigated. In addition, the relationship between the core height and the scan velocity measured in the experimentally fabricated waveguides is compared to the simulated results. In order to form the cores with the same size, the dispensing pressure is adjusted depending on the core monomer viscosity and the scan velocity.
To fabricate the waveguides, we use the materials introduced in section 2.1. Scan velocities of 15 mm/s and 80 mm/s are selected in order to compare with the simulation result. The core alignment in the waveguide is designed to have a cascaded core-height variation. In order to realize this alignment, the needle-tip height is set to 50 µm to form the first core and then the following 9 cores are located on heights with a 50-µm step to 450 µm, in addition to a 250-µm horizontal intercore pitch.
The relationship between the formed core height (y) and the needle-tip height (x) in the case of monomer B at a 15-mm/s scan velocity is shown in Fig. 9. A linear relationship is confirmed, and the approximate relationship between the different monomers and conditions is summarized in Table 2. The relationship under the conditions of monomer A at a 15-mm/s scan velocity and monomer E at an 80-mm/s scan velocity are not available, since the appropriate pressure does not exist to maintain the same core size due to too low or too high viscosity of the core monomer. It is found that the slope values at a 15-mm/s scan velocity are smaller than those under an 80 mm/s for all the monomers. The smaller slope value indicates that the core is formed on a lower position under the same needle-tip height condition, and thus, the height difference between the core and the needle-tip is smaller with increasing the scan velocity. It is confirmed theoretically and experimentally that the height of the formed core is higher with increasing the scan velocity. Also, the slopes of the monomer C under the two scan velocities (0.926 µm/µm under 15 mm/s, and 0.928 µm/µm under 80 mm/s) are almost the same values as the simulated values (0.953 µm/µm and 0.974 µm/µm, respectively). This is because the monomer flows are nearly identical to the simulated ones since the viscosity of the core monomer C is almost the same as the viscosity for the simulation condition. Slightly smaller slope values compared to the simulated one could be caused by the height decrease due to the volume shrinkage during the curing of the monomer included in the experimental result.
5. Core position arrangement
5.1 Core height correction
Since we obtained the relationship between the core height and the needle-tip height, in this section, we try to accurately control the core height by applying the obtained relationship. The needle-tip height setting is recalculated from the linear relationship obtained from the simulation result. It was already found from our previous research that the core position deviation from the designed value should be within ± 10 µm because the coupling efficiency between a 50GI-MMF and the waveguide decreases sharply when the core position shift exceeds 10 µm .
In order to demonstrate the ability to control the core height, the waveguide design is a multilayered structure (three layers): the core heights of the bottom, middle, and top layers are 150 µm, 250 µm, and 350 µm, respectively. A group of four cores composes each layer with a 250-µm horizontal intercore pitch, hence the 12 channels in total are formed. For the core monomer, monomer C (NP-832MF) is employed since the viscosity of the core is close to the simulation condition.
The cross-section of the fabricated waveguide is shown in Fig. 10(a) and the measured core height is shown in Table 3. For comparison, a cross-section of a waveguide fabricated without the needle-tip height correction (used for obtaining the relationship in Table 2) is shown in Fig. 10(b). Here, the heights of three cores in the waveguide dispensed under 150, 250, and 350-µm needle-tip heights are summarized in Table 3, compared to the average core heights for the waveguide shown in Fig. 10(a). The average core heights in Fig. 10(a) are controlled to 154.2 ± 1.1 µm, 258.0 ± 2.2 µm, and 356.4 ± 0.6 µm, for the bottom, middle and top layers, respectively. When the needle-tip height correction is not made, the core height deviates by 40 µm or higher. However, with the needle-tip height correction, the average core height deviations are reduced to 4.2 µm, 8.0 µm, and 6.4 µm, for the bottom, middle, and top layers, respectively. Thus, all the cores are formed in a designed height range (less than 10 µm deviation). It is confirmed that the core height correction using the simulation analysis works well to align the multilayered cores accurately.
5.2 Optical signal transmission
In order to evaluate the optical characteristics, the insertion loss of the fabricated waveguide shown in Fig. 10(a) is measured using the measurement setup shown in Fig. 11(a). The measured loss is shown in Fig. 12. The losses of Ch. 1 and Ch. 2 are unexpectedly high because of the accidental damage on those cores. The average loss of the other channels is as low as 1.2 dB for 4.9-cm long waveguide. It is confirmed that the insertion loss is low enough and independent of the formed height.
In order to confirm the accuracy of the core height from the point of optical characteristic, the near field patterns (NFPs) of the waveguide are measured under launching the four parallel cores on one layer simultaneously using a 12-channel, 50-µm core GI multimode fiber ribbon. In this measurement, a 12-channel 850-nm VCSEL based optical transceiver provided by Furukawa Electric Co., Ltd. is used, which is connected to the fiber ribbon, as shown in Fig. 11(b). At first, when the cores on the bottom layer are launched via the fiber ribbon, the NFP image is captured as shown in Fig. 13(a). Next, when a 100-µm upward shift is added to the fiber ribbon in the y-direction, the NFP image is also captured as shown in Fig. 13(b). Another 100-µm shift is added, and the NFP image coupled to the cores on the top layer is captured as shown in Fig. 13(c). In Figs. 13(a) and 13(b), an enlarged image of the cores is also indicated to confirm the intensity profile in each core. Only when the cores of each layer are coupled with the fiber ribbon, their optical fields can be observed. Here, since all twelve cores are not taken in one NFP photo, because of the size limitation of the CCD, the outermost two channels on the bottom and top layers (Ch. 1, 2, 11, and 12) are not involved in Figs. 13(a) and 13(c), respectively. However, we confirm the output light from them. Hence, it is verified that the cores on each layer are accurately aligned to the designed position in both horizontal and vertical directions.
The parameters to influence the height of the formed core in polymer optical waveguides fabricated using the Mosquito method were theoretically investigated using a fluid mechanics simulation. It was found that the calculated core position was influenced by the monomer wetting on the needle outer wall and by the needle-scan velocity. It was also confirmed from the experimentally fabricated waveguides that the height of the formed core tended to be higher when the needle-scan velocity was faster. The height of the formed core varied depending on the viscosity of the core monomer. We applied the obtained relationship between the core height and the needle-tip height from the simulation result to align the cores in multilayered waveguides. All the cores of each layer were found to be formed on the designed position from the observed cross-section and NFP images. Therefore, in the Mosquito method, core position control can be accomplished with few preliminary experiments or by just applying fluid analysis simulations.
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