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Abstract
We create a compact low-loss spot-size converter (SSC) which utilizes a tapered core polymer optical waveguide with circular cross-sectional graded-index (GI) core using the Mosquito method we developed. First, we theoretically analyze the mutual diffusion between the core and cladding monomers, which is a feature unique to the Mosquito method when forming GI cores. The monomer diffusion effect depends on the initial core diameter that is dispensed by a microdispenser and the diffusion time before UV curing: in a small core the monomer diffuses more rapidly than in a large core. Using this diffusion dependence on the initially dispensed core diameter, it is theoretically found that a tapered polymer waveguide based SSC can adiabatically convert the mode-field diameter between 4.0 and 8.6 μm at a 1550-nm wavelength waveguide as short as 4 mm. Next, the tapered waveguide based SSC with the designed structure is experimentally fabricated using the Mosquito method, and we confirm an 8-mm long tapered waveguide with an insertion loss of 1.83dB functions as a SSC that converts the MFD from 4.7 μm to 7.5 μm at 1550-nm wavelength.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the last couple of years, the drastic growth of cloud computing services has required higher bandwidth optical networks in datacenters [1]. Single-mode optical fiber (SMF) links operating with silicon (Si) photonics technologies are expected to replace the vertical cavity surface emitting laser (VCSEL) based multimode fiber links in order to attain much higher bandwidth distance product. Si photonics has the following attractive features: high compatibility with complementary metal oxide semiconductor (CMOS) process for their fabrication, ability for dense optical wiring due to the high optical confinement, and potential for higher bandwidth which can allow for low power consumption [2]. The Si photonics chips are typically integrated on-board, and SMFs connect these Si photonics chips. Hence, the signal light from the Si cores needs to be coupled to the SMFs and vice versa. Here, the mode-field diameter (MFD) of the propagating modes in the Si cores and conventional SMF cores differ significantly due to their core size and index contrast, which can cause a high coupling loss.
To address this high coupling loss issue, coupling devices such as grating couplers (GCs) [3] and spot-size converters (SSCs) [4] have been proposed. The characteristics of GCs strongly depend on the wavelength and the size of the connector with the GCs is relatively large due to the out-of-plane connection scheme. Contrastingly, the characteristics of SSCs are wavelength independent, which allows the device to operate within wavelength division multiplexing (WDM) links, and compact couplers between Si waveguides and SMFs [5,6] are expected to be created. Thus, in this paper, we focus on the SSCs composed of a polymer optical waveguide for an efficient coupling between Si photonics chips and SMFs.
As a fabrication method for the polymer waveguides to be applied to SSCs, the Mosquito method we have developed is applied [7,8]. The Mosquito method has unique features such as the ability to form circular cores enabling high coupling efficiency with the same circular core SMFs, to form axially tapering core maintaining its circular cross-sectional shape, and to form graded index (GI) profile by the interdiffusion between the core and the cladding monomers [8–10]. Figure 1(a) is the schematic design of the SSC composed of a polymer waveguide fabricated using the Mosquito method. Here, the axially tapered polymer core embeds the Si waveguide to realize an adiabatic coupling as shown in Fig. 1(b) while the tapered polymer waveguide core increases the MFD during the light propagation in the tapered core to the same size of the MFD in the SMF.
Fig. 1. (a) Design of the SSC to be fabricated using the Mosquito method and (b) Schematic illustration of adiabatic coupling between Si core and tapered SSC.
We previously succeeded in fabricating a 15-mm long tapered waveguide based SSC using the Mosquito method which showed an insertion loss of 2.77dB at 1550 nm [11]. However, for much higher link wiring density, SSCs need to be more compact to be integrated in a small connector. Thus, in this paper, we design the smallest possible SSC by theoretically simulating the MFD conversion in both radially and “axially” varying index profile (graded refractive index) formed during the procedure of the Mosquito method. Here, for the optimum design, we theoretically calculate not only the index profiles due to the monomer diffusion between the core and cladding, but also the outer shape of the tapered core. Finally, the optimally designed tapered waveguide is experimentally fabricated to create the smallest possible SSC.
2. Application of the Mosquito method to form axially tapered cores
2.1 Fabrication procedure
We have proposed the Mosquito method as a fabrication method for polymer waveguides, which uses a microdispenser and a syringe-scan desktop robot system. In the Mosquito method, a liquid core monomer in a syringe is dispensed from the needle by inserting its tip in another liquid cladding monomer coated on a substrate. Here, the needle horizontally scans while dispensing the core monomer to form the core-cladding structure. The tapered core waveguide fabrication procedure using the Mosquito method is illustrated in Fig. 2. The axially tapered cores are formed by accelerating the needle scan, as shown in Fig. 2(b). When we use miscible core and cladding monomers, the two monomers diffuse into each other during the interim time, which is defined as the time just after completing one core monomer dispense until the monomers are cured by UV-exposure (between Figs. 2(b) and 2(c)). The concentration distribution formed by the monomer diffusion is fixed after the monomers are cured in Fig. 2(c), leading to an index profile. Thus, the Mosquito method has a unique feature that the axially tapered core is formed while maintaining the shape of the core cross-section, namely an almost perfect circle. In addition, the Mosquito method can fabricate a 10-cm long tapered waveguide with four cores aligned in parallel in just less than 5 minutes.
2.2 Theoretical calculation for the tapered core
In order to find the optimum fabrication conditions for low loss tapered waveguide, we theoretically derive the outer shape of the tapered core formed in the Mosquito method. Equation (1) describes the monomer flow rate Q, which is derived by the Navier-Stokes equation [8].
Here, d represents the needle inner diameter, p represents the dispensing pressure, η represents the core monomer viscosity, and L represents the needle length. Theses parameters in the Mosquito method are depicted schematically in Fig. 3(a). In this paper, we focus on the initially dispensed core diameter a0 calculated by Eq. (2).Fig. 3. Parameters in the Mosquito method (a) when fabricating a straight core and (b) when fabricating a tapered core.
When fabricating tapered waveguides, the needle-scan velocity is accelerated from the initial velocity v0 with an acceleration rate of b, as shown in Fig. 3(b). Therefore, if the position where the acceleration starts is set to z = 0, the velocity at the position z (> 0) is described by Eq. (3).
From Eqs. (2) to (3), the initially dispensed (tapered) core diameter at the axial position z is described as Eq. (4).
Table 1. Fabrication conditions for a tapered waveguide.
3. Simulation of monomer diffusion
In the Mosquito method, the interdiffusion between the core and the cladding monomers during the interim time (defined in 2.1) allows for the formation of GI cores. In this paper, we demonstrate that this monomer interdiffusion is an important process for controlling the MFD in the tapered core. In the next section, the relationship between the interim time and the MFD is theoretically estimated applying diffusion analysis.
3.1 Estimation of the refractive index profile
In order to quantitatively evaluate the diffusion rate of the core monomer, first, a polymer plate sample is fabricated as follows: the core monomer, NP-005 (n1550 = 1.575, supplied by Nissan Chemical Corporation) and the cladding monomer, NP-213 (n1550 = 1.546, supplied by Nissan Chemical Corporation) are dispensed abutting vertically in the plate. Then both monomers are kept in contact for a certain interim time to allow the two monomers to diffuse, and the plate sample is cured under UV exposure. Next, the refractive index profile formed in the vicinity of the interdiffusion region is measured using a two-beam interference microscope (TDAS-12, Mizojiri Optical co., Ltd.). The concentration gradient of the core polymer (relative concentration C) is calculated from the measured index profile. Subsequently, by introducing the Fick's diffusion law expressed by Eq. (5), the relationship between the relative concentration C and the diffusion constant D of the core monomer is derived [12].
In addition, we develop a simulation program that is applied for predicting the monomer concentration distributions formed by the monomer diffusion after an arbitrary interim time. In the simulation, the relationship between the relative concentrations of the two monomers are derived by applying the concentration-dependent diffusion constant D(C) obtained by the above preliminary analyses. For the core and cladding monomers, NP-005 and OrmoClad (supplied by micro resist technology GmbH) are assumed to be used, because higher refractive index contrast is required for realizing an SSC. Since OrmoClad is a monomer of organic-inorganic hybrid resins similar to SUNCONNECT (NP-005 and NP-213) and these two monomers are miscible, the interdiffusion is observed, where we preliminary confirmed that the same diffusion constant D(C) was applicable to the new monomer combination by adjusting the interim time. In order to predict the index profile formed in the core dispensed in the Mosquito method, diffusion between the core with a circular cross-section surrounded by the cladding is programmed [12].At the moment when the core monomer is dispensed, the interim time and the core diameter are defined as 0 (a. u.) and the initially dispensed core diameter, a0, respectively. At this moment, the core should have an SI profile (i.e, no monomer diffusion has taken place). In this section and the next, the interim time is expressed with arbitrary units rather than seconds, and therefore we will leave the numbers unitless. This is because we apply the D(C) of NP-005 in NP-213 to the new monomer combination of NP-005 and OrmoClad, as mentioned above. We already confirmed that the interim time adjustment is good enough to simulate the diffusion between the new monomer system.
In the simulation, a0 is varied from 1.0 μm to 2.0 μm with a 0.1-μm step and also over the values 2.2 μm, 2.5 μm, 2.7 μm, 2.9 μm, and 3.0 μm. Then, the calculated relative concentration profile is converted to the refractive index profile: the relative concentration of 0 corresponds to the refractive index of OrmoClad (1.521), while the relative concentration of 1 is of NP-005 (1.575) by assuming the additive property.
Figures 5(a) and 5(b) show the calculated refractive index profiles when the initially dispensed core diameter a0 is 1.2 and 2.9 μm, respectively, after an interim time of 5.4. In this simulation, for simplicity, the monomer diffusion is assumed to progress only in the radial direction in the core cross-section, so the diffusion in the axial direction is neglected. We find from Fig. 5 that the refractive index difference Δn between the core center and the cladding decreases while the core diameter after diffusion a which is defined as the boundary of the area in which the core monomer exists increases due to the monomer diffusion. Here, when a0 is 1.2 μm, Δn decrease is faster than when a0 is 2.9 μm. Figure 6 shows the Δn variation with respect to the interim time. With decreasing the initially dispensed core diameter a0, Δn decreases more rapidly. Two examples are indicated in Fig. 6: when a0 is three times larger (1.0 and 3.0 μm), the interim time required to reduce Δn to 0.01 is almost 6 times longer (1.8 and 12.6).
Fig. 5. Calculated refractive index profiles after interim time of 5.4 (a. u.) with dispensed core diameter of (a) 1.2 μm and (b) 1.5 μm.
Figure 7 shows the variation of the core diameter after diffusion, a, with respect to the interim time. In Figs. 5 and 6, although we find the rapid decrease of Δn in the core with small a0, the rate at which a increases appears to be nearly independent of a0, as shown in Fig. 7. Hence, the magnitude relationship of a0 is preserved in a that experiences the same interim time.
By combining the refractive index profiles of various a0 values with interim time t and the relationship between a0 and z shown in Fig. 4, the 3-dimensional refractive index profile in the tapered waveguide fabricated by the Mosquito method after a certain interim time is depicted in Fig. 8. When t = 0 in Fig. 8(a), because the monomer diffusion does not progress, the tapered waveguide has an SI core at any positions z and has a constant Δn. Meanwhile, when the monomer diffusion progresses after a certain interim time as shown in Figs. 8(b) and 8(c), not only does the core diameter increase, but also Δn decreases along with the z position because the monomer diffusion rate depends on a0 as mentioned. Thus, it is revealed that the Mosquito method is able to fabricate tapered waveguides in which both the core diameter and Δn vary in the axial direction by accelerating the needle-scan velocity.
Fig. 8. 3-dimensional refractive index profiles of tapered waveguide by the Mosquito method with interim time of (a) 0 (a. u), (b) 2.7 (a. u.), and (c) 8.1 (a. u.).
3.2 MFD variation after monomer diffusion
As mentioned above, the core monomer dispensed into the cladding monomer forms a GI profile during which Δn decreases while the core diameter increases. Based on the calculated refractive index profiles after a certain interim time as shown in Fig. 8, we investigate how the MFDs of the cores in the fabricated waveguides change as the interim time increases. For the MFD calculation, we use a mode solver FIMMWAVE (Photon Design).
Figure 9 shows the calculated results of the MFDs of the fundamental (LP01) mode by incorporating the calculated refractive index profiles on FIMMWAVE as an input parameter. Here, almost all the cores (except for the cores with a0 of 2.9 μm and 3.0 μm, just after being dispensed) satisfies the single-mode condition at 1550 nm, while the cores with a0 larger than 3.0 μm support multiple propagating modes after an interim time within the range shown in Fig. 9. As shown in Fig. 6, the cores with small a0 show a rapid decrease in Δn, and therefore the MFD also increases more rapidly when a0 is small, because the lower Δn increases the evanescent field of the mode due to the low light confinement. On the other hand, when a0 is large, Δn decreases slowly, resulting in the slow MFD variation because the light is tightly confined in the core. Therefore, the MFD variation with respect to the interim time largely depends on the initially dispensed core diameter a0. As a0 is deliberately varied along the optical axis to fabricate a tapered waveguide, the optimum tapered shape should be designed for a compact (short) waveguide type SSC.
4. Structural design of the waveguide-based SSC
In this section, we theoretically deign the optimum structure of the tapered waveguide based SSC, where we derive the minimum tapered waveguide length that allows for efficient conversion of the MFDs. Currently some Si photonics chips have a tapered core structures (e.g., SSCs) on their ends to extend the MFD to a few micrometers. So, we fix the MFD of the tapered waveguide on the Si photonics chip side as 4.0 μm at 1550 nm, which should be converted on the other end to an MFD (8.5 μm experimentally measured at 1550 nm) of a typical SMF (PA-A2, Sumitomo Electric Industry), compliant to ITU-T G.657.A2. While designing the structure of the SSC, the insertion loss of the waveguide, including the coupling and propagation losses, is estimated.
4.1 Waveguide length
First, we focus on the optimum value of a0 on both ends of the taper, where the large and small core sides are defined as aL0 and aS0, respectively, as shown in Fig. 10. Here, since the needle scan velocity actually forming the tapered core is relatively quite fast, as shown in Table 1, the interim time is regarded to be identical on both ends of a 4-cm long core. In Fig. 9, two dashed lines indicate the MFDs of Si photonics chip and SMF, which should coincide with the MFDs of the SSC. Hence, there are several candidates for the combination of aL0 and aS0 found from Fig. 9 as the intersecting points between the curves and the dashed lines. Here, when an interim time longer than 3.6 is applied, aL0 is fixed to 3.0 μm, since the cores with a0 larger than 3.0 μm do not satisfy the single-mode condition after monomer diffusion. Next, using Eq. (4) and Table 1, the z position at which a0 coincides with aS0 is calculated. As the needle scan starts accelerating at z = 0, the tapered waveguide length for the SSC is determined as the z value difference at which a0 = aL0 and a0 = aS0, as shown in Fig. 10.
When the interim time is short, a shows little difference from a0. Hence, a smaller a0 is required to extend the MFD to couple to the SMF, resulting in longer waveguide length for the SSC. On the contrary, by applying the long interim time, a large difference in Δn is obtained between both ends (large and small core ends), as shown in Fig. 5. Thus, applying the appropriate interim time allows the MFD to extend wider even if a0 is set to be relatively large. Figure 11 shows the relationship between the waveguide (SSC) length and interim time calculated by the above steps. We find from Fig. 11 that the required waveguide length decreases with increasing the interim time. Therefore, for creating an SSCs with a short waveguide length, the interim time should be appropriately long.
4.2 Coupling loss
The dependence of the coupling loss between the tapered waveguide and fibers on the interim time is calculated by using the mode solver FIMMPROP (Photon Design). As the smaller core end of the SSC is assumed to be coupled to an SMF (PA-A2) as mentioned above, the MFD should be 8.5 μm at 1550-nm wavelength. Meanwhile, although the larger core end of the SSC should be coupled to a Si waveguide, an ultra-high-NA single-mode fiber (UHNA1, Thorlabs) whose MFD is experimentally measured as 4.0 μm at 1550 nm is assumed to be coupled to the SSC. In the later section, the UHNA1 fiber is used for experimentally evaluating the fabricated tapered waveguides, as previously performed in [11,13]. So, the input parameters for the calculation relating to UHNA1 and PA-A2 are summarized in Table 2. The coupling losses on both ends of the SSC are calculated by an overlap integral of the mode fields of the LP01 modes in the waveguide and fiber.
Table 2. Optical characteristics of UHNA1 and PA-A2.
Figure 12 shows the calculated result. It is noteworthy that significantly high coupling losses are obtained particularly on the small core end when the interim time is shorter than 2.7. Although the coupling loss on the small core end dominates the insertion loss of the waveguide, it decreases monotonically over a range of the interim time from 0 to 12.6, and the lowest coupling loss is observed at an interim time of 12.6. On the other hand, the loss on the large core end is almost one tenth of the total coupling loss under the short interim time conditions, which indicates less contribution on the insertion loss. Here, all the tapered waveguides have the MFDs coinciding with those of the two SMFs. Nevertheless, high coupling losses are observed if the interim time is not appropriately applied. Even though the same MFDs as the fibers are assumed on the ends of the SSC, the high coupling loss is explained by the gap in the mode-field profiles between the waveguide and the fiber. Figure 13 shows the calculated 1-D profiles of the LP01 mode in PA-A2 compared to that of the waveguide on the small core end. Since the MFD is defined as the diameter at which the field intensity decreases to 1/e2 of the maximum intensity (generally observed at the core center), it is possible for the mode-field intensity profiles to have the same diameter only at the 1/e2 field intensity, although the field profiles differ in other regions. Actually, a large gap is observed between the two profiles at t = 0 in the range of 23.0 μm < x < 27.0 μm in Fig. 13 (a). On the small core end of the waveguide, because the core diameter is too small, the evanescent field extends significantly into the cladding. In particular, the field extends substantially into the cladding where the normalized intensity is lower than 0.2, resulting in the wide MFD. Meanwhile, most of the mode field is tightly confined in such a small core where the normalized intensity is higher than 0.2 due to high Δn (before monomer diffusion). However, since the core diameter after diffusion, a, increases and Δn decreases with increasing interim time, the light confinement conditions are closer to those in PA-A2. Then, the two mode-field distributions match identically after an interim time of 12.6, as shown in Fig. 13 (c), for which the calculated coupling loss is as low as 0.04 dB as shown in Fig. 12.
Fig. 13. Difference of the LP01 mode profiles between PA-A2 and the small core end of SSC after an interim time of (a) 0 (a. u.) (b) 5.85 (a. u.) (c) 12.6 (a. u.).
On the other hand, in Fig. 12, it is noted that little coupling loss is observed on the large core end when the interim time is in a range from 1.05 to 1.62. Figure 14 shows the calculated 1-D profiles of the LP01 mode in UHAN1 compared to those of the waveguide on the large core end. Here, with an NA of 0.28, UHNA1 is assumed to be coupled to the waveguide. Just after such a short interim time, the original high Δn is maintained in the waveguide on the large core end, and thus, the light confinement condition is kept close to UHNA1 to allow for better mode-field coupling to UHNA1 in Fig. 14 (b). After applying an interim time longer than 1.05, the coupling loss gradually increases because the mode-field profile in the waveguide tends to extend to show a profile gap with the UHNA1, as shown in Figs. 14(c)–14(e). However, in an interim time range from 3.6 to 5.85, the coupling loss decreases again, and finally shows another increase after 5.85 interim time. This oscillating coupling loss pattern is attributed to the variation of mode-field profile: when the core is just after dispensed (t = 0), the waveguide has a mode field narrower than that of UHNA1, and in a normalized intensity range between 1/e2 and 1.0, the profile of UHNA1 varies from wider to narrower compared to the profile of the waveguide when t increases from 0 to 3.6, while it returns to be narrower when t increases to 5.85.
Fig. 14. Difference of the LP01 mode profiles between UHNA1 and the large core end of SSC after an interim time of (a) 0 (a. u.) (b) 1.05 (a. u.) (c) 3.60 (a. u.) (d) 5.85 (a. u.) (e) 12.6 (a. u).
Then, as the interim time increases to 12.6 (a. u.), the difference of the mode-field profiles increases, to show high coupling loss. Therefore, as shown in Fig. 12, an interim time of 6.9 is the optimum value at which the total coupling loss is minimized to 0.28 dB.
4.3 Propagation loss
In this section, we investigate the dependence of the propagation loss of the tapered waveguide on the interim time. Here, the propagation loss is calculated by dividing the loss factor into two parts: one is the loss caused by the tapered core structure and the other is the loss inherent to the waveguide materials such as scattering and absorption losses. We first focus on the propagation loss caused by the tapered core structure.
For the loss simulation, the tapered structure needs to be quantitatively expressed as an input parameter to FIMMPROP. So, it is necessary to quantify how the core diameter after diffusion, a, and the refractive index difference, Δn, change depending on the interim time t as a function of the position z. In sections 3.1 and 3.2, the dependences of Δn and a on the interim time are calculated as shown in Figs. 6 and 7, respectively. In this section, the interim time is fixed, and the relationship between Δn and a0 as well as the relationship between a and a0 is obtained, which is shown in Fig. 15. Here, we focus on a range of a0 from aS0 to aL0. We find that Δn almost linearly increases with increasing a0, which is independent of the interim time, but the slope tapers off with increasing interim time (direction of arrow in Fig. 15 (a)). Meanwhile, the core diameter after diffusion, a, is originally identical to a0 at t = 0 because no diffusion has yet taken place, but if an interim time is applied, a exhibits a linear relationship with a0, as shown in Fig. 15(b). Hence, since the relationships between Δn and a0 are expressed by a linear approximation, a0 in Eq. (4) is substituted for Δn using the obtained linear approximation. Thus, Δn is expressed as a function of z-1/4. In addition, by the same calculation from the relationship between a and a0, a is also expressed as a function of z-1/4. Here, it is very important that Δn, which strongly affects the light confinement is dependent on the waveguide axis, z. This z-dependent Δn contributes to the efficient spot-size conversion.
The tapered structure approximated by the relationships between a and z, and the z-dependent Δn are entered into FIMMPROP, and then the lightwave propagation in the tapered waveguides is simulated as illustrated in Fig. 16. Here, the light intensity distribution on a plane perpendicular to the optical axis at the position z is dependent on the interim time since a and Δn at the same z position are also interim time dependent. In FIMMPROP, the light leakage loss during the tapered waveguide propagation is calculated, and the calculated propagation loss dependence on the interim time is shown in Fig. 17. It is found that the propagation loss due to the tapered structure is as low as 0.025 dB at 4.8 (a. u.). In Fig. 17, the propagation loss increases with increasing interim time to 4.8 and it declines after the interim time exceeds 4.8. This interim time dependence of the propagation loss is predominated by the absolute magnitude of Δn and the slope of the variation of Δn along the z direction. When the interim time is shorter than 4.8, Δn remains high over the whole z positions due to less monomer diffusion, which leads to strong light confinement, resulting in a low propagation loss. Meanwhile, when the interim time increases, Δn gradually decreases depending on the position z, as shown in Fig. 15(a), which lowers the light confinement to increase the propagation loss. Then, at an interim time of 4.8, the combination of low Δn, the larger slope of the Δn variation over the position z, and the tapered shape formed by the core diameter after diffusion, a, all contribute to the highest propagation loss. Finally, when the interim time exceeds 4.8, because the Δn variation is small with respect to a0, the Δn variation along with the optical axis comes to be moderate, and tapered shape with abrupt a variation over z is relaxed as well, thus, the propagation loss decreases. However, as mentioned above, even the highest calculated propagation loss at 4.8 (a. u.) is still much lower than the coupling loss shown in Fig. 12.
Next, we focus on the propagation loss inherent to the waveguide materials: the experimentally measured propagation loss of a single-mode polymer waveguide fabricated using the same core material by the Mosquito method is applied to the simulation. In our previous report [14], the propagation loss of the waveguide was measured applying the cut-back method to be 0.44 dB/cm at 1550-nm wavelength. At 1550 nm, the absorption loss due to the carbon-hydrogen bondings is the dominant factor, which shows a linear relationship with the waveguide length. Hence, the material inherent propagation loss is larger if the tapered length needs to be long.
The total insertion loss, which is a sum of the coupling and propagation losses, is shown in Fig. 18 with respect to the interim time. In Fig. 18, the waveguide length required to the spot-size conversion is also indicated. We find from Fig. 18 that the lowest loss of 0.40 dB is attained at an interim time of 9.3. Although the tapered waveguide length could be minimized by applying the interim time longer than 9.3, the coupling loss increases the total insertion loss compared to that at 9.3 (a. u.), as shown in Fig. 18. So, the shortest waveguide length is determined to be 2.4 mm, at which the lowest insertion loss is achieved. Thus, we theoretically confirm that the tapered waveguide fabricated by the Mosquito method realizes low loss spot-size conversion from 4.0 μm to 8.5 μm with an insertion loss of 0.40 dB at 1550-nm wavelength as short as 2.4 mm, which is small enough for packaging on a chip.
5. Experimental fabrication of tapered waveguide based SSC
In this section, we experimentally fabricate the tapered waveguides applying various interim times in the Mosquito method and evaluate their spot-size conversion functions.
Figure 19 shows the fabrication conditions in the Mosquito method. Three tapered cores to which the interim times of 2.7 s, 47.5 s, and 65.3 s are applied are fabricated by the fabrication procedure shown in Fig. 2 while maintaining the cladding monomer at 12.5°C. The interim times are corresponding to 0.3, 5.5, and 7.5 (a. u.) respectively. Here, a precise needle (SHN-0.1N, Musashi Engineering, Inc.) is applied. We already found that the smooth inner wall of the precise needle exhibited a high sensitivity to dispensing pressure compared to the straight needle we have used for the waveguide fabrication [15]. We compare the optical characteristics by measuring near-field patterns (NFPs) at 1550 nm: at first, we cut to shorten the waveguide from the large core side until the NFP of the LP01 mode with an MFD of 4.0 μm is clearly observed. Next, the NFP on the small core side is measured. If the MFD estimated from the NFP is larger than that of PA-A2 (8.5 μm), the waveguide is gradually shortened from the small core end until the same MFD as PA-A2 (8.5 μm) is observed to obtain an SSC between 4.0 and 8.5 μm.
Figure 20 shows the cross-sectional photos and observed NFP images on both ends of the fabricated tapered waveguides. From the cross sections, the core-cladding interface tends to blur as the interim time increases, which means the monomer diffusion progresses to form a GI profile. While the tapered waveguide to which a 2.7-s interim time is applied needs 26.5 mm in length to convert the MFD between 4.0 and 8.5 μm, by applying longer interim times such as 47.5 s and 65.3 s, the waveguide length to convert the MFD is remarkably short, which agrees well with the theoretically calculated result shown in Fig. 11.
Fig. 20. Cross sections and NFPs of the fabricated waveguide with the interim time of (a) 2.7 s, (b) 47.5 s, and (c) 65.3 s.
Figure 21(a) compares the measured 1-D NFPs on the large core side of the fabricated waveguides and UHNA1. While the waveguide to which 2.7-s interim time is applied shows almost the same NFP as that of UHNA1, as the interim time increases, the NFP difference between the waveguide and UHNA1 is large. On the other hand, as shown in Fig. 21(b), the NFP difference between the small core side of the waveguide and PA-A2 is the smallest when the interim time is 65.3 s because Δn of the waveguide decreases due to monomer diffusion. These experimentally obtained NFPs in Fig. 21 coincide with the simulation results in Figs. 13 and 14.
Fig. 21. NFP comparison of the fiber and the waveguides of (a) the large core side and (b) the small core side.
Finally, the insertion loss at 1550 nm is measured by connecting the UHNA1 and PA-A2 fibers to the large and small core ends of the fabricated waveguides, respectively. Figure 22 shows the result. The fabricated tapered waveguide to which a 47.5-s interim time is applied exhibits the lowest insertion loss of 1.83 dB while the waveguides to which 2.7-s and 65.3-s interim times are applied show insertion losses as high as 11.97 dB and 3.12 dB, respectively. The high loss of the waveguide to which a 2.7-s interim time is applied is due to the waveguide length of 26.5 mm: high absorption loss inherent to the waveguide material affects the total loss in such a long waveguide. In addition to the material inherent loss, two other loss factors are involved: one is the high coupling loss due to the mode field mismatch on the waveguide small core side as predicted in Fig. 12. The other one is the excess scattering loss at a rough core-cladding boundary due to an SI core which remained after such a short interim time [9]. Meanwhile, the waveguide to which a 65.3-s interim time is applied shows high insertion loss of 3.12 dB because of the excess coupling loss between UHNA1 and the waveguide on the large core end, since monomer diffusion leads to a mode-field mismatch between them. When a 47.5-s interim time is applied, the MFD is converted between 4.7 and 7.5 μm just in an 8-mm long tapered waveguide, resulting in the lowest insertion loss. The result that an adequate interim time should be applied to obtain a compact and highly efficient tapered waveguide SSC is consistent with the calculated results shown in Fig. 18.
Compared to the optimally designed waveguide in Fig. 18, the required length for spot-size conversion of the fabricated waveguide is longer, and the measured insertion loss is slightly higher. In Fig. 20(b), the mode-field on the small core side is not accurately adjusted to the mode field of PA-A2, which is confirmed in Fig. 21(b), as well. The waveguide ends that exhibit the same MFD as the fibers to be coupled are optimized manually (cut and shorten waveguides) as mentioned above. In addition, the measured insertion loss includes Fresnel reflection losses at the connections with fibers, which is another reason for the insertion loss discrepancy. We already confirmed a lower insertion loss by applying matching oil at the connection points between the fibers and waveguides, which reduces the Fresnel reflection loss.
The spot-size conversion function in the fabricated tapered waveguides is examined just by the edge coupling scheme with UHNA1 in this paper, which is different from the adiabatic coupler schematically illustrated in Fig. 1. We preliminarily confirmed the ability of low-loss adiabatic coupling in a configuration shown in Fig. 1 in theoretical simulation, where the waveguide has the same tapered structure as designed in this paper. Meanwhile, we need further experimental investigations on methodologies for embedding Si cores in the polymer tapered core during the Mosquito method. This topic will be published elsewhere after obtaining the designed embedded structure.
6. Conclusion
In this paper we theoretically investigate the conditions for fabricating low-loss and short tapered waveguides which function as SSCs by the Mosquito method. In the Mosquito method, there is diffusion between the miscible core and cladding monomers, which causes the Δn variation in the waveguide axis direction in tapered cores. When applying a long interim time, the optical confinement in the core that is dependent on Δn is different between the two ends of the tapered core, from which sufficient MFD conversion is possible even during a short distance propagation in the waveguide. Furthermore, the radial index profile as well as the axial Δn variation allows the mode-field intensity distributions on both sides of the waveguide to be fitted to fibers with different mode fields and to be connected with low coupling loss. Therefore, it is theoretically found that a core with a sufficiently long interim time exhibits SSC functionality with a length of 2.4 mm with a 0.40-dB total insertion loss at 1550 nm. In practice, we experimentally fabricate the tapered SSC using the Mosquito method by applying an interim time of 47.5 s. The fabricated SSC shows sufficient spot size conversion from 4.7 μm to 7.5 μm with 8-mm length and shows the low insertion loss of 1.83 dB. This result shows remarkable advancement in the insertion loss and the device size from our previous report in which the waveguide exhibited an insertion loss of 2.77 dB in a 15-mm length was fabricated without adjusting the interim time.
Funding
Japan Society for the Promotion of Science (JP18H05238); The Foundation for Technology Promotion of Electronic Circuit Board, Research Grant.
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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