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Abstract
We investigated the roughness-induced scattering loss (LossR) of small-core polymer waveguides fabricated using the photolithography method, both theoretically and experimentally. The dependence of LossR on the roughness parameter, waveguide dimension, operation wavelength, refractive index difference and distribution, polarization sensitivity, sidewall angle, and bending radius were studied. The surface roughness of both the sidewall and the top/bottom of the fabricated waveguides were measured using laser confocal microscope, and the results showed that the averaged sidewall roughness was approximately 60 nm, which is 3 times that of the top/bottom surface. As a result, the sidewall roughness-induced LossR is 9 times that induced by the top/bottom roughness. The calculated value of LossR agrees well with the measured value. LossR increases rapidly with the decrease in the waveguide width, especially when the waveguide width is reduced below 10 µm, at which the LossR is approximately 0.3 dB/cm. On the other hand, the dependence of LossR on the waveguide height is negligible. Our results provide guidance for developing single-mode polymer waveguides with low loss for optical interconnect applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The dramatic growth of data traffic in large-scale data centers and high-performance computers drives the rapid development of optical interconnects [1–3]. Compared with its electrical counterpart, optical interconnects have advantages in terms of transmission data rate, bandwidth, interconnect density, power consumption, and electromagnetic immunity [4,5].
Polymer waveguides are considered to be a promising transmission medium for high-speed on-board optical interconnects. It can achieve high density, high data throughput, and good compatibility with both printed circuit boards (PCBs) and fiber optics. Board-level optical interconnects based on the combination of multimode polymer waveguides and vertical cavity surface emitting lasers (VCSELs) have been successfully demonstrated [6,7]. The transmission loss of multimode polymer waveguides can be lower than 0.05 dB/cm at a wavelength of 850 nm [8]. High-speed non-return-to-zero (NRZ) signal transmission at a data rate of 30 Gb/s and single-channel 4-level pulse amplitude modulation (PAM4) signal transmission at a data rate of 56 Gb/s with a channel length of up to 1 m have been achieved [9,10]. However, the signal degradation due to the highly multimode nature is still a concern for further improvement of transmission capacity [11–13].
Single-mode polymer waveguides, which can avoid the intermodal dispersion in multimode waveguides and meet the increasing demand for dense photonic integration, are now under intensive investigation. High-function application-specific integrated circuits (ASICs), such as switch chips, employ silicon photonics technology operating in the conventional single-mode wavelength regions of 1310 nm or 1550 nm (O- or C-band) for larger channel numbers and greater throughput beyond 1 Tb/s [14]. Single-mode polymer waveguides can be used as low-loss and high-density polymer interposers that enable efficient coupling between standard single-mode fibers (SMFs) and silicon waveguides [15–17].
Despite these advantages, the applications of single-mode polymer waveguides operating in the O- or C-band are limited by their higher transmission loss when compared to multimode polymer waveguides operating at 850 nm. This is due to the fact that traditional polymer materials have strong C–H vibrational absorption in the infrared region (1000-1600 nm). As a result of the efforts to reduce absorption, polymer waveguide materials with high transparency, such as fluorinated polyimide, perfluorinated polyimide, perfluorinated methacrylates, and deuterated polyfluoromethacrylate, have been synthesized [18–21]. Another major reason for the high transmission loss is the existence of roughness and defects at the core/clad interface [22]. Some research groups have experimentally demonstrated that the formation of a refractive index gradient in the core can effectively reduce crosstalk and loss [23–27]. There have been many studies on waveguide defects and scattering loss of silicon waveguides [28–33] and some investigations on multimode polymer waveguides [34–37]. Although some preliminary results have been reported [38,39], there is a lack of a comprehensive study on the effect of roughness on a polymer waveguide with a small core size which is required in single-mode operation conditions. The core dimensions of single-mode waveguides are usually less than 10 µm, which implies that the scattering loss caused by the roughness becomes more significant due to the large proportion of modal power overlap at the core/clad interface. Moreover, the effects of top/bottom surface roughness and sidewall roughness are different owing to the differences in exposure and developing process conditions in photolithography, laser direct writing [40], and nano-imprint lithography [41].
In this study, we investigated the roughness-induced scattering loss (LossR) of polymer waveguides with a core size comparable to that of single-mode fibers fabricated by the photolithography method. We studied the dependence of LossR on the roughness parameter, waveguide dimension, operation wavelength, refractive index difference and distribution, polarization sensitivity, sidewall angle, and bending radius. LossR was calculated and measured accordingly, and the experimental results were found to agree well with the numerical calculations. We found that the LossR due to the sidewall roughness is 9 times that due to the top/bottom surface roughness. The LossR increases sharply with the decrease in the waveguide width, especially when the width of the waveguide is smaller than 10 µm. Our results provide guidance for the design and fabrication of low-loss polymer waveguides for single-mode optical interconnect applications.
2. Theoretical study and analysis
According to Marcuse’s coupled mode theory [42], the average power loss coefficient of a perturbed slab waveguide can be expressed as
Fig. 1. (a) Schematic of a rectangular waveguide with perturbation. (b) Y-Z cross section of the waveguide with rough interfaces.
According to the model described in [27,28], the scattering loss coefficient ${\alpha _{c{m^{ - 1}}}}$ resulting from the sidewall roughness can be expressed as
We set n1 and n2 to be 1.532 and 1.512 at 850 nm. These initial conditions coincide with our experimental conditions. The width, 2d, of the waveguide is set to 10 µm. We first calculated the dependence of LossR on σ and Lc using Eq. (5) by considering only the sidewall roughness because the sidewall roughness measured in our experiment was approximately 3 times that of the top/bottom surface roughness. Figure 2 shows the calculated results. The measured σ and Lc of the sidewall roughness in the experiment are also plotted (blue crossings) for comparison purposes. LossR is proportional to the square of σ, and it first reaches a maximum at Lc=4.07 µm and then starts to decrease with the increase in Lc. Under the initial conditions, σ should be less than 40 nm if a LossR caused by sidewall roughness is expected to be lower than 0.1 dB/cm.
The dependence of LossR on the waveguide width, wavelength, and refractive index difference was calculated using Eq. (5). The main calculation parameters are listed in Table 1. Figure 3(a) shows the results for the waveguide width. LossR was calculated by using the measured σ and Lc of the sidewall and top/bottom surface of the fabricated waveguides at 850 nm. σ and Lc of the sidewall are 60 nm and 1.79 µm, respectively. σ and Lc of the top/bottom surface of the waveguide are 20 nm and 2.21 µm, respectively. It can be observed that LossR decreases as the waveguide width increases. The dependency may be explained by the fact that LossR is dependent on the modal power overlap with the core/clad interface of the waveguide in the same operation wavelength, which is related to φ(d) in Eq. (2). As a result, the narrower waveguides that have a larger proportion of modal power overlap experience higher light scattering loss. Further, LossR due to sidewall roughness is much higher than that due to top/bottom surface roughness because LossR is proportional to the square of σ, as shown in Eq. (5). In the case of σ, the sidewall roughness is 3 times that of the top/bottom surface. As a result, the LossR of the sidewall was 9 times that of the top/bottom surface when Lc was similar.
Fig. 3. Calculated dependence of LossR on (a) waveguide width, (b) wavelength, and (c) refractive index difference.
Table 1. Main calculation and simulation parameters
The dependence of LossR on the operation wavelength is shown in Fig. 3(b). It can be observed that although LossR decreases with an increase in the operation wavelength, LossR is not negligible for a waveguide with a width less than 10 µm even under longer operation wavelengths such as 1310 nm or 1550 nm. Figure 3(c) shows the dependence of LossR on the refractive index difference. The width of the waveguide was set to 10 µm. LossR increases almost linearly with the increase in the refractive index difference.
The beam propagation method has also been employed to investigate the dependence of LossR on parameters such as refractive index distribution and core shape. The main simulation parameters are the same as the calculation parameters mentioned above and some additional simulation parameters are also added, as shown in Table 1. σ and Lc of the sidewall roughness were set to 60 nm and 1.79 µm, respectively, which is consistent with the experimental results. The top/bottom surface roughness was set to 0. To minimize the influence of the differences in coupling conditions, LossR was estimated using a cut-back method. We used the output beam from a 10 mm-long waveguide with the same structure as the input field for the waveguide under investigation.
The dependence of LossR on the waveguide height was also investigated. Figure 4(a) shows the results of the simulation. LossR decreases as the waveguide width increases. However, the dependence of LossR on the waveguide height is negligible compared with that on the waveguide width when there is no roughness on the top/bottom surface. The LossR of polymer waveguides with step and near-parabolic index distribution and schematics of their index profiles are shown in Fig. 4(b), respectively. Both the width and height of the waveguide are set to 10 µm. A near-parabolic refractive index fitted using a power-law equation with the best-fit index exponent of 2.5 [24], was adopted as the comparison standard for the step index profile. Compared with LossR of 0.15 dB/cm of the waveguide with a step index profile, the LossR of the waveguide with a near-parabolic index profile is 0.11 dB/cm, which agrees with the experimental results reported in [23,24].
Fig. 4. Dependence of LossR on (a) waveguide width, (b) refractive index distribution, (c) polarization, and (d) sidewall angle estimated using the beam propagation method.
The dependence of LossR of different waveguide widths on polarization is shown in Fig. 4(c). It can be observed that the effects of TE and TM polarized light on LossR are almost the same for different waveguide widths. This is because the refractive index difference between core and cladding is small. The dependence of LossR on the sidewall angle θ, as shown in the inset of Fig. 4(d) for different waveguide widths was studied. The bottom width and height of the waveguide are the same, and the top width varies with the angle of the sidewall. The sidewall angle-dependent loss (ADL) is defined as the difference between the LossR of a waveguide with a specific angle θ and angle θ of 0 degrees. It can be observed that the ADL increases with the increase in sidewall angle, especially when the waveguide width is small. In addition, the ADL with a waveguide width of more than 20 µm is negligible. The results imply that the fabrication tolerance is tighter when the waveguide width is small.
The effect of the sidewall roughness on the bending loss was investigated, and the results are shown in Fig. 5. The cross section of the waveguide is set to 10×10 µm2. It can be observed that the critical bending radius of the waveguide increases with increasing σ. The dependence of LossR on the bending radius for different waveguide widths was also studied, as shown in Fig. 6(a). σ and Lc were set to 60 nm and 1.79 µm, respectively. The bending loss without the consideration of roughness was also calculated by setting σ to 0 for comparison purposes, as shown in Fig. 6(b). The critical bending radius increases with the increase in sidewall roughness, especially when the waveguide width is larger. As a result, the practical minimum bending radius is approximately 15 mm for a 10 µm-width waveguide with σ of 60 nm.
Fig. 5. Bending loss with different sidewall roughness with waveguide dimension of 10×10 µm2 estimated using the beam propagation method.
Fig. 6. Bending loss with σ of (a) 60 nm and (b) 0 nm with different waveguide widths estimated using the beam propagation method.
3. Experimental results and analysis
Polymer optical waveguides were fabricated using one set of commercially available UV-curable resins (core: NTT-AT E3135 and clad: NTT-AT E3129) as the core and cladding materials by the standard photolithography method. The refractive indices of the core and cladding are 1.532 and 1.512, respectively, after the UV curing process at a wavelength of 850 nm. The viscosity of the core and cladding are 2900 mPa·s and 2200 mPa·s, respectively, at a temperature of 25°C. The height of the waveguides is 10 µm, and the width ranges from 6 µm to 40 µm. A schematic of the fabrication process is shown in Fig. 7. It was carried out at a temperature of 21°C and a relative humidity of less than 40%.
FR-4 boards with an area of 100×100 mm2 and thickness of 0.5 mm were used as substrates. The bottom cladding layer with a thickness of 50 µm was spin-coated on the substrate followed by UV curing for 8 min and baking at 80°C for 15 min. The core layer was spin-coated with a thickness of 10 µm and UV patterned for 70 s using a mask aligner. After that, the wafer was baked at 80°C for 1 min. The core pattern was developed in acetone for 30 s and dried with nitrogen. Finally, the top cladding layer with a thickness of approximately 50 µm was spin-coated and UV cured. The fabricated waveguide was post-baked for 10 min.
Under the same experimental conditions, the same photo mask was used to fabricate the waveguides without the top cladding for roughness measurement. A dicing saw (ADT 7100) with a 25 µm-thick cutting blade was used to cut the substrate at a distance of approximately 100 µm from the waveguide, as shown in Fig. 8, to maximally avoid damage to the core/clad interface of the waveguide. The waveguide was then rinsed with ethanol and dried carefully under nitrogen flow. A laser confocal microscope (Olympus OLS5000) was employed to directly observe the topography of the waveguide and to measure the σ and Lc of both the top/bottom surface and the sidewall of the waveguide.
Figure 9(a) shows an example of the observed three-dimensional topography of the fabricated waveguides without the top cladding. The area for measuring sidewall roughness is indicated by a yellow frame whose length and width are approximately 110 µm and 10 µm, respectively, as shown in Fig. 9(b). Figure 10 shows the measured results. The measured average σ and Lc of the sidewall and the top/bottom surface roughness are about 60 nm and 1.79 µm, and 20 nm and 2.21 µm, respectively, when the threshold of Lc is set to be 1/e. The variation range of σ on the sidewall and the top/bottom surface is 40 to 80 nm and 10 to 30 nm, respectively.
Fig. 9. (a) Three-dimensional image of optical waveguide. (b) An example of the area for measuring waveguide sidewall roughness.
Fig. 10. Measured σ and Lc by laser confocal microscopy of (a) sidewall and (b) top/bottom surface of the waveguide.
Using the experimental setup shown in Fig. 11(a), the insertion losses of the waveguide with the top cladding structure were measured. The waveguides have a length of 8.0 cm. The end facets of the waveguide were carefully polished, and one of their micrographs is shown in Fig. 11(b). The light from an 850 nm broadband laser diode was butt-coupled into the waveguide using a 4 µm-core single-mode fiber (HI-780). An OM3 graded-index multimode fiber was used to collect the output light to the power meter. The index-matching oil was applied to the end facets to maximally reduce the coupling loss. The averaged value was adopted to minimize the measuring errors.
Fig. 11. (a) Experimental setup for measuring insertion losses. (b) Polished end facet of the waveguide.
The transmission losses that we measured at a wavelength of 850 nm for different waveguide widths are plotted in red squares in Fig. 12. Each red square represents the averaged measured results of 8 channels of the waveguide with the same width. According to the overlap integral analysis, the fundamental mode carries most of the optical power in the regime where scattering loss is significant. This calculation is suitable for describing the experimental data. The calculated LossR is plotted with the same Lc of 1.79 µm and sidewall roughness σ of 40, 60, and 80 nm, respectively, which represent the calculated results using the minimum, average, and maximum σ of the experiments. The roughness-induced scattering loss is enhanced as the waveguide width decreases, and the measured transmission losses agree well with the calculated ones. As a result, in order to fabricate a polymer waveguide with a LossR less than 0.1 dB/cm, for example, the width of the waveguide should be larger than 10 and 25 µm when the sidewall roughness is 40 and 80 nm, respectively. The LossR is small when the waveguide width is larger than 20 µm. However, as the width of the waveguide is reduced to less than 10 µm, the LossR is enhanced rapidly. It should also be noted that the measured LossR also includes material absorption loss and coupling loss, which leads to a measured loss larger than the calculated LossR. In addition, the discrepancy between the measured transmission losses and the calculated LossR is larger when the waveguide width becomes smaller. A possible explanation is that the influence of the shape of the waveguide on LossR increases when the width of the waveguide reduces, making the fabrication tolerance tighter, as mentioned in Section 2.
4. Conclusion
We investigated the roughness-induced scattering loss (LossR) of polymer waveguides with a core size comparable to that of a single-mode fiber. A numerical model based on the coupled mode theory and the beam propagation method was adopted for the theoretical analysis. The dependence of LossR on the roughness parameter, waveguide dimension, operation wavelength, refractive index difference and distribution, polarization sensitivity, sidewall angle, and bending radius were studied. Both the sidewall and top/bottom surface roughness of the fabricated waveguides were measured using a laser confocal microscope, and the results showed that the averaged sidewall roughness was approximately 60 nm, which is 3 times that of the top/bottom surface. As a result, the sidewall roughness-induced LossR is dominant and is 9 times that due to the top/bottom surface roughness. The calculated value of the roughness-induced loss agrees well with the measured value. LossR increases rapidly with the decrease in the waveguide width, especially when the waveguide width is reduced below 10 µm, at which LossR is approximately 0.3 dB/cm. However, the dependence of LossR on the waveguide height is negligible. Our results provide guidance for the development of polymer waveguides with low loss for single-mode optical interconnect applications.
Funding
National Key Research and Development Program of China (2019YFB1802900); National Natural Science Foundation of China (61775138).
Acknowledgements
The authors thank Dr. Yoshihisa Sakai and Dr. Junya Kobayashi of NTT Advanced Technology Corporation for their advice and encouragement.
Disclosures
The authors declare no conflicts of interest.
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