Open Access
Add to BibSonomy
Abstract
A silicon-cored-fiber (SCF) is used in, what we believe to be, a novel way for coplanar light coupling from an incoming fiber to a silicon waveguide on a chip. Two schemes of utilizing SCFs are investigated, namely a tapered SCF coupler and a D-shaped SCF coupler. A tapered SCF coupler is chosen for further optimization, leading to a coupling efficiency of ∼97% obtained from the results of 3D FDTD simulation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photonic integrated circuits (PICs) have been considered promising schemes to realize modulation [1], detection [2], sensing [3,4], and even quantum computing [2,5]. By utilizing the mature silicon-based CMOS technologies, silicon photonics (SiPh) based on the silicon-on-insulator (SOI) platform is one of the popular choices for implementing PICs. The SOI optical interconnection provides wide bandwidth for on-chip applications and possesses low propagation loss. Aside from commonly-seen on-chip silicon waveguides, the emerging silicon-cored fibers (SCFs) can provide a promising alternative, owing to their easy integration advantage with commercial optical fiber devices. Furthermore, SCFs are compatible with traditional fiber processes such as tapering, chemical etching, and grinding.
Since Pier J. A. Sazio et al. first produced SCFs [6], there have been many SCF-based applications, such as super-continuum sources [7], solar cells [8], sensors [9], Schottky photodetector [10,11], etc. All the applications require light coupling from commercial single-mode fibers (SMFs) to the SCFs. Two light coupling methods enabling SCFs to be integrated into general fiber optic applications have been reported. One is the use of a tapered SCF with nano-spike and direct splicing with a tapered SMF [12]. The other is the use of microstructures on the end-faces of SCFs to reduce the Fresnel reflection loss between SCFs and commercial SMFs [13].
The fiber-to-chip coupling from a light source to an SOI platform is always a crucial topic in SiPh. Although the frequently used vertical coupling supported by a grating coupler has good misalignment tolerance, its coupling efficiency is averagely inferior to horizontal coupling. Its non-coplanar layout with silicon chips makes the whole setup bulkier and less compact [14]. The edge coupler is expected to have a better packing density and integration with silicon chips. However, if an SMF is directly applied to edge coupling, the large refractive index difference and mode size mismatch between the silicon chip and SMF pose challenging issues.
In this work, we propose what we believe to be, a novel SCF-based edge coupler to solve the issues. An SCF can be spliced with an SMF at one end with low loss [13], and the other end is to be connected with a silicon waveguide through edge coupling. Owing to the same material, the inherent Fresnel reflection loss is expected to be eliminated between SCF and silicon waveguide. Two kinds of SCFs are considered fiber-to-chip couplers, tapered SCFs and D-SCFs, and their characteristics are analyzed. Then a tapered SCF is chosen as a better coupler for further optimization because its effective mode index matches well with a single mode strip waveguide (Si SMWG), and almost unity integral value can be obtained for its modal overlapping with the Si SMWG in the electric field. Moreover, the total length of an optimized tapered SCF is only 50 µm from the input to the output ends, which is beneficial to compact device packing.
2. Comparison of two coupler designs
It has been reported that a tapered SCF with a sub-micrometer tip could be fabricated by sleeving the SCF into a hollow core fiber (HCF) before tapering process [7]. By further controlling the gap between the inner diameter of HCF and the outer diameter of SCF, our preliminary experimental results show that a tapered SCF with tip diameter less than 400 nm could be repeatedly obtained [15]. In addition, a length-controllable, low-roughness D-shaped region could be fabricated by modifying the side polishing techniques reported in Ref. [16], resulting a significant improvement on what have been reported in Ref. [10]. Based on the manufacturability of both tapering and polishing SCFs, two coupler designs are proposed: tapered SCF coupler, and D-SCF coupler. To investigate the two-dimensional (2D) cross-sectional electric field intensity distributions of tapered SCFs and D-SCFs, the finite element method (FEM) using Rsoft is applied. The structures and the defined terms used in the simulation are shown in Fig. 1. Because a tapered SCF only changes its diameter without varying its geometry, a tapered SCF could be viewed as a normal SCF in 2D simulation and is thus referred to as a normal SCF. In modal overlap integral calculation, for a normal SCF, the core diameter is increased from 300 nm to 1 µm at an equal interval of 10 nm. The cladding diameter is ten times the core diameter, representing a commonly-seen cladding-to-core ratio of SCFs. As for a D-SCF, the core diameter is increased from 300 nm to 1 µm at an equal interval of 20 nm, with the same cladding-to-core ratio as the normal SCFs. The remaining core height is directly related to the depth of polishing, and three groups are considered where the remaining core heights are: half of the core diameter, 50 nm more than half of the core diameter, and 50 nm less than half of the core diameter. The investigation of the remaining core height is to understand how the geometric change of the silicon core affects the light field distribution. The height and the width of Si SMWG are set to 220 nm and 500 nm, respectively, with a buried-oxide layer beneath the waveguide. The operating wavelength is 1550 nm; the refractive index of silicon is set to 3.45; the refractive index of silica is set to 1.45; the refractive index of air is set to 1.
Fig. 1. Schematic of (a) a normal SCF, representing the cross-section of a tapered SCF, and (b) a D-SCF used in the FEM simulation.
The 2D cross-sectional electric field intensity distributions of Si SMWG and both designs are shown in Fig. 2. It can be seen that the TE mode of Si SMWG shown in Fig. 2(a) is more matched to the first mode of normal SCF shown in Fig. 2(c). However, the TM mode of Si SMWG shown in Fig. 2(b) is more matched to the TM mode of D-SCF shown in Fig. 2(f). To further quantify the mode match of two designs with different parameters, the modal overlap integral η can be expressed as:
Fig. 2. The 2D cross-sectional electric field intensity distribution of the low-order mode, including (a) TE mode and (b) TM mode of Si SMWG; (c) 1st order mode and (d) 2nd order mode of a normal SCF with a 500 nm core diameter; and (e) TE mode and (f) TM mode of a D-SCF with a 500 nm core diameter and a 250 nm remaining core height.
3. Parameters optimization
Figure 5(a) shows the overall coupling scheme, including a tapered commercial SMF connected to a tapered SCF coupler as the input. Figure 5(b) shows the schematic of a tapered SCF coupler coupling to a Si SMWG. Figure 5(c) shows the defined parameters to be optimized for the tapered SCF coupler, including the tapered length of the tapered region and the tip diameter of the tapered SCF.
Fig. 3. The calculated effective mode index of the eigenmodes in Si SMWG, normal SCFs, and D-SCFs, showing the inherent advantage of SCF eliminating refractive index mismatch.
Fig. 4. The modal overlap integral between the lowest-order mode of (a) the normal SCF/D-SCF cut in half and the Si SMWG, where the core diameter is considered as the variable; and (b) the D-SCF with a core diameter of 420 nm and the Si SMWG, where remaining core height is considered as the variable.
Fig. 5. (a) Schematic of the overall coupling scheme, including an SMF spliced to the tapered SCF coupler. (b) Schematic of the tapered SCF coupler coupling to a Si SMWG. (c) The defined parameters to be optimized for the tapered SCF coupler, including the tapered length and the tip diameter, while the input length is fixed.
Firstly, it has been proved that adiabatic tapering can allow the mode field diameter of a commercial SMF to decrease with the diameter of the SMF [17–19]. And by employing techniques such as selective mode excitation [20], off-set launching [21], or mode field matched center launching [22], the higher-order modes excitation caused by the coupling between SMF and multimode fiber could be effectively avoided. Moreover, Fresnel reflection between a commercial SMF and an SCF can be significantly reduced by the microstructures made over the end-face of the SCF, as mentioned previously.
Next, the three-dimensional (3D) finite-difference time-domain (FDTD) method is applied to optimize the parameters and explore the difference between TE and TM. Based on the integral results from the previous section, the tip diameter is increased from 330 nm to 450 nm, with an equal interval of 20 nm. Also, based on the tapered angle, the tip diameter, and the input diameter usually achieved in experiments, the tapered length is defined as between 5 µm and 50 µm, with an increasing equal interval of 5 µm. The input length is defined as 1 µm.
Figure 6(a) shows the variation of coupling efficiency with the TE mode of Si SMWG as the tapered length and tip diameter change, respectively. The result shows that under the same tapered length, as the tip diameter gets closer to 430 nm, the interval difference of coupling efficiency becomes smaller and smaller. In addition, as the tapered length exceeds 20 µm, the coupling efficiency increases no more than 0.5%. Figure 6(b) shows that when the tapered length is fixed at 50 µm, the coupling efficiency reaches its peak at the tip diameter of 430 nm. The overall trend is in line with the expectation. When the tapered angle becomes smaller, the coupling efficiency increases more. Moreover, the short length of the tapered SCF coupler would benefit the compact packing. The optimized tip diameter slightly differs from the best value obtained from the modal overlap integral. This may be because the linear taper does not fully meet the adiabatic conditions and induce the coupling to the higher modes. The optimized tip diameter, therefore, doesn’t fully match the ideal situation in 2D simulation. However, the tapered SCF coupler still performs with excellent coupling efficiency. More importantly, the physical dimension can be obtained through experiments and has been proven in preliminary experiment.
Fig. 6. FDTD simulation shows the variation of coupling efficiency as (a) the tapered length and the tip diameter change, (b) the tip diameter changes when the tapered length is 50 µm.
The 3D FDTD simulation results in Fig. 7 show the electric field distribution change along the tapered SCF coupler. A promising low coupling loss of -0.11 dB is derived from the power monitors placed at the input of the tapered SCF coupler and the Si SMWG. To show the final results more clearly, Table 1 organizes the optimized parameters and the coupling loss for TE and TM modes. The polarization penalty is 1.8 dB, relatively comparable to other reported coupling method [14]. On the other hand, the simulation also shows little variation within the 1520∼1560 nm wavelength of C-band, due to the extremely small change in the refractive index of Si and SiO2. Furthermore, the misalignment tolerance of the optimized coupler is also calculated in FDTD, assuming the tolerable excessive loss for misalignment is -3 dB. Figure 8 shows that the x-axis misalignment tolerance is about 370 nm and the y-axis misalignment is about 340 nm. Overall, the low coupling loss promotes SCF to play a vital role in fiber-to-chip coupling. Moreover, the misalignment tolerance is large enough compared to the tip diameter of the tapered SCF coupler, which is beneficial to alignment between the tapered SCF coupler and Si SMWG.
Fig. 7. FDTD results show the electric field distribution along the propagation direction of the optimized design.
Fig. 8. Misalignment tolerance of the optimized tapered SCF coupler. The positive and negative directions of the two axes are plotted according to the definition in Fig. 5(b).
Table 1. The optimized parameters and the coupling loss for the optimized design
4. Conclusion
A novel SCF-based coupler for fiber-to-chip coplanar edge coupling is proposed. First, two kinds of couplers are investigated, namely a tapered SCF coupler and a D-SCF coupler, owing to the feasibility of their fabrication. A tapered SCF is then chosen for further optimization regarding its tip diameter and tapered length using 3D FDTD because the 2D modal overlap integral reveals that it exhibits higher coupler efficiency than a D-SCF. When operating in the C-band wavelength region, 97.5% coupling efficiency can be obtained from the optimized tapered SCF whose tapered length is 50 µm and tip diameter 430 nm. Such a compact, tapered-SCF-based coupler is expected to provide a novel alternative for light coupling commonly required between an incoming optical fiber and a silicon waveguide in silicon photonics.
Funding
National Science and Technology Council (111-2221-E-002-051-MY3, 111-2622-8-002-001, 111-2218-E-002-025, 111-2622-8-002-032, 111-3114-E-002-001, 111-2119-M-002-008, 112-2119-M-002-013, 112-2119-M-002-015, 112-2923-E-002-008-MY3); Chung-Shan Institute of Science and Technology (NCSIST-ACOM-111-6712002, NCSIST-ACOM-112-6712002); National Taiwan University (112L7860); NTUS Innovation Cooperation (11112071002); Powerchip Semiconductor Manufacturing Corporation (12H1004-C15, 12H1004-C16, 12H1004-C17); AU Optronics.
Acknowledgments
The authors are grateful for the financial assistance, supported in part by National Science and Technology Council (NSTC; the former Ministry of Science and Technology, MOST) of Taiwan, National Chung-Shan Institute of Science and Technology, National Taiwan University, NTUS Innovation Cooperation, and AU Optronics.
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.
References
1. P. Dong, J. Lee, Y. K. Chen, L. L. Buhl, S. Chandrasekhar, J. H. Sinsky, and K. Kim, “Four-channel 100-Gb/s per channel discrete multitone modulation using silicon photonic integrated circuits,” J. Lightwave Technol. 34(1), 79–84 (2016). [CrossRef]
2. C. P. Dietrich, A. Fiore, M. G. Thompson, M. Kamp, and S. Höfling, “GaAs integrated quantum photonics: Towards compact and multi-functional quantum photonic integrated circuits,” Laser Photonics Rev. 10(6), 870–894 (2016). [CrossRef]
3. K.-J. Lin and L. A. Wang, “Investigation of an In-Line Slot Waveguide Sensor Built in a Tapered D-Shaped Silicon-Cored Fiber,” Sensors 21(23), 7832 (2021). [CrossRef]
4. S. Arafin and L. A. Coldren, “Advanced InP photonic integrated circuits for communication and sensing,” IEEE J. Select. Topics Quantum Electron. 24(1), 1–12 (2018). [CrossRef]
5. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef]
6. P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V Badding, “Microstructured optical fibers as high-pressure microfluidic reactors.,” Science 311(5767), 1583–1586 (2006). [CrossRef]
7. A. C. Peacock, J. Campling, A. F. J. Runge, H. Ren, L. Shen, O. Aktas, P. Horak, N. Healy, U. J. Gibson, and J. Ballato, “Wavelength conversion and supercontinuum generation in silicon optical fibers,” IEEE J. Select. Topics Quantum Electron. 24(3), 1–9 (2018). [CrossRef]
8. F. A. Martinsen, B. K. Smeltzer, M. Nord, T. Hawkins, J. Ballato, and U. J. Gibson, “Silicon-core glass fibres as microwire radial-junction solar cells,” Sci. Rep. 4(1), 6283 (2014). [CrossRef]
9. Y. L. Yu, S. K. Laiw, H. Kishikawa, and N. Goto, “D-shaped silicon core fiber-based surface plasmon-resonance refractive index sensor in 2 µm,” Appl. Opt. 59(18), 5539–5546 (2020). [CrossRef]
10. W. C. Lu, C. H. Wu, C. Y. Yeh, C. H. Wu, C. L. Wang, and L. A. Wang, “D-shaped Silicon-cored fibers as platform to build in-line Schottky photodetectors,” IEEE Photon. Technol. Lett. 33(6), 317–320 (2021). [CrossRef]
11. Y. P. Huang and L. A. Wang, “In-line silicon Schottky photodetectors on silicon cored fibers working in 1550 nm wavelength regimes,” Appl. Phys. Lett. 106(19), 191106 (2015). [CrossRef]
12. H. Ren, O. Aktas, Y. Franz, A. F. J. Runge, T. Hawkins, J. Ballato, U. J. Gibson, and A. C. Peacock, “Tapered silicon core fibers with nano-spikes for optical coupling via spliced silica fibers,” Opt. Express 25(20), 24157–24163 (2017). [CrossRef]
13. J.-H. Chen, Y.-T. Sun, and L. A. Wang, “Reducing splicing loss between a silicon-cored optical fiber and a silica optical fiber,” IEEE Photon. Technol. Lett. 28(16), 1774–1777 (2016). [CrossRef]
14. G. Son, S. Han, J. Park, K. Kwon, and K. Yu, “High-efficiency broadband light coupling between optical fibers and photonic integrated circuits,” Nanophotonics 7(12), 1845–1864 (2018). [CrossRef]
15. Kai-Ju Lin, “The Design of Slot Waveguide Optical Fiber Sensor and Development of Tapered Waveguide Schottky Photodetector Based on D-Shaped Silicon Core Fibers,” GIPO Print 2021 (Graduate Institute of Photonics and Optoelectronics, National Taiwan University, 2021)
16. Q. Xie, Y. Chen, X. Li, Z. Yin, L. Wang, Y. Geng, and X. Hong, “Characteristics of D-shaped photonic crystal fiber surface plasmon resonance sensors with different side-polished lengths,” Appl. Opt. 56(5), 1550–1555 (2017). [CrossRef]
17. G. Son, R. A. Pradono, J. Choi, Y. Jeong, D. S. Han, M. Syahadi, Y. Jung, K. Kwon, H. Bae, and K. Yu, “Chemically-etched optical fiber tapers for adiabatic fundamental mode evolution over O-and C-bands,” J. Lightwave Technol. 40(14), 4832–4840 (2022). [CrossRef]
18. T. Alder, A. Stohr, R. Heinzelmann, and D. Jager, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000). [CrossRef]
19. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: Adiabaticity criteria,” IEE Proc. J Optoelectron. UK 138(5), 343–354 (1991). [CrossRef]
20. F. Dubois, P. Emplit, and O. Hugon, “Selective mode excitation in graded-index multimode fiber by a computer-generated optical mask,” Opt. Lett. 19(7), 433–435 (1994). [CrossRef]
21. L. Raddatz, I. H. White, D. G. Cunningham, and M. C. Nowell, “An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links,” J. Lightwave Technol. 16(3), 324–331 (1998). [CrossRef]
22. D. H. Sim, Y. Takushima, and Y. C. Chung, “High-speed multimode fiber transmission by using mode-field matched center-launching technique,” J. Lightwave Technol. 27(8), 1018–1026 (2009). [CrossRef]
