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We study the physical concept of utilizing a critical coupling to obtain a high-performance grating coupler with completely vertical emission on a silicon-on-insulator substrate. Following our design strategy, we numerically show that when our grating coupler is coupled to a standard single-mode fiber operating at 1310 nm wavelength, a −1.46 dB coupling loss, a 20 nm spectral full-width-half-maximum, and a −24 dB back reflection can be achieved at the same time without full optimization. A practical design that largely relaxes the stringent lithography requirement is also proposed and presented.
© 2015 Optical Society of America
1. Introduction
The recent advances in designing and fabricating high-performance silicon-on-insulator (SOI) grating coupler (GC) have enabled an efficient coupling between a single-mode fiber (SMF) and a sub-micron SOI waveguide. Such an approach makes low-cost packaging and wafer-level testing possible due to the fact that cleaving, polishing, and coating optical facets are no longer needed. In particular, a GC with completely vertical emission is vital for interfacing surface-emitting and receiving optoelectronic devices, and can largely reduce the packaging cost and complexity due to off-normal emission. Unfortunately, for a GC with completely vertical emission, it inevitably induces second-order diffraction that significantly enhances the backreflection and reduces the coupling efficiency. In the literature, a variety of approaches have been proposed to make a GC with completely vertical emission: Wang et al. [1] apply a slant grating configuration to reduce the second-order order diffraction; Schrauwen et al. [2] add a polymer wedge to bend the off-normal emission into completely vertical emission. Nevertheless, the compatibility of fabricating these devices with planar complementary metal-oxide-semiconductor (CMOS) processing techniques is unclear. Roelkens et al. [3] and Chen et al. [4] use a slit and a chirped grating respectively as a front mirror to cause a destructive interference between the second-order diffraction and the direct front mirror reflection; Covey et. al. introduce and optimize multi-stage gratings by a genetic algorithm [5]. Nevertheless, due to the small feature sizes, to optimally fabricate these devices often requires using e-beam lithography that is not suitable for high-volume manufacture; moreover, the designs of these devices highly rely on sophisticated numerical optimizations, and the underlying operation principle may not always applicable to general applications, e.g., when the wavelengths, polarizations, spot sizes or layer stacks are changed.
In this paper, we perform in-depth studies on a new approach to construct a high-performance SOI GC with completely vertical emission by utilizing a critical coupling [6]. The idea is based on achieving the critical coupling condition [7] between an external channel and a one-port cavity with its intrinsic loss caused by GC emission, which largely reduces the backreflection and enhances the coupling efficiency at the same time. Furthermore, our design can be regarded as a novel standing wave GC instead of the conventional traveling wave GC that exists in the literature. Using only a uniform grating, the GC field profile becomes step-function like that significantly reduces the mode-mismatch between a SMF and a GC and enhances the coupling efficiency at the same time.
In the following, we shall first discuss the physical concept and design strategy in details, and then numerically demonstrate a high-performance SOI GC with completely vertical emission. Based on the learnings, we finally propose and present a practical design that consists of only a uniform grating and a corner reflector, which largely relaxes the stringent lithography requirement while maintaining superior performances.
2. Physical concept and design strategy
Figure 1 illustrates the building blocks of our GC, in which an input waveguide is connected to a one-port cavity with a front partially reflecting mirror and a back perfectly reflecting mirror. A uniform grating is inserted into the cavity, and an output SMF is positioned above the GC. If we treat the GC emission as an intrinsic loss of the cavity, and when the cavity one-circulation loss is equal to the front mirror transmittance, a critical coupling occurs so the incident light is locked inside the one-port cavity with no backreflection returning to the input waveguide. Note that in this simplified picture, the interaction between the grating induced second-order diffraction and the recycled cavity field is unclear, which will be elaborated in the next section.
There are several key benefits of our GC. First, since we utilize a critical coupling, the backreflection that induces instability to on-chip hybrid lasers [8–10] can be in principle eliminated. Second, because the cavity field is quite uniform, an apodized grating modifying the field profile of a GC to match the mode profile of a SMF is not necessarily needed. The use of a uniform grating simplifies the GC fabrication process such as adjusting etch biases with varying grating line/space widths. Finally, our GC design concept is rather universal. A concrete design procedure can be devised and adapted to different wavelengths, polarizations, spot sizes or layer stacks.
We summarize the design procedure on how to optimize the proposed GC with completely vertical emission: 1) Select and design a back mirror featuring a close to 100% reflection. 2) Send in an optical signal to the input waveguide with the back mirror attached. Observe the standing wave pattern and identify its effective wavelength. 3) Add a grating structure on top of the waveguide, so that the grating period is almost the same as the effective wavelength of the standing wave pattern. Note that the grating length should be chosen to be comparable to the size of external coupling optics, e.g., a SMF in this paper. 4) Fine tune the grating parameters such as period, duty cycle, and etch depth, until a high directionality (i.e. “superstrate power” divided by “superstrate power plus substrate power”) and a zero far field angle (i.e. completely vertical emission) are reached at the same time. 5) Determine the one-circulation loss by measuring the power reflected from the grating structure with the back mirror attached, and then add a front mirror with transmittance equal to this one-circulation loss. Whether the condition of critical coupling is met or not can then be checked by the backreflection of the whole structure. 6) The coupling efficiency can finally be determined by measuring the power in the output SMF.
3. Exemplary design
As a proof of concept, we execute the above design procedure by simulating the structure shown in Fig. 2. All simulations done below are based on 2D or 3D finite-difference time domain (FDTD) method [11]. Transverse electric (TE) polarization is assumed. Starting with selecting a distributed Bragg reflector (DBR) as the back mirror, we design a tapered waveguide DBR to avoid the scattering loss at the waveguide-DBR boundary by gently transforming the single waveguide mode into the fundamental DBR Bloch mode [12]. The tapered waveguide DBR is constructed by 7 fully etched slits with space widths equal to 50 nm, 100 nm, 175 nm, 250 nm, and 234 nm x 4; line widths equal to 167 nm, 150 nm, 133 nm, 116 nm, and 107 nm x 3. A broadband reflection ~100% covering > 200 nm wavelength span is obtained by this arrangement. Next, a TE optical signal is sent into the waveguide with the tapered waveguide DBR attached to identify the standing wave pattern effective wavelength. The grating period of 420 nm is chosen accordingly, and the grating length of ~10 μm is chosen for later coupling to a standard SMF. To avoid the scattering loss at the waveguide-grating boundary, we apply a fin-like grating that stands on top of the silicon waveguide [13].
Fig. 2 Schematic plot of the GC with a single slit as the front mirror and a tapered waveguide DBR as the back mirror.
Before adding a single slit as the front mirror, we fine tune the grating fin height and duty cycle to optimize the GC directionality and far field angle. Note that the centers of grating fins are always positioned at the in-phase antinodes of a standing wave in these simulations. As shown in Fig. 3(a) and 3(b), it is clear that a GC featuring high directionality, i.e., the red region in Fig. 3(a), and zero far field angle, i.e., the green region in Fig. 3(b), can be found simultaneously. The reflection from the GC, i.e., 1 – one-circulation loss, is recorded in Fig. 3(c). Surprisingly, this reflection can be rather low while maintaining a high directionality and a zero far field angle at the same time, which is unexpected due to the inevitable presence of second-order diffraction. To have a deeper insight into this phenomenon, we plot the power reflected from and transmitted through the grating structure without the back mirror attached in Fig. 3(d) and Fig. 3(e), respectively. In can be observed that, in the region of zero far field angle, some fin height and duty cycle parameters (e.g. fin height of 140 nm and duty cycle of 0.7) can impose a strong grating strength causing a low transmission as well as a second-order diffraction induced high reflection. Usually, in designing a conventional traveling wave GC, such a configuration is used because a strong grating strength is required to produce a short GC field profile (~10 µm) that matches the SMF mode profile. On the contrary, in our standing wave GC, the attached back mirror creates a “double-pass” effect that allows the use of a weak grating strength (e.g. fin height of 180 nm and duty cycle of 0.55) yet still keeping a short GC field profile. Consequently, the second-order diffraction induced reflectance is diminished, and the simplified picture, e.g., treating the GC emission as the intrinsic loss of the cavity and neglecting the interaction between the second-order diffraction and the cavity field, applies reasonably well.
Fig. 3 The (a) directionality, (b) far field angle, and (c) reflection of the grating structure with the back mirror attached plotted as a function of grating fin height and duty cycle. The power (d) reflected from and (e) transmitted through the grating structure without the back mirror attached plotted as a function of grating fin height and duty cycle. Note that in all figures, the data for duty cycle < 0.2 correspond to effectively a thick (> 250 nm) SOI waveguide that shows multimode behavior and should be neglected. 2D FDTD simulations are used.
We now add a single slit as the front mirror. To design the front mirror properties, we first calculate the reflectance, transmittance and scattering loss of a single slit, and find that it’s necessary to have the slit width < 70 nm so a < 1% mirror scattering loss can be maintained. We choose the grating period/duty cycle/fin height to be 420 nm/0.54/180 nm that results into a 10.8% reflection before adding the single slit; the slit width and slit-grating distance equal to 38 nm and 188 nm are chosen accordingly. We calculate the optical powers emitted from the final GC as a function of wavelength in Fig. 4(a). The width of the GC is set to be 15 μm. It can be seen at 1310 nm wavelength, a high directionality of 85.3% can be obtained along with a low reflecting power. A Fabry-Perot fringe with a period slightly smaller than 30 nm can be observed, corresponding to a cavity length ~10 μm as expected. To calculate the coupling efficiency and the backreflection, we position a standard SMF (core index/radius = 1.45205/4.07 μm; cladding index = 1.44681; the fiber facet is coated with an anti-reflection coating) on top of the grating by 0.5 μm distance, inject a TE optical signal into the input waveguide, and then measure the mode powers into the output fiber and out of the input waveguide. In Fig. 4(b), the coupling loss, spectral full-width-half-maximum (FWHM), and backreflection are calculated as −1.46 dB, 20 nm, and −24 dB at 1310 nm wavelength, respectively. To the best of our knowledge, our GC performances are comparable to some of best GCs with off-normal emission in the literature (only one or a few etch steps involved; no bottom metallic or dielectric reflector added) in terms of coupling loss [14,15] and backreflection [13,16] but with a smaller spectral FHWM. In Fig. 4(c), we examine the near field of GC emission and a uniform plane wave with completely vertical emission can be observed. The strong field amplitude in the grating region suggests a cavity effect. In fact, the system can be conceptually regarded as a uniform “optical antenna” array in which all emitters are locked in phase, and hence a directional emission occurs at zero far field angle. In Fig. 4 (d), we examine the far field of GC emission and a nice circular pattern with its peak located at zero far field angle can be observed.
Fig. 4 (a) The optical powers emitted from the GC plotted as a function of wavelength. (b) The coupling efficiency (to SMF) and backreflection (to SM waveguide) plotted as a function of wavelength. The (c) near field and (b) far field of GC emission. All results are calculated by full 3D FDTD simulations.
4. Practical design
The example discussed in the last section has demonstrated all the essential features of our GC. However, the required fabrication accuracy due to the single slit and tapered waveguide DBR is similar to the previous proposals [3–5] in which e-beam lithography is needed. To simplify the fabrication effort, here we consider a practical design where only a uniform grating and a corner reflector present, so that the stringent lithography requirement can be relaxed. In Fig. 5(a), the concept is illustrated where a 90° corner reflector is attached after a fin-like uniform grating. Such a corner reflector functions as a retroreflector and can feature very high reflectivity given a sharp corner tip, which can be fabricated by separately etching the two corner reflector sides. It has been studied in the past to make on-chip III-V laser cavities without resorting to preparing optical facets [17]. We choose the grating period/duty cycle/fin height to be 420 nm/0.565/170 nm that results into a negligible reflection; this can be regarded as a special case of critical coupling where front mirror can be discarded. We calculate the optical powers emitted from the GC as a function of wavelength in Fig. 5(b). The width of the GC is set to be 15 μm. It can be seen at 1310 nm wavelength, a high directionality of 85.8% can be obtained along with a low reflecting power. A Fabry-Perot fringe with a period ~17 nm can be observed, corresponding to a cavity length ~17.5 μm as expected. In Fig. 5(c), the coupling loss, spectral FWHM, and backreflection are calculated as −1.66 dB, 12 nm, and −25.5 dB at 1310 nm wavelength, respectively. Again, to the best of our knowledge, our GC performances are comparable to some of best GCs with off-normal emission in the literature but with a smaller spectral FWHM. Note that although the spectral FWHM is narrower and so our GC may not be a good option for wafer-level testing purpose, it can still be used as a high-performance output coupler for single-frequency, on-chip hybrid lasers [8–10].
Fig. 5 (a) Schematic plot of the GC with a corner reflector as the back mirror. (b) The optical powers emitted from the GC plotted as a function of wavelength. (c) The coupling efficiency (to SMF) and backreflection (to SM waveguide) plotted as a function of wavelength. All results are calculated by full 3D FDTD simulations.
5. Summary
We study a new approach to construct a high-performance SOI GC with completely vertical emission by exploiting the critical coupling condition between an external channel and a one-port cavity with its intrinsic loss caused by GC emission. The physical concept and the design strategy are described in detail, and can be adapted to different wavelengths, polarizations, external coupling optics, or material platforms. To relax the stringent lithography requirement, a practical design is also introduced.
Acknowledgments
The work is supported by Forelux Inc. and National Tsing-Hua University (103A0109N6).
References and links
1. B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-on-insulator planar waveguides,” IEEE Photonics Technol. Lett. 17(9), 1884–1886 (2005). [CrossRef]
2. J. Schrauwen, S. Scheerlinck, D. Van Thourhout, and R. Baets, “Polymer wedge for perfectly vertical light coupling to silicon,” Proc. SPIE 7218, 72180B (2009).
3. G. Roelkens, D. V. Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32(11), 1495–1497 (2007). [CrossRef] [PubMed]
4. X. Chen, C. Li, and H. K. Tsang, “Fabrication-tolerant waveguide chirped grating coupler for coupling to a perfectly vertical optical fiber,” IEEE Photonics Technol. Lett. 20(23), 1914–1916 (2008). [CrossRef]
5. J. Covey and R. T. Chen, “Efficient perfectly vertical fiber-to-chip grating coupler for silicon horizontal multiple slot waveguides,” Opt. Express 21(9), 10886–10896 (2013). [CrossRef] [PubMed]
6. H.-L. Tseng, C.-W. Tseng, E. Chen, and N. Na, “A high-performance SOI grating coupler with completely vertical emission,” Proc. SPIE 8990, 899007 (2014).
7. T.-T. Wu, C.-Y. Chou, M.-C. M. Lee, and N. Na, “A critically coupled Germanium photodetector under vertical illumination,” Opt. Express 20(28), 29338–29346 (2012). [CrossRef] [PubMed]
8. A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y.-H. Kuo, and J. E. Bowers, “A distributed bragg reflector silicon evanescent laser,” IEEE Photonics Technol. Lett. 20(20), 1667–1669 (2008). [CrossRef]
9. A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, “A distributed feedback silicon evanescent laser,” Opt. Express 16(7), 4413–4419 (2008). [CrossRef] [PubMed]
10. J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15(11), 6744–6749 (2007). [CrossRef] [PubMed]
11. FDTD Solutions by Lumerical Solutions, Inc.
12. Ph. Lalanne and J. P. Hugonin, “Bloch-wave engineering for high-Q, small-V microcavities,” IEEE J. Quantum Electron. 39(11), 1430–1438 (2003). [CrossRef]
13. N. Na, H. Frish, I.-W. Hsieh, O. Harel, R. George, A. Barkai, and H. Rong, “Efficient broadband silicon-on-insulator grating coupler with low backreflection,” Opt. Lett. 36(11), 2101–2103 (2011). [CrossRef] [PubMed]
14. C. Li, H. Zhang, M. Yu, and G. Q. Lo, “CMOS-compatible high efficiency double-etched apodized waveguide grating coupler,” Opt. Express 21(7), 7868–7874 (2013). [CrossRef] [PubMed]
15. Y. Ding, H. Ou, and C. Peucheret, “Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals,” Opt. Lett. 38(15), 2732–2734 (2013). [CrossRef] [PubMed]
16. M. Antelius, K. B. Gylfason, and H. Sohlström, “An apodized SOI waveguide-to-fiber surface grating coupler for single lithography silicon photonics,” Opt. Express 19(4), 3592–3598 (2011). [CrossRef] [PubMed]
17. S. D. Smith, J. L. Fitz, and J. K. Whisnant, “CW operation of corner cavity semiconductor lasers,” IEEE Photonics Technol. Lett. 5(8), 876–879 (1993). [CrossRef]
