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Waveguide grating coupler with subwavelength microstructures Robert Halir,1,* Pavel Cheben,2,3 Siegfried Janz,2 Dan-Xia Xu,2 Íñigo Molina-Fernández,1 and Juan G. Wangüemert-Pérez1 1
Departamento Ingeniería de Comunicaciones, ETSI Telecomunicación, Universidad de Málaga, 29010 Málaga, Spain 2 Institute for Microstructural Sciences, National Research Council of Canada, Ottawa, Ontario, K1A 0RA, Canada 3
[email protected] *Corresponding author:
[email protected] Received February 9, 2009; revised April 1, 2009; accepted April 4, 2009; posted April 7, 2009 (Doc. ID 107347); published April 24, 2009 We propose a silicon waveguide-fiber grating coupler that uses a subwavelength microstructure to achieve a continuously variable grating strength yet can be fabricated using only a single etch step. By adjusting the subwavelength microstructure at every point along the grating, the grating coupler can be optimized to give high field overlap with the optical fiber mode and also minimize backreflections along the incident waveguide path. Our design example is optimized for quasi-TM mode in a silicon photonic-wire waveguide, as required for waveguide evanescent-field-sensing applications. A field overlap of up to 94% with a standard single-mode optical fiber (SMF-28) is achieved by coupler apodization. Backreflection from the grating is reduced to ⬃0.1%, and the total predicted photonic wire to fiber coupling efficiency is 50%. © 2009 Optical Society of America OCIS codes: 130.0130, 050.2770, 050.6624.
Grating couplers are an efficient means of coupling light between optical fibers and high-index-contrast waveguides [1,2]. By changing the propagation direction of light traveling in the planar waveguide to a near-normal orientation with respect to the chip surface, they enable coupling to an optical port, typically an optical fiber positioned over the coupler. In the case of an air cladding, the coupler efficiency may be estimated as C = Pu共1 − Rf兲Of ,
共1兲
where Pu is the power fraction of the incident waveguide mode that is directed toward the optical fiber, Rf is the Fresnel reflection coefficient between the fiber and the cladding medium, and Of is the overlap between the radiated field and the fiber mode. In the usual case of an air–SiO2 interface the Fresnel loss is Rf ⬃ 4%. To improve grating performance, special fabrication steps or techniques are often required. These include the use of Bragg mirrors [2], metal layers [3], subwavelength mirrors [4] or high-refractive-index claddings [5] to enhance the directionality of the grating. Backreflections due to second-order Bragg diffraction in vertically radiating structures can be suppressed with an extra trench with distinct etch
depth [6] or using slanted grating teeth [7]. Good overlaps of the radiated field with a Gaussian-like fiber mode are achieved when a second (shallow) etch depth in the grating region is combined with duty cycle apodization [2,5] and small feature sizes. Fabrication and tolerance control of such structures can, however, be challenging. In this Letter we present a single-etch grating coupler design in silicon-on-insulator platform for TM polarization, based on subwavelength gratings (SWGs), with high fiber-mode overlaps (94%) and backreflections of only 0.1%. The grating structure is shown schematically in Fig. 1(a), where the diffraction grating is formed in the longitudinal 共z兲 direction, whereas the nondiffractive SWG structure in the lateral 共x兲 direction acts as effective medium thereby controlling the strength of the grating. The waveguide core layer is fully etched to the bottom oxide cladding. Most of the previously reported designs focus on quasi-TE polarized light, since it is used in many applications involving silicon-wire waveguides. However, in evanescent-field waveguide-sensing application, TM polarization is required for maximum sensitivity [8]. Following the approach of [2], the width of grating 共W兲 was adjusted to maximize the overlap between the lateral 共x兲 profile of the
Fig. 1. (Color online) (a) Fiber-to-chip grating coupler with SWG in lateral direction. Decoupled model schematics for (b) the vertical dimension showing the first two periods of the grating and (c) the lateral dimension. 0146-9592/09/091408-3/$15.00
© 2009 Optical Society of America
May 1, 2009 / Vol. 34, No. 9 / OPTICS LETTERS
waveguide’s fundamental TM mode and the SMF-28 fiber mode (10.4 m mode diameter at 1 / e2 intensity), yielding a power overlap of 99% for W = 15 m. Since we are interested in TM polarization, the overlap was carried out with the Hx component instead of the Ex component used in [2]. The length of the taper required to create a transition with negligible loss between the 450-nm-wide Si-wire waveguide and the grating was found to be 300 m, using linear tapering. A simple grating without subwavelength microstructures was first designed as a reference structure. The operation wavelength is = 1.55 m. The duty cycle and pitch of the reference grating were determined with two-dimensional finite-difference time-domain (FDTD) simulations in the y – z plane using the RSoft simulator. The default choice for the duty cycle, which is defined as the ratio between the length of a silicon tooth and the pitch, was 50%. It was then optimized as a trade-off between reducing backreflections and maximizing the power radiated upward, for a radiation angle close to the grating vertical. The pitch 共⌳z兲 was finally adjusted to yield radiation angle of ⬃10° with respect to the grating normal. This resulted in a duty cycle of 70% and a pitch of ⌳z = 0.95 m. With this simple initial design, the fraction of incident power that is radiated upward is Pu = 55%, while about 15% is coupled to the backpropagating waveguide fundamental mode. A comparatively small 共Of = 35% 兲 power overlap is obtained for this structure because of the large grating strength. As shown in Fig. 2(a), the light is effectively radiated out of the waveguide within approximately 5 m of propagation in the grating region. The overall coupling efficiency of this structure is only C = 18%. To reduce the grating strength, we introduce a SWG structure in the lateral 共x兲 direction [Fig. 1(a)].
Fig. 2. (Color online) Radiated Hx field at a plane y = 1.5 m over the grating surface, for different coupler configurations: (a) without SWG, (b) with SWG. Fields have been shifted in the z direction for a maximum overlap with the fiber mode. The tilt angle of the fiber mode is 12° with respect to the grating normal 共y兲 in the y – z plane.
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The obvious advantage of this approach is that it requires a single etch step, hence simplifying fabrication, while it also allows for a gradual variation of grating strength, as required for apodization. Such single-etch apodization schemes have been demonstrated in integrated (Bragg) reflection gratings, where the reflection amplitude can be controlled interferometrically [9]. For our geometry [see Fig. 1(a)], assuming that the pitch of the grating in the lateral direction is ⌳x ⬍ 0 / max共neff兲, diffraction in the x – z plane is frustrated. Here 0 is the free-space wavelength and max共neff兲 is the maximum effective index encountered in the structure, which in this case is the effective index of the waveguide’s fundamental TM mode 共neff = 2.26兲. Since the grating’s width is much larger than its height, decoupled 2D models can be established in the vertical 共y兲 and lateral 共x兲 directions. As illustrated in Fig. 1(b), in the decoupled 2D model the subwavelength regions can then be approximated as effective media with effective indexes NSWG,i [10]. SWG structures have recently been implemented in edge-coupled microphotonic tapers [11] and antireflective waveguide boundaries and mirrors [12]. Since NSWG is an intermediate value between the refractive index of the cladding material (here air, n = 1) and silicon 共n = 3.476兲, the SWG effectively reduces the coupling strength of the grating. Referring to the decoupled model for the lateral 共x兲 direction in Fig. 1(c), the effective medium index of each SWG in the lateral 共x兲 direction 共NSWG,i兲 can be calculated as the effective index of the fundamental y-polarized (TM) mode of the corresponding multilayer slab [13]. We used an SWG with a rather conservative pitch of ⌳x = 300 nm and computed NSWG as a function of the width of the air gap between the silicon teeth, using the commercial Fimmwave package. The resulting effective index is shown in Fig. 3, revealing that a wide range of effective indexes can be synthesized. It is also observed (Fig. 3, inset) that effective index dispersion is very low for this SWG medium. Specifically, a gap size of 150 nm, which is easily attainable with e-beam lithography, yields NSWG = 2.73 for ⌳x = 300 nm. Using this subwavelength effective medium, we next designed a uniform grating with 17 periods arrayed along the longitudinal 共z兲 direction, consisting of alternating lines of silicon and the effective medium 共NSWG = 2.73兲, as illustrated in Fig. 1(b). Using the criterion described before, a 70% duty cycle was chosen in this case. The fiber mode
Fig. 3. (Color online) Refractive index of the effective medium created by a silicon SWG with a pitch of ⌳x = 300 nm, as a function of air gap. TM polarization is assumed.
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overlap was increased to 73% [Fig. 2(b)], which doubles the overlap attained without SWG. Since all grating teeth are identical, the radiated field is a plane wave, and hence its phase increases linearly along the grating [see Fig. 2(b)]. The mode overlap remains though limited by the exponential near-field profile along the z direction for this nonapodized grating, whose maximum theoretical overlap with the Gaussian profile is 80% [1]. The radiation angle for a pitch of ⌳z = 0.84 m is 11.5°, and the directivity of the grating does not vary appreciably, yielding an improved coupler efficiency of 38%. Furthermore, since the Fresnel reflection coefficient at the silicon– SWG boundary is now reduced, the power coupled to the backpropagating waveguide mode is ⬍1%. To further validate the performance of this structure, a three-dimensional (3D) FDTD simulation was carried out. Owing to computational constraints it was not possible to simulate the entire grating region. We overcame this limitation by simulating one period of the lateral SWG along the full length of the coupler using periodic boundary conditions, as illustrated in Fig. 1(a). This mimics a structure extending infinitely in the lateral 共x兲 direction, hence taking into account the effect of the SWG. We found that the radiated Hx field is virtually constant in the lateral 共x兲 direction, so that the SWG can indeed be considered an effective medium. The calculated overlap with the fiber mode is 74%, with a radiation angle of 11°, both being in excellent agreement with the 2D simulations. In the final step of coupler optimization, we use the SWG effect to continuously apodize the coupler in order to achieve a near-Gaussian outcoupled field matching the SMF-28 fiber. Using a variable SWG index along the grating requires that the pitch [⌳z,i, see Fig. 1(b)] of each longitudinal 共z兲 period be adjusted to eliminate phase errors; i.e., ensure that all elements radiate in the same direction [14]. Taking into account this consideration and using a linear variation from NSWG = 3.3 to NSWG = 2 along the 17 longitudinal 共z兲 periods of the grating, we obtained an excellent fiber mode overlap of 94% [see Fig. 2(b)], with a radiation angle of 12° with respect to the grating normal. These results were again verified by 3D FDTD simulations, yielding an overlap of 92% and a radiation angle of 11.5°. The phase of the radiated field is linear [see Fig. 2(b)], which shows that the pitch of each period was adjusted properly. With the default duty cycle of 50%, the coupler radiates Pu = 56% of the incident power upward, while only 0.1% of light is reflected back in the waveguide. These improved values are attributed to the grating apodization. Since in the design of the two previous grating structures we found that with the comparatively simple layer structure considered, achieving more than 55% of upward
power is difficult, no further duty cycle optimization was carried out. The total estimated coupling efficiency of this design is C = 50%. The grating directionality and thus overall efficiency could be further increased by techniques mentioned above; however, this would imply increased fabrication complexity. The coupling characteristics of this grating are adequate for many practical applications and are achieved with a simple structure, that does not require special etches or layer structures. Feature sizes are within the range of e-beam lithography and could still be increased by choosing a larger SWG pitch 共⌳x兲. The principle of grating engineering by SWG structuring demonstrated here is indeed of a broader relevance to other types of grating geometries and waveguide platforms. This work has been supported by the National Research Council of Canada (NRC) Genomics and Health Initiative, the Spanish Ministerio de Ciencia e Innovación under project TEC2006-02868, a Formación del Profesorado Universitario scholarship AP2006-03355, and by the Andalusian Regional Ministry of Science, Innovation and Business under project TIC-02946. References 1. T. Tamir and S. Peng, Appl. Phys. 14, 235 (1977). 2. D. Taillaert, P. Bienstman, and R. Baets, Opt. Lett. 29, 2749 (2004). 3. F. Van Laere, G. Roelkens, J. Schrauwen, D. Taillaert, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, in Optical Fiber Communication Conference and Exposition and The National Fiber Optics Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper PDP15. 4. P. Cheben, S. Janz, D.-X. Xu, B. Lamontagne, A. Delâge, and S. Tanev, IEEE Photon. Technol. Lett. 18, 13 (2006). 5. G. Roelkens, D. Van Thourhout, and R. Baets, Opt. Express 14, 11622 (2006). 6. G. Roelkens, D. Thourhout, and R. Baets, Opt. Lett. 32, 1495 (2007). 7. B. Wang, J. Jiang, and G. Nordin, IEEE Photon. Technol. Lett. 17, 1884 (2005). 8. A. Densmore, D. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. Schmid, and E. Post, IEEE Photon. Technol. Lett. 18, 2520 (2006). 9. T. Mossberg, C. Greiner, and D. Iazikov, Opt. Express 13, 2419 (2005). 10. S. M. Rytov, Sov. Phys. JETP 2, 466 (1956). 11. P. Cheben, D. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006). 12. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delâge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, Adv. Opt. Technol. 2008, 1 2008. 13. P. Lalanne and J. Hugonin, J. Opt. Soc. Am. A 15, 1843 (1998). 14. P. Bock, P. Cheben, A. Delâge, J. H. Schmid, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 16, 17616 (2008).
