We describe the coupling between optical modes of silicon-on-insulator SOI waveguides and Ge/SiGe quantum well modulators using an eigenmode expansion method. Laterally tapered features in the epitaxial layers are investigated for adiabatic optical coupling, and we find that there is a critical width range of the Ge/SiGe structure of 200–300 nm, where the taper angle should be minimised. We identify optimised taper profiles, which, for 1-μm-wide waveguides, allow the length of an adiabatic taper to be reduced from 250 μm for a simple linear profile to 40 μm for the optimised structure.
© 2012 Optical Society of America
There has been growing interest in Ge and SiGe active optical devices integrated with silicon-on-insulator (SOI) waveguides for applications including optical interconnects. Waveguide-integrated Ge and SiGe Franz-Keldysh electroabsorption modulators have recently been demonstrated [1–4], as well as considerable progress towards waveguide-integrated Ge/SiGe quantum well modulators [5, 6]. The recent demonstration of an electrically-pumped Ge-on-Si laser has intensified research efforts towards an SOI waveguide integrated Ge laser, which would be of particular interest both because of the wafer-scale epitaxial fabrication and because of the favourable predicted temperature performance of such devices .
The most common SOI waveguide platforms employ either 220 nm or 400 nm silicon layers . The inclusion of a Ge or SiGe layer on top of this SOI waveguide core, which is typically several hundred nanometers thick, results in a number of optical modes in the out-of-plane direction becoming allowed. Fig. 1 shows the fundamental optical modes for a 400-nm-thick SOI strip waveguide and a 900-nm-thick Si0.1Ge0.9 epilayer at 1550 nm, which is the typical total height of a Ge/SiGe quantum well modulator structure grown on a relaxed SiGe virtual substrate [9, 10].
The second and third order modes shown in Fig. 1 overlap strongly with the fundamental mode of the SOI waveguide. It follows that, if there were an abrupt transition between the two waveguide systems, optical power would couple from the fundamental mode of the SOI waveguide into multiple higher-order modes of the Ge/SiGe waveguiding section. These modes will propagate coherently, leading to multi-mode interference behaviour and the optical intensity will oscillate in the out-of-plane direction as it propagates along the SiGe-on-SOI waveguide, in a similar way to that described by Rouviere et al. for vertically-coupled Ge waveguide photodiodes . Such behaviour is not a significant problem for photodiodes as we do not wish to recover the incident light; however it is much more important in waveguide modulators where keeping the insertion loss to a minimum is one of the most critical design parameters. If the resulting optical intensity does not overlap well with the output SOI waveguide then most of the light will be reflected and a large insertion loss will result.
If the incident power is in the fundamental mode of the SiGe waveguide section, as may be expected for a SiGe waveguide modulator, most of the power at the SiGe-on-SOI/SOI interface will be reflected or scattered into the waveguide cladding layers, and only a small amount of the light will be transferred into the SOI waveguide.
Coupling between different optical waveguide core layers in III–V based photonic integrated circuits (PICs) is typically designed using the framework of coupled mode theory, where a low-refractive-index dielectric spacer layer is included between the two waveguide core layers. This allows the presence of the second waveguide core layer to be treated as a perturbation to the first . In hybrid integration of III–V lasers with SOI waveguides, tapered mode adaptors can be used to transform the modes between the waveguide and the device section [13, 14]. In the hybrid laser system, the gain medium and the underlying SOI waveguide are separated by a dielectric spacer layer. The system is typically designed so that either there is evanescent coupling between the SOI guided mode and the active layer , or to achieve phase matching between the two waveguides .
The Ge or SiGe epitaxial growth schemes that have been demonstrated for active photonics devices on silicon rely on a Ge or SiGe seed layer, which is grown directly onto the Si surface [9, 17]. Furthermore, the epitaxy does not allow for the insertion of a low-n dielectric spacer layer. In these epitaxial systems coupled mode theory is not a convenient description of the optical coupling between the SOI waveguide and the Ge or SiGe waveguiding layers, as we cannot consider the modes of the SOI waveguide and those of the SiGe device layer to be weakly interacting.
We study the optical mode propagation at the interfaces of a vertically-coupled SiGe-on-SOI waveguides using an eigenmode-expansion method . We focus on Ge/SiGe quantum well waveguide modulators and identify design criteria for efficient optical coupling between waveguides using lateral tapers, which may be fabricated using standard optical lithography and dry etching techniques. The vertically-coupled laterally-tapered device is shown schematically in Fig. 2, where the tapered SiGe waveguide section transforms the mode between that of the access waveguide and the device. The device is designed so that the power is always in the fundamental optical mode of the composite structure at all points along the taper. Furthermore, because the taper is discontinuous in one of the directions transverse to the propagation direction (i.e., the direction normal to the plane of the wafer, where there is a step change in the hight of the waveguiding structure) conventional adiabatic taper theory  does not adequately describe this system. The structure acts as an adiabatic mode converter  rather than the conventional adiabatic taper. First, we consider the optical coupling loss, which results from the optical coupling between the modes of the SOI waveguide and the modes of the larger SiGe-on-SOI waveguide (in other words, we examine the coupling efficiency between the fundamental optical mode of the SOI waveguide and the modes of the SiGe mesa active device). This is calculated by neglecting the material lossess that result from interband absorption and free carrier absorption. Then we calculate the overall insertion loss of the structures by including the material losses in the different layers.
The coupling loss as a function of the taper length for a vertically-coupled linearly-tapered SiGe layer is shown in Fig. 3(a) for an Si strip waveguide (and device) width of 1 μm. We find that the taper becomes adiabatic when the length reaches 250 μm. In general, it is desirable to have compact features for integrated optical devices, which reduces the area of semiconductor material required, and especially in a modulator where the overall length may place limits on the insertion loss, and may also place limits on the capacitance (as, for a given device width, the capacitance will scale with the length). Fig. 3(b) shows the fifteen lowest order TE modes of the structure as a function of the width of the SiGe layer, wSiGe. When wSiGe ∼ 0.2μm we can see that a number of higher order modes start to appear. These modes are the confined optical modes associated with the SiGe layer. Because this waveguide is considerably thicker than λ/2n, as wSiGe increases a number of vertical modes appear almost simultaneously. The sudden appearance of these vertical modes defines a region over which the dimensions of the structure must be varied slowly along its length; if the taper angle is too large here, the higher order modes will be excited by the incoming fundamental mode of the SOI waveguide. To prevent these higher order modes from being excited, it is important to maintain a shallow taper angle in this region where they appear, i.e., when wSiGe ∼ 0.2 μm. As wSiGe increases beyond about 0.3 μm, although more modes appear, these are higher order lateral modes of the structure, and as such tend not to be excited owing to the lateral symmetry of the structure and the parity of the modes. Therefore the taper angle can increase when wSiGe > 0.3 μm.
We can also gain some insight into how the taper behaves by analysing the electric field profile within the linear taper at the length when it becomes adiabatic. Figure 4 shows this in the 300-μm-long taper on the 1-μm-wide Si strip waveguide. The optical power transfer from the Si strip waveguide section into the SiGe occurs between 60 and 90 μm along the taper, i.e., when 0.2 < wSiGe < 0.3μm. Furthermore, because there is little power transferred when wSiGe < 0.2 μm, and since the bound optical modes of the SiGe epitaxial layer do not appear when wSiGe < 0.2 μm, it is not critical for the tip to be sharp. This has implications for the fabrication of such devices, as the tip of the structure can be up to 200-nm-wide without having a significant effect on the coupling loss. We arrive at an optimised taper function, shown in Fig. 5(a), such that there are no discontinuities in the taper angle, and where the taper angle is minimised in the range 0.2 < wSiGe < 0.3 μm.
The optical propagation through this taper profile is shown in Fig. 5(b) as a function of the length of the taper. The solid curve shows the coupling loss between the fundamental mode of the SOI waveguide and the fundamental mode of the device, and the dashed curve shows the coupling loss for a pair of tapers separated by a 100-μm-long SiGe-on-SOI mesa (i.e., S21 between incoming and outgoing SOI waveguides). We can see that, for tapers shorter than 40 μm, there are oscillations in the coupling loss, which indicates that multiple modes are excited. However, when the taper length exceeds 40 μm, these disappear, indicating that only the fundamental mode of the SiGe mesa is excited. The electric field intensity for a 40-μm-long taper using this profile is shown in Fig. 6. The optical coupling between the SOI waveguide and the device occurs throughout the length of the taper, and so we can consider it to be more efficient than the linear taper.
In order to determine the insertion loss of the tapers, we included layer losses for free carrier absorption in the doped layers and for indirect absorption in the MQW layers. The former are taken from Ref.  and the latter from Ref. , and are listed in Table along with the real part of the refractive indices used in the calculations. Including these layer losses results in the curves shown in Fig. 7, which show the insertion loss in coupling between the fundamental mode of the SOI waveguide and the fundamental mode of the Ge/SiGe waveguide, i.e., the loss from a single taper. The losses at the lengths corresponding to the point at which the tapers become adiabatic, i.e., 250 μm for the linear taper and 40 μm for the optimised taper, are 2.7 dB and 0.3 dB, respectively. The reason for the large improvement in the insertion loss that results from the use of the optimised tapers is that the taper can be so much shorter, which reduces the losses from the material absorption in the epitaxially-grown layers.
We have described a design approach to obtain short adiabatic vertically-coupled laterally-tapered mode adaptors. We find that, for Ge/SiGe on SOI waveguide modulators, the length required for adiabatic mode conversion between 1-μm-wide waveguides can be reduced from 250 μm to 40μm by optimising the design of the taper profile. When we included the material losses in the epitaxial layers, we find that this corresponds to a change from 2.7 dB to 0.3 dB per taper. For the Ge/SiGe-on-SOI structures considered here, we find that when wSiGe < 0.2 μm there is very little coupling between the SOI mode and the Ge/SiGe mode; that there is a critical width of 0.2 < wSiGe < 0.3 μm where the taper angle must be small; and furthermore, when wSiGe > 0.3 μm the angle can become much larger. Although we have focussed on Ge/SiGe waveguide modulators, the analysis also applies for vertically-coupled waveguide integrated Ge lasers and Ge Franz-Keldysh modulators.
This work has been funded by the Engineering and Physical Sciences Research Council (EPSRC) programme, “UK Silicon Photonics.”
References and links
1. J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008). [CrossRef]
2. A. E.-J. Lim, T.-Y. Liow, F. Qing, N. Duan, L. Ding, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Novel evanescent-coupled germanium electro-absorption modulator featuring monolithic integration with germanium p-i-n photodetector,” Opt. Express 19, 5040–5046 (2011). [CrossRef] [PubMed]
3. N. Feng, D. Feng, S. Liao, X. Wang, P. Dong, H. Liang, C. Kung, W. Qian, J. Fong, and R. Shafiiha et al., “30GHz Ge electro-absorption modulator integrated with 3μm silicon-on-insulator waveguide,” Opt. Express 19, 7062–7067 (2011). [CrossRef] [PubMed]
4. Y. Tang, J. D. Peters, and J. E. Bowers, “Over 67 GHz bandwidth hybrid silicon electroabsorption modulator with asymmetric segmented electrode for 1.3 μm transmission,” Opt. Express 20, 11529–11535 (2012). [CrossRef] [PubMed]
5. S. Ren, Y. Rong, S. Claussen, R. Schaevitz, T. Kamins, J. Harris, and D. Miller, “Ge/SiGe quantum well waveguide modulator monolithically integrated with SOI waveguides,” IEEE Photon. Technol. Lett. 24, 461–463 (2012). [CrossRef]
6. P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. L. Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20, 3219–3224 (2012). [CrossRef] [PubMed]
7. R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20, 11316–11320 (2012). [CrossRef] [PubMed]
8. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metaloxidesilicon nanophotonics,” Nano. Lett. 10, 2922–2926 (2010). [CrossRef] [PubMed]
9. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437, 1334–1336 (2005). [CrossRef] [PubMed]
10. L. Lever, Z. Ikonić, A. Valavanis, J. Cooper, and R. Kelsall, “Design of Ge-SiGe quantum-confined stark effect electroabsorption heterostructures for CMOS compatible photonics,” J. Lightwave Technol 28, 3273 –3281 (2010).
11. M. Rouviere, M. Halbwax, J.-L. Cercus, E. Cassan, L. Vivien, D. Pascal, M. Heitzmann, J.-M. Hartmann, and S. Laval, “Integration of germanium waveguide photodetectors for intrachip optical interconnects,” Opt. Eng. 44, 075402 (2005). [CrossRef]
12. L. Coldren, S. Corzine, and M. Mashanovitch, Diode Lasers and Photonic Integrated Circuits (Wiley, 2012). [CrossRef]
13. M. Lamponi, S. Keyvaninia, F. Pommereau, R. Brenot, G. de Valicourt, F. Lelarge, G. Roelkens, D. V. Thourhout, S. Messaoudene, J.-M. Fedeli, and G.-H. Duan, “Heterogeneously integrated InP/SOI laser using double tapered single-mode waveguides through adhesive die to wafer bonding,” Proceedings of Group IV Photonics22–24 (2010).
14. B. B. Bakir, A. Descos, N. Olivier, D. Bordel, P. Grosse, E. Augendre, L. Fulbert, and J. M. Fedeli, “Electrically driven hybrid Si/III-V Fabry-Pérot lasers based on adiabatic mode transformers,” Opt. Express 19, 10317–10325 (2011). [CrossRef] [PubMed]
16. X. Sun and A. Yariv, “Engineering supermode silicon/III-V hybrid waveguides for laser oscillation,” J. Opt. Soc. Am. B 25, 923–926 (2008). [CrossRef]
17. L. Colace, G. Masini, F. Galluzzi, G. Assanto, G. Capellini, L. Di Gaspare, E. Palange, and F. Evangelisti, “Metal–semiconductor–metal near-infrared light detector based on epitaxial ge/si,” Appl. Phys. Lett. 72, 3175–3177 (1998). [CrossRef]
18. “Photon Design,” www.photond.com.
19. J. Love, W. Henry, W. Stewart, R. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. I. adiabaticity criteria,” Optoelectronics, IEE Proceedings J 138, 343–354 (1991). [CrossRef]
20. T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-loss converters between optical silicon waveguides of different sizes and types,” IEEE Photon. Technol. Lett. 18, 709–711 (2006). [CrossRef]
21. J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44, 49–50 (2008). [CrossRef]