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New wide single mode strip and grating loaded waveguide on thin silicon-on-insulator CMOS compatible structure is proposed and analyzed. Waveguide is built by silicon nitride strip and gratings placed on silica cover of slab silicon. This structure is similar to conventional strip-loaded waveguide but differs by additional gratings near the strip sides. Numerical 3D simulations by FDTD and BPM prove that the side gratings with period 0.6 µm and depth 0.16 µm provide the high Figure of merit for higher order mode suppression and built quasi-single-mode waveguide with mode size ~10 µm and propagation loss ~0.3 dB/cm.
©2009 Optical Society of America
1. Introduction
Silicon photonics [1] belongs to the most perspective technologies to manufacture different optical elements that could find multiple applications in fiber-optic communication, sensors and optical data processing. Most of optical devices are based on the effect of optical interference and inherently use single-mode optical waveguides. Currently, the two types of such waveguide are practically used in silicon-on-insulator (SOI) structures: (1) rib etched in thick (~3–8 µm) slab silicon [2] and ridge silicon wire [3–5] built in thin (~220 nm) silicon (referred below as thin SOI). The first type of single-mode waveguides could be rather wide (~3–8 µm) that simplified coupling to optical fibers. Silicon wire has a small cross section (~450 nm) and its manufacturing is compatible with semiconductor CMOS technology [3].
Fiber-to-wire waveguide couplings are typically arranged by nano-size two-dimensional gratings [6] etched in thin SOI that also provide the possibility of polarization diversity [7] without polarization splitters and rotators. This 2D-grating element is very compact and couples orthogonal modes from the single-mode optical fiber into two quasi-TE modes of two crossed ridge waveguides, which could be connected to input/output of the photonic integrated circuit. However, the grating area in the ridge waveguide can be rather large, i.e. 10 µm, so experiencing a strongly multi-mode behavior. Thus, real devices contain adiabatic couplers that transform wide ridge waveguides to single-mode silicon photonic wires, ~450 nm wide. Wide optical waveguides are also needed to provide the small optical loss of waveguide crossing [8] as well as for implementation in multi-reflector filtering technology [9,10].
Unfortunately, the high index contrast of silicon/silica prevents manufacturing of wide single-mode waveguides on thin SOI structures that are most promising for the mass production and incorporating optical and electronic components on silicon substrate by CMOS compatible technology [3]. For example, the novel wide (~15 µm) and ultra-low loss (~0.006 dB/m) hollow-core waveguide [11] uses subwavelength high-contrast gratings as a high reflectivity glancing incidence mirror for the guided wave. But this multimode waveguide has a very small suppression of the first mode (loss ~0.057 dB/m) relative to the fundamental mode that makes the use of this waveguide impossible in many applications.
Recently we proposed [12–15] the new design of wide heterogeneous waveguide built in thin SOI. The advantage of heterogeneous waveguide comes from the use of additionally doped regions at both sides of wide (~20–35 µm) silicon rib that provides strongly mode-dependent optical propagation loss due to different penetration of optical field in the high loss doped regions with the high concentration (~9.2×1017 cm-3) of free charges. This makes a wide (mode size ~10 µm) heterogeneous waveguide quasi-single-mode. Heterogeneous waveguides are CMOS compatible and could be used with multi-reflector technology [13–15] to develop widely tunable filters and reconfigurable optical add/drop multiplexers (ROADMs) with thermo-optic control of multi-hundreds wavelength channels with 10 µs switching time. Unfortunately, these devices have not been experimentally demonstrated, as their manufacturing requires a parallel access to nanophotonic and microelectronic semiconductor technologies simultaneously.
The aim of the current paper it to set and to examine the new design of wide quasi-single-mode waveguide based on conventional optical technology. The new waveguide is expected to have superior parameters related to heterogeneous waveguide and will keep all the advantages of the latter. Namely, its technology has to be CMOS compatible and could be used in the future to manufacture multi-reflector filtering devices (filters and multiplexers) [13–15]. The new waveguide design was examined by multiple numerical simulations by finite difference time domain (FDTD) method and by beam propagation method (BPM) with the RSoft’s commercial software tools FullWAVE and BeamPROP, respectively [16].
2. Strip and grating loaded waveguides in thin SOI
From the very beginning of integrated optics, the great efforts had been made to develop the technologies of channel optical waveguides. Among the others, the strip-loaded waveguide [17] was introduced and studied. It contains a planar slab waveguide with the strip cover that has the refractive index higher than the surrounded media. Unfortunately, this technology could not be directly applied for devices based on the high-contrast SOI-structures that could contain deep isolating groves to prevent thermal spread [18]. Thus, strip cover can be built on a wide multi-mode rib waveguide that makes this strip loading waveguide also multimode.
In order to resolve the contradiction between the wide waveguide size (~10 µm) and the demand to have the single supported mode, we propose to use the similar conception as that used to construct a heterogeneous waveguide [12]. Namely, near the waveguide sides, we insert the additional high-loss areas built by the conventional gratings that radiate the light from the waveguide. The new design of strip and grating loaded (SGL) waveguide is shown in Fig.1. In order to simplify the manufacturing technology, we use the same film cover both for the loading strip and for the loading grating. The following notations for the structure design are used: h 0 is the rib height; hc is the depths for the buffer; d is the depth of the strip (and the grating); W, Wg0, and Wg are the width of strip, grating and spacing between strip and grating, respectively; W0=W+2(Wg0+Wg) is the total width of the rib part of waveguide.
Fig.1. General view of SGL waveguide and the field distribution of the two first guided TE-modes studied by 3D BPM. a) m=0; b) m=1. d=0.16 µm, hc=0.12 µm; W0=32 µm, W=10 µm, Wg=2 µm.
Fig.2. Simulation of rectangular shaped grating by FDTD. a) general view of the 2D waveguide with the grating loading; b) Optical loss in 2D waveguide with the grating for different values of hc and d (dots and curves corresponds to FDTD and BPM simulations, respectively); (c) Optical loss in 3D SGL waveguide obtained by different ways: 1- 3D FDTD, 2 – 3D BPM for equivalent waveguide; 3 - 3D BPM for equivalent waveguide with corrected (by 1.13) value of ni.
For the first examination of the device conception, we chose the silicon nitride (Si3N4) as the material for the loading film (refractive index n 2=2.0) and silica (n1=1.447) for the buffer between the rib silicon waveguide (h0=220 nm) and the loading. The description of manufacturing technology may be found elsewhere [4, 19]. A thick (~2 µm) buried oxide (BOX) layer of SOI (not shown on the Fig.1) prevents optical leakage into the silicon substrate. The grating (see Fig2a) has the period D=0.6 µm and the rectangular shape strips (with filing factor f=0.5) located perpendicular to the waveguide axis. It is proposed that grating is etched through the total height d of the cover film and then is over-covered by silica. This will eliminate the possible problem of precise stop of silicon nitride etching that otherwise could significantly disturb waveguide parameters.
We predict that SGL waveguide will have very small optical loss (~0.5 dB/cm) thus the total dimension of 3D structure under the study has to be very large, which makes it a great problem to apply directly any known software tool in order to examine its optical properties. At the same time, this waveguide arrangement is well suitable to examine by 3D BPM except the subwavelength grating areas that are out of the method possibilities. In order to find a reliable way to study this complicated optical task, we propose to substitute the real structure by the almost optically equivalent artificial model that replaces the grating by the properly designed strip with complex refractive index.
Let us follow the effective medium theory (EMT) [20] that approximates the subwavelength periodic structure by an optically anisotropic thin film. For ordinary and extraordinary optical waves, the refractive indexes are determined by weighted average of permittivities and reciprocal permittivities, respectively [20, 21]:
where f is the filling factor of the medium 2. The grating coupler in thin SOI waveguide typically works only with the single TE polarization [6, 7]. Here we also regard only TE polarization and thus equivalent structure has real refractive index no plus the imaginary part ni that is determined by the optical decay due to the coupling to radiation modes.
Note that a typical SGL waveguide has the high ratio of horizontal and vertical dimensions (W0/h0~100) that makes it possible to use 2D approximation and FDTD method for the study. The general view of the simulated structure is presented in Fig.2a. At first, using 2D FDTD we numerically determine the propagation loss in the grating loaded waveguide with arbitrary parameters d and hc (see Fig.2b). Then we replace grating by the film with the complex refractive index ng=no+ni and determine its effective mode index Nef by 2D BPM. By comparing the data obtained by FDTD and by BPM we find those values of ni that give the same values of loss (with 0.5% deviation) for all the parameters d and hc used.
The artificial model of the equivalent structure and the 2D approximation are verified by 3D FDTD numerical experiment with the simulation grid 0.4 µm, 0.04 µm, 0.05 µm along horizontal, vertical and propagation directions, respectively. At first, we find propagation loss in the test silicon rib waveguide with the grating loading. The loss is determined by the analysis of decay of the overlap integral of guided modes with FDTD field that was measured at 9 equidistant spacing cross sections. The test waveguide has the parameters: W0=10 µm, Wg0=9 µm, hc=0.12 µm, d=0.16 µm, Loss=37.5 dB/cm. Then, according to the above-described procedure, we find the parameters of the equivalent waveguide and determine optical loss by 3D BPM: no=1.7455, ni=0.0163, Loss=32.7 dB/cm. The comparison of this and the other results for different hc shows that equivalent model and the 2D approximation of the test strip waveguide with grating loading provides a moderate error about 13%. Note that the optical loss is a liner function of ni and for 3D case this error could be corrected by a 1.13 times increase in the equivalent value ni determined from 2D simulations.
The next stage is to get a general verification of the equivalent 3D model of strip and grating loaded waveguide. For this aim, we make simulations of optical loss in short SGL waveguide that contains 120 grating strips by 3D FDTD and in the equivalent waveguide by 3D BPM (see Fig.2c). Multiple simulations of SGL waveguide with different parameters show that the typical error of loss measurement by 3D FDTD of SGL structure is about 0.5 dB/cm. Data of Fig.2c proves that SGL waveguides are single mode, and the model of equivalent structure is correct and is suitable for detailed analysis of these waveguides by 3D BPM.
The typical optical field distributions for the two first guided modes are presented in Fig.1. One can see that the fundamental mode is confined within the area under the loading strip and only a small part of optical energy spreads out into the grating lossy areas. Conversely, the optical field of the first (and all other) mode has the great portion in the grating that causes a strong decay (similar to heterogeneous waveguide [12]). This effect produces strongly mode-dependent optical loss (see Fig.2c) and makes the foundation of SGL waveguide.
3. Optical properties of strip and grating loaded waveguides on SOI
Optical loss of strip and grating loaded waveguide depends on multiple parameters, namely, refractive indexes and sizes of all elements that form its structure. Actual waveguide will have a contribution to the optical loss caused by light scattering due to the technology imperfections. We will take into consideration the latter one by the phenomenological parameter of slab loss (SLoss). Our task is to find such a combination of these parameters which will provide small propagation optical loss for the fundamental mode and the high loss for all other modes. Our simulations show that for the most interesting cases the two first modes provide the minimum values of optical loss, thus only these two modes (m=0 and m=1) will be used for the further analysis. We choose the most reliable case that could be easily used for construction of slanted ROADM with high tuning rate that implement large spacing (>33 µm) of the waveguide array [13]. It should be mentioned that the larger total waveguide width W0, the smaller optical loss and the better figure of merit for higher order mode suppression. Thus, we use the sub-optimum value W0=32 µm for our analysis. It could be used for ROADM that will provide an increase at least by a factor of 5.5 (relative to other devices on the same material) in the wavelength tuning rate (δλ/δT) over the temperature [13–15]. Figure 3 presents the results of 3D BPM simulations of the equivalent SGL waveguide for different dimensions of the ideal structure with SLoss=0. One can see that the losses for the first two modes are strongly different and depend on the buffer height hc and lateral spacing Wg between the strip and the grating.
Fig.3. Simulated parameters of optical loss in ideal SGL waveguide (SLoss=0) studied by 3D BPM. a) For the fundamental mode (m=0); b) For the first mode (m=1). d=0.16 µm, W0=32 µm, W=10 µm.
In order to find a sub-optimum combination of structure parameters, let us analyze the Figure of merit for higher order mode suppression by introducing the parameter of the additional optical loss: AdLoss=Lc×Loss1- 3dB. It is stated as difference in loss of the first guided mode (Loss1) relative to the fundamental one (Loss0) that will take place for the waveguide of characteristic length Lc=3dB/Loss0 that corresponds to -3dB loss of the fundamental mode. Actual waveguide has some level of scattering loss (SLoss > 0) caused by the technology imperfections that has to be added to the simulated loss shown in Fig.3. The additional optical loss as the function of slab waveguide scattering loss is presented in Fig.4a. Very high waveguide quality (SLoss ~0.1 dB/cm) could be provided by the modern technology [22], thus for this case the best higher order mode suppression (~-60 dB) corresponds to the case Wg~3 µm. The results of simulation of the additional loss for the different waveguide parameters (for SLoss=0.1 dB/cm) are shown in Fig.4b. One can find that sub-optimum will be any SGL waveguide that has the buffer height hc ~0.12 µm. Depending on the spacing Wg one can obtain different loss for the fundamental mode as well as different Figure of merit for higher order mode suppression that is much higher than could be obtain for the heterogeneous waveguide (AdLoss ~20–30 dB) [13].
Fig.4. Simulated parameters of the additional optical loss in SGL waveguide studied by 3D BPM. a) as a function of waveguide spacing Wg for different Sloss (in dB/cm units) for hc=0.12 µm; b) as a function of hc for different Wg (SLoss=0.1 dB/cm). d=0.16 µm, W0=32 µm, W=10 µm.
For the design of any particular filter, ROADM or any other optical elements, one has to use the value of Wg that makes the best compromise between total optical loss and higher order mode suppression. Thus large Wg=3 µm that provides the best Figure of merit (see Fig.4a for SLoss=0.1 dB/cm) is preferable to use for the very long structures (L>3 cm). Say, L=3.1 cm provided the total loss -1 dB and the suppression of the first mode -20 dB (relative to fundamental one). The smaller structures need to use the smaller Wg in order to have sufficiently good higher order mode suppression through the device. For example, for the waveguide length 1.6 cm it is better to use Wg=2 µm that will provide also the small total loss -1 dB and moderate mode selection -14.5 dB. Note that the variation of the strip height d has a very small effect on the optical loss thus the waveguide parameters are very stable to the possible technology error in deposition of the silicon nitride film cover.
4. Conclusion
This paper presents the new design of novel strip and grating loading waveguide build by the silicon nitride strip and grating cover on the silica buffer over the slab SOI. In order to study optical properties of this 3D subwavelength structure the equivalent homogeneous waveguide was set up and analyzed by 3D BPM. The validity of this assumption was verified by direct 3D FDTD simulations. New waveguide could be manufactured by CMOS compatible technology and provides very small optical propagation loss (~0.5 dB/cm) and the high Figure of merit for higher-order mode suppression that makes wide waveguide (mode size ~10 µm) really single-mode. The new SGL waveguide is very interesting for practical implementation in multiple nanophotonic optical elements, including widely tunable ROADMs based on multi-reflector filtering technology, 2D grating couplers and different structures with waveguide crossing. We believe that this paper will stimulate intensive experimental investigations over strip and grating loading waveguides and their applications.
Acknowledgments
The author thanks Company RSoft Design Group, Inc. [16] for providing user license and technical support for Rsoft Photonic CAD Suite 8.0.
References and links
1. G. T. Reed, Silicon Photonics. State of the art (John Wiley & Sons, Ltd, 2008).
2. R. A. Soref, J. Schmidtchen, and K. Petermann, “Large Single mode rib waveguides in GeSi-Si and Si-on-SiO2,” J. Quantum Electronics 27(8), 1971–1974 (1991). [CrossRef]
3. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]
4. R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, “Low-loss silicon-on-insulator shallow-ridge TE and TM waveguides formed using thermal oxidation,” Appl. Opt. 48(5), 958–963 (2009). [CrossRef]
5. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009). [CrossRef]
6. D. Taillaert, Harold Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15(9), 1249–1251 (2003). [CrossRef]
7. W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, “A polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic wires,” Opt. Express 15(4), 1567–1578 (2007). [CrossRef]
8. W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 32(19), 2801–2803 (2007). [CrossRef]
9. A. V. Tsarev, “Tunable optical filters,” United States Patent No 6,999,639, February 14, 2006.
10. A. V. Tsarev, V. M. N. Passaro, and F. Magno, “Widely Tunable Reconfigurable Optical Add/Drop Multiplexers in Silicon-on-Insulator Technology: a New Approach,” in Silicon Photonics, V.M.N. PassaroEd., Research Signpost Publ., Trivandrum, Kerala, India: ISBN: 81-308-0077-2, 47–77 (2006).
11. Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “A novel ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Opt. Express 17(3), 1508–1517 (2009). [CrossRef]
12. A. V. Tsarev, “New type of heterogeneous nanophotonic silicon-on-insulator optical waveguides,” Quantum Electron. 37(8) , 775–776 (2007). [CrossRef]
13. A. V. Tsarev, “Thin heterogeneous optical silicon-on-insulator waveguides and their application in reconfigurable optical multiplexers,” Quantum Electron. 38(5), 445–451 (2008). [CrossRef]
14. A. V. Tsarev, F. De Leonardis, and V. M. N. Passaro, “Thin heterogeneous SOI waveguides for thermo-optical tuning and filtering,” Opt. Express 16(5), 3101–3113 (2008). [CrossRef]
15. F. De Leonardis, A. V. Tsarev, and V. M. Passaro, “Optical properties of new wide heterogeneous waveguides with thermo optical shifters,” Opt. Express 16(26), 21333–21338 (2008). [CrossRef]
16. www.rsoftdesign.com, Rsoft Photonic CAD Suite, ver. 8.0, single license (2007).
17. R. V. Ramaswamy, “Strip loaded film waveguides,” Bell Syst. Tech. J. 53, 697–704 (1974).
18. Y. He, L. Yang, Q. Fang, H. Xin, F. Li, and Y. Liu, “Influence of thermal isolating grooves on the performance of the Mach-Zehnder interferometer-type thermo-optic variable optical attenuator,” Opt. Eng. 44(4), 040504 (2005). [CrossRef]
19. N. Daldosso, M. Melchiorri, F. Riboli, M. Girardini, G. Pucker, M. Crivellari, P. Bellutti, A. Lui, and L. Pavesi, “Comparison Among Various Si3N4 Waveguide Geometries Grown Within a CMOS Fabrication Pilot Line,” J. Lightwave Technol. 22, 1734–1740 (2004). [CrossRef]
20. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
21. H. Kikuta, H. Toyota, and W. Yu, “Optical elements with subwavelength structured surfaces,” Opt. Rev. 10(2), 63–73 (2003). [CrossRef]
22. M. Borselli, Th. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef]
