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High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide Régis Orobtchouk, Abdelhalim Layadi, Hamid Gualous, Daniel Pascal, Alain Koster, and Suzanne Laval Light coupling into a sub-micrometer-thick waveguide is usually done through a grating coupler. Coupling efficiency is strongly enhanced by addition of a mirror above the grating. This new kind of coupler can be designed to achieve efficiencies as great as 80%. Numerical calculations for a high-angularspread Gaussian incident beam are compared with experimental results obtained for a standard siliconon-insulator waveguide. © 2000 Optical Society of America OCIS codes: 310.2790, 230.7390, 230.1950. 1. Introduction Although end coupling is usually used to inject light into integrated optical waveguides, it is not really achievable for sub-micrometer-thick waveguides, unless high insertion losses are accepted. The grating coupler is then a good alternative, because it can be monolithically integrated, at any point in the optical circuit. It can provide a good coupling efficiency regardless of the waveguide thickness. Moreover, only one mode of the guiding structure is resonantly excited. The grating parameters 共period and modulation depth兲 must be adjusted for a given waveguide structure to get the maximum coupling efficiency by means of limiting the number of diffracted orders. The grating period is usually chosen to get only the first diffracted order propagating in the waveguide and the transmitted and the reflected beams 共zero When this research was performed, the authors were with the Institut d’Électronique Fondamentale, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8622, Bâtiment 220, Université Paris-Sud, F-91405 Orsay cedex, France. R. Orobtchouk is now with the Laboratoire de Physique de la Matière, Centre Nationale de la Recherche Scientifique, Unité Mixte de Recherche 5511, Institut National des Sciences Appliquées, Bâtitment 502, 20 Avenue A. Einstein, F-69100 Villeurbanne cedex, France. H. Gualous is now with the Institut Génie Energétique, Université de Franche Comté, 12 rue des Entrepreneurs, F-90000 Belfort, France. A. Koster’s e-mail address is [email protected]. Received 9 February 2000; revised manuscript received 19 June 2000. 0003-6935兾00兾05773-05$15.00兾0 © 2000 Optical Society of America order兲 outside. Even at resonance the reflected and the transmitted beam intensities are not zero, and the maximum coupling efficiency is limited to ⬃40%. This can be greatly increased by addition of a mirror that reinjects the transmitted beam into the waveguide, provided a phase condition is fulfilled. Such an efficient coupler including a grating and a mirror has been studied both theoretically and experimentally. From a theoretical point of view, coupling efficiency for an incident Gaussian beam has been calculated following the method described by Nevière1 and used by other authors2,3 for low angular beam spread. In this paper we calculate the coupling efficiency for a Gaussian beam with high angular beam spread such that this could be applied to beams issued from an optical fiber, for instance. Experimental devices have been processed on different silicon-on-insulator 共SOI兲 substrates. SOI applications are increasingly developed in both microelectronics and optoelectronics.4 –7 Layadi et al. demonstrated that standard Simox substrates for microelectronics can be used to realize low-loss monomode waveguides at 1.3 m, although the guiding silicon film is only 0.2 m thick.8 The coupling efficiency was measured for various incident beam waists and compared with the calculated values.2 2. Device Description SOI Simox is obtained by deep oxygen ion implantation in a silicon substrate and thermal annealing, which create a buried silicon dioxide layer under a silicon film of good crystal quality. The standard layer thicknesses are 0.4 m for the buried dioxide and 0.2 m for the silicon film. Substrates were purchased from Soitec 共France兲. Gratings are de1 November 2000 兾 Vol. 39, No. 31 兾 APPLIED OPTICS 5773 Fig. 1. Schematic drawing of device and of spatial evolution of guided power. Coupling efficiency depends on the beam-waist value w0 with respect to the decoupling length of the coupler LC, and on the distance of the maximum of the incident beam from the grating edge. AR, antireflection coating. fined by holographic lithography. To get gratings only on limited areas, local variations of the reflection coefficient at the interface between the substrate and the photoresist are induced at the insolation wavelength 共0.4579 m兲 by means of multilayer coating9: a silicon dioxide layer 共260 nm兲, which is removed in the regions where gratings are to be present, followed by an antireflection coating consisting of 90 nm of silicon nitride and 45 nm of silicon oxide. The photoresist gratings are transferred into the silicon oxide and nitride and in a small fraction of the silicon layer 共30 nm兲 by means of reactive ion etching. Two gratings 共0.38 m period and 0.35 filling factor兲 separated by a noncorrugated waveguide are realized: The first enables light injection into the waveguide, whereas the second permits light decoupling. Coupling efficiency can be evaluated in this way. A silicon dioxide passivation layer is then deposited by plasma-enhanced chemical vapor deposition, followed by aluminium deposition above the input coupler grating to realize the mirror. The thickness of the silicon dioxide passivation layer 共0.46 m兲 was adjusted according to the numerical simulations presented hereafter to get a high coupling efficiency. As shown in Fig. 1, the incident light beam 共 ⫽ 1.3 m兲 reaches the grating through the substrate. Thus a Si3N4 antireflection coating had to be deposited on the entrance face. 3. Calculation of the Coupling Efficiency The method that we used is based on Nevière’s research,1 which considers a Gaussian beam incident on an infinite grating. The incident beam is described as a superposition of infinite elementary plane waves. In the vicinity of the resonant excita5774 APPLIED OPTICS 兾 Vol. 39, No. 31 兾 1 November 2000 tion of the guided mode the coupler response to an incident plane wave is given by a Lorentzian function of the incident angle, and the diffracted field can be assimilated to the guided-mode response. The coupler response for an incident beam is obtained by addition of the contributions of the elementary planewave spectrum and normalized to the incident intensity. The coupling efficiency is then given by the following formula,10,11 共z兲 ⫽ ⫻ ( 冦 2kp,z⬙ 兩r共z兲兩2 ⫹ 冉 冤 冉 冊 2 kp,z⬙ ⌳ 2k0 cos ⌰0 k0 sin ⌰0 ⫹ m ) 冊冧 Re关ir共z兲q*共 z兲兴 2 k0 sin ⌰0 ⫹ m ⌳ 兰 ⫹⬁ ⫺⬁ 冥 兩Em,y共kp,z⬘, x兲兩2dx , (1) where i. Em,y共kp,z⬘, x兲 is the complex amplitude profile of the mth diffracted order. It corresponds to the TE0 guided mode for m ⫽ ⫺1. ii. ⌳ is the grating period, and k0 ⫽ 共2兾兲 is the norm of the wave vector corresponding to the mean incidence angle ⌰0 of the Gaussian beam, where the beam wavelength, each of them measured in air. iii. kp,z ⫽ kp,z⬘ ⫹ ikp,z⬙ is the complex pole of the mth diffracted order field amplitude. At resonance Table 1. Refractive Index and Thickness of the Structure’s Various Layers Layers Indexes Thicknesses 共m兲 Al SiO2 共passivation兲 Si3N4 Si 共guide兲 Buried SiO2 Si 共substrate兲 Si3N4 共antireflection兲 1.3 ⫹ i14 0.2 1.45 Variable parameter 1.98 0.09 3.505 0.205 1.45 0.38 3.505 500 1.98 0.12 its real part is close to the wave vector of the guided mode propagating under the grating; i.e., kp,z⬘ ⬇ k0 sin ⌰r ⫹ m共2兾⌳兲. Its imaginary part is related to the characteristic decoupling length of the grating Lc, which can be measured from the 1兾e value of the light intensity decoupled outside when the guided mode arrives on the grating used as a decoupler: kp,z⬙ ⫽ 1兾2Lc. iv. q共z兲 is the Fourier transform of the incident field amplitude of a Gaussian beam in the local coordinates of the grating coupler12 共see Fig. 1兲, and q* denotes the complex conjugate of q, q共 z兲 ⫽ 兰 ⫹⬁ p共kz兲exp关i共kz ⫺ kp,z⬘兲z兴dkz, (2) ⫺⬁ where p共kz兲 ⫽ A kz k0,z ⫹ kx k0, x k0 kx 冋 exp ⫺ 册 w02共⫺kx k0,z ⫹ kz k0, x兲2 4k02 ⫹ i共kx dx ⫺ kz dz兲 , (3) where w0 is the beam waist, dx and dz give the distance of the beam center from the axis origin. kx is related to kz by kx ⫽ 共k02 ⫺ kz2兲1兾2. A is a constant associated with the incident beam power. v. The integral formula r共z兲 depicts the response of the grating coupler for the diffracted 共guided兲 field: r共z兲 ⫽ ⫺i 兰 ⫹⬁ ⫺⬁ p共kz兲 exp关i共kz ⫺ kp,z⬘兲z兴 dkz. kz ⫺ kp,z⬘ ⫺ ikp,z⬙ (4) The first factor in Eq. 共1兲 allows us to calculate the variations of the light power injected into the waveguide as a function of the coupler characteristic length LC, of the beam waist w0, and of the incidence conditions 共angle, distance between the waist and the device surface, distance between the coupler edge and the maximum of the incident beam兲. The second factor is usually referred to as a coupling term FC, which is often ignored in coupling efficiency calculations, depending on the characteristics of the whole structure through the diffracted field profile. Assuming that FC is equal to 1, we consider only the first factor to optimize the coupling efficiency. In the general case the integral equations 共2兲 and 共4兲 cannot be formally solved. For a Gaussian beam with low beam spread and assuming that the beam waist is on the device surface, the paraxial approximation is used to provide an analytical solution of these two equations.2,3 This allows us to determine the optimum resonant coupling efficiency, for a given coupler characterized by the decoupling length LC, as the beam parameters and position are varied. It is found that the optimum coupling of ⬃80% is obtained for a beam waist w0 ⫽ 1.37 LC cos ⌰r and when the distance d between the beam center and the coupler edge is approximately equal to LC. For a high angular beam spread the paraxial approximation is no longer valid, so the integral equations 共2兲 and 共4兲 must be solved numerically with a fast Fourier transform. For the highest angular beam spread considered it appears that we obtain the same optimum coupling conditions as calculated with the paraxial approximation. Let us now focus on the coupling factor FC, which determines the global coupling efficiency. The parameters that are to be optimized are the grating modulation depth h and the distance between the grating and the mirror, which corresponds to the thickness of the silicon dioxide passivation layer. The calculation is carried out with the rigorous differential method proposed by Vincent13 and used by Chang et al.14 For proper accounting of the metallic mirror and the large substrate thickness, we used an S matrix formalism,15 which avoids numerical divergence problems related to exponential terms in the equations. As the guided power varies with the incidence angle as a Lorentzian function, an analytical formula that directly gives the value of ⌰r is deduced from the calculation of three points of the resonance curve. This method is much less time consuming than pole research in the complex plane for the determination of the effective index of the guided mode under the grating as usually done, for example, in Ref. 1. The structure considered in the computation is represented in Fig. 1 and is used with m ⫽ ⫺1. The complex refractive index 共taken from Palik16兲 and the thickness of the various layers are given in Table 1. Since the coupler performances are mainly determined by the decoupling length LC and the coupling factor FC, these two parameters were calculated for various values of the grating modulation depth as a function of the thickness of the passivation silicon dioxide layer. The decoupling length LC is plotted in Fig. 2. The length decreases when the modulation depth increases, as the grating becomes more efficient, and it varies periodically with the silicon dioxide thickness. It can be confirmed from Fig. 2 that the period is determined by the optical path of the light between 1 November 2000 兾 Vol. 39, No. 31 兾 APPLIED OPTICS 5775 Fig. 4. Experimental setup. DFB, distributed feedback. Fig. 2. Characteristic length LC of coupler versus silicon dioxide thickness for various etching depth of grating in silicon. the grating and the mirror. The calculated period is 0.477 m, which is equal to 兾2n cos ⌰r, with ⫽ 1.3 m, n ⫽ 1.45, and ⌰r ⫽ 20°. The corresponding coupling factor is plotted in Fig. 3. Sharp resonances are observed for thickness values of the silicon oxide layer corresponding to a phase shift for the reflected light. Between these resonances the coupling factor is close to 1 over a large range of the passivation layer thickness. 4. Experimental Results The experimental setup is represented in Fig. 4. The light source is a distributed-feedback monomode laser diode from Hitachi, emitting at ⫽ 1.3 m. Its operating temperature is fixed by a Peltier device. A microscope objective and several lenses with different focal lengths allow us to get Gaussian beams whose waists can be varied from 14 to 48 m. Micropositioning elements are used to adjust the beam waists on the input coupler. An IR camera is used to locate the incident beam on the input coupler and to record the decoupled light intensity emerging from the output coupler. Photodetectors measure the light in- Fig. 3. Coupling factor FC versus silicon dioxide thickness for various etching depth of grating in silicon. 5776 APPLIED OPTICS 兾 Vol. 39, No. 31 兾 1 November 2000 tensities reflected on the input coupler and decoupled by the output grating. The light power that is decoupled from the waveguide decreases exponentially along the grating with the characteristic length LC. For the sample under consideration, with a grating etched in silicon 30 nm deep, measurements performed with the IR camera give a value LC ⫽ 23 m. This result is coherent with the calculated value for the passivation silica layer thickness of 0.46 m 共Fig. 2兲. The coupling factor is then equal to 0.97 共Fig. 3兲, which allows for a coupling efficiency of 78% for an optimum beamwaist value of 30 m. The reflected power on the input coupler was measured as a function of the incidence angle for various beam-waist values. Results are plotted in Fig. 5. The difference between the power measured off resonance and at resonance corresponds to the injected light power. Once it is normalized to the incident power, it gives the coupling efficiency. The experimental values exp are compared with the theoretical ones in Table 2. The maximum coupling efficiency is theoretically obtained for a 30-m waist, and the experimental results are in qualitative agreement with the calculated ones. Nevertheless, the measured values are smaller than the theoretical ones, in particular for Fig. 5. Measured values of device reflectivity as a function of incidence angle for various incident beam-waist values. Table 2. Comparison of the Experimental and Theoretical Values of the Coupling Efficiency for Various Beam Waists Waist w0 共m兲 Measured Coupling Efficiency exp 共%兲 Theoretical Coupling Efficiency th 共%兲 48 24 21 17 14 51 57 36 28 28 73.1 76.9 75.5 71.9 67.6 2. 3. 4. 5. the smallest waists. These results are consistent with the limitations of the one-dimensional model of divergence we used. Stronger diverging beams 共as issued from an optical fiber兲 will impose a twodimensional model. Further optimization of the coupler realization could lead to coupling efficiencies still closer to the theoretical limit, which is ⬃80%. The curves in Fig. 5 also show that the angular acceptance of such a coupler is ⬃1 deg, which permits easy alignment. 6. 7. 8. 9. 5. Conclusion We have demonstrated that high coupling efficiency is achieved by addition of a mirror above a conventional grating coupler. Nearly 60% of the incident light has been coupled into a sub-micrometer-thick SOI waveguide, with a strongly angular beam-spread Gaussian beam. The experimental results are coherent with the calculations. The latter take into account the case of strongly angular beam-spread Gaussian beams and predict, with the employed onedimensional model of divergence, coupling efficiencies as great as 80%. The authors acknowledge the contribution of B. Abécassis and C. Gousset for realization of the device. This study was supported by Centre National d’Etudes des Télécommunications—France Telecom contract 931B140. 10. 11. 12. 13. 14. 15. References 1. M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current 16. Physics 共Springer-Verlag, Berlin, 1980兲, Chap. 5, pp. 123– 157. D. Pascal, R. Orobtchouk, A. Layadi, A. Koster, and S. Laval, “Optimized coupling of a Gaussian beam into an optical waveguide using a grating coupler: comparison of experimental and theoretical results,” Appl. Opt. 36, 2443–2447 共1997兲. O. Parriaux, V. Sychugov, and A. Tischenco, “Coupling gratings as waveguide functional elements,” Pure Appl. Opt. 5, 453– 469 共1996兲. R. Soref, “Applications of silicon based optoelectronics,” MRS Bull. 23, 20 –24 共1998兲. E. A. Fitzgerald and L. C. Kimerling, “Silicon based microphotonics and integrated optoelectronics,” MRS Bull. 23, 39 – 47 共1998兲. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Randina, and F. Coppinger, “Advances in silicon on insulator optoelectronics,” IEEE J. Sel. Topics Quantum Electron. 4, 938 –947 共1998兲. A. J. Auberton-Hervé, J. M. Lamure, T. Barge, M. Bruel, B. Aspar, and J. L. Pelloie, “SOI materials for ULSI applications,” Semicond. Int. 18, 97–104 共1995兲. A. Layadi, A. Vonsovici, R. Orobtchouk, D. Pascal, and A. Koster, “Low-loss optical waveguide on standard SOI兾SIMOX substrate,” Opt. Commun. 146, 31–33 共1998兲. D. Pascal, R. Orobtchouk, S. Laval, and A. Koster, “Simple technique for fabricating limited coupler gratings by holographic method using standard thick photoresist,” Electron. Lett. 31, 914 –915 共1995兲. L. Li and M. C. Gupta, “Effect of beam focusing on the efficiency of planar waveguide grating couplers,” Appl. Opt. 29, 5320 –5325 共1990兲. R. Orobtchouk, “Modélisation et étude de composants pour l’optique intégrée silicium sur isolant 共Simox兲 à 1,3 m,” Ph.D. dissertation 4106 共Université Paris-Sud, Orsay, France, 1996兲. Em. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, “Diffraction of a Gaussian beam from a periodic planar screen,” J. Opt. Soc. Am. A 11, 630 – 636 共1994兲. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, R. Petit, ed., Vol. 22 of Topics in Current Physics 共Springer-Verlag, Berlin, 1980兲, Chap. 3, pp. 101–122. K. C. Chang, V. Shah, and T. Tamir, “Scattering and guiding of waves by dielectric gratings with arbitrary profiles,” J. Opt. Soc. Am. 70, 804 – 813 共1980兲. T. D. Visser, H. Blok, and D. Lenstra, “Modal analysis of a planar waveguide with gain and losses,” IEEE J. Quantum Electron. 31, 1803–1810 共1995兲. E. D. Palik, Handbook of Optical Constants of Solids 共Academic, New York, 1985兲. 1 November 2000 兾 Vol. 39, No. 31 兾 APPLIED OPTICS 5777