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Athermal silicon arrayed waveguide grating with polymer-filled slot structure
Optics Communications 282 (2009) 2841–2844
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Athermal silicon arrayed waveguide grating with polymer-filled slot structure Xiang Wang, Simiao Xiao, Weiwei Zheng, Fan Wang, Yubo Li, Yinlei Hao, Xiaoqing Jiang, Minghua Wang, Jianyi Yang * Department of Information Science and Electronic Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 18 November 2008 Received in revised form 10 April 2009 Accepted 10 April 2009
Keywords: Arrayed waveguide grating Silicon Slot Polymer Athermal
a b s t r a c t In this paper, an athermal silicon arrayed waveguide grating (AWG) with the assistance of a polymerfilled slot structure is proposed. Arrayed slot waveguides were used to replace arrayed silicon photonic wires (SPWs). By carefully controlling the temperature dependence of the effective index of the polymer-filled slot waveguides, the athermal silicon AWG is realized. Analysis shows that the center wavelength shift of the AWG can be down to 0.14 pm/°C. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Influence of temperature on silicon-based AWG
The arrayed waveguide grating (AWG) is a key component for wavelength division multiplexing systems and has been well developed [1–6]. In recent years, the silicon material received more and more attentions in the area of integrated optics because of its great potential for the realization of compact optical components and expected applications in optical interconnects. Several compact AWGs based on silicon photonic wires (SPWs) have been reported [7–10]. Temperature-independent AWGs are always required by practical systems. A lot of approaches have been proposed to fabricate silica-based athermal AWGs [11–15]. However, since the thermooptic (TO) coefficient of silicon is almost 20 times higher than that of silica, an SPW-based AWG is more sensitive to temperature than the silica AWG. As a result, it is hard to remove the temperature dependence and achieve athermal silicon AWGs when those approaches for the athermal silica AWGs were applied. In this paper, the slot waveguide [16,17] is applied into the part of arrayed waveguides in SPW-based AWGs and polymer material with high negative TO coefficient is filled into the narrow slot. Analysis shows that this design can remarkably reduce the temperature-dependent center wavelength shift (TD-CWS) and achieve athermal AWGs.
Fig. 1a shows a configuration of AWGs. The temperature dependence of its center wavelength can be written as [18]:
* Corresponding author. Tel./fax: +86 571 87952867. E-mail address: [email protected] (J. Yang). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.04.020
@kc kc @nc 1 @ DL ¼ þ nc @T ng @T DL @T
ð1Þ
where kc is the central wavelength, nc is the effective index of the arrayed waveguides, DL is the length difference between each successive waveguide, T is the temperature, and ng is the group index:
ng ¼ nc k
@nc @k
ð2Þ
Since the refractive index contrast of SOI is rather high, we use ng instead of nc here in Eq. 1, which has been reported to be more accurate [18] from both rigorous derivation and experimental data [19,20], unlike the cases with low index contrast [21,22]. If the center wavelength is independent on the temperature, the left item of Eq. 1 is zero and the athermal condition can be derived as follows:
1 @nc 1 @ DL ¼0 þ nc @T DL @T
ð3Þ
The second item of Eq. 3 corresponds to the coefficient of thermal expansion (CTE) asub of the substrate, which usually changes with the temperature. For the silicon material [23], an approximation can be given to represent the change of asub in the temperature range from 200 to 400 K as in Eq. 4, which covers the temperature range that devices commonly work:
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X. Wang et al. / Optics Communications 282 (2009) 2841–2844
Fig. 1. (a) Configuration of the polymer-assisted athermal silicon AWG with (b) a slot structure. (c) Structure of the slot waveguide.
n
o
3. Results and discussion
asub ðTÞ 3:75 106 1 exp½5:88 103 ðT 124Þ þ 5:548 1010 T
ð4Þ
Since the TO coefficient of silicon and silica are about 2.4 104 and 1.0 105 K1 respectively at the room temperature, Eq. 3 is hard to be satisfied for the AWGs formed by simple silicon waveguides with silica as the cladding. If the athermal condition given by Eq. 3 cannot be satisfied, the central wavelength will shift with the temperature as:
kc ¼ k0
nc exp nc0
Z
T
asub ðTÞdT
nc0 =ng0 ð5Þ
T0
where k0 and nc0 are the central wavelength and the effective index RT at the temperature of T0, respectively. The item T 0 asub ðTÞdT represents the interval integrals of Eq. 4 from temperature T0 to T. Analysis shows that the value of Eq. 6 can be omitted comparing with that of ng,
ng
ng0 @nc nc0 k nc ¼ nc k nc0 @k nc0
@nc0 @k
nc ¼
nc @nc0 @nc k k nc0 @k @k
Fig. 2. Temperature-dependent central wavelength shift of SPW.
In order to meet the requirement of Eq. 3 or to decrease the TDCWS, the temperature dependence of the effective index should be minimized, even turn to be a negative value to compensate the thermal expansion of the silicon substrate. It is known that polymers generally have a negative TO coefficient, and the value can reach more than 104 K1. However, simply using polymers as the cladding material can only slightly reduce the temperature dependence of the effective index of the SPWs because the light is mainly confined in the silicon core. To effectively take advantage of the negative TO coefficient of polymer to compensate the temperature dependence of silicon, employing the slot structure can be one of the solutions [18]. A schematic diagram employing slot waveguides to replace the part of the arrayed waveguides is shown in Fig. 1b above. To connect the slot structure with the simple SPW, low-loss structure transformers are designed. Fig. 1c gives the frame of a slot structure. When the width d of the silicon photonic wire pair and the width ws of the slot are small enough, large part of the electric field of the
ð6Þ
therefore, the following approximation of Eq. 7 is used above in Eq. 5 during deriving from Eq. 1:
ng
ng0 nc nc0
ð7Þ
The temperature-dependent central wavelength shift (TD-CWS) can be expressed as Eq. 8:
Dk ¼ k c k 0 ¼ k 0
nc exp nc0
Z
T
asub ðTÞdT
nc0 =ng0 k0
ð8Þ
T0
A SPW AWG with height of 320 nm and width of 450 nm has been reported in Ref. [8] without concerning temperature dependence. Here in Fig. 2, we illustrate the TD-CWS of the SPWs when the temperature changes, in which the width d of the silicon waveguides is 430, 450, and 470 nm, respectively, and the height h is 320 nm. It can be found that the TD-CWS almost reaches 5 nm when the temperature rises from 20 to 70 °C. The nearly 0.1 nm/°C wavelength shift is so huge that the traditional silicon AWG could not be used in practice if no temperature control system is applied.
Fig. 3. Temperature-dependent central wavelength shift of the slot waveguide with the variation of d and ws when the temperature rises from 20 to 70 °C. The height of the silicon photonic wire pairs is 320 nm.
X. Wang et al. / Optics Communications 282 (2009) 2841–2844
2843
quasi-TE mode will be confined in the narrow low-index slot. If polymer with a negative TO coefficient is filled in the slot, the TD-CWS can be tuned in a large range, from a positive value to a negative one, by properly choosing the structure parameters. As an example, Fig. 3 illustrates the TD-CWS with the variation of d and ws when the temperature rises from 20 to 70 °C. In the calculation, the height of the silicon photonic wire pairs is 320 nm. The polymer filled into the slot is assumed to be WIR30-490 [18] and
has a TO coefficient of 1.8 104 K1. As shown, with polymer filled and cladded, the arrayed slot waveguides can be used to control the TD-CWS of the AWG. The ‘‘athermal point” at a certain temperature, where the TD-CWS is zero, must truly exist. To design athermal silicon AWGs with the assistance of polymer-filled slot structure, the influence of the structural parameters ws, d, and h is analyzed. It was found that the change of three parameters exerted rather different influences on reducing the center wavelength shift in AWG. As shown in Fig. 4, the effect of changing the parameter d is most remarkable. In order to achieve the structural optimization, we first change the value of d as rough adjustment to find proper parameters that can make the TD-CWS minimum. After d is chosen, the parameters ws and h are changed as fine adjustment to find the optimum structure. With the polymer WIR30-490 filled in the slot, the optimum structure of the slot waveguide for achieving athermal silicon AWGs can be obtained with h = 320 nm, d = 220 nm, ws = 180 nm. As shown in Fig. 4c, the TD-CWS can be controlled below 7 pm at the temperature from 20 to 70 °C, smaller than 0.14 pm/°C. By using the BeamPROP AWG Utility, a software from RSoft, Inc., a 1 8 slot-assisted athermal AWG was simulated. The channel spacing is 1.6 nm, the number of arrayed waveguides is 32, DL is 46.1 lm, the grating order is 81, and the length of the free propagation region is 37.2 lm. Fig. 5a presents the spectrum of channel 6 when the temperature is 20and 70 °C. For comparison, a
Fig. 4. TD-CWS depending on (a) d = 210, 220, 230 nm, (b) ws = 170, 180,190 nm, and (c) h = 300, 320, 340 nm.
Fig. 5. Spectrum of (a) the slot-assisted athermal silicon AWG and (b) the traditional silicon AWG at different temperatures.
2844
X. Wang et al. / Optics Communications 282 (2009) 2841–2844
traditional AWG formed by SPWs was also simulated, and the spectrum of channel 6 at temperature 20, 45, and 70 °C are illustrated in Fig. 5b. It can be observed that the TD-CWS of slot-assisted AWG was effectively removed. 4. Conclusion A slot-assisted athermal silicon AWG is proposed. The key component of the athermal AWG for controlling the temperature dependence of the central wavelength is a series of arrayed polymer-filled slot waveguides. Analysis shows that the TD-CWS can be tuned in a large range, from a positive value to a negative one, by properly choosing the structure parameters. The CWS of this silicon AWG can be controlled down to 0.14 pm/°C when the structural parameters of the slot waveguide is properly set. Certainly, since the slot feature size of the slot-assisted AWG is at the level of 100 nm, the fabrication will be a challenge. Acknowledgement This work was supported by the Major State Basic Research Development Program under Grants 2007CB307003 and 2007CB613405, the Natural Science Foundation of China under Grants No. 60676028 and 6080835, and the Science and Technology Program of Zhejiang Province under Grant 2007C21022. References [1] M. Smit, Electron. Lett. 24 (7) (1988) 385.
[2] Y. Hibino, IEEE J. Sel. Top. Quantum Electron. 8 (8) (2002) 1090. [3] H. Bissessur, F. Gaborit, B. Martin, P. Pagnod-Rossiaux, J.-L. Peyre, M. Renaud, Electron. Lett. 30 (4) (1994) 336. [4] Y. Hida, Y. Inoue, S. Imamura, Electron. Lett. 30 (9) (1994) 959. [5] K. Jia, W. Wang, Y. Tang, Y. Yang, J. Yang, X. Jiang, Y. Wu, M. Wang, Y. Wang, IEEE Photon. Technol. Lett. 17 (2) (2005) 378. [6] J. Yang, X. Jiang, M. Wang, Y. Wang, Opt. Express 12 (6) (2004) 1084. [7] T. Fukazawa, F. Ohno, T. Baba, Jpn. J. Appl. Phys. 43 (5) (2004) L673. [8] K. Sasaki, F. Ohno, A. Motegi, T. Baba, Electron. Lett. 41 (4) (2005) 801. [9] P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, P. Jaenen, Opt. Express 14 (2) (2006) 664. [10] P. Cheben, J.H. Schmid, A. Delage, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, D.-X. Xu, Opt. Express 15 (5) (2007) 2299. [11] Y. Kokubun, N. Funato, M. Takizawa, IEEE Photon. Technol. Lett. 5 (11) (1993) 1297. [12] Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, S. Sumida, Electron. Lett. 33 (23) (1997) 1945. [13] Y. Kokubun, S. Yoneda, S. Matsuura, Electron. Lett. 34 (4) (1998) 367. [14] K. Maru, K. Matsui, H. Ishikawa, Y. Abe, S. Kashimura, S. Himi, H. Uetsuka, Electron. Lett. 40 (3) (2004) 374. [15] D. Li, C. Ma, Z. Qin, H. Zhang, D. Zhang, S. Liu, Opt. Appl. 37 (3) (2007) 305. [16] V.R. Almeida, Q. Xu, C.A. Barrios, M. Lipson, Opt. Lett. 29 (2004) 1209. [17] Q. Xu, V.R. Almeida, R.R. Panepucci, M. Lipson, Opt. Lett. 29 (2004) 1626. [18] J.-M. Lee, D.-J. Kim, G.-H. Kim, O.-K. Kwon, K.-J. Kim, G. Kim, Opt. Express 16 (5) (2008) 1645. [19] P. Dumon, Ultra-compact integrated optical filters in silicon-on-insulator by means of wafer-scale technology, PhD Thesis, Ghent University, 2007. [20] T. Baehr-Jones, M. Hochberg, C. Walker, E. Chan, D. Koshinz, W. Krug, A. Scherer, J. Lightwave Technol. 23 (2005) 4215. [21] Sai T. Chu, Wugen Pan, Shuichi Suzuki, Brent E. Little, Shinya Sato, IEEE Photon. Technol. Lett. 11 (1999) 1138. [22] N. Keil, H.H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, J. Schneider, Electron. Lett. 37 (2001) 579. [23] R. Hull, Properties of Crystalline Silicon, INSPEC, London, 1999, p. 91.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Athermal silicon arrayed waveguide grating with polymer-filled slot structure Xiang Wang, Simiao Xiao, Weiwei Zheng, Fan Wang, Yubo Li, Yinlei Hao, Xiaoqing Jiang, Minghua Wang, Jianyi Yang * Department of Information Science and Electronic Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 18 November 2008 Received in revised form 10 April 2009 Accepted 10 April 2009
Keywords: Arrayed waveguide grating Silicon Slot Polymer Athermal
a b s t r a c t In this paper, an athermal silicon arrayed waveguide grating (AWG) with the assistance of a polymerfilled slot structure is proposed. Arrayed slot waveguides were used to replace arrayed silicon photonic wires (SPWs). By carefully controlling the temperature dependence of the effective index of the polymer-filled slot waveguides, the athermal silicon AWG is realized. Analysis shows that the center wavelength shift of the AWG can be down to 0.14 pm/°C. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Influence of temperature on silicon-based AWG
The arrayed waveguide grating (AWG) is a key component for wavelength division multiplexing systems and has been well developed [1–6]. In recent years, the silicon material received more and more attentions in the area of integrated optics because of its great potential for the realization of compact optical components and expected applications in optical interconnects. Several compact AWGs based on silicon photonic wires (SPWs) have been reported [7–10]. Temperature-independent AWGs are always required by practical systems. A lot of approaches have been proposed to fabricate silica-based athermal AWGs [11–15]. However, since the thermooptic (TO) coefficient of silicon is almost 20 times higher than that of silica, an SPW-based AWG is more sensitive to temperature than the silica AWG. As a result, it is hard to remove the temperature dependence and achieve athermal silicon AWGs when those approaches for the athermal silica AWGs were applied. In this paper, the slot waveguide [16,17] is applied into the part of arrayed waveguides in SPW-based AWGs and polymer material with high negative TO coefficient is filled into the narrow slot. Analysis shows that this design can remarkably reduce the temperature-dependent center wavelength shift (TD-CWS) and achieve athermal AWGs.
Fig. 1a shows a configuration of AWGs. The temperature dependence of its center wavelength can be written as [18]:
* Corresponding author. Tel./fax: +86 571 87952867. E-mail address: [email protected] (J. Yang). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.04.020
@kc kc @nc 1 @ DL ¼ þ nc @T ng @T DL @T
ð1Þ
where kc is the central wavelength, nc is the effective index of the arrayed waveguides, DL is the length difference between each successive waveguide, T is the temperature, and ng is the group index:
ng ¼ nc k
@nc @k
ð2Þ
Since the refractive index contrast of SOI is rather high, we use ng instead of nc here in Eq. 1, which has been reported to be more accurate [18] from both rigorous derivation and experimental data [19,20], unlike the cases with low index contrast [21,22]. If the center wavelength is independent on the temperature, the left item of Eq. 1 is zero and the athermal condition can be derived as follows:
1 @nc 1 @ DL ¼0 þ nc @T DL @T
ð3Þ
The second item of Eq. 3 corresponds to the coefficient of thermal expansion (CTE) asub of the substrate, which usually changes with the temperature. For the silicon material [23], an approximation can be given to represent the change of asub in the temperature range from 200 to 400 K as in Eq. 4, which covers the temperature range that devices commonly work:
2842
X. Wang et al. / Optics Communications 282 (2009) 2841–2844
Fig. 1. (a) Configuration of the polymer-assisted athermal silicon AWG with (b) a slot structure. (c) Structure of the slot waveguide.
n
o
3. Results and discussion
asub ðTÞ 3:75 106 1 exp½5:88 103 ðT 124Þ þ 5:548 1010 T
ð4Þ
Since the TO coefficient of silicon and silica are about 2.4 104 and 1.0 105 K1 respectively at the room temperature, Eq. 3 is hard to be satisfied for the AWGs formed by simple silicon waveguides with silica as the cladding. If the athermal condition given by Eq. 3 cannot be satisfied, the central wavelength will shift with the temperature as:
kc ¼ k0
nc exp nc0
Z
T
asub ðTÞdT
nc0 =ng0 ð5Þ
T0
where k0 and nc0 are the central wavelength and the effective index RT at the temperature of T0, respectively. The item T 0 asub ðTÞdT represents the interval integrals of Eq. 4 from temperature T0 to T. Analysis shows that the value of Eq. 6 can be omitted comparing with that of ng,
ng
ng0 @nc nc0 k nc ¼ nc k nc0 @k nc0
@nc0 @k
nc ¼
nc @nc0 @nc k k nc0 @k @k
Fig. 2. Temperature-dependent central wavelength shift of SPW.
In order to meet the requirement of Eq. 3 or to decrease the TDCWS, the temperature dependence of the effective index should be minimized, even turn to be a negative value to compensate the thermal expansion of the silicon substrate. It is known that polymers generally have a negative TO coefficient, and the value can reach more than 104 K1. However, simply using polymers as the cladding material can only slightly reduce the temperature dependence of the effective index of the SPWs because the light is mainly confined in the silicon core. To effectively take advantage of the negative TO coefficient of polymer to compensate the temperature dependence of silicon, employing the slot structure can be one of the solutions [18]. A schematic diagram employing slot waveguides to replace the part of the arrayed waveguides is shown in Fig. 1b above. To connect the slot structure with the simple SPW, low-loss structure transformers are designed. Fig. 1c gives the frame of a slot structure. When the width d of the silicon photonic wire pair and the width ws of the slot are small enough, large part of the electric field of the
ð6Þ
therefore, the following approximation of Eq. 7 is used above in Eq. 5 during deriving from Eq. 1:
ng
ng0 nc nc0
ð7Þ
The temperature-dependent central wavelength shift (TD-CWS) can be expressed as Eq. 8:
Dk ¼ k c k 0 ¼ k 0
nc exp nc0
Z
T
asub ðTÞdT
nc0 =ng0 k0
ð8Þ
T0
A SPW AWG with height of 320 nm and width of 450 nm has been reported in Ref. [8] without concerning temperature dependence. Here in Fig. 2, we illustrate the TD-CWS of the SPWs when the temperature changes, in which the width d of the silicon waveguides is 430, 450, and 470 nm, respectively, and the height h is 320 nm. It can be found that the TD-CWS almost reaches 5 nm when the temperature rises from 20 to 70 °C. The nearly 0.1 nm/°C wavelength shift is so huge that the traditional silicon AWG could not be used in practice if no temperature control system is applied.
Fig. 3. Temperature-dependent central wavelength shift of the slot waveguide with the variation of d and ws when the temperature rises from 20 to 70 °C. The height of the silicon photonic wire pairs is 320 nm.
X. Wang et al. / Optics Communications 282 (2009) 2841–2844
2843
quasi-TE mode will be confined in the narrow low-index slot. If polymer with a negative TO coefficient is filled in the slot, the TD-CWS can be tuned in a large range, from a positive value to a negative one, by properly choosing the structure parameters. As an example, Fig. 3 illustrates the TD-CWS with the variation of d and ws when the temperature rises from 20 to 70 °C. In the calculation, the height of the silicon photonic wire pairs is 320 nm. The polymer filled into the slot is assumed to be WIR30-490 [18] and
has a TO coefficient of 1.8 104 K1. As shown, with polymer filled and cladded, the arrayed slot waveguides can be used to control the TD-CWS of the AWG. The ‘‘athermal point” at a certain temperature, where the TD-CWS is zero, must truly exist. To design athermal silicon AWGs with the assistance of polymer-filled slot structure, the influence of the structural parameters ws, d, and h is analyzed. It was found that the change of three parameters exerted rather different influences on reducing the center wavelength shift in AWG. As shown in Fig. 4, the effect of changing the parameter d is most remarkable. In order to achieve the structural optimization, we first change the value of d as rough adjustment to find proper parameters that can make the TD-CWS minimum. After d is chosen, the parameters ws and h are changed as fine adjustment to find the optimum structure. With the polymer WIR30-490 filled in the slot, the optimum structure of the slot waveguide for achieving athermal silicon AWGs can be obtained with h = 320 nm, d = 220 nm, ws = 180 nm. As shown in Fig. 4c, the TD-CWS can be controlled below 7 pm at the temperature from 20 to 70 °C, smaller than 0.14 pm/°C. By using the BeamPROP AWG Utility, a software from RSoft, Inc., a 1 8 slot-assisted athermal AWG was simulated. The channel spacing is 1.6 nm, the number of arrayed waveguides is 32, DL is 46.1 lm, the grating order is 81, and the length of the free propagation region is 37.2 lm. Fig. 5a presents the spectrum of channel 6 when the temperature is 20and 70 °C. For comparison, a
Fig. 4. TD-CWS depending on (a) d = 210, 220, 230 nm, (b) ws = 170, 180,190 nm, and (c) h = 300, 320, 340 nm.
Fig. 5. Spectrum of (a) the slot-assisted athermal silicon AWG and (b) the traditional silicon AWG at different temperatures.
2844
X. Wang et al. / Optics Communications 282 (2009) 2841–2844
traditional AWG formed by SPWs was also simulated, and the spectrum of channel 6 at temperature 20, 45, and 70 °C are illustrated in Fig. 5b. It can be observed that the TD-CWS of slot-assisted AWG was effectively removed. 4. Conclusion A slot-assisted athermal silicon AWG is proposed. The key component of the athermal AWG for controlling the temperature dependence of the central wavelength is a series of arrayed polymer-filled slot waveguides. Analysis shows that the TD-CWS can be tuned in a large range, from a positive value to a negative one, by properly choosing the structure parameters. The CWS of this silicon AWG can be controlled down to 0.14 pm/°C when the structural parameters of the slot waveguide is properly set. Certainly, since the slot feature size of the slot-assisted AWG is at the level of 100 nm, the fabrication will be a challenge. Acknowledgement This work was supported by the Major State Basic Research Development Program under Grants 2007CB307003 and 2007CB613405, the Natural Science Foundation of China under Grants No. 60676028 and 6080835, and the Science and Technology Program of Zhejiang Province under Grant 2007C21022. References [1] M. Smit, Electron. Lett. 24 (7) (1988) 385.
[2] Y. Hibino, IEEE J. Sel. Top. Quantum Electron. 8 (8) (2002) 1090. [3] H. Bissessur, F. Gaborit, B. Martin, P. Pagnod-Rossiaux, J.-L. Peyre, M. Renaud, Electron. Lett. 30 (4) (1994) 336. [4] Y. Hida, Y. Inoue, S. Imamura, Electron. Lett. 30 (9) (1994) 959. [5] K. Jia, W. Wang, Y. Tang, Y. Yang, J. Yang, X. Jiang, Y. Wu, M. Wang, Y. Wang, IEEE Photon. Technol. Lett. 17 (2) (2005) 378. [6] J. Yang, X. Jiang, M. Wang, Y. Wang, Opt. Express 12 (6) (2004) 1084. [7] T. Fukazawa, F. Ohno, T. Baba, Jpn. J. Appl. Phys. 43 (5) (2004) L673. [8] K. Sasaki, F. Ohno, A. Motegi, T. Baba, Electron. Lett. 41 (4) (2005) 801. [9] P. Dumon, W. Bogaerts, D. Van Thourhout, D. Taillaert, R. Baets, J. Wouters, S. Beckx, P. Jaenen, Opt. Express 14 (2) (2006) 664. [10] P. Cheben, J.H. Schmid, A. Delage, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, D.-X. Xu, Opt. Express 15 (5) (2007) 2299. [11] Y. Kokubun, N. Funato, M. Takizawa, IEEE Photon. Technol. Lett. 5 (11) (1993) 1297. [12] Y. Inoue, A. Kaneko, F. Hanawa, H. Takahashi, K. Hattori, S. Sumida, Electron. Lett. 33 (23) (1997) 1945. [13] Y. Kokubun, S. Yoneda, S. Matsuura, Electron. Lett. 34 (4) (1998) 367. [14] K. Maru, K. Matsui, H. Ishikawa, Y. Abe, S. Kashimura, S. Himi, H. Uetsuka, Electron. Lett. 40 (3) (2004) 374. [15] D. Li, C. Ma, Z. Qin, H. Zhang, D. Zhang, S. Liu, Opt. Appl. 37 (3) (2007) 305. [16] V.R. Almeida, Q. Xu, C.A. Barrios, M. Lipson, Opt. Lett. 29 (2004) 1209. [17] Q. Xu, V.R. Almeida, R.R. Panepucci, M. Lipson, Opt. Lett. 29 (2004) 1626. [18] J.-M. Lee, D.-J. Kim, G.-H. Kim, O.-K. Kwon, K.-J. Kim, G. Kim, Opt. Express 16 (5) (2008) 1645. [19] P. Dumon, Ultra-compact integrated optical filters in silicon-on-insulator by means of wafer-scale technology, PhD Thesis, Ghent University, 2007. [20] T. Baehr-Jones, M. Hochberg, C. Walker, E. Chan, D. Koshinz, W. Krug, A. Scherer, J. Lightwave Technol. 23 (2005) 4215. [21] Sai T. Chu, Wugen Pan, Shuichi Suzuki, Brent E. Little, Shinya Sato, IEEE Photon. Technol. Lett. 11 (1999) 1138. [22] N. Keil, H.H. Yao, C. Zawadzki, J. Bauer, M. Bauer, C. Dreyer, J. Schneider, Electron. Lett. 37 (2001) 579. [23] R. Hull, Properties of Crystalline Silicon, INSPEC, London, 1999, p. 91.