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Directional couplers are basic components for forming various kinds of photonic devices. In this paper, a directional coupler composed of two horizontal multiple-slotted waveguide structures with slanted sidewalls is characterized by using a full-vectorial finite element method in terms of the electric fields. The effective indexes of the even and the odd modes and the corresponding coupling lengths, both in quasi-TE and quasi-TM modes, are presented, where the strongly-hybrid nature of the guided-mode is effectively demonstrated. The results show that the coupling lengths in quasi-TE and quasi-TM modes exponentially increase with the increase of the gap between the coupled waveguides, where the value in quasi-TE mode is more sensitive to the variation of the angle of the sidewall, while the value in quasi-TM mode is more sensitive to variation of the height and the index of the slot. Properly choosing the structure and material parameters, polarization-independent directional couplers can be realized.
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Keywords:
- directional coupler /
- multiple-slotted silicon wires /
- slanted sidewalls /
- finite element method
[1] Paniccia M 2010 Nature Photon. 4 498
[2] Xu H H, Huang Q Z, Li Y T, Yu Y D, Yu J Z 2010 Chin. Phys. B 19 084210
[3] Xu Q, Almeida V R, Panepucci R R, Lipson M 2004 Opt. Lett. 29 1626
[4] Almeida V R, Xu Q, Barrios C A, Lipson M 2004 Opt. Lett. 29 1209
[5] Feng N N, Michel J, Kimerling L C 2006 IEEE J. Quantum Electron. 42 885
[6] Sun R, Dong P, Feng N N, Hong C Y, Michel J, Lipson M, Kimerling L 2007 Opt. Express 15 17967
[7] Xiao J B, Liu X, Sun X H 2008 Jpn. J. Appl. Phys. 47 3748
[8] Guider R, Daldosso N, Pitanti A, Jordana E, Fedeli J M, Pavesi L 2009 Opt. Express 17 20762
[9] Baehr-Jones T, Hochberg M, Wang G, Lawson R, Liao Y, Sullivan P A, Dalton L, Jen A K Y, Scherer A 2005 Opt. Express 13 5216
[10] Figi H, Bale D H, Szep A, Dalton L R, Chen A 2011 J. Opt. Soc. Am. B 28 2291
[11] Fujisawa T, koshiba M 2006 IEEE Photon. Technol. Lett. 18 1246
[12] Fujisawa T, Koshiba M 2006 Opt.Lett. 31 56
[13] Xiao J B, Liu X, Sun X H 2008 Appl. Opt. 47 2687
[14] Xiao J B, Liu X, Sun X H 2007 Opt. Express 15 8300
[15] Barrios C A, Gylfason K B, Sanchez B, Griol A, Sohlstrom H, Holgado M, Casquel R 2007 Opt. Lett. 32 3080
[16] Claes T, Molera J G, Vos K D, Schacht E, Baets R 2009 IEEE Photon. J. 1 197
[17] Kargar A, Chao C 2011 J. Opt. Soc. Am. A 28 596
[18] Koshiba M, Maruyama M S, Hirayama K 1994 J. Lightwave Technol. 12 495
[19] Li D U, Chang H C 2000 IEEE J. Quantum Electron. 36 1251
[20] Lusse P P, Stuwe P, Schule J, Unger H G J. Lightwave Technol. 12 487
[21] Xiao J B, Sun X H, Zhang M D 2006 Chin. Phys. 15 143
[22] Sacks Z S, Kingsland D M, Lee R, Lee J F 1995 IEEE Trans. Antennas Propagat. 43 1460
[23] Jin J 2002 The Finite Element Method in Electromagnetics 2nd ed. (New York: John Wiley & Sons) p22
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[1] Paniccia M 2010 Nature Photon. 4 498
[2] Xu H H, Huang Q Z, Li Y T, Yu Y D, Yu J Z 2010 Chin. Phys. B 19 084210
[3] Xu Q, Almeida V R, Panepucci R R, Lipson M 2004 Opt. Lett. 29 1626
[4] Almeida V R, Xu Q, Barrios C A, Lipson M 2004 Opt. Lett. 29 1209
[5] Feng N N, Michel J, Kimerling L C 2006 IEEE J. Quantum Electron. 42 885
[6] Sun R, Dong P, Feng N N, Hong C Y, Michel J, Lipson M, Kimerling L 2007 Opt. Express 15 17967
[7] Xiao J B, Liu X, Sun X H 2008 Jpn. J. Appl. Phys. 47 3748
[8] Guider R, Daldosso N, Pitanti A, Jordana E, Fedeli J M, Pavesi L 2009 Opt. Express 17 20762
[9] Baehr-Jones T, Hochberg M, Wang G, Lawson R, Liao Y, Sullivan P A, Dalton L, Jen A K Y, Scherer A 2005 Opt. Express 13 5216
[10] Figi H, Bale D H, Szep A, Dalton L R, Chen A 2011 J. Opt. Soc. Am. B 28 2291
[11] Fujisawa T, koshiba M 2006 IEEE Photon. Technol. Lett. 18 1246
[12] Fujisawa T, Koshiba M 2006 Opt.Lett. 31 56
[13] Xiao J B, Liu X, Sun X H 2008 Appl. Opt. 47 2687
[14] Xiao J B, Liu X, Sun X H 2007 Opt. Express 15 8300
[15] Barrios C A, Gylfason K B, Sanchez B, Griol A, Sohlstrom H, Holgado M, Casquel R 2007 Opt. Lett. 32 3080
[16] Claes T, Molera J G, Vos K D, Schacht E, Baets R 2009 IEEE Photon. J. 1 197
[17] Kargar A, Chao C 2011 J. Opt. Soc. Am. A 28 596
[18] Koshiba M, Maruyama M S, Hirayama K 1994 J. Lightwave Technol. 12 495
[19] Li D U, Chang H C 2000 IEEE J. Quantum Electron. 36 1251
[20] Lusse P P, Stuwe P, Schule J, Unger H G J. Lightwave Technol. 12 487
[21] Xiao J B, Sun X H, Zhang M D 2006 Chin. Phys. 15 143
[22] Sacks Z S, Kingsland D M, Lee R, Lee J F 1995 IEEE Trans. Antennas Propagat. 43 1460
[23] Jin J 2002 The Finite Element Method in Electromagnetics 2nd ed. (New York: John Wiley & Sons) p22
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