本論文提出一種新的共振器耦合器結構，主要利用S型彎曲波導所造成的彎曲損失將能量耦合進入微米小球共振腔，此結構可積體化構裝於Si晶片上具有較佳的機械強度等優點。
在實驗模擬上我們得到與微米小球的耦合效率最高可達35%以上，而實驗的量測上，S型彎曲波導在彎曲半徑為1500微米且彎曲角度為41度時的彎曲損失約為13dB/cm，而在角度為40度時彎曲損失開始明顯上升的趨勢，與利用光束傳播法模擬所得之結果吻合。

We have designed and fabricated an S-bend waveguide structure which enables one to excite the Whispering Gallery Modes (WGMs) in microspheres. The highest coupling efficiency found is estimated to be about 35%, and the designed structure has high position and wavelength tolerance. By misplacing the microsphere by 15um only results in 6% coupling efficiency degradation; while 10nm wavelength drift results in 3dB/cm coupling efficiency degradation.
Preliminary experimental result shows that the design is in close agreement with the simulation using beam propagation method (BPM). II

[1] B.E. Little, J.-P. Laine, D. R. Lim, and H. A. Haus,
“ Pedestal antiresonant reflecting waveguides for robust coupling to microsphere resonators and for microphotonic circuits” OPTICS LETTERS, Vol.25, No.1,pp.73,January 2000
[2] M. L.Gorodetsky and V.S.Ilchenko“ Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes”J.Opt.Soc.Am.B ,Vol.16,No.1/January 1999
[3] J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks“Phase-matched excitation of whispering-gallery-mode
resonances by a fiber taper” Optics Letters, Vol. 22, Issue 15, pp. 1129-1131 ,August 1997
[4] Vladimir S. Ilchenko, X. Steve Yao,and Lute Maleki,
“Pigtailing the high-Q microsphere cavity: a simple fiber
coupler for optical whispering-gallery modes”Optics Letters,Vol.24,No.11,pp.723, June 1999
[5] N. Dubreuil , J.C. Knight , D. K. Leventhal , V.Sandoghdar , J. Hare , and V. Lefevre, “Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres”OPTICS LETTERS, Vol.20,No.8,pp.813,April 1995
[6] M.L.Gorodetsky,A.A.Savchenkov,and V.S.Ilchenko“Ultimate Q of optical microsphere resonators”,Optics Letters,Vol.21,No.7,1996
[7] Ming Cai,Guido Hunziker,and Kerry Vahala,Member,IEEE“Fiber-Optic Add–Drop Device Based on a Silica
Microsphere-Whispering Gallery Mode System”IEEE photonics technology letters,Vol.11,No.6,1999
[8] M.Haraguchi,M.Fukui,Y.Tamaki,T.Okamoto“Optical switching due to whispering gallery modes in dielectric
microspheres coated by a Kerr material”Journal of Microscopy,Vol.210,Pt 3 June 2003,pp.229-233
[9] Yigit O. Yilmaz, Student Member, IEEE, Abdullah Demir, Student Member, IEEE, Adnan Kurt, Member, IEEE,and Ali Serpengüzel, Senior Member, IEEE“Optical Channel Dropping With a Silicon Microsphere” IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 8, AUGUST 2005
[10] Meint K. Smit, Erik C. M. Pennings, Member, ZEEE, and Hans Blok“A Normalized Approach to the Design of Low-Loss Optical Waveguide Bends”JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 11, NO. 11, NOVEMBER 1993
[11] Mordehai Heiblum and Jay H.Harris,“Analysis of Curved Optical Waveguides by Conformal Transformation”IEEE JOURNAL OF QUANTUM ELECTRONICS,VOL.QE-11, NO.2, pp.75,FEBRUARY 1975
[12] Robert G.Hunsperger“Integrated Optics:Theory and Technology”,pp.102-103,Springer,2002.
[13] Vijaya Subramaniam, Gregory N.De Brabander,David H.Naghski and Joseph T.Boyd, ”Measurement of Mode Field Profiles and Bending and Transition Losses in curved Optical Channel Waveguides,” Jounal of lightwav.
[14] http://web2.ctsh.hcc.edu.tw/~s9311104/u4.html
[15] A.N.Oraevsky “whispering-gallery waves”Quantum Electronics,Vol.32,No.5,pp.377 2002
[16] Brent E. Little, Member, IEEE, J.-P. Laine, and Hermann A. Haus,“Analytic Theory of Coupling from Tapered Fibers
and Half-Blocks into Microsphere Resonators”,JOURNAL OF LIGHTWAVE TECHNOLOGY,VOL.17,NO.4,APRIL 1999
[17] http://metrology.hut.fi/courses/s108-j/ Nano2.pdf.
[18] Orazio Svelto, Principles of Lasers, 3rd, Plenum Publish,
New York (1989), p161
[19] M.Cai,O.Painter,and K.J.Vahala“Fiber-coupled microsphere laser”,Optics Letters, Vol.25,No.19, pp.1430,2000
[20] RSoft Design Group, Inc,“User Menu”.
[21] K. Kawano, T. Kiton,“Introduction to Optical Waveguide
Analysis: Solving Maxwell’s Equations and the Schrodinger Equation”, WILEY, 2001.
[22] Duke Scientific corporation,“User Menu”.
[23] C. Y. Tai, B. Unal, J. S. Wilkinson, M. A. Ghanem, and P.
N. Bartlett“Optical coupling between a self-assembled microsphere grating and a rib waveguide”,Appl. Phys. Lett., 2004, Vol. 84, pp. 3513-3515
[24] Robert G.Hunsperger“Integrated Optics:Theory and Technology”,pp.114-119,Springer,2002.
[25] http://metrology.hut.fi/courses/s108-j/ Nano3.pdf.