Abstract

We present a compact and efficient design for slanted grating couplers (SLGC’s) to vertically connect fibers and planar waveguides without intermediate optics. The proposed SLGC employs a strong index modulated slanted grating. With the help of a genetic algorithm-based rigorous design tool, a 20µm-long SLGC with 80.1% input coupling efficiency has been optimized. A rigorous mode analysis reveals that the phase-matching condition and Bragg condition are satisfied simultaneously with respect to the fundamental leaky mode supported by the optimized SLGC.

© 2004 Optical Society of America

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Appl. Opt. (6)

Appl. Phys. (1)

T.Tamir and S. T. Peng, �??Analysis and design of grating couplers,�?? Appl. Phys. 14, 235 (1977).
[CrossRef]

IEEE J. Lightwave Technology (1)

T. Liao, S. Sheard, M. Li, J. Zhuo, and P. Prewett, �??High-efficiency focusing waveguide grating coupler with parallelogramic groove profiles, �?? IEEE J. Lightwave Technology 15, 1142 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. Mesel, and R. Baets, �??An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,�?? IEEE J. Quantum Electron. 38, 949 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

B. Mersali, A. Ramdane, and A. Carenco, �??Optical-mode transformer: A III-V circuit integration enabler,�?? IEEE J. Sel. Top. Quantum Electron. 3, 1321 (1997).
[CrossRef]

IEEE J. Select. Topics Quantum Electron. (1)

I. Moerman, P. P Van Daele, and P.M. Demeester, �??A review on fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,�?? IEEE J. Select. Topics Quantum Electron. 3, 1308 (1997).
[CrossRef]

IEEE Photon. Tech. Lett. (1)

P.V. Studenkov, M.R. Gokhale, and S.R. Forrest, �??Efficient coupling in integrated Twin-waveguide lasers using waveguide tapers,�?? IEEE Photon. Tech. Lett. 11, 1096 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. W. Ang, et al., �??Effects of grating heights on highly efficient unibond SOI waveguide grating couplers,�?? IEEE Photon. Technol. Lett. 12, 59 (2000).
[CrossRef]

IEEE Photonics Technology Letters (1)

G. Z. Masanovic, V. M. N. Passaro, and T. R. Graham, "Dual grating-assisted directional coupling between fibers and thin semiconductor waveguides," IEEE Photonics Technology Letters 15, 1395 (2003).
[CrossRef]

Integrated Photonics Research 1994 (1)

L. C. West, C. Roberts, J. Dunkel, G. Wojcik, and J. Mould, Jr., �??Non uniform grating couplers for coupling of Gaussian beams to compact waveguides, �?? Integrated Photonics Research Technical Digest, Optical Society of America, 1994.

Integrated Photonics Research 2003 (1)

D. M. Chambers, B. Wang, G. P. Nordin, and J. Jiang, �??Stratified grating coupler for waveguide applications,�?? Integrated Photonics Research Topical Meeting in Washington, DC, USA on June 16-18, 98-100, 2003.

J. Comput. Phys. (1)

J. P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (4)

Journal of Lightwave Technology (1)

J. K. Bulter, S. Nai-Hsiang, G. A. Evans, L. Pang, and P. Congdon, "Grating-assisted coupling of light between semiconductor glass wavwguides," Journal of Lightwave Technology 16, 1038 (1998).
[CrossRef]

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386 (6621), 143-149 (1997).
[CrossRef]

OFC 2001 (1)

Y. Hibino, �??High contrast waveguide devices,�?? Conf. Opt. Fiber Commun. Tech. Dig. Ser. 54, WB1/1 (2001).

Opt. Commun. (1)

M. Li, S. J. Sheard, �??Waveguide couplers using parallelogramic-shaped blazed gratings,�?? Opt. Commun. 109, 239(1994).
[CrossRef]

Opt. Eng. (2)

M. Li, and S. J. Sheard, �??Experimental study of waveguide grating couplers with parallelogramic tooth profiles,�?? Opt. Eng. 35, 3101 (1996).
[CrossRef]

V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and O. Parriaux, �??Optimization and control of grating coupling to or from a Silicon-based optical waveguide,�?? Opt. Eng. 35, 3092 (1996).
[CrossRef]

Opt. Lett. (3)

Optics Letter. (1)

J. Jiang, J. Cai, G. P. Nordin, and L. Li, �??Parallel micro-genetic algorithm design of photonic crystal and waveguide structures,�?? Optics Letter. 28, 2381 (2003).
[CrossRef]

Proc SPIE (2)

K. Krishnakumar, �??Micro-genetic algorithm for stationary and non-stationary function optimization,�?? SPIE 1196, 289 (1989).

A. V. Tishchenko, N. M. Lyndin, S. M. Loktev, V. A. Sychugov, and B. A. Usievich, �??Unidirectional waveguide grating coupler by means of parallelogramic grooves,�?? SPIE 3099, 269 (1997).
[CrossRef]

Other (8)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton University Press, Princeton, N.J., 1995).

Personal communications with Dr. Mark Hoffbauer in Los Alamos National Laboratory about slant etches using atomic oxygen technique.

T. Tamir, Integrated Optics, (Springer Verlag, 1975).

Z. Michalewicz, Genetic Algorithm + Data Structures + Evolution Programs, (Springer-Verlag, Berlin, 1992).

D. E. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning, (Addison Wesley, Massachusetts, 1989).

R. Petit, Electromagnetic Theory of Gratings, (Springer-Verlag, Berlin, 1980).
[CrossRef]

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Massachusetts, 1995).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 90, (Cambridge University Press, 1996).

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Figures (11)

Fig. 1.
Fig. 1.

3D geometry of the SLGC for the normal coupling between fiber and waveguide.

Fig. 2.
Fig. 2.

2D cross sectional geometry of SLGC used in the 2D FDTD simulation.

Fig. 3.
Fig. 3.

(a) Geometry of uniform SLGC optimized by µGA. (b) 2D FDTD result of magnitude squared time averaged Ez component for the uniform SLGC.

Fig. 4.
Fig. 4.

(a) Same as Fig. 3. (a), except for non-uniform SLGC. (b) Same as Fig. 3. (b), except for non-uniform SLGC.

Fig. 5.
Fig. 5.

Fill factor distribution of µGA optimized grating along x direction for the non-uniform SLGC shown in Fig. 4.

Fig. 6.
Fig. 6.

Lateral shift sensitivity analysis of the non-uniform SLGC design.

Fig. 7.
Fig. 7.

2D FDTD simulated spectrum response of the non-uniform SLGC design.

Fig. 8.
Fig. 8.

Infinite periodic version of the SLGC for leaky mode finding with RCWA approach.

Fig. 9.
Fig. 9.

K- vector diagram of the uniform fill-factor SLGC presented in Section 3.1, the inset shows the slanted grating.

Fig. 10.
Fig. 10.

Phase distribution from 2D FDTD simulation on the uniform SLGC.

Fig. 11.
Fig. 11.

(a) k-vector diagram of non-uniform SLGC. (b) 2D FDTD phase distribution of the non-uniform SLGC design.

Tables (1)

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Table 1. µGA optimization of a uniform SLGC

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

η RCE = P RCE P i × MOI
η j = P j P i , with j = R , T , LCE
f = c ( 1 η RCE )
n m = β m k 0
β qx = k ix + q · 2 π Λ , q = 0 , ± 1 , ± 2
n ave = [ n 1 2 × ( fillfactor ) + n 2 2 × ( 1 fillfactor ) ] 1 2

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