Abstract

This paper reports on the modeling of arrayed-waveguide gratings (AWGs) by means of Fourier optics where the coupling between the grating waveguides and defocus of the star couplers is taken into account as well. Special interest is drawn to the geometrical modeling of AWGs. The paraxial approximation for the free-space propagation within the star couplers, the exact calculation of the coupling coefficients for the star couplers by an orthonormal basis (ONB) expansion, and the drawbacks due to the nonunitary transfer matrix provided by the Green's functions approach for the coupling between the grating waveguides,as well as possible improvements thereof, are identified as crucial points. An efficient orthonormalization procedure by means of an eigenvector decomposition is presented. A unitary approximation of the transfer matrix, which is in itself approximate but in general not unitary, introduced within the impulse response method, is obtained. The presented simulation technique allows for ab initio simulations, which do not fall back on any experimental input, for the spectral response of AWGs, which are found in good agreement with experimental results.

© 2003 IEEE

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  1. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis-A Signal Processing Approach , New York: Wiley, 1999.
  2. P. Munoz, D. Pastor and J. Capmany, "Modeling and design of arrayed waveguide gratings", J. Lightwave Technol., vol. 20, pp. 661-674, Apr. 2002 .
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  18. J. C. Chen and C. Dragone, "A proposed design for ultralow-loss waveguide grating routers", IEEE Photon. Technol. Lett., vol. 10, pp. 379-481, Mar. 1998.
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J. Lightwave Technol. (2)

C. Dragone, "Efficient N × N star couplers using Fourier optics", J. Lightwave Technol., vol. 7, pp. 479-489, Mar. 1989.

P. Munoz, D. Pastor and J. Capmany, "Modeling and design of arrayed waveguide gratings", J. Lightwave Technol., vol. 20, pp. 661-674, Apr. 2002 .

Other (17)

C. R. Doerr and C. H. Joyner, "Double chirping of the waveguide grating router", IEEE Photon. Technol. Lett., vol. 9, pp. 776 -778, June 1997.

R. Scarmozzino, A. Gopinath, R. Pregla and S. Helfert, "Numerical techniques for modeling guided-wave photonic devices", IEEE J. Select. Topics Quantum Electron. , vol. 6, pp. 150-162, Jan./Feb. 2000.

R. März, Integrated Optics-Design and Modeling, Norwood, MA: Artech House, 1995.

J. W. Goodman, Introduction to Fourier Optics, New York: McGraw-Hill, 1996.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis-A Signal Processing Approach , New York: Wiley, 1999.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1993.

C. Dragone, "An N× N optical multiplexer using a planar arrangement of two star couplers", IEEE Photon. Technol. Lett., vol. 3, pp. 812-814, Sept. 1991 .

C. Dragone, C. A. Edwards and R. C. Kistler, "Integrated optics N× N multiplexer on silicon", IEEE Photon. Technol. Lett., vol. 3, pp. 896-899, Oct. 1991.

F. Pizzato, G. Perrone and I. Montrosset, "Arrayed waveguide grating demultiplexers: A new efficient numerical analysis approach", in Proc. SPIE, vol. 2620, 1999, pp. 198-206.

J. Gehler and W. Spahn, "Dispersion measurement of arrayed waveguide gratings by Fourier spectroscopy", Electron. Lett., vol. 36, pp. 338-339, 2000.

A. Klekamp and R. Wessel, "Influence of phase errors on the spectral response of AWG multiplexers", J. Opt. Commun., vol. 23, pp. 170-177, 2002.

K. Takada, Y. Inoue, H. Yamada and M. Horiguchi, "Measurement of phase error distributions in silica-based arrayed waveguide grating multiplexers by using fourier transform spectroscopy", Electron. Lett., vol. 30, pp. 1671-1672, 1994.

M. Reed and B. Simon, Methods of Modern Mathematical Physics I, New York: Academic, 1980.

M. Born and E. Wolf, Principles of Optics , 7 ed. Cambridge: U.K.: Cambridge Univ. Press, 1999.

A. Klekamp and R. Münzner, "Imaging errors in arrayed waveguide gratings", Optical Quantum Electron., vol. 35, pp. 333-345, 2003.

J. C. Chen and C. Dragone, "A proposed design for ultralow-loss waveguide grating routers", IEEE Photon. Technol. Lett., vol. 10, pp. 379-481, Mar. 1998.

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical recipes in C, 2 ed. Cambridge: U.K.: Cambridge Univ. Press, 1997.

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