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K. Maru, T. Hakuta, Y. Abe, M. Ito, S. Himi, H. Uetsuka, T. Mizumoto, "Spot-size converter using vertical ridge taper for low fiber-coupling loss in 2.5%-$\Delta$ silica waveguides," Electron. Lett. 42, 219-220 (2006).

K. Maru, M. Okawa, Y. Abe, T. Hakuta, S. Himi, H. Uetsuka, "Silica-based 2.5%-$\Delta$ arrayed waveguide grating using
simple polarisation compensation method with core width adjustment," Electron. Lett. 43, 26-27 (2007).

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. QE-9, 919-933 (1973).

C. Dragone, "Theory of wavelength multiplexing with rectangular transfer functions," IEEE J. Sel. Topics Quantum Electron. 8, 1168-1178 (2002).

C. R. Doerr, R. Pafchek, L. W. Stulz, "Integrated band demultiplexer using waveguide grating routers," IEEE Photon. Technol. Lett. 15, 1088-1090 (2003).

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foy, L. T. Gomez, "Low-loss rectangular-passband multiplexer consisting of a waveguide grating router synchronized to
a three-arm interferometer," IEEE Photon. Technol. Lett. 17, 2334-2336 (2005).

C. R. Doerr, M. A. Cappuzzo, E. Y. Chen, A. Wong-Foy, L. T. Gomez, L. L. Buhl, "Wideband arrayed waveguide grating with three low-loss maxima per passband," IEEE Photon. Technol. Lett. 18, 2308-2310 (2006).

K. Maru, Y. Abe, M. Ito, H. Ishikawa, S. Himi, H. Uetsuka, T. Mizumoto, "2.5%-$\Delta$ silica-based athermal arrayed waveguide
grating employing spot-size converters based on segmented core," IEEE Photon. Technol. Lett. 17, 2325-2327 (2005).

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer
," IEEE Photon. Technol. Lett. 11, 581-583 (1999).

C. R. Doerr, L. W. Stulz, R. Pafchek, S. Shunk, "Compact and low-loss manner of waveguide grating router passband flattening and demonstration in a
64-channel blocker/multiplexer," IEEE Photon. Technol. Lett. 14, 56-58 (2002).

T. Mizuno, T. Kitoh, M. Itoh, T. Saida, T. Shibata, Y. Hibino, "Optical spotsize converter using narrow laterally tapered waveguide for planar lightwave circuits
," J. Lightw. Technol. 22, 833-839 (2004).

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interferometers," J. Lightw. Technol. 6, 1003-1010 (1988).

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$\hbox{SiO}_{2}$ waveguides on Si," J. Lightw. Technol. 6, 1011-1015 (1988).

P. Muñoz, D. Pastor, J. Capmany, "Modeling and design of arrayed waveguide gratings," J. Lightw. Technol. 20, 661-674 (2002).

K. Maru, T. Mizumoto, H. Uetsuka, "Modeling of multi-input arrayed waveguide grating and its application to design of flat-passband
response using cascaded Mach–Zehnder interferometers," J. Lightw. Technol. 25, 544-555 (2007).

C. Dragone, "Efficient techniques for widening the passband of a wavelength router," J. Lightw. Technol. 16, 1895-1906 (1998).

C. Dragone, "Efficient $N \times N$ star couplers using Fourier optics
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M. Kawachi, "Silica waveguides on silicon and their application to integrated-optic components," Opt. Quantum Electron. 22, 391-416 (1990).

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