Abstract

A numerical technique for analyzing multireflector optical resonators with an arbitrarily large number of mirrors is applied to the design of ripple-free, flat-top bandpass filters. The algorithm determines unique values for the mirror reflectances Rj, j= 1, ... N, subject to a constraint on a contradirectional coupling strength parameter Z defined as Z= Sum^N j=1 zeta j with zeta j=tanh^-1(sqrt Rj) . The method is applied to the design of resonators with N as high as 12. Transmittance and dispersion spectra are presented for two cases that represent relatively weak and relatively strong contradirectional coupling. These spectra illustrate that, for a fixed -20-dB width of the transmittance spectrum, the -3-dB spectral widths increase monotonically with N, while the central portion of the group refractive-index spectrum becomes flatter and wider as N increases. These designs are compared with those obtained using a Chebyshev formula to determine the mirror reflectances. Application of these multireflector resonators as bandpass filters, slow-wave electrooptic modulators, and nonlinear optical devices are discussed.

© 2005 IEEE

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Opt. Lett. (1)

Other (15)

N. Shaw, W. J. Stewart, J. Heaton and D. R. Wright, "Optical slow wave resonant modulation in electrooptic GaAs/AlGaAs modulators", Electron. Lett., vol. 35, pp. 1557-1558, 1999.

A. Melloni, F. Morichetti and M. Martinelli, "Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures", Opt. Quantum Electron. , vol. 35, pp. 365-379, 2003.

T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms, Englewood Cliffs, NJ: Prentice-Hall, 2000, pp. 608-608.

L. E. Sarles, Introduction to Non-Linear Optimization, New York: Springer-Verlag, 1985, ch. 8, 9, 12.

K.-Y. Wu and J.-Y. Liu, "Programmable wavelength router", U.S. Patent 5 867 291, Feb. 2, 1999.

K. Jinguji and M. Oguma, "Optical half-band filters", J. Lightw. Technol., vol. 18, no. 2, pp. 252-259, Feb. 2000.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno and Y. Hibino, "Passband-width broadening design for WDM filter with lattice-form interleave filter and arrayed-waveguide gratings", IEEE Photon. Technol. Lett., vol. 14, no. 3, pp. 328-330, Mar. 2002.

H. van de Stadt and J. M. Muller, "Multimirror Fabry-Pérot interferometers", J. Opt. Soc. Amer. A, vol. 2, pp. 1363-1370, 1985.

J. Stone, L. W. Stulz and A. A. M. Saleh, "Three-mirror fiber Fabry-Pérot filters of optimal design", Electron. Lett., vol. 26, pp. 1073-1074, 1990.

G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion and S. B. Poole, "Wide-band Fabry-Perot-like filters in optical fiber", IEEE Photonics Technol. Lett., vol. 7, pp. 78-80, 1995.

S. Li, K. T. Chan, J. Meng and W. Zhou, "Adjustable multi-channel fiber bandpass filters based on uniform fiber Bragg gratings", Electron. Lett., vol. 34, pp. 1517-1519, 1998.

J. U. Kang, X. Xie and J. Khurgin, "Group velocity modified Ti-diffused LiNbO3 waveguides with dual Bragg gratings", Electron. Lett., vol. 38, pp. 1049-1051, 2002.

H. F. Taylor, "Design of multireflector resonant bandpass filters for guided wave optics", J. Lightw. Technol., vol. 19, no. 6, pp. 866-871, Jun. 2001.

A. Melloni and M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems", J. Lightw. Technol., vol. 20, no. 2, pp. 296-303, Feb. 2002.

H. F. Taylor, "Enhanced electrooptic modulation efficiency utilizing slow-wave optical propagation", J. Lightw. Technol., vol. 17, no. 10, pp. 1875-1883, Oct. 1999.

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