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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 4 — Apr. 1, 2010
  • pp: 895–910

Extended active optical lattice filters: filter synthesis

Mieczyslaw Dabkowski, Amr El Nagdi, Louis R. Hunt, Ke Liu, Duncan L. MacFarlane, and Viswanath Ramakrishna  »View Author Affiliations


JOSA A, Vol. 27, Issue 4, pp. 895-910 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000895


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Abstract

In this paper, we study the synthesis of asymptotically stable filters from a unit cell of a two-dimensional tunable lattice filter architecture consisting of four four-port couplers and four waveguides containing semiconductor optical amplifiers. Upper bounds on the number of gains that will produce a filter with a priori prescribed poles, for a specific system, are obtained. We also provide sufficient conditions on the reflection-type coefficients, characterizing each four-port coupler, which ensure that real-valued gains, taking values in [0,1], exist so that the filter is asymptotically stable. Finally, we motivate the notion of a transmission zero of a filter and discuss the possibility of simultaneously placing both poles and transmission zeros for the unit cell.

© 2010 Optical Society of America

OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(130.3120) Integrated optics : Integrated optics devices
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(070.5753) Fourier optics and signal processing : Resonators
(070.7145) Fourier optics and signal processing : Ultrafast processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: November 12, 2009
Revised Manuscript: January 29, 2010
Manuscript Accepted: February 3, 2010
Published: March 31, 2010

Citation
Mieczyslaw Dabkowski, Amr El Nagdi, Louis R. Hunt, Ke Liu, Duncan L. MacFarlane, and Viswanath Ramakrishna, "Extended active optical lattice filters: filter synthesis," J. Opt. Soc. Am. A 27, 895-910 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-4-895

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