title: Extended active optical lattice filters: filter synthesis.
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.
authors.affiliation: Department of Mathematical Sciences, University of Texas at Dallas, P.O. Box 830688,Richardson, Texas 75083, USA.
authors.forename: Mieczyslaw
authors.initials: M
authors.lastname: Dabkowski
authors.forename: Amr
authors.initials: A
authors.lastname: El Nagdi
authors.forename: Louis R
authors.initials: LR
authors.lastname: Hunt
authors.forename: Ke
authors.initials: K
authors.lastname: Liu
authors.forename: Duncan L
authors.initials: DL
authors.lastname: Macfarlane
authors.forename: Viswanath
authors.initials: V
authors.lastname: Ramakrishna