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.

Active Integrated Filters for RF-Photonic Channelizers

“…The eigenvalues of the A matrix are computed by solving the characteristic equation det[ zI − A ] =0. Further discuss of stability of the systems can be found in our previous work [ 21 , 22 ].…”