Dabkowski Mieczyslaw, El Nagdi Amr, Hunt Louis R, Liu Ke, Macfarlane Duncan L, Ramakrishna Viswanath
Department of Mathematical Sciences, University of Texas at Dallas, P.O. Box 830688,Richardson, Texas 75083, USA.
J Opt Soc Am A Opt Image Sci Vis. 2010 Apr 1;27(4):895-910. doi: 10.1364/JOSAA.27.000895.
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.
在本文中，我们研究了由四个四端口耦合器和四个包含半导体光放大器的波导组成的二维可调晶格滤波器结构的一个单元合成渐近稳定滤波器的问题。针对特定系统，获得了产生具有先验规定极点的滤波器的增益数量的上限。我们还给出了表征每个四端口耦合器的反射型系数的充分条件，这些条件确保存在取值于[0,1]的实值增益，使得滤波器渐近稳定。最后，我们引出滤波器传输零点的概念，并讨论在单元中同时放置极点和传输零点的可能性。
