1458 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 45, NO. 8, AUGUST 1997 Synthesis of All-Optical Microwave Filters Using Mach–Zehnder Lattices Thomas A. Cusick, Student Member, IEEE, Stavros Iezekiel, Member, IEEE, Robert E. Miles, Member, IEEE, Salvador Sales, Associate Member, IEEE, and Jos´ e Capmany, Senior Member, IEEE Abstract— A synthesis algorithm which generates the set of coupling ratios required to produce a desired time-domain win- dow response using an all-optical Mach–Zehnder lattice network is presented. The analysis assumes incoherent interference of the lightwaves within the structure. The window coefficients are dictated by the coupling ratios of the couplers forming the lattice, leading to a simple structure comprising only passive components. Since its impulse response (IR) is finite, the filter will be stable, and the algorithm is capable of generating a wide range of responses in terms of their extinction ratios and passbands. The theory has been validated by experiment. Index Terms—Microwave filters, optical-fiber delay lines. I. INTRODUCTION T HE ANALYSIS of all-optical structures for microwave signal processing has been the subject of much research over the past decade [1]–[3]. However, it is only recently that the synthesis of such structures has been considered [4]–[7]. Synthesis of infinite impulse-response (IIR) filters using pos- itive coefficients was considered in [4]. The limitations of positive coefficient IIR design were overcome in [5], [6] by employing differential optical detection. Nevertheless, these methods still lead to complex IIR structures—the stability of which cannot be guaranteed. Finite impulse-response (FIR) structures on the other hand are always stable. Synthesis techniques for FIR optical delay-line filters were presented in [7], using cascaded fixed coupling ratio couplers, and in [8], which relied upon optical amplifiers to generate the coefficients. The disadvantage of such an approach is that the use of optical amplifiers significantly increases the cost and complexity of the filters. In contrast, the synthesis technique presented in this paper allows FIR structures to be designed which incorporate only passive components. The resulting all- optical microwave filters are, therefore, robust, economical, and simple to manufacture. By ensuring incoherent optical interference, the output impulses of the filter are restricted to positive-only values. This then allows the application of data windows (which have all-positive coefficients [9], [10]) to the synthesis problem. Manuscript received November 29, 1996; revised April 30, 1997. T. A. Cusick, S. Iezekiel, and R. E. Miles are with the Microwave and Terahertz Technology Group, Department of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, U.K. S. Sales is with the Escuela Optical Communications Group, Departamento de Communicaciones., Universitaria de Gandia, Gandia, Valencia, Spain. J. Capmany is with the Grupo de Comunicaciones ´ Opticas, Departamento de Comunicaciones, ETSI Telecomunicaci´ on, 46071 Valencia, Spain. Publisher Item Identifier S 0018-9480(97)05992-9. Fig. 1. The Mach–Zehnder lattice topology with unit delay length . The structure used by the design algorithm is the sim- plest of the all-optical FIR topologies, the feed-forward, or Mach–Zehnder lattice [1]. This is presented along with a new and rigorous analysis of the optical-intensity impulse response (IR), and its relationship with the coupling ratios in the structure. Based on the results of this analysis, a novel technique for synthesizing symmetrical time-domain IR’s is then described, and a set of the algorithm’s output values is included. Finally, the results of the microwave characterization of such a structure are shown and discussed. II. THE MACH–ZEHNDER LATTICE A. Analysis A single optical Mach–Zehnder section consists of two directional couplers separated by two unequal optical paths. A Mach–Zehnder lattice is produced when several such sections are cascaded [1], as in Fig. 1. In the analysis which follows, the couplers are optical-fiber directional couplers whose behavior is modeled using [1, eq. (3)]. The unit time delay—the difference between the two path lengths—introduces a factor of to the path transmittance, and is realized by a length of optical fiber. Assuming the input port to be the upper arm of the first coupler, we shall now consider the general form of the IR of this structure. For a lattice containing couplers, there are, in total, possible forward paths between the input port and each of the output ports. Since each of these paths must pass once through each of the couplers, with the th coupler introducing a transmittance factor of either when the path couples across the coupler, or when the path travels directly through it, the magnitude of each of the path transmittances will be a product of factors, such that for to (1) Here, is the th forward-path graph transmittance, and will be equal to either or , depending on the route taken by the path. These path transmittances contribute to the 0018–9480/97$10.00  1997 IEEE