Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1243 Optimization of Coherence Multiplexed Coding for High Density Signal Processing S. Elwardi 1, 2 , M. Zghal 1 , and B.-E. Benkelfat 2 1 Cirta’Com Laboratory, Engineering School of Communication of Tunis (Sup’Com) University of Carthage, Ghazala Technopark, Ariana 2083, Tunisia 2 Institut T´ el´ ecom, T´ el´ ecom SudParis SAMOVAR UMR INT-CNRS 5157 9 rue Charles Fourier 91011 Evry Cedex, France Abstract— In this paper, we study the effects of the divergence of a Gaussian beam in coher- ence multiplexed coding technique. We use this optical system for high density signal parallel arithmetic operations. We illustrate the variation of the measurement coherence length as func- tion of the angular divergence for different wavelength λ, beam-waist W 0 , and z 1 , the distance travelled by the first beam of the interferometer. We show that the divergence of a Gaussian beam introduces an additional crosstalk between light fields. 1. INTRODUCTION Real time optical arithmetic operation of signals has found a wide range of applications in both temporal and spatial domain. The most commonly used method for this fundamental arithmetic uses interferometric configurations [1], a noninterferometric method [2] and also the basic joint transform correlator architecture [3]. In our research work, in a novel and original application of coherence multiplexed coding tech- nique, we propose a high density signal processing [4]. Coherence multiplexed technique is an interesting alternative method among the existing different techniques for optical communication and signal processing. It has been used for sensing of high intensity and wideband electric fields [5], for transmitting simultaneously a several signals through a single light beam [6] and also for pro- cessing data such as faster matrix-vector, matrix-matrix products [7, 8]. Let’s recall briefly that the N -multiplexed coherence system is composed by a cascade of N encoding modules (EM ) and a decoding module (DM ). Each EM i is formed by a birefringent electro-optic modulator (EOM i ) and a birefringent slab Q i set between two polarizers (P ) and introducing a static optical path difference (OPD i ), i =1,...,N . The main condition to have coherence modulation is the choice of the static OPD, which must be larger than the coherence length of the source (Lc) [6]. In this paper, in the context of increased need of optimization and performance in optical coherence multiplexed technique, and in order to reduce noise and crosstalk, we study the effect of diffraction in coherence multiplexed systems. In the second section, by using a simple Gaussian model, we report the measurement of the coherence length of the source as function of the angular divergence θ for difference value of the distance traversed by the first beam z 1 , wavelength λ and beam-waist size W 0 . Finally, we find out the value of the additional crosstalk introduced in the coherence multiplexed system as function of the divergence and suggest a solution based on the optical properties of the birefringent elements to reduce the crosstalk. 2. DIFFRACTION EFFECT ON COHERENCE LENGTH MEASUREMENT To have coherence modulation of light, it is mandatory to introduce a static OPD greater than the coherence length of the source. In this context, we have performed a numerical study of the measurement of coherence length L c,meas of the source, which is usually measured, in laboratory, through the Michelson interferometer. The schematic diagram of this interferometer is illustrated in Fig. 1(a). As we can see, that the incident light is splitted into two equal parts via the beam splitter (BS ). They traverse, respectively, the distance z 1 = z m +2D 1 and z 2 = z m +2D 2 . As a result, the important parameter that characterizes the interference pattern, at the output of the Michelson interferometer, is the fringe visibility V . If we consider, a cylindrical coordinates system (ρ, z ), After some approximations the fringe visibility will take the form [9, 10], V ≈ 2 W 1 W 2 + W 2 W 1 (1)