Analysis of EM Sources Behavior in Closer Proximity Cahit Karakuş Ertuğrul Bolcal Çağatay Aydın Doğu Çağdaş Atilla Ramazan Köprü B. S. Yarman Istanbul Kültür University Istanbul, Turkey Istanbul Kültür University Istanbul, Turkey Istanbul University Istanbul, Turkey Istanbul University Istanbul, Turkey Istanbul Technical University Istanbul, Turkey Istanbul University Istanbul, Turkey Abstract— Determination of position, direction and radiation characteristics of an electromagnetic source is an important issue in radar and wireless sensor applications. Basically, in order to increase performance of antenna radiation in wireless communication, radar and remote sensing optimization is required. Hence, it must be analyzed the electromagnetic power from the source to the free space with minimum loss of energy and maximum efficiency. Electromagnetic Gaussian beam is used to solve the electromagnetic radiation and scattering problems in electromagnetic simulation tools. In this work, characteristics of electromagnetic sources in close proximity are studied. Schwarzian Derivative Method is employed to investigate the chaotic behavior of dynamics of electromagnetic sources. Experimental results show that Schwarzian derivative facilitates the computation of the chaotic behavior of a function. Keywords- electromagnetic source; antenna array; chaotic behaviour; Schwarzian derivative; Gaussian beam. I. INTRODUCTION In recent, design of antenna arrays has increasingly become important in wireless communications systems. The major advantages of antenna arrays are securing the capability of a steerable beam, providing a high gain by using simple antenna elements. Furthermore array antennas provide high gain in multipath signal reception and enable array signal processing [1]. On the other hand, a dynamical system can be called as chaotic if its orbit or position is unstable, it is sensitive to initial conditions and it evolves with time [2,3]. The purpose of this work is to investigate chaotic behavior of radiation pattern of the antenna array that depends on the distance between antenna elements. Pattern of the antenna array can be obtained by multiplying the element pattern by the array factor [1]. The Gaussian function is used as radiation pattern of unit antenna element. Gaussian beam is generated by approximating transverse electric field and intensity distributions of a beam of electromagnetic radiation by Gaussian functions. The mathematical function that describes the Gaussian beam is a solution to the paraxial form of the Helmholtz equation. The solution, in the form of a Gaussian function, represents the complex amplitude of the beam's electric field. The electric field and magnetic field together propagate as an electromagnetic wave. A description of just one of the two fields is sufficient to describe the properties of the beam. Gaussian beam is used to compute the near/far fields of antennas radiation when they are illuminated by a feed with a radiation pattern [4-6]. II. ANALYTICAL DEFINITION OF CHAOTIC BEHAVIOUR OF RADIATION PATTERN OF ANTENNA ARRAY One of the most important characteristic of an array is the change of its radiation pattern as response to variety of excitations of its antenna elements. The radiation pattern of the antenna array, called the array pattern, can be changed upon exciting its elements both current magnitudes and current phases in contrast to a single antenna having fixed radiation pattern. Hence, one can simply has a freedom of design a certain desired array pattern from an array, without changing its physical dimensions. Moreover, we can achieve many signal processing functions such as spatial filtering, interference suppression, gain enhancement, target tracking, etc. by manipulating the received signals from the individual antenna elements in variety of ways. Therefore given an antenna array of identical elements, the radiation pattern of the antenna array can be calculated according to the pattern multiplication theorem given below [1].           Array Element Pattern is described as the pattern of the individual array element and Array Factor is a function depends only on the geometry of the array and the excitation (amplitude, phase) of the elements. Moreover, based on the above equation, normalized array function can be obtained as,       ቀ   ቁ  ቀ   ቁ (1) where,  is the element number of the antenna array,    ,  is separation distance between two antenna elements and  is polar angle. The normalized element field pattern for the antenna as a Gaussian Function is,    (     ) (2) In this equation,  is the amplitude and  is the beamwidth of Gaussian Function. For a broadside array, in order to satisfy above equation along the z-axis main lobe is at     . A plane wave