Published in IET Communications Received on 22nd October 2011 Revised on 20th June 2012 doi: 10.1049/iet-com.2011.0773 ISSN 1751-8628 Characterisation of bifurcation and chaos in silicon microring resonator I.S. Amiri 1 R. Ahsan 2 A. Shahidinejad 3 J. Ali 1 P.P. Yupapin 4 1 Institute of Advanced Photonics Science, Nanotechnology Research Alliance, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Malaysia 2 Department of Computer, Islamic Azad University, Qom branch, Qom, Iran 3 Faculty of Computer Science & Information Systems (FCSIS), Universiti Teknologi Malaysia (UTM), 81300 Johor Bahru, Malaysia 4 Advanced Research Center for Photonics, Faculty of Science King Mongkut’s Institute of Technology Ladkrabang Bangkok 10520, Thailand E-mail: isafiz@yahoo.com Abstract: This study investigates the non-linear behaviours of light known as bifurcation and chaos during the propagation of light inside a non-linear silicon microring resonator (SMRR). The aim of the research is to use the non-linear behaviour of light to control the bifurcation and chaos of SMRR, which are used in engineering, biological and security systems. Bifurcation and chaos control deals with the modification of bifurcation characteristics of a parameterised non-linear system by a designed control input. The parameters of the SMRR cause bifurcation to happen in smaller round-trips among the total round-trip of 20 000 or input power. Effective parameters such as the refractive indices of a silicon waveguide, coupling coefficients (k) and the radius of the ring (R) can be selected properly to control the non-linear behaviour. Simulated results show that rising non-linear refractive indices, coupling coefficients and radii of the SMRR lead to descending input power and round-trips when bifurcation occurs. Therefore bifurcation behaviour can be seen at a lower input power of 44 W, where the non-linear refractive index is n 2 ¼ 3.2 × 10 220 m 2 /W. The smallest round-trips of 4770 and 5720 can be seen for the R ¼ 40 mm and k ¼ 0.1, respectively. 1 Introduction In the last few years, power system dynamics have been studied from a non-linear dynamics point of view through bifurcation theory. Non-linear behaviour of light inside a silicon microring resonator (SMRR) occurs when a strong pulse of light is input into a ring system, a process used for many applications in signal processing and communication [1]. Bifurcation controls with various objectives have been implemented in experimental systems and simulated theoretically, as well as used in a great number of optical [2–4], engineering [5] and biologically designed systems [6]. The bifurcation properties of a ring system can be modified via various control methods. Theoretical studies of ring systems have shown that these systems have the same traits as ring cavities [7, 8] and the Fabry–Pe ´rot system [9–11]. Nakatsuka et al. [12] have shown that chaotic signal behaviour can be seen after generating bifurcation. Additionally, Yupapin et al. [13] demonstrated the non- linearity behaviours of a travelling pulse inside a fibre ring resonator. The behaviour of light travelling in a non-linear ring resonator is well described by Yupapin and Suwancharoen [14]. Laser Gaussian pulse input propagates inside the ring resonators system, which is introduced by the non-linear Kerr effect. More details about these phenomena have been explained by Ferreira [15]. One such phenomenon, known as bifurcation, has been used in digital coding applications [16, 17]. Several works have been done to show the applications of chaos and bifurcation, which can be seen in the [18–22]. In this work, the bifurcation performance of light in a fibre microring resonator device is analysed and characterised. Controlling bifurcation behaviour can be implemented by controlling the round-trip and input powers of the ring system by variating parameters. Bifurcation control not only is important in its own right, but also suggests a viable and effective approach for chaos control that can be used to generate secure codes in digital information processing. Therefore bifurcation and chaos are usually twins [23, 24]. 2 Theory of propagation of light inside SMRR The non-linearity of the fibre ring is of the Kerr-type, wherein the non-linear refractive index is given by n = n 0 + n 2 I = n 0 + n 2 A eff   P (1) where n 0 and n 2 are the linear and non-linear refractive indices, whereas I and P are the optical intensity and optical field power, respectively. The effective mode core area of the fibre is A eff , which ranges from 0.1 to 0.5 mm 22 . In the simplest microring structure, a waveguide is coupled to a IET Commun., 2012, Vol. 6, Iss. 16, pp. 2671–2675 2671 doi: 10.1049/iet-com.2011.0773 & The Institution of Engineering and Technology 2012 www.ietdl.org