Modeling of Yb 3+ /Er 3+ -codoped microring resonators Juan A. Vallés a,⇑ , Ramona Ga ˘la ˘tus ß b a Department of Applied Physics and I3A, Faculty of Sciences, University of Zaragoza, C/P. Cerbuna 12, 50009 Zaragoza, Spain b Department Basis of Electronics, Optoelectronics and Optical Integrated Components Group, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania article info Article history: Available online 4 November 2014 Keywords: Active integrated microring resonator Yb 3+ /Er 3+ -codoping Energy-transfer inter-atomic mechanisms Design requirements abstract The performance of a highly Yb 3+ /Er 3+ -codoped phosphate glass add–drop microring resonator is numer- ically analyzed. The model assumes resonant behaviour of both pump and signal powers and the depen- dences of pump intensity build-up inside the microring resonator and of the signal transfer functions to the device through and drop ports are evaluated. Detailed equations for the evolution of the rare-earth ions levels population densities and the propagation of the optical powers inside the microring resonator are included in the model. Moreover, due to the high dopant concentrations considered, the microscopic statistical formalism based on the statistical average of the excitation probability of the Er 3+ ion in a microscopic level has been used to describe energy-transfer inter-atomic mechanisms. Realistic param- eters and working conditions are used for the calculations. Requirements to achieve amplification and laser oscillation within these devices are obtainable as a function of rare earth ions concentration and coupling losses. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction Microring resonators (MRR) have attracted much attention as multifunctional components for signal processing in optical communication systems [1–4]. Recently, due to their fabrication scalability, functionalization and easiness in sensor interrogation MRR with chip-integrated linear access waveguides have emerged as promising candidates for scalable and multiplexable sensing platforms, providing label-free, highly-sensitive and real-time detection capabilities [5–8]. The near infrared spectral range and, in particular, the 1.5-lm wavelength band is already employed in several bio/chemical sensing tasks using MRR [9–11]. If gain is incorporated inside the ring, losses (intrinsic absorp- tion, scattering, bend, etc.) can be compensated, filtering and amplifying/oscillating functionalities are combined [12,13] and the sensing potentialities of the device become enhanced [14]. Due to their excellent spectroscopic and solubility characteristics phosphate glass is a suitable host for rare earth (RE) high doping and Yb 3+ /Er 3+ -codoped phosphate glass integrated waveguide amplifiers and lasers provide a compact, efficient and stable performance [15]. However, when the host material of an MRR is Yb 3+ /Er 3+ -codoped the modeling of the performance of the active structure increases its complexity, due to the coupled evolution of the optical powers and the RE ions population densities. More- over, the high RE-doping levels that the device dimensions require enhance the Er 3+ -ion efficiency-limiting energy-transfer inter- atomic interactions (homogeneous upconversion and migration) which have to be considered for an optimized design [16]. In the literature models describing RE-doped microfiber ring lasers can be found [17] but the dopant concentrations were much lower than those needed in MRRs and some simplified models for RE-doped MRR have been published where the energy-transfer mechanisms reinforced by the high RE-dopant concentrations were simply ignored [18]. In a preceding paper we reported some results of the optimized active performance of this device when the effect of high dopant concentrations was incorporated [19]. How- ever, in that paper not only the gain coefficient was averaged along the amplifier total length but also the pump resonant behaviour inside the ring and the influence of coupler additional losses were neglected. In this paper we present a much more detailed model of the performance of a highly Yb 3+ /Er 3+ -codoped phosphate glass add/ drop filter that overcomes previous models deficiencies. In Section 2 the model for an active MRR is described by using a formalism for the intensity rates of the optical powers (pump and signal) at res- onance affected by their interaction with the dopant ions through absorption/emission processes. In Section 3 we calculate the per- formance of an active MRR, in order to analyze its optimized design and to determine the conditions to achieve amplification and oscillation. http://dx.doi.org/10.1016/j.optmat.2014.10.028 0925-3467/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +34 976 762444; fax: +34 976 761233. E-mail address: juanval@unizar.es (J.A. Vallés). Optical Materials 41 (2015) 126–130 Contents lists available at ScienceDirect Optical Materials journal homepage: www.elsevier.com/locate/optmat