ORIGINAL ARTICLE European Journal of Applied Physics www.ej-physics.org DOI: http://dx.doi.org/10.24018/ejphysics.2021.3.1.43 Vol 3 | Issue 1 | January 2021 6 I. INTRODUCTION Stochastic Resonance (SR) is a topic of increasing interest in several scientific domains [1]-[4], being intensively investigated since it has been referred for the first time in 1981 [1], [2]. Recent works have shown that this subject is also relevant in linear systems [5]-[6], suggesting that the effect of SR on signal-to-noise ratio (SNR) calculations can be included in laser simulation models [7], for the analysis of the electric signal current modulation and the electro-optical signal conversion inherent to the laser emission process. This may be particularly important in the area of Optical Communication Systems (OCS), where one of the main goals is to insure the single longitudinal mode (SLM) operation, by an adequate design of the laser structure [8]-[15]. In section II of the present paper, we extend the analysis described in [7] to non-rectangular waveguides, by considering a more realistic situation that takes into account a non-linear optical gain versus carrier concentration dependence for the semiconductor description [8]-[15]. In section III, some results concerning the power spectrum and the SNR of the photon density are presented and discussed, considering the device geometry. Finally, in section IV, some conclusions and future work are summarized. II. MODEL The starting point corresponds to the single-mode rate equations for semiconductor lasers that include the Langevin noise sources. They are given by:   =   −    −   () +   (1)   =[   Γ() −   ℎ ]  + Γ    +  (2) where J is the current density, N is the carrier density, S the photon density, q is the modulus of the electron charge, d is the active layer thickness,   is the spontaneous-emission lifetime of carriers, τph is photon lifetime, c is the light velocity in vacuum,   and   are the carrier and photon noises, respectively, βsp is the spontaneous-emission factor, Γ is the optical confinement factor and g is the optical gain. The photon lifetime depends on the total optical loss, which includes the internal losses and the mirror losses; the spontaneous emission factor is a measure of the fraction of the spontaneous emission that is coupled to the lasing mode, which is typically in the range 10 −3 to 10 −4 . The Langevin Numerical Analysis of Dielectric Optical Waveguides João Paulo N. Torres, Carlos A. F. Fernandes and Ricardo A. Marques Lameirinhas ABSTRACT The stochastic resonance (SR) in direct-modulated laser diodes is investigated using an analytical approach based on the laser rate equations for the carrier and photon densities, that include the cross correlation between the photon and carrier noises. This subject may be particularly important in the domain of Optical Communication Systems, where increasing demands on laser performance have led to the fabrication of more and more complex structures. In viewing the development of the associated technology, the importance of the simulation tools revealed of crucial importance. Keywords: Lasers, Optical Communications, Optics, Optoelectronic Devices, Ring Waveguides. Published Online: January 4, 2021 ISSN: 2684-4451 DOI :10.24018/ejphysics.2021.3.1.43 João Paulo N. Torres Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisbon, Portugal. Instituto de Telecomunicações, Lisbon, Portugal. (e-mail: joaotorres tecnico.ulisboa.pt) Carlos A. F. Fernandes Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisbon, Portugal. Instituto de Telecomunicações, Lisbon, Portugal. (e-mail: ffernandes tecnico.ulisboa.pt) Ricardo A. Marques Lameirinhas* Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisbon, Portugal. Instituto de Telecomunicações, Lisbon, Portugal. (e-mail: ricardo.lameirinhas tecnico.ulisboa.pt) *Corresponding Author @ @ @