Self-pulsing laser as oscillator Toda: approximations through elementary functions

Abstract

A simple model of self-pulsation in lasers is considered. The laser is described by the system of two ordinary differential equations for the number of photons in the cavity and the number of excitations in the active medium, leading to the equation for the oscillator Toda with damping. For the case of strong spiking, the damping is considered as perturbation; the estimates in terms of elementary functions are suggested for the period of pulsation, damping rate, amplitude and phase of pulsation, quasi-energy and the output power. These estimates are compared to the numerical solution and to the experimental data.

Non-uniform black strings and the critical dimension in the 1/D expansion

“…This is equivalent to the differentiated version of the effective equation obtained in [16]. 7 As pointed out in [16], eq (4.17) is the system equivalent to the undamped Toda oscillator [24].…”

Verified solutions of two-point boundary value problems for nonlinear oscillators

“…For u ∈ H 1 0 (0, 1), (9), (11), and (12) supply (as implicitly already shown in the proof of Lemma 1)…”

“…If ||v −û|| H 1 0 < 2α, ||w −û|| H 1 0 < 2α, and thus ||v −û|| ∞ < α, ||w −û|| ∞ < α by (9), this means using Conditions 1 d), e), Remarks 1 and 2, (9) and c := ||û|| ∞ + α:…”

“…The Toda oscillator with small damping parameters 0 < η, ζ 1 was used in[9] as a model of self-pulsation in lasers 6. The computation with this large number of grid points was only carried out for u 2 .…”

Kinetics and mechanism of sodium (Z)-3-(5-chloro-2-((5-chloro-3-(3-sulfonatopropyl) benzothiazol-2(3H)-ylidene)methyl)benzo-thiazol-3-ium-3-yl)propane-1-sulfonate adsorption on gold nanoparticle colloids of different properties and size

“…Eksponencijalna funkcija drugog reda ima primenu u teoriji brojeva [178][179][180], fizici [181], teorijskoj biologiji [182] i kod tumačenja kompleksnih algoritama [183,184]. Pored toga eksponencijalna funkcija drugog reda je korišćena za ispitivanje različitih kinetika, kao što su kinetika hetrogene i enzimske katalize [185], adsorpcije [186], interpolimernih kompleksa [187], termo-indukovanih prelaza u micelarnim sistemima [188], fluorescencije kod polimernih koloida [189], kinetika odgovora pH senzora zasnovanog na koloidnom templatu [190] itd.…”