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International Conference Laser Optics (ICLO)

Analysis of the processes of interection of photons in the spectral of the pump and laser radiation with Yb3+ fiber amplifier medium

Mariya G. Slobozhanina, A.V. Bochkov

Published Nov 2, 2020• 0 citations
Publisher

Abstract

The paper presents kinetic equations based on conservation laws describing the changes in ion populations over energy states, and a sequential derivation of equations describing the changes in the intensity of optical radiation in the core of the active fiber. The physical limitations of this approach are indicated.
DOI
10.1109/iclo48556.2020.9285739

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An analysis is made of some processes that occur under conditions of accumulation of population inversion due to the 4 I 13/2 – 4 I 15/2 resonant transition in Er 3+ ions in ytterbium–erbium (Yb–Er) glasses of various compositions. Methods of measuring the parameters of direct and reverse excitation energy transfer between Er 3+ and Yb 3+ ions are also studied. It is found that, under certain conditions achieved in practice, appreciable bleaching of the medium should be observed at the frequency of the pump radiation, particularly under conditions of high-intensity reverse transfer of excitation energy from Er 3+ to Yb 3+ ions. This is typical of glasses having a low rate of intracenter relaxation of Er 3+ ions. It is also shown that nonsteady-state rate equations that assume a linear relationship between the rate of interionic transfer and the ground state population of the acceptor consistently describe the energy characteristics of the excitation processes of Yb–Er glasses. In this case, it is not necessary to introduce in the calculation model additional excitation losses that increase nonlinearly with the pump radiation.
Decoupling of equations for the diagonal and nondiagonal elements of the density matrix of laser radiation is used in an analysis of the interaction of the radiation field with an active medium. An algorithm for the calculation of the eigenvalues and eigenvectors is proposed for the diagonal elements describing the radiation field statistics. The first minimal (in respect of the magnitude) eigenvalues are calculated and nonequilibrium distribution functions are found for the dynamics of a transition from a vacuum to an equilibrium state; the results agree well with those obtained in machine (numerical) experiments. The equations for the nondiagonal elements of the density matrix are used to find the characteristic times of changes in these elements and to determine the emission line width.
The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The fundamental concern of this investigation is the spectral behavior of the radiation in the nonlinear regime; hence, the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. These expressions should be easily susceptible to detailed experimental observations. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed with some detail. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is extensively explored in several numerical examples. The connections of this study with the time-domain work of Risken and Nummedal, on self-pulsing in a ring-laser configuration, are clearly established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ("Raman-type terms"), and saturation phenomena. The predicted narrowing-rebroadening rate is compared with expressions found in previous literature.
POPULATION RATE EQUATIONS From the discussion in the preceding chapter, it is clear that population inversion is the basic condition for an optical gain. For any system in its normal state in thermal equilibrium, a low-energy level is always more populated than a high-energy level, hence there is no population inversion. Population inversion in a system can only be accomplished through a process called pumping by actively exciting the atoms in a low-energy level to a high-energy level. If left alone, the atoms in a system relax to thermal equilibrium. Therefore, population inversion is a nonequilibrium state that cannot be sustained without active pumping. To keep a constant optical gain, continuous pumping is required to maintain population inversion. This condition is clearly consistent with the law of conservation of energy: amplification of an optical wave leads to an increase in optical energy, which is possible only if the required energy is supplied by a source. Pumping is the process that supplies energy to the gain medium for the amplification of an optical wave. There are many different pumping techniques, including optical excitation, electric current injection, electric discharge, chemical reaction, and excitation with particle beams. The use of a specific pumping technique depends on the properties of the gain medium being pumped. The lasers and optical amplifiers of particular interest in photonic systems are made of either dielectric solid-state media doped with active ions, such as Nd:YAG and Er:glass fiber, or direct-gap semiconductors, such as GaAs and InP. For a dielectric gain medium, the most commonly used pumping technique is optical pumping using either an incoherent light source, such as a flashlamp or a light-emitting diode, or a coherent light source from another laser. A semiconductor gain medium can also be optically pumped, but it is usually pumped by electric current injection. In this section, we consider the general conditions for pumping to achieve population inversion. Detailed pumping mechanisms and physical setups are not addressed here because they depend on the specific gain medium used in a particular application. The net rate of increase of the population density in a given energy level is described by a rate equation. As we shall see below, pumping for population inversion in any practical gain medium always requires the participation of more than two energy levels.
"Doping a part of the optical fiber core by (Er3+ ) ions in presence of external pumping power will lead to form the erbium-doped fiber amplifier (EDFA).The performance of this optical amplifier depends on (the power and the wavelength of the pumping laser, the power and wavelength of the input signal, amplifier length, ion concentration). These parameters will affect the characteristics of EDFA such as amplifier gain, gain saturation, noise figure and output power. However, these characteristics can be determined by solving the EDFA propagation and rate equations. The solution of these equations of two-level laser medium can be done numerically. In this paper, we are proposed a novel method to solve these equations. The reconstructed results are perfectly coincided the well known numerical results.