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Journal of the Optical Society of America B

Classification of power-degrading mechanisms in an optically pumped four-level laser: an analytical approach

Alphan Sennaroğlu

Published Jul 22, 2019• 18 citations
Publisher

Abstract

In this paper, coupled power-gain equations were derived and solved to investigate the role of different power-degradation mechanisms on the continuous-wave power performance of a laser in the absence of thermal effects. Nine different power-degradation cases were considered, including a low-gain ideal four-level operation, ground-state reabsorption, pump excited-state absorption with and without storage, laser excited-state absorption with and without storage, intermediate storage, and Auger-type energy transfer upconversion with and without storage. There were three distinct types of laser performance identified, in terms of how the output power varies as a function of the pump power. Explicit analytical expressions were derived for the threshold pump power Pth, slope efficiency η, and the product Pthη/T as a function of output coupler transmission T and other physical parameters that describe the power degradation mechanism. The analytical approach developed here provides valuable insight about the role of major power degradation mechanisms in lasers, and it should be applicable to the analysis of a wide range of low-power, optically pumped laser media, including solid-state, fiber, and ceramic lasers.

DOI
10.1364/josab.36.002202

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In this paper, coupled power-gain equations were derived and solved to investigate the role of different power-degradation mechanisms on the continuous-wave power performance of a laser in the absence of thermal effects. Nine different power-degradation cases were considered, including a low-gain ideal four-level operation, ground-state reabsorption, pump excited-state absorption with and without storage, laser excited-state absorption with and without storage, intermediate storage, and Auger-type energy transfer upconversion with and without storage. There were three distinct types of laser performance identified, in terms of how the output power varies as a function of the pump power. Explicit analytical expressions were derived for the threshold pump power Pth, slope efficiency η, and the product Pthη/T as a function of output coupler transmission T and other physical parameters that describe the power degradation mechanism. The analytical approach developed here provides valuable insight about the role of major power degradation mechanisms in lasers, and it should be applicable to the analysis of a wide range of low-power, optically pumped laser media, including solid-state, fiber, and ceramic lasers.
An analytic model for the cw diode pumped alkali laser is developed by considering the longitudinally averaged number densities of the ground 2S1/2 and first excited 2P3/2, and 2P1/2 states. The pump intensity to reach threshold requires fully bleaching the pump transition and exceeding optical losses, typically about 200 Watts/cm2. Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95 - 0.98. For marginal cavity transmission losses, peak performance is achieved for low output coupling. For efficient operation, the collisional relaxation between the two upper levels should be fast to prevent bottlenecking. By assuming a statistical distribution between the upper two levels, the limiting analytic solution for the quasitwo level system is achieved. For properly designed gain conditions, the quasi two level solution is usually achievable and represents ideal performance.
Continuous-wave lasers in which the emitted photon energy may be up to three times greater than that of the incident pump light by virtue of cooperative (coupled atom) upconversion processes are reported for the first time in this thesis. Cw upconversion laser action was obtained at wavelengths of 0.55μ\muμm, 0.70μ\muμm, 0.85μ\muμm and 2.8μ\muμm using infrared excitation in the range λ\lambdaλ = 1.48-1.70μ\muμm in concentrated crystals of Er:CaF$\sb2$ and Er:LiYF$\sb4$. Detailed aspects of the behavior and internal dynamics of these systems have been considered both experimentally and theoretically in this work. Two limiting approaches were applied to gain theoretical insight into possible unique features of cooperative upconversion lasers. These corresponded to strong and weak coupling theories. A density matrix approach describing the strong coupling limit predicted several new results of cooperative interactions, including enhanced quantum efficiency, enhanced energy transfer, and cooperative instabilities. A rate equation analysis appropriate to weaker coupling was used to confirm that cooperative upconversion lasers can operate continuously on self-terminating transitions and established threshold conditions for pair- and trio-pumped lasers. Time dependent upconversion fluorescence measurements were performed to investigate the pumping mechanism of the new lasers experimentally. These observations and measurement of the intensity dependence of upconversion emission established that the inversion mechanism was exclusively cooperative in nature. Upconversion laser instabilities were also studied and related to nonlinear, cooperative dynamics. Unique features of cooperative upconversion lasers were identified, compared with other upconversion pumping schemes, and exploited to demonstrate the first cw mode-locked solid state laser operating in the visible spectral range. On the basis of this work, it may be concluded that cooperative upconversion provides a practical means of generating coherent radiation in new spectral regions, even on self-terminating transitions.
Laser cooling of rare-earth doped solids has been demonstrated across a wide range of material platforms, inspiring the development of simple phenomenological models such as the four-level model to elucidate the universal properties of laser cooling under various operating conditions. However, these models usually require the input of full absorption spectra that must be provided experimentally or by additional complicated atomic modeling. In this Letter, we propose that a four-level model, when extended to admit effective energy levels adaptive to the pumping photon energy, can accurately predict the cooling efficiency as a function of temperature and pumping frequency using only few inputs such as the absorption coefficient measured at a single frequency and temperature. Our model exploits the quasi-equilibrium properties of the excitation of rare-earth ions for the determination of the effective four energy levels. The model is validated against published experimental results for a span of materials including ytterbium/thulium-doped glass and crystals. With the verified model, we derive explicit expressions for the optimal frequency and the operating bandwidth of pumping lasers. Our model significantly simplifies the modeling process of laser cooling and is expected to stimulate further development of optical refrigeration.
Based on an analysis of kinetic processes in the continuous-wave (CW) single-wavelength two-photon pumped Rb-vapor laser (Rb-TPAL), a three-dimensional computational model is established using the rate equation. Based on the application of the model to cavity-enhanced Rb-TPAL [Yuanet al.,Optics Express29, 4858 (2021)], the calculated and measured dependences of the laser power on the pump power show good agreement. We simulate the Rb-TPAL pumped by a high-power CW laser diode and analyze the effects of temperature, vapor cell length, pump waist, vapor cell transmission, and output mirror reflectance on the characteristics of the blue laser. The results suggest that the output power and efficiency of blue laser can be improved by optimizing the above parameters; however, the particles in the52D5/25^{2}\text{D}_{5/2}52D5/2​level face difficulty to transition to the62P3/26^{2}\text{P}_{3/2}62P3/2​level, and this limits the further improvement of blue laser efficiency; therefore, an approach is proposed to improve the efficiency of Rb-TPAL. This study can be useful for designing a two-photon pumped alkali metal laser with high-power output.
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.
Exact and approximate theoretical models of the small-signal single-pass gain in single-mode three-level laser fibers are presented. These models are relevant to the behavior of rare-earth-doped (in particular Er/sup 3+/) silica-based fibers. They account for the effects of both the pump and signal-mode structures and pump excited-state absorption (ESA), the latter being present for some pump wavelengths in Er-doped silica fibers. By relying on the modal overlap integral formalism for four-level lasers, relatively simple closed-form expressions for the pump absorption and the gain are derived. These expressions are also applicable to four level laser fibers by a simple adjustment of some of the model parameters.>