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IEEE Journal of Quantum Electronics

Amplified spontaneous emission in spherical and disk-shaped laser media

Amos A. Hardy, D. Treves

Published Sep 1, 1979• 10 citations
Publisher

Abstract

Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.

DOI
10.1109/jqe.1979.1070212

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Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell's equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.

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Flashlamp Pumped Dye Amplifiers

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The major purpose of the work described in this thesis is the experimental and theoretical study of the amplification of the spontaneous emission in dye amplifiers. This work falls into three distinct sections: (a) the study of high-current short-pulse flashtubes operating in (or near) the ablation regime; (b) the study of the amplification process of the spontaneous emission in a homogeneously broadened medium, such as a dye material, in the thin cell case, where there is no variation of the pumping across the cell; and, (c) the study of the amplification of the spontaneous emission in the thick cell case, where gain and index of refraction inhomogeneities exist across the cell thickness. In each case, we have developed theoretical models and compared their predictions with the experimental results. In particular, for the ablation-type flashlamps, it is shown that their behaviour is well represented by an analysis in which the discharge plasma is supposed to radiate as a blackbody at the temperature of the plasma. This model accounts for the fact that the light output from a flashlamp saturates whereas the current does not, provides a more accurate value for the plasma resistivity as a function of temperatures and gives a useful design criterion for determining the physical dimensions of an ablation-type flashlamp. With respect to the amplification of the spontaneous emission in a thin cell, it is mainly shown that (i) the spontaneous emission propagating along the gain medium is subject to narrowing along with shifting of its peak wavelength; (ii) even at moderate pumping the population of the excited singlet state, which determines the gain of the system, is non-uniform along the cell; (iii) it is possible to calculate the unsaturated gain by calculating the intensity of a particular wave-length and its spectral narrowing both as a function of the exciation and compare them with the same quantities measured experimentally; (iv) it is also possible to develop a semianalytic system independent method to measure the gain approximately. The theory developed to account for the propagation of the amplified spontaneous emission (ASE) has been partly extended to cover the case of the propagation and spectral narrowing of the ASE in a thick cell, where non-uniformities of the index of refraction and the gain are important along with the diffraction losses. In this particular case, it is shown that a model, which assumes an index step variation across the cell, and solves the Maxwell's equation for the field propagation along the cell, can account for the spatial distribution of the field across the cell and its manifestation at the far field. Most of the predictions of the model are verified experimentally. In particular, it is shown that (i) in a thick cell, part of the ASE propagates outside the gain medium, because of the lensing effect caused by heating of the lasing material; (ii) the field across the cell can exhibit stable spatial modes, which can produce a far field far from the amplifying cell axis; (iii) it is possible to improve the spectral narrowing of the ASE since saturation can be delayed to higher pumping than before and most of the narrowing occurs below saturation of the gain; (iv) it is also possible to measure the temperature and the index of refraction change due to heating by measuring the far field angle, and estimate the diffraction losses involved in the propagation of the ASE in a thick cell. Finally, a number of suggestions on further research are proposed.

•Oct 1, 1978•0 citations
Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.
Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell's equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.
The output of pulsed, homogeneously broadened amplified spontaneous emission (ASE) lasers operating under conditions of strong saturation is considered. An expression for the maximum power (energy) per unit volume that may be extracted from steady-state (pulsed) systems is derived and shown to be independent of the saturation intensity. Numerical calculations of the temporal evolution of the populations in the laser levels and the growth in the ASE fluence, peak intensity, and spectral width are presented for three types of laser system: quasi steady state, short pump pulses, and self-termination. In all cases the growth in the fluence of the ASE pulse is found to agree with an analytic solution derived for conditions of strong saturation. The calculated growth in intensity of the ASE pulse is compared with expressions derived by Pert [J. Opt. Soc. Am. B11, 1425 (1994)] for the steady-state case. As expected, good agreement is found for the quasi-steady-state system, but in the limit of strong saturation significant differences occur for the short pump pulse and self-terminating laser systems considered. For all cases considered, the variation of the spectral width of the ASE pulse is found to be in reasonable agreement with that predicted by Pert for steady-state conditions.
We formulate a second-quantized theory of propagation in laser-active media and apply it to the description of amplified spontaneous emission for the case of homogeneously broadened three-level atoms in a rodlike geometry with arbitrary Fresnel number. The electromagnetic field is treated in paraxial approximation by an ad hoc quantization scheme, and spontaneous emission into off-axis modes is described by noise operator methods. We show by a scaling (dimensional) analysis how to derive the characteristic fields and lengths for superfluorescence and amplified spontaneous emission. The results show that dye media can be used as experimental analogs for x-ray lasers.
Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.
The major purpose of the work described in this thesis is the experimental and theoretical study of the amplification of the spontaneous emission in dye amplifiers. This work falls into three distinct sections: (a) the study of high-current short-pulse flashtubes operating in (or near) the ablation regime; (b) the study of the amplification process of the spontaneous emission in a homogeneously broadened medium, such as a dye material, in the thin cell case, where there is no variation of the pumping across the cell; and, (c) the study of the amplification of the spontaneous emission in the thick cell case, where gain and index of refraction inhomogeneities exist across the cell thickness. In each case, we have developed theoretical models and compared their predictions with the experimental results. In particular, for the ablation-type flashlamps, it is shown that their behaviour is well represented by an analysis in which the discharge plasma is supposed to radiate as a blackbody at the temperature of the plasma. This model accounts for the fact that the light output from a flashlamp saturates whereas the current does not, provides a more accurate value for the plasma resistivity as a function of temperatures and gives a useful design criterion for determining the physical dimensions of an ablation-type flashlamp. With respect to the amplification of the spontaneous emission in a thin cell, it is mainly shown that (i) the spontaneous emission propagating along the gain medium is subject to narrowing along with shifting of its peak wavelength; (ii) even at moderate pumping the population of the excited singlet state, which determines the gain of the system, is non-uniform along the cell; (iii) it is possible to calculate the unsaturated gain by calculating the intensity of a particular wave-length and its spectral narrowing both as a function of the exciation and compare them with the same quantities measured experimentally; (iv) it is also possible to develop a semianalytic system independent method to measure the gain approximately. The theory developed to account for the propagation of the amplified spontaneous emission (ASE) has been partly extended to cover the case of the propagation and spectral narrowing of the ASE in a thick cell, where non-uniformities of the index of refraction and the gain are important along with the diffraction losses. In this particular case, it is shown that a model, which assumes an index step variation across the cell, and solves the Maxwell's equation for the field propagation along the cell, can account for the spatial distribution of the field across the cell and its manifestation at the far field. Most of the predictions of the model are verified experimentally. In particular, it is shown that (i) in a thick cell, part of the ASE propagates outside the gain medium, because of the lensing effect caused by heating of the lasing material; (ii) the field across the cell can exhibit stable spatial modes, which can produce a far field far from the amplifying cell axis; (iii) it is possible to improve the spectral narrowing of the ASE since saturation can be delayed to higher pumping than before and most of the narrowing occurs below saturation of the gain; (iv) it is also possible to measure the temperature and the index of refraction change due to heating by measuring the far field angle, and estimate the diffraction losses involved in the propagation of the ASE in a thick cell. Finally, a number of suggestions on further research are proposed.