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Soviet Journal of Quantum Electronics

Laser threshold of viscous active media in the presence of induced absorption at stimulated emission wavelength

Gleb A. Abakumov, L T Makarova, Alexander P. Simonov

Published Nov 30, 1976• 2 citations
Publisher

Abstract

A calculation is made of the stimulated emission threshold of organic dye solutions as a function of the diffusion coefficient, intensity of induced singlet–singlet or triplet–triplet absorption at the stimulated emission wavelength, steepness of the leading edge of pump pulses, and other parameters. It is shown that, if the dipole moment of a fluorescence transition is perpendicular to the dipole moments of associated induced singlet–singlet or triplet–triplet absorption transitions, the laser threshold of high–viscosity solutions is considerably lower than that of low-viscosity systems. The maximum value of the ratio of the cross sections of the singlet-singlet absorption and stimulated emission, at which a given molecule ceases to emit stimulated radiation, increases from 1 to 3 when the rotational diffusion coefficient decreases from ∞ to 0.

DOI
10.1070/qe1976v006n11abeh012002

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 14, 2006•0 citations
A calculation is made of the stimulated emission threshold of organic dye solutions as a function of the diffusion coefficient, intensity of induced singlet–singlet or triplet–triplet absorption at the stimulated emission wavelength, steepness of the leading edge of pump pulses, and other parameters. It is shown that, if the dipole moment of a fluorescence transition is perpendicular to the dipole moments of associated induced singlet–singlet or triplet–triplet absorption transitions, the laser threshold of high–viscosity solutions is considerably lower than that of low-viscosity systems. The maximum value of the ratio of the cross sections of the singlet-singlet absorption and stimulated emission, at which a given molecule ceases to emit stimulated radiation, increases from 1 to 3 when the rotational diffusion coefficient decreases from ∞ to 0.
The problem about two-photon induced fluorescence of organic dye active molecules located in spherical transparent microparticles at the ultrashort laser pulses influence was theoretically investigated. The system of kinetic equations for laser generation was written taking into account stimulation transitions. Generation regimes of stimulated radiation were found. Resonator properties of spherical microparticles were theoretically investigated using the method of expanding optical fields into series of eigenfunctions. The breakdown of the beginning of stimulated radiation in the microparticle was determined. It was shown that stimulated radiation intensity depends on degree of its spatial overlap with all other modes of the pump radiation. The interpretation of experimental data of two-photon induced fluorescence in the particles with organic dye was carried out.
In several recent experiments, isotropic lasing action was observed in paints that contain rhodamine 640 dye molecules in methanol solution as gain media and titania particles as optical scatterers. These so-called paint-on laser systems are extraordinary because they are highly disordered systems. The microscopic mechanism for laser activity and the coherence properties of light emission in this multiple-light-scattering medium have not yet been elucidated. In this paper we derive the emission intensity properties of a model dye system with excited singlet and triplet electronic energy levels, which is immersed in a multiple-scattering medium with transport mean free path l*. Using physically reasonable estimates for the absorption and emission cross section for the singlet and triplet manifolds, and the singlet-triplet intersystem crossing rate, we solve the nonlinear laser rate equations for the dye molecules. This leads to a diffusion equation for the light intensity in the medium with a nonlinear intensity-dependent gain coefficient. Using this model we are able to account for nearly all of the experimentally observed properties of laser paint reported so far when l*\ensuremath{\gg}${\ensuremath{\lambda}}_{0}$, the emission wavelength. This includes the dependence of the peak intensity of amplified emission on the mean free path l*, the dye concentration \ensuremath{\rho}, and the pump intensity characteristics. Our model recaptures the collapse of the emission linewidth at a specific threshold pump intensity and describes how this threshold intensity varies with l*. In addition, our model predicts a dramatic increase in the peak intensity and a further lowering of the lasing threshold for the strong scattering limit l*\ensuremath{\rightarrow}${\ensuremath{\lambda}}_{0}$. This suggests a striking enhancement of the characteristics of laser paint near the photon localization threshold in a disordered medium. \textcopyright{} 1996 The American Physical Society.
The problem about two-photon induced fluorescence of organic dye active molecules located in spherical transparent microparticles at the ultrashort laser pulses influence was theoretically investigated. The system of kinetic equations for laser generation was written taking into account stimulation transitions. Generation regimes of stimulated radiation were found. Resonator properties of spherical microparticles were theoretically investigated using the method of expanding optical fields into series of eigenfunctions. The breakdown of the beginning of stimulated radiation in the microparticle was determined. It was shown that stimulated radiation intensity depends on degree of its spatial overlap with all other modes of the pump radiation. The interpretation of experimental data of two-photon induced fluorescence in the particles with organic dye was carried out.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
The threshold pump power density for lasing in dye solutions is found to depend on the photon energy of pumping radiation. An increase in the pumping photon energy can significantly lower the threshold pump power of dye lasers. For an ethanol solution of rhodamine 6G with a concentration of 4×10 18 cm −3 , the threshold power density for pumping radiation with a wavelength of 532 nm is 20-fold higher than for pumping radiation with a wavelength of 347 nm. This phenomenon is associated with the competition of collective spontaneous emission, which can lead to the efficient deactivation of excited molecules in femtosecond times, and the dephasing of excited molecules due to the intramolecular nonradiative processes of absorbed-energy conversion. An increase in the dephasing rate with the increasing energy of exciting photons lowers the efficiency of collective spontaneous emission and increases the concentration of dephased excited molecules responsible for lasing.
The problem about fluorescence of organic molecules located in micropartical-cavity at two-photon absorption in the condition of laser pulse radiation influence taking into account stimulated transitions was theoretically investigated. The approach based on the metod of open-resonator theory with light fields expanded in series of quasinormal vibrational eigenmodes of a dielectric full sphere was used. For active molecules in microcavity the model of generalized two-level system noted with processes of two-photon absorption and emission, spontaneous and stimulated emissions on stokes frequencies was considered. The kinetic equations solution were obtained.