Semi-classical Model And Numerical Analysis On Anti-Stokes Radiation Cooling For Tm Doped Solids

Laser cooling of solids is regarded as the interaction between solid-state and laser material.It is to remove phonon energy from the solid matrix material by means of optical radiation,so as to achieve the purpose of cooling the temperature of the solid material.Laser cooling of solids is usually based on the physical principle which is that the luminescence center induced by laser produces anti-Stokes fluorescence radiation.It is an all-optical refrigeration technology with no vibration,no noise,no electromagnetic pollution and other unique advantages.Therefore,it has a very broad application background in the field of refrigeration technology of aerospace and electronic chip.In this paper,we present a theoretical scheme of anti-Stokes fluorescence cooling in Tm-doped rare earth ions,based on the theory of semi-classical and radiative thermal balance,combined with the energy level structure of Tm ion luminescence center,and the semi-classical model of non-coherent anti-Stokes fluorescence cooling is developed,at the same time,the mechanism of coherent radiation is introduced,then the radiation cooling performance of thulium-doped solids is numerically analyzed.By the analysis of density matrix,the semi-classical theory model to describe the anti-Stokes fluorescence cooling with Tm-doped solids is established.With 1.9 ?m laser to induce Tm ions so as to produce 1.8 ?maverage fluorescence wavelength radiation,the typical three-level atomic system can be adopted to deal with anti-stokes excitation radiation process for Tm ion,the Hamiltonian of anti stokes excitation radiation of a three-level atomic system can be given under the electric dipole interaction approximation,and the motion equation of density matrix can be established by making use of the perturbation method and the rotating wave approximation of quantum mechanics.Combined with the thermal balance analysis of fluorescence radiation refrigeration,then the semi-classical theory in cooling power and cooling efficiency of the fluorescence radiation can be described in details.From the perspective of statistical average quantum mechanics,anti-stokes single atomic fluorescence radiation refrigeration capacity can be revealed.Taking into account the spontaneous collective coherent effect between atoms in the excited state of Tm ions system,the coherent anti-Stokes superradiance system is introduced,the nonequilibrium cooling model of superradiance which can give consideration to the anti-Stokes radiation effects and the process of internal thermal excitation is established,and the superradiance refrigeration capacity of Tm-doped is analyzed numerically.As for Tm doped ZBLAN glass,we adopt the union scheme of using the continuous-wave pump laser at 1.9 ?m and the pulse pump laser at 1.8 ?m.The radiation thermal equilibrium parameter equation of superradiance is provided,the number of population dynamics response of the system of superradiance cooling is numerically simulated,and the laser cooling power and the cooling efficiency in the scheme of anti-Stokes superradiance system are numerically calculated.The superradiance cooling performance of Tm doped solids is theoretically evaluated,further to discuss that the superradiance cooling scheme has the potential advantage in improving the laser refrigerating capacity of Tm doped solid materials.