Photon avalanche and the mean-field approximation

Abstract

Starting from a microscopic description, we show the analogy between photon avalanche and second-order phase transition. This justifies the validity of the mean-field approximation. Then we show that the rate equations reproduce quantitatively the experimental results as soon as the Gaussian intensity profile of the input beam is taken into account. Moreover, we apply the general Landau theory to the photon avalanche: the absorption between the excited state is the control parameter of the transition whereas the ground-state absorption is an external field. By this way the impact of the residual nonresonant ground-state absorption is clarified.

Photon-Avalanche Effect of Y₂O₃:Er,Yb Nanoparticles Prepared by Laser Ablation in Liquid

“…The increase in upconversion luminescence is very important for the application of nanoparticles. Similar phenomena of bulk of other materials were observed [17][18][19][20]. The mechanism of photon-avalanche would be the followings; Three-photon process of the upconversion luminescence would occur as shown in Fig.…”

“…In general, the upconversion intensity is weak. Previously photon-avalanche effect of bulk upconversion material was reported, which increased upconversion intensity significantly [17][18][19][20]. The photon-avalanche effect of bulk upconversion nanoparticles Y 2 O 3 :Er,Yb was investigated hereby.…”

Violet Upconverted Luminescence via Photon-Avalanche Pumping in Monoclinic LiKYF5:Nd3+ Single-Centered Laser Crystals

“…A number of papers provide a general and theoretical approach to the PA (see, for example, [1 to 6]). More recently, by comparing this nonlinear upconversion process to a second-order phase transition and using the general Landau-Lifshitz theory [7], the fundamental physics associated with this upconversion process has been elucidated [8]. It has been demonstrated in LiYF 4 :1 at% Nd 3 single crystal [8] that excitation at % 603 nm wavelength ( I 11/2 ), but only at low temperature ( 60 K).…”

“…More recently, by comparing this nonlinear upconversion process to a second-order phase transition and using the general Landau-Lifshitz theory [7], the fundamental physics associated with this upconversion process has been elucidated [8]. It has been demonstrated in LiYF 4 :1 at% Nd 3 single crystal [8] that excitation at % 603 nm wavelength ( I 11/2 ), but only at low temperature ( 60 K). The excitation power threshold increases with temperature essentially due to the evolution of the ESA cross-section which decreases from 3X5 AE 0X4 Â 10 À20 cm 2 at 6 K to 1X7 AE 0X2 Â 10 À20 cm 2 at 55 K [3].…”

VUV Laser Spectroscopy of Trivalent Rare-Earth Ions in Wide Band Gap Fluoride Crystals

“…The second method applies upconversion pumping arrangement with all solid state laser elements [10][11][12], which greatly simplifies the experimental ob stacles arising from the VUV pumping. The radiative interconfigurational d-f transitions of the RE activated ions, in the wide band gap of dielectric crystals, offer the possibility that these materials can be used in a variety of applications and for generating coherent VUV or UV light.…”