TY - JOUR

T1 - Solution of the Holstein equation of radiation trapping in one-dimensional geometries by the geometric quantization technique

AU - Bezuglov, N. N.

AU - Molisch, A. F.

AU - Klucharev, A. N.

AU - Fuso, F.

AU - Allegrini, M.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We solve the Holstein equation of radiation trapping in an atomic vapor cell by the geometric quantization technique (GQT). In the GQT, the rate equation for the excited-state density is transformed into an “equivalent” Schrödinger equation for an associated quasiparticle. The problem of finding the complete set of radiation escape factors is thus reduced to searching quantized energy values for the quasiparticle locked into the vapor cell. We combine already known solutions for the trapping factors at high opacities with new results for the phase jump at the vapor cell boundary to arrive, within the framework of the GQT technique, at solutions that are valid at all opacities. The phase factors are independent of geometry, and we derive an explicit representation for them by the Wiener-Hopf technique in the most simple geometry, a half-space. Our approach enables an analytical computation of the trapping factors in all practically occurring line shapes (including Voigt lines and hyperfine-split lines), all opacities, and all modes in one-dimensional (1D), 2D, and 3D geometries allowing for variable separation. We present results obtained in 1D geometries at all opacities that show discrepancies within 5% for the lowest-order trapping factor and even less (at the level of approximately 0.1%) for higher-order modes, in agreement with the predictions of the GQT theory that has been developed.

AB - We solve the Holstein equation of radiation trapping in an atomic vapor cell by the geometric quantization technique (GQT). In the GQT, the rate equation for the excited-state density is transformed into an “equivalent” Schrödinger equation for an associated quasiparticle. The problem of finding the complete set of radiation escape factors is thus reduced to searching quantized energy values for the quasiparticle locked into the vapor cell. We combine already known solutions for the trapping factors at high opacities with new results for the phase jump at the vapor cell boundary to arrive, within the framework of the GQT technique, at solutions that are valid at all opacities. The phase factors are independent of geometry, and we derive an explicit representation for them by the Wiener-Hopf technique in the most simple geometry, a half-space. Our approach enables an analytical computation of the trapping factors in all practically occurring line shapes (including Voigt lines and hyperfine-split lines), all opacities, and all modes in one-dimensional (1D), 2D, and 3D geometries allowing for variable separation. We present results obtained in 1D geometries at all opacities that show discrepancies within 5% for the lowest-order trapping factor and even less (at the level of approximately 0.1%) for higher-order modes, in agreement with the predictions of the GQT theory that has been developed.

UR - http://www.scopus.com/inward/record.url?scp=0001207798&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.57.2612

DO - 10.1103/PhysRevA.57.2612

M3 - Article

AN - SCOPUS:0001207798

VL - 57

SP - 2612

EP - 2624

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 4

ER -