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Journal of the Optical Society of Korea

Analytical Solutions of Birefringence and Dichroism Spectroscopy for the Jg = 0 → Je = 1 Transition

Heung‐Ryoul Noh

Published Aug 25, 2014• 0 citations
Publisher

Abstract

We present accurate analytical solutions of the lineshapes of birefringence (rotation) and dichroism (absorption) spectroscopy for a circular anisotropic medium composed of atoms of the transition $J_g=0{\rightarrow}J_e=1$ . The susceptibility of a weak probe beam was analytically calculated and was averaged over a Maxwell-Boltzmann velocity distribution. The lineshapes of the two spectroscopies were then presented in analytical forms at arbitrary values of the linewidths of the inhomogeneous (Doppler) broadening and the homogeneous (natural) broadening of the atoms.

DOI
10.3807/josk.2014.18.4.365

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We present accurate analytical solutions of the lineshapes of birefringence (rotation) and dichroism (absorption) spectroscopy for a circular anisotropic medium composed of atoms of the transition Jg=0→Je=1J_g=0{\rightarrow}J_e=1Jg​=0→Je​=1 . The susceptibility of a weak probe beam was analytically calculated and was averaged over a Maxwell-Boltzmann velocity distribution. The lineshapes of the two spectroscopies were then presented in analytical forms at arbitrary values of the linewidths of the inhomogeneous (Doppler) broadening and the homogeneous (natural) broadening of the atoms.
We present an analytical study of susceptibility in pump–probe laser spectroscopy for an atomic medium composed of two-level atoms in the Doppler-broadened limit. We derive an accurate analytical formula for susceptibility up to the first (arbitrary) order at the Rabi frequency of the probe (pump) beam. This is expressed in a succinct single term rather than as a complicated summation, as presented in previous papers. We also derive analytical solutions for the linewidth and peak value of the absorption spectrum of the probe beam.
We present an analytical calculation of the susceptibility in Doppler-broadened three-level atomic systems using a diagrammatic method. The optical coherences responsible for the susceptibility of the probe field are obtained from the optical Bloch equations for Ladder (lower or upper transition probed), V and Λ-type three-level atoms up to the first (arbitrary) order in the probe (coupling) field Rabi frequency, and are then averaged over a Maxwell–Boltzmann velocity distribution. Finally, we obtain analytical solutions of the susceptibility for four different three-level atomic systems. In particular, the general expressions of the susceptibility are obtained where the wavelengths of the probe and coupling fields are different from each other.
This work presents a theoretical study on the analytical calculation of the lineshape of polarization spectroscopy (PS) for the transition line 5s2  1S0→5s5p  1P15s^2\;^1S_0{\rightarrow}5s5p\;^1P_15s21S0​→5s5p1P1​ of 88Sr^{88}Sr88Sr . From the obtained analytical form of the PS spectrum, we were able to identify how the saturation affected the lineshape of the PS spectrum. The results obtained will be useful for polarization spectroscopy experiments using the alkaline-earth atoms such as Sr or Yb.
We present an analytic calculation for linear susceptibility in pump-probe spectroscopy for a Doppler broadened atomic vapor. The analytic form of the population of each magnetic sublevel of a 87Rb^{87}\mathrm{Rb}87Rb atom, illuminated by a weak circularly polarized pump beam, was calculated for the lowest order of laser intensity and used in the calculation for the susceptibility of a counterpropagating (copropagating) probe beam. The obtained analytic results for the susceptibility can be used for calculating the absorption or the refractive index of the probe beam as functions of pump beam diameter and intensity.
The effect of level degeneracy on saturated absorption in a resonant medium is considered using a simple but realistic three-level system to model $J=1\ensuremath{\rightarrow}J=0$ atomic transition. Assuming homogeneous broadening and exact resonance, an analytic nonperturbative expression for the medium susceptibility is obtained and used to study propagation of an arbitrarily polarized optical field. Optical saturation affects considerably Zeeman-coherence-induced circular dichroism. The analysis may find application in high-resolution spectroscopy and other branches of nonlinear optics.