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Optics Communications

Susceptibility for inhomogeneously broadened three-level atomic systems: Simple analytical solutions using Lorentzian distribution

Heung‐Ryoul Noh, Han Seb Moon

Published Jul 18, 2013• 0 citations
Publisher
DOI
10.1016/j.optcom.2013.07.020

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One characteristic normally used to distinguish inhomogeneous broadening from homogeneous broadening is the saturation behavior occurring when irradiation takes place at line center. The usual behavior found is that the absorption coefficient decreases as a negative power of 1 + I/Isat; a power of −1 indicates homogeneous broadening and a power of −½ denotes inhomogeneous broadening. It is shown here that, in the rate equation limit, this behavior is followed in most cases even though the homogeneous and inhomogeneous absorption profiles can have any line shape. The homogeneous line shape, in particular, need not be Lorentzian; its line center saturation behavior will be the same as that of a Lorentzian, however. If the inhomogeneous broadening is due to a distribution of atomic center frequencies, in the inhomogeneous limit the usual line center saturation behavior will be found no matter what the combination of homogeneous and inhomogeneous line shapes. However, if the broadening is inhomogeneous because of a distribution, among the individual atoms, in any property of the absorption profile other than center frequency (for example, the homogeneous linewidth), the saturation properties are not as simple, and in fact the inhomogeneous limit may not even exist.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
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.
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.
One characteristic normally used to distinguish inhomogeneous broadening from homogeneous broadening is the saturation behavior occurring when irradiation takes place at line center. The usual behavior found is that the absorption coefficient decreases as a negative power of 1 + I/Isat; a power of −1 indicates homogeneous broadening and a power of −½ denotes inhomogeneous broadening. It is shown here that, in the rate equation limit, this behavior is followed in most cases even though the homogeneous and inhomogeneous absorption profiles can have any line shape. The homogeneous line shape, in particular, need not be Lorentzian; its line center saturation behavior will be the same as that of a Lorentzian, however. If the inhomogeneous broadening is due to a distribution of atomic center frequencies, in the inhomogeneous limit the usual line center saturation behavior will be found no matter what the combination of homogeneous and inhomogeneous line shapes. However, if the broadening is inhomogeneous because of a distribution, among the individual atoms, in any property of the absorption profile other than center frequency (for example, the homogeneous linewidth), the saturation properties are not as simple, and in fact the inhomogeneous limit may not even exist.