Annual Meeting Optical Society of America

Generalized line broadening and saturation behavior

Albert T. Rosenberger

Published Jan 1, 1989• 0 citations

Abstract

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.

DOI: 10.1364/oam.1989.mgg6

Related papers

Saturation broadening by inhomogeneous fields

James C. Camparo

According to the standard Karplus-Schwinger theory of saturation broadening, saturated line shapes are Lorentzians with linewidths that increase linearly with the perturbing field strength. This, however, is not what is observed experimentally when the saturating field is inhomogeneous. If the saturating field strength varies significantly over the experimental signal volume, we find that the saturated line shapes are strikingly non-Lorentzian. The ``sharpness'' of the experimental line shapes is quantified by an ``effective linewidth,'' which is the half width at half maximum of a Lorentzian that approximates the experimental line shape near line center. For certain classes of inhomogeneous fields, we find that this effective linewidth increases approximately as the square root of the saturating field strength, rather than linearly. We show that this class of inhomogeneous fields is distinguished by the presence of a node in the field geometry, and that the effect arises because the line shape near line center is dominated by the atomic population in the vicinity of the node. These results indicate the importance of understanding and accounting for inhomogeneous field effects when extracting physical information from experimental line shapes.

Physical Review AJan 1, 198913 citations

Inhomogeneous broadening

Luigi Lugiato, Franco Prati, Massimo Brambilla

Up to this point we have always assumed that all the atoms which interact with the radiation field have the same atomic transition frequency, with an atomic linewidth given by γ ⊥ . This configuration is called homogeneous broadening. However, in the great majority of lasers the linewidth is inhomogeneously broadened , because the atomic frequency follows a distribution. For example, in solid-state lasers such as the ruby laser and fiber lasers the inhomogeneity is due to the imperfections in the crystalline structure of the material. In gas lasers, where the atoms or molecules are free to move, the inhomogeneous broadening is due to the Doppler effect, for which a molecule moving with velocity v in a field of frequency ω and wave vector k experiences an effective frequency ω ′ = ω − k · v [8]. Since what matters is the difference between the atomic transition frequency and the field frequency, we can keep the field frequency fixed and imagine that the field interacts with different groups of atoms that move with different velocities and therefore have different transition frequencies. The realistic velocity distribution is a Gaussian, for which the corresponding distribution for the modulus of the velocity is Maxwellian. However, in the following we will mainly analyze the case of a Lorentzian distribution for the atomic transition frequency, because this allows an analytical treatment. Again for the sake of simplicity, we will limit our analysis to the case of a ring cavity. In Section 15.1 we will generalize to the inhomogeneous-broadening configuration the modal equations for the case of homogeneous broadening, which were formulated in Chapter 12. In Section 15.2 we will specialize to the single-mode model and discuss its stationary solutions for the laser case. Multimode dynamical equations The atomic transition frequency of the generic group of atoms is given by ω a + δ D , where ω a is the central atomic frequency and δ D takes positive and negative values. We call ω c the frequency of the cavity mode nearest to ω a and denote by δ ac the difference ω a − ω c .

Cambridge University Press eBooksFeb 28, 20152 citations

Understanding the characteristics of gain saturation for homogeneously broadened laser medium from the point of view of the bandwidth

Geguo Du

It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δν = √1+Iν1 / IsΔνH for condition 2). Here, Iν1 and Is are the intensity of the large signal and the saturation intensity at the center frequency ν0, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEAug 3, 20150 citations

Understanding the characteristics of gain saturation for homogeneously broadened laser medium from the point of view of the bandwidth

Geguo Du

It is very important to understand the characteristics of gain saturation for homogeneously broadened laser medium. Assuming a Lorentzian lineshape function with a linewidth of ΔνH, we have derived the analytical functions of the gain coefficient under three different conditions: 1) a small and 2) a large signal incident on the medium respectively, and 3) a small signal accompanied by a large signal simultaneously incident on the medium. We have found that the bandwidth Δν of the gain coefficient is equal to the linewidth ΔνH for condition 1) and 3) while it is Δ ν = 1 + I ν 1 / I s Δ ν H for condition 2). Here, I v 1 and Is are the intensity of the large signal and the saturation intensity at the center frequency Vo, respectively. The reasons are also presented for such results. For condition 2), gain saturation effect is strongly dependent on the frequency of the large signal: the more the frequency deviates from the center frequency, the weaker the gain saturation effect. This results an increase of the bandwidth. For condition 3), the intensity of the large signal only changes the distribution of populations on the upper and lower energy levels. Hence, the shape of the gain coefficient does not change with the gain reduction of the small signal, thus, its bandwidth remains the same.

Education and Training in Optics and PhotonicsJan 1, 20070 citations

Transition from inhomogeneous to homogeneous broadening at a lasing prethreshold

I. S. Pashkevich, Iliya V. Doronin, E. S. Andrianov +1 more

The emission linewidth in active medium emerges due to homogeneous and inhomogeneous broadening. We demonstrate that in lasers with inhomogeneous broadening there is a critical pump rate, above which the special mode forms. This mode consists of locked-in oscillations of cavity mode and of the active atoms with different transition frequencies. Below the critical value of the pump rate, the radiation spectrum of the laser has a Gaussian profile, provided that inhomogeneous broadening is dominant. Above the critical value of pump rate, the special mode mostly determines the laser radiation spectrum. As a result, the spectrum attains Lorentz shape characteristic for homogeneous broadening. The formation of the special mode precedes lasing and that the critical pump rate plays the role of lasing prethreshold. We suggest a system where such a transition could be experimentally observed separately from lasing. We obtain expressions for the threshold and generation frequency of a single-mode laser where both homogeneous and inhomogeneous broadening are present.

arXiv:2312.03890Physical Review AMar 6, 20241 citation

Theory of two-photon Doppler-broadened probe absorption

Barbara A. Capron, A. S. Marathay, M. Sargent

We generalize the two-photon probe-absorption coefficient to include any amount of Doppler broadening and an arbitrarily intense saturator wave. By analytically performing integrals over a Lorentzian velocity distribution we are able to examine the transition from homogeneous broadening to extreme Doppler broadening for both zero and nonzero Stark shifts. For Doppler widths much larger than the saturator Rabi flopping frequency, the probe-absorption spectrum approaches a Doppler-free Lorentzian with width equal to the homogeneous linewidth and center displaced by the dynamic Stark shift.

Optics LettersFeb 1, 19862 citations