Experimental observation has shown that it is no simple matter to make a homogeneously broadened laser operate in a single longitudinal mode. However, elementary theoretical treatments of homogeneously broadening predict that such lasers can operate in only a single mode, because all of the atoms constituting the gain medium experience identical degrees of saturation.

Topical Meeting on Optical Bistability (OB)Jan 1, 19831 citation

Spectral Properties of a Single-Mode Ruby Laser: Evidence of Homogeneous Broadening of the Zero-Phonon Lines in Solids

Carson L. Tang, H. Statz, G. A. deMars +1 more

Physical ReviewOct 5, 196453 citations

Springer eBooks

The Single-Mode Homogeneously Broadened Laser II: Phase-Space Analysis

H. J. Carmichael

Published Jan 1, 1999• 1 citation

Publisher

DOI: 10.1007/978-3-662-03875-8_8

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The Single-Mode Homogeneously Broadened Laser I: Preliminaries

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Theory of intensity and phase fluctuations of a homogeneously broadened laser

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Single-mode and multimode operation in inhomogeneously broadened lasers

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.

Cambridge University Press eBooksFeb 28, 20150 citations

Intrinsic Instabilities in Homogeneously Broadened Lasers

Lloyd W. Hillman, Robert W. Boyd, Jerzy S. Krasiński +1 more

Topical Meeting on Optical Bistability (OB)Jan 1, 19831 citation

Spectral Properties of a Single-Mode Ruby Laser: Evidence of Homogeneous Broadening of the Zero-Phonon Lines in Solids

Carson L. Tang, H. Statz, G. A. deMars +1 more

According to several recent studies, the width of the sharp zero-phonon lines in the electronic spectra of impurities in solids, such as the $R$ lines of ruby, is due to Raman scattering of phonons by the impurity ions. The question whether such zero-phonon lines are homogeneously broadened is an important one, both for its own interest and for optical-maser applications. From a detailed study of the stimulated-emission spectra of a ruby laser operating in the traveling-wave modes, we obtain conclusive evidence that such zero-phonon lines are homogeneously broadened. Because the ${R}_{1}$ line of ruby is essentially homogeneously broadened at room temperature, the traveling-wave laser oscillates for all practical purposes only in a single mode. The spectral width of the laser emission is extremely sharp. It is less than 0.005 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature as compared to a width of the order of 1 ${\mathrm{cm}}^{\ensuremath{-}1}$ for conventional ruby lasers of comparable intensity. In addition, the output intensity no longer shows random spikes but shows a predictable train of regularly spaced spikes which agree well with theory.According to several recent studies, the width of the sharp zero-phonon lines in the electronic spectra of impurities in solids, such as the $R$ lines of ruby, is due to Raman scattering of phonons by the impurity ions. The question whether such zero-phonon lines are homogeneously broadened is an important one, both for its own interest and for optical-maser applications. From a detailed study of the stimulated-emission spectra of a ruby laser operating in the traveling-wave modes, we obtain conclusive evidence that such zero-phonon lines are homogeneously broadened. Because the ${R}_{1}$ line of ruby is essentially homogeneously broadened at room temperature, the traveling-wave laser oscillates for all practical purposes only in a single mode. The spectral width of the laser emission is extremely sharp. It is less than 0.005 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature as compared to a width of the order of 1 ${\mathrm{cm}}^{\ensuremath{-}1}$ for conventional ruby lasers of comparable intensity. In addition, the output intensity no longer shows random spikes but shows a predictable train of regularly spaced spikes which agree well with theory.

Physical ReviewOct 5, 196453 citations

According to several recent studies, the width of the sharp zero-phonon lines in the electronic spectra of impurities in solids, such as the

R

lines of ruby, is due to Raman scattering of phonons by the impurity ions. The question whether such zero-phonon lines are homogeneously broadened is an important one, both for its own interest and for optical-maser applications. From a detailed study of the stimulated-emission spectra of a ruby laser operating in the traveling-wave modes, we obtain conclusive evidence that such zero-phonon lines are homogeneously broadened. Because the

{R}_{1}

line of ruby is essentially homogeneously broadened at room temperature, the traveling-wave laser oscillates for all practical purposes only in a single mode. The spectral width of the laser emission is extremely sharp. It is less than 0.005 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature as compared to a width of the order of 1 ${\mathrm{cm}}^{\ensuremath{-}1}$ for conventional ruby lasers of comparable intensity. In addition, the output intensity no longer shows random spikes but shows a predictable train of regularly spaced spikes which agree well with theory.