Historical note on spatial hole burning and twisted-mode laser resonators

R. M�ller

Mark P. Jelonek, Won B. Roh

Philip Goldberg, Peter W. Milonni, Bala Sundaram

The theory of the laser linewidth is formulated to account for arbitrarily large output couplings and spatial hole burning. We show explicitly that the linewidth can be interpreted in terms of either spontaneous-emission noise or the amplification of vacuum field modes leaking into the cavity, depending on the ordering of operators in the correlation function determining the laser spectrum. This allows us to derive the Petermann K factor associated with ``excess spontaneous-emission noise'' in a physically transparent and mathematically simple way, without the need to introduce adjoint modes of the resonator. It also allows us to straightforwardly include spatial-hole-burning effects, which are found to increase the K factor and the linewidth in high-gain systems appreciably.

Daniel F. Walls, K. J. McNeil

David A. Holm, Murray Sargent, Lois M. Hoffer

The effects of inhomogeneous broadening, spatial hole burning, and Gaussian beams are calculated for the four coefficients derived in previous papers in this series [Phys. Rev. A 31, 3112 (1985); 31, 3124 (1985)] on the quantum theory of multiwave mixing. These coefficients uniformly describe how one or two strong classical-field modes and one or two weak quantum-field modes interact in a two-level medium. The phenomena for which this theory is applicable includes resonance fluorescence, Rayleigh scattering, laser and/or optical bistability instabilities, and phase conjugation. The averaged formulas are illustrated by resonance-fluorescence spectra. We find the sidepeaks can be ``washed out'' and that asymmetries can occur.

Hans Günter Danielmeyer

The rate equation for the population inversion of homogeneously broadened 4-level lasers is solved for the cases of small and large mobility of excited states. Considered are drift and diffusion, i.e., collective and random motions along the laser axis. Both drift and diffusion smooth spatial holes which are burned into the population inversion by standing-wave fields. A drift results also in a drag effect, i.e., a phase lag between the population inversion and the standing-wave field. For homogeneously broadened lasers, sufficient smoothing of spatial holes will result in spontaneous full-power single-frequency operation. This is examined by calculating the unsaturated gains of secondary modes as a function of the excitation, drift, and diffusion parameters. Spatial hole burning is insignificant for gas lasers because of their large carrier diffusion. Furthermore, ionic drift in gas-ion lasers alone could effectively quench spatial hole burning. This is in contrast to dye lasers where drifts, i.e., longitudinal flow rates of the order of the sound velocity, would be required to obtain a single-frequency output. In solid-state lasers like ruby and Nd: YAG, energy diffusion between lattice sites is shown to significantly reduce spatial hole depths although the matrix elements for the exchange are quite small. An experiment is described which confirms the theory and allows the measurement of small diffusion constants of excited laser states. For the 4F3/2 level in Nd: YAG a value of 5×10−7 cm2/sec is obtained. This energy exchange among Nd3+ sites contributes 0.3 GHz to the homogeneous linewidth. Implications for axial mode selection and single-frequency oscillation of various lasers are discussed.