Acta Optica Sinica

Nonresonant operation of a two-mode laser in three level atomic system

Shiwei Zhu

Published Jan 1, 1983• 0 citations

Abstract

The master equation of a nonresonant two-mode laser in three level atomic system with equal detune for each mode is deduced. The influences of the detune over the laser operation are discussed. It is found that the gain and saturation coefficients are reduced by factors L and L2 separately. The influence of the detune is appreciable at slightly above the threshold operation and is fading away far above. The effect of the two-photon process is comparatively enhanced in detune case.

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Acta Optica Sinica

Nonresonant operation of a two-mode laser in three level atomic system

Shiwei Zhu

Published Jan 1, 1983• 0 citations

OpenAlex

Abstract

Related papers

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The quantum theory of the three-energy-level two-mode laser in which all the levels are being pumped is investigated and the master equation of the laser operation is obtained. It contains two variables, ${n}_{1}$ , the photon number of the first mode, and ${n}_{2}$ , the photon number of the second mode. There appear four terms in the master equation which represent two-photon processes between the two modes, the absorption of a photon from one mode, and emission of a photon to the other. They are absent in the single-mode case and in the two-mode case with pumping only to the upper level. The master equation can be represented by a diagram of probability in two dimensions which can be extended to infinity, and each arrow of it represents a term on the right-hand side of the master equation. By summing each variable ( ${n}_{1}$ or ${n}_{2}$ ) of the master equation, two equations can be obtained. Each equation contains only one variable, and can be expressed by a diagram of probability flow in one dimension. By considering the correspondence between macroscopic equilibrium and microscopic detailed balance the equations of motion in the steady state are obtained. By introducing a parameter $H$ , the equation of motion is simplified and a formal solution can be deduced which is dependent on $H$ . It appears that the parameter $H$ cannot be fully determined, but some properties of it can be deduced which prove that the introduction of $H$ is reasonable. The operation characteristics of the laser under different conditions are discussed on the basis of the formal solution: among them are the threshold condition, the condition for one-mode operation, and the change of the photon-statistical distribution. We especially discuss the laser output power curves under two-mode operation above threshold. The curve of one mode, which oscillates first, shows a bending-down phenomenon as the excitation increases when the other mode goes beyond its threshold as demonstrated experimentally by Otsuka. This phenomenon is explained qualitatively and is attributed to the two-photon processes between the two modes.The quantum theory of the three-energy-level two-mode laser in which all the levels are being pumped is investigated and the master equation of the laser operation is obtained. It contains two variables, ${n}_{1}$, the photon number of the first mode, and ${n}_{2}$, the photon number of the second mode. There appear four terms in the master equation which represent two-photon processes between the two modes, the absorption of a photon from one mode, and emission of a photon to the other. They are absent in the single-mode case and in the two-mode case with pumping only to the upper level. The master equation can be represented by a diagram of probability in two dimensions which can be extended to infinity, and each arrow of it represents a term on the right-hand side of the master equation. By summing each variable (${n}_{1}$ or ${n}_{2}$) of the master equation, two equations can be obtained. Each equation contains only one variable, and can be expressed by a diagram of probability flow in one dimension. By considering the correspondence between macroscopic equilibrium and microscopic detailed balance the equations of motion in the steady state are obtained. By introducing a parameter $H$, the equation of motion is simplified and a formal solution can be deduced which is dependent on $H$. It appears that the parameter $H$ cannot be fully determined, but some properties of it can be deduced which prove that the introduction of $H$ is reasonable. The operation characteristics of the laser under different conditions are discussed on the basis of the formal solution: among them are the threshold condition, the condition for one-mode operation, and the change of the photon-statistical distribution. We especially discuss the laser output power curves under two-mode operation above threshold. The curve of one mode, which oscillates first, shows a bending-down phenomenon as the excitation increases when the other mode goes beyond its threshold as demonstrated experimentally by Otsuka. This phenomenon is explained qualitatively and is attributed to the two-photon processes between the two modes.

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{n}_{1}

, the photon number of the first mode, and

{n}_{2}

, the photon number of the second mode. There appear four terms in the master equation which represent two-photon processes between the two modes, the absorption of a photon from one mode, and emission of a photon to the other. They are absent in the single-mode case and in the two-mode case with pumping only to the upper level. The master equation can be represented by a diagram of probability in two dimensions which can be extended to infinity, and each arrow of it represents a term on the right-hand side of the master equation. By summing each variable (

{n}_{1}

{n}_{2}

) of the master equation, two equations can be obtained. Each equation contains only one variable, and can be expressed by a diagram of probability flow in one dimension. By considering the correspondence between macroscopic equilibrium and microscopic detailed balance the equations of motion in the steady state are obtained. By introducing a parameter

H

, the equation of motion is simplified and a formal solution can be deduced which is dependent on

H

. It appears that the parameter

H

cannot be fully determined, but some properties of it can be deduced which prove that the introduction of

H

is reasonable. The operation characteristics of the laser under different conditions are discussed on the basis of the formal solution: among them are the threshold condition, the condition for one-mode operation, and the change of the photon-statistical distribution. We especially discuss the laser output power curves under two-mode operation above threshold. The curve of one mode, which oscillates first, shows a bending-down phenomenon as the excitation increases when the other mode goes beyond its threshold as demonstrated experimentally by Otsuka. This phenomenon is explained qualitatively and is attributed to the two-photon processes between the two modes.