Photon Statistics of an m-photon Laser with k-photon Losses

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Abstract
With the help of an approximation scheme valid for n ≫ 1 and Δ n2 ≪n -2 (where n is the mean value and Δ n2 the variance of the photon number), the photon statistics of an m-photon laser with k-photon losses (m,k = 1, 2, …) is studied theoretically for arbitrary values of the atomic population inversion s produced by an external pumping source. For m>k, m = k and m < k, the dependences of the steady-state values of the mean photon number and of the quantity Δ n2 / n on gain and saturation are investigated. In the limit of strong saturation (well above the threshold for m > k) the photon statistics are characterized by the steady-state value Δ n2 / n = (1/2) (1 + m/ks).

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