NUMERICAL SIMULATIONS OF LASING WITHOUT POPULATION INVERSION IN TWO- LEVEL OPTICALLY DENSE MEDIUM
R.M. Arkhipov1,2, M. V. Arkhipov2, S.A. Pulkin2
1 Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e.V,
Berlin, Germany
2 Physics Faculty, Saint-Petersburg State University, Saint-Petersburg, Russia
The behavior of two-level system in strong optical fields for over 40 years has been attracting the attention of the researchers [1- 10]. Practical interest of such problems is connected with the occurrence of narrow and ultra-narrow resonances of light amplification, and the possibility of obtaining amplification and lasing without population inversion in such systems [6-10].
Typically amplification and lasing without population inversion has been studied experimentally and theoretically in the 2 following cases. In the 1st case the frequency of a strong monochromatic pumping field coincides with the frequency of the resonant transition of two-level system, and a weak probe radiation can be amplified if its frequency is close to the Rabi frequency of monochromatic field. In the 2nd case two-level system interacts with 2 fields having the same amplitude and equal frequency detuning, which is symmetric in respect to the transition frequency (biharmonic pumping). In this case if the frequency detuning of biharmonic field is close to it’s Rabi frequency a weak resonant probe field can be amplified.
Effects of lasing without population inversion have been observed experimentally in the cases of monochromatic and biharmonic pumping in the paper [11]. The results of theoretical investigations of gain without inversion for the explanation of these experiments have been used. In this approach propagation of the electric field in the length medium, placed into the optical cavity is not taken into account. So to explain the results of the real experiment it is necessary to take into account effects of spatial propagation of the electric field in the medium, multimode properties of radiation, transition processes and intermode interaction.
Thus the main purpose of this work is the numerical modeling of the generation without population inversion in two-level system, placed in the ring optical cavity. In our model effects of spatial propagation of the electric field in the medium are taken into account and the transition processes are included in the consideration. The basic system of equations in our model is the system of Maxwell-Bloch equations, describing the behavior of slow envelopes of the electric field, polarization and population differences of two-level system [1-5]. For modeling of the results of the real experiment numerical simulations of these equations in the cases of monochromatic, quasi-monochromatic and biharmonic pumping have been performed.
During to the numerical simulations spatial and temporal dynamics of the electric field amplitude, polarization and population difference in the medium were analyzed. The arising of the new spectral components in the medium radiation which are not contained in the pumping field spectrum, was interpreted as the generation without population inversion. Due to our simulations it has been shown that the effects of amplification without population inversion of radiation by optically thin layer and effects of generation in optical cavity have different mechanisms. It was shown that there is no generation without population inversion in the case of monochromatic pumping. Lasing without inversion aroused only in the cases of quasi-monochromatic and biharmonic pumping.
Finally we demonstrated that the arising of the new spectral components in the medium radiation (lasing without population inversion) is due the redistribution of energy within the spectrum of the pumping field. This redistribution is due to the coherent effects of interaction of the laser radiation with optically dense, extended medium.
The support from EU FP7 ITN PROPHET is gratefully acknowledged (Grant No. 264687).
REFERENCES
1. L. Allen, J. H. Eberly. Optical Resonance and Two-level Atoms. Dover Publications, INC., New York, 1987.
2. A. Yariv. Quantum Electronics, Wiley, New York, 1975.
3. J. D. Macomber. The Dynamics of Spectroscopic Transitions, Wiley, New York, 1976.
4. Kryukov P. G., Letokhov V. S. Propagation of a Light pulse in a Resonantly amplifying (absorbing) medium.
Sov. Phys. Usp. 12, 1970, pp. 641–672.
5. Poluektov I. A., Popov Yu. M., Roitberg V. S. Self-induced transparency effect. Sov. Phys. Usp. 18, 1975, pp. 673–690.
6. B.R. Mollow. Phys. Rev A, V. 5(5), 1972, pp. 2217-2222.
7. S. Ezekiel, F.Y. Wu. Sov. Journal Quantum Electron. 8(8), 1978, pp. 978-980.
8. G. S. Agarwal. J. Opt. Soc. Am. B . Vol. 8, No. 5, 1991, pp. 1163-1167.
9. Yoon T.H., Pulkin S.A., Park J. R., Chung M.S., Lee H.W. Phys.Rev. A, V.60 (1), 1999, pp. 605-613.
10. N. B. Manson, C. Wei, J. P. D. Martin. Phys Rev. Lett., V. 76, № 21, 1996, pp. 3943-3946
11. Gaida L.S, Zeilikovich I. S., Pulkin S. A., Fradkin E. S. Opt. and Spectr., 65 (4), 1988, pp. 802-804.
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