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Acta Physica Sinica

Threshold and saturation properties of two-dimensional random lasers and mode selection

Jinsong Liu, Liu Hai, Chun Wang, Jiantao Lü, Fan Ting, Xiaodong Wang, 华中科技大学激光技术国家重点实验室，武汉 430074

Published Jan 1, 2006• 4 citations
Publisher

Abstract

Based on the time dependent theory of random lasers, which was established via combining Maxwell equations with the rate equations of a four-level atomic system, the output intensity of lasing modes varying with the pump rate and area as well as the medium's size and shape is simulated for two-dimensional random media by use of the finite difference time domain method. Results show that the pump-rate dependence of the output intensity presents not only a threshold property, but also a saturation property, just like that of the lasing modes in conventional lasers. Based on the dependence of mode property on the medium's and pump's parameters, the mode-selection approaches are proposed for two-dimensional random lasers, which are quite different from those performed in conventional lasers.

DOI
10.7498/aps.55.4123

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Based on the time dependent theory of random lasers, which was established via combining Maxwell equations with the rate equations of a four-level atomic system, the output intensity of lasing modes varying with the pump rate and area as well as the medium's size and shape is simulated for two-dimensional random media by use of the finite difference time domain method. Results show that the pump-rate dependence of the output intensity presents not only a threshold property, but also a saturation property, just like that of the lasing modes in conventional lasers. Based on the dependence of mode property on the medium's and pump's parameters, the mode-selection approaches are proposed for two-dimensional random lasers, which are quite different from those performed in conventional lasers.
Based on the time dependent theory of random lasers, which was built via combining Maxwell equations with the rate equations of a four-level atomic system, the output intensity of a lasing mode varying with the pumping rate is simulated for a two-dimensional random active medium by use of the finite difference time domain method. Results show that the pumping rate dependence of the output intensity presents not only a threshold property, but also a saturation property, just like that of lasing modes in conventional lasers. Charactering the mode's localization extent via the mode's area indicates that the stronger the mode's localization extent is, the lower the mode's threshold is. However, such a relation is not a one-to-one correspondence, meaning that the mode's localization extent is an important fact to determine the mode's threshold, but is not alone.
A model of random laser with semi-classical theory is presented.It couples Maxwell's equations with density matrix of excited atom in a disordered system.So Maxwell-Bloch equations for random laser are obtained.A finite-difference time-domain method is used to solve Maxwell-Bloch equations directly.We studied the pattern of field and localized modes of random laser.A critical pumping rate W~c_p exists for the appearance of the lasing peaks in random system.The number of lasing modes increases with the pumping rate and it is saturated finally.
By numerically solving Maxwell’s equations and rate equations in a two-dimensional (2D) active random media made of ruby grains with a three-level atomic system, the threshold gain behavior for a THz random laser is investigated. The spectral intensity variation with the pumping rate is calculated for both the transverse magnetic (TM) field and the transverse electric (TE) field. The computed results show that THz random lasing could occur in a 2D disordered medium for both the TM and TE cases. Further analysis reveals that the THz lasing threshold for TM fields is lower than that for TE fields.
By numerically solving Maxwell’s equations and rate equations in a two-dimensional (2D) active random media made of ruby grains with a three-level atomic system, the threshold gain behavior for a THz random laser is investigated. The spectral intensity variation with the pumping rate is calculated for both the transverse magnetic (TM) field and the transverse electric (TE) field. The computed results show that THz random lasing could occur in a 2D disordered medium for both the TM and TE cases. Further analysis reveals that the THz lasing threshold for TM fields is lower than that for TE fields.
Laser action in the regime of Anderson localization is investigated by coupling Maxwell's equations in a strongly scattering medium with the rate equations of a four-level atomic system. We find that the localized modes of the passive medium are not modified by the presence of gain and serve as resonant microcavities of the random laser. The spectrum of laser emission is shown to depend on the location of the external pump. These results are similar to the recent experimental observations in semiconductor powder [Cao et al., Phys. Rev. Lett. 82, 2278 (1999)]. We show that local pumping of the system allows selective excitation of individual localized modes.
We simulate the transition from amplified spontaneous emission (ASE) to lasing in random systems with varying degrees of mode overlap. This is accomplished by solving the stochastic Maxwell-Bloch equations with the finite-difference time-domain method. Below lasing threshold, the continuous emission spectra are narrowed by frequency-dependent amplification. Our simulations reproduce the stochastic emission spikes in the spectra. Well-defined peaks, corresponding to the system resonances, emerge at higher pumping and are narrowed by stimulated emission before lasing takes place. Noise tends to distribute pump energy over many modes, resulting in multimode operation. Well above the lasing threshold, the effects of noise lessen and results become similar to those without noise. By comparing systems of different scattering strength, we find that weaker scattering extends the transition region from ASE to lasing, where the effects of noise are most significant.