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Journal of Modern Optics

Theoretical investigation on the threshold properties of localized modes in two-dimensional random media

Jinsong Liu, Hai Liu

Published Apr 27, 2006• 7 citations
Publisher

Abstract

We present a detailed calculation to analyse the threshold properties of individual localized modes in two-dimensional random media. Some long- and short-life localized modes are selected and indicated from the spectral intensity of a passive system. By pumping the system, the pumping rate dependence of the peak intensity of the indicated modes is obtained. Results identify that these modes have a typical threshold gain behaviour, and the pumping thresholds of long-life modes are lower than those of short-life modes. By calculating the energy decay rate, the lifetime is obtained for each mode, and the results show that there exists a certain correspondence between the mode threshold and lifetime and that, the longer the lifetime, the lower the threshold is.

DOI
10.1080/09500340600552109

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We present a detailed calculation to analyse the threshold properties of individual localized modes in two-dimensional random media. Some long- and short-life localized modes are selected and indicated from the spectral intensity of a passive system. By pumping the system, the pumping rate dependence of the peak intensity of the indicated modes is obtained. Results identify that these modes have a typical threshold gain behaviour, and the pumping thresholds of long-life modes are lower than those of short-life modes. By calculating the energy decay rate, the lifetime is obtained for each mode, and the results show that there exists a certain correspondence between the mode threshold and lifetime and that, the longer the lifetime, the lower the threshold is.
The model based on the method of finite-difference time-domain is applied to calculate the general feature of localized modes in active random media. The evolution of the localized modes from passive random media to active ones is investigated. By varying the gain lineshape for an active random medium, we have observed a selective excitation of localized modes, including both single-mode and multi-mode excitations. When the eigenfrequencies for some localized modes are near the centre of the gain spectrum, the optical gain offers coherent amplification to them so that they can obtain more amplification and have stronger field amplitude than other modes. The pumping level dependence of the field amplitude of the localized modes exhibits a threshold behaviour.
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.
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.
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.
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.