Abstract
The spatial formation of coherent random laser modes in strongly scattering disordered random media is a central feature in the understanding of the physics of random lasers. We derive a quantum field theoretical method for random lasing in disordered samples of complex amplifying Mie resonators which is able to provide self-consistently and free of any fit parameter the full set of transport characteristics at and above the laser phase transition. The coherence length and the correlation volume respectively is derived as an experimentally measurable scale of the phase transition at the laser threshold. We find that the process of stimulated emission in extended disordered arrangements of active Mie resonators is ultimately connected to time-reversal symmetric multiple scattering in the sense of photonic transport while the diffusion coefficient is finite. A power law is found for the random laser mode diameters in stationary state with increasing pump intensity.
Highlights
The research for random lasers is an emerging research field [1,2,3,4,5,6,7,8,9,10,11], which recently has been extended to highly flexible [12] and unconventional materials and setups [13,14]
We find that the process of stimulated emission in extended disordered arrangements of active Mie resonators is connected to time-reversal symmetric multiple scattering in the sense of photonic transport while the diffusion coefficient is finite
Random lasers are operated in absence of any external feedback or mirror system, it is of principal importance that a high contrast of the refractive index between scatterer and background is given in order to enhance multiple scattering and photonic transport and as a result of the accumulation of a high number of photons in the sample
Summary
The research for random lasers is an emerging research field [1,2,3,4,5,6,7,8,9,10,11], which recently has been extended to highly flexible [12] and unconventional materials and setups [13,14]. Monodisperse Mie spheres can become in certain configurations extremely sensible systems, especially when the scatterers are large compared to the transport wavelength. Energy conservation laws are implemented by means of a generalized Ward identity [40] We couple this framework to the microscopic laser rate equations for quantum cascades, see Figure 1b, that ensure particle conservation on the microscopic level. (d) The irreducible vertex includes all kk orders of maximally crossed diagrams (Cooperon) which represent all quantum-coherent interference contributions due to multiple scattering in presence of disorder. We derive in the following a self-consistent frame which provides systematic results free of any fit parameter that are directly measurable in random laser experiments
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