Hidden modes in open disordered media: Analytical, numerical, and experimental results

Weexplore numerically, analytically, and experimentally the relationship between quasi-normal modes (QNMs) and transmission resonance (TR)eaks in the transmission spectrum of onedimensional (1D) and quasi-1D open disordered systems. It is shown that for weak disorder there exist two types of the eigenstates: ordinary QNMs which are associated with a TR, and hiddenQNMswhich do not exhibiteaks in transmission or within the sample. The distinctive feature of the hidden modes is that unlike ordinary ones, their lifetimes remain constant in a wide range of the strength of disorder. In this range, the averaged ratio of the number of transmissioneaks Nres to the number of QNMs N_mod,N_res N_mod, is insensitive to the type and degree of disorder and is close to the value √2/5 ,which we derive analytically in the weak-scattering approximation. Thehysical nature of the hidden modes is illustrated in simple examples with a few scatterers. The analogy between ordinary and hidden QNMs and the segregation of superradiant states and trapped modes is discussed. When the coupling to the environment is tuned by an external edge reflectors, the superradiance transition is reproduced. Hidden modes have been also found in microwave measurements in quasi-1D open disordered samples. The microwave measurements and modal analysis of transmission in the crossover to localization in quasi-1Dsystems give a ratio of N_res N_mod close to √2/5 . In diffusive quasi-1D samples, however, N_res/N_mod falls as the effective number of transmission eigenchannels M increases. Once N_mod is divided by M, however, the ratio N_res N_mod is close to the ratio found in 1D.