Probing the total density of states in a photonic crystal with different number density distributions of luminescent molecules

Abstract

The dynamical characteristics of the spontaneous decay of a single excited atom or molecule depend strongly on its position within a photonic crystal (PC) and the relative orientation of its dipole and the electric field there. Measuring its dynamical characteristics of the spontaneous decay in a PC can only obtain the local density of states (DOS) in the PC, but cannot reflect the total DOS in the PC. It is found, theoretically, that using different number density distributions of luminescent molecules within the PC, one can probe the partial information or even all of the total DOS in the PC. In this paper, we separate, for the first time to our knowledge, the total DOS into two parts, DOS in the scatterer and DOS in the matrix of the Wigner-Seitz unit cell, according to their origin, and demonstrate that a special number density distribution of fluorescent molecules can reflect the total scatterers DOS or total matrix DOS or even both of them, i.e. the total DOS in the PC. This is meaningful in explaining and designing the experiments of prohibiting and enhancing the spontaneous emission of excited molecules.