However, the effect of the PC slab thickness on the quality factor has not been reported. Besides the quality factor, another important

parameter for the realization of the strong coupling interaction is the mode volume of the nanocavity. Traditionally, the mode volume is calculated by click here simulating and then integrating the electric field distribution of the 3-MA mouse nanocavity mode around the whole nanocavity region [24–26, 29] (see Equation 6). This is a rather time-consuming and difficult task. Obviously, a simple and efficient numerical method for the calculation of mode volume is desirable and remains a challenge so far. In this paper, we present an extremely simple method to determine the volume of a nanocavity mode and investigate the effect of the slab thickness on the quality factor

and mode volume of the PC slab selleck kinase inhibitor nanocavities based upon projected local density of states for photons [30]. It is found that the mode volume monotonously expands with the increasing slab thickness. As compared with the previous structure finely optimized by introducing displacement of the air holes, via tuning the slab thickness, the quality factor can be enhanced by about 22%, and the ratio between the coupling coefficient and the nanocavity decay rate can be enhanced by about 13%. Our work provides a feasible approach to manipulate the quality factor and mode volume in the experiment. This is significant for the realization of the strong coupling interaction between the PC slab Ketotifen nanocavity and a quantum dot, which has important applications in quantum information processing [21–23]. Methods The optical properties of an arbitrary dielectric nanostructure can be characterized by the projected local density of states (PLDOS) [30], which is defined as follows: (1) where r 0 is the location; ω, the frequency; , the orientation; and E

λ (r) and ω λ , the normalized eigen electric field and eigen frequency of the λth eigenmode of the nanostructure, respectively. In an ideal single-mode nanocavity without loss, the PLDOS can be expressed as follows: (2) where E c (r) and ω c are the normalized eigen electric field and eigen frequency of the nanocavity mode, respectively. Considering the loss, the PLDOS of a realistic single-mode nanocavity can be generalized to Lorentz function [31] as follows: (3) where κ = ω c / Q is the decay rate of the realistic nanocavity with loss and Q represents the quality factor. Apparently, when κ is infinitely small, Equation 3 of the loss nanocavity approaches to Equation 2 of the lossless nanocavity.