Bloch mode reflection and lasing threshold in semiconductor nanowire laser arrays

We use a plane-wave-based transfer-matrix method to investigate the dispersion and intrinsic reflection coefficients of electromagnetic guided waves at the facets of single isolated semiconductor nanowires and one-dimensional periodic nanowire arrays. The knowledge of such reflection losses can help people to understand the intrinsic threshold of laser operation in these nanowire laser systems. We find that the dispersion of guided modes in a nanowire array is not sensitive to the interwire distance, while the reflection coefficients of Bloch guided modes strongly depend on this interwire distance, and can be much different from that in a single isolated nanowire. The reflection spectrum also differs much for different polarization modes in the nanowire array. We also find that the quantitative features of these complex reflection spectra cannot be adequately explained by only considering the energy flux and field profiles of the guided mode itself that is involved in the reflection. A satisfactory physical model should involve the leaky wave modes supported by the nanowire. The contribution from both the propagating guided modes and decaying leaky modes has been fully described within the framework of the transfer-matrix method.