Distribution of optical emission between guided modes and free space in a semiconductor nanowire

We study the distribution of the emitted power between the free-space modes and guided modes in a semiconductor nanowire. We analyze all possible dipole orientations and nanowire radii in the range from very small to comparable to the wavelength. Our theoretical approach is based on the Fourier transform technique and equivalent to the construction of Green's function for a dipole at an arbitrary location inside the nanowire. We show that the total emitted power can exhibit rather pronounced oscillations as a function of the frequency and radius. The far-field pattern is also very sensitive to the frequency and radius, especially in the regime when leaky (or whispering gallery) modes with finite axial wave numbers are excited. We discuss the enhancement of emission into guided modes due to formation of Fabry-Ṕrot cavity in a finite length nanowire. Our results yield directly the extraction efficiencies and angular distribution of radiation of light-emitting diodes made of nanowires.