Diffraction of a Waveguide Mode in a Nanowire

Despite recent progress in fabrication and investigation of submicron-sized optical fibers known as nanowires or nanofibers, the lack of theory which could describe their optical response adequately prevents from fundamental understanding of experimental results. Although diffraction in a nanowire can be calculated numerically, such an approach does not allow comprehensive analysis of the problem.

In the present talk, the rigorous theory of reflection and diffraction of a waveguide mode at the end of a semi-infinite dielectric circular cylinder is developed. The theory assumes an arbitrary ratio between the cylinder radius and the wavelength and hence it can be used for the description of the nanowire optical properties. An exact solution of this problem is found by the use of fictitious electric and magnetic current sheets located at the end of the cylinder. The solution has the form of the Fourier integral along the integration path in the complex plane of propagation constants. Deforming this path, one obtains either the field reflected from the nanowire end or the diffracted field in the outer space. The case when the incident wave is a TM or TE waveguide mode is analyzed in detail. It is shown that the polarization of the electromagnetic field is not changed upon reflection and its amplitude is zero in the far-field limit. The extension of this approach to the case of a nanowire of a finite length is also discussed. The normal modes of such a resonator which are analogs of the Fabry-Perot modes dictate possible wavelengths of nanolaser generation.