Recent BICEP2 detection of low-multipole B-mode polarization anisotropy in the cosmic microwave background radiation supports the inflationary universe scenario and suggests a large inflaton field range. The latter feature can be achieved with axion fields in the framework of string theory. We present such a helical model which naturally becomes a model with a single cosine potential, and which in turn reduces to the (quadratic) chaotic inflation model in the super-Planckian limit. The slightly smaller tensor/scalar ratio $r$ of models of this type provides a signature of the periodic nature of an axion potential. We present a simple way to quantify this distinctive feature. As axions are intimately related to strings/vortices and strings are ubiquitous in string theory, we explore the possibility that cosmic strings may be contributing to the B-mode polarization anisotropy observed.