In immersive augmented reality (IAR), users can wear a head-mounted display to see computer-generated images superimposed to their view of the world. IAR was shown to be beneficial across several domains, e.g., automotive, medicine, gaming and engineering, with positive impacts on, e.g., collaboration and communication. We think that IAR bears a great potential for software engineering but, as of yet, this research area has been neglected. In this vision paper, we elicit potentials and obstacles for the use of IAR in software engineering. We identify possible areas that can be supported with IAR technology by relating commonly discussed IAR improvements to typical software engineering tasks. We further demonstrate how innovative use of IAR technology may fundamentally improve typical activities of a software engineer through a comprehensive series of usage scenarios outlining practical application. Finally, we reflect on current limitations of IAR technology based on our scenarios and sketch research activities necessary to make our vision a reality. We consider this paper to be relevant to academia and industry alike in guiding the steps to innovative research and applications for IAR in software engineering.