We consider a voltage-biased Normal metal-Insulator-Superconductor (NIS)tunnel junction, connected to a high-temperature external electromagneticenvironment. This model system features the commonly observed subgap leakagecurrent in NIS junctions through photon-assisted tunneling which is detrimentalfor applications. We first consider a NIS junction directly coupled to theenvironment and analyze the subgap leakage current both analytically andnumerically; we discuss the link with the phenomenological Dynes parameter.Then we focus on a circuit where a low-temperature lossy transmission line isinserted between the NIS junction and the environment. We show that the subgapleakage current is exponentially suppressed as the length, $\ell$, and theresistance per unit length, $R_0$, of the line are increased. We finallydiscuss our results in view of the performance of NIS junctions inapplications.
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