Free-field realizations of $\mathcal{N} = 1$ supersymmetric $\mathcal{W}$-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$

We extend the recursive construction of free-field realizations proposed by Ide, Ito, and Miyazaki to the $\mathcal{N} = 1$ supersymmetric $\mathcal{W}$-algebras $\mathcal{SW} B (n - 1 , n)$ and $\mathcal{SW} B (n , n)$, associated with the Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$, respecti