Wannier functions from non-bloch bands of 1D non-Hermitian photonic systems

Non-Hermiticity profoundly alters wave function behavior in photonic systems due to finite size effects and open boundary conditions (OBC). A primary consequence is the emergence of non-Hermitian skin modes, which fundamentally redefine the system’s response. We apply non-Bloch theory to formulate Wannier functions (WFs) and to describe non-Hermitian photonic structures explicitly. We find that individual left and right WFs in a 1D photonic structure are inherently gauge-dependent and non-unique, exhibiting artificial spatial shifts when the reference position parameter is varied. In contrast, we find that the biorthogonal Wannier density is invariant upon a cancellation of the position-dependent factor under the smooth biorthogonal gauge-fixing procedure adopted in this work. It is a numerically stable quantity that serves as the natural biorthogonal spatial weighting function associated with the non-Hermitian Wannier functions. The Wannier density also shows robust exponential localization in systems with complex OBC spectra, while its real-space distribution is intrinsically linked to the non-Bloch winding number of the generalized Brillouin zone (GBZ). Our comprehensive framework provides a powerful tool for investigating light-matter interactions and topological polarization in open, asymmetrically-coupled, non-Hermitian photonic systems.