Discrete diffraction and Bloch oscillations in non-Hermitian frequency lattices induced by complex photonic gauge fields

Non-Hermitian lattice systems with unconventional transport phenomena and topological effects have
attracted intensive attention recently. Non-Hermiticity is generally introduced by engineering on-site gain/loss
distribution or inducing asymmetric couplings by applying an imaginary gauge field. Here, we extend the
concept of non-Hermitian lattices from spatial to frequency dimension and emulate various non-Hermitian
transport phenomena arising from asymmetric coupling in synthetic dimension. The non-Hermitian frequency
lattice is created by introducing complex gauge potentials through appropriate complex modulations in a slab
waveguide. This complex gauge potential can induce asymmetric couplings among spectral modes and give rise
to various non-Hermitian transport phenomena such as amplified and decayed frequency diffraction, refraction
and non-Hermitian Bloch oscillations. The latter manifest themselves as both power oscillation and asymmetric
oscillation patterns, and can be exploited to probe in the bulk the non-Hermitian skin effect. Frequency-domain
Bloch oscillations with both exponentially growing oscillation amplitude and energy are also predicted. Our
results pave the way towards emulating non-Hermitian transport phenomena and topological effects in synthetic
dimension on a photonic platform, with potential applications to spectral manipulation of optical signals and
energy harvesting