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.

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