Nonlinear effects may play a crucial role in addressing optical nonreciprocal behaviors in scattering media. Such behaviors are however typically observed within a single transmission channel and predominantly in media with fixed optical structures, which inherently restrict the tunability of a nonreciprocal response. We suggest to combine the (intrinsic) nonlinearities of a coherent multilevel medium with a tailored driving geometry that relies on two phase-mismatched standing-wave (SW) beams. This combination is essential for creating extra scattering channels over which, in addition, fully tunable optical nonreciprocal reflection can be attained. Our general approach is adapted here to four-level double-$\mathrm{\Lambda }$ atoms that are found to exhibit distinct forms of nonreciprocal multichannel scattering and to be quite sensitive to easily tunable parameters of two SW driving beams. The numerical results we present offer valuable insights into the field of non-Hermitian optical scattering and arise indeed from the interplay of interference among scattering processes and Bragg reflection.

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• Effects of atomic coherence on light propagation
• Non-reciprocal propagation
• Nonlinear optics
• Optical coherence
• Quantum optics
• Atomic systems