Fig. 1: Shaping nonlinear energy flow in a non-Hermitian nonlinear multimode cavity.
From: Non-reciprocal frequency conversion in a non-Hermitian multimode nonlinear system
a Tight-binding schematic of nearest-neighbor couplings in a frequency multimode system with second-order nonlinearity. The interplay between nonlinear Hermitian coupling (NL) mediated by a common idler mode and the anti-Hermitian coupling generated by amplitude modulation (AM) at the idler frequency breaks reciprocity in the frequency conversion (κ+ ≠ κ−), which can create unidirectional energy flow in the frequency dimension. b The presence of anti-Hermitian coupling through AM or Hermitian coupling through NL alone is insufficient to break symmetry in the frequency conversion process. However, the presence of both couplings simultaneously generates an effective non-Hermitian system that can bias frequency downconversions and create an asymmetric frequency comb. c In the nonlinear, non-Hermitian system, the interplay between NL and AM is reflected in the temporal dynamics of the modal amplitudes since the nonlinear coupling is time-dependent, βaT(t). The initial frequency conversion is symmetric since κ+ = − κ− (purely AM coupling). As the idler mode is populated, βaT → κ. A threshold is reached where reciprocity in upconversion/downconversion is broken and an NHSE-type phenomenon in the frequency dimension occurs, with all energy flowing to the chiral mode aN. In (b, c), 2N + 1 = 19, β0 = 2 × 10−4 J−1/2, κ = 7.8 × 109 s−1, Q0 = 9 × 105, μ = 0.1γ, QT = 103, and ℏω0∣s0∣2 = 5 MW. In this system, the pump frequency ω0 = 2π ⋅ 282 THz, and the idler frequency ωT = 2π ⋅ 1.06 THz.
