Fig. 4: Robustness of non-reciprocal frequency conversion to defect and disorder.
From: Non-reciprocal frequency conversion in a non-Hermitian multimode nonlinear system
a A random low Q-factor defect is introduced in the frequency comb. The non-reciprocal frequency conversion is robust to strong defects, though the strongest defects result in the skin effect terminating just before the defect mode. Here, the modal energy En = ℏωn∣an∣2 is plotted for various defect strengths Qdefect/Q0 = x, where Q0 denotes the Q factor of the remaining modes in the frequency comb. b Robustness of non-reciprocal frequency conversion to disorder. Here, the Q factor of all frequency modes in the comb is sampled uniformly from [xQ0, Q0]. Nsamp = 100 samples are drawn from this uniform distribution and individually simulated, with the shaded regions denoting ± 1σ standard deviation from the mean modal energies. Shown in the inset is the robustness of the energy of the chiral mode aN, plotted as the standard deviation normalized by the mean (coefficient of variation), fN ≡ σN/〈EN〉, where 〈EN〉 denotes the ensemble average over Nsamp samples. In the absence of amplitude modulation κ = 0, the disorder affects fN much more strongly than the case κ ≠ 0, where reciprocity breaking helps stabilize the modal energy in the chiral mode. System parameters include 2N + 1 = 19, β0 = 5 × 10−4 J−1/2, κ = 2π ⋅ 350 MHz, Q0 = 8.86 × 109, QT = 500, μ = 0.9γ, ℏω0∣s0∣2 = 5 MW, ω0 = 2π ⋅ 282 THz, and ωT = 2π ⋅ 1.06 THz.
