Fig. 3: Coherent injection-locking effect.

a A comb spectrum showing five observed modes. b–d Spectrum maps obtained by sweeping the injection frequency f_inj around f₇ at a fixed power (P_inj = −82 dBm), and at various sensing modes m_sen = 6 (b), 7 (c), and 9 (d), respectively. The emission signals are locked within the range Δf_inj and Δf_sen. e–g Comparison of spectra between free-running (black) and injection-locking (red) states. Insets show the linewidth, which is ≤1 Hz for all locked modes. h–j Spectra maps obtained by varying injection power (P_inj) with an off-resonance tone (f_inj = f₇-Δf_off; f₇ = 5.26 GHz, Δf_off = 8 MHz). The shifts of the locked tone from the free-running tones are indicated by Δf_lock. The long-dashed lines in (b–d, h–j) are fittings to extended Alder’s Eq. (2). k–m Plots of Δf_inj and Δf_off (k), Δf_sen (l), and Δf_lock (m) as functions of mode number m.