Period-Two Dynamics of an Optically Injected Semiconductor Laser for Range-Sensitive Resonance Detection

Period-doubling nonlinear dynamics of a laser is experimentally found to be highly sensitive for ranging the distance of an optoelectronic feedback loop. The semiconductor laser is first optically injected for period-one (P1) dynamics at a fundamental frequency ƒ₀. The optoelectronic feedback then induces period-doubling bifurcation in yielding period-two (P2) dynamics at the subharmonic frequency ƒ₀/2. By adopting current modulation, the periodic dynamics adiabatically exhibits frequency-modulated continuous-wave (FMCW) behavior in general, but a resonance is unveiled when the modulation frequency ƒ_m matches the reciprocal of the feedback delay τ. Such a resonance is manifested through broadening the FMCW comb around the fundamental and concurrently suppressing the P2 dynamics at the subharmonic. It can be detected by simply monitoring the subharmonic power without frequency mixing. It allows for measuring τ to determine the effective absolute distance of the feedback loop with a microwave path included. It is also highly sensitive to fine changes in distance without being limited by the FMCW microwave coherence length. For the laser operating at ƒ₀ = 15 GHz with feedback of 1/τ = 17 MHz, the resonance is sensitive to fractional changes of the order of 10^-4 in τ. Ranging at 8.8 m is demonstrated with the capability to resolve down to 1 mm, where the required bandwidth is no more than 3 GHz. The novel form of resonance as detected through the P2 suppression enables the applications of range-sensitive nonlinear dynamics. © 2026 IEEE.