Fiber lasers have gained widespread adoption in scientific, industrial, and medical applications due to their superior beam quality, thermal management, compact design, and minimal maintenance requirements. Passively mode-locked fiber lasers serve as essential platforms for investigating soliton interactions. Soliton molecules, extensively studied in optics and physics, emerge through attractive or repulsive forces between solitons. The intricate internal dynamics of soliton molecules have been revealed through dispersive Fourier transform (DFT) technology, enabling high-resolution, real-time monitoring. Through DFT, researchers have identified two primary types of relative phase dynamics in soliton molecules: phase drifting and relative phase oscillation. These investigations have illuminated the formation and manipulation of soliton molecules. Current research has predominantly focused on controlling and analyzing the relative phase of individual soliton molecules. This paper demonstrates effective control of the relative phase of two-soliton molecules by introducing a modulation signal into the pump driving current of a passively mode-locked fiber laser. The implementation of a modulation signal to the pump driver current facilitated the transition from a regular mode-locked pulse to a soliton molecule exhibiting relative phase oscillation. By adjusting the modulation signal amplitude, dual soliton molecules with co-directional and counter-directional relative phases are achieved. DFT technology enables the study of relative dynamic processes within these soliton molecules, leading to analysis of the mechanisms underlying various soliton molecule formations.

The experimental configuration utilizes a 980 nm semiconductor laser diode (LD) as the pump source. A square-wave modulation signal, generates by a signal generator, is applied to the pump driver to regulate soliton dynamics through electronic modulation. The pump light entered the laser cavity via a 980 nm/1550 nm wavelength division multiplexer. The cavity contained a 3.3 m long erbium-doped fiber serving as the gain medium. A polarization-independent isolator (ISO 1) is incorporated to ensure unidirectional light propagation within the cavity. The system employs a polarization controller for adjusting the cavity light’s polarization state, and a 60% output coupler extracts the laser output. Single-walled carbon nanotubes function as a saturable absorber to achieve mode-locking. Standard single-mode fiber comprises the remaining cavity fiber, totaling approximately 12.2 m. An additional polarization-independent isolator (ISO 2) is positioned outside the cavity to prevent external light reflection re-entry. The DFT technique implementation incorporates dispersion-compensating fiber with approximately 660 ps/nm dispersion, a 24 GHz photodetector, and a 59 GHz high-speed real-time oscilloscope to monitor real-time soliton dynamics within the laser cavity.

Without modulation signal application, a soliton singlet emerged at a pump driver current of 43 mA (Fig. 2), exhibiting a central wavelength of approximately 1530 nm. Upon introducing a square-wave modulation signal to the pump driver current while maintaining 43 mA, a soliton molecule formed, displaying periodic variations in both relative phase and temporal separation (Fig. 3). The function generator provides a modulation signal with 0.266 V amplitude, 99% duty cycle, and 17 kHz frequency. These conditions produce periodically varying interference fringes in the real-time spectrum. When the modulation amplitude increased to 0.701 V, maintaining constant pump current, duty cycle, and frequency, dual soliton molecules with co-directional relative phase variations are observed (Fig. 4). The solitons maintaine approximately 16 ns temporal separation, both exhibiting interference fringes with nearly identical fringe periods. Further increasing modulation amplitude to 0.719 V while maintaining other driving parameters produce dual soliton molecules with counter-directional relative phase oscillations (Fig. 5). The temporal separation between solitons increase to approximately 24 ns. The relative phase evolution diagrams indicate similar oscillation periods of approximately 38 round trips for both solitons, despite significant differences in phase dynamics.

This research demonstrates successful generation and control of soliton molecules exhibiting periodic changes in relative phase and spacing within a passively mode-locked fiber laser using pump modulation techniques. The relative phase and spacing variations of soliton molecules are effectively controlled through modulation signal amplitude adjustments in the pump drive current. DFT technology enables real-time observation of internal relative phase and spacing variations within the soliton molecules. The experiments produce three distinct types of vibrating soliton molecules under varying modulated signal amplitudes: single soliton molecules with phase vibration, double soliton molecules with in-phase vibration, and double soliton molecules with out-of-phase vibration.