Recently, supercontinuum sources have garnered considerable attention as a critical technology that plays an essential role in various high-precision scientific research fields, including spectroscopy [1], optical imaging [2], and frequency-comb technologies [3]. The unique combination of high spectral brightness, broad spectral coverage, and coherence makes them ideal for various research studies and industries [4,5]. Spectral broadening is commonly achieved by propagating light pulses through various nonlinear media, including solids, gases, and waveguides [[6], [7], [8]]. Among them, the utilization of specialty optical fibers for ultrafast pulse-pumped nonlinear spectral broadening presents a simple and compact approach to generating broadband coherent supercontinuum light, enabling broadband spectral generation from ultraviolet to mid-infrared [9,10]. Furthermore, given the increasing demands and advancements in high-speed, high-sensitivity spectroscopic detection and imaging techniques, considerable efforts have been undertaken to improve the noise properties, spectral stability, and temporal characteristics of fiber-based supercontinuum sources [[11], [12], [13]].

Coherent injection of mode-locked femtosecond fiber lasers has been reported to generate stable supercontinuum sources with multiple-octave, high-brightness, single-mode output [14,15]. In particular, compact fiber oscillators employing nonlinear amplifying loop mirrors as saturable absorbers have demonstrated a pulse train with sub-femtosecond timing jitter and low integrated relative intensity noise (RIN) [16]. However, the gain dynamics and soliton dynamics during power amplification and spectral broadening have led to nonlinear noise amplification, which has become one of the fundamental limitations of broadband amplitude noise in supercontinuum spectra [17,18]. The noise dynamics of these nonlinear processes cause unique amplitude-frequency and phase-frequency responses for the transmission of RIN, which deserves a detailed study for thorough analysis of nonlinear dynamics. In general, direct seed control via an acousto-optic modulator is a straightforward approach for measuring the RIN transfer function, generating desired intensity noise on the power spectral density of an initial laser [19]. This method enables a continuous frequency sweep of desired noise, allowing for the acquisition of complex frequency-dependent responses while avoiding interference from other noise sources [20]. Further, this method could provide insights into the nonlinear dynamics in continuous and pulsed laser systems, which have helped clarify the noise transmission of designed active feedback loops [[21], [22], [23], [24]]. Therefore, applying this method to measure and comprehend the nonlinear dynamics of noise transfer is a valuable tool for designing low-noise, robust supercontinuum sources.

In this letter, we showed a systematic measurement of RIN nonlinear transfer dynamics observed in an ytterbium-doped fiber amplifier and photonic crystal fiber (PCF) supercontinuum. The amplitude-frequency and phase-frequency responses of the RIN were obtained by employing a weak sinusoidal amplitude modulation into the seed pulses. As expected, the frequency-dependent response of the seed modulation resembled that of a damped high-pass filter, which saturated at low Fourier frequencies within the fiber amplifier and reached a 26-dB suppression factor at 700-mW pump power. Moreover, the long-term spectral stability and short-term RIN transfer function measurement results indicated the wavelength and frequency correlation of the nonlinear noise transformation in the spectral output. The coupling of soliton-dispersion waves (DWs) and soliton-soliton self-frequency shift (SSFS) considerably enhanced input laser fluctuations, exhibiting anticorrelation with spectral broadening. Finally, we presented the combined RIN transfer functions of fiber amplification and supercontinuum generation stages, which were considerably influenced by gain and soliton dynamics. These findings can provide valuable guidelines for the design of low-noise fiber supercontinuum sources.