3.1 Single-stage RFL with a full-open cavity

The output spectrum of the SC was collected by two optical spectrum analyzers (Yokogawa, AQ6374 and AQ6375) with spectral bands of 350–1750 and 1200–2400 nm, respectively. The measured spectra were spliced together by aligning the spectral intensity.

Firstly, the broadband coupler is removed and the idle fiber output end of the HR-FBG is cleaved at an angle of 8° to prevent end feedback. The output end of the HR-FBG is defined as the backward output direction. The output performances of the RFL with a full-open cavity are measured. The spectral evolutions of the forward and backward output laser are recorded in Figure 2. The zero-dispersion wavelengths (ZDWs) of 25/400 μm YDF and GDF are about 1.3 μm. When the pump is located in the normal dispersion region of the fiber, the Raman effect dominates the initial spectrum expansion^[Reference Ma, Xu, Ye, Zhang, Huang, Yao, Leng, Pan and Zhou^16]. The spectrum of Figure 2(a) shows three Raman peaks at the maximum pump power, which lie around 1134, 1193 and 1259 nm, and they all correspond to a 13.2 THz downshift of the previous signal wavelength. The higher-order Raman peak has the larger spectral bandwidth, benefiting from the broadband Raman gain spectrum of the Raman effect^[Reference Ilev, Kumagai, Toyoda and Koprinkov^17]. For the backward output spectrum in Figure 2(b), the intensity of the 1134 nm first-order Raman peak is about 28 dB higher than that of the pump peak, which indicates that the backward output laser is basically concentrated in the first-order Raman peak.

Figure 2 Output spectral evolution of pump laser power in the RFL with a full-open cavity: (a) forward direction and (b) backward direction.

The forward and backward laser output powers are measured to quantitatively observe the laser output performance. Figure 3(a) plots the laser output powers versus the pump laser power in the forward and backward directions, and corresponding conversion efficiencies are shown in Figure 3(b). At first, the forward laser output power increases almost linearly with the injecting of the pump laser. When the pump laser power reaches 575 W, the forward laser output power reaches the threshold for backward Rayleigh scattering, and the backward laser starts to appear. The backward laser obtains the active gain when it passes through the YDF, which is because the wavelength of the backward laser (1134 nm) is located in the ytterbium ion radiation range of 1000–1200 nm. With the pump laser power increasing to 1185 W, the backward output power is amplified to 298 W with the aid of the distributed Raman gain and the active gain. In this process of power scaling, the conversion efficiency of the forward laser decreases. The forward first-order Raman laser and the pump laser have opposite intensity distributions along the GDF, resulting in the saturation of forward first-order Raman gain. The Raman gain saturation becomes increasingly obvious with the increase of the pump laser power^[Reference Vatnik, Churkin and Babin^18]. As the pump laser power reaches the maximum value, the conversion efficiency of the forward laser descends to 59% and the forward output power almost stops growing. This is caused by the combination effect of the Raman gain saturation of the forward laser and the quantum defect occurring in the process of wavelength conversion in the forward direction. In Ref. [Reference Vatnik, Churkin and Babin18], the backward first-order Raman output power always is higher than the forward first-order Raman output power due to the Raman gain saturation of the forward laser. However, in our full-opened RFL at the maximum pump laser power, the calculated forward and backward first-order Raman output powers by the method of spectral integration are 443 and 294 W, respectively. The lower backward first-order Raman output power is due to insufficient distributed backward scattering and the existence of the walk-off effect^[Reference Zhang, Wu, Wan, Wang, Yang, Xi, Wang and Zhou^11]. If further increasing the pump laser power, the energy pump may be completely transferred to the backward output laser due to the enhanced backward scattering, the Raman gain saturation of the forward laser and the quantum defect in the forward direction.

Figure 3 (a) Laser output power and (b) conversion efficiency of the RFL with a full-open cavity in both directions. The green background area is the growth area of the backward output power; the yellow background area shows that the forward output power stops increasing.

3.2 Single-stage RFL with a half-open cavity

It can be seen from the discussion above that the backward output power is rather high in the single-stage RFL with a full-open cavity. To solve this problem, a broadband coupler is installed before the pump laser to form a half-opened RFL. It is noted that in the RFL with a full-open cavity, the strong backward laser is obtained by the weak backward Rayleigh scattering light combined with the distributed Raman gain and ytterbium ion active gain. When the coupler is added, gain competition occurs between the forward feedback light and the weak backward Rayleigh scattered light in the transmission process along the fiber. Part of the energy is transferred to the forward laser and the backward output power is reduced, which means that the coupler does not need to withstand too much power. It is roughly estimated by monitoring the coupler temperature and the result shows that the temperature of the coupler has no obvious rise in the whole process of power scaling. Figure 4 shows the compared output spectra of RFLs with a full-open cavity and a half-open cavity under the same pump power of 964 W. The inset displays the forward and backward output power in both structures. The results demonstrate that the backward output light is fed back into the forward direction with the aid of the broadband coupler, promoting forward output power and conversion efficiency. The output spectrum of the half-opened RFL is greatly expanded compared to that of the full-opened RFL under the same pump power. This is because the boosting of forward output power facilitates the interaction among nonlinear effects, such as the Raman effect, phase-matched four-wave mixing and group-velocity-matched dispersive wave, thus promoting the conversion among wavelengths.

Figure 4 Compared output spectra of RFLs with a full-open cavity and a half-open cavity under the same pump power of 964 W.

In the following, the output performances of the RFL with a half-open cavity are analyzed in detail. Figure 5 presents the output spectral evolution. The mechanism of the initial spectrum expansion is similar to that of the full-opened RFL, which is dominated by the cascaded Raman effect. The modulation instability (MI) starts to work and gives birth to a train of ultra-short pulses when the long wavelength edge of the spectrum is extended beyond the ZDW of the fiber^[Reference Abeeluck and Headley^19]. In the short wavelength direction, the whole Raman substrate is connected under the combined action of dispersive waves trapped by soliton and phase-matched four-wave mixing^[Reference Travers, Rulkov, Cumberland, Popov and Taylor^20]. In the long wavelength direction, the extension of the spectrum is induced by the soliton self-frequency shift and soliton fission^[Reference Frosz, Bang and Bjarklev^21]. With the further increasing pump power, these effects are stimulated more effectively and together enhance the broadening of spectrum. Although with the combination of the CW pump and the LMA fiber with a low nonlinear coefficient it is difficult to excite various nonlinear effects, the spectrum is broadened in effect, which benefits from the high pump power and the long interaction length of various nonlinear effects increased by random distributed feedback^[Reference Qi, Yang, Li, Yan, Gong and Xiao^6]. When the pump power reaches 1847 W, a broadband spectrum covering 887–1920 nm is then obtained.

Figure 5 Output spectral evolution with pump laser power in the RFL with a half-open cavity.

Figure 6 presents the laser output power and the conversion efficiency versus the pump laser power in the half-opened RFL. When the pump power reaches 1847 W, the SC output power reaches 1300 W. The conversion efficiency decreases with the increase of pump power due to the quantum defect occurring in the whole process of wavelength conversion. Concerning that for the final SC, the laser conversion efficiency reaches 66%, which is the highest conversion efficiency in a reported RFL output SC with the same spectral range. Such a high conversion efficiency is benefited by the introduced position of feedback in our structure. The feedback is introduced between the pump laser and the passive fiber, and thus the SC output power is difficult to increase and the SC output spectrum and conversion efficiency are also relatively poor (see the supplementary material for details). In our structure, the feedback is introduced before the pump laser, and the backward scattered light passes through the YDF and experiences the ytterbium ion gain in the bandwidth range of 1000–1200 nm. Then, both the 1000–1200 nm wavelength range backward light and the 1080 nm signal light extract energy from the 940 nm pump light, promoting the conversion of the pump light and enhancing the conversion efficiency. The bandwidth of the coupler is 1120–1200 nm. The light in the wavelength range will pass through the YDF multiple times due to the presence of the coupler with broadband strong feedback, further enhancing this effect. In addition, the bandwidth of the coupler covers the strong radiation wavelengths of backward light (1134 nm backward first-order Raman and 1193 nm backward second-order Raman). The coupler is fabricated by the fused taper technique. The light located in the bandwidth of the coupler obtains strong feedback, and the light located outside the bandwidth of the coupler obtains relatively weak feedback. With the aid of the coupler, the backward light loss is reduced and the conversion efficiency is improved.

Figure 6 (a) Laser output power and (b) conversion efficiency in the RFL with a half-open cavity.

The temporal behaviors of the half-opened RFL are measured in the output end by an InGaAs photo-detector with a bandwidth of 1 GHz and an oscilloscope with a bandwidth of 1.5 GHz. The standard deviation (STD) values displayed are used to characterize the temporal dynamics. The results are shown in Figure 7. The RFL has the advantage of suppressing the self-pulsing effect^[Reference Zhang, Huang, Zhou, Wang, Xu and Xu^22]. In self-pulsing dynamics, the photon lifetime in the cavity plays a major role. The longer the photon lifetime in the cavity τ _c, the more stable the time domain due to the suppression of self-pulsing. It can be calculated by the following formula^[Reference Upadhyaya, Kuruvilla, Chakravarty, Shenoy, Thyagarajan and Oak^23]:

$$\begin{align*}{\tau}_{\mathrm{c}}=\frac{2 nL}{c\left(-\ln {R}_1{R}_2+2\alpha l\right)}\end{align*}$$

Figure 7 Normalized temporal signal of the RFL with a half-open cavity: (a) spectrum expansion below the ZDW; (b) spectrum expansion near the ZDW; (c) spectrum expansion above the ZDW; (d) maximum spectrum broadening. The recording time window is set to 100 ms.

where L is the length of the resonator, l is the length of the gain fiber, n is the refractive index of the fiber, R ₁ and R ₂ are the two-side reflectivities of the resonator and α is the scattering loss. The length of the gain fiber is relative to the pump light. It refers to the fact that when the length of the gain fiber is long, the saturable absorption effect in the weakly pumped portion of the gain fiber triggers a strong self-pulsing effect initiated by the relaxation oscillations, corresponding to the reduction of the intracavity photon lifetime in the formula^[ Reference Upadhyaya, Kuruvilla, Chakravarty, Shenoy, Thyagarajan and Oak ^{23 ]}. However, the length of the resonator is relative to the signal light. Concerning the cavity of the RFL, multiple scattering caused by random distributed feedback increases the length of the resonator, thus enhancing the photon lifetime in the cavity and leading to a stable CW operation^[ Reference Ma, Liu, Fang and Fan ^{24 ]}. With the increase of pump power, Rayleigh scattered light based on random distributed feedback is strengthened. On the one hand, the part of the backward Rayleigh scattered light at 1080 nm is amplified in the oscillator, reducing the time domain fluctuation of the 1080 nm signal light, and the corresponding time domain properties are transferred from the signal light to subsequent Raman lights. On the other hand, the random distributed feedback of Raman light enhances the intracavity photon lifetime. Based on the above two aspects, a stable Raman laser output is obtained. As shown in Figures 7(a) and 7(b), the STD values indicate that the output laser becomes more and more stable with the increasing pump power during the whole conversion process of the Raman peak. When the spectrum extends beyond the ZDW of the fiber, a slight time domain fluctuation could be observed in Figure 7(c), which tends to be caused by nonlinear effects involving the process of SC broadening, such as soliton fission. Because the generated pulse originating from the soliton fission has random duration and energy, a pulse train with periodic modulation is not observed in the time domain. With the further increase of pump power, the time domain becomes more stable again owing to the increasing intracavity photon lifetime caused by enhanced random distributed feedback, which is shown in Figure 7(d). The results indicate that this scheme could produce a stable SC laser source, especially during high-power operation.