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Abstract
Inspired by the chirped pulse amplification technique, herein, we show an efficient method to improve the distribution probability of dissipative soliton and noise-like pulse in all-normal-dispersion fiber lasers by using an intracavity pulse power editing (PPE) technique for the first time. The dissipative-soliton fiber laser is thus simplified into three parts: a PPE link, a saturable absorber (SA), and a spectral filter. Pulse with different peak powers can be edited in the PPE link, then undergo the positive- or reverse-saturable absorption of the SA, and finally pass through the filter. Further, just by assigning the length of single-mode fiber (SMF) at different positions in the PPE link with a fixed cavity length, four pulse patterns, including dissipative soliton (DS), DS molecules, a bound pattern of DS and noise-like pulse (NLP), and pure NLP, can be controllably produced in fiber lasers. The observed bound pattern of DS and NLP is a new addition to the pulse dynamic pattern family. It is found that the longer the SMF after the gain fiber is, the pulse will be severely broadened. This pulse can easily enter the positive-saturable absorption region of most saturated absorption curves, which will increase the probability of DS radiation; if the SMF behind the gain fiber is shorter, the pulse is not severely broadened. The pulse has a high probability of entering the reverse-saturable absorption range of most saturated absorption curves, resulting in a higher likelihood of generating NLP. In experiments, it is only necessary to increase the SMF length between the gain fiber and the isolator to build a DS fiber laser; however, to construct an NLP fiber laser, only the SMF length between the gain fiber and the isolator needs to be shortened. The experimental results agree well with the numerical predictions. The results significantly broaden the design possibilities for pulse lasers, making them much more accessible to produce specific pulse patterns.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The prediction and production of nonlinear dynamic patterns in dissipative systems are essential in many scientific fields, including hydrodynamic systems [1], plasma physics [2], and nonlinear optics [3–5]. As optical fiber’s response is nonlinear at higher optical power, fiber lasers can provide an excellent framework for the production of different pulse patterns such as dissipative soliton (DS) [6], DS molecules [7,8], noise-like pulses (NLPs) [9,10], and rogue waves [11,12].
The propagation of the pulse in the fiber part of fiber lasers can be well modeled by the cubic-Ginzburg-Landau equation (CGLE). The solution of the CGLE can be characterized as a dissipative soliton (DS) with large, net-normal cavity dispersion. Specifically, the DS pattern’s energy, profile, and chirp are predetermined by the cavity parameters rather than the initial conditions. Generally, the pulse pattern variety is considerably wider than imagined and approximated [3]. Hence, an extended exploration in the parameter space can reveal numerous pulse patterns.
The DS fiber laser generally includes the following optical components: pump source, fibers (active fiber, passive fiber), saturable absorber (SA), spectral filter, polarization controller, output coupler, etc. Numerical calculations are performed under the condition that each optical device in the resonant cavity is regarded as an independent variable. The role of the spectral gain bandwidth on the multiple pulsing was initially investigated in [13]. Li et al. have shown numerically that the multipulse and dissipative soliton resonance (DSR) can be formed only by changing the bandwidth of the spectral filter while fixed other parameters of the resonant cavity [14]. The influence of the exact position of fibers with constant fiber length has been previously introduced in the framework of DSR [15]. Du et al. reported that all-normal-dispersion mode-locked fiber laser could produce multipulse, bound-state pulse, or NLP under different filter bandwidths and pump powers [16]. Xu et al. investigated the impact of spectral filtering on pulse breaking up and NLP generation in all-normal-dispersion fiber lasers. [17]. By changing the filter bandwidths, Gupta et al. also demonstrated the generation of stable DSs, multiple soliton explosions, and a stable multi-pulsing state [18].
The role of optical fiber always focuses on dispersion and nonlinearity effects. As two crucial properties of optical fibers, dispersion and nonlinearity, have been studied separately. By increasing the net cavity dispersion from anomalous to net-normal and then to all-normal, conventional soliton [19], stretched pulse [20], similariton [21], and the DS [22] have been found in the sequence. On the other hand, by increasing the mode area and thereby reducing the self-phase modulation (SPM) effect, mode-locking pulses with higher pulse energy have been achieved. Meanwhile, various pulse patterns, which came from pulse splitting and were caused by the excessive accumulation of the nonlinear phase shift, have also been observed [23].
For the role of the SA, pulse peak-power-limiting effect (PPLE) in the resonant cavity has been put forward [24,25]; recent studies show that the pulse PPLE is mainly caused by the reverse saturable absorption (RSA) of the SA in fiber lasers [26–29]. Some researchers have also pointed out that monotonic or periodical SA is closely related to the formations of the multipulse, DSR, and NLP [26–29]. Therefore, the generation and detour of the specific pulse patterns need a compelling set of more complex cavity parameters, and numerical simulation is often required to guide the experimental design.
Enlightened by chirped pulse amplification (CPA), in this work, we introduce an intracavity pulse power editing (PPE) technique, which can efficaciously edit the pulse power by assigning the single-mode fiber (SMF) length at different positions of the PPE link. In this case, the fiber’s nonlinear effect and dispersion effect are considered comprehensively for the first time. Therefore, different pulse power would be provided before the pulse entered the SA. Due to the various functions of the positive or the reverse saturated absorption effect, the pulse would own different pulse duration and spectral width before entering the filter. Affected by the filtering and cumulative nonlinear effect, several pulses and dispersive waves will be trimmed. After these pulses and dispersive waves circulated in the resonant cavity, different pulse patterns–including DSs, DS molecules, a bound pattern of DS and NLP, and pure NLP–have been controllably produced in fiber lasers for the first time. This can assist in understanding the mechanism of pulse-pattern generation and define a compelling way to manipulate the DS cavity parameters in an orderly manner. It gives an effective method to quickly realize the DS or NLP fiber laser and does not require numerical simulation to guide the experimental design.
The paper is organized as follows. Section 2 describes the concept of the in-cavity PPE link; section 3 demonstrates in detail the orderly and controllable generation of pulse patterns, while section 4 gives the experimental setup, observation, and discussion of four fiber lasers with different pulse patterns. Section 5 summarizes the conclusions.
2. Concept description
The round-trip laser cavity model comprises a PPE link, a periodical SA, and a spectral filter, as shown in Fig. 1. The PPE link, which consists of a sandwich fiber structure of SMF1 /gain fiber (GF)/ SMF2 with a fixed sum of fibers length, precisely edits the pulse peak power in the PPE link by assigning the length of the SMFs. Assumed only one pulse with lower pulse power was output from the band-pass filter (BPF) at first. This original pulse will experience the dispersion effect when it propagates along the SMF1 and extend its duration according to the pulse broadening formula, ΔT = DLΔλ, where D is the dispersion parameter, L is the fiber length of the SMF1, and Δλ is the 3-dB spectral width of the pulse. As the original pulse owns lower peak power, dispersion will alone increase its duration when it propagates through the SMF1. This stretched pulse will be amplified, and its peak power will increase while it passes through the gain fiber. When the pulse with higher peak power transmits in the adjacent fiber of the SMF2, the combined effect of dispersion and nonlinearity would further broaden the pulse width. Compared with SMF1, where only the dispersion effect stretches the pulse, the SMF2 broadens the pulse even more since the pulse propagates along with the normal-dispersion fiber. Therefore, for a certain length of SMF (SMF1 + SMF2), to obtain a high peak-power pulse at position B, one should use the combination of long SMF1 and short SMF2. On the contrary, the combination of short SMF1 and long SMF2 will produce the pulse with broader pulse width and lower peak pulse power. From Fig. 2, we can see that the PPE link can form various pulses with different peak power of 367.8 W, 473.4 W, 578.2 W, and 799.9 W at position B only by setting SMF1 and SMF2 at different lengths.
Fig. 1. Conceptual schematic of a fiber laser comprising a spectral filter, a PPE link and a periodical saturable absorber. The transmittance curve (inset) of the saturable absorber is the product of the instantaneous pulse power and transmissivity versus the instantaneous power. [Inset parameters of sequentially dark yellow (solid line), green (dashed line), and blue (dotted line) used in the simulation are Δφ0 = 0.05 π, δλ/λs = 0, L/Lb = 80, θ = 0.268 π, ψ = 0.167 π; Δφ0 = 0.05 π, δλ/λs = 0, L/Lb = 80, θ = 0.263 π, ψ = 0.177 π; Δφ0 = 0.05 π, δλ/λs = 0, L/Lb = 80, θ = 0.259 π, ψ = 0.177 π, respectively.]
Fig. 2. Four pulse evolution processes using SMF layout with a fixed sum of fibers length in the PPE link. A Gaussian pulse with 160-fs pulse width and 150-W peak power after BPF (The BPF has a bandwidth of 8 nm and a central wavelength of 1030 nm.) was edited by the PPE link at a gain of 115 dB. The pulse with the correspondingly edited power at positions P3, B is shown on the right side of (a), (b), (c), (d), respectively.
Since the pulse with different pulse peak power would have extra spectral width, and the broader spectrum includes more wavelength components, that is to say, when these pulses propagate along with the fiber, they may produce dispersive waves. The higher the pulse peak power, the broader the spectrum, correspondingly, and more dispersive waves will form. When pulse and the dispersive waves pass through the SA, the SA can make the pulse peak power suffer higher losses than dispersive waves do if the pulse peak power passes over the critical saturation power (CSP). In this regard, after consecutive roundtrips, the dispersive waves will be amplified significantly. Furthermore, when these dispersive waves circulate in the resonant cavity, they will also be strengthened by the YDF, the new pulses form. Since the pulses before entering the filter own different spectral widths, then a different number of dispersive waves will be created. As a result, different pulse patterns – including DSs, DS molecules, a bound pattern of DS and NLP, and pure NLP – can all be formed.
3. Numerical simulation
The generalized nonlinear Schrödinger equation (GNLSE) is used to model the pulse propagation inside the SMF and YDF in the presence of stimulated Raman scattering [30,31]. The GNLSE shown as Eq. (1) is valid under the approximation of a slowly varying envelope, in which A(z, t) is the slowly varying electric field envelope. t is the local time, z is the propagation distance, and Ω is related to the gain bandwidth. The quantity β2 is 2-order dispersion coefficients. γ is the nonlinear coefficient of the optical fiber. g(Epulse) represents the amplification coefficient for the gain fiber and can be modeled according to Eq. (2). Generally, the small-signal gain g0 is set according to the pump power. The pulse energy Epulse is given by Eq. (3), where τ is the cavity round-trip time. The nonlinear response function can be separated into an instantaneous and a delayed part. The delayed molecular response gives rise to stimulated Raman scattering. TR is related to the slope of the Raman gain spectrum and is given by Eq. (4). The relative contribution of the instantaneous and delayed parts to Raman scattering is given by fR, where fR = 0.18 in fused silica. A simple model for the delayed response hR(t-t′) of Eq. (5) is a single damped harmonic oscillator, represented by a Lorentzian vibrational line with a phonon period τ1 and an inverse linewidth τ2. For silica, the values are τ1 = 12.2 fs and τ2 = 32 fs.
The lumped NPR’s transmission function [32] can be expressed as in Eq. (6). Here, θ and ψ represent the azimuth angles of the polarizer and the analyzer, respectively, concerning the fast axis of the fiber. ΔφL and ΔφNL denote the linear and nonlinear phase delays, respectively, which can be expressed as ΔφL = Δφ0 + 2π(1-δλ/λs)L/Lb, and ΔφNL = 2γLPcos(2θ)/3. Here, Δφ0 denotes the initial phase delay between the two orthogonal modes propagating in the fiber; λs is the central wavelength of the pulse; δλ is the wavelength detuning for λs; L, Lb, and γ are the total length of the cavity, birefringence beat length, and nonlinear coefficient of the fiber, respectively, and P is the instantaneous power of the optical pulse. Therefore, the instantaneous power P’ after the pulse is subjected to saturated absorption is shown in Eq. (7).
The round-trip resonant cavity model and the SA transmission curve are shown in Fig. 1 and the solid line (dark yellow) of the inset of Fig. 1, respectively. The PPE link comprises a segment of SMF1, a 60-cm-long YDF, and another segment of SMF2, in that order. The group-velocity dispersion of the SMFs and YDF is assumed to be the same of 23 ps2/km (ignoring higher-order dispersion effects). The nonlinear coefficients of the SMFs and YDF are 4.68 W−1km−1 and 9.3 W−1km−1, respectively; the gain bandwidth of the YDF is 45 nm, and the gain saturation energy is 1441 pJ. The stimulated Raman scattering, a higher-order nonlinear effect, is also considered. The filter, which has a Gaussian shape with a spectral filter bandwidth (SFBW) of 8 nm and a central wavelength of 1030 nm, is modeled as Eq. (8). Here, ω is the instantaneous angular frequency, and δω = 2πc[δλ/(1.665λ2)], where c is the speed of light in vacuum, δλ is the SFBW, λ is the central operating wavelength. The lumped linear cavity loss is 22%. In the simulation, by distributing the lengths of SMF1 and SMF2 and fixing the other parameters, we have obtained different pulse dynamic patterns in YDF lasers, as shown in Table 1 and Figs. 3–7.
Table 1. Controllably produced pulse patterns in fiber lasers. (DS: dissipative soliton, NLP: noise-like pulse)
3.1 Single DS
At first, we set the length of SMF1 and SMF2 to be 480 cm and 1250 cm, respectively. On this occasion, one can simulate the peak power of the original output pulse from the PPE link as 854.7 W when g0 = 95 dB (see Table 1), which is just over the CSP value of 691.7 W. In this case, when the pulse passes the SA, the SA would present a positive-saturable absorption (PSA) and a small portion of RSA. Therefore, the pulse is in the form of a double peak after SA at position C, as shown in Fig. 3. The spectral filtering effect then cuts the pulse to a single peak structure. Since the pulse before entering the filter has lower pulse peak power, wide pulse duration, and narrow spectral width, almost no dispersive waves are produced when they propagate along with the fiber. And then, the formed initial pulse continually circulates in the cavity and undergoes shaping in the PPE link, SA, and filter, and finally, a stable DS is produced.
Fig. 3. Calculated single steady-state DS’ buildup in time [(a), (b), and (c)] and spectral [(d), (e), and (f)] domains for cavity positions B, C, and P1, respectively. The spectral, temporal, and autocorrelation trace of the numerical DS (g) at position B from the last round trip.
3.2 DS molecules
Varied the lengths of SMF1 and SMF2 from 480 to 680 cm and 1250 to 1050 cm, respectively, also fixed g0 to 95 dB, in this case, the peak power Pp of the output pulse from the PPE link as the number of cycles increases so does the spectral width. The small pulse will form when this Pp value is higher enough, as shown in Fig. 4(a).
Fig. 4. Calculated steady-state DS molecules’ buildup in time [(a), (b), and (c)] and spectral [(d), (e), and (f)] domains for cavity positions B, C, and P1, respectively. The spectral, temporal, and autocorrelation trace of the numerical DS molecules (g) at position B from the last round trip.
We can understand this pulse evolution as follows, since the peak power is higher, i.e., γPpT2≫β2 (γ is the fiber nonlinear parameter; Pp is the peak power of the pulse; T is the pulse duration, and β2 is the GVD parameter), so the self-phase-modulation (SPM) effect dominates the GVD effect during the initial stages of pulse evolution. As we all know, the SPM effect will widen the spectrum, with the increase of the pulse circulated in the resonant cavity, the broader the spectrum. When this width exceeds a specific value, the dispersive waves near the arrows on the leftmost (Fig. 4(a)) pulse evolution of Fig. 4 (position B) were formed [7]. The small dispersive waves are subjected to the PSA of the SA while propagating along the cavity because of their lower peak power until the laser system reaches steady-state, and bound DSs (DS molecules) are finally formed.
Note that because the laser is operated in the normal GVD regime (β2 > 0), the red-shifted light located near the leading edge travels faster, whereas the blue-shifted light located near the trailing edge travels slower; when the red-shifted light overtakes the blue-shifted light in the forward tail of the pulse, interference occurs and interference fringes are formed. Compared the Fig. 3(g) and Fig. 4(g), we can see that the optical spectrum of the DS molecules shown in Fig. 4(g) is strongly modulated as a direct consequence of the coherence of the two DSs. The separation distance between the DSs is 45.0 ps (The middle graph in Fig. 4(g)), which also equals the delay time from the central- to the side-peaks in the autocorrelation trace (The rightmost picture in Fig. 4(g)).
The edited pulse peak power at position B here is 889.5 W at the 40th round-trip, which is higher than the CSP of 691.7 W; i.e., more instantaneous power enters into the RSA range of the SA.
3.3 Bound pattern of DS and NLP
Further increased the length of SMF1 from 680 cm to 880 cm and decreased the SMF2 size from 1050 cm to 850 cm, and fixed g0 to 95 dB. In this case, the peak power Pp of the output pulse from the PPE link is 1976 W. From the above analysis, we can see that, with the increase of the SMF1, the peak power of the output pulse from the PPE link at position B will increase, so does the spectral width. Accordingly, this broader spectrum would induce more dispersive waves, as shown in Fig. 5. In addition, the fine-structure oscillations in the pulse caused by the RSA of the SA would also coincide [32].
Fig. 5. The buildup of the bound pattern of DS and NLP in the time domain [(a), (b), and (c)] (Inset: Pulse pattern for the 199th round trip), spectral-domain [(d), (e), and (f)], and five randomly extracted autocorrelation traces [(g), (h), and (i)] at cavity positions B, C, and P1, respectively. The spectral, temporal, and autocorrelation trace of the numerical bound pattern of DS and NLP (j) at position B from the last round trip.
On the other hand, considering the stimulated Raman scattering effect, the laser energy would be transferred from a 1030-nm pump wave to a 1078-nm Stokes wave (downshifted by approximately 13 THz). Therefore, the front pulse preferentially undergoes energy downshifting. Then the tiny dispersive waves and the front pulse will enjoy more gain and experience the RSA of the SA while propagating along the cavity until a bound pattern of DS and NLP is formed, as shown in Fig. 5.
From Fig. 5(j), we can see that the spectrum of the bound pattern of DS and NLP retains the sharp-edged shape of the DS at short wavelengths but has more oscillations at long wavelengths, which is consistent with the NLP spectrum. The traces in the temporal domain also demonstrated that the leading edge of the pulse has an NLP pattern, and the trailing edge of the pulse had a typical DS pattern (The middle graph in Fig. 5(j)). In this case, the auto-correlation function has a non-usual triple (femto-, pico-, and picosecond) scale shape (The rightmost picture in Fig. 5(j)). Though this autocorrelation trace is similar to that of the bound NLPs [see Fig. 3 of [33]], however, their temporal domain structure is entirely different [see Fig. 10(a) of [33]].
If the length of SMF1 is further increased from 880 cm to 1080 cm, whereas that of SMF2 was decreased from 850 cm to 650 cm with the 95-dB g0 and SMF length sum. A bound pattern of DS and NLP would still be generated in the cavity, as shown in Fig. 6. A comprehensive study was given in Ref. [34] concerning the possibility of generating a wide variety of pulse patterns. The bound pattern of DS and NLP can be maintained in a wide range of SMF length distribution and therefore is a new addition to the pulse pattern family.
Fig. 6. The buildup of the bound pattern of DS and NLP in time (upper graphs) and spectral (lower graphs) domains at cavity positions B, C, and P1.
3.4 NLP
The length of SMF1 was further increased from 1080 cm to 1480 cm, whereas that of SMF2 was decreased from 650 cm to 250 cm in the PPE link with the 95-dB g0. As the pulse amplitude was further amplified when the pulse passed through the YDF, the peak power of the pulse from the PPE link also increased caused by the pulses experiencing little dispersion. It is around 1200 W at position B. This value is greater than the CSP of the saturable absorber, indicating that it is wholly located in the first saturable absorption region; i.e., when the entire pulse passes through the SA, the low-power portion undergoes less absorption, while the high-power portion undergoes considerable absorption. The pulse experiences the RSA effect while propagating in the cavity until the system reaches equilibrium; consequently, NLPs are formed, as shown in Fig. 7. Figure 7(g) presents well-known features of isolated NLP, which with extremely variable wavelength emission intensity, an irregular set of noisy-like peaks, and a double-structured autocorrelation trace (femto- and pico-second).
Fig. 7. Calculated NLP buildup in time [(a), (b), and (c)] and spectral [(d), (e), and (f)] domains at cavity positions B, C, and P1, respectively. The spectral, temporal, and autocorrelation trace of the numerical NLP (g) at position B from the last round trip.
From the above investigation, we can see that controllable pulse patterns including DS, DS molecules, the bound pattern of DS and NLP, and pure NLP can be obtained by increasing the length SMF1 while decreasing SMF2 in the PPE link with a fixed gain. As described in a recent study on nonlinear transmission [35], NPR effect can provide many saturable absorption curves, such as in the upper block diagram of Fig. 1 with different CSP values varying the saturated absorption model parameters. We can still give effective methods to increase DS and NLP distribution probability. The longer the SMF2 is, the pulse will be severely broadened. This pulse can easily enter the PSA region of most saturated absorption curves, which will increase the probability of DS radiation; if the SMF2 is shorter, the pulse is not severely broadened. The pulse will have a high likelihood of entering the reverse-saturable absorption range of most saturated absorption curves, resulting in a higher likelihood of generating NLP. Considering the change of the saturable absorption curve, we draw significant conclusions about the controllable generation of DS and NLP. Without numerical simulation guidance, a short SMF1 and a longer SMF2 are required to obtain a DS. More specifically, when other components in the resonant cavity are selected, increasing the length of SMF2 in the PPE link can generate DS under a specific pump power. On the other hand, if the goal is to obtain an NLP, a long SMF1 and a shorter SMF2 should be chosen.
4. Experimental results
We constructed fiber ring lasers, as shown in Fig. 8, for the experiment. Briefly, they comprise a PPE link, a BPF with 8-nm 3-dB width and an NPR mode locker. The PPE link includes a 976/1030-nm WDM, 850-mW LD, a variable-length SMF1, a 0.6-m YDF, a 10% OC, and another variable-length SMF2. The NPR includes two PCs used for finely adjusting the cavity intensity-dependent losses. The SMF length between PC2 and the BPF should be minimum; by adjusting the length of the SMF between points BPF and A (Fig. 8) in the experiments, the length of LBPF-A was made to correspond to the SMF1 length in the numerical simulation, along the operating direction of the laser. By adjusting the length of the SMF between points B and C, length LBC was made to correspond to the SMF2 length in the simulation, also.
Fig. 8. Schematic of the mode-locked fiber laser setup. LD: laser diode, WDM: wavelength-division multiplexer, YDF: Yb-doped fiber, 10% OC: 10% output coupler, PC: polarization controller, PD-ISO: polarization-dependent isolator, NPR: nonlinear polarization rotation, BPF: band-pass filter.
Corresponding to the numerical simulation parameters, we performed experiments using four different fiber lasers with approximately uniform SMF lengths. The experimental results are summarized in Table 2.
Table 2. Controllable pulse patterns generated in the experiments.
A single DS was generated when the pump power was 269.0 mW, as shown in Fig. 9(a). Visualization 1 recorded the measured spectrum, oscilloscope curve, autocorrelation trace, and RF spectrum of the DS. The repetition rate of the DSs was 12.20 MHz, and the signal-to-noise ratio (SNR) was greater than 65 dB, indicating that the DS laser operated in a stable regime. It is worth mentioning that it is challenging to obtain NLP radiation under this cavity length ratio structure and within this pump range unless a pump power higher than 310 mW is used. Further, we cut 2 m of the SMF from the LBC of the DS cavity and fused it with the LBPF−A to build another fiber laser. By carefully adjusting the PC states, DS molecules were obtained when the pump power was increased to 268.3 mW, as shown in Fig. 9(b). The optical spectrum is modulated by a two-DS interference pattern with a contrast approaching unity as shown on the expanded portion of the spectrum in the inset of Fig. 9(b). This high-contrast interference pattern remains stable for hours, indicating that the two DSs comprising the bound-pulse have a fixed phase relationship. The period of the spectral modulation is Δλ = 0.142 nm, which implies a pulse separation of Δτ = 25 ps (ΔτΔλ = -λ2/c, λ=1033 nm in Fig. 9(b)). The autocorrelation trace shown in Fig. 9(b) also confirms this separation, with the two side peaks situated at 25 ps from the central peak. Visualization 2 and Visualization 3 recorded the measured spectra, oscilloscope curves, autocorrelation traces, and RF spectra of the DS molecules in different spectral measurement spans. The repetition rate of the DS molecules was 12.15 MHz, and the SNR was greater than 70 dB, indicating that the DS-molecule laser operated in a stable regime.
Fig. 9. Experimental results of pulse patterns for controllable generation in the all-normal-dispersion fiber lasers. Optical spectrum and autocorrelation trace (inset) of the single DS (a) (see Visualization 1). Optical spectrum and autocorrelation trace (inset) of the DS molecules (b) (see Visualization 2 and Visualization 3). Optical spectrum and autocorrelation trace (inset) of the bound pattern made up of DS and NLP (c) (see Visualization 4). Optical spectrum and autocorrelation trace (inset) of the NLP (d) (see Visualization 5 and Visualization 6).
Note that in addition to DS molecules, other pulse patterns, such as the DS and NLP, can also be obtained by appropriately adjusting the pump power and the state of the PCs in the same cavity. We can qualitatively understand these phenomena as follows: in addition to the discreet cavity structure design, the change in the nonlinear transmission curve of the NPR mainly depends on the PC rotation angle. Generally, a single DS is easily produced if the NPR transmission curve has a high CSP [32]. Assuming that the gain saturation of the gain fiber is sufficiently large, the pulse can be rapidly amplified in a very short gain fiber. Therefore, depending on the nonlinear effect of the fiber, pulse-breaking occurs easily in an all-normal-dispersion fiber laser [36,37]. In this case, multiple pulse states, including DS molecules, are easily generated [13,25,38–40]. If the pump power is increased with a lower gain saturation of the gain fiber, the pulse does not break. When the peak power of the pulse exceeds the CSP of the NPR transmission curve considerably, the pulse can easily evolve into DS molecules or an NLP, depending on the RSA effect. Therefore, using the PPE link and NPR-saturated absorption and guided by numerical simulation, it is easier to achieve the approximate transmission curve used in the simulation by adjusting the PC in the experiment. The produced DS molecules’ pattern is displayed in Fig. 9(b).
A 2-m length of the SMF was cut from LBC of the DS molecule cavity and fused with LBPF−A to build the third fiber laser. The experimental results are shown in Fig. 9(c) confirm the existence of the bound pattern of DS and NLP in the fiber laser, as depicted in Figs. 5 and 6. In particular, the autocorrelation trace of the bound pattern of DS and NLP exhibits a triple (femto-, pico-, and picosecond) scale shape and a dynamically variable shape as a function of the round-trip cavity period; however, due to the superimposed recording of the autocorrelator, the autocorrelation trace in the experiment was recorded as shown in the inset of Fig. 9(c), which is in good agreement with the numerical simulation (see also Fig. 5(g)-(j)). Visualization 4 recorded the measured spectrum, oscilloscope curve, autocorrelation trace, and RF spectrum of the bound pattern of DS and NLP. The repetition rate of the bound pattern of DS and NLP was 12.1744MHz, and the SNR was greater than 40 dB, indicating that the bound pattern of DS and NLP operated in a stable regime.
Then 6 m of the SMF was further cut from LBC the cavity of the bound pattern of DS and NLP and fused with LBPF−A to build the last fiber laser. As previously mentioned, the pulse peak power was edited largely in the NPR RSA region. Increasing the pump power to 282.5 mW, an NLP produced, its autocorrelation trace has a signature NLP signal, i.e., a narrow spike riding on a broad pedestal [41,42]. It is worth noting that a difference is that in the simulation results, the NLP spectra exhibit a prickly shape as a function of the round-trip cavity period, as shown in Fig. 7(g); however, the experiment’s spectral shape was stable and smooth due to the optical spectrum analyzer's superimposed recording, as shown in Fig. 9(d). Visualization 5 and Visualization 6 recorded the measured spectrum, oscilloscope curve, autocorrelation trace, and RF spectrum of the pure NLP at the same pump power and different PCs’ states. It indicated that the narrowband pure NLP (see Fig. 9(d), Visualization 5) had a smaller SNR of around 30 dB, showing that the laser operated in a less stable regime. However, by carefully adjusting the PCs, the spectra of the NLP and the Raman conversion part could be connected. Consequently, a broadband NLP with around 60-nm spectral width could be formed (see Visualization 6). In this case, the SNR was greater than 50 dB, indicating that the laser operated in a stable regime. Otherwise, it is challenging to obtain DS radiation under this cavity length ratio structure and within this pump range. It is worth noting that after obtaining the NLP, the DS can be obtained with a small probability by carefully reducing the pump power. The above experimental results are consistent with the theoretical predictions.
5. Conclusion
In conclusion, we have presented a concise mechanism, the intracavity pulse power editing (PPE) link, to improve the distribution probability of dissipative soliton (DS) and noise-like pulse (NLP) in all-normal-dispersion fiber lasers. Different pulse patterns can be produced by simply assigning the length of the SMF in the laser. The two critical characteristics of optical fiber, dispersion and nonlinearity, are not studied separately in the PPE link. To the best of our knowledge, a bound pattern of DS and NLP has been produced controllably for the first time. Our work dramatically broadens the design possibilities in terms of technology and provides convenient architectures for DS and NLP fiber lasers. The intracavity PPE link also offers new perspectives on complex pulse dynamics and may inspire innovative cavity designs.
Funding
National Natural Science Foundation of China (12074098, 61605040); Natural Science Foundation of Hebei Province (F2020205016, A2020205009); Scientific Research Special Fund of Hebei Normal University (L2021T03).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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