Mechanism of noise-like pulse in all-normal dispersion all-fiber laser based on nonlinear polarization rotation

Jiajing Lang; Jiajing Lang; Chenyue Lv; Chenyue Lv; Baole Lu; Baole Lu; Baole Lu; Jintao Bai; Jintao Bai; Jintao Bai

doi:10.1364/OE.508074

1. Introduction

Fiber lasers have the advantages of excellent beam quality, high energy conversion efficiency, compact structure, and superb heat dissipation, which can be operated in anomalous dispersion [1], near zero dispersion [2], and normal dispersion [3]. All-normal dispersion (ANDi) mode-locked fiber lasers are widely studied for their potential to achieve high power, high energy ultrashort pulses [3–5]. Based on the various nonlinear effects in ANDi fiber lasers, different types of pulses can be obtained, such as dissipative soliton (DS) [3], dissipative soliton resonance (DSR) [6,7], and noise-like pulses (NLP) [8]. NLP is a pulse envelope with a broad spectrum and low temporal coherence, containing many ultrashort pulses with different peak powers and pulse widths. Therefore, NLP has a wide range of applications in sensing [9], optical coherence tomography [10], laser-induced breakdown spectroscopy [11], and supercontinuum generation [12,13]. With the continuous exploration of the application areas, the intrinsic mechanisms of NLP generation have equally attracted wide interest.

The generation of NLP is not limited to the mode-locking methods of the laser, the operating wavelength, and the dispersion region [14–17]. NLP was first reported by Horowitz et al. in an erbium-doped mode-locked fiber laser based on nonlinear polarization rotation (NPR), which operates in the anomalous dispersion regime [1]. Tang et al. pointed out that NLP in dispersion-managed erbium-doped fiber ring lasers resulted from a combination of soliton collapse and positive feedback [2]. Zhang et al. demonstrated that the anti-saturable absorption introduces amplitude modulation and peak-power-clamping (PPC) effect of NPR, which play a key role in the formation of NLP [18]. Mou et al. fixed the polarization state and found that the operating state of the fiber laser can be switched between DS and NLP by only increasing the pump power [19]. Wang et al. proposed an effective method to form NLP in ANDi fiber laser by weakening spectral filtering [20]. The results showed that NLP is widely distributed in the region of weaker spectral filtering. Kobtsev et al. achieved switching between DS and NLP by changing the polarization controller (PC) by combining experiment and simulation [21]. Few studies investigated the role of the polarization state between DS and NLP switching. As far as we know, previous studies only suggested that the polarization state affects the pulsed state from DS to NLP, but the specific mechanism remains unclear.

This letter focuses on the role of polarization states in the DS to NLP transition. We find that variation in the polarization state changes the positive and negative feedback states in the cavity, leading to the transition from DS to NLP. In other words, the critical saturation power (CSP) is changed. In the experiment, a birefringent fiber filter is used to achieve wavelength switching, which has the advantages of a simple structure. The numerical simulation results are in good agreement with the experimental results, further demonstrating the function of the change of polarization state in the transition from DS to NLP.

2. Theoretical model and numerical simulation

2.1 Theoretical model

To investigate the specific mechanism of polarization state in DS and NLP transition, we build an ideal ANDi all-fiber laser based on NPR and perform numerical simulations, as shown in Fig. 1. The simulated cavity consists of 0.3 m ytterbium-doped fiber (YDF), 7.3 m single-mode fiber (SMF), an NPR mode-locker, a Lyot filter (or a birefringent fiber filter), and a coupler with a 30% output. The lengths of SMF1, SMF2, and SMF3 are 3.6 m, 2.6 m, and 1.1 m, respectively. The Lyot filter consists of 0.3 m PMF, a polarizer, and an analyzer. The polarizer and analyzer also form the NPR mode-locker.

Fig. 1. Simulation model of the ANDi all-fiber laser.

Download Full Size | PDF

The pulse transmission process within the fiber is simulated using the coupled Ginzburg-Landau equations shown below:

(1)$$\begin{array}{l} \frac{{\partial {\varphi _x}}}{{\partial z}} ={-} i\frac{{{\beta _2}}}{2}\frac{{{\partial ^2}{\varphi _x}}}{{\partial {t^2}}} + i\gamma \left( {{{|{{\varphi_x}} |}^2} + \frac{2}{3}{{|{{\varphi_y}} |}^2}} \right){\varphi _x} + \frac{{i\gamma }}{3}\varphi _x^\ast \varphi _y^2 + \frac{{g - l}}{2}{\varphi _x} + \frac{g}{{2\Omega _g^2}}\frac{{{\partial ^2}{\varphi _x}}}{{\partial {t^2}}}\\ \frac{{\partial {\varphi _y}}}{{\partial z}} ={-} i\frac{{{\beta _2}}}{2}\frac{{{\partial ^2}{\varphi _y}}}{{\partial {t^2}}} + i\gamma \left( {{{|{{\varphi_y}} |}^2} + \frac{2}{3}{{|{{\varphi_x}} |}^2}} \right){\varphi _y} + \frac{{i\gamma }}{3}\varphi _y^\ast \varphi _x^2 + \frac{{g - l}}{2}{\varphi _y} + \frac{g}{{2\Omega _g^2}}\frac{{{\partial ^2}{\varphi _y}}}{{\partial {t^2}}} \end{array}$$

where β₂ is the group velocity dispersion (GVD) coefficient, γ denotes the nonlinear coefficient of the fiber, and g represents the saturable gain coefficient of the gain fiber. For undoped fiber, g = 0. l denotes the loss coefficient of the fiber, and Ω_g is the gain bandwidth. The saturated gain coefficient can be expressed using the following formula:

(2)$$g = {g_0}\exp \left( { - \frac{{\int {({{{|{{\varphi_x}} |}^2} + {{|{{\varphi_y}} |}^2}} )dt} }}{{{P_{sat}}}}} \right)$$

where g₀ is the small-signal gain coefficient and P_sat denotes the saturation energy. In the simulation, a weak Gaussian pulse is used as the initial input field to avoid temporal randomness in the generation of NLP.

Assuming the polarization state of the light passing through the polarizer is in line with the y axis, the transmission matrix of the polarizer is J_P. The matrix of light propagating along the fiber is J_F, and the transmission matrix of the analyzer is expressed as J_A. The transmission matrix of the NPR can be expressed as shown below [18,22]:

(3)$${T_{NPR}} = {J_A} \cdot {J_F} \cdot {J_P} = \left[ {\begin{array}{cc} {\cos \psi }&{\sin \psi }\\ { - \sin \psi }&{\cos \psi } \end{array}} \right] \cdot \left[ {\begin{array}{cc} {{e^{\frac{{i\Delta \varphi }}{2}}}}&0\\ 0&{{e^{\frac{{ - i\Delta \varphi }}{2}}}} \end{array}} \right] \cdot \left[ {\begin{array}{cc} {\cos \theta {e^{\frac{{i\Delta {\varphi_0}}}{2}}}}&{\sin \theta {e^{\frac{{i\Delta {\varphi_0}}}{2}}}}\\ { - \sin \theta {e^{\frac{{ - i\Delta {\varphi_0}}}{2}}}}&{\cos \theta {e^{\frac{{ - i\Delta {\varphi_0}}}{2}}}} \end{array}} \right] \cdot \left[ {\begin{array}{c} 1\\ 0 \end{array}} \right]$$

where θ and ψ are the azimuth angles of the polarizer and analyzer compared to the fast axis of the fiber, respectively. $\Delta \varphi = \Delta {\varphi _L} + \Delta {\varphi _{NL}}$ is the total phase delay, $\Delta {\varphi _L} = 2\pi ({1 - {{\delta \lambda } / {{\lambda_0}}}} ){L / {{L_b}}}$ and $\Delta {\varphi _{NL}} ={-} 2\gamma LP\cos (2\theta )/3$, denote the linear phase delay and nonlinear phase delay, respectively. Δφ₀ is the initial phase delay. λ₀ and δλ are the central wavelength and wavelength detuning, respectively. L, L_b, γ, P is the length of the cavity, birefringence beat length, nonlinear coefficient of the SMF, and instantaneous power of the pulse, respectively. The instantaneous power P’ after the pulse is subjected to saturated absorption is shown in Eq. (4) [23].

(4)$$P^{\prime} = PT = P{|{{T_{NPR}}} |^2}$$

Because the polarizer and analyzer are the same as those used in the NPR mode-locker. The filtering effect of a Lyot filter can be expressed as [24,25]:

(5)$${|{{T_{Filter}}} |^2} = {\sin ^2}(\theta )+ {\sin ^2}(\psi ) + {\cos ^2}(\theta )+ {\cos ^2}(\psi ) + \frac{1}{2}\sin ({2\theta } )\sin (2\psi )\cos ({\Delta {\varphi_{L1}} + \Delta {\varphi_{NL1}}} )$$

The linear phase delay and nonlinear phase delay can be expressed as $\Delta {\varphi _{L1}} = \Delta {\varphi _0} + 2\pi {{{L_{PMF}}\Delta n} / \lambda }$ and $\Delta {\varphi _{NL1}} ={-} 2{\gamma _{PMF}}{L_{PMF}}P\cos (2\theta )/3$, respectively, L_PMF is the length of the PMF, Δn is the birefringence difference of PMF, λ is the operating wavelength, and γ_PMF is the nonlinear coefficient of the PMF. Since the filter uses the same polarizer and analyzer as the NPR mode-locker, θ, ψ, and Δφ₀ are the same as Eq. (3). The above model is solved by Matlab using the fourth-order Runge-Kutta method. To accelerate the convergence of the calculation to a stable operating state, a weak Gaussian-shaped pulse with a full-width at half-maximum of 50 ps and peak power of 1 W is used as the initial pulse. To avoid the effect of different initial fields on the simulation results, we use the noise field as the initial field for the simulation and find no significant effect on the results. In order to compare the simulation with the experiment and to make it more reliable, we chose the relevant parameters as shown in Table 1.

Table 1. Parameters used in the simulation of ANDi all-fiber laser.

View Table

2.2. Numerical simulation

We fix the other parameters while varying only the θ value and show the pulse evolution in Fig. 2 for θ values of 40° and 35°, respectively. The results of DS and NLP can be obtained at different θ, and for the obviousness of the comparison, we chose two of them to discuss in detail. The time taken for the simulation is 396.45 s when θ=40° and 404.32 s when θ=35°, respectively. Figures 2(a)-2(c) illustrate the evolution of the spectrum and pulse towards a stable DS pulse at θ=40°. From the local amplified Fig. 2(b), it becomes evident that after the 20th roundtrip, the initial weak Gaussian pulse transforms into a stable DS pulse. The autocorrelation trace of the output pulse is depicted in Fig. 2(d). At θ=35°, the initial weak Gaussian pulse gradually evolves into NLP, as shown in Figs. 2(e)-2(g). After the 20th roundtrip, the pulse exhibits random sub-pulses within the wave packet, forming an NLP. The output pulse has a double-scale autocorrelation trace, as shown in Fig. 2(h). The intensity ratio of spike-to-pedestal in the NLP is smaller due to the higher density of sub-pulses within the wave packet. Increasing the density of sub-pulses in the wave packet, the NLP spike-to-pedestal ratio becomes smaller [26].

Fig. 2. Numerical simulation results. When θ=40°, (a) Spectrum evolution, (b) Local amplified spectrum evolution, (c) Pulse evolution, and (d) Autocorrelation trace; When θ=35°, (e) Spectrum evolution, (f) Local amplified spectrum evolution, (g) Pulse evolution, and (h) Autocorrelation trace.

Download Full Size | PDF

Furthermore, the positive feedback state within the cavity is demonstrated in Fig. 3(a) and 3(b) according to Eq. (3) and (4). Positive feedback means the transmission of the cavity increases as the peak power of the pulse increases, also known as positive saturation absorption. Negative feedback is the opposite. The blue curve is the transmission curve at different θ (corresponding to Eq. (3)), and the red curve is the transmitted power after NPR, which is the product of intracavity transmission and instantaneous power (corresponding to Eq. (4)).

Fig. 3. Intracavitary transmission (blue curve) and the product of instantaneous power and transmission (red curve). (a) θ=40°; (b) θ=35°.

Download Full Size | PDF

The power corresponding to the critical point of positive and negative feedback is called the CSP [27]. Considering that the transmissivity T is related to the feedback state in the cavity, the CSP from positive to negative feedback is at the maximum product of the instantaneous power P and the corresponding transmissivity [18,20,23,28]. When the peak power is lower than the CSP, the pulse with higher peak power will encounter a smaller NPR attenuation, which is called positive feedback. Points A, C, and E in Fig. 3 represent the CSP positions. When the peak power of the pulse exceeds the CSP, negative feedback plays a role, leading to the PPC effect. It has been shown that the PPC is mainly caused by the negative feedback of the saturable absorber in the fiber laser [6,18,23,29], and the NPR is also a saturable absorber.

In Fig. 3(a), the CSP is located at point A means that when the peak power of the pulse before NPR is lower than 388.09 W, the intracavity transmission is in a positive feedback state, whereas when the peak power of the pulse before NPR is higher than 388.09 W, the negative feedback will come into play, and the peak power of the pulse will be clamped down to 279. 47 W. As can be seen from Fig. 3(a), when the peak power of the pulse is lower than the instantaneous power corresponding to point B, the highest peak power after passing through NPR will also be clamped below 279.47 W. In Fig. 3(b), the CSP is located at point C, which means that the intracavity transmission is in a positive feedback state when the peak power of the pulse before passing through the NPR is lower than 198.91 W. Negative feedback comes into play when the peak power of the pulse before the NPR is higher than 198.91 W, and the peak power of the pulse is clamped at 142.96 W. Similarly, when the peak power of the pulse before the NPR is lower than the peak power at point D, the peak power of the pulse after the NPR is also clamped at 142.96 W. At this point, the extra gain in the cavity will not enhance the soliton energy but amplify the background noise or dispersive waves [28,30]. The pulse keeps circulating in the cavity and the initial weak Gaussian pulse becomes an NLP. For the same gain condition, there is positive feedback in the cavity at θ=40° and the initial weak Gaussian pulse forms a stable DS pulse. While, the negative feedback comes into play and the peak power of the pulse is clamped due to the change in polarization state at θ=35°, leading to the formation of an NLP.

To verify the influence of the polarization state on the type of output pulses by the laser, we extract the intracavity pulse, which is the pulse before passing through the NPR, and the pulses after passing the NPR. At θ=40°, DS is eventually formed, as depicted in Fig. 4(a). The peak power of the pulse is 345.47 W, which is lower than the CSP of 388.09 W. The initial weak Gaussian pulse passes through the gain medium and is amplified. However, during this amplification process, the peak power of the pulse remains lower than the CSP. The laser cavity is in a positive feedback state. The pulse is compressed, while the peak power of the pulse remains below the CSP, and eventually stable DS pulse is formed. The DS spectrum after NPR is shown in the inset in Fig. 4(a). However, at θ=35°, it can be observed from Fig. 4(b) that at the 3rd roundtrip, the peak power of the pulse is 97.11 W, which is lower than the CSP of 198.91 W. The cavity is in a positive feedback state, the pulse continues to be transmitted, and the peak power of the pulse increases. At the 4th roundtrip, the peak power of the pulse exceeds the CSP of 198.91 W, the negative feedback will come into play, and the peak power of the pulse is clamped at 142.96 W, as shown in Fig. 4(c). It can be seen that there is a depression in the middle of the pulse after NPR, which is because although the peak power of the pulse is clamped at 142.96W, this is the maximum peak power P’ after NPR, and different peak powers P correspond to different P’ after NPR. Other peak powers P correspond to P’ less than 142.96W, thus leading to the appearance of the depression. After that, the pulse continues to be transmitted and is amplified after passing through the YDF, as shown by the blue line in Fig. 4(d). The peak power of the pulse is clamped after passing through the NPR, and more small depressions are generated, as shown by the red line in Fig. 4(d). Afterward, the cycle is repeated (see Figs. 4(d)–4(f)), and finally the NLP is formed, which consists of ultrashort pulses with different peak powers and pulse widths. The NLP spectrum after NPR is shown in the inset in Fig. 4(i). We see that the spectrum is messy because this is a real-time spectrum, and the OSA used in the experiment is used to obtain the average spectrum. So there are some differences in the spectrum obtained in the experiment. This formation of NLP can be observed in Figs. 4(g)–4(i).

Fig. 4. The pulses before and after passing through the NPR at different θ. (a) Stable DS at θ=40°; (b)-(i) Pulse of 3rd, 4th, 5th, 6th,16th, 26th,36th, 46th roundtrip at θ=35°.

Download Full Size | PDF

We also find that if switching DS and NLP by only adjusting the θ value, g₀ needs to be higher or equal to a constant threshold. Below this value, DS is formed in both cases. The reason for this transition is that only when g₀ is sufficiently large, at θ = 35°, the peak power of the pulse is likely to exceed the CSP. Ultimately, the NLP is formed. As g₀ continues to increase, the initial weak Gaussian pulse also evolves into NLP at θ = 40°. Thus, a suitable g₀ value needs to be selected in the simulation, which is 38.3. By constructing a theoretical model and performing numerical simulations, the transition from DS to NLP is found to be caused by the change in intracavity polarization state. This alteration affects the intracavity positive and negative feedback states, thereby changing the transmission curve in the cavity. At this point, the intracavity conditions can allow the energy of a single pulse to exceed its CSP, negative feedback and the PPC effect come into play, so the transition from DS to NLP can be achieved by changing the intracavity polarization state.

3. Experimental setup and results

3.1 Experimental setup

The schematic of the ANDi fiber laser based on NPR is shown in Fig. 5. The 980 nm laser diode pumps the 0.3 m YDF (Liekki Yb1200, GVD = 24.22 ps²/km) through a 980/1060 nm wavelength division multiplexer (WDM). The polarization independent isolator (PI-ISO), PCs (PC1 and PC2), and in-line polarizer (ILP) are combined to NPR structure in the cavity enabling the passively mode-locking. At the same time, the PI-ISO guarantees the unidirectional propagation of pulses in the cavity. The optical coupler (OC) splits the 30% of light pulse energy for measurement. While 70% of light continues to transmit in the cavity. The 0.3 m PMF (PM980, GVD = 24.8 ps²/km) is added between the ILP and PC1 to form a Lyot filter. All other components are made of SMF (HI1060, GVD = 21.91 ps²/km) with a total length of 7.3 m. The total length of the cavity is approximately 7.9 m. The difference between the experiment and the simulation model is the position of the OC, which is located after the NPR in the simulation but before the NPR in the experiment. However, this does not affect our experimental results.

Fig. 5. Schematic of the ANDi fiber laser. LD: laser diode; WDM: wavelength division multiplexing; PI-ISO: polarization-independent isolator; PC1 and PC2: polarization controllers; ILP: in-line polarizer; OC: optical coupler.

Download Full Size | PDF

The PCs change the polarization state by squeezing and twisting on the fiber. This leads to a shift in the transmission peak of the Lyot filter, facilitating wavelength switching. Figure 6(a) and 6(b) depict the transmission spectrum of the Lyot filter at different θ angles and measures in the experiment, which we can see the free spectral range is basically consistent with the simulation. Manual fiber PCs are used in the experiment, so we could not measure the variation of angles in the experiment. The filter curves at different θ in Fig. 6(a) are obtained by simulation based on Eq. (5). The net cavity dispersion was normal with a value estimated to be 0.17 ps². A high-speed real-time oscilloscope (OSC, Agilent, DSO9104A) is used to track temporal information. The optical spectrum of the laser is recorded by an optical spectrum analyzer (OSA, Yokogawa, AQ6370C) with a resolution of 0.02 nm. The radio frequency (RF) spectrum is recorded by an RF spectrum analyzer (Keysight, N9000BCXA signal analyzer), and the width of pulses is measured with an autocorrelator (APE, PulseCheck-50).

Fig. 6. Transmission spectrum. (a) Simulated Lyot filter at different θ; (b) Experimental measurements.

Download Full Size | PDF

3.2 Wavelength switchable dissipative soliton

The wavelength switching of DS is achieved by adjusting the PCs at a pump power of 200 mW. The mode-locked spectrum of DS exhibits a central wavelength of 1041.06 nm and a 3-dB bandwidth of 9.95 nm, as shown in Fig. 7(a). The 3-dB bandwidth can be obtained from the OSA. Figure 7(b) displays the RF spectrum with a fundamental frequency of 25.73 MHz, which corresponds to the cavity length of 7.9 m. The signal-to-noise ratio (SNR) is 71 dB, indicating that the laser is in a stable mode-locked state [31,32]. The pulse train of the oscilloscope is exposed in Fig. 7(c). The time interval between adjacent pulses is 38.9 ns, corresponding to a fundamental frequency of 25.73 MHz, and the inset of Fig. 7(c) is the real pulse train recorded by the oscilloscope in the range of 50 µs, which also shows that the laser is in a stable mode-locked state. The pulse autocorrelation trace in Fig. 7(d) demonstrates a pulse width of 4.09 ps under Gaussian fitting and a time-bandwidth product (TBP) of 11.2568.

Fig. 7. Typical experimental results of DS mode-locking at the pump power of 200 mW. (a) Spectrum of DS; (b) RF spectrum of DS (inset: RF spectrum within 600 MHz); (c) Pulse train (inset: time-domain plot of 50 µs); (d) Autocorrelation trace.

Download Full Size | PDF

Figure 8(a) is the mode-locked spectrum of the DS, which exhibits a wavelength switch from 1041.06 nm to 1033.83 nm by rotating the PCs while keeping the pump power fixed. The 3-dB bandwidth is only 10.21 nm, which can be obtained from the OSA. The RF spectrum is shown in Fig. 8(b), revealing a fundamental frequency of 25.73 MHz and an SNR of 70 dB. Figure 8(c) displays a time interval of 38.9 ns between adjacent pulses, whose inset is the real pulse train recorded by the oscilloscope in the 50 µs range, indicating that the laser is in a stable mode-locked state. The pulse autocorrelation trace in Fig. 8(d) shows a pulse width of 4.35 ps under Gaussian fitting and a TBP of 12.4577. The mode-locked spectrum exhibits asymmetry due to various factors that affect the shape of the DS, such as nonlinear interactions, dispersion, and self-phase modulation [5,33]. However, it is important to note that these asymmetries do not impact our experimental results.

Fig. 8. Typical experimental results of DS mode-locking at the pump power of 200 mW. (a) Spectrum of switchable DS; (b) RF spectrum of DS (inset: RF spectrum within 600 MHz); (c) Pulse train (inset: time-domain plot of 50 µs); (d) Autocorrelation trace.

Download Full Size | PDF

3.3 Transition from dissipative soliton to noise-like pulse

The transition of the DS to NLP can be achieved by adjusting only PC2 while keeping the pump power at 200 mW. Figure 9(a) illustrates that NLPs have a spectrum with a central wavelength of 1041.90 nm and a 3-dB bandwidth of 8.79 nm. The RF spectrum is presented in Fig. 9(b), the fundamental frequency is 25.73 MHz. The SNR is 52 dB, which is lower than that of the stable mode-locking. The noise pedestal is one of the typical characteristics of NLP, primarily caused by amplitude noise. Amplitude noise is the variation of the pulse amplitude, which can be observed on the oscilloscope. As seen in Fig. 9(c), the time interval between adjacent pulses is 38.9 ns, and the amplitude is unstable, which is evident from the pulse train in the range of 50 µs. Figure 9(d) illustrates the double-scale autocorrelation trace of the NLP, revealing a pedestal width of 4.52 ps and a spike width of 246 fs. It is noteworthy that this is the shortest pedestal width of NLP directly generated in the ANDi all-fiber laser based on NPR so far.

Fig. 9. Typical experimental results of NLP at the pump power of 200 mW. (a) Spectrum of NLP; (b) RF spectrum of NLP (inset: RF spectrum within 600 MHz); (c) Pulse train (inset: time-domain plot of 50 µs); (d) Autocorrelation trace (inset: autocorrelation trace of the spike).

Download Full Size | PDF

By retaining the pumping power and the state of PC1, the DS can undergo a gradual transformation into an NLP through the adjustment of PC2. The transition process from DS to NLP is illustrated in Figs. 10(a)–10(h). We observe that this transition is continuous and reversible. The continuous wave (CW) component appears during the transition from DS to NLP. The appearance of the CW component can be attributed to nonlinear effects and redistribution of energy. The energy of the DS is concentrated in the center of the pulse and the width of the pulse is relatively narrow. However, the light energy begins to distribute more widely in the frequency domain as the transition to NLP, leading to a broader spectrum and the formation of CW components. Polarization states play a crucial role in influencing nonlinear effects and energy distribution. The adjustment of the PC2 influences the polarization state, subsequently affecting the nonlinear effects and energy distribution. By returning the PC2 to its initial state, the transition from NLP back to DS can be achieved.

Fig. 10. Transformation of DS to NLP. (a)-(d) Spectrum; (e)-(h) Autocorrelation traces of the pulses.

Download Full Size | PDF

To enhance the visibility of spectral broadening, we indicate a 20-dB bandwidth in Figs. 10(a)–10(d). It is clear that the spectrum undergoes a progression from the stable mode-locked state to the emergence of the CW component. However, the oscilloscope still displays the mode-locked state. A slight narrowing of the pulse width from 4.09 ps to 4.00 ps can be observed, which can be attributed to the subtle broadening of the spectrum, as depicted in Fig. 10(e) and 10(f). Subsequently, the CW component diminishes (compare the CW components in Fig. 10(b) and Fig. 10(c)). As the NLP regime appears gradually, the width of the pulse increases, and its autocorrelation trace pulse width increases to 4.16 ps. This transition is shown in Figs. 10(b)–10(c), and Figs. 10(f)–10(g), respectively. Ultimately, the CW component disappears completely, forming the experimentally measured NLP, as shown in Fig. 10(d) and 10(h). The output NLP has a pedestal width of 4.52 ps.

4. Conclusion

Overall, we find that the transition mechanism between DS and NLP in ANDi all-fiber laser based on NPR is due to the change of the polarization state, which changes the positive and negative feedback states in the cavity. With the same gain condition, the peak power of the pulse will be clamped as the change of polarization state causes the negative feedback comes to play, resulting in the formation of NLP. In the experiment, the PMF is combined with polarization devices to form a Lyot filter, which constructs a wavelength-switchable and pulse-type switchable fiber laser. This study combines numerical simulations and experiment to investigate the mechanism of NLP generation in ANDi all-fiber laser based on NPR. The mechanism is an effective method for DS to NLP transition by changing the polarization state and is attractive for practical applications such as optical coherence tomography, supercontinuum generation, and micromachining.

Funding

Shaanxi Key Science and Technology Innovation Team Project (2023-CX-TD-06); National Natural Science Foundation of China (62375220); National Key Scientific Instrument and Equipment Development Projects of China(51927804)

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.

References

1. M. Horowitz, Y. Barad, and Y. Silberberg, “Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser,” Opt. Lett. 22(11), 799–801 (1997). [CrossRef]

2. D. Y. Tang, L. M. Zhao, and B. Zhao, “Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser,” Opt. Express 13(7), 2289–2294 (2005). [CrossRef]

3. A. Chong, J. Buckley, W. Renninger, et al., “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006). [CrossRef]

4. A. Chong, W. H. Renninger, and F. W. Wise, “All-normal-dispersion femtosecond fiber laser with pulse energy above 20nJ,” Opt. Lett. 32(16), 2408–2410 (2007). [CrossRef]

5. P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012). [CrossRef]

6. Z. Cheng, H. Li, H. Shi, et al., “Dissipative soliton resonance and reverse saturable absorption in graphene oxide mode-locked all-normal-dispersion Yb-doped fiber laser,” Opt. Express 23(6), 7000–7006 (2015). [CrossRef]

7. Z. Wang, H. Li, J. Li, et al., “Generation and vector features of pulsating dissipative-soliton-resonance pulses in a figure-of-eight fiber laser,” Opt. Laser Technol. 161, 109132 (2023). [CrossRef]

8. N. Paul, C. P. Singh, Bhuvnesh, et al., “Noise-like pulses from all-normal dispersion ytterbium doped all-fiber oscillator with semiconductor saturable absorber,” J. Opt. 24(6), 064015 (2022). [CrossRef]

9. S. Keren and M. Horowitz, “Distributed three-dimensional fiber Bragg grating refractometer for biochemical sensing,” Opt. Lett. 28(21), 2037–2039 (2003). [CrossRef]

10. Y. J. You, C. Wang, P. Xue, et al., “Supercontinuum Generated by Noise-like Pulses for Spectral-domain Optical Coherence Tomography,” in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (Optical Society of America, 2015), paper JW2A.94.

11. G. J. Parker, D. E. Parker, B. Nie, et al., “Laser-induced Breakdown Spectroscopy and ablation threshold analysis using a megahertz Yb fiber laser oscillator,” Spectrochim. Acta, Part B 107, 146–151 (2015). [CrossRef]

12. X. Zhu, D. Zhao, B. Zhang, et al., “Spectrally flat mid-infrared supercontinuum pumped by a high power 2 µm noise-like pulse,” Opt. Express 31(8), 13182–13194 (2023). [CrossRef]

13. A. Zaytsev, C. H. Lin, Y. J. You, et al., “Supercontinuum generation by noise-like pulses transmitted through normally dispersive standard single-mode fibers,” Opt. Express 21(13), 16056–16062 (2013). [CrossRef]

14. S. Smirnov, S. Kobtsev, S. Kukarin, et al., “Three key regimes of single pulse generation per round trip of all-normal-dispersion fiber lasers mode-locked with nonlinear polarization rotation,” Opt. Express 20(24), 27447–27453 (2012). [CrossRef]

15. Y. Mashiko, E. Fujita, and M. Tokurakawa, “Tunable noise-like pulse generation in mode-locked Tm fiber laser with a SESAM,” Opt. Express 24(23), 26515–26520 (2016). [CrossRef]

16. B. Ren, C. Li, T. Wang, et al., “Stable noise-like pulse generation from a NALM-based all-PM Tm-doped fiber laser,” Opt. Express 30(15), 26464–26471 (2022). [CrossRef]

17. P. Tang, M. Luo, T. Zhao, et al., “Generation of noise-like pulses and soliton rains in a graphene mode-locked erbium-doped fiber ring laser,” Front. Inf. Technol. Electron. Eng. 22(3), 303–311 (2021). [CrossRef]

18. X. Li, S. Zhang, M. Han, et al., “Fine-structure oscillations of noise-like pulses induced by amplitude modulation of nonlinear polarization rotation,” Opt. Lett. 42(20), 4203–4206 (2017). [CrossRef]

19. X. Cheng, Q. Huang, Z. Huang, et al., “Multi-shuttle behavior between dissipative solitons and noise-like pulses in an all-fiber laser,” J. Lightwave Technol. 38(8), 2471–2476 (2020). [CrossRef]

20. Z. Zhang, S. Wang, Y. Pu, et al., “Improving the formation probability and stability of noise-like pulse by weakening the spectrum filtering effect,” Opt. Express 30(18), 31998–32009 (2022). [CrossRef]

21. S. Kobtsev, S. Kukarin, S. Smirnov, et al., “Generation of double-scale femto/pico-second optical lumps in mode-locked fiber lasers,” Opt. Express 17(23), 20707–20713 (2009). [CrossRef]

22. W. S. Man, H. Y. Tam, M. S. Demokan, et al., “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17(1), 28–33 (2000). [CrossRef]

23. X. Li, S. Zhang, J. Liu, et al., “Using reverse saturable absorption to boost broadband noise-like pulses,” J. Lightwave Technol. 38(14), 3769–3774 (2020). [CrossRef]

24. T. Wang, W. Ma, Q. Jia, et al., “Passively mode-locked fiber lasers based on nonlinearity at 2-µm band,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–11 (2018). [CrossRef]

25. Z. Zhang, L. Zhan, K. Xu, et al., “Multiwavelength fiber laser with fine adjustment, based on nonlinear polarization rotation and birefringence fiber filter,” Opt. Lett. 33(4), 324–326 (2008). [CrossRef]

26. J. Ratner, G. Steinmeyer, T. C. Wong, et al., “Coherent artifact in modern pulse measurements,” Opt. Lett. 37(14), 2874–2876 (2012). [CrossRef]

27. Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, et al., “On the formation of noise-like pulses in fiber ring cavity configurations,” Opt. Fiber Technol. 20(6), 575–592 (2014). [CrossRef]

28. X. Li, S. Zhang, J. Liu, et al., “Efficient method to improve the distribution probability of dissipative soliton and noise-like pulse in all-normal-dispersion fiber lasers,” Opt. Express 30(4), 6161–6175 (2022). [CrossRef]

29. Z. Cheng, H. Li, and P. Wang, “Simulation of generation of dissipative soliton, dissipative soliton resonance and noise-like pulse in Yb-doped mode-locked fiber lasers,” Opt. Express 23(5), 5972–5981 (2015). [CrossRef]

30. Y. Zhou, X. Chu, Y. Qian, et al., “Investigation of noise-like pulse evolution in normal dispersion fiber lasers mode-locked by nonlinear polarization rotation,” Opt. Express 30(19), 35041–35049 (2022). [CrossRef]

31. B. Wang, H. Han, L. Yu, et al., “Generation and dynamics of soliton and soliton molecules from a VSe2/GO-based fiber laser,” Nanophotonics 11(1), 129–137 (2021). [CrossRef]

32. Z. Dong, J. Lin, H. Li, et al., “Er-doped mode-locked fiber lasers based on nonlinear polarization rotation and nonlinear multimode interference,” Opt. Laser Technol. 130, 106337 (2020). [CrossRef]

33. Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, “Two-dimensional dissipative solitons supported by localized gain,” Opt. Lett. 36(1), 82–84 (2011). [CrossRef]

Mechanism of noise-like pulse in all-normal dispersion all-fiber laser based on nonlinear polarization rotation

Abstract

1. Introduction

2. Theoretical model and numerical simulation

2.1 Theoretical model

2.2. Numerical simulation

3. Experimental setup and results

3.1 Experimental setup

3.2 Wavelength switchable dissipative soliton

3.3 Transition from dissipative soliton to noise-like pulse

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (10)

Tables (1)

Equations (5)

Optics Express

Parameters	Numerical value	Parameters	Numerical value
P_sat	45 W	L/ L_b	2
γ_SMF	4.67 W^-1km^-1	g₀	38.3
γ_PMF	1.4 W^-1km^-1	Δφ₀	π/6
Ω_g	40 nm	ψ	2π/9
β_2SMF	21.91 ps²/km	λ₀	1040 nm
β_2YDF	24.22 ps²/km	δλ/λ₀	0
L_PMF	0.3 m	Δn	3.429 × 10⁻⁴