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Abstract
Controlling emission of light in random structures/disordered systems, e.g., implementing mode-locked pulses in a laser system with a random structures/disordered systems, is a complex task. Usually, the generation of laser pulse by mode locking needs a stable fixed-length cavity that determines a specific repetition rate of the mode-locked pulses. Here, mode-locking laser pulses with selectable repetition rates are achieved in a typical one-dimensional disordered laser by passive mode locking. The laser includes disordered reflectors to provide multiple resonant modes associated with different cavity length. The regular pulses with adjustable repetition rates can be generated and selected by a nonlinear polarization rotator and a semiconductor saturable absorber mirror. The proposed work utilizing the advantages of multiple resonances in random lasers could pave a new way for regulating emission of light in the random structures/disordered system. And it displays an effective and realistic technical route to study ultrafast pulses generation and optical soliton dynamics in random structures/disordered systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Controlling emission of light in the random structures/disordered systems is a profound topic recently. Particularly, controlling random fiber lasers (RFLs) emission with reflection from random structures/disordered systems, e.g., disordered array of fiber Bragg gratings (FBGs) is of great significance [1,2]. And this kind of RFL is coherent. It can generate multiple resonant modes with random mode intervals, which enables mode locking and pulses generation of variable repetition rates corresponding to different cavity length. Thus, this paper demonstrates mode locking of a coherent random fiber laser assisted by the reflection from the disordered array of FBGs, which could be a typical sample for controlling emission of light, realizing the ultrafast pulses generation and exploring optical soliton dynamics in the random structures/disordered systems.
Being combination of random lasers and fiber lasers, RFLs provide new opportunities for development of two laser communities. They inherit advantages of the fiber lasers such as good beam quality, large length-volume ratio and proven gain mechanisms (e.g., rare earth doping and fiber nonlinearity) [2–4]. Compared with traditional random lasers, they have better directional emission, higher pump efficiency and simpler structure (i.e., free of high-quality cavities) [5–7]. In recent years, RFLs have gained remarkable research attention in applications such as optical communication, sensing and speckle-free imaging [8–11]. These studies mostly focused on continuous-wave emission of RFLs. Pulsed RFLs also requires innovative fundamental research and applications, e.g., light control/regulation in the random structures/disordered systems, full-field optical coherence tomography, high resolution sensors and frequency metrology [12–15].
Random distributed feedback in fibers could be either incoherent (e.g., Rayleigh scattering) or coherent (e.g., the reflection from disordered array of FBGs). The incoherent RFLs are ‘modeless’, and do not support passive mode-locking, so external modulation or self-pulsing based on Q-switched effect has been proposed to generate laser pulses [16–18]. On the contrary, due to multiple resonant modes caused by disordered array of FBGs in coherent RFLs, realizing the mode-locking pulses of variable repetition rates corresponding to different cavity length is realistic in this RFLs. Thus, to achieve mode locking pulses in coherent RFLs is still a variable work that deserves further study. Recently, mode locking between different localized modes of nanoparticle-film random lasers has been reported by designing a patterned pump/gain profile without concerning pulsed emission [19]. Furthermore, a quasi Q-switched mode-locking regime of coherent RFL is obtained, and the repetition rate of the mode locking pulses varies randomly in different Q-switched envelopes [20].
Here, a stable mode-locking coherent RFL with selective/controllable repetition rates is proposed and realized for the first time to the best of our knowledge. The RFL is formed in a ring cavity configuration in combination with a typical one-dimensional disordered structure, e.g., random distributed array of FBGs, to produce coherent random distributed feedback. On account of the light localization in the disordered cavity, several resonant modes with random mode separations are formed [21–23]. The collective mode locking mechanisms of mode-sensitive nonlinear polarization rotation and saturable absorption are implemented together to realize stable mode locking laser pulses in the proposed structure, due to strong mode competition, the narrow reflection spectrum of the employed disordered FBGs and limited performances of devices. And our experimental results validate that regular mode-locked pulses with different repetition rates can be obtained in the same cavity. The Q-switched, fundamental and second-order harmonic mode-locking regimes can also be observed by changing the power of pump. Most important of all, this work demonstrates an effective technical route to obtain the ultrafast pulses and offers a general method to control/regulate the optical soliton dynamics in the random structures/disordered systems. Besides, the amazing feature of tunable repetition rate and structure-marked pulse (e.g., the achievable pulse rates are determined by the unique structure of the disordered cavity) taking advantages of the disordered cavities, make the pulsed RFL a good supplement to traditional pulsed fiber lasers, and a good candidate for flexible and special applications ranging from laser coding to ultrafast spectroscopy.
2. Results and analyses
2.1 Experiment setup and fundamental of the work
The experimental setup is shown schematically in Fig. 1(a) and further details are provided in the method section. Random distributed feedback and resonant modes are provided by the disordered reflectors, i.e., random distributed FBGs. As a result, the cavity supports pulses of the various repetition rates related to the random resonant modes. When pump is applied, those resonant modes with positive net gain will be emitted, i.e., the so called coherent random lasing. Initially, the output waveform fluctuates irregularly due to phase mismatch of the modes.
Fig. 1. Experimental setup and output characteristics. (a) Schematic of the tunable repetition rate mode-locked RFL, with WDM (wavelength division multiplexer), EDF (Erbium-doped fiber), CIR (circulator), TFBGs (tilted fiber Bragg gratings), PC (polarization controller), SESAM (semiconductor saturable absorber mirror), and Disordered reflectors (random distributed fiber Bragg gratings). (b) Phase shift $\Delta {\phi _{xy}}$, in the parameter space of l and $\rho$. (c) pulse train with repetition rate of 5.452 MHz. (d) RF spectrum of (c). (e) Enlargement of (c). (f) Enlargement of (d). (g) Pulse train with repetition rate of 5.457 MHz. (h) pulse train with repetition rate of 5.447 MHz. The pump power is 127 mW. And the output power is 0.02 mW.
Mode locking of different random lasing modes could be controlled and selected by setting the nonlinear polarization rotator (NPR, integration of a tilted FBG and PCs 1 & 2). The NPR is used to pass a specific resonant mode with polarization rotation according to its setting. Besides, the NPR also compresses width of pulses. For example, the light is forced to be linearly polarized when passing through the tilted FBG, and transforms into elliptical one by setting PC 2. Then, the light passes through the fiber and experiences polarization rotation that occurs due to nonlinear phase shift. The nonlinear phase shift arises from intensity-dependent self-phase modulation and cross-phase modulation. As the peak and wings of pulse undergo different degree of polarization rotation, the NPR is set to pass centre part and hinder the wings of pulse. This shortens the pulse and facilitates self-starting of the mode-locking regime [24–27]. It is also worth noting that different random lasing modes correspond to different cavity lengths, and they amass additional amounts of polarization rotation, i.e., linear phase shift. Thus, adjusting the NPR can select some certain modes to circulate through the cavity.
Theoretically, the polarization phase shift ($\Delta {\phi _{xy}} = {\phi _x} - {\phi _y}$) of the pulse includes the linear ($\Delta {\phi ^L}$, loop length dependent) and nonlinear ($\Delta {\phi ^{NL}}$, power dependent) parts [27], which can be expressed as:
Equation (1) clearly shows that the total polarization phase shift depends on the loop length (mode-sensitive) and the pulse profile in time domain (intensity sensitive). In our work, I has a typical value of ∼105 W/cm2, and $\Delta {\phi _{xy}}$ as a function of l and $\rho$ is shown in Fig. 1(b). It shows that variation of l (in the scale of centimeters or tens of centimeters for different random lasing modes) and $\rho$ (from −1 to 1) will cause considerable phase shift (from −50 to 150 degree), which can be used for selective mode-locking. For example, only pulses with a specific value of $\Delta {\phi _{xy}}$ are allowed to circulate in the cavity, i.e., the pulse width will be compressed and the pulse repetition rate will be selected.
2.2 Selective mode-locking of the random lasing modes
Mode-locking regime of the coherent RFL starts when pump power is increased above 82 mW. One typical case with the pump power of 127 mW is shown in Figs. 1(c)–1(h). A regular pulse train is observed, with pulse-width of 8.8 ns, pulse separation of 183.40 ns and peak-power fluctuation less than 1.47%, seeing Figs. 1(c) and 1(e). The RF spectrum calculated by Fast Fourier Transform (FFT) of waveform shows up to 100th-order harmonics, and the fundamental mode has signal-to-noise ratio of up to 40 dB, seeing Figs. 1(d) and 1(f). All of these manifest high stabilities of the mode-locked pulses.
Even for a fixed pump power, different random lasing modes undergo different polarization rotations, since the polarization rotation is related to loop-length. Thus, the repetition rate of the mode-locked pulses can be selected/tuned by resetting the two PCs of the NPR. As shown in Figs. 1(e), 1(g) and 1(h), the pulse repetition rates are found to be 5.452, 5.457, 5.447 MHz respectively. This corresponds to the loop length of 37.48, 37.45, and 37.52 m respectively. It is well known that the change in the cavity length induced by temperature and stress is usually on the order of micrometer which is much smaller than centimeter level [28]. Thus, the variation in Figs. 1(e), 1(g) and 1(h) manifests selective locking of random lasing modes that arise from different feedback loops.
For further corroboration of the mode tunability originating from the disordered structure, two regular ring-cavity structures are tested. In Figs. 2(a) and 2(c), the cavity is integrated with the same NPR, while the FBGs array together with the CIR 1 are replaced by an optical isolator. The cavity length is 15.51 m constructed by 6 m EDF and 9.51 m SMF, and the net cavity dispersion is −96.09 ps2/km. It is found that a typical mode-locking regime is realized, e.g., regular pulses, and Kelly sideband. In Figs. 2(b) and 2(d), similar results are obtained when the semiconductor saturable absorber mirror (SESAM) is added. In this case, the cavity length is 26.38 m with 12 m EDF and 14.38 m SMF, and the net cavity dispersion is −85.09 ps2/km. Separation between the first Kelly sideband and centre wavelength (1553 nm) of spectrum is calculated to be 15.5 nm [27], which exceeds spectrum range. So, there is no Kelly sideband appearing in Fig. 2(d).
Fig. 2. Output characteristics when a regular ring cavity (i.e., the disordered reflector is removed) is used. (a) and (c) are the waveform and optical spectrum respectively, when only the NPR is included in the cavity. (b) and (d) are the waveform and optical spectrum respectively, when both the NPR and the SESAM are included in the cavity.
In the two cases, repetition rate of the laser pulses keeps unchanged when adjusting the pump power or the NPR. All these prove that the proposed disordered cavity accounts for the tunability.
2.3 Second-harmonic and Q-switched mode locking of random laser
By setting the two PCs of the NPR, the cavity loss can be altered, and second-harmonic mode locking is obtainable, as shown in Figs. 3(a) and 3(b). The pulse-to-pulse period is 91.76 ns, and the corresponding repetition rate is 10.897 MHz. This value is much smaller than Fabry-Perot resonances between the FBGs, e.g., separations of the FBGs are within sub-centimeter. While it is close to twice of the pulse repetition rate obtained in Fig. 1. Thus, it should be second-harmonic mode locking pulse of the fundamental frequency around 5.448 MHz.
Fig. 3. Output characteristics of the second-harmonic and Q-switched mode-locking regimes. (a) Waveform of the second-harmonic mode-locking regime for pump power of 127 mW. (b) RF spectrum of (a). (c) Waveform of the Q-switched mode-locking regime for pump power of 70 mW. (d) RF spectra of (c). (e) Enlargement of (c). (f) Enlargement of (d).
Moreover, Q-switched mode-locking is also obtainable when lower value of pump power is used [29,30]. Figures 3(c)–3(f) depict a typical example of the Q-switched mode-locking regime when pump power is 70 mW. In Fig. 3(c), a series of Q-switched envelopes with period of 14.8 µs are observed. The enlarged view of one single Q-switched envelope is given in Fig. 3(e), wherein mode-locked pulses with period of 182.92 ns is obtained. The FFT spectrum in a large (Fig. 3(d)) and a small (Fig. 3(f)) frequency scales show clearly the frequency separations of 5.467 and 0.0675 MHz respectively, corresponding to repetition rates of the mode-locked pulses and the Q-switched envelopes respectively. By resetting the NPR, both the repetition rates of the Q-switched envelopes and the mode-locked pulses can also be tuned, and the results are not shown here.
2.4 Stability of mode locking of random laser
The stability of mode-locking is also tested by monitoring the output every 5 minutes. The spectrum in Fig. 4(a) remains constant over time, showing good stability of the mode-locking regime. The spectral width (less than 0.2 nm) is greatly reduced compared to regular ring cavity, which is due to the filtering effect of disordered array of FBGs. The output spectral bandwidth is 0.058 nm. And it is worth noting that when resetting the NPR to a different mode locking regime (i.e., tuning the repetition rate), there is a tiny center wavelength shift, as shown in Fig. 4(b). Besides, initial mode-locking state can be disturbed by pump power variations, and the NPR (i.e., the two PCs) needs to be reset to observe mode-locking. This is because that the amount of nonlinear polarization rotation varies with pump power, as demonstrated by Eq. (1).
Fig. 4. The output spectrum. (a) The optical spectrum of the mode-locking regime that correspond to Fig. 1(c). (b) the optical spectra of the mode locking regimes of Figs. 1(e), 1(g) and 1(h) respectively.
3. Discussion
It is worth to note that technically mode locking regime could be obtained with either the NPR or the SESAM saturable absorber. However, due to the strong mode competitions and the narrow transmission/reflection spectrum (see Fig. 5) of the employed disordered array of FBGs, even the limited performances of the devices, the above two mode locking mechanisms have to be combined together to realize stable and highly efficient mode locking laser pulses here. In this research we mainly focus on the characterization of the unique mode locking operation in the proposed random coherent feedback cavity. The optimization of the mode locking mechanism that enabled by only one of the NPR or the other passive saturable absorbers is of great interest for further study. The detailed requirements to realize highly efficient mode locking regime for a random structure/disordered systems deserve further investigation.
Fig. 5. Component characteristics of the RFL. (a) Reflection characteristics of the disordered FBGs. (b) Reflection characteristics of the TFBG. (c) Reflection characteristics of the disordered FBGs together with the TFBG. (d) The nonlinear reflectivity of SESAM. The dots are the experimental data and the curve is fitted from the experimental data.
4. Method
To facilitate pulse generation, the laser cavity is designed to have the net dispersion of −208.14 ps2/km, i.e., 22.38 m single mode fiber (G.652) and 15 m EDF (EDFC-980-HP, Nufern), with dispersion parameter of 18 and −16 ps/km/nm respectively. Furthermore, the ring-shaped resonant configuration of the cavity is also helpful for mode locking through mode pulling effect [31,32].
The disordered reflector, i.e., disordered array of FBGs consist of 20 FBGs with the same central wavelength of 1552.5 nm, reflectivity about 4% and length of 3 mm for each FBG, which is fabricated in EDF through hydrogen loading and ultra-violet exposing technique [33,34], is integrated into the fiber loop through an optical circulator (CIR1) to provide random distributed feedback. The characteristic optical spectra of different components are shown in Fig. 5. The reflection spectrum of TFBG is flat, which also reflects that the transmission spectrum is flat. This means that the TFBG can pass light with wavelength from 1552.3 to 1552.8 nm (the range of the reflection spectrum of the disordered FBGs) almost equally. Meanwhile, comparing the Fig. 5(b) with Fig. 5(c), it could be known that the spectral characteristics of the whole system are mainly determined by the disordered FBGs.
A 1480 nm laser is used as the pump, which is coupled into the EDF via a 1480/1550 nm WDM. The NPR and SESAM with absorbance of 32% and relaxation time of 18 ps are inserted successively into the fiber loop to support self-start mode locking operation. The nonlinear reflectivity of the SESAM versus power is shown in Fig. 5(d), revealing that its modulation depth is 7%. The NPR is formed by inserting a 45° tilted FBG between two polarization controllers (PCs). The tilted FBG has polarization extinction ratio of 26 dB, and can discard the s-polarization component and enable the p-polarization component to be transmitted according to Brewster’s law, which is combined with the PCs to realize mode-locking [35,36].
The laser output is monitored through the 1% port of a 1:99 coupler by photodetector (Conquer, 75 MHz bandwidth), oscilloscope (Rohde & Schwarz, 1 GHz bandwidth and 5 GSa/s sampling rate), optical spectrum analyzer (OSA, Ando, spectral resolution of 0.01 nm), and power meter.
5. Conclusion
In conclusion, we have experimentally demonstrated a mode locking random fiber laser with tunable repetition rate. The NPR offers mode-sensitive saturable absorption, and the SESAM enhances saturable absorption and rectifies the mode locking. Their combined influence makes it possible to implement stable regular laser pulses with variable pulse repetition rates via selective mode locking of the random lasing modes. Thus, mode locking with controllable repetition rate, Q-switched mode locking and high-order harmonic mode locking are demonstrated successively by changing the setting of NPR and pump power. The disordered cavity and NPR are the basic physical origins of our tuning scheme, which provides, respectively, various modes of random separations and the selection mechanism through mode/power dependent polarization rotation. This work opens up a way of controlling emission of light and provides an innovative method to realize ultrafast pulses in the random structures/disordered systems. Meanwhile, it reveals an effective and realistic technical route to study the optical soliton dynamics in the random structures/disordered systems.
Funding
Sichuan Science and Technology Program (2018HH0148); National Natural Science Foundation of China (11974071, 61575040, 61635005).
Acknowledgement
We thank Prof. Lin Zhang in Aston University who provides the TFBG.
Disclosures
The authors declare no conflicts of interest.
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