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Abstract
We investigate a promising approach to the energy scaling of mode-locked erbium fiber lasers. It consists in a special cavity design, comprised of a really long polarization maintaining (PM) part and a short non-PM part. Two separate fiber parts ensure the principle of space division for highly chirped dissipative soliton formation and NPE-based self-amplitude modulation effects. As a result, the pulse energy was increased up to 4 nJ with an estimated transform-limited pulse duration of 150 fs. It was also found that further energy scaling is limited by transition to a noise-like pulse generation regime. Numerical simulations revealed that this transition is associated with a contrast of the employed spectral filter and the amplifier noise level, which agrees well with the experiment.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Today ultrafast lasers form a wide class of instruments for various high power or precision applications from CARS [1], few-cycle pulse synthesis [2] and frequency metrology [3] to THz-wave generation [4] and telecommunications. One of the possibilities to achieve energy of several nanojoules directly from the master oscillator is generation of highly-chirped dissipative solitons (HCDS). Such pulses acquire strong linear frequency modulation (chirp), which helps to reach high energy values. Two main requirements should be satisfied for the generation of this type of pulses: normal net cavity dispersion and presence of strong spectral filtering. Substantial HCDS energy increase has been obtained previously in Yb-fiber all-fiber nonlinear polarization evolution (NPE) mode-locked cavity containing polarization maintaining (PM) and non-PM parts [5], while transferring this approach to Erbium fiber lasers remains a challenging task. The first attempt resulted in pulses with the energy of 0.93 nJ compressed down to 165 fs [6]. At the same time, we were faced with a limited availability of PM fibers with a normal dispersion at 1550 nm. As a result, non-PM DCF38 fiber was used to provide a large net normal dispersion and nonlinear polarization evolution (NPE) simultaneously, which destroyed the original idea about an energy scaling due to cavity lengthening. We have found several types of fibers that can be used to provide a large net normal dispersion, including Fujikura DS-15, OFS PM Raman and Thorlabs PMDCF. These are special fibers but some of them are quite expensive. In this situation, numerical simulations based on the proven models [7,8] can help to choose the most suitable type of fiber for energy scaling and achieving the Raman threshold. The latter opens up wide opportunities for further research like Raman dissipative soliton [9,10] and spectral comb of highly-chirped pulses [11] generation.
In this work we are doing the next step in extending the cavity length and improving stability of operation in the NPE mode-locked Erbium fiber laser, where NPE effect occurs in a relatively short section of non-PM single-mode fiber. Different types of fibers were compared numerically and the most suitable one was used to build the experimental setup. Complex optimization in terms of the lengths of different types of fiber has been performed. In addition, influence of the spectral filter on laser performance and pulse generation regime has been investigated.
2. Fibers comparison
Two new types of fibers were considered for energy scaling and achieving the Raman threshold: Thorlabs PMDCF and OFS PM Raman. Fujikura DS-15 fiber has a low anomalous dispersion, which has been measured with a white light interferometry technique (see Table 1). Therefore we did not consider that it can be used for a lengthening alone. To choose the most suitable fiber among them we estimated the intra-cavity SRS threshold $E_{\textrm {cr}} \approx \ln (P/P_{\textrm {sp}})\delta \nu ^{-1}/g_R$, where $P$ is the HCDS power, $P_{\textrm {sp}}$ is the spontaneous emission at the Stokes wavelength, $\delta \nu ^{-1} = \nu _{\textrm {HCDS}}^{-1} - \nu _{R}^{-1} \approx \beta _2 (\omega _{\textrm {HCDS}} - \omega _R)$ is the group velocity difference between the HCDS and Raman pulse due to dispersion in PMF, and $g_R \approx 2.5$ W${}^{-1}$km$^{-1}$ is the Raman gain coefficient. The Raman threshold in OFS PM Raman is about 10 nJ, which is 5 times lower than in Thorlabs PMDCF. In numerical simulations the HCDS intracavity energy reached 24 nJ in presence of noisy Raman pulse in fiber cavity comprised of 50-meters long OFS PM Raman (Fig. 1, blue line). Detailed description of the scalar numerical model and the laser cavity used in simulations is given in [8]. In the PMDCF-based cavity the same energy was reached with 12-meters long fiber. However, HCDS demonstrates relatively narrow spectrum without Raman component. One of the potential applications of the laser can be generation of the coherent Raman pulses, so-called Raman dissipative solutions [9], directly from the oscillator. So, keeping in mind such possibility and taking into account the minimum achievable pulse duration, we considered OFS PM Raman fiber for further experimental realization of the laser setup despite the lower SRS threshold.
Numerical modelling results showed the advantages of the OFS PM Raman fiber for the purposes of current research. All the experimental data have been obtained with this fiber.
Fig. 1. Calculated spectra inside the laser cavity comprised of 50-meters long PM Raman fiber and 12-meters long PMDCF, corresponding to equal 24 nJ intractivity energy.
Table 1. Parameters of the fibers at 1.55 µm.
3. Laser scheme
We applied to the laser cavity the technique of spatial division of mode-locking and soliton formation sections. The first section is a relatively short single mode fiber to enable NPE and eliminate environmental perturbations. Such approach allows to change the length and configuration of the cavity without affecting the mode-locking state and demonstrates applicability both in Yb and Er spectral regions [5,6]. The experimental laser setup is shown in Fig. 2(a). Two pumping schemes were implemented with copropagating and counterpropagating pump direction relatively to the signal pulse. Conceptually, the laser cavity includes two different parts: short single mode part (blue dashed line) where NPE takes place and the rest polarization maintaining (PM) part (solid black lines).
Fig. 2. (a) Experimental setup in copropagation (1) and counterpropagation (2) configurations: WDM — wavelength division multiplexer, EDF — Erbium doped fiber, PC — polarization controller, DCF — dispersion compensating fiber (DCF38), PBS — polarization beam splitter, PF — polarization (Lyot) filter, ISO — isolator, LD — laser diode, (b) Typical spectrum of Lyot filter measured on spontaneous emission radiation.
The pump source is a 976 nm single mode laser diode (LD), which radiation is injected via wavelength division multiplexer into Erbium doped PM fiber. Active medium produces the light in 1530-1560 nm spectral range. The polarization sensitive isolator (ISO) strictly determines the propagation direction of the signal radiation and acts as polarization analyser for the filter. We used all-fiber Lyot filter consisted of polarised input, birefrigent part, i.e. a piece of PM fiber spliced under the angle of 45° to main axis of the resonator, and analysing part. Such configuration of the filter produces periodical $\cos ^2$ transmission spectrum [12] and the length of the birefrigent fiber piece defines the period of the spectrum (see e. g. Figure 2(b)). To make net cavity dispersion normal, 50 m of PM Raman fiber is spliced inside the resonator. Also, this fiber is the main part where generating pulse evolves. The polarization controller (PC) gives the possibility to adjust incoming polarisation state for the mode-locked regime search. Polarisation beam splitter (PBS) plays a role of artificial saturable absorbing element and main output of the laser.
4. Experiment
It is known, that the energy scaling can be realized by lengthening the cavity or mode area increase [13,14]. However, for the 1.5 µm region only the first case is possible for HCDS generation as the material dispersion of silica-based fibers is anomalous and it is just impossible to manufacture a large-mode-area fiber with the normal one. So, the lengthening took place in the PM-fiber section of the cavity with several fiber alternatives (Fujikura DS-15, PM 1550-XP, OFS PM Raman). We have found previously that PM Raman fiber is the most suitable for our experiment because of its high normal dispersion in the 1550 nm spectral region. As a result, the repetition rate was decreased from 17.2 MHz to 3.2 MHz which is more than 5 times lower than in [6] and comparable with the repetition rate reported in [15] where the pulse duration was only 750 fs. In our experiment we could achieve generation of highly chirped pulses with the estimated Fourier transform limited pulse duration of 150 fs. In the co-propagating pumping scheme the energy of the obtained HCDS pulses was 3.3–3.7 nJ (Fig. 3(a). It was easier to achieve a self-start of single pulse mode-locking regime in comparison with the configuration described in [6], because we could decrease the length of the SMF part and overcome the NPE overdriving effect [16].
Fig. 3. (a) Typical experimental optical spectra of HCDSs with 3–4 nJ energy in a pulse and noise-like operation regime with 5.1–5.9 nJ; (b) ACF for the noise-like pulses.
Further energy increase seemed possible by changing the direction of the pump [17]. Energy of the generated pulses in mode-locked regime reached the level of 5.1–5.9 nJ. However, the spectral form has changed dramatically: it became smoother and wider relatively to the previously generated HCDS (Fig. 3(a)). The generation of such pulses was observed in a wide range of parameters, i.e. dispersion, pump power and filter widths. That is why the characterization of the regime became very important. Besides the optical spectrum, we also measured the autocorrelation function (ACF). It helped to characterize the generated pulses and showed a very wide pedestal (about 10 ps) with a relatively narrow peak above. The duration of the peak was less than 200 fs. Such two-scale shape of the ACF is a feature of so-called double-scale or noise-like (NL) pulse family [18,19]. It worth to note that only change in pump direction made it impossible to obtain any stable HCDS generation. The reasons of such behaviour were investigated numerically and presented in the next section.
5. Reasons of noise-like transition
For numerical simulation of pulse propagation inside the laser cavity we employed hybrid model, full description of which is given in [8]. Generalized nonlinear Shrödinger equation (NLSE) describes evolution of the optical field in Raman PM fiber under influence of stimulated Raman scattering, while the system of coupled NLSEs describe evolution inside non-PM fibers. The point-action cavity elements are described by their transmission functions. The amplifier noise is simulated with complex ’white’ Gaussian noise with mean 0 and standard deviation $\sigma$, which is added to the amplitude of the electromagnetic field after its amplification at each round trip. The $\sigma$ was chosen in such a way that spectral noise level was equal to ${-}60$ dB relative to DS power The main goal of the simulation was to identify the conditions of transition from a stable HCDS operation regime to noise-like (NL) pulse generation.
During the modelling we varied the Lyot filter parameters: central wavelength, bandwidth, and contrast - the relation between the maximum and minimum values of the transmittance in dB. The filter spectral transmission function was approximated with a cosine function. We have found a series of solutions in the range of filter center wavelength from 1530 to 1553 nm and filter bandwidth from 31 to 44.5 nm. Previously, such transition was studied and described from the other point of view. In [20,21] the authors describe the modulation depth of a saturable absorber transmission function and pump power defining the transition from the DS to NL pulses. Du with a coauthor [22] described the multipulse formation and NL pulse generation in ANDi lasers relatively to pump strength and filter bandwidth balance. However, these parameters do not determine HCDS-NL transition clearly. The closest to our understanding research was the work of Xu and his coauthors [23], described the influence of the multi pulse soliton break and NL pulse formation depending of the filter spectral shape and also saturation power of the amplifier. In our work, it has been observed for the first time, according to our knowledge, that an amplifier noise level and Lyot filter contrast have a significant influence on the mentioned transition. The threshold of the filter contrast for HCDS-NL transition was about 7.6 dB at ${-}60$ dB noise level, whereas the filter central wavelength and bandwidth were fixed (see inset in Fig. 4(b)). At lower filter contrast NL pulses were generated. The HCDS and NL pulses are shown in Fig. 4 in spectral and time domain. The results were obtained for the following parameters: Lyot filter center wavelength is 1550 nm, filter bandwidth is 34 nm, half and quarter wave plates operating angles $\chi =0.1\pi$, $\psi =0.45\pi$. In time domain one can see that the distribution of the peak power during the pulse is stochastic which is exactly relevant for NL pulses.
Fig. 4. (a) Comparison of the experimental noise-like (NL exp) pulse spectra with the numerical HCDS and NL spectra; (b) Power distribution along the pulse for numerical NL to HCDS transition. Inset: map of the HCDS-NL transition in the plane of filter contrast and noise level.
Further increase of noise level ($\sigma > -50$ dB, inset in Fig. 4(b)) leads to generation of NL pulses regardless of the Lyot filter contrast. It means that the contrast of the filter and amplifier noise can be considered as a couple of counteractive parameters in relation to this transition. The higher active medium noise can be "compensated" only by higher filter contrast with fixed power level. From the optical communications it is known that the backpropagating pump in EDFA produces not only higher signal power but also higher ASE noise level [24]. Thus, a change of the pump direction leads not only to gain increase, but also to increase of the noise amplitude. It shifts the balance and, according to our modelling, leads to the HCDS-NL transition. Therefore, filter contrast is one of the most important parameters for stable HCDS generation and it should be improved for our laser.
6. Non periodic filter
We replace the Lyot filter with a higher contrast spectral filter (see Fig. 5(a)). A combination of a dual fiber collimator (DFC) and a bulk reflective diffraction grating (BDG) mounted in a Littrow configuration can produce a parabolic spectral shape (in the logarithmic scale) of the filter which was used in the master oscillator. The filter is non periodic in contrast to Lyot filter. Its additional feature is a possibility to change the central wavelength of the generated pulses via grating and collimator relative angle adjustment. It can be seen in Fig. 5(b), showing tunability of the filter center wavelength in the range of 1490–1610 nm. The filter bandwidth did not change significantly via tuning and was about 12 nm at the level of $-3$ dB. It can be varied by changing the grating constant (number of lines per mm). The measured contrast exceeds 35 dB that is limited only by the optical spectrum analyser (OSA) noise level (Yokogawa AQ6370) and a brightness of used home-made ASE source. The total transmittance losses were no more than 3 dB. The similar approach was demonstrated previously in [25], but unlike that work, we use the PM version of the DFC, so that the filter comply to the whole cavity design. It also should be noted that despite the use of a bulk element in the cavity we gained a lot of advantages in comparison with all-fiber Lyot spectral filter, namely a high contrast and nearly Gaussian non-periodic shape, tolerance to the temperature influence and simple tuning of the central wavelength within $>50$ nm bandwidth. The last thing is very important for further matching the wavelengths of generated pulses and amplifier gain bandwidth.
Fig. 5. (a) Experimental setup with non-periodic filter: BDG — bulk reflective diffraction grating, PM DFC — polarization maintaining dual fiber collimator, MTC — Corning MetroCor fiber; (b) Tunability demonstration of the filter transmittance based on bulk diffraction grating and dual-fiber collimator.
In principle, the laser scheme shown in Fig. 5(a) remains the same as in Fig. 2. The spatial division technique is also used and pump direction is copropagating. Right after PBS the pulse propagates through long PM part of the cavity, experiencing spectral broadening and chirping, then it is filtered before the WDM. Obsolete DCF38 fiber was replaced with more widely used Corning MetroCor (MTC), 5 meters long DS-15 fiber was also used for additional lengthening of the cavity. Fiber lengths were optimized for stable and self-starting mode-locking operation. In addition, a fiber coupler with the ratio of 30/70 was inserted into the cavity before the filtering and amplifying sections to have an output at the point, where pulses obtain the widest spectrum during the roundtrip.
In the new laser scheme a stable HCDS generation with ability of the central wavelength tuning was demonstrated (Fig. 6(a)). The optical spectra were measured by OSA and presented in Fig. 6(a). Pulses with the energy of 2.54-nJ and ${\sim }30$ nm bandwidth at ${-}10$ dB level were obtained with a repetition rate of 6.7 MHz. They were also characterized with FROG traces (Fig. 6(b)) that have been measured by a commercial device (Mesaphotonics Ltd.). The retrieved spectral and temporal pulse shapes are presented in Fig. 6(c)-(d) together with phase curves. The measured and retrieved spectra show a good agreement (solid and dashed lines in Fig. 6(c) correspondingly) despite the fact that the data were obtained in a slightly different time. Parabolic shape of the intrapulse phase indicates the presence of strong linear frequency chirp in the pulse. Thereby, we assume that the pulse may be effectively dechirped down to approximately 250-fs duration.
Fig. 6. (a) Output spectra of pulses with central wavelength tuning via filter adjustment; (b) Measured and retrieved FROG traces; (c) Comparison of the retrieved and experimental spectral pulse shapes; (d) Retrieved temporal pulse shape and phase distribution at the 1530 nm wavelength.
7. Conclusion
In this work we presented a numerical and experimental study of energy scaling in the net normal dispersion Erbium-doped fiber laser. We have demonstrated the ability to increase energy via cavity lengthening, which proves the advantage of self-amplitude and pulse evolution spatial division technique. The energy of the ultrashort pulses with estimated transform limited duration of 150 fs increased up to 3.3–3.7 nJ via cavity lengthening by PM Raman fiber. Further energy scaling was limited by the transition to NL pulses generation. Using the numerical simulation, we have found that filter contrast and amplifier noise are the main factors responsible for a stable operation regime. At the same time, dynamic of HCDS-NL transition is more complicated that it was reported so far. We considered new experimental scheme, in which all-fiber Lyot filter was replaced with a diffraction grating based one. As a result, generation of the HCDSs with tunable wavelength and 2.5 nJ energy was achieved. This improvement opens the way to further development of high power pulse generation directly from the master oscillator.
Funding
Russian Foundation for Basic Research (19-32-90227, 20-32-70093); Russian Science Foundation (17-72-30006).
Acknowledgments
This work was supported by the Russian Foundation for Basic Research (Research Project No. 20-32-70093). The work of I.Zh. was also supported by the Russian Foundation for Basic Research (Research Project No. 19-32-90227). The work of A.E.B. was supported by the Russian Science Foundation (Grant No. 17-72-30006).
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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