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Abstract
We experimentally demonstrate a pulsed operation in a random fiber laser operation via self-gain-switching. The pulses have low timing jitter and high average output power. We show that repetition rate switches abruptly while varying the pump power, and introduce a simple formula for oscillation frequencies.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Random lasers are the type of lasers where feedback is provided by the randomly distributed inhomogeneities within the media. Since the first demonstration of the random fiber laser based on Rayleigh backscattering in optical fibers [1] the field has undergone extensive development. This is due to ability of such lasers to operate at any desirable wavelength [2,3], high efficiency [4–6] and other surprisingly useful properties such as low spatial coherency for imaging [7,8] and low time coherency for temporal ghost imaging [9].
Such promising properties together with a simple laser design prompted the investigations of new regimes including pulse generation. Namely, apart of active modulation of the inner parameters to get active Q-switched regime [10–12], several studies were devoted to studying the self-pulsed operation in random distributed feedback lasers (RDFL). The first demonstration was given in [13], where Q-switched regime established with randomly appearing pulse trains each of millisecond duration. Repetition rate for the pulse trains varied considerably – up to 20%. Further it was shown that special time-delayed feedback can be used to control the repetition rate [14]. Finally, stable high repetition rates were achieved in random Bragg grating based RFL [15] and in Rayleigh backscattering based RFL [16]. Most of the works attributed stimulated Brillouin scattering as the driving force of the passive Q-switched regime [17–19]: the interplay between the pump and the Stokes waves results in modulation of the Brillouin gain in time. Recently, it was demonstrated in a simple model that the same Q-switching occurs due to Raman scattering gain modulation in Rayleigh backscattering based RFL [16]. The authors proposed a setup that would enable very stable modulation of the output power for the Stokes wave.
In the current work we take this research further and experimentally demonstrate the self-gain-modulation induced pulsed operation in random fiber laser with varying repetition rate between fixed values. We introduce a simple formula describing frequencies of the output power oscillations that are achievable. The frequencies differ from the repetition rate defined by the roundtrip time in a conventional cavity. The demonstrated switchable regime given its low timing jitter is promising for reconfigurable high average power applications.
2. Experimental setup
The setup is a simple two-armed configuration of a random fiber laser with backward pumping [20], see Fig. 1. It consists of a piece of fiber pumped from both ends with two 1455 nm Raman fiber pump lasers, so the lasing occurs at the first Stokes wavelength at around 1550 nm. Two wavelength division multiplexing couplers are used to couple the pump power into the fiber, and 4 isolators, two for the pump lasers and two for the outputs. This allows to minimize back-reflections into the cavity and to prevent the laser output from affecting the pump laser. Pump and output isolators provide at least 25 dB and 55 dB return loss correspondingly. IPG Raman fiber lasers were used as the pump lasers, each reaching up to 5 W of optical power. In the experiment the pump powers were always set to be equal. Anomalous dispersion TrueWave fiber (D=7.8 ps/nm/km) was used in the experiment, with length of the fiber varying in the range from 27 to 72 km. All connections were made by splicing to minimize parasitic reflections. Temporal dynamics of the output radiation were monitored simultaneously from both ends using 50 GHz DC coupled photodetectors, a 6 GHz oscilloscope, and a 13.6 GHz radio-frequency electrical spectrum analyzer (ESA).
The typical spectrum of the output radiation (see Fig. 2(a)) is the double peak Raman spectrum with peaks at 1555 nm and 1566 nm. The 1566 nm peak starts to dominate once the pump power exceeds ∼4-5 W of total pump power due to energy transfer from the 1555 nm peak [21]. The observed spectra are not affected by the fiber length showing the same spectrum behavior over pump power. However, the asymmetry in pump powers for the left and right end does change the power distribution between spectral peaks. We measured the total output power (that the sum of the generation power at both outputs) against the total pump power (that is the sum of powers of two input pump waves) for three different fiber lengths, see Fig. 2(b). The power dependence happened to be remarkably identical for all fiber lengths, demonstrating high efficiency and linearity in good agreement with the model [22]. Note that despite the high output powers of the first Stokes component there were no cascaded generation of higher order components. There was no residual pump at the output as well.
Fig. 2. a) Optical spectrum measured from one side for different pump powers for fiber length of 48 km b) Total output Stokes power for different fiber lengths versus total pump power.
3. Numerical model for power dynamics
The numerical modelling of the experiment was performed with the equations for the intensities of pump and Stokes waves in Raman fiber laser described in [23,24] with Rayleigh backscattering terms, according to [20] and cascaded Raman scattering excluded:
Here $P_{p,s}^ \pm $ are powers of pump (p) and Stokes (s) waves, $+ $ and $- $ superscripts are used for forward and backward waves. ${\alpha _p},{\alpha _s}$ are the losses for pump and Stokes beams at the fiber length $L$, ${g_R}$is the Raman gain, ${\lambda _{p,s}} = 2\pi c/{\omega _{p,s}}$ are the wavelengths, $\Delta {\omega _s}$ is the Raman gain linewidth, ${R_s}$ is Rayleigh backscattering coefficient. We used ${\alpha _s} = 0.046k{m^{ - 1}},{\alpha _p} = 0.055k{m^{ - 1}},L = 45km,{g_R} = 0.6k{m^{ - 1}}{W^{ - 1}},{R_s} = 0.002{a_s}$
In these equations $z\; $is normalized to L so $0 < z < 1$, and the temporal scale is normalized to round-trip time $T = 2L/{v_{gs}}$, where ${v_{gs}}$ is the group velocity of Stokes wave. We considered only sufficiently long pulses so the dispersion is omitted from the model. Moreover, for the simplicity, we also assumed the equality of Stokes and pump wave velocities ${v_{gs}} = {v_{gp}}$.
The boundary condition are as follows: $P_p^ + (0 )= {P_0}/2,P_p^ - (1 )= {P_0}/2$, $P_s^ + (0 )= RP_s^ - $, $P_s^ - (1 )= RP_s^ + $, where ${P_0}$ – total input pump power. It was also possible to introduce nonzero R (reflection from fiber ends) to study an influence of conventional point-like reflectors such as fiber Bragg gratings of parasitic reflections.
4. Results
The dynamics of the output Stokes power at both forward and backward outputs well above the threshold turned out to demonstrate multi-scale behavior. At the short time scales there are stochastic pulses with durations less than the measurement system response time of 200 ps. Such random dynamics of generation intensity is typical for Raman fiber lasers with random feedback [20] or different type of fiber lasers with pointlike feedback [25,26] possessing uncorrelated broad spectrum of generation. Given the generation linewidth of ∼1 nm, the pulse duration might be as small as 10 ps. At the same time, slowly varying envelope clearly demonstrates pulsating behavior, Fig. 3(a-c). Despite the stochastic nature of the pulse filling, the pulse’s envelope is rather stable: consequent pulses have qualitatively similar pulse shape. Moreover, we have measured time dynamics simultaneously from both opposite laser outputs and found similar pulse shapes from both ends. Numerical simulation confirms this, Fig. 3(d-f). While pump power increases, the pulse envelope changes its shape both in experiment and modelling.
Fig. 3. (a)-(c) – Experimentally measured time traces from opposite laser outputs, L = 48 km. Total pump powers are 3 W, 4 W, 4.4 W correspondingly. Darker green/red overlay shows the average value of intensity. (d)-(f) – numerical simulations for the same pump powers. Different colors code time traces from opposite laser outputs.
Further increase of the pump power leads to changes in time dynamics, and a sudden increase of the repetition rate (compare Fig. 3(b) with Fig. 3(f)). Moreover, after such repetition rate change the previously in-phased pulses from opposite fiber outputs (compare red and blue curves at Fig. 3(d)) becomes to be anti-phased (Fig. 3(f)). We observe changing phases between counter-propagating generation waves both in experiment and numerical modelling. Interestingly the time dynamics do not depend on the order in which pump power lasers are switched on, or how fast. At any given pump power the repetition rate, and pulse shape would be the same.
The more detailed information about the repetition rate one can obtain from radio-frequency spectrum measurements. The rf-spectrum demonstrates clearly pulsed nature of the generated random radiation with OSNR of more than 90 dB for the first-order rf peak. We have found that rf-spectrum peak is surprisingly narrow: the full width at 10 dB level is around 2 Hz (see inset at Fig. 4(a)). In the demonstrated configuration of random fiber laser unlike in other Q-switched and gain-switched lasers, the pulses have incredibly low timing jitter. This stability may could be attributed the insensitivity to pump power fluctuations, which partly explains high OSNR value. Increase in pump power leads to increase in repetition rate, while preserving its stability and peak spectral width (Fig. 4(b)).
Fig. 4. Radio-frequency generation spectrum measured for a laser of L = 48.7 km at pump power of (a) 4 W and (b) 4.4 W. At inset: zoomed first rf-peak.
We studied in details how the repetition rate depends on laser parameters: both on pump power and laser length. We repeat experiments for pump power levels between 2 and 7 W and for laser length between 27 and 73 km and found very consistent behavior for the repetition rate, Fig. 5, despite the fact that repetition rate hops while pump power increases. We found that the laser operates at fixed repetition rates if measured in universal $c/4Ln$ units, where c is the speed of light and n is the refractive index. For example, at the pump power range 5.6-6 W, the laser operates at repetition rate of 9.1 kHz, 8.5 kHz, 7.9 kHz, 7.4 kHz for the laser length L = 39.7 km, 42.6 km, 45.8 km, 48.7 km. All these various frequencies, however, correspond to the same value of $5c/4Ln$.
Fig. 5. Repetition rate of depending on pump power for different random fiber laser lengths. Black solid line – a case of a conventional cavity with point-like reflectors.
In general, the repetition rate pattern follows the simple empirical formula:
The range of possible repetition rates for a given setup depends on the laser length. For the shortest length of 27 km used in the experiment, only the lowest frequency of ${\nu _1}$ is achievable in our experiments given the available maximum pump power of 7.2 W. It could be possible that frequency hops for short laser length occur at higher powers. For longer fiber lengths, the system shows the tendency to jump to higher frequencies more readily. At the lengths larger than ∼40 km oscillations for any pump level start with ${\nu _2}$ skipping principal frequency ${\nu _1}$. We also found that for odd k numbers pulses leave the laser simultaneously, and for even k numbers pulses leave the opposite laser outputs in anti-phase for all our experimental data, similar to shown on Fig. 3.
In general, the reason for such “relaxation” oscillations is due to counter propagating Stokes wave competition [23]. Those may appear when a Stokes wave propagating towards the pump origin depletes it at the one output, which leads to a decrease in the gain for the associated Stokes wave, which also depletes the pump wave, but mainly at another output of the laser. The period of such oscillations is related to the travel time of the co- and counter propagating Stokes waves and the pump wave along the fiber, but differs markedly from the fiber round-trip time which determines the repetition rate in a standard cavity based on point-like reflectors at the outputs. To emphasize this, we have also measured repetition rate for the laser made of fiber Bragg gratings placed at the output (see black solid line at Fig. 5). Such a discrepancy is associated with the superluminal pulse propagation in a medium with high stimulated Raman scattering gain.
We have also performed the numerical analysis to check if the regime relies on Rayleigh backscattering. It was found that at low levels of ${R_s}$, comparable to the level of signals of spontaneous Raman scattering, Rayleigh backscattering can be neglected but oscillations still exist. In this way, the Rayleigh backscattering doesn’t play a role in the development of the pulsed regime, although it remains crucial in shaping power and spectral properties. At the same time, this configuration showed very high sensitivity to the parasitic back reflections, which can ruin the self-gain-switching regime completely. Even the inclusion of small reflections R at the ends of the fiber at a level of ${10^{ - ({2 \div 3} )}}$ drastically changes the dynamics, significantly increasing the threshold for the onset of oscillations. Thus the conventional feedback based on point-like reflection ruins the observed pulsed regime completely, making frequency hops unachievable.
5. Conclusion
In this work we showed that radiation of random fiber laser could be driven into pulsed operation via self-gain-switching. The regime is characterized by small time jitter. The oscillations of the output power arise due to counter-propagating Stokes waves competing for the same pump wave that results in modulation of the gain in time. Moreover, we demonstrated experimentally as well as in numerical simulations that with pump power increase the repetition rate switches to higher frequencies. The repetition frequencies are universal for lasers of different lengths and for different pump power if measured in universal units and are given by $({2k + 1} )c/4Ln$.
We found that the repetition rate is defined by the properties of the Raman gain and relies on competition between counter propagating Stokes waves depleting the same pump. Nevertheless, random distributed feedback is crucial for the generation defining spectral and power properties of the generation as well as allows achieve observed pulsed behavior. On the contrary, even small conventional point-based feedback ruins the pulsed regime. That is why frequency hops are not achieved in conventional Raman fiber lasers with fixed cavity.
Funding
Russian Science Foundation (19-12-00318).
Disclosures
The authors declare no conflicts of interest.
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