1. Introduction

Lasers with a continuously tunable wavelength (so-called tunable lasers) are usually based on a cavity with multiple longitudinal modes within a spectral profile of gain media and tuning/filtering elements, which select a narrow spectral interval and scan its central wavelength along the gain profile [1]. As the generation can hop from one mode to another during the tuning process, rather complicated optoelectronic techniques for selecting a single mode and providing its continuous hop-free tuning are implemented [1, 2]. Such single-frequency lasers with continuous tuning in a broad spectral range are in great demand for advanced applications such as coherent communication and/or physical parameter sensing via fiber optics links [3, 4]. To the moment, diode lasers with a tuning range of tens of nanometers in a telecom spectral window near 1.5 μm with linewidth of ≤1 MHz have been developed for such applications [5–7]. Their operation is based on external cavity micro-electromechanical tuning and active elimination of mode hops by means of rather complicated synchronization of several electrical control circuits [6]. Another approach is based on a naturally mode-hop-free single-frequency distributed feedback (DFB) configuration with expansion of the tuning range by means of integration of DFB lasers of different wavelengths into a monolithic array [7]. Recent developments of these technologies further improve the device performances. First, nanoelectromechanical tuning has led to drastic reduction of the tuning element size and mass thus increasing the tuning/switching speed beyond the MHz level [8]. Second, all-fiber tunable DFB lasers have provided a broad tuning range for a single laser source and easy integration to fiber links, see [9] and citation therein.

An alternative to active frequency selection and continuous tuning techniques is self-induced scanning of laser frequency based on internal physical mechanisms inside the laser without tuning elements. The effect of self-induced periodic scanning (or self-sweeping) of laser frequency was first observed in a ruby laser in 1962 [10]. More than 50 years later, the effect was re-discovered in fiber lasers [11–13] featured by two-orders of magnitude broader scanning range than that in ruby lasers and by a possibility of obtaining single-frequency regime, which makes them potentially competing with actively tuned single-frequency lasers. The self-sweeping effect is shown to be determined by formation of dynamical phase and gain gratings induced by spatial hole burning in population inversion of the active medium by the field of a standing wave formed in a Fabry-Perot cavity [14]. The gratings arisen from individual longitudinal cavity modes are long-lived. Therefore, one lasing mode affects the generation of subsequent modes thus leading to specific mode dynamics with self-sweeping of the central frequency in the generated spectrum. Despite small amplitude of the dynamics gratings they create significant reflection thanks to a large length (order of several meters) [15]. The effect has several features identified by now. First, the generation wavelength can either increase [11–14] or decrease [13, 16] in time repeatedly returning to its initial value, whereas the sweeping range can exceed 20 nm [14]. Second, the generation is pulsed (regular or stochastic) while the spectrum may be multi-frequency or single-frequency (single longitudinal mode) during the generation of each pulse, depending on the laser cavity design [14]. In spite of the fact that the majority of publications describe the studies of the effect in an Ytterbium-doped fiber laser operating in the spectral range near 1 µm, several attempts to broaden the operating wavelength range of self-sweeping lasers by using other active fibers are known. For example, wavelength self-sweeping is successfully obtained in a Thulium-Holmium codoped fiber laser [17] demonstrating a sweeping range of 17 nm near 1.9 µm. On the other hand, in an Erbium-doped fiber laser, it appears difficult to reach a sweeping range beyond 1 nm, which prevents practical applications of the laser, albeit sweeping is principally possible [13]. Bismuth (Bi) doped active fibers may be treated as an alternative to Erbium-doped fibers in the telecom spectral range allowing one to build fiber lasers and amplifiers operating in the range extended to 1.15-1.78 µm [18–20]. Such a broad spectral range makes this new active material principally different from conventional rare-earth-doped fibers. At the same time, Bi-doped fiber lasers exhibit very specific generation features that have attracted much attention recently, see [18, 19] for a review.

In this paper, we report on the first realization of quasi-continuous self-sweeping in a single-frequency regime with an all-fiber all-PM laser based on Bi-doped active medium, which demonstrates its unique features with a great potential for applications.

2. Experiment

As high-quality Bi-doped fibers have low dopant concentrations, much longer active fibers are usually used for laser construction [18, 19]. It is very attractive from the viewpoint of the self-sweeping regime as the intermode spacing is inversely proportional to the cavity length. The following experimental setup has been assembled for the first study of the self-sweeping effect in Bi-doped fiber lasers, see Fig. 1. A polarization-maintaining (PM) Bi-doped fiber (made in FORC [21]) with a maximum available length of about 60 m is used as a gain medium. The fiber comprises Panda-type stress rods for PM operation. The measured beat length in the fiber is ~2.5 mm at a wavelength of ~650 nm. The fiber cut-off wavelength is near 0.9 µm. The Bi concentration is below 0.1 wt%. The fiber core is also doped with ~4 mol% of GeO₂ to form a waveguide structure. The index difference between the core and cladding is Δn ~6.4·10⁻³. The absorption of Bismuth active centers peaked around 1395 nm is ~1.2 dB/m.

 

Fig. 1 Experimental scheme of the PM Bi-doped fiber laser.

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To obtain the self-sweeping regime, a low-Q laser cavity is formed by means of a PM fiber loop mirror (FLM) based on 50/50 (at 1550 nm) fused coupler at one cavity end and the Fresnel reflection at the other end. The fiber is pumped through the FLM by a home-made Raman fiber laser operating at 1310 nm [22]. The FLM has high reflection for signal radiation (R = 55% at 1460 nm) and high transmission for pump radiation (R = 12% at 1310 nm). A polarization beam splitter (PBS) with a normally cleaved end is used as a polarizer and a broadband reflector on the other side of the cavity. An additional section of the Nufern PM1550 fiber is used to increase the cavity length by 30 m, thus providing narrow spacing between the longitudinal cavity modes: $\Delta \nu =c/2Ln\approx$1.1 MHz for the net cavity length L = 90 m. The laser generation starts at a low pump threshold (less than 20 mW) and has a relatively high differential efficiency of 33% (Fig. 2). Self-induced laser line sweeping is observed in the pump power range P = 50-300 mW. The process is easily observable on a standard optical spectrum analyzer (OSA) due to a rather slow sweeping rate (Fig. 3). At that, the signal to noise ratio is about 50 dB.

 

Fig. 2 Generated output power from the cleaved end side versus pump power: experimentally measured data (dots), and a linear fit (line).

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Fig. 3 Laser wavelength dynamics measured by OSA at pump power of 200 mW.

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In the short time scale, the dynamics of intensity looks like periodic self-pulsations [Fig. 4(a)]. Each pulse is well approximated with the squared hyperbolic secant function $I(t)=I_0{\text{sech}}^2\left(t/{\tau }_0\right)$ [14]. When the pump power P increases from 50 to 300 mW the pulse width ${\tau }_0$ and the pulse spacing T decrease from 3.7 to 2.0 μs and from 30 to 10 μs, respectively. At high pump powers the pulses become overlapping and thereby strongly modulated.

 

Fig. 4 Intensity dynamics in a short time scale at different pump powers: 150 mW (red) and 300 mW (black) (a). Reconstructed frequency dynamics for lasing at a pump power of 300 mW (b).

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Thus, the temporal dynamics of intensity is similar to that observed in [14]. A heterodyne technique with a narrowband (<100 kHz) single-frequency laser was applied in [14] to measure fast wavelength dynamics in a self-sweeping Yb-doped laser. For application of the heterodyne technique in our case, one needs a single-frequency laser generating around 1460 nm. As no narrowband source generating within the range of Bi-laser self-sweeping is available, a Mach-Zehnder fiber interferometer is applied to measure the instantaneous wavelength, see Appendix for details.

The reconstructed dynamics of frequency for one of the pulse trains is shown in Fig. 4(b). It exhibits a pulse to pulse frequency shift equal to one intermode spacing ($\Delta \nu =c/2Ln\approx$1.1 MHz) and a specific frequency change during the pulse. To study the intra-pulse frequency dynamics more accurately, averaging over a large number of pulses (>20) was performed, the results of averaging are presented in Fig. 5. In addition, the spectral dynamics was measured by interferometers of two different lengths (69 and 250 m) with free spectral ranges of 2.9 MHz and 0.8 MHz, respectively. The results appear to be similar (see Appendix).

 

Fig. 5 Averaged spectral dynamics measured by a 250-m long interferometer for different levels of the pump power in (a) normal and (b) normalized scales: Experiment (dots), and theoretical fit (lines).

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Such heterodyne measurements were carried out at pump power levels from 50 to 300 mW. Though the pulse-to-pulse frequency hop is equal to one intermode beating frequency of the laser (about 1.1 MHz) at all pump power levels, the interval of the frequency modulation (chirp) within the pulse varies with the pump power. The averaged data on the intra-pulse frequency chirp are presented in Fig. 5(a). The reason for the chirp $\delta \nu \left(t\right)$ is the change of the refractive index $\delta n\left(t\right)$ in the Bi-doped fiber because of population inversion variation during the pulse generation [14]. The change of refractive index $\delta n\left(t\right)$ in an active fiber of length l in a cavity of length L leads to generation frequency change for a cavity mode:

Thus the expression for the frequency chirp can be represented also in dimensionless units $\delta \nu \left(t\right){\tau }_0=A\tan h\left(t/{\tau }_0\right)$.

The data of Fig. 5(a) are represented in Fig. 5(b) in the dimensionless units. One can see that all the curves at different pump powers practically coincide (especially in the central region). The slope of the curves in the center is defined by constant A. The best-fit value of A is equal to 1.064 (for Yb-doped fiber laser the value is equal to 0.55 [14]). The difference between the experimental results and the theory at pulse edges ($t>{\tau }_0$) can be explained by the influence of adjacent modes given that the single-mode radiation is required for frequency reconstruction. The theoretical fitting curves calculated in the normal units are presented in Fig. 5(a) by the dashed lines for a comparison with the corresponding experimental data. The comparison clearly shows that the range of the frequency chirp within the pulse increases from 0.4 to 0.8 MHz with the pump power increase from 50 to 300 mW. At the pump power of 300 mW the intra-pulse frequency chirp becomes comparable with the pulse-to-pulse frequency hops. Thus, at all levels of the pump power each generated pulse consists of a single longitudinal mode. Herewith, the frequency is scanned along the pulse sequence almost continuously with a relatively small instant bandwidth (<1 MHz), see Fig. 4(b), because the values of pulse bandwidth and pulse-to-pulse frequency shift are comparable. It is also noted that the influence of the Kerr nonlinearity on frequency variation is insignificant due to a low peak power of pulses.

One purpose of the work is to obtain the smallest possible value of the intermode beating frequency, which becomes close to frequency chirp in the studied laser configuration. One can see from Eq. (6) that increasing of cavity length by means of a piece of passive fiber leads not only to the reduction of intermode beating frequency, but also to the decrease of chirp amplitude. So, long active fiber is a key factor for the demonstrated regime. Indeed, similar results have been obtained for the laser without additional section of the passive fiber with a length of 30 m (Fig. 1). The main distinction for such a laser with a shorter cavity is an increase of the pulse-to-pulse frequency change inversely proportional to the cavity length and the chirp value proportional to the ratio of the active fiber length and cavity length ($l/L$~2/3 and ~1 for the long and short cavity, respectively). The best-fit value of A for the short cavity is equal to 1.55, which is by one half more than that for the long cavity. Based on this value, the polarizability difference of Bismuth active centers in ground and excited states $\Delta p$ can be estimated when cross sections become available.

An interesting question is about the phase of each mode-pulse. Is it random or not? To answer this question, we have extracted AC component from the intensity trace shown in Fig. 6(a), defined by the beating frequency of consecutive modes. Corresponding maximum points $t_i$ of the obtained sinusoid [Fig. 6(b)] have been found and compared with the maximum points ${\tilde{t}}_i$ of the trace shifted exactly by one pulse period. Then the difference between corresponding maxima $\Delta t_i=t_i-{\tilde{t}}_i$ is normalized by the modulation period, thereby finding relative phase shift of corresponding maxima, $\Delta {\phi }_i=\Delta t_i/\left(t_{i+1}-t_i\right)=\left(t_i-{\tilde{t}}_i\right)/\left(t_{i+1}-t_i\right)$. These data are shown in Fig. 6(c). One can see that the phase is nearly constant with variations which are much less than the modulation period. Root-mean square deviation is found to be 0.17π.

 

Fig. 6 Intensity trace at different 300 mW pump power (a); its AC component (black) and that one shifted by pulse period (red) (b); and calculated phase shift between black and red traces (c).

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3. Conclusion

Thus, we have demonstrated for the first time nearly continuous tuning of a linearly-polarized single-frequency laser with a narrow bandwidth (<1 MHz) in a broad spectral range (>10 nm) without any filtering/tuning element (in the self-sweeping regime), see Figs. 3 and 4. Such a regime is obtained in a simple, reliable and efficient configuration of a Bi-doped fiber laser featured by long cavity (~100 m) and small intermode spacing (~1 MHz), whose performance greatly outperforms that of conventional rare-earth-doped fiber lasers. Though the intensity of such a laser is pulsed, the pulses become overlapping with increasing pump power (Fig. 4), so the temporal characteristics approach to a quasi-continuous regime. The pulse-to-pulse frequency change is equal to one intermode spacing (~1 MHz) independent of the pump power with intra-pulse frequency variation below this value. So the sweeping process is also quasi-continuous, and the scan rate increases with the pump power because of decreasing period of pulses. At that, the phases of consecutive pulse modes are close (with RMS deviations of 0.17π), so the obtained regime is nearly equivalent to the mode-hop free continuous tuning of single-frequency radiation, but without any selector and/or tuning element. The self-sweeping Bi laser has also much simpler design and much narrower bandwidth than the Bi-doped fiber laser with intra-cavity spectral filtering [24] provided by a narrow-band fiber Bragg grating and two fiber integrated Fabry-Perot filters resulting in 4-GHz linewidth.

Further improvements of the self-sweeping Bi laser characteristics seem to be feasible. First, the pulse-to-pulse frequency shift may be further decreased by lengthening the cavity beyond 100 m. It is also potentially possible to change the scanning direction (for example, by changing the pump wavelength [25]) thus providing matching of the intra-pulse chirp and the average shift between the pulses with reduction of the instant linewidth/frequency shift to 0.1 MHz and below. Better fitting to the telecom window (1.5-1.6 μm) is also possible with the Bi-doped fiber if longer-wavelength pumping is provided [18–20]. In addition to telecommunications and sensing, potential applications of the realized laser include spectral characterization of optical elements [26], RADAR systems with stepped-frequency modulation [27, 28], bio-medicine and astrophysics.

We anticipate that new advances in fundamental research, as well as new applications will emerge from further development of this concept.

Appendix Measurements of fast spectral dynamics

For measuring the instantaneous wavelength dynamics of a Bismuth-doped self-sweeping fiber laser, a Mach-Zehnder fiber interferometer is used. The interferometer is made of two 50/50 couplers and a spool of a SMF-28e fiber. Two interferometers with a fiber length difference of its arms of 69 m and 250 m with free spectral ranges of 2.9 MHz and 0.8 MHz, respectively, are used in the experiments. An additional polarization controller inside the interferometer is used to increase the visibility of interferograms. The input and two output signals are measured for frequency reconstruction. In accordance with classical theory of the Mach-Zehnder interferometer [29], the optical powers in output channels 1 and 2 can be written as:

(7)$$I_{1,2}(\nu )=\frac{I_{in}}{2}\left(1\pm V\cos \left(2\pi \frac{\nu }{\Delta \nu }\right)\right),$$

where $I_{in}$ is the input power, V is the visibility, $\nu$is the laser frequency, $\Delta \nu$is the interferometer free spectral range. Taking into account the power conservation $I_1+I_2=I_{in}$ one can obtain another equation for the optical frequency:

(8)$$\cos \left(2\pi \frac{\nu }{\Delta \nu }\right)=\frac{1}{V}\frac{I_1\left(\nu \right)-I_2\left(\nu \right)}{I_1\left(\nu \right)+I_2\left(\nu \right)}.$$

Cosine is an even periodic function, thus the actual laser frequency is determined up to an integer number m of free spectral ranges:

(9)$$\nu =\pm \frac{\Delta \nu }{2\pi }\mathrm{arc}\cos \left(\frac{1}{V}\frac{I_1\left(\nu \right)-I_2\left(\nu \right)}{I_1\left(\nu \right)+I_2\left(\nu \right)}\right)+m\cdot \Delta \nu$$

Let us demonstrate in detail the process of frequency reconstruction for the 250-m long interferometer with the visibility $V\approx$ 0.9. The measured input signal [Fig. 7(a)] that passed through the interferometer is divided into two output channels [Fig. 7(b)]. The power in each channel depends on the laser frequency. According to Eq. (9), one can calculate the laser frequency values from the data of Fig. 7(b). Four roots of Eq. (9) are presented in Fig. 7(c). Taking into account a continuous frequency change during each pulse (so-called “chirp”) shown by bold black line in Fig. 7(c), and additionally assuming that the frequency hops between pulses are equal to one beating frequency of the laser cavity (1.1 MHz), one can find the full spectral dynamics of the laser [Fig. 7(d)]. Thus, the measured wavelength sweeping rate is equal to 0.355 nm/s, which is in good agreement with the rate of 0.36 nm/s measured by OSA. This fact confirms that the frequency change between the pulses is equal to one intermode beating frequency. It should be noted that the sweeping rate can be measured by another Mach-Zehnder interferometer with larger free-spectral range (much more than the pulse-to-pulse frequency change) as in [26].

 

Fig. 7 Description of frequency reconstruction at a pump power of 100 mW: (a) input signal, (b) two output signals, (c) frequencies calculated using Eq. (9), (d) reconstructed dynamics of frequency.

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Note that the frequency changes within one pulse measured by two interferometers have similar shapes, as well as the frequency and time scales (Fig. 8). The similarity of the results obtained by two different interferometers confirms their reliability.

 

Fig. 8 Averaged spectral dynamics within one pulse for a pump power of 100 mW measured by two interferometers with an arm length difference of 69 and 250 m (red and black dots, respectively)

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Acknowledgments

The study is supported by Russian Science Foundation (project No. 14-22-00118). The work of I.A.L. is supported by RFBR grant 14-42-08026 r_ofi_m.

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