1. Introduction

Regime of spontaneous laser line sweeping (SLLS) was observed in fiber lasers recently [1–4]. The SLLS is characterized by periodic drift of the laser wavelength within spectral interval as long as ~20 nm. This spectacular effect was attributed to spatial-hole burning caused by standing-wave in the laser cavity [1–3]. The laser wavelength sweeping from shorter towards longer wavelengths was observed in the first detailed reports on SLLS [1–3]. The so-called reverse direction of sweeping was observed later too [5, 6]. The SLLS laser output is not a continuous-wave signal but it is a train of self-sustained relaxation oscillations with pulse width ranging from microseconds to tens of microseconds. Another important feature of the SLLS is narrow linewidth given by single- or few-longitudinal mode nature of oscillation [7]. The SLLS fiber lasers are attractive tunable sources of narrow-line radiation that offers high output power and cost effectivity thanks to low complexity of the fiber laser design. The potential applications include, e. g., component testing, laser spectroscopy, and optical fiber sensor arrays. The self-swept fiber lasers were used for characterization of narrow-band features of fiber Bragg gratings that cannot be resolved by monochromator-based spectrometers [8]. Just recently they were used as a test signal for demonstration of fast optical spectrum analyzer with high spectral resolution [9]. Deeper understanding of SLLS may also help to reveal physical origins of triggering the giant pulse generation through self-Q-switching. Indeed, the Q-factor of the laser resonator can be increased by transient fiber Bragg gratings (FBGs) that are created during the self-sweeping regime along the active medium. Reflectivity close to 100% can be reached in such weakly modulated but long FBGs [10–12]. It was experimentally demonstrated that the SLLS is a prerequisite for the self-Q-switched operation at least in some fiber laser arrangements [3]. Most of the reports on SLLS dealt with ytterbium fiber laser where the self-swept regime can be readily established. The SLLS was reported also in thulium- [13], and bismuth fiber lasers [14]. Surprisingly, it seems difficult to obtain SLLS in erbium-fiber lasers; only one successful experiment has been reported so far [5]. Laser wavelength of all the SLLS fiber lasers reported until now was below 2 μm. With this paper we extend the group of self-sweeping lasers by holmium fiber laser around 2100 nm. The self-sweeping was recorded using Fourier transform infrared (FTIR) spectrometer.

2. Experimental setup

The active medium of the fiber laser was a holmium fiber fabricated in house using modified chemical vapor deposition and solution doping methods. The fiber core is designed so that it is single mode at 1.95 μm, i. e., for both the pump and signal radiation. The core diameter and numerical aperture were 11 μm and 0.13, respectively. The peak holmium absorption at 1950 nm band was 40 dB/m, which corresponds to Ho³⁺ concentration of about N_tot = 1600 mol ppm. The measured spectral shape of the holmium fiber absorption corresponds well to the absorption cross section spectrum σ_a reported by Simakov et al. [15] and is shown in Fig. 1(a) together with the emission cross section σ_e. The two spectra σ_a and σ_e from reference [15] were fitted by linear combination of Gaussian functions for the sake of estimation of the active fiber gain and its first derivative in the next section. The laser wavelength range of 2.1 μm is located in the region of considerable losses due to OH^- and SiO₂ infrared absorption. The OH^- content was estimated as 5 mol ppm from the attenuation of 0.31 dB/m at the 1383-nm peak, see Fig. 1(b). In order to determine the OH^- concentration, we used the attenuation 62.7 dB/(ppm × km) at the OH^- peak in silica fibers [16]. The spectral variation of attenuation due to 5 mol ppm of OH^- according to [16] and due to the SiO₂ infrared absorption according to [17] is also shown in Fig. 1(b). The basic laser characteristics were tested in Fabry-Perot arrangement with a high-reflective FBG at 2100 nm at the pump end of the holmium fiber and with a perpendicularly cleaved fiber at the other end working as an output mirror with 3.5% reflectance. With the pump at around 2020-2030 nm we found the optimum fiber length, laser threshold, and slope efficiency with respect to the absorbed pump power to be 4.5 m, 0.6 W and 64%, respectively. Details about the active fiber performance in continuous-wave and mode-locked fiber lasers can be found in [18, 19]. In the case of the used fiber we measured smaller slope efficiency and shorter fluorescence lifetime of the level ⁵I₇ than in the case of holmium fiber with lower holmium concentration and similar core composition [18]. Therefore, we anticipate that energy transfer upconversion (ETU) processes caused the lower slope efficiency of the holmium fiber laser, namely the process ⁵I₇,⁵I₇ → ⁵I₈,⁵I₅, see Fig. 1(c).

 

Fig. 1 (a) Holmium fiber absorption and emission spectra. The values of the cross sections are taken from Simakov et al. [15]. (b) Background losses due to OH^- content (5 mol ppm OH^-) and infrared SiO₂ absorption. (c) Simplified energy level diagram of Ho³⁺.

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The holmium fiber laser for investigation of the possible self-sweeping regime was built in all-fiber Fabry-Perot arrangement shown schematically in Fig. 2. The pump radiation from a thulium fiber laser in ring arrangement (maximal output power around 4 watts in continuous regime) was coupled into the holmium fiber via specialty Wavelength Division Multiplexer (WDM) for combining 1950 nm and 2100 nm wavelengths. Although the thulium fiber laser used for pumping emitted within 2020-2030 nm, the transmission of the WDM was still more than 50% at the pump wavelength [19]. The output mirror of the Fabry-Perot resonator was formed by a perpendicularly cleaved active fiber end with about 3.5% reflectance. The high reflective mirror (around 90% at 2.1 μm) of the resonator was formed by fiber-loop mirror (total length around 1.5 m) using specialty broadband coupler with 50/50 coupling ratio within the range from 1.77 to 2.04 µm. The specialty WDM and broadband coupler were fabricated by fused biconical tapering technique [17]. The residual part of the radiation in the fiber-loop mirror was coupled out from the cavity through the other branch of the coupler. This branch was used for monitoring of the laser signal in the cavity and correspondingly for monitoring of the laser output temporal behavior. The photodiode (Thorlabs PDA10D) was connected either through a circulator and FBG at 2100 nm, so that only laser signal in close proximity to 2100 nm was detected; or, the laser signal without spectral filtration was detected. Optical spectra were recorded by means of Nicolet 8700 FT-IR Spectrometer with linear scan velocity of 2.53 cm/s.

 

Fig. 2 (a) Holmium fiber laser setup. One port of the fiber loop mirror was used to monitor the laser light either through a circulator and FBG at 2100 nm (b); or directly, so that the series of relaxation oscillations (c) and longitudinal mode-beating (d) could be observed.

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3. Results and discussion

Various lengths of the active fiber were tested. The self-sweeping was not observed for a fiber length around 5 m, i. e., for the optimum fiber length in terms of maximum slope efficiency in the given pump source and mirror reflectances. The self-sweeping regime was observed for 8 m-long fiber and it was studied by means of temporal traces (oscillograms) and spectrograms.

Temporal traces of the SLLS regime have several characteristic features on different time scales. By using a narrowband spectral filter, e. g., a monochromator of optical spectrum analyzer, one can observe a signal with time period equal to the sweeping period [3, 5]. In our case, the narrowband filter was formed by the FBG and the circulator. The recorded temporal trace with period of ~4.5 s is shown in Fig. 2(b). The SLLS laser output pulse train of self-sustained relaxation oscillations is shown in oscillogram in Fig. 2(c). The output pulses were of several tens of microseconds long. Single- or few-mode nature of the SLLS regime is apparent in temporal trace by mode-beating between the neighboring modes. The mode-beating signal in Fig. 2(d) had a period of 273 ns that corresponded to the interference of i and i + 3 longitudinal mode of ~9 m-long fiber laser resonator.

Although the SLLS regime is distinguished by its characteristic temporal behavior, the confirmation of SLLS should be made by recording the time evolution of the laser output spectra. The laser output spectra are shown in Fig. 3 for the pump power of 0.8 W, i. e., slightly above the holmium fiber laser threshold. The corresponding output power of the self-swept laser was 0.2 W. The saw-like temporal behavior is apparent from the color-contour graph in Fig. 3(a). Cuts of the color-contour graph for selected time instants are shown in Fig. 3(b). Note that we set intentionally the low resolution of the spectrometer of about 3 nm. The lower was the spectral resolution the shorter was the sweep of the movable interferometer arm inside the FTIR spectrometer. Therefore, the reading of a single spectrum could be fast and we could get both sufficient spectral samples within one sweeping period and less distortion of the spectrum due to the laser wavelength sweep. The stability of the SLLS regime lost its periodicity in several minutes. The periodic self-sweeping operation was recovered after several hours of cool-down of the laser setup when the optical pump was switched off. With increasing pump power the regime transited into a self-Q-switching regime. The spectra in Fig. 3 were taken soon after establishing the SLLS regime and the sweeping occurred in ~4 nm interval with a rate of ~0.7 nm/s in the so-called reverse direction from longer towards shorter wavelengths.

 

Fig. 3 (a) Recording of time series of the laser output spectra. (b) Spectrograms for selected time instants. The resolution of the spectrometer was set to 8 cm⁻¹ (~3 nm).

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Let us discuss the sweeping direction in more detail. The sweeping direction is determined before the single sweeping interval starts. This is because the direction is hold by the transient grating burned into the active medium during the sweeping [1, 6, 7]. Several effects may play role in determination of the sweeping direction. The effects discussed so far in open literature can be divided into two categories: the effects of spectral gain profile [1, 6] and the effects of transient refractive-index grating inscribed into the active media [7, 10–12]. The effect of spectral gain profile was discussed in [1, 6] for the case of ytterbium fiber lasers. In the reference [1] it was assumed that differences in metastable level population before and during the single sweeping interval are high enough so that at the beginning, the peak spectral gain is located always at a wavelength shorter than the peak spectral gain corresponding to the metastable level population later during the sweeping. This can explain the so-called normal sweeping direction (from shorter towards longer wavelengths), but not the reverse one. On the contrary, Navrátil et al. [6] assumed that the changes of the metastable population are negligible and the sweeping direction is given only by the spectral gain profile at given population of the metastable level. It means that lasing would start at the wavelength of maximum gain and sweeping would occur in the direction where the gain declination is lower. In other words, the absolute value of the first derivative of the gain with respect to wavelength is lower in the direction of sweeping than in the other direction. Using the theoretical model described in [6] and the parameters of the holmium fiber and laser cavity listed above, the spectral gain profile and its first derivatives for various length-averaged populations N₂ on metastable level are estimated in Fig. 4. For given metastable level population N₂, ground state population N₁ and fiber length L, the gain is estimated as G ≈4.34 ΓL (N₂ σ_e − N₁ σ_a − α). The parameter Γ accounts for the overlap of the laser signal with the core doped with holmium and the parameter α accounts for the silica and OH^- losses shown in Fig. 1(b). For the relative population N₂/N_tot = 28% and above we found that the absolute value of the gain derivative is lower at the shorter wavelengths' side of the peak gain. It can explain the observed direction of sweeping from the longer towards the shorter wavelengths, the so-called reverse sweeping. The control of the sweeping direction by the pump wavelength and pump power (and correspondingly the population inversion) was demonstrated in the case of self-swept ytterbium fiber laser [5,6]. Therefore, we tried to pump the holmium fiber laser also at another pump wavelength. The pump at 1940 nm was tested, but the self-sweeping regime was not observed in this case. The sweeping direction can be affected also by the refractive-index transient gratings inscribed into the active fiber. It was found that this effect can be even higher than the effect of the spectral gain profile [7]. In addition, the spectral reflectance of the transient FBG was found to be asymmetric to the wavelength at which the grating was inscribed [10–12] thus the reflectance of the transient grating would support the laser light generation on the pre-selected side with a higher reflectance. Investigation of the effect of the refractive-index transient grating to the sweeping direction is beyond the scope of this paper.

 

Fig. 4 (a) Estimation of the holmium fiber gain for various average relative population on the metastable level. (b) Corresponding first derivative of the gain.

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4. Conclusions

We have reported self-sweeping of the laser wavelength in a holmium fiber laser. It extends the group of self-swept fiber lasers demonstrated so far by the wavelength range near 2.1 µm. The sweeping occurred in the so-called reverse direction from longer towards shorter wavelengths. in the interval of about 4 nm with sweeping rate of ~0.7 nm/s. However, the stability of the SLLS regime was short-lived; it lasted for about couple of minutes and become gradually unstable. It is in the contrast with ytterbium fiber lasers where periodic SLLS operation with good stability can be readily achieved. Deeper understanding of heating effects in the active medium on the SLLS operation, optimization of the cavity of the holmium fiber lasers and investigation of the effect of refractive index grating to the sweeping direction require further research effort.