1. Introduction

A self-sweeping of laser frequency was observed in ruby laser [1] just one year after demonstration of the first laser. Later the effect was studied and described in detail, see e.g [2]. The authors of paper [2] found that for explanation of this regime it is necessary to take into account the spatial hole burning (SHB) effect in longitudinal distribution of the laser gain. In addition, the SHB was found to lead to self-sustained relaxation oscillations and therefore the laser generation occurs in the spiking mode. A maximum wavelength tuning range was measured to be as small as 0.07 nm [2]. Although fiber lasers are studied extensively in the last two decades, similar effects in their operation have not been observed until the last year.

Recently, observation of the laser frequency self-sweeping in fiber lasers has been reported simultaneously in papers [3,4]. The authors of paper [3] report on self-induced sweeping of the laser frequency in the Yb-doped fiber laser operating in the quasi-continuous mode that utilizes an active fiber with two-element cladding and a cavity formed by Fresnel reflection from two cleaved fiber ends. In our paper [4] the effect of self-sweeping is observed in a widely used laser configuration with a double-clad Yb-doped fiber and a cavity formed by a fiber Bragg grating (FBG) and Fresnel reflection from one cleaved (output) end. In contrast to [3], in our experiments the frequency self-sweeping was accompanied by the self-sustained relaxation oscillations, similarly to [1,2]. Note that the regime of self-sustained relaxation oscillations in fiber lasers is being studied in various aspects [5–9]. We have also found that the sweeping range is limited by the spectral width of the FBG.

In the present paper we report on the self-sweeping effect observed in the configuration with the fiber loop mirror (FLM) having a broadband reflection compared to the FBG. In the cavity with the FLM we have obtained the self-sweeping in the range as large as 16 nm, whereas the measured laser line width is found to be less than 1 pm. The details of the self-sweeping regime in presence of self-pulsations are studied and a model describing interplaying dynamics of laser frequency and self-pulsing laser power is proposed.

2. Experiment

A schematic of the studied broad-range self-sweeping of narrow-line Yb-doped laser is shown in Fig. 1 . The laser is based on single-mode octagonal double-clad Ytterbium-doped active fiber 1 (Nufern SM-YDF-5/130) with following parameters: mode field diameter is d_mode = 6.4 µm @ λ_signal = 1060 nm, cladding diameter is d_clad = 130 µm, absorption is 1.7 dB/m @ λ_pump = 976 nm, length is l = 2.6 m. The fiber is pumped by multimode laser diode 2 (Lumics) via pump combiner 3. The laser cavity is formed by Fresnel reflection (4%) from the cleaved end 4 at one side of the fiber, and fiber Bragg grating 5 (FBG) with resonant wavelength at 1066 nm or broad-band fiber loop mirror 6 (FLM) [10] at the other side. The FLM consists of the fiber coupler 7 (with 50/50 coupling ratio at wavelength of 1065 nm) and polarization controller (PC) 8. The PC is adjusted to obtain minimum transmission of power through the FLM. To increase total cavity length a passive single-mode fiber 9 (Nufern XP1060) with length up to 40 m is inserted into the fiber cavity. The output beam is collimated by aspherical lens 10 and then is divided into signal and unabsorbed pump beams by couple of dichroic mirrors 11 (“a scheme with the collimator”). To obtain all-fiber configuration with fiber output, the additional 50/50 coupler 12 is spliced instead of the collimator. One end of the coupler 13 is cleaved to supply feedback in the laser cavity. Another part of the power passes through the isolator 14 to avoid back reflection and then through WDM (980/1060 nm) coupler 15 to divide generation and spontaneous emission (“a scheme with the fiber output”). In contrast to the scheme with reflection from the cleaved end, this scheme has an effective reflection of about 1%. The scheme allows one to use measuring equipment having fiber input without launching significant losses.

 

Fig. 1 Schematic of the broad-range self-sweeping of narrow-line Yb-doped laser.

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Study of the temporal dynamics of the laser was performed with a fast InGaAs photodetector (Thorlabs DET01CFC, 2 GHz) and a digital oscilloscope (Tektronix TDS 3032B, 300 MHz). Figure 2 shows that the laser operates in the self-pulsing regime. The microsecond pulses are modulated with the intermode beating frequency $c/2Ln$ (inset to Fig. 2). It is known that the self-pulsations are caused by relaxation oscillations [11] with a frequency determined by the photon lifetime in the cavity ${\tau }_c$ and the pump power $P_p$ [9]:

 

Fig. 2 Typical temporal dynamics of self-pulsations and high-frequency modulation of the pulses (inset).

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Fiber vibration, temperature fluctuation or spatial inhomogeneity of the inversion population [11] may eliminate damping of the relaxation oscillations. In the other words [12], a composition of the generated modes may be changed after switching from one pulse to another thus leading to self-pulsations.

Average frequency, measured at the peak value of the Fourier transformation of the temporal signal, increases as square root of the output power (Fig. 3(a) ). In addition, the average frequency of relaxation oscillations is found to decrease with increasing cavity length. Figure 3(a) presents three curves for different lengths of the passive fiber (9 in Fig. 1): 0.5, 10, 40 m. Corresponding intermode beating frequency is $c/2Ln$ = 16.9, 6.6, 2.3 MHz, respectively (taking into account the lengths of active fiber, the pump combiner fiber and FLM). The solid lines in Fig. 3(a) correspond to the square root approximation in accordance with Eq. (1). It has been also observed that the regime of self-pulsations transforms into CW mode at a significantly increased power and/or cavity length. These results are in agreement with the results of papers devoted to the self-pulsation mode of fiber lasers [5–9]. The results presented in Fig. 3(a) were obtained in the “scheme with the collimator” and the FLM, but it should be noted that similar dependences were also observed in the “scheme with the fiber output” as well as in schemes involving FBG. In Fig. 3(b) the average sweeping rate versus laser power is also shown, determined from the spectral measurements described below.

 

Fig. 3 The average frequency of the relaxation oscillations ${\nu }_{oscill}$ (a) and the sweeping rate ${\alpha }_{sweep}$ (b) versus the output power of the laser at different cavity lengths (corresponding intermode frequency $c/2Ln$ is given) in the scheme with the collimator and FLM. Lines – square root approximation. Arrows indicate the instability thresholds of the self-sweeping regime.

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The measurement of the spectral characteristics of the laser was performed using LSA and WS-U devices (Angstrom/HighFinesse). The measurements show that the laser operates in wavelength self-sweeping regime. The LSA allows one to record spectra in the wavelength range of 600-1120 nm at a rate up to 350 Hz and to observe dynamics of the laser spectrum in real time with a rate of 20 Hz. An exposure time was about 1 ms. Some examples of measured temporal dynamics of the generated wavelength are shown in Fig. 4 . It has been found that the range of the periodic sweeping is limited by the spectral width of the cavity mirror: for FBG it is about 0.1 nm (Fig. 4(a)), for FLM it is more than 10 nm (Fig. 4(b)). The lasing wavelength increases linearly with time at a sweeping rate varying from 0.5 to 16 nm/s for different pump power and cavity lengths values. The resulting dependence for the scheme with the collimator and FLM is shown in Fig. 3(b). The average sweeping rate increases as square root of the average output power (Fig. 3(b)) similar to the average frequency of relaxation oscillations (Fig. 3(a)). It was also found that an increase of the cavity length leads to decrease of sweeping rate. Figure 3(b) presents three dependences for different lengths of the buffer fiber (9 in Fig. 1): 0.5, 10, 40 m. Note that the self-sweeping regime becomes unstable or completely disappears at a significantly increased power. The stability limit of the self-sweeping regime increases with decreasing cavity length: For the laser with FLM and intermode frequency $c/2Ln$ = 2.3, 6.6 and 16.9 MHz the power limit amounts to 50, 170 and 270 mW respectively (arrows in Fig. 3(b)). It should be noted that we observed unstable wavelength sweeping even above this limit that may be measured during some periods of time. Therefore Fig. 3(b) also shows the data for power that exceeds the stability limit.

 

Fig. 4 Temporal dynamics of wavelength for the FBG (a) and the FLM (b) cavities. Red and black curves correspond to different configuration of PC.

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From the data presented in Figs. 3(a) and 3(b) we find that average pulse to pulse change of lasing frequency is $\Delta \nu$ = 25.9, 17.7, 24.0 MHz for the cavity intermode frequency $c/2Ln$ = 16.9, 6.6, 2.3 MHz respectively. Thus average pulse to pulse frequency change corresponds to one to ten intermode spacings.

The sweeping range, as well as the sweeping rate, depends on the power. It is rather short at laser threshold. The range increases with pump power and amounts to about 10 nm at 40 mW output power level with cavity involving FLM. In Fig. 4(b) one can see that the sweeping range is slightly changed over time, but sweeping rate is nearly constant. It should be also noted that the sweeping rate and range depend strongly on the PC configuration (8 in Fig. 1). At a certain PC configuration we were able to increase the sweeping range up to 16 nm at the rate of 4 nm/s (red curve in Fig. 4(b)).

Spectra measurement with LSA showed that the instantaneous linewidth $\delta \lambda$ is less than 0.01 nm. Moreover, the width was measured independently with the wavelength meter WS-U having free spectral range 1.9 GHz and finesse 5. The device has an option of narrow line measurements relaying on its instrument’s function broadening. This option allows us to measure the width as small as 100 MHz. For these measurements higher input power are desirable, therefore we used “scheme with the fiber output”. It was found that even for the high precision device the linewidth lies close within the sensitivity limit of the WS-U wavelength meter $\delta \nu$~100 MHz, that means $\delta \lambda$~0.3 pm.

Such a narrow generated spectrum should consist of only a few longitudinal modes leading to intermode beatings. Indeed, some pulses are strongly modulated with the intermode frequency (see inset in Fig. 2). The RF spectrum is also measured. It consists of less than ten intermode beating peaks that confirm that only a few longitudinal modes take a part in lasing at the same time. It is in agreement with the fact mentioned in [11] that the regime of irregular and sustained pulsations associates with a small number of simultaneously generating longitudinal modes. The small number of modes detected in RF spectra is in good agreement with optical spectra measurements ($\delta \nu$~100 MHz). It should be noted that much broader linewidth $\delta \lambda$~0.1 nm is indicated in [3]. This value is more than two orders greater than for our laser.

As it is mentioned above, the narrow-line self-sweeping regime at high powers becomes unstable. The transition scenario depends on the spectral width of the cavity mirror. The generated spectrum is stabilized at the Bragg wavelength and is significantly broadened up to 0.1 nm in quasi-CW mode after disappearance of the self-sweeping effect in the case of FBG mirror. In the case of FLM mirror, the stimulated Brillouin scattering (SBS) is observed with increasing pump power. SBS manifests itself in the temporal dynamics as well as in the spectrum. Giant SBS-induced pulses appear in temporal dynamics, similar to the pulses mentioned in [5,7]. Additional narrow line peak separated by 15.6 GHz from the main peak is observed in the spectrum that corresponds to SBS Stokes shift. It is also observed that this spectral component is also sweeping in front of the main line. Further power increase leads to transition to stochastic lasing: giant irregular pulses and unstable spectrum are observed. As shown in [7] laser instability is related to cascaded Brillouin process. The appearance of Brillouin scattering may be also treated as an indication of the narrow width of the sweeping line.

3. Discussion

It is well known that one can obtain the regime of self-sustained pulsation with cavity having low Q-factor [3,4]. Taking into account that the sweeping rate and frequency of self-pulsation have similar dependence on the power and cavity length in our experiments (see Figs. 3(a) and 3(b)), and that there is no sweeping without self-pulsations, we believe that the self-sweeping is related to the relaxation oscillations. As we observed the self-sweeping effect in the presence of self-pulsations only, we are not sure that the effect can be obtained in a CW laser. It is found that during the evolution of a single pulse small number of longitudinal modes takes a part in lasing. We assume that there is a mechanism defining the initial direction of the wavelength sweeping and the wavelength initially increases. Let us consider further dynamics of wavelength taking into account SHB. For simplicity let’s assume that there is only one longitudinal mode during a single pulse with wave vector $k_m=2\pi /{\lambda }_m=2\pi /{\lambda }_0+\pi m/L$, where ${\lambda }_0$ and ${\lambda }_m$ are wavelengths for modes with numbers 0 and m respectively, L is the cavity length. The intensity distribution of the standing wave $I_m(x)=I_m^0{\sin }^2(k_{m}x)$ with the spatial vector $k_m$leads to SHB in inversion and in corresponding saturated gain $g_s$ in the active medium$g_m(x)=-2g_m^0{\sin }^2(k_{m}x)=-g_m^0+g_m^0\cos (2k_{m}x)$, where x is longitudinal coordinate, $I_m^0$and $g_m^0$ are amplitudes of the generated field intensity and of the holes, respectively. For simplicity assume that the mean value of $g_m(x)$ is added to a saturated gain$g_s$ and the alternating part is called as “grating” and is associated with the hole burning effect. It is shown further that this renormalization leads to appearance of the effective additional gain at adjacent frequencies. Note that the lifetime of gain grating is determined by the lifetime of the upper level of the laser transition, ${\tau }_0$~0.8 ms, and the lifetime of the mode m is determined by the time of several relaxation oscillations $T=1/{\nu }_{oscill}$~10 µs. One can estimate the amplitude of grating in the gain as $g_m^0/g_s\sim IT/I_s{\tau }_0$ ~10⁻¹-10⁻² whereI, $I_s$ are the average generation and the saturation power, respectively. Saturation power for our laser is $I_s$~10 mW, while the average output power is I<500 mW. It means that longitudinal mode writes only weak grating in the medium. The spatial grating controls appearance of other longitudinal modes. Let us consider how it affects the mode n. The effective gain for the mode is proportional to the overlap integral between the grating which is written by the mode m and the intensity distribution for the mode n along the length of active medium l [2]:

 

Fig. 5 Effective gain as a function of the wavelength difference ${\lambda }_j-{\lambda }_0$ (bottom) or the mode index j (top) in accordance with Eq. (3). The curves correspond to generation of one mode (#1), three modes (#2) and hundred modes (#3). Index of the last generated mode is 0. The curves are plotted for the case $L/l$ = 8.

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Therefore mode with number $j^{\prime }=j-3L/4l$should arise after modej. One can show that the change in frequency in the interval between pulses is

As mentioned above, grating’s lifetime is limited by the lifetime of the upper level ${\tau }_0$, thus number of modes affecting a new mode j can be estimated as $N\sim {\tau }_0/T$~100. Hence we can estimate the full width of the hole in the gain spectrum as $\delta \nu \sim N\cdot \Delta \nu$~3 GHz or $\delta \lambda$~0.01 nm.

Since frequency changes from one pulse to another, the temporal dynamics of lasing wavelength is determined by the temporal dynamics of relaxation oscillations. One can see from Eqs. (1) and (4) that the sweeping rate can be estimated as${\alpha }_{sweep}=\Delta \lambda /T\propto \sqrt{I/L}/l$, i.e. the rate increases as square root with an average lasing power and decreases with cavity length.

Let’s discuss possible mechanisms defining the initial direction of wavelength changes on the base of the above model taking into account deformation of the gain spectral profile. It is known [13] that the position of maximum gain depends on the value of population inversion. The gain maximum shifts to shorter wavelengths with increasing population inversion. In the case of pulsed generation, the gain fluctuates around the average level which corresponds to the loss level. A fast decrease of inversion (and gain) after pulse is followed by a gradual growth during the time between pulses. In our case there is a gradual growth of the population until the lasing starts when the gain becomes higher than the cavity losses. Let us assume that in the moment of appearance of the first pulse the population is greater than for a continuous generation (upper curve of Fig. 6(a) ). Thus lasing begins at shorter wavelength. After generation of the first pulse population of upper level is decreased and the gain contour is shifted to longer wavelength (lower curve of Fig. 6(a)). The pulse also burns a hole in the gain in accordance with Eq. (3). Then the second pulse is generated at the wavelength corresponding to the right main peak in the SHB-induced oscillations thus defining sweeping direction. The following pulses also burn holes in the gain contour at the corresponding lasing wavelengths (Fig. 5). This leads to a gradual increase of the population inversion and a shift of the contour maximum to shorter wavelength (Fig. 6(b)). Spatial grating in the gain is “washed out” during the lifetime of the upper level${\tau }_0$. As noted above, it determines the width of the hole in the gain spectrum. Figure 6(b) shows a smoothed contour without oscillations. Sweeping continues as long as the lasing wavelength reaches the point where the short-wavelength maximum of the gain becomes larger than long-wavelength one (Fig. 6(b)). At this moment lasing wavelength hops to shorter one instantly and the process repeats again.

 

Fig. 6 Qualitative dynamics of the gain contour against loss level at self-sweeping: a – after generation of the first pulse, b – before wavelength hopping, after many pulses when the tail of the grating is “washed out” (oscillations are not shown), gain is presented in log scale. The scale of holes is changed for convenience.

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It should be mentioned that the presented consideration is qualitative in nature. In our paper we don’t take into account signal inhomogenity along the length and dynamic phase gratings. As shown in [14] the phase gratings are very strong in Yb-doped fibers and have to be accounted for correct description of the laser dynamics. For a detailed comparison with the experiments one should perform numerical calculations of full equation set for modes and level populations, taking into account the temporal dynamics of the processes. It is beyond of frames of the present work.

One can also suggest another mechanism defining the initial long-wavelength change which is connected with the generation of the Stokes components in a nonlinear process such as stimulated Raman-like scattering on the transverse sound [15].

4. Conclusion

Thus the new effect of narrow-line self-sweeping in fiber lasers is described in detail. In addition to the fact that the laser line moves periodically from shorter to longer wavelengths, it has been found that it is very narrow amounting to δν ~100 MHz that is equal to several times of mode spacing. The regime is observable in various cavity configurations based on FBG or fiber loop mirror and cleaved fiber end. An all-fiver cavity formed by broad-band fiber loop mirror and ~1% fiber reflector has been also realized. In such configurations a sweeping range as large as 16 nm has been demonstrated. Though these parameters concede to those in modern active scanning laser configurations [16] with scanning range up to 200 nm at 200 kHz scanning frequency, the studied self-sweeping laser has one important advantage: it doesn’t needs special elements providing scanning. We also hope that its parameters may be further improved. The developed source can be used in various applications requiring tuning, e.g. for interrogation of FBG sensors.

To describe the observed phenomena a model of the self-sweeping effect has been developed based on the non-stationary spatial hole burning in the longitudinal distribution of gain for a small number of generated modes. The corresponding dynamics of the saturated gain profile has been analyzed. It has been found that the frequency shift between two pulses in self-pulsations series is defined in the first-order approximation by the length of the active medium. This agrees well with the experimental results. Further investigations both experimental and theoretical are necessary for description of fine details.