1. Introduction

Recently, an all-fiber Erbium laser has been shown to operate in the self-Q-switched regime [1], where self Q-switching (SQS) is owing to the nonlinear thermal lensing effect stemming from the presence of excited-state absorption in the Erbium active fiber at the laser wavelength [2]. However, apart from this fact, it was noted in [1,2] that even at continuous-wave (CW) operation, preceding at low pump powers the SQS regime (the latter appears suddenly at some higher pump rate), the laser output power is weakly modulated at the relaxation frequency. It is a quite surprising fact, since it is known that the Erbium fiber laser, being a class-B laser, has to be free from such oscillations under the CW pumping. On the other hand, as shown in [3,4], the Erbium fiber laser demonstrates, with the modulated pump, all the expected nonlinear-dynamics properties (e.g., the quasi-periodicity regimes, generation of multiple attractors, transition to chaos, etc.), i.e., the pump modulation is the source of the laser modulation and establishes the characteristic pulsed regimes [3].

In the present Letter, we show experimentally that the mentioned self-modulation of the autonomous CW-pumped Erbium fiber laser [1,2] on the relaxation frequency has a similar physical origin as the pump-modulated Erbium fiber laser [3,4], but the source of the modulation is now the amplitude noise launched from the pumping diode laser.

2. Experimental results and discussion

An experimental set-up is shown in Fig. 1. The laser has been arranged as a simple splice of a heavily doped (2300 mol. ppm) Erbium fiber (SCL110-01; IPHT-Jena, Germany) with length of 152 cm and two fiber Bragg gratings (FBGs) as the output couplers, both with reflectivity of 92% (total length of the intra-cavity FBGs’ tails was 181 cm). The active Erbium fiber was pumped through a WDM multiplexer by a standard commercial low-power pigtailed CW diode laser (JDS Uniphase; wavelength, 978 nm); a fiber attenuator was used in the scheme for control over the optical pump level, while keeping the current of the pumping diode laser fixed. A driver of the pumping diode laser allowed us to control the pump current as well as to apply to the laser diode an additional (white) noise of controllable magnitude. Signals corresponding to the powers of the pumping diode laser and Erbium fiber laser were measured either with a power-meter, or with a set of 125 MHz photo-detectors and recorded by an oscilloscope and RF spectrum analyzer. The diode laser pump power depended linearly on the applied current. The Erbium fiber laser operated at the wavelength 1560.4 nm with the efficiency (measured as a sum of signals from both the laser outputs) not exceeding 6.5%. The optical spectrum bandwidth of the Erbium fiber laser was less than 0.1 nm (the resolution of an optical spectrum analyzer).

 

Fig. 1. Experimental set-up.

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The Erbium fiber laser in the all-fiber configuration (Fig. 1), where only the active fiber is placed inside the cavity, supports either the quasi-CW operation at the low pump rates, starting from the “first” laser threshold, 33.8 mA (where the output power is weakly modulated on the laser relaxation frequency), or the mentioned above SQS regime at pump powers exceeding the “second” threshold [1,2], ~250 mA. The characteristic snapshots (1–6) of the laser output power, recorded at the different pump powers, are shown in Fig. 2(a) (these graphs have been obtained for the case where neither a noise voltage is applied to the pumping diode driver, nor any attenuation set by the attenuator). The ESA/thermal-lensing assisted SQS regime [2] appears above the second laser threshold and is depicted in Fig. 2(a) by graphs 5 and 6. Meanwhile, the quasi-CW operation of the Erbium fiber laser with self-modulation of the output power at the relaxation frequency (pump powers, 33.8–250 mA, graphs 1, 3, and 4) is replaced, a bit above the first laser threshold (at the pump power, 34.7±0.8 mA), by another pulsed regime (graph 2). We shall concentrate further attention on the investigation of the source of the self-modulation effect only (see snapshots 1–4), i.e., on the fiber laser operation at the relatively small pump levels, before the thermally-induced pulsing (snapshots 5 and 6) is self-switched on (recall that the last regime is addressed in detail in [1,2]).

We have suspected that the self-modulation of the Erbium fiber laser is a consequence of the pumping diode laser amplitude noise, which is inevitably reflected in the characteristics of the pumped Erbium fiber laser. The evidences for this conclusion stem from Figs. 3–6 discussed below.

Figure 3 shows the noise features of the pumping diode laser as measured at five different spectral components of the noise versus pump power. These components (each labeled by the central frequency in the 250-Hz band provided by the RF spectrum analyzer) were chosen to be within the range of the characteristic relaxation frequencies of the Erbium fiber laser, which, in turn, are dictated by the pump level. An inset to Fig. 3 shows the overall noise spectra of the pumping diode laser, which have been measured with the RF spectrum analyzer for several pump powers (no additional noise voltage was applied to the laser diode driver in this experiment). Note that such noise characteristics of the pumping diode laser are possibly related to the modal properties of the laser diode, which are dependent on the diode pump level. In Fig. 4(a), are shown the dependences of the Erbium fiber laser output power modulation versus pump power within the same (as in Fig.3) range; for completeness, in Fig. 4(b) are shown the dependences of the relaxation frequency and output power versus pump power. The curves composed of filled circles relate to the case of no additional noise signal applied to the driver; while the curves composed of empty triangles correspond to the case of additional white noise voltage (of the magnitude of 1 and 2V, respectively) applied.

 

Fig. 2. Oscillograms of output power of the Erbium fiber laser for the different pump driver currents (in brackets - an excess over the first laser threshold). The sets of snapshots (1–6) on each graph (a,b) correspond, respectively, to the cases of non-attenuated (a) and attenuated (b) pump power, i.e., to the same excess over the threshold, but to the different levels of amplitude noise of the pump diode laser.

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Fig. 3. Relative (to the pump power, in %) amplitudes of the noise spectral components (measured at 5, 10, 30, 60, and 90 kHz) of the pumping diode laser as a function of applied current of the diode driver. Inset shows overall views of absolute magnitude of the diode noise within the interval 0–100 kHz for the different pump currents (1 - the detector noise, 2–13 mA/1.7 mW, 3–25 mA/8.1 mW, 4–50 mA/22.7 mW, 5–175 mA/99.3 mW, 6–275 mA/153 mW).

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A comparison of Fig. 3 and Fig. 4 allows one to conclude that, especially at the low pump powers, ≤50 mW (≤100 mA), where the diode noise-to-signal ratio is the highest, the pumping diode noise causes the observed self-modulation effect in the Erbium fiber laser. Meanwhile, note that the “integral” characteristics of the fiber laser (the output power and relaxation frequency) do not change with the variation in the diode noise magnitude. Indeed, one can see that the noise local maximum (nearly 10 mW, or 40 mA) corresponds to the maximum modulation of the Erbium fiber laser and even to the establishment of the self-pulsing (Fig.2(a), snapshot 2). The latter is the phenomenon resembling the pulsed regimes observed recently in the Erbium fiber laser under pump modulation [3], but in the present case the role of pump modulation is played by the correspondent spectral component(s) of the noise, corresponding to the relaxation frequencies at the given pump rates. Further, an increase of the noise magnitude (at the fixed diode pump level; compare the curves labeled as 0, 1, and 2V in Fig. 4(a)) directly leads to an increase of the modulation of the Erbium fiber laser power. Finally, the spiking region observed near the first laser threshold (see snapshot 2 in Fig. 2(a)) was expanding with the increase in the noise magnitude. Moreover, as it is seen from Fig. 5(a), the amplitude of the pulses obviously increases as the noise magnitude rises. However, the re- gime of giant pulses (SQS), observed above the second laser threshold and, remember, caused by the ESA-assisted thermo-lensing, is non-sensitive to the noise amplitude (Fig. 5(b)).

 

Fig. 4. Dependences of Erbium fiber laser power modulation (a) and its relaxation frequency/output power (b) versus the pumping diode power. Filled circles answer to the case where no additional noise is applied (0V); empty triangles correspond to the two different levels of additional white noise applied (1 and 2 V, which correspond, for instance, to the additional noise power of 7 and 14 µW in 250 Hz bandwidth at frequency 50 kHz). The modulation parameter (Fig.4(a)) is calculated as the peak-to-peak to average voltage ratio. No attenuation is set by the attenuator.

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We have performed an additional experiment for confirming the above-formulated evidence regarding the role of the pumping diode noise in the establishing of the power self-modulation in the Erbium fiber laser. With the help of the attenuator, we could fix the pump power launched from the diode laser at some level, but at different noise levels of the pump (see Fig. 3). For the condition where the attenuation coefficient in the attenuator was about 40%, we have measured the dependences (plotted in Fig. 6) of the output power/relaxation frequency (Fig. 6(b)) and output power modulation (Fig. 6(a)) on the excess of the pump power over (first) laser threshold. As it is seen from Fig. 6(b), the integral parameters of the Erbium fiber laser are kept non-changed - either with the pump attenuated, or not. At the same time, one can see that the self-modulation effect (Fig. 6(a)) is essentially different in these two cases because of the different levels of the pump noise magnitude. It is remarkable that if the noise magnitude is weak enough (as given by the pump attenuation), the regime of self-spiking is not observed at all - compare the corresponding snapshots in the cases of non-attenuated (Fig. 2(a)) and attenuated (Fig. 2(b)) pump power.

 

Fig.5. (a) Snapshots of output power of the Erbium fiber laser operating in the first self-pulsing regime (near the 1-st threshold, 34.5 mA) established due to the influence of the corresponding spectral component of the pumping diode noise as the external ruling parameter. (b) Similar snapshots of the laser operating in the second self-pulsing regime (owing to the ESA-assisted thermal lensing effect in the active fiber [2]), 400 mA. The traces 1, 2, and 3 correspond to the different magnitudes (0, 1, and 2 V) of the additional white noise applied to the diode driver.

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3. Conclusion

The experimental data presented allows us to conclude a notable role for amplitude noise in a standard pumping diode laser in the appearance of self-modulation and self-spiking effects in a diode-pumped Erbium fiber laser. The diode laser amplitude noise is composed of spectral components, which resonantly interact with the relaxation frequency (given by the pump rate) of the Erbium fiber laser. This results, even at the extremely weak noise magnitudes, in that the relaxation oscillations of the Erbium fiber laser to become non-dumped. The latter appears as self-modulation and self-pulsing of the Erbium fiber laser output power. A separate experimental investigation, performed with other pumping diode sources and other Erbium fibers (with the much lower, 300 ppm, concentration of Erbium ions in the active fiber), has confirmed this conclusion. Thus, one can, by attenuating pump power and/or applying noise voltage to the diode driver, either minimize (and even eliminate) the self-modulation effect in the pumped Erbium fiber laser, or, vice versa, force the laser to work in a pulsed regime, which may be useful in applications.

 

Fig. 6. Dependences of the Erbium fiber power modulation (a) and its relaxation frequency/output power (b) versus an excess over the first laser threshold. Filled and empty circles relate to, correspondingly, the cases where no attenuation is set by the attenuator and 40%-attenuation. The modulation parameter (Fig. 6,a) is calculated as the peak-to-peak to average voltage ratio. The case of natural noise level of the pumping diode laser is shown (i.e., no additional noise is applied to the diode driver).

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