The output pulse characteristics of Q-switched Yb-doped fiber lasers have been investigated experimentally. It has been observed that for any typical modulation frequency, the pump power and the modulator OFF-time govern the shape of the output Q-switched pulse. At a fixed modulation frequency, with a fine adjustment of acousto-optic modulation window ON-time, pump power and cavity mirror position, it was possible to obtain modulation free single-peak pulse, multi-peak pulse, mode-locked resembling pulse and multi-pulse structured pulse shapes in a Q-switched fiber laser output. These observations have been analyzed and explained. Our investigations show that multi-peak pulse output is due to onset of nonlinear phenomena like SBS and SRS. Similarly, we have found that the mode-locked resembling periodically modulated output pulse shape is due to mode beating between the zeroeth order and the first order diffracted beams of the intra-cavity acousto-optic Q-switch.
©2007 Optical Society of America
High energy and short pulse single-mode Q-switched double-clad fiber lasers are attractive for many applications such as range finding, remote sensing, optical time domain reflectometry, medical and industrial processing due to their high efficiency, reliability, beam quality and compactness [1–4]. Electro-optic and acousto-optic modulators have been widely used for active Q-switching of fiber lasers in linear Fabry-Perot and ring cavity configurations [1–8]. For most of the applications, it is desirable to have a temporally smooth modulation free single peak pulse with a well defined time interval between pulses. However, quite often multiple random pulsing as well as Q-switched pulses with multi-peak or split pulse structure and mode-locked resembling periodically modulated pulse shapes have been reported in these lasers [1, 3–20]. Several earlier studies have attempted study of generation processes of such pulse shapes [4,7–20]. In reported Q-switched pulse shapes with multi-peak or split pulse structure, there are a few peaks in Q-switched pulse envelope with moderate depth of modulation [1, 4, 6–16]. These peaks in multi-peak structured pulses were claimed to have been separated by round trip time based on the presence of a peak corresponding to cavity mode spacing in FFT of these pulses [10–15]. Further, the observed optical spectrum in one of the reports  shows a band width of 0.16 nm, which corresponds to about 24.5 ps mode-locked pulses. However, the observed pulse widths of individual pulses in multi-peak structured Q-switched pulses are very large compared to the inverse of the gain bandwidth. Wang et. al. [12–14] have predicted that the formation of multi-peak structured Q-switched pulses may not be avoided if the width of a Q-switched envelope is greater than one round trip time and schemes to achieve single peak pulses have been proposed. To analyse observation of multi-peak phenomena, simulation of Q-switched fiber lasers have been carried out and the effect of modulation rise-time has been investigated [4, 7–13]. Based on these analyses, perturbation induced by quick switching of acousto-optic modulator (AOM) along with a series of pulse reflections from cavity mirrors has been shown to create multi-peak pulse shapes. In case of periodically modulated mode-locked resembling Q-switched pulse shapes, which were attributed to mode-locking process, the pulses within one Q-switched envelope were not separated by cavity round trip time or its sub-harmonic time [17, 18]. Myslinski et. al.  have claimed observation of such stable and efficient ‘simultaneously Q-switched and self-mode locked’ pulses in erbium doped fiber laser by carefully adjusting the rear mirror position. The mechanism of formation of mode-locked resembling pulse was explained on the basis of self-phase modulation (SPM), self-focusing, the Kerr lens effect and the aperture effect. In literature, multi-peak structured pulses with separation equal to or not equal to round-trip time and mode-locked resembling pulses with separation not equal to round trip time have been treated similarly. In spite of a large number of studies, in our opinion, a consistent picture about the mechanism of generation of pulses of different shapes is still lacking as different types of pulse shapes have been generated under different operating conditions. To the best of our knowledge, no one has reported observation of modulation free single-peak, multi-peak, mode-locked resembling, and multi-pulse type of Q-switched pulses with the same experimental set-up. Also, the effect of modulation window-time on the output pulse shape of high peak-power acousto-optic Q-switched Yb-doped fiber lasers has hardly been reported.
In this paper, we experimentally demonstrate the generation of a variety of pulse shapes under controlled operating conditions in a single set-up. It has been shown that by a fine adjustment of modulation window ON- and OFF-time, pump power and the cavity mirror position, various output pulse shapes such as multiple pulses within one modulation period, single-peak modulation free pulses, split or multi-peak pulses and periodically modulated mode-locked resembling Q-switched pulses can be generated. We also present a qualitative analysis to explain the shapes of the observed pulses, and a physical mechanism that leads to the generation of these pulses.
2. Experimental setup
Figure 1 shows the experimental set-up of an acousto-optic (AO) Q-switched fiber laser. In the experimental set up, a 20 W fiber-coupled laser diode at 975 nm has been used to end-pump 18 meters of Yb-doped double-clad fiber. The fiber used has a uniformly doped core with a homogeneous dopant concentration, and hence a uniform Yb-doping profile giving a step-index refractive index profile in the core region. The doped-fiber has a core diameter of 10 µm with a numerical aperture (NA) of 0.075 and an octagonal inner-clad diameter of 400 µm with an NA of 0.45. It has an inner-clad pump absorption of 0.8 dB/m at 975 nm. The laser resonator consists of a linear Fabry-Perot cavity with a rear mirror of ~100% reflectivity, and the cleaved facet at the other end with 4% Fresnel reflection acts as the output coupler. A dichroic mirror, which is highly transmitting at 975 nm and highly reflecting in a broadband from 1064–1140 nm, has been used to couple out the Q-switched laser beam. To achieve faithful Q-switching, one of the fiber ends has been angle polished at 10° to prevent any feedback and spurious lasing between the pulses. Here, the term ‘faithful Q-switching’ has been used to mean regular Q-switched pulses with a well-defined time spacing and repetition rate. Also, between the pulses there should not be any cw lasing, and hence cw power due to Fresnel reflection from fiber end-facets, which reduces pulse peak power. Further, several authors have reported random self-pulsing behaviour with irregular gigantic output pulses in feedback suppressed (by the use of angle-cleaved end face) fiber configurations [21–23]. Although, we have also observed random self-pulsing behaviour in the absence of AO Q-switching mechanism, these random self-pulses cannot be called ‘faithfully Q-switched’ pulses unless special measures are taken to make them regular. In our experiment, initially, the resonator was aligned for maximum CW laser output power, where in a maximum power of 10.75 W at an input pump power of 17.2 W, with a slope efficiency of 73%, was obtained. The pump threshold was 1.2 W. Further, the beam was collimated using a lens of 10 mm focal length, and Q-switching was achieved by using an intra-cavity AO modulator. The AO switch was kept near the rear mirror end at a distance of 0.5 m, and a radio frequency wave at 27.12 MHz with modulation rate of 1–100 kHz with variable duty cycle was applied in the study of Q-switching action. The AO modulator provides a diffraction efficiency of about 60% with a Bragg angle of 7.68 mrad. When the RF is turned OFF (i.e. low Q), the light beam within the cavity does not undergo deflection, leading to a build-up of population inversion; the laser pulse is emitted when the RF is turned ON (i.e. high Q) after some delay, equal to the pulse build-up time. Rise and fall time of the modulating signal were 22.5 ns and 22 ns respectively, which are very small compared to the cavity round-trip time (174 ns). The average output power was measured using a thermal detector and the Q-switched pulses were recorded using a 1 GHz photo-receiver and a 500 MHz digital storage oscilloscope. Effects of RF ON- and OFF-timing have been observed by modulating the Q-switch driver externally through a signal generator.
3. Results and discussion
3.1 Observation of single and multi-pulse output
At a typical modulation frequency of 20 kHz with 22 µs modulator OFF-time and 17.12 W pump power, a maximum average output power of 4.5 W with a single un-modulated pulse of 225 µJ pulse energy and 240 ns full-width at half-maximum (FWHM) pulse duration was achieved. We first studied the effect of AO Q-switch ON- and OFF-timings on the output pulse shape. Figures 2(a)–2(d) shows typical multi-pulse appearance in the output at 20 kHz modulation frequency. The pump power was 11.72 W. The number of post pulses in the output decreases with increase in the modulator OFF-time. When the modulator OFF-time was increased from 5.2 µs to 32 µs, number of post pulses reduced from five to nil. Pulse build-up time of the principal pulse also decreases with increase in modulator OFF-time; the peak power of the principal pulse increases with reduction in the number of post pulses, and finally a desired single pulse output is observed. When the modulator OFF-time was further increased, the principal pulse amplitude stability became poor.
When the modulator OFF-time (i.e. low Q) is large enough, population inversion and hence gain builds up in the system. A large initial gain facilitates the formation of a single Q-switched pulse (Fig. 2(d)). As the modulator OFF-time is reduced considerably, the initial gain available for pulse build-up is reduced and full energy extraction may not be possible. As a result smaller satellite pulses are also generated. Thus, for very small modulator OFF-timings, the additional available gain is so small that normal Q-switching process is disturbed and the laser output breaks into relaxation oscillations as shown in Figs. 2(a)–2(c). In this case multiple pulses are observed with a pulse separation of about 10–12 µs, which can be understood by considering a slight loss modulation in the cavity and the resultant fluctuation of population inversion. As the pulse build-up time also depends on initial gain, hence one can see the reduction in the pulse build-up time from 5.2 µs to 3.88 µs as the modulator OFF-time is increased from 5.2 µs to 32 µs. Since, it is possible to increase the gain in the system by using higher pump powers. Indeed, as the pump power and hence gain increases, the modulator OFF-time could be considerably reduced before the laser output changes from a single pulse to multiple pulses due to relaxation oscillations, which is as one would expect. As the modulator OFF-time is increased beyond a certain optimum limit, probably the large gain in the system causes ASE generation, which leads to amplitude fluctuations in the Q-switched output. This shows that for a given pump power, there is an optimum value for modulator OFF-time for generation of a stable single pulse output in Q-switched fiber lasers.
3.2 Observation of multi-peak structured pulse output
We further investigated the dependence of output pulse shape on pump power for a fixed modulation frequency and modulator OFF-time. Figures 3(a)–3(f) show output pulse shapes observed at 20 kHz modulation frequency at a fixed modulator OFF-time of 32 µs for pump powers from 10.13 W to 13.97 W. When the pump power is increased, initially the pulse is distorted and then a multi-peak structured pulse appears in the output. There is a continuous decrease in pulse build-up time with increase in pump power as expected. With an increase in pump power, modulation of pulse envelope is enhanced. With further increase in pump power Q-switched pulse breaks up in short duration giant pulses with a very high peak power as shown in Fig. 3(f). We show later that this multi-peak or split pulse appearance is due to the occurrence of nonlinear phenomena like stimulated Brillouin scattering (SBS) and Simulated Raman Scattering (SRS). These multi-peak pulses are similar to those observed by Wang et. al.  and were said to be ‘simultaneously Q-switched and mode-locked’ pulses with spacing of the split pulses in Q-switched envelope equal to one round trip time. However, the time separation of individual pulses in multi-peak pulses was not measured. This was concluded on the basis of observation of a frequency peak in FFT of these pulses, which was at the mode separation frequency of the laser resonator. We also found a peak at 5.75 MHz in the FFT of these pulses, which corresponds to the inverse of the round trip time of our resonator (174 ns). However, the spacing between peaks in the Q-switched envelope was not always equal to round trip time.
We also recorded the output spectrum corresponding to these pulse shapes which are shown in Figs. 4(a)–4(d). It can be seen that for a temporally undistorted pulse, the output wavelength spectrum is also smooth in a wavelength range of 1067–1108 nm with peak at 1093 nm. At higher input pump powers, the temporal envelope starts distorting and a new peak at 1049 nm starts appearing in the output spectrum with a range between 1040–1077 nm (Fig. 4(b)). This new peak and wavelength range is probably due to ASE generation at higher pump powers. As the highly reflecting feedback mirror does not provide feedback in this wavelength range, its amplitude remains lower even with increase in pump power. With further increase in pump power a peak shifted by about 56 nm from laser signal peak starts appearing, which is accompanied by a second peak at about 1200 nm with further increase in pump power. The position of these peaks corresponds to the primary and secondary Stokes component due to stimulated Raman scattering in silica . The spectral data clearly shows the existence of nonlinear scattering beyond a threshold pump power. The intensity dependent nonlinear distortion of the intra-cavity pulses is further supported by control of modulator OFF-time. For any pump power, a smooth transition from a temporally distorted to a clean pulse shape was possible with decrease in modulator OFF-time. This decrease in modulator OFF-time reduces the intra-cavity intensity and thus prevents the nonlinear distortion of the circulating Q-switched pulse. Thresholds for nonlinear phenomena SBS and SRS are given by 
where, Aeff is the effective core area and Leff is the effective fiber length given by
Brillouin and Raman gain coefficients in silica are gB=5×10-11 m/W and gR=1×10-13 m/W respectively . ΔνB=30 MHz is the Brillouin gain bandwidth and Δνs=5.06 THz is the signal bandwidth corresponding to signal linewidth of Δλs=20 nm in our experiments. αs=5×10-3 m-1 is the scattering loss at signal wavelength. For our case, with Aeff=7.85×10-11 m2 and L=18 m, the calculated values of SRS and SBS thresholds are 730 W and 194 kW respectively. These values approximately match with the observed thresholds for these phenomena. From Eqs. (1) and (2), it is clear that SRS and SBS thresholds depend on fiber parameters and spectral width of the pump beam, so these values will be different in different experimental conditions as reported by several authors like Wang, et. al. and Ye, et. al. [24, 25].
Similar temporal and spectral distortions in pulses were observed at 10, 15 and 25 kHz modulation frequencies. Figures 5(a)–5(g) shows single and multi-peak pulse shapes at 25 kHz modulation frequency at a fixed modulation window ON-time of 28.8 µs with variation in pump power from 10.55 W to 14.83 W. Figure 5(h) shows output wavelength spectrum corresponding to split pulse in Fig. 5(g). Output spectrum at lower pump powers has a similar behaviour as at 20 kHz modulation frequency, but there is an increase in pump threshold for appearance of another wavelength range (1040–1067 nm) and spectral peaks due to nonlinear scattering, namely SRS and SBS.
The pump power threshold for distortion and multi-peak structure appearance in output pulse shape increases as the modulation frequency increases. The pulse distortion occurs at a higher pump power since the intra-cavity intensity per pulse reduces as the modulation frequency is increased. It is apparent that the pulse splitting or multi-peak nature of pulses is due to the high intra-cavity pulse peak power and consequent nonlinear phenomenon like SRS and SBS and may not be due to fast rise time or switching induced perturbation [10–13]. In the high power AO Q-switched fiber lasers, the feedback is generally provided by the frequency shifted first order Bragg diffracted beam from the AOM. Cutler  has shown by simulation of a wide band oscillator that a continuously changing phase shift (a fixed frequency shift) in the feedback path produces a response that resembles mode-locking or split peak pulses. However, this theory can not explain multi-peak pulses observed in electro-optic Q-switched fiber lasers [6, 16], where unlike AOM there is no frequency shift in the feedback path of the laser. On the other hand, the onset of intra-cavity nonlinear scattering due to high intra-cavity peak power is able to explain the pulse splitting in case of electro-optic Q-switched as well as AO Q-switched fiber lasers. Renaud, et. al.  and Alvarez-Chavez, et. al.  have also reported observation of split or distorted pulses with increase in length of fiber. The pump thresholds for nonlinear phenomenon like SRS and SBS decreases with an increase in effective fiber length, hence the multi-peak pulse appearance might have started in their experiments on increase in fiber lengths. Unfortunately none of the authors have reported the output wavelength spectrum of Q-switched fiber lasers, when the pulse distortion or splitting starts appearing in the output. We may conclude that a single-peak output pulse could be observed in Q-switched fiber lasers, when the signal peak power is below SRS and SBS thresholds.
3.3 Observation of mode-locked resembling pulse output
Myslinski, et. al. [17, 18] have observed periodic modulation within the Q-switched envelope, which was attributed to ‘simultaneous Q-switching and mode-locking’ in AO Q-switched fiber laser due to SPM. It was also stated that these periodic modulations appeared only after a careful adjustment of the mirror. We were able to reproduce similar pulse shapes by carefully adjusting the position of mirror near the AOM. Figure 6(a) shows a periodically modulated mode-locked resembling pulse shape at 32 kHz modulation frequency and input pump power of 12 W. The FWHM pulse width of Q-switched envelope is 260 ns with an average output power of 3.2 W. One can note that the separation between individual pulses within the Q-switched envelope is about 18–20 ns (pulse repetition frequency of about 50 MHz), which is much smaller than the 174 ns cavity round trip time corresponding to the cavity mode spacing of 5.75 MHz. Thus, the pulse repetition frequency of 50 MHz is neither equal to cavity mode spacing nor equal to its harmonics as one would expect in case of mode-locking of a laser. The pulse width of the individual pulses within the envelope was about 8 ns. It was also observed that the modulation depth of mode-locked resembling pulse can be increased or decreased, when modulation window ON-time and mirror alignment is adjusted carefully. Figure 6(b) shows the output spectrum corresponding to the pulse shape of Fig. 6(a). The recorded pulse band-width of 42.9 nm corresponds to about 100 fs mode-locked pulses in contrast to the observed pulse duration of 8 ns.
Several mechanisms of generation have been proposed for observation of mode-locked resembling pulses in AO Q-switched fiber lasers. A proposed explanation for self mode-locking in these lasers is based on self-phase modulation . The spectral broadening caused by the self-phase modulation for an un-chirped Gaussian pulse with the length ΔτFWHM is given by 
where ΔνNL is the full width at the 1/e intensity point, T0 is the half width at 1/e intensity point and for a Gaussian pulse it is related with ΔτFWHM by ΔτFWHM=2(ln2)1/2 T0, and zeff is the effective distance of the guided pulse propagation. The nonlinear coefficient γ is defined by 
λ0 is the pulse wavelength in vacuum, n2 is the fused-silica nonlinear refractive index (n2=3.2×10-20 m2/W) and Aeff is the effective fiber core-area. For our case, Aeff=7.85×10-11 m2 and λ0=1089.5 nm, providing the value of γ=2.35×10-3 W-1m-1. The effective distance can be taken to be equal to one round trip propagation through the fiber zeff=36 m. For a peak power of P0=385 W, the corresponding spectral broadening due to self-phase modulation is ΔνNL=57 MHz, which is much larger than the cavity mode-spacing (5.75 MHz). Thus, in our case a large spectral broadening due to SPM may cause axial mode coupling to force self mode-locked operation . However, the separation between these mode-locked type of pulses in our case, as well as in the reports by Myslinski, et. al.  is not equal to the round-trip time or its sub-harmonic time as one would expect in case of mode-locking. In another explanation in Ref. 20, it has been mentioned that the shape of the Q-switched pulses in fiber lasers are modulated at the round trip frequency and this modulation arises from the difference in optical power on the two sides of the AOM before it is opened. This difference in power is retained during lasing, with the result that spikes at the round-trip frequency appear in the output and the observed modulation depth is limited by the response time of the detector. However, this concept is unable to explain large modulation depths which are not at round trip frequency observed by us and Myslinski, et. al. [17,18]. Further, its generation can not be explained by conjectures that there are harmonics of the modulation frequency that correspond to the cavity mode-spacing, which stimulates the laser and forces the formation of mode-locked pulses from noise, after the AOM is switched ON . Thus, the pulse repetition frequency, the large lasing band-width and long pulse duration of individual pulses in Q-switched pulse envelope indicate that the observed periodic modulation is probably not due to mode-locking phenomena. Hence, additional studies seem necessary to probe the cause of mode-locked resembling periodic modulation of the Q-switched envelope.
We show that the mode-locked resembling periodic modulation of Q-switched envelope is due to mode beating between the zeroeth order and the first order (frequency shifted) diffracted beams from the AOM. As stated earlier, the periodic modulation could be obtained by ‘carefully adjusting the rear mirror position’. We then systematically recorded the output pulse as the highly reflecting rear mirror was moved closer and farther away from the AOM. When the rear mirror was far away (~0.5 m) from AOM, the output pulse was smooth without any modulation. When the mirror was brought nearer (~0.1 m) to AOM, periodic modulation appeared in the Q-switched envelope on adjustment of modulation window ON-time and mirror tilt. The mode-locked resembling periodic modulation of the pulse envelope was also observed at 20, 24, 27 & 30 kHz modulation frequencies. If ω and Ω are the frequencies of laser and radio frequencies (RF) applied to the AO cell, the first order diffracted beam will have a frequency ω+Ω. After feedback it passes again through the AO cell and gets diffracted again to give ω+2Ω in the first order, in a direction in which the laser beam was propagating before the Q-switch. Now, the two signals at ω and ω+2Ω will give a mode beat at 2Ω with a maximum modulation depth if both signals have similar intensities. On observation of the mode-locked resembling Q-switched pulses obtained in our experiment, we found that the separation between individual pulses within the Q-switched envelope is about 18–20 ns (measurement limited by detection system), which corresponds to mode beat at 50–55.5 MHz. The RF wave applied to the Q-switch in our case was 27.12 MHz, and corresponds to 2Ω=54.24 MHz, which matches with the observed beat frequency. As the angular separation between the zeroeth and the first order (frequency shifted) diffracted beams are rather small, such a mixing of zeroeth order and first order diffracted beams can occur due to the mirror near the Q-switch, which was meant for providing feedback using the first order diffracted beam. If we now look at the mode-locked type of pulses reported by Myslinski, et. al , the separation between pulses within the Q-switched envelope is about 6.25 ns, which corresponds to mode beat at 160 MHz, and in their report the AO modulator induced round-trip frequency shift is also 160 MHz. Since they have not specified the position of the feedback mirror in their experiment, it might be possible that during the ‘careful adjustment of feedback mirror’, feedback occurred from both the zeroeth and the first order diffracted beams, leading to the formation of mode-locked resembling pulses, as in our case. Further, in our experiments, we could change the modulation depth by changing the ratio of feed back from the first and the zeroeth order beams by means of slight adjustment of the mirror alignment. This further confirms the proposition of mode-beating. Thus, our experimental observations, as well as observations by Myslinski, et. al. , could be explained with the above proposition. This identifies the physical phenomenon responsible for the occurrence of mode-locked resembling pulses within the Q-switched pulse envelope, and is attributed to mode-beating between the round-trip frequency-shifted beam at ω+2Ω and the original (un-deviated) beam at ω.
In conclusion, we have experimentally investigated the output pulse characteristics of Q-switched Yb-doped fiber laser. Different pulse shapes were observed by varying the modulation window ON- and OFF-time, pump power and mirror position in the same experimental set-up. It has been found that mode-locked resembling pulse shapes and multi-peak structured Q-switched pulse shapes observed by us, and also by several researchers in rare earth doped fiber lasers, is not because of the generation of ‘simultaneously Q-switched and mode-locked pulses’ that occurs in other solid-state lasers wherein simultaneous Q-switched and mode-locked pulses have pulse-durations and separations corresponding to their bandwidths. We have provided a new insight to the generation of multi-pulse, multi-peak (or split pulse), and mode-locked resembling pulses in the output of Q-switched fiber lasers. Occurrence of nonlinear effects like SBS and SRS have been shown to cause multi-peak structure in the case of Q-switched fiber lasers; the mode beating between round-trip frequency-shifted beam at ω+2Ω from the AO Q-switch and the original (un-deviated) beam at ω, has been shown to cause the mode-locked resembling output pulses. Thus, in order to achieve single peak Q-switched pulses, modulation window-time, pump power and mirror position has to be optimized to avoid any intra-cavity nonlinear interactions, mode beating and multi-pulse appearance.
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