A high power passively Q-switched dual wavelength Yb fiber laser using a Cr4+:YAG saturable absorber has been realized. Two wavelengths centered at 1040 nm and 1070 nm are generated directly from the cladding pumped Yb doped fiber laser. The pulse trains exhibit regions of stability and instability dependent on the pump power. At a pump power of 7.8 W, 1040 nm and 1070 nm pulses are generated alternatively, with pulse durations of 105 ns, pulse-repetition rates of 32 KHz and average pulse energies of 56 μJ and 47 μJ, respectively. A theoretical model is developed to simulate the two-wavelength Q-switched operation, which gives qualitative agreement with the experimental observations.
© 2008 Optical Society of America
Recently there has been considerable interest in studying Yb doped fiber lasers because of their beneficial properties for a number of applications. With a small quantum defect, Yb doped fiber lasers are suitable for high power operation with reduced thermal loading. The relatively long upper-state lifetime of Yb enables more efficient pumping from a given diode pump source and storage of a large amount of energy which is of benefit for Q-switching operation. A number of actively and passively Q-switched double-clad Yb fiber lasers have been reported to date [1-6]. The emission spectrum of Yb is also broad which allows wide wavelength tuning or multi-wavelength lasing. Recently a few multi or two-wavelength Yb doped fiber lasers have been demonstrated, with different configurations for the wavelength selection and stabilization. These include the use of spatial mode beating in multimode fiber , a few-mode fiber Bragg grating (FBG) together with polarization control working as a filter , dual frequency generation using the birefringence of a polarization-maintaining (PM) FBG , dual wavelength operation using a FBG stabilized by four wave mixing , and a Mach–Zehnder interferometer (MZI) operating as a comb filter . All the above lasers operated in the CW region. In many cases, pulsed lasers operating at high peak power are of interest for applications such as laser micromaching and laser sensing. Hu et. al.  reported a dual wavelength nanosecond Yb doped fiber laser based on the mechanism of stimulated Brillouin scattering (SBS) induced self-Q-switching. The two wavelengths 1109.6 nm and 1127.6 nm were reportedly due to the birefringence in the fiber and the pulse energy was relatively low (~nJ) in this case. In this paper we present a high power multi-μJ two-wavelength passively Q-switched Yb fiber laser based on a Cr4+:YAG saturable absorber (SA). The two wavelengths centered at 1040 nm and 1070 nm were generated without using any spectral control mechanism and arise from the natural peaks in the net gain curve. A theoretical model is developed and the resultant simulations could explain the two-wavelength operation reasonably well.
2. Experimental setup
The laser configuration is shown in Fig. 1. A Yb doped single-mode double-clad fiber with a length of ~1.9 m was used as a gain medium. The fiber core/inner cladding diameters (numerical aperture NA) were 10/125 μm (0.08/0.46). Cladding absorption at 976 nm was approximately 6.5 dB/meter. The pump laser was a fiber coupled diode laser with a center wavelength of 976 nm. The Pump light was coupled into the active fiber by two collimating lenses L1, L2 and a dichroic mirror (DM) with >96% transmission at 976 nm and >99% reflectance at 1030-1100 nm. End-caps were put onto both ends of the fiber to avoid unnecessary reflection and damage. A broadband high-reflection (HR) mirror at the left side and a mirror with 4% reflection on the right side were used as a rear mirror and an output coupler, respectively. Lenses 3 and 4 were used to focus the laser through the SA (T0=30% at 1064 nm) with a focal spot diameter of ~15 μm. A diffraction grating (1180 g/mm) was used for spectral separation of the laser output. To detect the dynamics of the two wavelength output two fast photodiodes were placed at a distance of ~2 m from the grating where the spectrum displayed two well separated peaks. Each photodiode was centered on the corresponding peak and connected to a two channel digital oscilloscope.
3. Experimental results
The gain and absorption spectra of Yb fiber are shown in Fig. 2. During operation two output wavelength components were observed as shown in Fig. 3. The dependency of the average output power at 1040 nm and 1070 nm and the total output power on pump power was measured with a power meter and is shown in Fig. 4. Two-wavelength emissions appeared when the pump power was 3.5 W or higher; below this power, only one output wavelength at 1040 nm existed. The spectral positions of two-wavelength peaks were stable with pump power, with a minor shift of the short wavelength peak from 1040 nm to 1042 nm when the pump power increased up to 9.9 W. A total output power of 4.2 W was obtained at a pump power of 9.9 W, with a slope efficiency of 44%. The ratio of average power at the two wavelengths was determined by measuring the two beams in the first diffraction order from the grating. As can be seen in the figure, the 1040 nm power at first increased with the pump power; reached a maximum at a pump power of 7.8 W and then decreased. The 1070 nm output increased steadily with the pump power.
At a pump power of 4.5 W, the pulse trains for both wavelengths exhibited a period-doubled behavior; a big-small 1040 nm pulse pattern was accompanied with a big-small 1070 nm pulse pattern, as shown in Fig. 5(a). The average powers for 1040 nm and 1070 nm were 1.4 W and 0.4 W; and pulse durations (Fig. 5(b)) were about 100 ns and 300 ns, respectively. At this pump power, the 1040 nm emission dominates in the wavelength competition, experiencing higher gain, and achieving higher pulse energy and shorter pulse duration. As also can be seen in Fig. 5(b), the 1070 nm pulse was ~500 ns later than 1040 nm pulse.
With an increase in pump power, the output at 1070 nm increased significantly; the big-small and big-small pulse patterns became unstable and changed to big-small small-big patterns for the two wavelengths respectively: a strong 1040 nm pulse was accompanied with a weak 1070 nm pulse, and vice versa. At a pump power of 7.8 W, the weak pulse almost disappeared in the pattern and the two-wavelength pulses appeared alternatively. The 1040 nm pulse train still exhibited period-doubled shape and the 1070 nm pulse train was stable, as shown in Fig. 6(a). Average outputs of 1.8 W and 1.5 W have been obtained for 1040 nm and 1070 nm, with a pulse repetition rate of 32 KHz and average pulse energies of 56 μJ and 47 μJ. Considering their same pulse durations of 105 ns, the peak powers of two wavelengths pulses were 533 W and 448 W, respectively. At this pump power, the two wavelengths achieved a balance in competition in gain and dominated alternatively with every second pulse. With further increase in the pump power, the output at 1070 nm increased further and the pulse pattern became more complicated. A new stable pattern was formed at a pump power of ~9.9 W; in this case period-2 for 1040 nm and period-6 for 1070 nm output was observed, as shown in Fig. 6(b). The dual wavelength operation also depended on fiber length;longer fibers would lase primarily around 1070 nm while shorter fibers would lase around 1040 nm. However similar behavior was observed for fibers with approximate lengths from ~1.6 m to ~2.0 m.
4. Theoretical analysis and discussions
Yb doped fiber lasers have a very broad emission spectrum from approximately 970 nm to 1200 nm. In the case of homogenous broadened medium, the wavelength with the highest net gain will build up the quickest and deplete the inversion number thus suppressing the gain for other wavelengths. However Q-switching is not a static process; the gain for each wavelength is changing with time as well as the position along the fiber. To understand this behaviour, we have theoretically simulated the Q-switched operation using a multi-wavelength model. For Yb doped double clad fiber, the equations are :
where N0 is the total Yb dopant concentration (Provided by LIEKKI); N1 and N2 are ground and excited number densities. Pp - represents the backward propagating pump power.Pk ±are the forward and backward propagating laser radiation. k is a spectral index allowing multiple simultaneous wavelengths to grow and interact within the laser cavity. To simulate the behaviour observed experimentally only the two wavelengths at 1040 nm and 1070 nm were chosen and retained in order to explore the system dynamics. σαp, σep, σαk, σek are the absorption and emission cross sections of Yb ion at pump wavelength and each emission wavelength, respectively (shown in Fig. 2). The pump (emission) and fiber core overlap factors Γp(s) were calculated with Gaussian shape assumption for signal waves. For the spontaneous emission bandwidth we have used Δλk=30 nm for each of the two components.The fiber refractive index was set as n=1.5 and the pump and emission group velocities vp and vk were both set to c/n, where c is the speed of light in vacuum. h is the plank constant, τ is the lifetime of Yb, and αp(k) is the fiber attenuation at pump (emission) wavelength.
For Cr4+:YAG SA, we have used a point model :
where Nsa is the total ion doping, N1 sa and N2 sa are the ground and excited level number intensities; Tk(t) is the instantaneous two way transmission of the SA, and σgsa, σesa are the ground-state and excited-state-absorption cross sections, respectively. Lsa is the thickness of the SA (~4.5 mm). Asa is the focal spot area on the SA; τsa is the lifetime of the excited state. Nsa was calculated based on Lsa, initial transmission T0=30% and σgsa=4.3×10-18 cm2  at 1064 nm. T0 was measured to be 26% at 1040 nm and 35% at 1070 nm, so σgsa can be estimated at the two wavelengths. For the ratio of σgsa/σesa, we have used 6 and 4 for 1040nm and 1070 nm as approximate values . Because the SA is relatively thick and the focused beam was not uniform in the SA; the positions far from the focal spot may not be well saturated and thus would contribute towards the non-saturable loss rather than acting as a saturable absorber. In the simulation we have used Lsa=3.5 mm and an averaged focal spot diameter dsa=70 μm to represent the central region of SA where the saturation is expected. The above equations are solved under the boundary conditions given by:
where P0 is the pump power, L is the fiber length, Roc=0.04 is the reflectivity of the output coupler, η is the loss at the high reflector end ( ~15% one way) due to the non-saturable loss of the saturable absorber, Fresnel reflection from the end-cap, coating loss and lens coupling loss, etc.. The values of parameters used in simulation are shown in Table 1.
The simulation results show that the two emission wavelengths can co-exist in the Q-switched operation; the ratio of the power between two wavelengths depended on the fiber length and pump power; long fibers and higher pump will favour 1070 nm radiation. We have fixed the fiber length L=190 cm and investigated the Q-switching characteristics at different pump powers, which are shown in Fig. 7(a-f). At a pump power of 5 W, the 1040 nm dominates in the output, achieving much higher peak power (~560 W compared with ~5 W).With an increase of pump power to 8 W, the 1070 nm wavelengths observes higher gain and starts to induce instabilities to the pulse train: An alternative big-small pulse pattern starts to be evident. At a pump power of 11 W, the weak pulse almost disappears in the big-small pattern, and the two wavelengths appear alternatively, which is similar to the experimental results shown in Fig. 6(a). With further increase to a pump power to 18 W, the pulse intensities return to constant values; the 1070 nm wavelength dominates the output and achieves higher peak power (~580 W compared with ~115 W for 1040 nm). The time delay of 1070 nm pulse to 1040 nm pulse is shown in Fig. 7(b) and 7(f). The output at 1040 nm precedes the output at 1070 nm similar to that in Fig. 5(b).
Since the Yb ion inversion number is changing with time and position in the fiber, we can define a position averaged inversion number density as:
The two-way signal gain (loss) for each wavelength with fiber and SA at an instantaneous time can be estimated as:
With a relatively larger σe, there is higher gain at 1040 nm when N̲2(t) is higher; also with much smaller σα, the lasing threshold for1070 nm is lower: N̲2 th 1070<N̲2 th 1040. Thus there exists a critical value N̲2 c above which g1040nm>g1070nm and below which g1070nm> g1040nm. At an early stage of each pulse when N̲2(t) is its maximum (N̲2 0), g1040nm> g1070nm; the 1040 nm wavelength pulse can build up and bleach the SA more quickly, and lead to emission at 1040 nm early in time. With the decrease of N̲2(t) throughout the pulse to N̲2 c, higher gain is observed at 1070 nm sometime later during the pulse. With lower threshold, the 1070 nm wavelength continues to see gain even after the 1040 nm wavelength is no longer amplified.Thus the 1070 nm pulse can deplete N̲2(t) to a deeper final level N̲2 f, which explains why the 1070 nm pulse could lase well after 1040nm pulse, as shown in Fig. 5(b) and Fig. 7(b, f). Fig. 8 shows an example of how the inversion number along the length of fiber changes during the stages discussed above for a pump power of 18 W; the times t1 to t6 are defined in Fig. 7(f). As shown in the figure, the gain drops below threshold at t3 and t4 for 1040 nm and 1070 nm wavelengths respectively. In the period of time from t5 to t6 the 1070 nm laser pulse continues to deplete the inversion number after the 1040 nm pulse has finished. If we increase the fiber length without changing other parameters, the overall inversion number will be distributed over a longer fiber. Thus N̲2 0 will decrease and the 1070 nm emission will dominate sooner. If the fiber is long enough then N̲2 0 drops below N̲2 th 1040, and the 1040 nm emission will completely disappear.
The situation is further complicated by the recovery time and spectral characteristics of the saturable absorber. At a low pump power, the pulse repetition rate is low and the time period between pulses is long; so the saturable absorber recovers to its thermal equilibrium state between pulses. Thus N̲2 0 is high to overcome the large initial absorption in the saturable absorber and the 1040 nm wavelength dominates in each pulse. At a high pump power, the pulse separation time and the recovery time for saturable absorber is short, thus N̲2 0 is lower in order to reach the switching threshold, and emission at 1070 nm wavelength will become stronger. The 1040 nm (1070 nm) pulse will dominate only when the pump power is very low (high). For a medium pump power, the two wavelengths both see net gain; they dominate in the output alternatively and big-small pulse patterns are observed. Fig. 9 shows the dynamics of g1040(t), g1070(t), N̲2(t) and N̲2 sa with the 1040 nm and 1070 nm output pulses at a pump power of 11W. As can be seen in the figure, after a stronger 1070 nm pulse, the inversion number is depleted to a deeper level. It takes longer time for the pump to restore the inversion number. At the same time the saturable absorber has more time to recover and N̲2 sa reaches a lower value for the start of the next pulse. Thus N̲2 0 will be higher for the next pulse and the 1040 nm wavelength will dominate. After the strong 1040 nm pulse the inversion number is not depleted so deeply and the time to buildup to the next pulse time is shorter, thus 1070 nm will dominate in turn for next pulse. So the two wavelengths dominate alternatively as shown in Fig. 6(a) and Fig. 7(d). In the figures, there is a longer time period between pulses after a 1070 nm pulse compared to after a 1040 nm pulse, which also agrees with the above explanation. Figure 10 shows an expanded view of the details of the changes in g1040(t),g1070(t) within the time duration of the pulses themselves. As depicted in Fig. 9 g1040(t) becomes higher than g1070(t) sometime preceding the pulses and then drops below g1070(t) sometimes during the pulse. For the 1070 nm dominated case shown in Fig. 10(a), the 1070 nm output overcomes 1040 nm output all the time during the pulse, although g1040(t) is slightly higher than g1070(t) during a relatively short period.
The above modeling and discussion can explain the coexistence of the two peak wavelengths, with longer fibers and higher pump powers favoring 1070 nm output, as well, the pulse instabilities such as the two wavelengths lasing alternatively in the pulse train.However we have not reproduced all the pulse patterns in the experiment, such as big-small and big-small pattern for the two wavelengths respectively in Fig. 5(a) and period-6 behaviors in Fig. 6(b). In a passive Q-switched laser, pulse instabilities due to nonlinear dynamics have been reported and investigated recently [18-20]. In , a period-doubled route to chaotic pulse trains have been observed in a passively Q-switched Nd:YAG laser operating under specific cavity configurations and pump powers. The nonlinear behavior arose from including the rapid relaxation between levels in the lower manifold. In the modeling, in addition to the two-level model for the Nd ion that was conventionally used, the authors included splitting of the ground level with a relaxation lifetime of ~30 ns (compared to an upper level lifetime of ~230 μs). The period-doubling to chaotic pulse shapes could be observed in the simulation under certain pump conditions. Fig. 11 shows the Yb ion energy levels in a fiber involved in the lasing output around 1050 nm. The upper and lower manifolds include three and four stark shifted levels, respectively. The 1040 nm and 1070 nm output radiation correspond to transitions from the bottom of upper level to two different sublevels of the lower manifold.Due to the strong broadening of Yb ions in glass at room temperature, the transitions between the sublevels are not fully resolved . A complete simulation of two wavelength operation would require a more advanced model, in which transitions between the sublevels should be considered, and will be the subject of future work.
A high power two-wavelength passively Q-switched Yb doped fiber laser has been demonstrated with a very simple cavity configuration. Single transverse mode output at 1040 nm and 1070 nm was obtained with tens of micro-joule pulse energies and hundred nanosecond pulse durations. The two-wavelength generation can be achieved for particular configurations where the effective net gains seen by both wavelengths are comparable and is dependent on fiber length, pump power and cavity Q. A theoretical simulation model qualitatively explains the dynamics of the two wavelengths behavior observed in the experiment indicating that longer fibers and higher pump powers favor 1070 nm laser output and reproduces the pulse pattern where two wavelength pulses alternate at an intermediate pump power. A more advanced model will be required to obtain more quantitative agreement with the details observed in the experiment.
Financial support from MPB Technologies Inc. and the Natural Sciences and Engineering Research Council is gratefully acknowledged.
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