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In this paper, we propose hybrid-pumped resonant gain-switched thulium fiber lasers to realize high-average-power and high-pulse-energy 2-μm laser emissions. Based on numerical simulation, laser dynamics (pulse peak power, pulse energy, pulse duration, etc.) of this kind of laser system are investigated in detail. By taking advantages of the 793 nm continuous wave pump and the 1900 nm pulsed pump, performance of the laser emission can be significantly improved, with the highest average power of 28 W, peak power of 3.5 kW, pulse energy of 281 μJ, and narrowest pulse duration of 92 ns, all of which can be further optimized through designing the cavity parameters and the pumping circumstance. Compared with the pump pulses, two times improvement in pulse energy and average power has been achieved. This hybrid resonant gain-switched system has an all-fiber configuration and high efficiency (low heat load), and can be steadily extended into the cladding pump scheme, thus paving a new way to realize high power (>100 W average power) and high pulse energy (>1 mJ) 2 μm thulium fiber lasers.
© 2015 Optical Society of America
1. Introduction
Owing to the spectral overlap with the absorption peaks of several major molecules in air (e.g., H2O, CO2), ~2-μm laser sources are now playing a more and more important role, and have been applied in various areas, such as remote sensing, light detection, industry, military and medical treatment [1–6]. In addition, they are also excellent pump sources for 2.4 μm solid state lasers [7] and 3-5 μm optical parametric oscillators. For achieving high-power 2-μm laser emission, fiber lasers are found to be much more preferable to solid-state bulk lasers due to lesser requirement of thermal management (large surface-to-volume ratio of fibers), more robustness, high beam quality, and etc. Tm-doped fiber lasers (TDFLs) have been generally adopted and are good candidates to obtain high power 2-μm laser emission owing to the advantages of high quantum efficiency, broad emission band, and easy availability of high-power 793-nm pump sources (AlGaAs laser diodes) [8]. Taking advantage of the ‘two-for-one’ cross relaxation process [9–11], TDFLs can operate with quantum efficiency larger than unity, and have achieved over 1 kilowatts output power from a single fiber oscillator [12].
To realize pulsed operation of 2-μm fiber lasers, gain-switching is a good and efficient alterative and has stimulated extensive researches in recent years [10, 13–22]. In addition to all the general advantages of fiber lasers, gain-switched fiber lasers have their own specific virtues. Unlike the traditional Q-switching method, gain-switching doesn’t need any intra-cavity modulation components, thus can provide all-fiber configurations. Another outstanding advantage of gain-switched fiber lasers is that nearly all the laser emission characteristics can be actively controlled through tuning the switching seed source, thereby rendering this kind of system high flexibility and controllability.
During the development process, 2-μm gain-switched TDFLs have achieved ~10 mJ pulse energy [14, 15], 4 kW peak power [18], and ~10 ns pulse duration [16]. Furthermore, the spectral bandwidth of gain-switched TDFLs can also be narrowed to less than 1 nm by integrating fiber Bragg gratings (FBGs) to the laser cavity [18]. In the conventional operations, gain-switched TDFLs usually suffer from output pulse relaxation instability and comparatively low average power. Through introducing fast gain-switching [16], the output pulsing instability can be effectively solved. For achieving high average output power, we have previously proposed hybrid-pumped gain-switched technique and have augmented the output power to over 10 W [18]. While over 80% slope efficiency has been achieved from a singly pulse-pumped resonant gain-switched fiber laser [17], the seed pulse energy put a limit on the achievable output pulse energy.
In this Letter, we propose a new hybrid resonant gain-switched 2-μm thulium fiber laser through combining a high power 793 nm continuous wave (CW) pump source and a high power 1900 nm pulsed pump source. Theoretical simulation shows that this system possesses the advantages of both hybrid gain-switched lasers (high average output) and resonant pumped lasers (high efficiency). Under the help of the CW pump, 15 W of 1900 nm pulsed pump source can stimulate ~28 W pulsed laser emission at 2 μm with a slope efficiency of >90%. Pulsing dynamics including pulse peak power, pulse energy and pulse width, are investigated in detail, and the influence of the pulse duration and repetition rate of the pump pulse on the output characteristics is also observed. A rational pump range associating the tolerable pump level of the CW source and the pulsed seed source is established and in deep analyzed. In operation, peak power >3 kW, pulse energy >28 μJ, and pulse width <100 ns can be steadily achieved. This high power, high pulse energy, ~100 ns 2-μm fiber laser system show great improvement compared with the previous reports, and can provide an all-fiber configuration. Furthermore, this hybrid resonant gain-switched concept can be steadily extended into the cladding pumping situation with fiber combiners, thus provide great potential for average power and pulse energy scaling of 2-μm fiber lasers.
2. Theoretical modeling
The system of our proposed theoretical model is shown in Fig. 1. We combine a 793 nm CW laser diode (LD), and a 1900 nm pulsed TDFL, as a hybrid-entity to pump the 2μm TDFL. With the aid of the 793 nm CW pump, the stimulated Tm-doped fiber (population inverted) first acts as a power amplifier to amplify the 1900 nm pulse source (pulse energy). Then (nearly the same time), the amplified 1900 nm pulses will be absorbed by the Tm fiber and function as a gain-switch to switch on and off the 2 μm TDFL, thus achieving 2 μm pulse output. A pair of fiber Bragg gratings (FBGs) at 2020 nm is used to select the oscillating wavelength and improve the cavity gain.
Different from traditional fiber amplifiers [23, 24], where seed pulse is only amplified, the 1900 nm seed pulse here is not only amplified by the gain fiber but also performs as a switch to temporally/periodically tune the gain of the fiber. The addition of the 793nm CW pump helps to reduce the lasing threshold and raise the output average power, peak power and single pulse energy. Another advantage of this system is that the Tm gain fiber is a double-cladding large mode area fiber, which not only facilitates high launch power but also mitigates nonlinear effects incurred by high pump intensity.
2.1 Rate equation model
According to the proposed system in Fig. 1, two pump transitions of 3H6 → 3F4 and 3H6 → 3H4 are included in our model, although there are many other pump options (such as 1064 nm, 1090 nm, 1.5 μm, etc. [25].) for TDFLs to achieve 2 μm laser emissions.
The simplified energy diagram of Tm3+ ions and all involved transitions are demonstrated in Fig. 2. The dash lines are used to separate the processes related to the two different pump transitions, and different color arrows represent different physical processes. The dark blue, light blue, black, green and red are the pump transition, excited-state absorption, cross relaxation(CR) and energy transfer upconversion (ETU), non-radiative decay, and the 2 μm stimulated emission, respectively.
Based on Fig. 2, the rate equations that govern the population transfer can be expressed as [25]
CR1 and CR2 are the cross relaxation processes included in the 793nm pumping and are governed by N is the ion concentration of the Tm3+ cations. N1, N2, N3, N4 are the population densities on the energy level 3H6, 3F4, 3H5, and 3H4, respectively. W14 is the stimulated absorption coefficient of the pump. W34 is the ESA coefficient of the laser from 3H5 to 3H4 [7]. W12 and W21 are the stimulated absorption and emission rates of the pump and laser emission. k1242, k1232, k2124, k2123 are the CR and ETU coefficients. τ2, τ3 and τ4 are the energy-level life-times of 3F4, 3H5, 3H6, respectively. βij are the branch ratios from level i to level j.The stimulated absorption and emission coefficients can be written as follows:
where σ14, σ21, σ34 are absorption and emission cross sections. λpi and λs are the central wavelength of pump and laser. h is the Planck constant. c is the light velocity in vacuum. Pf,r1 and Pf,r2 represent the forward direction and reverse direction pump power of the LD and TDFL, respectively. Sf,r are the optical powers of the laser. The subscript f and r represent the forward propagation direction and backward propagation direction. LD pump is a kind of cladding pump with the filling factor Γpclad, which is defined as Γpclad = Acore/Aclad, where Acore and Aclad are the area of the fiber core and clad, respectively. As for the core pump, the filling factor Γp or the filling factor of laser Γs can be deduced by the follow function [26, 27] where rc is the radius of the fiber core.2.2 Optical power propagation equations
Complete description of laser behavior in fibers should include equations for the beam propagation and amplification as follows
Note that the positive sign relates to the forward ( + z) direction and negative sign to the reverse (-z) propagating direction. vg = c/n is the group velocity in the fiber, and n is index of refraction of silica fiber. αpi and αs are intrinsic losses of the host glass at each pump and laser wavelengths. ΔλASE is the bandwidth of the amplified spontaneous emission (ASE) [13].
The pump radiations are subject to the boundary conditions:
Rp1i, Rp2i are input and output reflectivities of the fiber Bragg gratings for each pump, respectively. Pfi are launched pump power into the fiber for each pump.The intracavity laser field is subject to the boundary conditions:
Rs1, Rs2 are reflectivities related to the laser wavelength. L is the length of the gain fiber.2.3 Simulation process
The parameters adopted in the simulation are listed in Table 1. The thulium gain fiber (25/400μm, NA = 0.09) is a step-index double clad fiber with thulium ion doping concentration of ~4wt.%. The fiber length used is 3.08 m. The 793nm LD is continuous wave, while the 1900 nm TDFL is a pulse source. In the simulation, the numerical method is basically the finite difference in time-domain (FDTD) method. Time step size and space step size in our simulation are 0.1 ns and 0.02 m, respectively. The populations of each level at a specific moment and position are determined by the populations at this position but in the previous moment. The optical power at a specific moment and position is determined by the populations of the energy levels at this moment and position, the optical power at this moment but previous position, and the optical power at this position but in the previous moment. Such calculations proceed first along the positive direction and then along the negative direction, iteratively. After many times of iterations, the solution will converge to a stable value, and consequently the information (population inversion, pump power, laser power, etc.) at each position and each moment is obtained.
Table 1. Constants Employed in the Numerical Simulation
3. Numerical results and discussion
We first set the repetition rate of the 1900 nm pump source to 100 kHz and pulse width to 100 ns (with the duty ratio of 1%), which will be changed thereafter (the last simulation). Under various combinations of the 793 nm CW pump and the 1900 nm pulse pump, the 2-μm output dynamics together with the population evolution of the upper laser level (N2) are shown in Fig. 3. When the two pumps are both at a low level, e.g., set the power of 1900 nm to 5 W and that of 793 nm to zero, there will be a ‘pulse missing’ during every two pumping periods [Fig. 3(a)]. This is because that when only the pulse pump (at a low level) is adopted (set the 793 nm CW pump to zero), the upper-laser-level population (ULP) will decrease after each pulse excitation due to both radiative and non-radiative relaxations. After emitting a huge laser pulse, the ULP cannot be excited to above the laser threshold by the next pump pulse. Only after two pump pulses excitation, the ULP is raised to a high enough level to trigger the next laser pulse.
Fig. 3 Temporal dynamics of the 2-μm laser (blue line), 1900 nm pump (green line) and the population density of the upper laser level (red line) for 793 nm pump power of (a) 0 W, (b) 10 W and (c) 30 W. The pulsed pump at 1900 nm has an average power level of 5 W, repetition rate of 100 kHz, and pulse width of 100 ns.
The situation will be completely different when the 793 nm CW pump source is employed to compensate the ULP relaxations, as shown in Fig. 3(b) with 10-W 793 nm pump power. In this case, the ULP increases instead of decreases between two adjacent pump pulses, leading to a high population inversion level before the arrival of the next pump pulse. Consequently, every 1900 nm pump pulse is strong enough to improve the ULP above laser threshold, thus trigger a sole laser pulse. This is denoted as the ‘single pulsing’ regime, i.e. one output laser pulse per pump period. The addition of 793 nm CW pump can significantly reduce the threshold of the hybrid gain-switched TDFL, but it can also lead to problems when its power is too high. With 30 W of 793 nm pump, the output result is shown in Fig. 3(c). In each exciting period, another small pulse appears except for the main pulse. Such additional/satellite pulses were defined as ‘trailing spikes’ [13]. The emergence of the ‘trailing spike’ is due to that the ULP is increased to above laser threshold by the 793 nm pump between two adjacent pump pulses. Therefore, more trailing spikes will appear if the 793 nm pump is further increased. These trailing spikes will deplete the stored energy (consumed a lot of inverse population) before the generation of the next main laser pulse, thereby will not only damages the waveform, changes the repetition frequency, but also reduces the peak power of the laser pulse, and ultimately decrease the laser efficiency.
We also simulated the process with only the 1900 nm pulse pump source, and found that simply improving the pulse pump power to over 16 W can effectively address the ‘pulse missing’ problem thus achieve stable 2-μm pulsing output (not shown here). The evolution of both the output and the population inversion is very similar to that of Fig. 3. However, a 16-W pump source at 1900 nm with peak power of 1.6 kW is itself a complicated system and challenge demanding.
For a certain given 1900 nm pump power, there is a ‘limitation range’ for the 793nm CW pump, only within which the laser output lies in the single pulsing regime. When the 793 nm CW pump is too high (low), the laser will transit to the trailing spike (pulse missing) state. As shown in Fig. 4, this limitation range for the 793nm CW pump steadily increases with the 1900 nm pulse pump power. Therefore, excellent single pulsing regime can be maintained under the combination of both high pumping at 793 nm and 1900 nm. This gives rise to great potential for achieving high power 2 μm pulse laser output with such kind of hybrid resonant gain-switched scheme. In Fig. 4, the deviation of the data points from the fitting lines is due to that we determine the stable pulsing state (observe the simulated output pulse shape) through increasing/decreasing the both pump sources by 1 W. This comparatively large changing step size of the pump power leads to certain amount of error. This also accounts for the situation in Fig. 9.
Within the single pulsing region, we calculate various laser output characteristics including average power, pulse width, peak power and single pulse energy, and the results are shown in Figs. 5 and 6. As shown in Fig. 5, fixing either the 1900 nm pump or the 793 nm pump, the average laser output power increases linearly with the other pump power (793 nm or the 1900 nm pump). Under 15 W 1900 nm and 28 W 793 nm pump, the maximum average output power is ~28 W. For a given 793 nm pump [Fig. 5(a)], the slope efficiency of laser output is about 92% with respect to the 1900 nm pump. If we fix the 1900 nm pump power, the laser slope efficiency is about 53% with respect to the 793nm pump. This difference in slope efficiency can be easily understood providing that the quantum efficiency for the 793 nm (1900 nm) pump transition is ~39.3% (~94%). In fact, the 53% slope efficiency is still very high (considering the low quantum efficiency of the 793 nm pump), which can be attributed to the ‘two-for-one’ cross relaxation process [9–11].
Fig. 5 Average out power of the hybrid gain-switched fiber laser under various combinations of the 793 nm CW pump and the 1900 nm pulse pump.
Fig. 6 Output laser pulse characteristics of the hybrid gain-switched fiber laser versus the 793 nm CW pump under several 1900 nm pump levels.
As shown in Fig. 6(a), increasing the pump power of, 793 nm and/or 1900 nm, will reduce the output laser pulse width from >1 μs to ~100 ns. With increasing 1900 nm pump power, the 793 nm pump dependence of the pulse width will weakens, and pulse width less than 100 ns (~92 ns) can be obtained under the pump combination of 15 W of 1900 nm and 28 W of 793 nm. Under various 1900 nm pump powers, both pulse peak power and single pulse energy increase with the 793 nm pump. The maximum pulse peak power and pulse energy are ~3 kW and 281 μJ, respectively. Considering the 1900 nm pump pulse (100 ns) has an average power of 15 W, peak power of 1.5 kW, and pulse energy of 150 μJ, our hybrid gain-switched fiber laser can improve the average power, peak power and single pulse energy nearly twice. In fact, further increasing both the 793 nm pump and the 1900 nm pump can produce even higher average power, peak power and pulse energy of 2 μm laser pulses.
When we fix the 793 nm pump and also fix the power and repetition rate of the 1900 nm pump, while change the pulse width of the 1900 nm pump, the output dynamics are shown in Fig. 7. The output pulse shows nearly no difference when the pump pulse width is changed from 10 ns to 100 ns, being ~312 ns and 311 ns, respectively. The output pulse width increases, however, when the pump pulse width is broadened to 2 μs [Fig. 7(c)] and beyond. At 2 μs pump width, the laser pulse width increases to ~326 ns. When the pump pulse width is large, at the instant of the laser pulse emitting, the fiber still absorbs the pump pulse thus leads to successive accumulation of population inversion. Consequently, the over-threshold population inversion will occupy a longer time period, thereby leading to broadened output laser pulses (decrease of the peak power). It is clear there is tolerable pulse duration for the 1900 nm pump pulse. When the pump pulse width is smaller than 2 μs (or equals 2 μs), stable single pulsing regime can be achieved. However, when the pump pulse width is increased to 4 μs and beyond the output pulses has trailing spikes, and under CW pumping (1900 nm) the laser transits to CW mode after a short period of relaxation oscillation. On the other hand, too narrow pump pulses (<10 ns) will induce strong nonlinearity in the fiber by themselves [30]. Based on calculation with the equation from [31], it is found that 28 W (10 ns) 1900-nm pulse pump (corresponding to peak power of 28 kW) will trigger stimulated Raman scattering.
Fig. 7 Laser output characteristics of the hybrid gain-switched fiber laser under 10 W 793 nm pump and with 1900 nm pump power of 5W (100 kHz) in pulse width of (a) 10 ns, (b) 100 ns, (c) 2 μs, (d) 4 μs and (e) CW mode.
The repetition rate of the 1900 nm pump pulse also has significant influence on the laser output dynamics of the hybrid gain-switched fiber laser. When the repetition rate of the 1900 nm pump is increased to 200 kHz (the pulse width of the pump is still 100 ns), the output pulse characteristics are shown in Fig. 8. Compared with the results obtained with the 100 kHz pump [Figs. 5 and 6], higher pump pulse repetition rate (200 kHz) will lead to a much larger pump tolerable range, thus giving a much higher output average power. However, higher pump pulse repetition rates give rise to obvious decrease in pulse energy and peak power while increase the laser pulse width.
Fig. 8 Output characteristics of the hybrid gain-switched fiber laser when the 1900 nm pump source has repetition rate of 200 kHz.
In fact (based on the above analysis), the pump repetition rate has important role in the output laser dynamics and the limitation range for the single pulsing regime. The tolerable pump combination behavior under several pump pulse repetition rates are shown in Fig. 9.
Increasing the pump pulse repetition rate can effectively expand the 793nm pump range and also the maximum pump power, thus leading to higher output average power. This can be well explained based on Fig. 3(b). When the pump repetition rate decreases, the time interval between two adjacent pump pulses broadens, and there is more time for the ULP to increase. Therefore, it is much easier for the CW pump to cause the ‘trailing spike’, thus the maximum tolerable CW pump power (in the single pulsing regime) will decrease. Conversely, while the repetition rate rises, the time between two adjacent pump pulses becomes smaller. Therefore, higher 793 nm CW power is required to compensate the depletion of population inversion, thus promoting the tolerable CW pump power to a very high level. In the case of higher pumping repetition rate of the 1900 nm (keep its average power constant), the single pump pulse energy will be reduced in every pump period. To avoid the ‘pulse missing’ problem, more CW pump is needed to promote the population inversion, so the minimum of the rational pump at 793nm increases a lot under higher pumping rates (the red dashed line).
4. Conclusion
We propose a hybrid resonant gain-switched 2 μm fiber laser and theoretical analyze (based on the FDTD method) its output dynamics under various pumping circumstances. By combining a 793 nm CW pump and a 1900 nm pulse pump, this laser system can produce high average laser power (tens of watts) with high pulse-transformation efficiency (>90% efficiency from the 1900 nm pulses to the 2 μm laser pulse). This will open a new way to achieve high power 2 μm pulsed laser sources with very low heat load.
In such hybrid gain-switched systems, there exists a pump limitation range, where the CW pump and the 1900 nm pulse pump should increase all together to improve the 2 μm pulse output. Too high or too low pumping at either the 1900 nm pump or the 793 nm CW pump will lead to the laser departing from the stable single pulsing regime, transiting to the trailing spike state or the pulse missing mode. Under the 15 W 1900 nm and 28 W 793 nm pump combination, the maximum 2 μm average output power is ~28 W. The laser pulse width, peak power, and single pulse energy can be effectively tuned through changing either the 793nm or the 1900nm pump source. In the current simulation, the maximum pulse energy, peak power and the narrowest pulse width are 281 μJ, ~3 kW and 92 ns, respectively, all of which can be further improved. In addition, the 1900 nm pump pulse has a limitation in the pulse width, which is approximately within the 10 ns→2 μs range. Too broad (>2μs) pump pulse will cause trailing spikes while too narrow (<10 ns) pump pulse can induce strong nonlinear effects. Increasing the pump pulse repetition rate has a compromise between improving the output average power and decreasing the pulse energy (peak power) and broadening the pulse width.
The pump tolerable range can be further increased through changing the pump pulse’s repetition rate, and all the output pulsing dynamics can also be further optimized through optimization of relevant pumping parameters. In all, this kind of hybrid resonant gain-switched 2 μm fiber laser can produce high average power, high peak power (several kilo watts), high pulse energy (hundreds of micro-joules) nanosecond laser emissions, which can find wide applications in various areas.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61138006, 61275136, and 11121504) and the Research Fund for the Doctoral Program of Higher Education of China (No. 20120073120085).
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