1. Introduction

Interest in pulsed 3 µm, diode pumped lasers is driven primarily by material processing, medical and environmental applications, spectroscopy and laser technology in general [1,2].

In erbium-doped materials, the most efficient 3 µm laser operation on ⁴I_11/2 → ⁴I_13/2 luminescent transitions, see Fig. 1, is achieved under direct, resonant pumping into the upper-state [3]. The biggest drawback of this simple pump-lase scheme is that the lifetime of the bottom laser level is much longer than that of the upper one, which makes laser action self-terminating and inefficient [4–6]. This limitation can be abated by speeding up the de-population of the bottom laser level and can be achieved with two different methods.

 

Fig. 1 Energy levels in Er:YLF, after [5]. Solid arrows denote absorption and laser transitions. Dashed arrows denote energy transfer processes. Broken, arrows denote heat generating non-radiative decay. Also listed on the right are the lifetimes of the levels involved in numerical simulations.

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The first method makes use of high erbium concentration in laser materials to intensify energy transfer up-conversion (ETU) process which depopulates the lower laser level ⁴I_31/2. The majority of the reported CW and Q-switched lasers used this approach [7–9]. However, high Er-doping brings its own issues: (i) deterioration of thermo-optic properties of the host materials, and (ii) inevitable heating of the laser media. These factors reduce the power scaling potential of this pump-lase scheme, though, several attempts were made to optimize erbium concentration to mitigate these drawbacks and increase laser efficiency [10,11].

The second approach enables 3 µm + 1.6 µm cascade lasing: ⁴I_11/2 → ⁴I_13/2 → ⁴I_15/2 [12], which de-populates ⁴I_13/2 much faster than ETU and spontaneous decay do. Contrary to the first method, high Er-concentration is detrimental to the ⁴I_13/2 →⁴I_15/2 lasing at 1.6 µm because (i) the stronger ground state absorption (GSA) increases its threshold and (ii) the same ETU now depopulates the upper laser level for the ⁴I_13/2 → ⁴I_15/2 transition. Thus, any meaningful implementation of the cascade requires low Er³⁺ content.

The main advantage of cascade schemes with low Er-concentration is in the considerable reduction in heating of the laser media and preservation of their thermo-optic parameters. The obvious drawbacks are relatively weak pump absorption and more complex laser design.

To the best of our knowledge, the 3 + 1.6 µm cascade lasing scheme in Er-doped materials was first suggested in [10] and was implemented in several free running lasers, including those performed at cryogenic temperatures [13–16].

Even more complex, the 3-wavelength cascade process, involving additional 1.7 µm lasing from the ⁴S_3/2 level was demonstrated in Er-doped fibers [17]. This process can benefit 3 um lasing in the Q-switched mode, by re-populating its upper laser ⁴I_11/2 level.

However, as far as we know, there were no reported studies of the cascade lasing in the Q-switched mode in any Er-doped crystalline laser media. Q-switching with 3 µm + 2.1 µm cascade was demonstrated in Ho-doped ZBLAN fiber laser [18]. The laser output consisted of a combination of 3 µm Q-switched and 2.1 µm gain-switched pulses.

In this work we numerically analyzed the impact of the cascade mechanism on the 3 µm, Q-switched lasing and performed the first experimental demonstration using Er:YLF in a dual-cavity setup. We showed that the 1.7 µm lasing helps to increase energy stored in the upper level for the 3 µm transition. The 1.6 µm cascade lasing, manifests itself as gain-switched lasing, increases the average power of the 3 µm, Q-switched operation, but does not affect its pulse energy. Both 1.6 and 1.7 µm cascade lasing reduce heating of the laser media.

2. Energy transfer processes and modeling of cascade lasing

We performed numerical modeling of the Q-switched, cascade operation using Er:LiYF₄ (Er:YLF) as an example of laser gain medium. Among the variety of Er-doped materials used to obtain 1.6, 1.7 and 2.6 – 3 µm lasing, we selected this particular crystal for two reasons. First, it happened to be the most studied laser material in this wavelength range with the majority of material and spectroscopic properties, such as, emission and absorption cross-sections, ETU and CR rates, etc. readily available in the literature [2,5,19–25]. Secondly, its ⁴I_11/2 radiation lifetime, ~4.8 msec [21], is long enough to provide adequate energy storage for Q-switched operation. Figure 1 shows an energy level scheme of Er:YLF from its ground state ⁴I_15/2 (level 0) up to the energy level ⁴F_7/2 (level 6). The energy level ²H_11/2 is thermally coupled with the ⁴S_3/2 and in the modeling we considered both as one level (level 5). This figure also shows all the radiative (solid arrows) and non-radiative (dashed and broken arrows) processes that were accounted for in the numerical model.

The most important non-radiative process, affecting both 1.6 and 3 um lasing is ETU₁: (⁴I_13/2 + ⁴I_13/2) → (⁴I_15/2 + ⁴I_9/2) with the rate of W₁₁.

The next process is ETU₂: (⁴I_11/2 + ⁴I_11/2) → (⁴I_15/2 + ⁴F_7/2). The ⁴F_7/2 rapidly decays to the ⁴S_3/2 energy level, so its population can be equaled to zero and attributed to the ⁴S_3/2. The exited state absorption (ESA) at the pump wavelengths λ_P acts with ETU₂ in tandem, de-populating the ⁴I_11/2 level. However, for the λ_P ~972 nm ESA is weak [7] and may be ignored.

The last important process is cross-relaxation CR₁: (⁴S_3/2 → ⁴I_9/2) + (⁴I_15/2 → ⁴I_13/2). It strongly depends on the Er³⁺concentration, and for the Er-doping exceeding 10%, it becomes the dominant process of depopulating the ⁴S_3/2 level.

The ⁴I_11/2 population loss of can be partially recovered by recycling the energy intermittently stored in ⁴S_3/2 back via ⁴S_3/2 → ⁴I_9/2 lasing at 1.7 µm. Without this important process, only a smaller amount of this intermittently stored energy will reach ⁴I_11/2.

We solved a system of rate equations [5] which describe the kinetics of the primary energy levels of Er³⁺ as well as photon densities corresponding to three laser transitions in the Er:YLF cascade laser: the ⁴I_11/2 → ⁴I_13/2, ⁴I_13/2 → ⁴I_15/2 and the ⁴S_3/2 → ⁴I_9/2 (at the 2.6 - 2.8, 1.62 and the 1.73 µm correspondingly).

Taking into account that the lifetimes of ⁴F_9/2 and ⁴I_9/2 (microseconds) are much shorter than those of ⁴S_3/2, ⁴I_11/2 and ⁴I_13/2 levels, and both of them quickly feed the ⁴I_11/2, we can consider their populations, N₃ and N₄ equal to zero. As a result, we reduced the total number of rate equations to just six - three for the population densities N_i (i = 1, 2, 5) and three equations for the photon densities φ_2.8, φ_1.7 and φ_1.6 at 2.8, 1.7 and 1.6 µm wavelengths:

Here we used the following notations:

The numerical values of the parameters used in simulations are listed in Table 1.

Table 1. Selected Er(1%):YLF parameters used in numerical simulations.

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The system of Eqs. (1) – (10) was solved using the Bulirsch-Stoer algorithm for stiff ordinary differential equations. In the first step, we suggested that during pumping (regime of energy accumulation at the ⁴I_11/2 level), the laser cavity for the 2.8 µm emission has a high loss and the photon density φ_2.8 could be initially set to zero.

However, if a free running laser operation at 1.7 µm and 1.6 µm is allowed by designing a laser cavity with a low loss at these wavelengths, then the photon densities φ_1.7 and φ_1.6 could grow with pumping.

For the 2.8 µm ⁴I_11/2 → ⁴I_13/2 transition, the stored energy $E_{2.8}^{ST}$ is given by Eq. (11) [26]:

3. Simulations results

Figure 2 shows how populations of the laser levels: ⁴S_3/2, ⁴I_11/2 and ⁴I_13/2, as well as the coefficient of amplification α_2.8, change in the pre-Q-switch, energy accumulation stage, when the cavity loss is high and the 2.8 µm lasing is not possible. Here we can compare two distinctive cases: (i) - when the cavity loss is high for all 3 lasing wavelengths of interest, and (ii) - when the loss is high only for the 2.8 µm lasing, while the loss for 1.62 and 1.73 µm lasing is low.

 

Fig. 2 Population dynamics of the ⁴I_11/2, ⁴I_13/2, and ⁴S_3/2 levels, top row, (in red, blue and green correspondingly). Dynamics of the coefficient of amplification α_2.8 is shown in the bottom row. Frames (a) & (b) represent the case of high cavity loss for all 3 wavelengths. Frames (c) & (d) represent the case of high cavity loss only for the 2.8 µm emission, while lasing at the 1.73 and 1.62 µm wavelengths is allowed. Cavity parameters: R_1.6 = 0.99, R_1.7 = 0.97, G_1.6 = G_1.7 = 0.033, L_CR = 15 mm, Pump = 80W.

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One can see that in the case of high losses for all 3 wavelengths, the coefficient of amplification of the 2.8 µm transition α_2.8 reaches its maximum of 0.85 cm⁻¹, with about 1 msec delay after pumping began, long before the ⁴I_11/2 lifetime expires, see Fig. 2(b).

But when 1.73 µm lasing is enabled, then the 2.8 µm amplification reaches its maximum much later, at ~1.9 msec, see Fig. 2(d), and at the 30% higher magnitude of 1.1 cm⁻¹. Thus, enabling 1.73 um lasing leads to larger stored energy in the ⁴I_11/2 level and should result in higher energy per pulse for Q-switched operation at the 2.8 µm. The reason for this effect is that the 1.7 µm lasing on the ⁴S_3/2 - ⁴I_9/2 transition, followed by the fast ⁴I_9/2 → ⁴I_11/2 decay, populates the upper laser level ⁴I_11/2 of the 2.8 µm laser much faster than it would be populated by CR₁ alone, in the absence of 1.7 µm lasing. The speed of depopulation of the ⁴I_11/2 level, however, remains approximately the same for both cases. Eventually, α_2.8 gain saturates and stays almost constant, see Fig. 2(d). Therefore, for the Q-switching at the 2.8 um, it is meaningless to extend pump pulsewidth beyond a certain timeframe, which of course varies with pump power, but typically remains noticeably shorter than the ⁴I_11/2 luminescent lifetime (~4.8 msec). In other words, longer pump pulses do not lead to increase in the output pulse energy, but only contribute to the heating of the laser gain media.

Knowing the coefficient of amplification, we can now calculate the expected Q-switched pulse energy using Eqs. (11) - (14), see the results in Fig. 3. Predictably, the Q-switched pulse energy follows the behavior of the coefficient of amplification.

 

Fig. 3 Simulation of the 2.8 µm pulse energy vs time at different pump powers. (a) 2.8 µm lasing only; (b) 2.8 µm lasing with 1.6 + 1.7 µm cascade.. Cavity parameters: R_1.6 = 0.99, R_1.7 = 0.97, G_1.6 = G_1.7 = 0.033, L_CR = 15 mm.

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When the 2.8 µm gain reaches its maximum, the Q-switch modulator sharply lowers the 2.8 µm cavity loss and the process of the pulse build up begins. It is described by Eqs. (1) – (6) where initial conditions come from the final set of values N₁, N₂, N₅ and φ_2.8, φ_1.7 and φ_1.6, calculated for the last moment of the pre-Q-switch stage. We assumed that the Q-switch operates in a step function manner and the cavity loss remained low only for 5 µsec.

Figure 4 shows the simulated development of the Q-switched and gain-switched pulses at the 2.8 and 1.6 µm correspondingly. The first pulse instantaneously populates ⁴I_13/2 level and creates conditions for the development of the giant, gain-switched pulse at 1.62 μm. It appears a few microseconds later (16 µsec for the particular 80 W pump power). The gain-switched pulse, in its turn, empties the ⁴I_13/2 much faster than ETU₁ does, creating preferable conditions for the next 2.8 μm Q-switch pulse faster as well. As a result, with the 2.8 + 1.6 µm cascade lasing, the 2.8 μm Q-switching can operate at a higher pulse repetition rate.

 

Fig. 4 Simulation of the Q-switched + Gain-switched, ⁴I_11/2 → ⁴I_13/2 → ⁴I_15/2 cascade lasing at the 2.8 and 1.62 µm wavelengths. Cavity parameters: R_1.6 = 0.99, R_1.7 = 0.97, R_2.8 = 0.8, G_1.6 = G_1.7 = 0.033, L_CR = 15 mm, Pump = 80W.

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4. Experimental setup

Until now, the reported 3 + 1.6 µm and 1.7 + 3 + 1.6 µm cascade lasers used a single-cavity design where all three lasing channels shared the same optical path between cavity mirrors, thus, the spatial overlap was automatically achieved, see Fig. 5(a). Fiber lasers belong to this category too. However, a Q-switched laser with cascade requires spatial separation of the 3 µm laser channel/arm from the 1.6 and 1.7 µm arm outside the gain media. This split-channel or dual-cavity design, where both channels overlap only inside the active media, ensures that the Q-switching in the 3 µm arm does not affect cavity loss in the other channel. In other words, when the loss in the ‘3 µm’ cavity is high, the lasing on the 1.6 and 1.7 µm transitions is still possible. An example of such a split-channel optical layout, where 3 and 1.6 + 1.7 µm arms are separated by an intracavity dichroic mirror is shown in Fig. 5(b). This setup requires tighter alignment to provide spatial overlap between 1.6 + 1.7 and 3 um cavity’s arms, which is not automatic anymore.

 

Fig. 5 Simplified schematics of (a) single-cavity and (b) spilt-channel cascade lasers.

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To validate our numerical model we implemented this new, split-channel cavity layout, which more detailed schematic is depicted in Fig. 6.

 

Fig. 6 Er:YLF cascade laser experimental layout. Spectral overlap of the pump emission and Er:YLF absorption is pictured on the left. Pump spectrum was measured with Yokogawa Optical Spectrum Analyzer 3624 and Er:YLF π-absorption spectrum was collected with Cary 600 spectrometer (resolution 0.5 nm).

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A 15 mm long Er(1%):YLF rectangular slab (3 x 6 mm cross-section) was clamped between two copper, water cooled plates (T_WATER = 16 C^O). The crystal was cut to have its c-axis normal to the optical axis of the crystal. It was end-pumped by a fiber coupled laser diode module (90 W at the 971 nm). The pump was delivered into the crystal using a dichroically coated mirror DCM1 and a pair of collimating and focusing (f = 150 mm) spherical lenses. Spectral matching of the pump and Er:YLF π-polarized absorption was not ideal, as can be seen in Fig. 6(inset). By placing a power meter behind the cavity high reflector HR_LAS (HR at 1.6 + 2.8 um, AR at 971 nm) we directly measured that only half of pump was absorbed in a single pass. An unabsorbed portion of pump, that left the cavity was reflected back by a concave mirror HR2 with the radius of curvature R_CC = 300 mm. After accounting for all transmission and reflection losses, we conservatively estimated that the total pump absorption was about 70%.

Another dichroically coated mirror DCM2 splits the cavity into the two channels – for 1.6 + 1.7 and 2.8 µm. Both arms shared the same flat, dichroically coated high reflector HR_LAS. Both cavity arms had the same length ~240 mm and the same radii of curvature of their respective output couplers (OCi) – 250 mm. However, the reflectivity of the OC2 in the arm2 was 99% at the 1.62 µm wavelength and 97% for the 1.73 µm, while the reflectivity of the OC1 (in arm1) was 80% at the 2.8 µm. Such low output coupling in the 1.6 µm channel was chosen intentionally in order to minimize the lasing threshold. No attempts were made to optimize OC1 reflectivity neither in the QCW or Q-switched modes of operation

5. Experimental results

The Er:YLF crystal was first pumped by the fiber coupled laser diode module producing 10 msec long pulses with 20% duty cycle. When losses were low for 2.8 and 1.6 + 1.7 µm cavity channels, a free running QCW cascade lasing was observed with expected performance, see Fig. 7. At the 12W QCW pump power, lasing on the ⁴I_11/2 → ⁴I_13/2 transitions began with less than a hundred microseconds delay, see Fig. 7(a), indicating that the threshold was low.

 

Fig. 7 Er(1%):YLF cascade laser performance in the free running, QCW operation. (a) – Oscilloscope traces of pump (grey), 2.8 µm (red) and 1.62 µm lasing (blue). (b) – Wavelength resolved cascade laser output vs the absorbed pump. Inset shows output spectrum consisting of the 2.66, 2.72 and 2.81 µm lines. Δt_PUMP = 10 msec, PRF = 20 Hz.

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After about 1.75 milliseconds, cascade lasing was observed on the ⁴I_13/2 → ⁴I_15/2 transition at 1.62 µm. Its boosting impact on 2.8 um was clearly visible in Fig. 7. Similar laser behavior was first reported in [12].

The relatively low slope efficiency of the 2.8 µm lasing could be explained by the high transmission loss introduced by DCM2 (~8% per pass) and un-optimized output coupling provided by OC1.

The spectrum of the QCW laser output consisted of 3 laser lines - 2.66, 2.72 and 2.81 µm, see the inset in Fig. 7(b), as was observed in [27]. A study of the time resolved spectral behavior was outside the scope of this paper.

In the free running mode we did not observe any lasing at 1.73 µm. Indeed, its upper laser level ⁴S_3/2 can be populated only by the ETU₂ process, which depends on the population of the ⁴I_11/2. CW lasing at the 2.8 µm keeps the population of the ⁴I_11/2 at the (low) threshold level, denying the “supply” to ⁴S_3/2 and keeping its population below threshold for 1.72 µm lasing.

In the pre-Q-switched stage, a high loss in the 2.8 µm arm prevents lasing on the ⁴I_11/2 → ⁴I_13/2 transition. As a result, the population of the ⁴I_11/2 is not “clamped” any more and it keeps increasing with pump until either Q-switching occurs or it reaches some stationary value. As the population of the ⁴I_11/2 grows, so does the population of the ⁴S_3/2 until it reaches a threshold value for lasing on the ⁴S_3/2 → ⁴I_9/2 transition at 1.73 µm.

As a Q-switch device, we used a simple mechanical modulator - a fast rotating disk with a slit, similar to that described in [28]. When it was inserted into the 2.8 µm arm of the cavity, we observed the following behavior of the Q-switched cascade laser, see Fig. 8. The 1.73 µm lasing began with about 450 µsec delay and lasted until the Q-switching at 2.8 µm interrupted it sharply. Within 10 to 20 µsec after the appearance of the 2.8 µm pulse, a gain-switched pulse at the 1.62 µm followed.

 

Fig. 8 Er(1%):YLF cascade laser performance (1.6 + 1.7 + 2.8 µm) in the Q-switched mode. Shown are the oscilloscope traces of the pump (grey), 2.8 µm (red), 1.73 µm (green) and 1.62 µm lasing (blue). Pump pulsewidth Δt_PUMP = 1.25 msec, PRF = 160 Hz. Inset shows 1.62 and 1.73 µm laser spectral lines.

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As we expected, fast de-population of the ⁴I_11/2 by Q-switching instantly “chokes” the ETU₂ process and ends the 1.73 um lasing. The “giant” 1.6 µm pulse depletes the lower level for the ⁴I_11/2 → ⁴I_13/2 laser transition at the 2.8 µm, restoring the above threshold condition faster for the next Q-switching event.

When the 1.6 + 1.7 µm arm of the cavity was blocked, preventing the cascade lasing, the energy per pulse at the 2.81 µm dropped by about 20%.

A significant mechanical jitter of the Q-switch modulator prevented us from making precise measurements of output power. However the goal of this work was to demonstrate a concept of the cascade-assisted Q-switch lasing in Er-doped crystalline material. The existing setup could be considerably improved by using a more stable and much faster Electro- or Acousto-optical Q-switching in lieu of an unstable mechanical one. Output coupler should be optimized and dichroic coatings should be improved as well.

One of the most important factors influencing cascade laser is Erbium doping concentration, which should be a subject of the future performance optimization.

6. Conclusions

We modeled a Q-switched operation at the 2.8 µm, assisted by cascade lasing at the 1.6 and 1.7 µm, in Er(1%):YLF. We showed that enabling CW lasing at the 1.7 µm, in the pre-Q-switch energy accumulation stage, not only reduces heating of the laser media, but also boosts the inversed population of the ⁴I_11/2 → ⁴I_13/2 laser transition, and increases output energy of the 2.8 µm pulses. A gain-switched, cascade operation at the 1.62 µm also reduces heating. However, while it does not affect the Q-switched pulse energy, it provides faster de-population of the ⁴I_13/2 level and enables the 2.8 µm Q-switching at a higher repetition rate, i.e. increases its average output power. The first 2.8 µm Q-switched laser with cascade, based on Er-doped crystalline material, was experimentally demonstrated in a dual-cavity setup. We found that cascade operation in Er(1%):YLF increased energy per pulse by 20-25%.