1. Introduction

Currently, there exists a need for high-power coherent light sources operating in the mid-infrared region (MIR) of the electromagnetic spectrum, between 2 – 5 μm, to address a plethora of applications [1]. To this extent, rare-earth-doped zirconium and indium fluoride-based (ZrF₄ and InF₃) glass fiber lasers have become interesting candidates for specific MIR applications given their power scalability, near-diffraction-limited beam quality, ruggedness and small footprint design. Beyond 3 μm, three rare-earths have shown impressive continuous-wave (CW) output power in fluoride fiber architectures: a record power of 10.1 W was demonstrated in Dy³⁺-doped ZrF₄ (Dy³⁺:ZrF₄) at 3.24 μm [2], 5.6 W in Er³⁺:ZrF₄ at 3.55 μm [3] and nearly 200 mW in Ho³⁺:InF₃ at 3.92 μm [4]. Among these transitions, the 3.5 μm transition in Er³⁺:ZrF₄ has gathered interest for polymer processing [5] and remote sensing of methane [6], both of which rely on resonant excitation of the C-H vibrational bond located between 3.3-3.5 μm.

Efficient laser emission at 3.5 μm in Er³⁺:ZrF₄ was enabled by the advent of the dual-wavelength pumping (DWP) scheme proposed by Henderson-Sapir et al. [7]. As shown in Fig. 1, DWP uses a 976 nm pump to populate the long-lived ⁴I${ }_{11/2}$ state, which serves as a virtual ground-state (VGS) from which the ions are pumped at 1976 nm to the ⁴F${ }_{9/2}$ state, the upper-level of the 3.5 μm transition. Since the pioneering demonstration of Henderson-Sapir et al. [7], DWP has been successfully used to produce 5.6 W of CW output power in a monolithic Er³⁺:ZrF₄ all-fiber laser at 3.55 μm [3] and to demonstrate some of the widest reported tunability from a fiber laser, i.e. from 3.33 μm to 3.78 μm [8]. More recently, Q-switched, gain-switched and mode-locked operation in DWP 3.4 μm fiber lasers have also been demonstrated, although modest performances were achieved [9–11]. Finally, in order to gain insight into the dynamics of the laser system and to further its optimization, numerical models for both CW and pulsed operation of DWP 3.5 μm fiber lasers have been developed and spectroscopic investigations of the DWP Er³⁺:ZrF₄ system were conducted [12–14]. However, the role of the Er³⁺ concentration on the efficiency of DWP 3.5 μm fiber lasers has not been extensively studied given all demonstrations have used either 1 mol% or 1.5 mol% Er³⁺-doped ZrF₄ fibers, yet 10 mol% Er³⁺-doped fibers are commercially available [15]. Moreover, although Luo et al. have simulated 3.5 μm laser emission in 10 mm long 6 mol% doped Er³⁺:ZBLAN waveguides [16], their modeling results did not consider the deleterious effect of quenching (VESA in Fig. 1) [13] and was not aimed towards power scaling of DWP 3.5 μm class fiber lasers.

 

Fig. 1 Energy level diagram of the Er³⁺:ZrF₄ system with relevant processes for 3.42 μm laser emission through DWP. The lifetimes of the different energy levels are given on the right. GSA, ground-state absorption at 976 nm; ESA, excited-state absorption at 976 nm; VGSA, virtual ground-state absorption at 1976 nm; VESA, virtual excited-state absorption at 1976 nm; W_ij, ion-pair ET process; MPR, multiphonon relaxation. Circled numbers indicate the progression of the ions during the excitation trapping mechanism detailed in section 4.3.

Download Full Size | PDF

In the present work, we investigate the laser emission capabilities of a 7 mol% Er³⁺:ZrF₄ fiber laser emitting at 3.42 μm. Bounded by two intracore fiber Bragg gratings and core-pumped in contra-propagation at 1976 nm, the monolithic cavity emits a maximum output power of 3.4 W with no sign of output power quenching and achieves a record efficiency of nearly 39 % with respect to the launched 1976 nm pump power. Through numerical modeling, we demonstrate that the high Er³⁺ concentration enhances ion-pair energy transfer processes to prevent quenching. We also simulate the power scaling capabilities of 1 mol%, 4 mol% and 7 mol% Er³⁺:ZrF₄ fiber laser cavities. Moreover, we report on the formation of a periodic luminescent grating upon DWP within the core of the 7 mol% Er³⁺:ZrF₄ fiber. The grating remained visible without deterioration over time under 1976 nm core pumping after the 976 nm pump was removed. We demonstrate that the period of this grating is consistent with the transverse mode-beating associated with the 1976 nm core pump and show through numerical modeling that the grating’s luminescent maxima are caused by trapped excitation within the metastable energy levels of the Er³⁺:ZrF₄ system. Finally, our experimental investigation also shows the occurrence of output power bistability of the fiber laser.

2. Experimental setup

The schematic of the DWP 3.42 μm monolithic Er³⁺:ZrF₄ fiber laser is depicted in Fig. 2. The laser cavity is made of a 2.5 m long segment of double-clad 7 mol% Er³⁺:ZrF₄ fiber manufactured by Le Verre Fluoré. The fiber core has a diameter of 15 μm along with a numerical aperture ($N{A}_{\text{core}}$) of 0.126, ensuring single-mode operation above 2.5 μm. Coated with a low-index fluoroacrylate to enable multimode light guidance, the fiber cladding has a circular diameter of 260 μm and is truncated by two parallel flats separated by 240 μm.

 

Fig. 2 Schematic of the DWP monolithic 7 mol% Er³⁺:ZrF₄ fiber laser cavity at 3.42 μm. L₁ - L₂, 12.7 mm plano-convex aspheric ZnSe lenses; M₁, gold mirror; DM₁ – DM₂, dichroic mirrors transmitting at 976 nm and 3.4 μm and reflecting at 1976 nm; RCPS, residual cladding pump stripper; BD, beam dump; L₃, f=25.4 mm convex lens; LD, multimode 976 nm laser diode.

Download Full Size | PDF

Similarly as in [3], the fiber laser cavity was bounded by a pair of intracore fiber Bragg gratings (FBGs) photo-inscribed through the active fiber’s polymer coating with 800 nm femtosecond pulses using the phase-mask technique [17, 18]. Figure 3(a) presents the transmission spectra of both the high-reflectivity (HR) and low-reflectivity (LR) FBGs characterized with a 0.2 nm resolution in the 3415 – 3435 nm region while Fig. 3(b) presents the broadband HR-FBG’s transmission from 1800 nm to 3400 nm. The narrow HR-FBG was written using a uniform pitch phase mask and was stabilized through thermal annealing for 5 minutes at 80 °C. This resulted in a peak reflectivity of >96 % (limited by the noise level of the characterization setup) at 3424.3 nm along with a full-width at half maximum (FWHM) of 2.1 nm. The HR-FBG possesses scattering losses of around 1.4 dB at the laser wavelength of 3425 nm, as estimated through its transmission value at 3435 nm, hence indicating partial type-II (damage) modification of the Er³⁺:ZrF₄ core [19]. This fact is further supported by the high transmission losses of the HR-FBG in the NIR as shown in Fig. 3(b). This grating can therefore not support co-pumping [3], given it would induce 3.7 dB of losses at the 1976 nm core pump wavelength. In order to ensure a good spectral overlap with the narrow HR-FBG, a broad LR-FBG was written with a chirped phase mask and had a reflectivity of around 55 % at 3425 nm along with a FWHM of 5.3 nm. It was stabilized through thermal annealing for 5 minutes at 70 °C. The low out of band losses (< 0.1 dB) of the LR-FBG enable it to support core-pumping at 1976 nm.

 

Fig. 3 (a) Transmission spectra around 3425 nm of the HR and LR-FBGs measured with a 0.2 nm resolution and (b) broadband transmission spectrum of the HR-FBG from 1800 to 3400 nm.

Download Full Size | PDF

As shown in Fig. 2, the DWP scheme was implemented by injecting the 1976 nm light in the core of the Er³⁺:ZrF₄ fiber at the output end of the laser cavity (counter-directional) while the 976 nm light was injected in its cladding at the entrance of the cavity (co-directional). Both the 1976 nm and 976 nm pump sources are identical to the ones used in [3]. Injection into the core of the Er³⁺:ZrF₄ fiber was achieved with a set of 12.7 mm ZnSe plano-convex aspheric lenses (L₁ and L₂), a gold mirror (M₁) and a 45 ° dichroic mirror (DM₁) having a high reflectivity at 1976 nm and high transmission around 3.42 μm. The 976 nm pump was injected into the cladding using a standard 25.4 mm convex lens (L₃). In order to protect the 976 nm laser diode (LD) from the residual counter-propagating pump at 1976 nm, a dichroic mirror (DM₂) was placed between L₃ and the entrance of the Er³⁺:ZrF₄ fiber cavity to redirect the 1976 nm pump in a beam dump (BD). The Er³⁺:ZrF₄ fiber cavity was passively cooled on an aluminum plate and the FBGs were fixed with adhesive copper tape. A residual cladding pump stripper (RCPS), made by applying high-index UV-cured polymer on the bare Er³⁺:ZrF₄ fiber, was placed at the output of the cavity to filter out the 976 nm pump. Finally, the output fiber tip was cleaved at a 7 ° angle to prevent parasitic lasing at around 2.8 μm on the ⁴I${ }_{11/2} w{ }^4$I${ }_{13/2}$ transition.

The output power at 3.42 μm was collected and measured after the DM₁ with a thermopile power detector (Gentec-EO, UP19K-30H-H5-D0). A monochromator (Digikrom, DK480) equipped with a liquid nitrogen cooled InSb detector (Judson, J10DM204-R01M-60) covering the 1.5-5.5 μm spectral range was used to analyze the laser’s spectrum. The slits of the monochromator were adjusted to a 0.2 nm resolution.

3. Numerical modeling

Modeling, based on the numerical model and algorithm detailed in [13], was used to validate experimental results and gain insight into the kinetics of the energy level populations. Figure 1 presents the partial energy level diagram, adapted from [13], of the Er³⁺:ZrF₄ system with relevant optical transitions, ion-pair energy transfers (ETs) and energy level lifetimes. Laser emission at 3.42 μm on the ⁴F${ }_{9/2} \to { }^4$I${ }_{9/2}$ transition is excited when resonant ground-state absorption (GSA, ⁴I${ }_{15/2} \to { }^4$I${ }_{11/2}$) at 976 nm and resonant virtual-ground-state absorption (VGSA, ⁴I${ }_{11/2} \to { }^4$F${ }_{9/2}$) at 1976 nm simultaneously occur. Excited-state absorption (ESA, ⁴I${ }_{11/2} \to { }^4$F${ }_{7/2}$) at 976 nm and virtual-excited-state absorption (VESA, ⁴F${ }_{9/2} \to { }^4$F${ }_{7/2}$) at 1976 nm are parasitic upconversion processes. While VESA is non-resonant, it was experimentally and numerically demonstrated to induce quenching of the output power of 1 mol% DWP 3.4 μm fiber lasers in both CW and pulsed operation regimes [3, 10, 13]. The differention-pair ETs occurring in the Er³⁺:ZrF₄ system are represented by their respective W_ij parameter, where i and j represent the initial levels of the two ions participating in the ET. Finally, MPR stands for multiphonon relaxation which occurs between closely spaced energy levels.

The numerical model used in the present work uses identical spectroscopic parameters, i.e. cross-sections, lifetimes and branching ratios, to those reported in [3, 13]. As for the ET parameters W_ij, the strongly interacting (SI) values reported in [14] for different Er³⁺ molar concentrations were used and are presented in Table 1. In order to achieve a good agreement with experimental results, a value of $0.28\times {10}^{-26}$ m² was used as absorption cross-section for the VESA process in the modeling. The effective reflectivity of the HR-FBG as seen by the 3.42 μm light, taking into account scattering losses, was fitted to 85 % while the reflectivity of the LR-FBG was fitted to 50 %. Finally, the fiber was discretized in 200 elements, i.e. 1.25 cm per fiber element, to model adequately the gain distribution in the laser cavity.

Table 1. ET parameters (W_ij) used in the numerical model for different Er³⁺-doping concentrations.

View Table

4. Results and discussion

4.1. Laser performance

The output power of the fiber laser as a function of the launched 1976 nm pump power, for different launched 976 nm pump powers, is exhibited in Fig. 4(a). For pump powers of 1.73 W and 10.4 W at 976 nm and 1976 nm, respectively, a maximum output power of 3.4 W at 3.42 μm was achieved. Further power scaling was limited by the availability of the 1976 nm pump provided by the Tm³⁺:silica fiber laser. The slope efficiency with respect to the launched 1976 nm core pump power is 38.6 % while the overall power conversion efficiency, accounting for both the launched 976 nm and 1976 nm pumps, is around 28 % at maximum output power. These values are slightly higher than the previous efficiency records achieved with a DWP 1 mol% Er³⁺:ZrF₄ monolithic all-fiber laser, i.e. 36.9 % and 26.4 % [3]. Moreover, the threshold of the laser is located at around 1.5 W of launched 1976 nm pump, which is 0.5 W less than that achieved in 1 mol% Er³⁺:ZrF₄ [3]. The cavity’s lower threshold can be attributed to the higher reflectivity of its HR and LR-FBG, i.e. 99 % and 55 %, respectively, compared to those of the 1 mol% Er³⁺:ZrF₄ cavity, i.e. 90 % and 30 %, respectively. Nonetheless, these results clearly indicate that heavily-doped Er³⁺:ZrF₄ fibers are as efficient in producing 3.42 μm laser emission as their lightly-doped counterparts, and that ET processes could benefit laser emission.

 

Fig. 4 (a) Laser output power at 3.42 μm as a function of the launched 1976 nm core pump for different launched 976 nm cladding pump. (b) Laser output power at 3.42 μm as a function of the launched 976 nm cladding pump for different launched 1976 nm core pump. Scattered points represent experimental data while numerical modeling results are given by solid lines.

Download Full Size | PDF

When decreasing the launched 976 nm pump from 1.73 to 0.75 W, the slope efficiency of the laser in Fig. 4(a) is seen to decrease while the threshold of the laser remains constant. Further reducing the 976 nm pump down to 0.42 W not only further reduces the slope efficiency but also increases the threshold of the laser from 1.5 W up to 9 W of launched 1976 nm pump. This behavior is drastically different from the quenching phenomenon that has been reported in low-concentration fibers [3, 13]. In the latter, when decreasing the 976 nm pump, the slope efficiency along with the 1976 nm pump threshold remained fairly constant. However, as the 1976 nm pump power was increased up to a certain point, the 3.4 μm output underwent quenching, i.e. a reduction of the output power. In the case of the heavily-doped-Er³⁺:ZrF₄ fiber laser used in the current work, it was not possible to induce any quenching of the output power. Figure 4(b) presents the 3.42 μm output power of the DWP fiber laser as a function of the launched 976 nm pump power for different launched 1976 nm pump powers. Similar to 1 mol% Er³⁺:ZrF₄ cavities, the 3.42 μm output power shows a steep increase once the 976 nm threshold is reached and then immediately saturates. However, in contrast, the 976 nm pump threshold increases as the 1976 nm pump is decreased. This feature clearly indicates that no quenching occurs in the 7 mol% Er³⁺:ZrF₄ fiber laser since no output power reduction can be expected for increasing 1976 nm pump powers. This can be understood by drawing a vertical line, representative of increasing 3.42 μm output power, in Fig. 4(b) and noticing that the laser curves it intersects always have increasing 1976 nm pump power. The same does not hold for 1 mol% Er³⁺:ZrF₄ cavities for low 976 nm pump powers [3].

 

Fig. 5 Spectrum of the DWP Er³⁺:ZrF₄ fiber laser at different output powers.

Download Full Size | PDF

The output spectrum of the 3.42 μm fiber laser is presented in Fig. 5. At low output powers, the spectrum of the fiber laser coincides with the peak reflectivity of the HR-FBG, i.e. 3424.3 nm. The spectrum’s FWHM is 0.2 nm, i.e. identical to the resolution of the monochromator, hence suggesting that it is narrower in reality. As the output power of the laser is increased, the emission wavelength suddenly shifts by more than a nanometer up to 3425.7 nm due to heating of the fiber and expansion of the FBGs therein. Thermal imaging revealed that the temperature of 7 mol% Er³⁺:ZrF₄ fiber during laser operation was between 40 – 50 °C. Since the HR and LR-FBGs were fixed with an adhesive copper tape, we believe that above a certain temperature the gratings must have moved under the tape, hence accounting for the discrete wavelength shift in Fig. 5. Finally, for output powers of 2.4 and 3.4 W, the spectrum shows signs of symmetric broadening. The origin of this broadening has not been determined, but will be investigated in the future.

4.2. Numerical modeling results and cavity optimization

Numerical modeling results, represented by solid lines, are presented alongside experimental data in Fig. 4(a) and 4(b). Generally, the numerical model is able to reproduce with good accuracy all the features of the experimental laser curves such as slope efficiencies, laser thresholds with respect to the 1976 nm and 976 nm pumps as well as output power saturation above a certain 976 nm pump power. This agreement justifies the use of the numerical model for optimization and to gain insight into the laser’s dynamics.

As discussed above, the high Er³⁺ concentration in the current ZrF₄ fiber is able to prevent quenching of the 3.42 μm output power. To understand this, numerical simulations were run where individual ETs were de-activated. Doing so, it was found that it was only when ET W₅₀ was de-activated that the output power curves of the 7 mol% Er³⁺:ZrF₄ cavity showed quenching and became identical in behavior to the laser curves obtained with 1 mol% Er³⁺:ZrF₄ cavities. As shown in Fig. 1, ET W₅₀, enhanced by the high Er³⁺ concentration, counteracts quenching by effectively redistributing the bottlenecked ions in the (²H${ }_{11/2}$, ⁴S${ }_{3/2}$) levels that were upconverted by VESA.

The numerical model was also used in order to compare the power scaling capabilities of 1, 4 and 7 mol% Er³⁺:ZrF₄ fiber cavities. For this purpose, co-directional pumping at 1976 nm and 976 nm was assumed given that such a pumping scheme enables an all-fiber cavity design such as in [3]. Figure 6 compares the maximum output power, slope efficiency, threshold and heat load at the HR-FBG of the different 3.42 μm fiber lasers as a function of the peak reflectivity of the LR-FBG. In each case, the HR-FBG reflectivity was fixed at 99 % and the launched 1976 nm core pump was 50 W, co-directional with the 976 nm pump. The length of the cavity and the 976 nm cladding pump power were optimized beforehand by verifying that the totality of the launched 1976 nm pump was absorbed when the LR-FBG had a minimal reflectivity of 4 %. It should be noted that shorter fiber lengths and lower 976 nm pump powers could be used when increasing the reflectivity of the LR-FBG, given that more 3.42 μm intracavity light promotes the absorption of the 1976 nm pump. The heat load was calculated by taking into account non-radiative decay from the excited energy levels and by considering exothermic/endothermic heat generated by ETs according to:

In Eq. (1), q is the heat generated per unit length [W m⁻¹], A_c is the area of the active fiber [m²], N_i is the population density in energy level i [m⁻³], ω_i is the non-radiative decay rate of level i [s⁻¹] while E_i is the energy of level i and $\delta E_{ij}$ is the exothermic or endothermic energy associated with ET W_ij, in [J]. The non-radiative decay rates ω_i were taken from [20] while the position of the different energy levels E_i were taken from [21]. Based on these energy levels, the following exothermic/endothermic ET energies were found: $\delta E_{11}=$ 591 cm⁻¹, $\delta E_{22}=$ -214 cm⁻¹, $\delta E_{50}=$ -146 cm⁻¹ and $\delta E_{42}=$ 127 cm⁻¹. Finally, the heat load was calculated at the location of the HR-FBG, i.e. z = 0.

 

Fig. 6 (a) Simulated output power, (b) slope efficiency, (c) threshold and (d) heat load at the HR-FBG as a function of the reflectivity of the LR-FBG of 3.42 μm DWP Er³⁺:ZrF₄ fiber cavities using 1, 4 or 7 mol% Er³⁺ concentrations. The reflectivity of the HR-FBG was fixed at 99 % while the co-directional launched 1976 nm core pump was fixed at 50 W. The 976 nm cladding pump and the cavity’s length were adjusted beforehand for each concentration.

Download Full Size | PDF

From Figs. 6(a) and 6(b), it is clear that similar power scaling can be achieved with 1, 4 and 7 mol% Er³⁺:ZrF₄ fibers. For each simulated concentration, the maximum 3.42 μm output power is around 20 W while the slope efficiency with respect to the 1976 nm pump exceeds 40 %. However, while heavily-doped 3.4 μm cavities possess slightly higher 1976 nm pump thresholds as shown in Fig. 6(c), they offer the significant advantage of requiring less fiber length and less 976 nm cladding pump. Indeed, for both the 4 and 7 mol% Er³⁺:ZrF₄ cavities, less than 3 m of fiber and 5 W of 976 nm cladding pump are required while for the 1 mol% Er³⁺:ZrF₄ cavity, 4 times more fiber and 3 times more cladding pump are needed to achieve similar performances. On the other hand, Fig. 6(d) shows that the heat load experienced by the HR-FBG significantly increases as the Er³⁺ concentration increases. For a LR-FBG reflectivity of 50 %, the heat load in the 1, 4 and 7 mol% cavities are 5, 33 and 69 W m⁻¹, respectively. In each case, the dominant contribution to the heat load is non-radiative relaxation from the ⁴I${ }_{9/2}$ level. This can be understood by noticing that for each 3.42 μm photon that is generated by the cavity, the energy equivalent of a 4.6 μm photon on the ⁴I${ }_{9/2} \to { }^4$I${ }_{11/2}$ level is emitted in the form of phonons (MPR). Since a similar amount of 3.42 μm photons are generated in 1, 4 and 7 mol% Er³⁺:ZrF₄ fibers, it is obvious that heavily-doped fibers possess a higher heat load than lightly-doped fibers given the same total generated heat is spread over a shorter fiber length. This issue clearly indicates that future power scaling of 3.42 μm DWP fiber laser cavities should rely on lightly-doped Er³⁺:ZrF₄ fibers to reduce the heat load on the HR-FBG and ensure the cavity’s stability.

 

Fig. 7 (a) Photograph of the luminescent grating in the core of the Er³⁺:ZrF₄ fiber when only the 1976 nm pump was activated and increased slightly above the excitation trapping threshold ($\approx$ 5 W); no image processing was used to enhance the quality of the picture. (b) Simulated intensity distribution of the 1976 nm pump within the core of the Er³⁺:ZrF₄ fiber.

Download Full Size | PDF

4.3. Mode-beating and excitation trapping

During the laser experiment, a periodic red luminescent grating (LG) was seen within the core of the 7 mol% Er³⁺:ZrF₄ fiber, as shown in Fig. 7(a). For the LG to appear, both the 976 nm and 1976 nm were at first activated and then the 976 nm was turned off. When the 1976 nm core pump was in excess of 5 W of launched power, the LG remained visible and without fading away over time. For lower pump powers at 1976 nm, the LG’s visibility gradually decreased within a time span of a few seconds. Through image analysis, the periodicity of the LG’s dark and bright (red) fringes was evaluated to be around 391 μm.

Given the manufacturer’s specifications of the 7 mol% Er³⁺:ZrF₄ fiber (${\oslash }_{\text{core}}$ = 15 μm, $N{A}_{\text{core}}$ = 0.126 and n_core = 1.49), one finds that the V-number of the fiber core at 1976 nm is 3.005 and that it therefore allows the propagation of the LP₀₁ and LP₁₁ transversal modes, with respective effective indices n₀₁ = 1.49347 and n₁₁ = 1.49096. The simulated intensity profile of the 1976 nm pump inside the Er³⁺:ZrF₄ fiber, considering the propagation of equal amplitude LP₀₁ and LP₁₁ modes, is shown in Fig. 7(b). While the modal beat length between both modes is 785 μm ($\lambda /\left[n_{01}-n_{11}\right]$), the separation between two intensity maxima is 393 μm, i.e. in good agreement with the period of the luminescent grating of Fig. 7(a). It is therefore clear that the LG is related to transverse mode-beating of the 1976 nm core pump and that the bright luminescence is caused by increased 1976 nm pump intensity at the maxima of the mode-beating pattern. Such a LG caused by transverse mode-beating has already been reported in a large-mode area ytterbium-doped rod-type fiber used in the context of high-power amplifiers around 1 μm, although the LG’s period was around a few centimeters due to the smaller effective index difference [22]. Moreover, the LG observed in this current work shows that the 1976 nm pump intensity distribution within the fiber core varies significantly in both the transverse and longitudinal direction. This phenomenon can therefore have a significant impact on the gain characteristics of the 3.4 μm laser transition.

The occurrence of visible luminescence at the maxima of the transverse mode-beating pattern, and its persistence over time, can be explained through numerical modeling. As such, the population rate equations of the different energy levels were solved in the steady-state regime with only the 1976 nm core pump applied. In order to reproduce an initial 976 nm pumping, the initial guess for the energy level populations assumes that a certain fraction of the Er³⁺ions are evenly distributed over the six excited energy levels (⁴I${ }_{13/2}$ up to ⁴F${ }_{7/2}$). It should be noted that the choice of initial guess for the ion distribution did not affect the steady state solution of the rate equations. Figure 8(a) presents the population of the different excited energy levels as a function of the 1976 nm pump intensity. For intensities below 11 MW/cm², a trivial solution is found where all the Er³⁺ ions are in the ground-state. However, once the 1976 nm pump intensity exceeds this threshold, the excited energy levels begin to build-up a significant steady-state population, hence indicating that the 1976 nm pump is able to trap the initial excitation provided by the 976 nm pump.

 

Fig. 8 (a) Normalized population in the excited energy levels of the 7 mol% Er³⁺:ZrF₄ system as a function of the 1976 nm pump intensity. (b) Normalized population inversion on the ⁴F${ }_{9/2}{\to }^4$I${ }_{9/2}$ transition at 3.4μm as a function of the 1976 nm pump intensity for different Er³⁺ concentrations. The colored curves are representative of the color of the fluorescence emitted by their associated levels.

Download Full Size | PDF

We propose that this threshold behavior for excitation trapping, combined with mode-beating, is at the origin of the LG shown in Fig. 7(a). We believe the dark fringes of the LG are regions within the Er³⁺:ZrF₄ fiber core where the 1976 nm core pump intensity is below the excitation trapping threshold and therefore produce no luminescence, while the bright fringes of the LG are regions where the 1976 nm core pump intensity is above the excitation trapping threshold. As a result, these latter regions produce spontaneous visible emission associated with radiative decay from the excited energy levels to the ground-state. Additionally, the model predicts the red color of the LG shown in Fig. 7(a), i.e. when the 1976 nm pump intensity is close to the excitation trapping threshold. Indeed, it is seen in Fig. 8(a) that for pump intensities between the excitation trapping threshold and three times this value, the population of the ⁴F${ }_{9/2}$ energy level, which emits red fluorescence around 655 nm [20], is significantly higher than the population of the (²H${ }_{11/2}$, ⁴S${ }_{3/2}$) levels which emit fluorescence around 550 nm (green). This prediction is further confirmed by analyzing the side fluorescence produced by the fiber shown in Fig. 7(a) with a visible OSA. The main peak of the fluorescence spectrum was centered at 655 nm whereas the peak around 550 nm was significantly ($\approx$ 6 dB) weaker.

Upon further numerical modeling, it was found that by de-activating either VGSA, VESA, W₅₀ or W₁₁ in the model, no excitation trapping could occur and this for any given 1976 nm pump power. As for the other processes, i.e. ESA at 976 nm, W₂₂ and W₄₂, varying their strength would only shift the excitation trapping threshold and affect the ion distribution within the excited energy levels. These results allow us to propose the following excitation trapping mechanism, illustrated with the help of numerical labels in Fig. 1: given an initial population in the ⁴I${ }_{11/2}$ level, the 1976 nm core pump excites the ions successively in the ⁴F${ }_{9/2}$ and the ⁴F${ }_{7/2}$ levels through VGSA (1) and VESA (2), respectively. The ions in the ⁴F${ }_{7/2}$ level then undergo MPR (3) to reach the thermally coupled levels (²H${ }_{11/2}$, ⁴S${ }_{3/2}$). Due to the long lifetime of these levels (530 μs), a significant population can build-up and efficient ET W₅₀ can occur, which promotes the upconversion of ions from the ground state to the ⁴I${ }_{13/2}$ level (4). Finally, the ions in the ⁴I${ }_{13/2}$ level can be upconverted through ET W₁₁ to the ⁴I${ }_{9/2}$ level (5), hence re-entering the 1976 nm pump cycle. Additionally, the threshold intensity for excitation trapping can be seen as the point at which the 1976 nm pump intensity is sufficient to generate a net influx of ions in the ⁴I${ }_{11/2}$ level to balance out the outflux of ions caused by radiative and non-radiative decay, W₂₂ and W₄₂. This net influx of ions is provided by the concurrent effects of VGSA, VESA, W₁₁ and W₅₀ which are driven by the 1976 nm pump.

Figure 8(b) presents the population inversion by excitation trapping on the ⁴F${ }_{9/2}{\to }^4$I${ }_{9/2}$ transition at 3.4 μm as a function of the 1976 nm core pump intensity for Er³⁺ concentrations from 2.5 to 10 mol%. Firstly, one can see that the excitation trapping threshold increases as the Er³⁺ concentration decreases. This can be attributed to the fact that the magnitude of ET processes scales with the square of the ion concentration and that the value of the W_ij parameter of each ET process also increases with concentration [14]. It should be noted that for a 1 mol% concentration of Er³⁺, modeling showed that no excitation trapping could occur for any given 1976 nm pump intensity. This is in agreement with prior demonstrations of DWP 3.4 μm 1 mol% Er³⁺ fiber lasers where no evidence for excitation trapping has been reported. Secondly, Fig. 8(b) shows that population inversion on the 3.4 μm transition is directly reached once excitation trapping occurs, therefore hinting at the possibility of operating the 3.4 μm laser through the use of excitation trapping.

 

Fig. 9 Experimentally observed bistability of the 3.42 μm output power from the DWP 7 mol% Er³⁺:ZrF₄ fiber laser depending on which pump is activated first.

Download Full Size | PDF

4.4. Laser output power bistability

The measured output power of the 3.42 μm DWP 7 mol% Er³⁺:ZrF₄ fiber laser showed signs of bistability depending on the order of activation of the 976 nm and 1976 nm pumps, as shown in Fig. 9. For varying power combinations of the 976 nm and 1976 nm pumps, the 3.42 μm output power was measured when the 1976 nm pump was activated after the 976 nm pump (red data) and vice-versa (blue data). As can be seen, once the 1976 nm core pump power exceeds a certain threshold, roughly 7 W, the 3.42 μm output power is significantly higher when the 1976 nm core pump is activated after the 976 nm cladding pump. In the case of Fig. 9(a) for a 1976 nm pump power of 8 W, a 0.65 W discrepancy exists between both laser curves which amounts to a 23 % variation with respect to the 3.42 μm output power. Interestingly, the slope efficiency of both the blue and the red data points are fairly identical and remain constant over the whole 1976 nm pumping range, except in the transition zone. It should be noted that the curves were recorded from the highest output power down to the laser’s threshold.

We believe bistability occurs since the order in which the pumps are activated determines how the ions are distributed within the energy levels of the Er³⁺:ZrF₄ system. For instance, when the 1976 nm pump is activated after the 976 nm pump, the ions are mostly pumped from the ⁴I${ }_{11/2}$ level to the ⁴F${ }_{9/2}$ level through VGSA, and only weak VESA occurs given that most 1976 nm photons are consumed for VGSA. However, when the 976 nm pump is activated after the 1976 nm pump, very few ions are present in the ⁴I${ }_{11/2}$ state in the first few moments while a comparatively large number of photons are present at 1976 nm. Hence, every ion in the ⁴I${ }_{11/2}$ state undergoes successive excitation to the ⁴F${ }_{9/2}$ and ⁴F${ }_{7/2}$ state through VGSA and VESA. This has the net effect that, in the steady-state regime, a considerable amount of ions are stuck in the (²H${ }_{11/2}$, ⁴S${ }_{3/2}$) levels and cannot participate in 3.42 μm laser emission. To date, the steady-state numerical model was not able to reproduce the bistability phenomenon, however we believe that using a transient model may provide the means to do so in the future.

5. Conclusion

We have studied in this work a DWP 7 mol% Er³⁺:ZrF₄ monolithic fiber laser cavity in order to investigate the potential of heavily-doped Er³⁺:ZrF₄ fibers for laser emission around 3.4 μm. Achieving a record efficiency of 38.6 %with respect to the launched 1976 nm core pump, along with a maximum output power of 3.4 W at 3.42 μm, our cavity demonstrates that heavily-doped fibers can achieve similar laser performances at 3.4 μm compared to their lightly-doped counterparts. However, the high Er³⁺ concentration significantly increased the heat load in the fiber, therefore limiting the laser’s power scaling potential. The performance of the 7 mol% cavity was well reproduced through numerical modeling, which was subsequently used to validate that equivalent 3.4 μm output powers and slope efficiencies can be reached with 1, 4 or 7 mol% Er³⁺:ZrF₄ fibers, albeit with increasingly higher heat loads. Based on these results, it is therefore clear that future power scaling of DWP 3.4 μm fiber laser cavities must rely on lightly-doped Er³⁺:ZrF₄ fibers in order to minimize the heat load and ensure the stability of the FBGs. However, heavily-doped Er³⁺:ZrF₄ cavities at 3.4 μm require 4 times less fiber and 3 times less 976 nm cladding pump compared to their lightly-doped counterparts, making them a cost-effective option for low-power applications. Moreover, this investigation has shown that 7 mol% fibers prevent output power quenching of 3.4 μm fiber lasers. Heavily-doped Er³⁺:ZrF₄ fibers can therefore be of great interest for gain-switched DWP 3.4 μm fiber lasers where quenching was shown to be a major bottleneck in achieving stable and high-power pulses [10].

This work also reports the formation of a luminescent grating in the core of the 7 mol% Er³⁺:ZrF₄ fiber as a result of the combined effects of transverse mode-beating associated with the 1976 nm core pump and excitation trapping within the metastable energy levels of the Er³⁺:ZrF₄ system. Through numerical modeling, it is shown that the excitation trapping phenomenon possesses a 1976 nm pump threshold which can be met by relying on constructive interference of the LP₀₁ and LP₁₁ modes at 1976 nm. This is confirmed given that the periodicity of the luminescent grating, 391 μm, is in agreement with the transverse mode-beating interference pattern. Finally, this work also reports on the bistability of the 3.42 μm output power depending on which pump wavelength was activated first.