1. Introduction

Rare-earth doped ZBLAN glasses enable access to mid-IR fiber laser wavelengths, since their transmission windows have long-wavelength edges extending to ∼4 µm [1], much further than the ∼2.2 µm edge of traditional fused-silica fibers [2]. Er:ZBLAN fiber is one of the most successful gain medium for fiber laser operation in mid-IR partly due to its convenient pumping band, accessible with widely available, reliable, and efficient telecom-grade InGaAs laser pump diodes operating at 976 nm. Furthermore, Er-doped ZBLAN fibers can reach very high optical pumping efficiencies (up to 49.5% [3]) using these 976 nm diodes by utilizing energy transfer up-conversion processes in heavily doped erbium fibers, which enable one-to-two pump-to-signal photon conversion processes with efficiencies exceeding quantum defect limit of ∼35% for this pump and signal wavelength combination. This facilitates achieving high average powers in mid-IR – up to 70W has been reported so far [4].

Generation of high energy short (ns-range) pulses using Er:ZBLAN fiber lasers operating at ∼2.8µm has been a very active research direction [5–9] due to numerous potential applications of efficient and high-power pulsed sources in mid-IR in spectroscopy, sensing, medicine, defense, and other areas [10]. For many such applications it is highly preferable to maintain a diffraction-limited output beam quality. However, the highest pulse energies achieved in a diffraction-limited output beam are all below ∼100 µJ, limited by the largest single-mode core sizes available with Er:ZBLAN fibers. For example, in 2018 Pascal, et al [5] reported generation of 80 µJ and 170 ns pulses using a gain switched 15 µm core Er:ZBLAN fiber laser. In 2022, Nikolai, et al [6] demonstrated 52 µJ energy and sub-10 ns duration pulses from a single mode 15µm core Er-fluoride fiber amplifier. Achieving higher energies was only possible by resorting to larger core but multimode output Er:ZBLAN fiber lasers or amplifiers. For example, in 2017 Shen et al. [7] reported generation of 150 µJ and ∼100-ns duration pulses in a multimode output beam from a 33 µm core Er:ZBLAN Q-switched fiber laser. In 2020 we reported [8] multimode beam amplification of ∼10 ns pulses to ∼230 µJ using a 30 µm core, and to ∼0.67 mJ using a 70 µm core Er:ZBLAN fiber amplifiers. More recently, in 2021 Aydin, et al [9] reported highly multimode beams of ∼1 ns pulses reaching ∼0.5 mJ from a 85 µm core, and ∼1 mJ from a 115 µm core Er³⁺: ZrF4 fiber amplifiers.

In this paper we demonstrate that it is possible to achieve and maintain single transverse mode operation with high energy pulses at ∼2.8µm from large core Er:ZBLAN, even with cores supporting multiple higher-order modes, and thus to exceed energy limitations of single-mode core Er:ZBLAN fibers by approximately an order of magnitude. We report diffraction-limited beams of ∼100 ns pulses reaching up to 0.75 mJ from a 50-µm core, and up to 420 µJ from a 30-µm core Er:ZBLAN fiber amplifiers, which to our knowledge represents the highest energies in a single transverse mode achieved from a mid-IR fiber laser or amplifier to date.

2. Single-mode operation of large mode area Er:ZBLAN fiber amplifiers

Single transverse mode operation of large multimode core fibers is routinely used in NIR with so called large mode area (LMA) fibers. LMA fibers lack any specially-designed internal structure to sustain such an operation, and achieve it via some external to the fiber mode management. One such technique is higher-order mode (HOM) filtering using fiber coiling [11], which at ∼1 µm NIR wavelengths is limited to fiber cores smaller than ∼25 µm, and which requires relatively low numerical aperture (NA) cores (typically NA < 0.07). For LMA fibers with larger cores and/or higher core numerical apertures HOMs cannot be completely filtered out using fiber coiling, and diffraction-limited output beams can be achieved only by using the single-mode excitation technique [12,13]. This technique relies on careful fundamental mode (FM) matching when exciting signal at the fiber input, and it requires that the fundamental mode is preserved when propagating along the fiber, which is achievable under certain conditions. These conditions, as we show below, scale favorably with increasing wavelength, thus allowing us to demonstrate sustained nearly diffraction-limited output from 50 µm core high-energy mid-IR fiber amplifiers.

First let’s consider under what conditions fundamental mode can be preserved while propagating in an LMA fiber core. Quantitatively, fundamental mode can be considered to be preserved after propagating a finite length (typically few meters or less) of a fiber amplifier, when only a sufficiently small portion of the total signal power is coupled into HOMs at the fiber output. According to the Telecommunications Industry Association standard TIA-455-80 [14] fiber output is strictly single mode when its HOM power content is below 1% of the total power. In practice, however, fiber output can be considered to be sufficiently close to the diffraction limit when the power contained in all HOMs is not exceeding few % of the total [13]. Both external, i.e. packaging, conditions and internal structural properties of an LMA fiber influence whether the fundamental mode will propagate sufficiently undisturbed, and will reach the amplifier output without significant HOM content. However, when the internal scattering is sufficiently low it is always possible to carefully package an LMA fiber without causing any significant externally-caused HOM content [13]. Therefore, suitability of an LMA fiber for an unperturbed fundamental mode propagation is determined by its internal properties.

Internal mode scattering in LMA fibers is caused by intrinsic random refractive-index perturbations distributed along a fiber. This longitudinal distribution can be described by its Fourier spectrum S$(\Lambda ),$ where $\Lambda $ is a spatial period [12]. For an LMA fiber only the coupling between the fundamental LP₀₁ and the nearest higher order mode LP₁₁ needs to be considered. This coupling is caused by the spectral component $S({{L_{\textrm{LP}01 - \textrm{LP}11}}} )$ whose spatial period Λ is matching the mode beat length L_LP01-LP11 = 2π/(β_LP01 - β_LP11) between these two modes. Here β_LP01 and β_LP11 are the corresponding mode propagation constants. Strength of this coupling can be described by the mode power coupling coefficient η = (λ/2nd_core)²·h, where h measures the power fraction transferred from the FM to this HOM per unit propagation length [15], n is the fiber core refractive index, d_core is the core diameter, and λ is the wavelength. For a step-index fiber it can be shown [12] that η $(\Lambda $) = (1/2)(n/π)²·S(Λ).

It is known [12] that intrinsic refractive-index perturbations can occur due to random stresses induced in the fiber during its fabrication process, as well as due to micro-bends associated with the limited mechanical stiffness of a fiber structure [12]. However, as it is shown in [12] perturbations due to random stresses can be made negligible by a proper choice of fiber fabrication process, in which case only the micro-bending caused scattering will remain the dominant mechanism in such LMA fibers. Since micro-bending depends on mechanical stiffness of a fiber, perturbation spectrum S$(\Lambda )$ rapidly decreases in magnitude with decreasing spatial period Λ, vanishing at spatial periods comparable to the outer diameter of a fiber D_outer. It has been shown that this dependence can be approximated as S$(\Lambda )\; \sim \; {\Lambda ^4}/D_{outer}^6$ [12]. The beating length between the LP₀₁ and the LP₁₁ modes far from cutoff can be approximated by L_LP01-LP11 ≈ $2.2nd_{c\textrm{ore}}^2/\lambda $ [16], indicating that the beat length increases with increasing fiber core diameter. Therefore, in order to preserve fundamental mode propagation in an LMA fiber it is necessary to select proper fiber parameters so that this beat length would be short enough to be within the spatial period range of sufficiently small perturbation spectral magnitude. Substituting this beat length into the above expressions for S$(\Lambda )$ and η $(\Lambda $) we obtain the following approximate dependence of the mode power coupling coefficient between LP₀₁ and LP₁₁ on fiber core and outer diameters: η ∝ d_core⁸/(D_outer⁶·λ⁴) [12], indicating that mode scattering can be effectively reduced by choosing a suitably large outer diameter of a fiber. These theoretical expectations have been extensively confirmed at ∼1 µm NIR wavelengths, where single-mode operation via single-mode excitation is routinely achieved in LMA fibers with ∼30 µm core diameters, and near diffraction-limited operation of Yb-doped silica fiber amplifiers was reported for core sizes as large as ∼65 µm [13], with fiber outer diameters typically ∼400 µm. Implication of this experimental evidence for NIR and the η ∝ λ^-4 dependence for the LP₀₁-LP₁₁ mode power coupling coefficient given above is that this single mode excitation technique should be performing robustly for larger core sizes of Er:ZBLAN fiber amplifiers operating at ∼2.85 µm MIR wavelengths than what has been achieved at shorter, NIR wavelengths.

Since the single mode excitation technique does not rely on any mode filtering mechanism it is essential to ensure that only the fundamental LP₀₁ mode is excited at the input of the fiber [12]. For this it is necessary to precisely match the profile, position and direction of the incident beam to those of the fundamental mode of an LMA fiber. Mode profile matching requires a pure diffraction-limited input beam and a careful selection of the input optics to focus this beam at the fiber input to the spot size precisely equal to the mode diameter of the LMA fiber. Position and direction of the excitation beam needs to be carefully aligned to accurately match the transverse position of the LP₀₁ mode and should be strictly co-linear with the LMA core axis. This can be achieved by using a proper measurement to quantify the purity of single-mode excitation, serving as a feedback to the excitation beam alignment. The basic idea proposed in [12] is to use the mode-matched beam coupling into a test single-mode (SM) fiber for quantifying beam quality of the LMA fiber output, where the SM fiber acts as a spatial filter which only transmits the LP₀₁ mode and filters out any higher order modes. This can be set up as shown in Fig. 1. A gaussian beam is coupled into an LMA fiber, and the LMA fiber output is coupled into a SM test fiber with a pair of a collimating and a focusing lenses which controls the focused beam diameter into this test fiber. Not shown in this figure are two mirrors that must be inserted between the two lenses in order to control the test fiber excitation-beam position and direction. Similar two mirrors must also be used for the same purpose in the gaussian beam path at the input of the LMA fiber. The measured power transmission through the test SM fiber quantifies the percentage of the fundamental mode content, and therefore the mode quality of the LMA fiber output [12]. Alignment procedure consists of several iteration cycles, switching forth and back between repetitively re-aligning LMA input to maximize SM test fiber throughput, and repetitively re-aligning test fiber input to continuously maximize LMA-to-test fiber LP₀₁ mode matching.

 

Fig. 1. Schematic of an arrangement implementing the single mode excitation technique in an LMA fiber, using a single-mode fiber as a spatial LP₀₁ mode filter.

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3. Experimental setup and results

Experimental setup for demonstrating single mode operation of a high-energy short pulse fiber amplification system in Mid-IR, is shown in Fig. 2. The setup is built using Er:ZBLAN fibers, and consists of four parts: a Q-switched laser seed source, a single mode fiber pre-amplifier, an LMA fiber amplifier, and a single mode (undoped ZBLAN) fiber based LP₀₁ mode filter setup for aligning amplification stage excitation into a single transverse mode. Q-switched laser uses 3m single-mode doubled-cladding Er:ZBLAN fiber (FiberLabs, Inc) with a highly-doped core (6 mol. % Er3 + concentration), and is configured as a ring cavity. It was pumped with 5W at 976nm from a fiber-pigtailed (105µm diameter and 0.22NA) laser diode. This laser is setup to generate 95ns and 30µJ pulses at λ = 2.78µm with a variable repetition rate tunable between 100Hz to 5kHz. The generated seed pulse energy, duration and central wavelength are kept constant at all these repetition rates by adjusting pump power accordingly. These output pulses are exiting the ring cavity of the Q-switched laser via a polarizing beam splitter, and thus are linearly polarized.

 

Fig. 2. Experimental setup of the Er:ZBLAN LMA fiber high energy pulse amplification system.

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After passing through an isolator, these seed pulses are coupled into the single-mode core and double-clad fiber pre-amplifier using CaF2 lenses. This single-polarization isolator (ISO-5-2700-MP) transmits 70% of the signal, resulting in 20µJ seed pulses at the preamplifier input. This input was also linearly polarized, with the polarization orientation adjusted with a λ/2 waveplate placed after the isolator. Preamplifier is built using a 3m long non-PM Er:ZBLAN fiber with 6 mol% doping (FiberLabs, Inc). Fiber core diameter is 18 µm with 0.09 NA, and with the LP₁₁ mode cut-off at 2.5 µm. It is therefore strictly single mode at the seed wavelength of 2.78 µm. Both non-PM ZBLAN fiber ends are protected with ∼650µm long AlF₃ endcaps to eliminate fiber-end degradation and damage. The endcaps are polished to $12^\circ $ angle to avoid amplifier lasing. Although the fiber is not polarization preserving, but we find that it robustly maintains linearly polarized output for the input signal linearly polarized in the plane of the fiber coiling. Fiber cladding is 250µm in diameter with NA > 0.5, surrounded by a low-index polymer coating with the outer diameter of 450µm. This amplifier was pumped at 976nm from a fiber pigtailed (400µm/0.22NA) diode laser, the 976 nm pump light was divided to two beam via using the 50:50 beam splitter to achieve the dual-end pump for the preamplifier. Preamplifier output energies for 20µJ seed pulses at 1kHz repetition rate with pump power varying from 2W to 11W are shown in Fig. 3. Amplified signal spectrum is shown in the insert of this figure. Note that the highest achieved pulse energies of 176µJ are more than two times higher than the highest single-mode Er:ZBLAN fiber amplifier energies of 80µJ reported previously in [5].

 

Fig. 3. Amplified 95 ns pulse energies from the single mode 18 µm core Er:ZBLAN fiber pre-amplifier for 20µJ seed. Amplified pulse spectrum is shown in the insert.

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As it is shown below, these energies are more than enough for seeding LMA fiber high energy amplifiers, and in practice we only used a fraction of the available maximum energy. This pre-amplified seed signal is launched into an LMA fiber amplifier after passing several mirrors, a single-polarization isolator (ISO-5-2800-MP), a f = 25.4 mm focal length CaF₂ lens collimating the preamplifier output, a two 20-mm focal length CaF₂ lens telescope, a λ/2 waveplate, and a f = 40mm focal length CaF₂ lens for focusing signal into the LMA amplifier fiber. Due to various losses in these components the overall power transmission between the pre-amplifier output and the LMA amplifier fiber input was measured to be ∼50%. The highest loss is in the isolator, which was measured to transmit only 65% of the seed signal. The isolator was rotated axially to match the linear polarization from the single-mode pre-amplifier. The waveplate, placed right before the power amplifier input, is used to set the linear polarization of the seed signal into the coiling plane of the LMA fiber to achieve its linearly polarized output. LMA-amplified beam PER was not characterized, however, due to the lack of extra polarizers at the time of the experiment. The purpose of the two-lens telescope is to re-collimate the signal beam, to offset diffraction spreading accumulated in its free-space path. The focal lengths of the collimating and focusing lenses is chosen to match the mode sizes of the single-mode pre-amplifier fiber and the 50 µm core power amplifier fiber, necessary for achieving single-mode excitation in this LMA fiber.

The power amplifier uses a 3.2 m long highly doped (6 mol.% Er³⁺ concentration) 50 µm diameter and 0.12 NA core Er:ZBLAN LMA fiber from FiberLabs, Inc. The polymer-coated double-clad LMA fiber inner cladding diameter is 250 µm with >0.5 NA, and the outer cladding diameter is 460 µm. Both LMA ZBLAN fiber ends are protected with ∼570µm long AlF₃ endcaps to eliminate fiber-end degradation and damage. The endcaps are polished to $12^\circ $ angle to avoid amplifier lasing. Up to 75 W of pump power at 976 nm was available from a laser diode coupled into the 400 µm and 0.22 NA delivery fiber, output of which was split into two equal-power paths for pumping the Er:ZBLAN fiber from the two ends.

The single-mode excitation procedure, described earlier, was carried out for this 50 µm core Er:ZBLAN LMA fiber amplifier. As a spatial filter we used 14 µm and 0.12 NA core ZFG single-mode fiber from Le Verre Fluoré. To achieve mode matching between the LMA and the single-mode filter fibers we used CaF₂ lens with f = 40 mm for collimating the LMA output, and another CaF₂ lens with f = 12.7 mm for focusing into the single-mode fiber. The chosen focal length ratio is sufficiently close to the ratio between the calculated mode field diameters of the two fibers (MFD = 14.5 µm for the SM, and MFD = 40µm for the LMA fibers). To avoid damaging this single-mode fiber, we carried out the iterative single-mode excitation procedure at relatively low pulse energies of ∼100µJ. This procedure included iterative alignments of the inputs into the LMA and single-mode fibers, by adjusting each fiber-end XYZ positions, adjusting angles of the two beam-steering mirrors in the LMA-input and SM-input paths (as shown in Fig. 2), and by adjusting the telescope in the LMA-input path. Alignment procedure was completed once the highest coupling efficiency of ∼58% from the LMA into the SM-test fiber was reached. Note that this coupling efficiency is similar to the maximum coupling efficiency previously measured for coupling from the single-mode ZBLAN fiber pre-amplifier into the same ZFG single-mode fiber. After completing the alignment we use the micro-bolometer array camera (WinCamD-FIR8-14-HR) to visually inspect the beam profile, and verify the nearly diffraction-limited quality of the LMA output beam via M² measurements, results of which are shown in the Fig. 4(b). We used the standard moving knife-edge method to measure the beam size at the 1/e² peak-intensity level at different longitudinal positions.

 

Fig. 4. (a) Amplified 95 ns pulse energies from 3.2 m long 50 µm core Er:ZBLAN fiber amplifier, at various pump powers and repetition rates. Seed energy at the amplifier input was kept constant at 30µJ. All energy measurements were performed while maintaining the single mode operation of the LMA fiber amplifier. Amplified pulse spectrum and pulse profile are shown in the insert. (b) Beam quality measurement of the LMA amplifier output at ∼0.75mJ energy. Measured near-field beam profile is shown in the insert.

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Once the single-mode output from the 50 µm core LMA fiber was achieved, we carried out the high energy amplification experiments, while maintaining the diffraction-limited output beam at all achieved energies and powers. The amplified output energies for varying pump powers from ∼3W up to 21W are shown in Fig. 4(a), which were measured using a pyroelectric energy meter (PE 10-C P/N 7Z02932). We explored power amplifier performance at various repetition rates in the range from 500 Hz to 5kHz. Seed pulse energy at the LMA amplifier input was kept constant at 30µJ (corresponding to 61µJ directly from the pre-amplifier) by adjusting single-mode fiber pre-amplifier pumping power accordingly. The highest average power of 1.75W was achieved at 5kHz when pumping with 21W (corresponding pulse energy is 350µJ). The highest pulse energy achieved was 0.743mJ at both 1kHz and 500 Hz repetition rates, when pumping with 21W. Amplified signal spectrum is shown in the insert of the Fig. 4(a). Note that even at the highest energies no spectral broadening was observed compared to the seed pulse spectra from the single-mode preamplifier, shown in Fig. 3. The 95 ns pulse measured at the highest pulse energies is also shown in the Fig. 4(a) inset. The near diffraction-limited output beam was verified at the highest pulse energies of ∼0.75mJ: the output beam quality measurements shown in Fig. 4(b) indicate that M² ∼1.172 was achieved. Note that since the pulse energies at this pump power do not change when reducing pulse repetition rate below ∼1kHz, but decrease with repetition rate increasing to 2kHz, the gain recovery time of this LMA fiber at ∼21W of 976 nm pumping should be approximately 1 ms, much shorter than the 6.9 ms spontaneous emission lifetime of this ∼2.8 µm Er³⁺-ion laser transition in ZBLAN glass host [17].

We also carried out stored energy measurements for this 50 µm core Er:ZBLAN LMA under various pumping levels. For this we used the Frantz-Nodvik model [18], which describes amplification in a saturated short-pulse amplifier. In this model measured pulse gain g_p = E_out/E_in can be expressed as a function of the energy extraction efficiency η and the small-signal gain g₀ [19] of the amplifier. Here η = (E_out – E_in)/E_stored = E_in (g_p – 1)/E_stored, where the corresponding subscripts indicate amplifier output, input and stored energies. Therefore, by measuring the small-signal gain g₀ at a certain pump power P_pump, and then measuring g_p for several E_in values at the same pump power, one can use this functional dependence to calculate the corresponding η value for each E_in at this P_pump, and thus the stored energy E_stored. The measured small-signal gain and the corresponding stored energies are shown in Fig. 5 for several pump power ranging from 7W to 21W. The important conclusion here is that at the highest pump powers of around 20W the extracted pulse energies of ∼0.75mJ constitute approximately 80% of the stored energy of ∼0.9mJ in this 50 µm core Er:ZBLAN LMA fiber.

 

Fig. 5. Measured small signal gain and stored energy in the 3.2 m long 50 µm core Er:ZBLAN fiber amplifier.

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We also performed an additional set of high-energy single-mode amplification experiments, in which the 50-µm core fiber was replaced with a 30 µm core LMA fiber. Specifically – we used 1.9 m of highly doped (6 mol. % Er³⁺ concentration) Er:ZBLAN double cladding fiber (FiberLabs, Inc), with the 30µm diameter and 0.12-NA LMA core. The polymer-coated double-clad fiber inner cladding diameter is 300 µm with >0.5 NA, and the outer cladding diameter is 460µm. Both 30µm ZBLAN fiber ends are protected with ∼600µm long AlF₃ endcaps to prevent fiber-end degradation and damage. The endcaps are polished to $12^\circ $ angle to avoid amplifier lasing. We use the same pump diode and two-side pumping arrangement shown in the Fig. 2, as was used for the 50 µm core LMA fiber amplifier. The single-mode excitation was achieved by the same method as for the 50 µm core LMA, but required different choices of collimating and focusing lenses to achieve the mode matching. The measured amplified output energies for varying pump powers of up to 35W, seeded with 89.5µJ pulses at 5kHz repetition rate, are shown in Fig. 6(a). The highest obtained pulse energy is 420µJ, limited by the excessive heating of the fiber ends. Amplified signal spectrum is shown in the insert of the Fig. 6(a), indicating the same wavelength and bandwidth as from the single-mode preamplifier (shown in Fig. 3). Output beam M² measurement, shown in Fig. 6(b) was carried out at 410µJ of amplified pulse energy, and indicates a near diffraction-limited beam with M² = 1.289.

 

Fig. 6. (a) Amplified 95 ns pulse energies from 1.9 m long 30 µm core Er:ZBLAN fiber amplifier at various pump powers, and at 5kHz repetition rate. Seed pulse energy was kept constant at the amplifier input at 89.5µJ. All energy measurements were performed while maintaining the single mode operation of the LMA fiber amplifier. Amplified pulse spectrum is shown in the insert. (b) Beam quality measurement of the LMA amplifier output at 410µJ of amplified energy. Measured near-field beam profile is shown in the insert.

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4. Conclusion

In summary, we had demonstrated high energy single-mode amplification in LMA core Er:ZBLAN fibers producing near diffraction-limited output beams with M² ∼1.2-1.3, and with up to 0.75mJ per pulse at ∼2.8 µm and pulse durations of 95 ns. These highest achieved energies from a 50 µm core LMA fiber are nearly equal to the previously reported ∼1mJ record from a highly multi-mode 115 µm core Er:ZBLAN fiber [9]. This demonstrated performance constitutes an order of magnitude increase in single-mode output energies from a Mid-IR fiber amplifier or laser. Demonstrated single-mode operation is robust, and is sustainable over many hours of operation (in our experiments lasting for up to 6 hours of continuous use). A complete restart of the system from the “power-off” conditions would typically require a quick (15-20 minute) single-mode excitation realignment. This result enables high energy femtosecond pulse amplification in Mid-IR using LMA fibers, where single-mode operation is critical. We anticipate that this demonstration is only the first step in exploring other methods of achieving single-mode operation in large core Er:ZBLAN fibers in Mid-IR spectral range.