Kerr-Lens Mode-Locked Yb:BaF₂ Laser

Abstract

We present sub-50 fs soliton pulse generation from a diode-pumped Kerr-lens mode-locked laser based on an Yb³⁺-doped BaF₂ crystal. Utilizing a spatially single-mode, fiber-coupled InGaAs laser diode at 976 nm as a pump source, the Yb:BaF₂ laser generates pulses as short as 46 fs at 1060.1 nm with an average output power of 45 mW at a pulse repetition rate of ~65.6 MHz via soft-aperture Kerr-lens mode locking. To the best of our knowledge, this represents the first demonstration of Kerr-lens mode-locked operation of the Yb:BaF₂ crystal, as well as the shortest pulse duration ever achieved from any diode-pumped mode-locked laser based on an Yb³⁺-doped alkaline-earth fluoride crystal.

1. Introduction

Ytterbium (Yb³⁺)-doped alkaline-earth fluoride crystals with the chemical formula Yb:MF₂, where M = Ca²⁺ [1], Sr²⁺ [2], and Ba²⁺ [3] or their mixtures [4], are promising laser gain media for developing high-power, femtosecond solid-state lasers at ~1 μm. These crystals belong to the cubic class and feature the so-called fluorite-type structure (sp. gr. Fm$\overline{3}$m). The MF₂ crystals exhibit a wide transparency spectral range spanning from the UV to the mid-IR, low refractive index, exceptionally high thermal conductivity with a moderate dependence on the Yb³⁺ doping concentration, negative thermo-optic coefficients resulting in weak negative thermal lensing, and low phonon energies [5]. Because of their congruent melting and relatively low melting points, MF₂ crystals with large volumes can be grown by the Bridgman–Stockbarger and Czochralski approaches. Furthermore, they can also be used in the form of laser ceramics [6,7]. The Yb³⁺ dopant ions in MF₂ crystals have a tendency to form clusters [8,9], which results in profound inhomogeneous broadening of their absorption and emission bands, an effect often referred to as a “glassy-like” spectroscopic behavior [6]. Compared to cubic oxides, e.g., Yb³⁺-doped garnets or sesquioxides, they feature extremely broad, smooth, and flat gain profiles which could spectrally support sub-50 fs pulse generation via passive mode locking [5]. Nevertheless, the potential of the gain bandwidth of Yb:MF₂ crystals seems to be not fully exploited, which is probably due to the relatively low-gain cross-sections as well as the relatively long fluorescence lifetime (>2.4 ms [5]) counteracting soliton stabilization. In the case of using “slow” saturable absorbers (SAs) such as SEmiconductor Saturable Absorber Mirrors (SESAMs), the strong tendency of Q-switching makes it difficult to stabilize continuous-wave mode-locked (CWML) lasers. To overcome this limitation, the enhanced Kerr-lensing effect can be employed for stabilizing SESAM mode-locked operation and achieving shorter pulses. A SESAM ML Yb:CaF₂ laser generating 99 fs pulses was stabilized by the Kerr-lensing effect in [10]. Slightly shorter pulses (65 fs) were obtained from an Yb:CaF₂ laser operating in a hybrid Kerr-lens and SESAM ML regime [11]. A SESAM was employed for starting and maintaining soliton-like pulse shaping; 52 fs pulses were generated at 1058.2 nm from a diode-pumped Yb:BaF₂ laser with an average output power of 129 mW and a pulse repetition rate of 79.5 MHz [12].

Kerr-lens mode locking (KLM) provides an approach to better exploit the gain bandwidth of Yb³⁺-doped laser crystals for achieving shorter pulse durations. It represents a well-established passive mode-locking technique that relies on self-focusing in conjunction with an intracavity aperture. This induces an intensity-dependent quasi-instantaneous self-amplitude modulation (SAM) serving as an artificial “fast” SA, which supports the generation of few-optical-cycle pulses without the drawbacks associated with non-saturable loss of “slow” SAs and their inherent bandwidth limitations. However, the Kerr self-focusing effect requires very high peak power to induce a noticeable modification of the spatial mode through nonlinear refractive index variation. Such modification is proportional to the intensity of the electric field, Δn = n₂I, where n₂ is the nonlinear refractive index. In fact, due to their larger band-gaps, alkaline-earth fluoride crystals exhibit a very low value of the nonlinear refractive index at ~1 μm, e.g., 2.85 × 10⁻²⁰ m²/W for BaF₂ [13], 1.9 × 10⁻²⁰ m²/W for CaF₂ [13], and 1.34 × 10⁻²⁰ m²/W for SrF₂ [14], which suppresses the nonlinear SAM effect.

A straightforward solution for achieving KLM operation of Yb:MF₂ lasers would increase the laser intensity by maintaining a tight focusing over a long crystal using a high-brightness pump source. Utilizing a 6 mm long Brewster-angle-cut Yb:CaF₂ crystal as the gain medium, Sévillano et al. demonstrated a 7 W Yb-fiber laser-pumped KLM Yb:CaF₂ laser producing 68 fs pulses at 1049 nm with a maximum average output power amounting to 2.3 W [15]. By scaling the available pump power of the Yb-fiber laser to 12 W, the same authors demonstrated 48 fs pulse generation at 1046 nm via soft-aperture KLM, which corresponds to a slightly higher average power of 2.7 W [16]. More recently, Su et al. realized a low-threshold soft-aperture KLM operation using a 5 mm long Brewster-cut compositionally “mixed” Yb,Gd:(Ca,Sr)F₂ crystal. Employing a 976 nm single-transverse-mode, fiber-coupled InGaAs laser diode as the pump source, the KLM Yb,Gd:(Ca,Sr)F₂ laser produced 57 fs pulses at 1060.8 nm, with an average output power of 26 mW and a laser threshold of 200 mW [17]. Furthermore, by utilizing a 5 W high-brightness Yb-fiber laser at 976 nm, pulses as short as 46 fs at 1049 nm were generated from the KLM laser based on the same laser crystal with a maximum average power of 620 mW [18]. So far, no KLM operation of Yb³⁺-doped BaF₂ crystals has been reported in the literature.

The barium fluoride (BaF₂) crystal features the highest nonlinear refractive index of the MF₂ compounds. It also presents a lower melting point as compared to the other MF₂ crystals [19]. In the present work, we explore further pulse shortening with this laser material, reporting soliton pulses as short as 46 fs at 1060.1 nm via soft-aperture KLM. To the best of our knowledge, this presents the first report on the KLM laser operation for the Yb:BaF₂ crystal.

2. Experimental Setup

A high-quality Yb:BaF₂ crystal was grown by the Bridgman–Stockbarger method having an actual Yb³⁺ concentration of 2.12 at.% (ion density = 3.56 × 10²⁰ cm⁻³). A cubic sample with an edge length of 3 mm was cut from the as-grown bulk crystal. The input and output faces of the sample were polished with high parallelism without anti-reflective coating. The schematic of the diode-pumped KLM Yb:BaF₂ laser is shown in Figure 1. The Yb:BaF₂ crystal was mounted in a copper holder and placed at the Brewster angle between two concave dichroic folding mirrors M₁ and M₂ (radius of curvature, RoC = −100 mm) in an X-shaped astigmatically compensated linear cavity without active cooling.

The pump source was a spatially single-mode, fiber-coupled InGaAs laser diode emitting non-polarized radiation with a maximum incident pump power of 1.38 W. It was equipped with a Fiber Bragg Grating (FBG) for wavelength locking across the entire operational range at 976 nm, with a spectral emission linewidth (full width at half-maximum, FWHM) of 0.2 nm, and a measured beam propagation factor (M²) of ~1.02. The pump beam was reimaged into the laser crystal by using an aspherical lens L₁ (focal length: f = 25.4 mm) and a spherical lens L₂ (f = 75 mm), which results in beam waist radii of 15 and 26.7 μm in the sagittal and tangential planes, respectively. For KLM operation, one cavity arm was terminated by a flat end mirror M₄, while the other arm was terminated by two flat dispersive mirrors (DMs) and a plane-wedged output coupler (OC). All cavity mirrors, including the OC, were designed to have a low group delay dispersion (GDD). The intracavity GDD was managed by incorporating two or three flat DMs characterized by the following GDD per bounce: DM₁ = −100 fs², and DM₂ = DM₃ = −250 fs². The overall negative GDD value was varied by adjusting the number of bounces on the DMs or by substituting the flat end mirror M₄ with DM₃. The geometrical cavity length of the KLM laser was ~2.3 m, corresponding to a pulse repetition rate of ~65 MHz.

3. Kerr-Lens Mode-Locked Operation

Initially, the KLM operation was studied at the maximum incident pump power of 1.38 W by utilizing three DMs (DM₁–DM₃), as illustrated in Figure 1. This resulted in an overall round-trip negative GDD of −1650 fs². The M₁–M₂ separation was initially aligned for optimum CW laser performance with a 1.6% OC. Under the absorbed pump power of 782 mW, the maximum CW output power of the Yb:BaF₂ laser reached 500 mW. To distinguish between CW and KLM operation, the separation between M₁ and M₂ was aligned toward the edge of the stability region via shifting folding mirror M₂ by several hundred micrometers away from the pump mirror M₁ to maximize the SAM induced by soft-aperture Kerr effect. However, in this cavity configuration, the CW output power significantly dropped to 98 mW. After a careful cavity alignment, stable KLM operation was initiated by gently tapping the OC or adjusting the DM₃. When ML, the Yb:BaF₂ laser exhibited a sudden power surge from 98 to 111 mW, corresponding to an absorbed pump power of 744 mW. The optical spectrum of the laser pulses, depicted in Figure 2a, revealed a spectral bandwidth (FWHM) of 24.8 nm centered at 1054 nm, assuming a sech²-shaped spectral profile. The intensity autocorrelation trace based on second-harmonic generation (SHG) yielded a deconvolved pulse duration of 48 fs (FWHM), assuming a sech²-shaped temporal pulse profile, as illustrated in Figure 2b. Consequently, the time-bandwidth product (TBP) was calculated as 0.321, slightly surpassing the Fourier transform-limited value of 0.315. At a pulse repetition rate of 65.7 MHz, the corresponding peak power reached ~30.9 kW. The optical efficiency, relative to the absorbed pump power, was measured at 14.9%. Furthermore, the beam propagation factor (M²) of the laser pulses was determined to be 1.02.

A distinct change in the laser mode between the CW and KLM operation regimes was evident through monitoring the far-field beam profiles with a camera positioned approximately 0.8 m away from the OC. The reduction in the far-field beam diameter, from 2.32 × 2.07 mm² to 1.99 × 1.91 mm², as depicted in Figure 3, indicated a pronounced soft-aperture Kerr-lensing effect and self-focusing within the Yb:BaF₂ laser crystal.

The pulse duration underwent further reduction by decreasing the transmittance of the OC to 0.8% and optimizing the total negative GDD value. The shortest pulse duration was obtained by substituting DM₃ with the flat end mirror M₄, resulting in an overall negative GDD of −1400 fs², as illustrated in Figure 1. The pulse characteristics are detailed in Figure 4. The optical spectrum of the laser pulses exhibited a bandwidth (FWHM) of 26.1 nm at a central wavelength of 1060.1 nm, assuming a sech²-shaped spectral profile, as depicted in Figure 4a. The observed satellite peak around 1.1 μm stemmed from the unmanageable intracavity GDD at the long-wave spectral wing and the non-optimized spectral reflectivity of the cavity mirrors. This could be rectified by appropriately managing the overall intracavity GDD across the entire spectral bandwidth of the ML laser. The measured SHG-based intensity autocorrelation curve closely matched a sech²-shaped temporal profile, yielding a deconvolved pulse duration of 46 fs, as presented in Figure 4b. The corresponding TBP of 0.320 indicated the generation of nearly Fourier-transform limited pulses. The long-scale SHG-based intensity autocorrelation scan of 50 ps, displayed in the inset of Figure 4b, affirmed single-pulse CW-ML operation. The maximum average output power reached 45 mW at an absorbed pump power of 729 mW, corresponding to an optical efficiency of 6.2%. The soliton pulses exhibited a peak power of 13.2 kW at a pulse repetition rate of 65.6 MHz. However, despite effort, further reduction in pulse duration proved unattainable through either decreasing the transmittance of the OC or reducing the overall negative round-trip GDD in our laser configuration.

The steady-state pulse train corresponding to the achieved shortest pulses was characterized using a microwave spectrum analyzer. Two microwave spectra were presented to confirm clean CW-ML operation. The first beat-note was detected at 65.63 MHz with a high signal-to-noise ratio above 70 dBc for a resolution bandwidth (RBW) of 300 Hz, as illustrated in Figure 5a. This, together with the consistent 1-GHz harmonic beat-notes depicted in Figure 5b, serves as evidence of clean fundamental ML operation of the Yb:BaF₂ laser without any occurrence of Q-switching or multiple pulse instabilities.

4. Conclusions

In conclusion, we report on the first demonstration of a diode-pumped Kerr-lens mode-locked Yb:BaF₂ laser. Soliton pulses as short as 46 fs were delivered at 1060.1 nm via soft-aperture Kerr-lens mode locking. The corresponding average output power amounted to 45 mW at ~65.6 MHz. Given the relatively low nonlinear refractive index of the BaF₂ crystal, our results represent significant progress for an Yb:BaF₂ laser crystal with thickness as small as 3 mm employed as a Kerr medium for effective soft-aperture Kerr-lens mode locking. They indicate the possibility for power scaling and pulse shortening towards sub-40 fs durations for Yb:BaF₂ lasers when employing high-power and high-brightness Yb fiber laser as pump sources.