1. Introduction

YSr₃(PO₄)₃ (YSP) is a representative of a large family of eulytite-type structure orthophosphate crystals REM₃(PO₄)₃, where the passive rare earth (RE³⁺) can be Y, La, or Gd, and M²⁺ = Ca, Sr, Ba, etc. [1–4]. These crystals are cubic with non-centrosymmetric point group, $\bar{4}$3 m and space group $T_d^6$ – I$\bar{4}3$d [4]. They exhibit local structure disorder due to the random distribution of RE³⁺ and M²⁺ cations over the same 16c Wyckoff sites. The structural units consist of isolated PO₄ tetrahedra and edge-sharing RE|M octahedra, arranged in a manner that shares common apexes. Optically active RE³⁺ ions, such as Ce³⁺_­, Pr³⁺, Nd³⁺, Eu³⁺, Tb³⁺, Dy³⁺, Er³⁺ Tm³⁺, or Yb³⁺ replace the passive RE³⁺ host-forming cations. The resulting inhomogeneous spectral broadening of the absorption and emission bands is manifested in a “glassy-like” spectroscopic behavior [4–8].

In addition to the broadband emission characteristics exhibited by the dopant RE³⁺ ions, the YSP crystal, serving as a host matrix, possesses notable attributes, including chemical stability, a substantial specific heat capacity (1.17 J/gK), a modest thermal expansion coefficient (13.7 × 10⁻⁶ K^-1), and a high laser damage threshold (1.15 GW/cm² using a 10-ns pulses at 1064 nm). Despite its disordered structure leading to a relatively low thermal conductivity (1.53 W/mK at room temperature), a high-quality Yb³⁺-doped YSP crystal has recently been grown by the Czochralski (Cz) method [1,9]. A radiative lifetime of 0.92 ms was estimated for 4.8 at.% Yb:YSP in [9] from the measured absorption spectrum. The measured fluorescence lifetime of 1.267 ms for the same doping level was obviously affected by reabsorption [9]. The zero-phonon line of Yb:YSP at 976 nm features an absorption bandwidth of 6.4 nm (full width at half maximum, FWHM) which renders this material suitable for pumping by InGaAs laser diodes near 980 nm.

Due to the inhomogeneous spectral line broadening, Yb:YSP displays a wide, flat, and smooth gain profile, which is promising for wavelength tunable operation and generation of sub-100 fs from passively mode-locked (ML) lasers around 1 µm. To date, only CW lasing of Yb:YSP has been reported. Employing a multi-transverse-mode InGaAs laser diode at 976 nm for pumping, a maximum output power of 2.72 W was achieved at 1054 nm, and the maximum slope efficiency (vs. the absorbed pump power) reached 66.9% [10]. The current study is devoted to passive mode-locking in the femtosecond regime. Using a SEmiconductor Saturable Absorber Mirror (SESAM), the diode-pumped Yb:YSP laser produces sub-100 fs soliton pulses at 1062.7 nm. Utilizing a Semiconductor Saturable Absorber Mirror (SESAM), the diode-pumped Yb:YSP laser produces sub-100 fs soliton pulses at 1062.7 nm.

2. Laser set-up

The schematic of the diode-pumped Yb:YSP laser is shown in Fig. 1. A parallelepipedic sample was cut from the as-grown bulk with an aperture of 4 × 4 mm² and a thickness of 3 mm. The actual Yb³⁺ doping concentration in the crystal was measured by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) to be 4.8 at.% (Yb³⁺ ion density: N_Yb = 1.61 × 10⁻²⁰cm^-3 [9]). The uncoated sample was mounted in a copper holder without active cooling and placed at Brewster’s angle between two dichroic concave mirrors M₁ and M₂ (radius of curvature, RoC = -100 mm) in an X-shaped astigmatically compensated standing-wave cavity. The pump source was a spatially single-mode, fiber-coupled InGaAs laser diode delivering a maximum incident power of 1.34 W at 976 nm (unpolarized radiation). Its emission wavelength was locked by a fiber Bragg grating (FBG) resulting in a spectral linewidth (FWHM) of 0.2 nm. The beam propagation factor (M²) of the pump radiation at the maximum output power was measured to be 1.02 indicating near diffraction limited beam. The pump beam was collimated by an aspherical lens L₁ (focal length: f = 26 mm) and focused into the laser crystal through the M₁ mirror by a spherical focusing lens L₂ (f = 75 mm), which yielded a beam waist (radius) of 15.8 μm × 31.1 μm in the sagittal and tangential planes, respectively.

 

Fig. 1. Schematic of the diode-pumped Yb:YSr₃(PO₄)₃ laser. LD: fiber-coupled InGaAs laser diode; L₁: aspherical collimating lens; L₂: spherical focusing lens; M₁, M₂ and M₄: dichroic curved mirrors; M₃: flat rear mirror for CW laser operation; DM₁ – DM₂: flat dispersive mirrors; OC: output coupler; SESAM: semiconductor saturable absorber mirror.

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A four-mirror cavity was used to evaluate the laser performance of the Yb:YSP crystal in the CW regime. One cavity arm terminated with a flat rear mirror (M₃), while the other featured a plane-wedged output coupler (OC) with a transmission (T_OC) ranging from 0.2% to 4.5% at the laser wavelength. The fundamental mode size within the laser crystal was determined using the ray transfer matrix formalism, yielding a beam radius of 21.4 μm × 35.3 μm in the sagittal and tangential planes, respectively. Under lasing conditions, the measured single-pass pump absorption exhibited a slight decrease from 45.8% to 37.7% with T_OC, attributed to the diminishing recycling effect at lower intracavity intensity.

In the ML regime, a commercial SESAM (BATOP, GmbH) featuring a modulation depth of 3%, a non-saturable loss of 2% and a time constant of approximately 6 ps (at ∼1 µm), was incorporated instead of the flat rear mirror (M₃). Its primary function was to initiate and sustain the ML operation. An additional concave mirror (M₄) was introduced to create a second beam waist (with a spot radius of ∼73 μm) on the SESAM, ensuring efficient bleaching. To manage the material dispersion of the Yb:YSP crystal (estimated from the dispersion curves to be +60.4 fs²/mm at 1060 nm for a refractive index n of 1.658 [1]), and balance the self-phase modulation (SPM) for soliton pulse shaping, two flat dispersive mirrors (DMs) were integrated into the other cavity arm leading to an overall round-trip negative group delay dispersion (GDD) of -1220 fs². The geometrical cavity length of the ML laser was approximately 2.24 m.

3. Experimental results

3.1 Continuous-wave laser operation

The input-output characteristics and the laser emission spectra of the diode-pumped Yb:YSP laser in the CW regime are presented in Fig. 2(a). The maximum output power amounted to 333 mW at 1045.8 nm for T_OC = 1.6% at an absorbed pump power of 598 mW. This corresponds to an optical efficiency of 55.7% and a slope efficiency η of 60.9% (with respective to the absorbed pump power). The laser threshold gradually increased with the output coupling, from 22 mW (T_OC = 0.2%) to 82 mW (T_OC = 4.5%). The observed emission spectra displayed a monotonic blue-shift in the 1027-1061 nm range with increasing T_OC, as illustrated in Fig. 2(b), which corresponds to the quasi-three-level Yb³⁺ laser scheme.

 

Fig. 2. Diode-pumped Yb:YSP laser in the CW regime: (a) Input-output dependences for different OCs, η – slope efficiency; (b) Laser emission spectra.

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The overall round-trip cavity loss δ (excluding reabsorption losses) and the intrinsic slope efficiency η₀ (considering mode-matching and quantum efficiencies) were determined through Caird analysis. This involved fitting the measured laser slope efficiency as a function of the output coupler reflectivity, R_OC = 1-T_OC [11]. With an estimated intrinsic slope efficiency (η₀) of 73.1 ± 3.3% and a total round-trip cavity loss (δ) of 0.23 ± 0.05%, as depicted in Fig. 3(a), it is evident that the laser crystal employed in our study exhibits excellent optical quality.

 

Fig. 3. Diode-pumped Yb:YSP laser in the CW regime: (a) Caird analysis: slope efficiency vs. R_OC = 1 – T_OC; (b) tuning curve obtained using a Loyt filter with a 0.2% OC.

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The wavelength tuning characteristics of the diode-pumped CW Yb:YSP laser were investigated by introducing a 2-mm thick quartz-based Lyot filter at Brewster’s angle near the OC. The incident pump power in this case was 1.34 W. The emission was continuously tunable from 1007 nm to 1104 nm, of across a range of 97 nm at the zero-power-level. The smooth and broad tuning curve observed suggests a promising potential for generating sub-100 fs pulses in the ML regime.

3.2 SESAM mode-locked laser operation

Stable and self-starting ML operation of the diode-pumped Yb:YSP laser was easily attained through precise cavity alignment, including the DMs and the SESAM. The shortest pulse duration was achieved with a 1% OC. Soliton-like pulses were generated at 1062.7 nm with a spectral bandwidth of 20 nm (FWHM), assuming a sech²-shaped spectral profile, as illustrated in Fig. 4(a).

 

Fig. 4. Diode-pumped SESAM ML Yb:YSP laser with T_OC = 1%. (a) Optical spectrum and (b) measured SHG-based intensity autocorrelation (AC) trace, inset-long-scale (50-ps) AC trace.

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In Fig. 4(b), the pulse duration was measured by a second harmonic generation (SHG) based background-free intensity autocorrelator. The curve exhibits an excellent fit with a sech²-shaped temporal profile, resulting in an estimated pulse duration (FWHM) of 61 fs. With this OC, the laser emitted an average output power of 38 mW at an absorbed pump power of 514 mW, corresponding to a peak power of 8.2 kW and an optical efficiency of 7.4%. The associated time-bandwidth product (TBP) was 0.324, very close to the Fourier-transform-limited value of 0.315. The inset in Fig. 4(b) shows a long-scale (50-ps) background-free intensity autocorrelation trace, providing evidence of single-pulse CW-ML operation.

Figure 5 displays the measured radio frequency (RF) spectra of the shortest pulses. In Fig. 5(a), a remarkably sharp peak is evident at the fundamental beat-note near 66.69 MHz, boasting a high extinction ratio exceeding 75 dBc above the noise level. The 1-GHz wide frequency span measurement shown in Fig. 5(b) reveals uniform harmonics of the fundamental beat in the RF signal. These findings provide confirmation of stable single-pulse CW-ML operation of the diode-pumped Yb:YSP laser, with no indications of Q-switching instabilities or multiple pulses.

 

Fig. 5. RF spectra of the diode-pumped SESAM ML Yb:YSr₃(PO₄)₃ laser: (a) fundamental beat note at 66.69 MHz measured with a resolution bandwidth (RBW) of 300 Hz; (b) harmonics on a 1-GHz frequency span (RBW = 100 kHz). T_OC = 1%.

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To validate the underlying pulse shaping mechanism, far-field beam profiles of the Yb:YSP laser were recorded in both CW and ML regimes using an IR camera positioned at approximately 0.6 m from the OC. A subtle cavity misalignment facilitated a seamless transition between the CW and ML regimes. Remarkably, minimal changes in the far-field beam diameters were observed during this transition, as illustrated in Fig. 6. The absence of indication of Kerr-lensing, coupled with the superb sech²-shaped spectral and temporal profiles of the shortest pulses, strongly suggests that soliton mode-locking was dominant pulse shaping mechanism.

 

Fig. 6. Measured far-field beam profiles of the diode-pumped Yb:YSP laser: (a) CW regime; (b) ML regime.

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4. Conclusion

In summary, we demonstrate sub-100 fs pulse generation in a diode-pumped SESAM mode-locked Yb:YSr₃(PO₄)₃ laser. Soliton pulses, with a nearly Fourier-transform-limited duration of 61 fs, were generated at 1062.7 nm. The average output power was 38 mW at a pulse repetition rate of ~66.7 MHz. This represents the first demonstration of passively mode-locked operation in the Yb:YSr₃(PO₄)₃ crystal. The limitation for scaling the average output power is mainly limited by the relatively low pump absorption as well as a very low available pump power of laser diode. Leveraging the unique “glassy-like” spectroscopic properties of Yb:YSr₃(PO₄)₃, we anticipate further advancements in pulse shortening and power-scaling through Kerr-lens mode-locking, particularly by utilizing high-power, single-transverse-mode Yb-fiber lasers as pump sources.