Mode-locked lasers with GHz repetition rates have a plethora of promising applications, for example in clocking, RF referencing, and frequency comb spectroscopy [1,2]. For the latter, a high repetition rate in combination with high average power and low noise levels enables widely spaced, powerful single comb lines, which is beneficial for increasing signal-to-noise ratio in spectroscopy. GHz femtosecond lasers in many wavelength regions are nowadays successfully applied in time or comb-resolved spectroscopy [3,4]. In addition, high-power GHz repetition rate lasers also showed great potential for material processing to improve the ablation efficiency while maintaining the ablation quality [5].

For all these applications, significant efforts were made to generate GHz ultrashort pulses with high average powers. In this regard, many realizations were done with fiber lasers [6,7], while bulk lasers can provide an attractive combination of average power and low noise operation [8]. Most efforts in this direction were realized in the 1-µm wavelength region [3,4,9] with a state-of-the-art average power of 6.9 W from a Yb bulk oscillator [9]. Meanwhile, there is an increasing interest in operating at longer wavelengths >1.5 µm for many of these applications, e.g., for spectroscopy, to directly address greenhouse gas detection [10] or even >2 µm to efficiently reach the molecular fingerprinting region via nonlinear conversion. To date, most 2-µm GHz lasers are based on Tm fibers and Cr:ZnS bulk lasers. In terms of fiber geometry, scaling the average power from GHz oscillators is still a challenge due to the low gain provided by short fibers, with typical average power in the mW regime [7]. Therefore, multi-stage amplifiers are needed to achieve watt-level average power, making the laser systems complex and typically increasing the noise level. Mode-locked bulk lasers provide a promising alternative to reach watt-level average power directly from a GHz oscillator. Recently, a SESAM mode-locked Cr:ZnS oscillator was reported with a repetition rate of 2 GHz, an average power of 0.8 W, and a pulse duration of 155 fs [11]. In this laser, a specially designed SESAM is necessary to achieve stable mode-locking. In [12], a Kerr-lens mode-locked Cr:ZnS oscillator with an adjustable repetition rate generated 120 mW of average power in 50-fs pulses at 1.2 GHz, and 1.2 W was obtained at 1 GHz with a slightly longer pulse duration of 75 fs, representing thus far the highest average power from a 2-µm GHz oscillator. However, average power scaling is generally challenging due to the special thermal properties of the Cr:ZnS [13]. Therefore, it is a well-justified task to seek other materials that can achieve high-power, short-pulse mode-locking in this wavelength region. Furthermore, the emission wavelength of the Cr:ZnS laser is at 2.4 µm, and a variety of applications desire efficient, high-power lasers in the atmospheric transmission window at 2.1 µm. In this regard, Ho³⁺-doped bulk materials are excellent candidates. In particular, the disordered Ho:CaGdAlO₄ (Ho:CALGO) crystal features excellent thermal properties [14], and has been proven to support femtosecond pulse duration with watt-level average power [15,16] at repetition rates <100 MHz. However, Ho-based gain materials typically feature millisecond-level fluorescence lifetimes at 2 µm, which constitutes a challenge for stable mode-locking at a higher repetition rate because of likely Q switching instabilities [17,18], preventing significant progress in the mode-locked GHz operation.

In this work, we demonstrate the first mode-locked Ho:CALGO bulk laser at a GHz fundamental repetition rate. The repetition rate is 1.179 GHz with a maximum average power of 1.69 W and an optical-to-optical efficiency of 12.4%. This is the first GHz Ho-bulk laser system and represents the highest average power from a GHz oscillator at 2 µm. The average power scaling to even higher levels will be possible in the near future by optimizing the crystal size and heat sink. The pulse duration is as short as 92 fs benefiting from the large gain bandwidth of the Ho:CALGO crystal, representing the first sub-100-fs pulse duration from a Ho-based oscillator.

Figure 1 shows the experimental setup of our Kerr-lens mode-locked GHz Ho:CALGO laser. We used a 10-mm long a-cut 3.1 at.% doped Ho:CALGO crystal (provided by the Electro-Optics Technology Inc. (now Coherent Corp.)) as the laser gain medium. The aperture of the crystal is 4 mm × 4 mm. Both end surfaces were anti-reflection-coated for the wavelength range of 1900 to 2200 nm. To ensure good heat dissipation and avoid condensation on the end faces, the cooling temperature of the crystal was kept at 16°C. At the GHz fundamental repetition rate, the cavity length should be less than 15 cm for a standing wave cavity. However, instead of a standing wave cavity, we used a ring cavity to increase the repetition rate in a resonator that is easier to handle. In this way, the laser only passes through the crystal one time for every round trip, but the resonator design is relaxed. In addition, the total round trip group delay dispersion (GDD) can be lower, which is beneficial for achieving shorter pulse durations.

 

Fig. 1. Experimental setup of the GHz fundamental repetition rate Ho:CALGO laser. M1 and M2, input mirror; DM, dispersive mirror, −1000 fs² per bounce; OC, output coupler. The arrows next to the crystal are the crystal axes. Counterclockwise and clockwise outputs are marked as output 1 and output 2, respectively.

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The two concave mirrors M1 and the output coupler (OC) have the same radius of curvature (RoC) of −50 mm. M1 has a high-transmission coating at the pump wavelength and exhibits high reflectivity (HR) at the laser wavelength. The OC is HR-coated at the pump wavelength and exhibits 0.5% transmission at the laser wavelength. The plane mirror M2 has the same reflectivity at the laser emission range as M1, allowing for single-pass absorption in the laser crystal. To achieve stable soliton mode-locking, the total round trip GDD was optimized and amounted to −1550 fs², including −1000 fs² from the dispersive mirror (DM) and −550 fs² from the 10-mm Ho:CALGO crystal (σ-polarization). With this arrangement, the fundamental repetition rate of this ring cavity is around 1.2 GHz. A single mode unpolarized 1940-nm Tm fiber laser was used as the pump source. The calculated pump beam waist has a radius of 55 µm inside the crystal. The maximum pump power was limited to 18 W to avoid thermal damage. The single-pass pump absorption of the crystal was estimated by the difference between the incident pump power and the leaked pump power behind the M2.

The cavity was first aligned in a continuous-wave (CW) operation. The crystal was placed closer to the OC, as shown in Fig. 1. Then the OC was aligned to achieve the highest output power for a fixed incident pump power. In this case, the laser works in a bidirectional mode, i.e., output 1 and output 2 in Fig. 1 operate simultaneously. Both outputs have nearly the same output power and slope efficiency. A total output power of 3.7 W was obtained at the incident pump power of 18 W (single-pass absorption 61.7%). The natural birefringence of the Ho:CALGO crystal enables a linearly polarized laser output (E⊥c, σ-polarization) at 2133 nm for both outputs.

To achieve mode-locking, the OC was slightly moved toward the crystal by ∼940 µm. In this case, the CW output power decreases rapidly. As a reference, the power of output 1 will reduce from 1.44 to 0.4 W at 13.6 W of the incident pump power. To start the mode-locking, the incident pump power was increased to 18 W, then the self-starting counterclockwise mode-locking was observed. The unidirectional operation is due to the different Kerr nonlinearities in the crystal for the two opposite directions. In this way, one oscillation direction sees a preferential gain and is thus favored [19]. When the laser self-starts, the laser spectrum exhibits a clear CW breakthrough peak. However, the incident pump power can be safely reduced while maintaining stable and robust mode-locking to operate the laser without a CW background.

Figure 2 shows the average output power and pulse duration of the counterclockwise oscillation (output 1) at different incident pump powers. Stable mode-locking can be achieved starting from an incident pump power of 12.4 W (single-pass absorption 60.3%) to a maximum value of 13.6 W (single-pass absorption 59.2%). The corresponding output power ranges from 1.55 to 1.68 W, resulting in an optical-to-optical efficiency of 12.4% at the maximum output power. In this range, the pulse duration decreases from 99 to 93 fs, and the output laser remains linearly polarized in the σ-polarization. When the pump power is further increased, the output power saturates accompanied by a slight increase in pulse duration. This is because in a mode-locking condition, the mode beam radius will shrink below the pump radius at a higher pump power, resulting in a slight mismatch between the pump and the laser mode, which leads to the saturation of the amplitude modulation and the generation of higher-order transverse modes. We confirmed the generation of higher-order transverse modes by the beating frequencies in the radio frequency spectrum [20]. This eventually limits the further increase of intra-cavity intensity and reduction of the pulse duration. At 1.68 W of output power, the output pulses have a fitted (sech²) full width at half-maximum spectral bandwidth (FWHM, Δλ) of 55 nm at the center wavelength of 2159.1 nm, as shown in Fig. 3(a). The pulse duration (Δτ) was measured by a second harmonic generation-based intensity autocorrelator (PulseCheck, A.P.E. GmbH), and a FWHM pulse duration of 93 fs is extracted assuming the soliton of shaped pulses, as shown in Fig. 3(b), resulting in a peak power of 13.4 kW. The corresponding time–bandwidth product (TBP) is 0.329, which is close to the TBP (0.315) of an ideal soliton (sech² fitting). The slight chirp most likely stems from the substrate of the OC and a subsequent collimation system. Further, the ring cavity tends to prevent the generation of satellite pulses [19]; we also did not find multi-pulsing in the 16-ps autocorrelation scan, as shown in Fig. 3(b).

 

Fig. 2. Average output power and pulse duration of the counterclockwise oscillation at different incident pump powers. The dashed line marks the incident pump power for shortest pulse duration in stable mode-locking.

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Fig. 3. Laser properties of the counterclockwise oscillation at 1.68 W of output power. (a) Laser spectrum; (b) autocorrelation measurement result, inset is 16-ps autocorrelation scan; (c) radio frequency spectrum in the 10-GHz range. RBW, resolution bandwidth; (d) radio frequency spectrum of the fundamental beat note.

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To characterize the mode-locking stability, the radio frequency spectrum was measured with a 12.5-GHz photodiode (EOT-5000, Coherent Inc.) and recorded by a 20-GHz radio frequency analyzer (MS2720 T, Anritsu Corp.). The beat notes in Fig. 3(c) exhibit only a slight reduction in intensity due to the limited bandwidth of the photodiode and are free of multi-transverse modes beating in a 10-GHz scanning range, indicating stable single-transversal-mode mode-locking [21]. The fundamental repetition rate was measured to be 1179.22 MHz with a spurious free dynamic range of more than 70 dBc, as shown in Fig. 3(d).

In order to operate the oscillator in a clockwise direction (output 2), the crystal was moved slightly toward mirror M1. The mirrors DM and OC were realigned to achieve the highest laser output power. The laser exhibited a similar behavior to that of the counterclockwise oscillation when it starts the mode-locking, i.e., self-starting in CW at 18 W of incident pump power. Figure 4 shows the average output power and pulse duration at different incident pump powers in a clockwise direction. Only slightly different from the results of the counterclockwise oscillation in Fig. 2, the incident pump power for the stable mode-locking ranges from 12.8 W (single-pass absorption 58%) to 13.6 W (single-pass absorption 56.9%) corresponding to an average output power of 1.58 to 1.69 W (σ-polarization). At the maximum output power, the optical-to-optical efficiency is 12.4%. The change in output power and single-pass absorption is induced by the change of the pump-laser mode matching. This occurs because the laser oscillation direction can be adjusted by adjusting the loss and gain of the resonator in one direction [22]. However, multi-transverse mode beating here is also the reason that limits stable mode-locking at a higher pump power. Figure 5 shows the laser properties at 1.69 W of the average output power. The central wavelength is 2159.4 nm with a spectral bandwidth of 54.6 nm (FWHM, Δλ), while the pulse duration is 92 fs (FWHM, Δτ), resulting in a TBP of 0.323. No multi-pulsing was found in the 16-ps autocorrelation scan, as shown in Fig. 5(b). The clean radio frequency spectra in Figs. 5(c) and 5(d) show stable single transverse-mode mode-locking. The fundamental repetition rate was measured to be 1179.13 MHz with a spurious free dynamic range of more than 70 dBc. A slight reduction of the fundamental repetition rate was induced by the change of the cavity length.

 

Fig. 4. Average output power and pulse duration of the clockwise oscillation at different incident pump powers. The dashed line marks the incident pump power for the shortest pulse duration in stable mode-locking.

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Fig. 5. Laser properties of the clockwise oscillation at 1.69 W of average output power. (a) Laser spectrum; (b) autocorrelation measurement result, inset is 16-ps autocorrelation scan; (c) radio frequency spectrum in the 10-GHz range; (d) radio frequency spectrum of the fundamental beat note.

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During our experiment, we did not observe bidirectional mode-locking when we tried to adjust the cavity. In addition, the potential risk of crystal damage at a higher pump power to start the mode-locking limited the power scaling with a higher output transmission. At the maximum output power level, mode-locking in both directions was observed to be stable for hours. Especially, the stability of our GHz laser in the clockwise direction was characterized in detail. We measured the average output power at 1.69 W for 1 h which resulted in an RMS power stability of 0.09%, indicating excellent long-term stability, as shown in Fig. 6(a). Furthermore, the amplitude and phase noises of the laser were measured at a carrier frequency of the first harmonic with a phase noise analyzer (FSWP50, Rohde & Schwarz), as shown in Figs. 6(b) and 6(c). The noise peaks at low frequency (<1 kHz) from the relative intensity power spectral density (RIN PSD) of amplitude noise should come from the mechanical vibration. The weak and broadband noise at an offset frequency of 350 kHz is most likely produced by the relaxation oscillation of the Tm fiber laser we used as a pump [16]. The integrated RIN of the GHz laser is 0.08% in the integration interval from 10 Hz to 10 MHz. Regarding the phase noise, the free-running integrated timing jitter is 13 ps (RMS phase noise, 96 mrad) in the integration interval from 10 Hz to 10 MHz. Affected by a high repetition rate and low intra-cavity pulse energy, the phase noise becomes higher at the GHz repetition rate compared with the phase noise of our bulk oscillator at the 100-MHz repetition rate [8,16]. The measured phase noise is comparable to a previously reported GHz-Cr:ZnS laser [11].

 

Fig. 6. Stability and noise measurement of the GHz Ho:CALGO laser at 1.69 W of average power. (a) Power stability in 1 h; inset is a zoom-in view of the output power in 6 min; (b) amplitude noise. RIN, relative intensity. PSD, power spectral density; (c) phase noise.

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In conclusion, we have demonstrated a Kerr-lens mode-locked Ho:CALGO laser with watt-level average power at a 1.179 GHz fundamental repetition rate, representing the highest average power GHz oscillator demonstrated to date in the 2-µm wavelength region. The ring laser works in a stable and adjustable unidirectional output. For the counterclockwise oscillation, the average power was 1.68 W with 93 fs of pulse duration; while for the clockwise oscillation, the average power was 1.69 W with 92 fs of pulse duration. This also represents the first sub-100-fs Ho laser demonstrated so far. The laser shows excellent power stability and low noise. However, as our mirrors are optimized for the central wavelength of 2100 nm, a dramatic drop of its reflectivity at a longer wavelength can be predicted, which will induce strong GDD variation [23]. The difficulty in managing the dispersion at a longer wavelength in our case will limit the generation of shorter pulse duration. In the near future, we believe significantly shorter pulses in the sub-50 fs regime can be achieved with optimized coatings and Kerr strength. Further power scaling can be considered by better thermal management of the crystal to enable mode-locking with a higher output transmission at higher pump power. The demonstrated laser should be an excellent candidate for the repetition frequency and the carrier-envelope offset-frequency stabilization to achieve a stable GHz frequency comb. Furthermore, the current laser system offers also interesting perspectives for other applications, e.g., in material processing.