1. INTRODUCTION

Coherent ultrafast pulse lasers in the visible wavelength region are useful light sources in spectroscopy, material processing, medicine, and biology. Conventionally, visible ultrafast laser pulses can be generated as a second harmonic of near-infrared laser pulses by employing frequency conversion techniques. However, ideally, we can replace them with all solid-state direct oscillating visible laser systems for improving compactness and cost effectiveness.

Trivalent praseodymium ion (${\mathrm{Pr}}^{3+}$) is a unique laser gain material that has many optical transitions in a wide range of the visible region from 480 to 720 nm. Because of its utilities for miniaturization or efficiency improvement, ${\mathrm{Pr}}^{3+}$-doped laser media are gathering attention because they permit oscillation in the visible region without frequency conversion.

For room temperature operation of a ${\mathrm{Pr}}^{3+}$ laser, host materials of low phonon energy are required, and laser actions of ${\mathrm{Pr}}^{3+}$ lasers are obtained with fluoride hosts, such as YLF (${\mathrm{LiYF}}_4$) [1], LLF (${\mathrm{LiLuF}}_4$) [2], KYF(${\mathrm{KY}}_3{\mathrm{F}}_{10}$) [3] crystals, and ZBLAN [4] and ${\mathrm{AlF}}_3$ [5] fibers. Since ${\mathrm{Pr}}^{3+}$-doped fluorides have absorption peaks around 440 nm, they can be pumped by InGaN blue laser diodes (LDs) whose output power and efficiency have been making significant progress [6]. In particular, a ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{LiYF}}_4$ (YLF) laser was reported with high efficiencies (slope efficiency up to $\sim 60\%$) and a low threshold [7,8]. The ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser enabled direct oscillations at deep red ($\sim 720$, $\sim 700\mathrm{nm}$), red ($\sim 640\mathrm{nm}$), orange ($\sim 610\mathrm{nm}$), and green ($\sim 520\mathrm{nm}$) transitions have been realized at room temperature.

Regarding the pulsed oscillation of ${\mathrm{Pr}}^{3+}$ lasers, passive $Q$-switching was reported with a semiconductor saturable absorber mirror (SESAM) [9], ${\mathrm{Cr}}^{4+}\text{:}\mathrm{YAG}$ crystal [10,11], gold nanoparticles [12], and nanosheets of transition metal dichalcogenides (TMDs) [13,14] as saturable absorbers. Kerr-lens mode-locking of ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ lasers at 607 and 640 nm was realized with argon-ion laser pumping [15,16].

Recently, using a SESAM, Gaponenko et al. successfully demonstrated a passively mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser pumped by a frequency-doubled optically pumped semiconductor laser ($2\omega$-OPSL) operating at the red wavelength [17]. The maximum averaged output power reached 16 mW at an incident pump power of 3.75 W with a mode-locked pulse width of 18 ps (FWHM). Due to the narrow gain bandwidth of the transition (${}^3{\mathrm{P}}_0\to {{}^3\mathrm{F}}_2$) in the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$, generating mode-locked subpicosecond pulses is challenging.

In this paper, to the best of our knowledge, we report the first SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser that is directly pumped by InGaN LDs. On the other hand, since broadband SESAMs are not available, and high-power laser operation is prohibited due to the low damage threshold of SESAMs, pure Kerr-lens mode-locking of ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ lasers is still desired. However, for multimode diode pumping, obtaining sufficient self-focusing cannot be expected because of relatively low intracavity intensity. Moreover, multimode diode pumping tends to induce multimode laser oscillation. For solving these problems, in this work, we employed an SF57 glass as a Kerr medium and attempted a hard-aperture Kerr-lens mode-locking [18].

2. SESAM MODE-LOCKING OF ${\mathsf{Pr}}^{\mathsf{3}+}\text{:}\mathsf{YLF}$ LASER AT 640 nm

A. Experimental Setup

The experimental setup of a SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser is depicted in Fig. 1. A 5-mm-long ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ crystal (Unioriental Inc.) doped with ${\mathrm{Pr}}^{3+}$ at a concentration of 0.5 at. %, which was cut parallel to the c-axis, was placed in front of the plane pumping mirror. As pump sources, we used two InGaN blue LDs (Nichia Inc.). Each output power reached 3.5 W. The LD’s emitter size was $1\times 30\mathrm{\mu m}$ with a divergence angle of $2\theta$ of $45.9\times 13.9°$, which corresponded to $M^2=1.5\times 13$ (fast axis × slow axis). To maximize the absorbed power, the wavelength of each LD was tuned to 444 and 442 nm by Peltier devices, since the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ crystal respectively has absorption peaks at 444 and 442 nm for polarization parallel to the c- and a-axes [19]. The pump beam from each LD was collimated by an aspherical lens with a focal length of 4.6 mm and expanded along the slow axis by a cylindrical lens pair ($f=-20$ and 100 mm). Then the beam was focused into the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ crystal through a lens whose focal length was 75 mm. At 444 and 442 nm, the absorption coefficients of the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ crystal were measured to be 3.54 and 1.16/cm, which respectively corresponded to absorbed pump powers of 2.2 and 1.6 W. Therefore, the total absorbed pump power reached 3.8 W.

 

Fig. 1. Schematic view of cavity configuration for a SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser: polarization beam splitter (PBS); half-wave plate (HWP); dichroic mirror (DM); and output coupler (OC).

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The SESAM in this experiment contained three 6-nm-thick GaInP quantum wells that were embedded within an AlGaInP cavity and placed on top of a 40-pair AlGaAs/AlAs distributed Bragg reflector (DBR) (RefleKron Ltd.) that had a center reflection wavelength of 640 nm, a response time of 300 ps, and an unsaturated reflectivity of 97%. According to the $2\omega$-OPSL pumped ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ mode-locked laser reported by Gaponenko et al. [17], who used the same SESAM as we used, the necessary intensity of the SESAM for achieving stable mode-locking was estimated to be $\sim 23\mathrm{MW}/{\mathrm{cm}}^2$.

The 1.4-m-long Z-folded laser cavity consists of four mirrors: an output coupler M1 (OC) with 10% transmission; two high-reflectivity (HR) concave mirrors, M2, M3 (${\mathrm{ROC}}_{\mathrm{M}2}=100\mathrm{mm}$, ${\mathrm{ROC}}_{\mathrm{M}3}=75\mathrm{mm}$); and a plane mirror M4 (HR mirror or SESAM). To obtain stable mode-locking, the SESAM intensity must be higher than the estimated saturation intensity. For designing the cavity mode of ${\mathrm{TEM}}_{00}$, we used the cavity design proposed by Qiao et al. [20] to compensate for the astigmatism on the SESAM and to reach sufficiently high intracavity intensity. Equations (1) and (2) express the effective focal lengths of a concave mirror in the sagittal and tangential directions when the angle of incidence is $\theta$ [21]:

When a Gaussian beam is focused by a lens with a focal length of $f$, Eqs. (3) and (4) provide the relationship between a spot size and a distance from the concave mirror to the spot [22]:

Using these equations, a Z-folded cavity, in which the astigmatism can be compensated at the focal spots, is designed in the following three steps: (1) set a spot size ($w_1$); (2) set a concave mirror (M2) at a position where the Gaussian beam radius corresponds to the beam radius after being transcribed by a concave mirror (M3) in both the sagittal and tangential planes; and (3) set an M2 angle to correspond to the transcribed spot size ($w_2^{\prime }$) in the sagittal and tangential planes. In this experiment, we designed a cavity so that the beam waist spot size became $10\mathrm{\mu m}\times 10\mathrm{\mu m}$. The mode-matching efficiency between the pump and cavity modes was calculated to be 78%. With this cavity, the estimated value of the averaged output power, that we had to obtain for reaching the SESAM’s saturation intensity, was 14 mW.

B. Experimental Results and Discussion

With an M4 HR mirror, we obtained an averaged CW output power of 550 mW and replaced the plane M4 mirror by a SESAM to achieve mode-locked oscillation. Figure 2 shows the output power as a function of the absorbed pump power. From an absorbed pump power of 2.8 W, stable mode-locking started. At a maximum absorbed pump power of 3.8 W, we obtained the highest averaged output power of 65 mW at a pulse repetition rate of 108.7 MHz. The mode-locked pulse width was measured as 45 ps (FWHM) by a streak camera (Hamamatsu C4334, 15-ps resolution) (Fig. 3). Figure 4 shows a spectrum measured by a spectrum analyzer (ADVANTEST Q8384 Optical Spectrum Analyzer, 0.01-nm resolution) under mode-locked operation. The center wavelength was 639.7 nm, and the spectral width (FWHM) was 0.1 nm, which corresponded to a transform-limited pulse width of 4.2 ps. Gaponenko et al. obtained a pulse width of 18 ps (FWHM) with SESAM mode-locking [17]. The reason for such a longer pulse width far from the Fourier transform limit remains an open question. The actual spectrum width might be much narrower than our measurement where the spectrum was integrated over $\sim 1\mathrm{s}$ by the optical spectrum analyzer. In fact, the measured spectrum shows some internal structures (Fig. 4). The stable mode-lock oscillation was maintained for more than a half hour.

 

Fig. 2. Output power of SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser as function of absorbed pump power.

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Fig. 3. Single pulse trace of SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser. Inset shows pulse train in microsecond time scale.

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Fig. 4. Optical spectrum of a SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser measured at maximum absorbed pump power of 3.8 W. Spectral resolution was 0.01 nm.

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3. KERR-LENS MODE-LOCKING

A. Experimental Setup

Figure 5 shows a schematic view of a Kerr-lens mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser cavity. A 4-mm-long, 0.5 at. % doped ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ crystal was cut at a Brewster’s angle of 55.5°. As a Kerr medium, we employed an SF57 glass, which had a huge nonlinear refractive index of $4.1\times {10}^{-19}{\mathrm{m}}^2/\mathrm{W}$ [23]; the nonlinear refractive index of YLF was $1.4\times {10}^{-20}{\mathrm{m}}^2/\mathrm{W}$ [24]. The 2-m-long cavity consists of six mirrors: a plane end mirror, M1; a pair of concave mirrors, M2, M3 (${\mathrm{ROC}}_{\mathrm{M}2,3}=75\mathrm{mm}$); two pumping concave mirrors, M4, M5 (${\mathrm{ROC}}_{\mathrm{M}4,5}=100\mathrm{mm}$); and an OC of 1.2%. We employed optical isolators to protect the LDs from any backreflected beams and unabsorbed opposite pump beams, which were polarized parallel to the c-axis of the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ and focused into the gain crystal by lenses with a 100-mm focal length.

 

Fig. 5. Schematic view of a Kerr-lens mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser with SF57 glass.

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In this experiment, we designed a cavity so that the mode size at the aperture changes significantly in the pulsed operation and realizes fine hard-aperture Kerr-lens mode-locking. The cavity stability depends on the two independent distances between the two pairs of concave mirrors that were placed on both sides of the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ rod and the SF57 glass. Since we expected to obtain the maximum mode size change at the end mirror, we calculated the change in mode radius normalized to the CW mode radius on the end mirror as the parameters of the distances between the two pairs of mirrors placed at both sides of the ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ rod and the SF57 glass with an ABCD matrix method, based on the Kerr lens effect.

An effective focal length of the Kerr lens is given by Eq. (5):

 

Fig. 6. The change in mode radius normalized to the CW mode radius in the sagittal direction of the end mirror with a SF57 glass. At darker range, larger beam radius change is expected. ${\delta }_{\mathrm{YLF}}$ and ${\delta }_{\mathrm{NL}}$ express differences from confocal length of two concave mirrors placed on both sides of ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ and SF57 glass, respectively. Averaged output power of 20 mW was assumed with a pulse width of 15 ps.

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In Fig. 7, we compared the change in the mode radius on the OC with fused silica as the nonlinear medium with that with a SF57 glass. We assumed averaged output power of 20 mW. The nonlinear refractive index of the fused silica was $2.5\times {10}^{-20}{\mathrm{m}}^2/\mathrm{W}$ [25]. Since its nonlinear refractive index was much lower than that of the SF57 glass, the maximum change in a beam radius of 26% from the fused silica was smaller.

 

Fig. 7. Change in mode radius normalized to the CW mode radius in the sagittal direction of the end mirror with a fused silica. At darker range, larger beam radius change is expected. ${\delta }_{\mathrm{YLF}}$ and ${\delta }_{\mathrm{NL}}$ express differences from a confocal length of two concave mirrors placed on both sides of ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ and fused silica, respectively. Averaged output power of 20 mW was assumed with a pulse width of 15 ps.

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B. Experimental Results and Discussion

We obtained a CW laser power of $\sim 1\mathrm{W}$ at a highest absorbed pump power of 4.2 W with the optimal cavity adjusted for CW operation. Figure 8 shows an output pulse train when a knife edge is inserted in front of the OC in the sagittal direction as well as the recorded pulse train. We observed $Q$-switch mode-locking with the averaged output power of $\sim 50\mathrm{mW}$. The $Q$-switched pulse repetition rate was measured as 120 kHz. The pulse width was measured as 1 ns. The pulse repetition rate was measured as 151 MHz, which is double the value calculated from a cavity length of 2 m. Presumably because the Kerr lens effect became too strong, the oscillation condition shifted to a state with a higher pulse repetition rate to reduce the pulse peak power. Then, instead of an SF57 glass, we employed fused silica to decrease the nonlinear effects. However, in this case, we failed to achieve even $Q$-switch mode-locking.

 

Fig. 8. (a) Output pulse of a $Q$-switch mode-locked laser in microsecond time scale. Inset shows the $Q$-switch pulse train in tens of microseconds time scale. (b) Pulse train in tens of nanoseconds time scale measured by a photodiode.

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Figure 9 shows the pulse train obtained when we tapped an end mirror M1 with the SF57 glass. The pulse train, which was only measured immediately after tapping, soon switched back to the pulses shown in Fig. 8 within a several seconds. However, the pulse repetition rate of 75 MHz obtained by the pulse train in Fig. 9 equaled the value calculated from the cavity length. In addition, the pulse width was shortened to $\sim 400\mathrm{ps}$ (the measurement limit value of our photodiode), which is much shorter than before tapping the mirror. These experimental results suggest that we may be able to achieve stable mode-locking at more stable cavity condition for mode-locking. Presumably, since the proper Kerr-lens mode-locking condition attained such a limited condition near the unstable cavity condition, as shown in Fig. 6, no self-sustained Kerr-lens mode-locking occurred in our cavity design.

 

Fig. 9. Output pulse train measured only just after vibrating M6.

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We calculated again the beam radius reductions at the Kerr lens formation for higher intracavity laser intensities. The results are shown in Fig. 10. As the averaged output power increased from 20 to 80 mW, the cavity condition, where the beam size was reduced by more than 60%, extended to a wider area. Therefore, we may be able to attain a stable mode-lock cavity condition at high-power laser operations.

 

Fig. 10. Change in mode radius normalized to the CW mode radius in the sagittal direction of the end mirror when we assume 15-ps pulse width with the following averaged output power: (a) 20 mW (original condition), (b) 40 mW, (c) 60 mW, and (d) 80 mW. Scale of color bar was changed for (b), (c), and (d).

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Very recently, we noticed that a thermal lens assisted KLM was achieved by Zhang et al. [26] with a $\mathrm{Pr}\text{:}{\mathrm{GdLiF}}_4$ laser crystal pumped by InGaN LDs in a short laser cavity. Since the Kerr nonlinearity of ${\mathrm{GdLiF}}_4$ is much higher than that of YLF, this scheme will also be suitable for ultrashort pulse generation by ${\mathrm{Pr}}^{3+}$ lasers.

4. CONCLUSIONS

In this paper, to the best of our knowledge we reported the first SESAM mode-locked ${\mathrm{Pr}}^{3+}\text{:}\mathrm{YLF}$ laser that is directly pumped by InGaN LDs. Stable mode-locked operation started from absorbed pump power of 2.8 W. At absorbed pump power of 3.8 W, a maximum averaged output power of 65 mW was obtained with a pulse width of 45 ps (FWHM) at a pulse repetition rate of 108 MHz. By employing a SF57 glass as a Kerr medium, we also tried LD-pumped Kerr-lens mode-locking. In this approach, however, we could not achieve self-sustained CW mode-locking and only obtained a $Q$-switch mode-locked pulse train whose pulse repetition rate was doubled. The laser operation only switched to CW mode-locking immediately after we tapped an end mirror. Our model calculations predicted that a stable mode-locking cavity condition could be found with larger Kerr effects at high-power laser oscillation.