1 Introduction

The 27Al+ ion clock has been recognized as a high-accuracy optical clock based on the 1S0↔3P0 transition [1–6] because of its good physical properties, such as narrow natural linewidth (8 mHz), immunity to magnetic fields and electric field disturbances in ion traps [1], and small room-temperature blackbody radiation shift [2]. However, the ion cannot currently be directly laser cooled due to the lack of an accessible laser at 167 nm, corresponding to the 1S0↔1P1 transition in the 27Al+ ion. To overcome the difficulty, a method of quantum logic spectroscopy (QLS) [1–5] was utilized, where an auxiliary ‘logic ion’ takes over the requirement of laser cooling. The coupled motion of the two ions allows for sympathetic cooling [3], and 27Al+ optical clock has been achieved with a fractional frequency inaccuracy of 8.6 × 10−18 [4]. Unfortunately, some mechanisms [4, 5, 6], such as the mass mismatch between logic ion and the 27Al+, excess micromotion (EMM) in Paul trap near trap drive frequency and harmonic oscillator motion (HOM) at ions normal mode frequencies, shift the clock from its optimal frequency, which degrades the clock accuracy. It is reasonable that there is potential for 27Al+ optical clock to achieve higher accuracy. Clearly, the direct Doppler cooling through the 1S0↔1P1 transition [3, 7, 8] is expected for a 27Al+ ion. With the combination of the resolved-sideband laser cooling [9] through 1S0↔3P1 transition [8], the merits of direct Doppler cooling over QLS are obvious. The 27Al+ optical clock system and the interrogation process of 27Al+ state are simplified. Furthermore, it is possible to reduce the EMM and HOM, thus a higher-accuracy optical clock with fractional frequency inaccuracy proximity to 10−19 is expected.

The most crucial difficulty of direct Doppler cooling is that 1S0↔1P1 transition emits light of 167.0787 nm [3, 8], which is in the DUV region and it is unavailable in the past. Until now, efficient laser output around 167.0787 nm has never been available.

Fortunately, the development of KBBF crystal provides a possible way for generating efficient 167.0787-nm laser. The KBBF crystals have the proven abilities for generating deep-ultraviolet (DUV) laser (<200 nm) [10, 11] by cascaded second-harmonic generation (SHG). Recently, our lab has obtained a picosecond 167-nm laser by KBBF crystal [12]. Thus, the eighth-harmonic generation of 1336.630-nm laser by KBBF is a candidate scheme for 167.0787-nm laser as long as the fundamental laser at 1336.630 is available.

In order to be qualified as the pumping beam [6] for 27Al+ ion optical clock, the properties of the fundamental laser (FL) at 1336.630 nm, such as narrow linewidth (about 0.48 pm which is (2√2)3 times the natural linewidth of 27Al+ of 0.02 pm), high wavelength stability (fluctuation less than 0.48 pm), fine tunability and good beam quality, should be satisfied.

An appropriate laser crystal is very important which must have the emission spectrum around 1336.6 nm. At present, the only report on 1336.6-nm laser is based on the Nd-doped gadolinium yttrium scandium gallium garnet (Nd:GYSGG) crystal [13]. Nd-doped gadolinium scandium gallium garnet (Nd:GSGG) is another candidate crystal. By comparison, the two crystals possess similar emission spectra and similar fluorescence branch ratios of about 0.10 at 1.3-μm region [14, 15], while the measured peak of the emission spectrums at 1.3-μm region in our lab is 1336.0 nm for Nd:GYSGG [13] and 1336.2 nm for Nd:GSGG, which clearly reveals that the Nd:GSGG crystal is favorable to produce 1336.6-nm laser compared to Nd:GYSGG. Furthermore, other advantages of Nd:GSGG include the higher segregation coefficient of 0.65 [15] than that of Nd:GYSGG of 0.60 [14], and the higher thermal conductivity of 6.0 W/m K than that of Nd:GYSGG of 4.3 W/m K [14–16]. As is well known, it is likely to produce higher pulse energy for a gain medium with higher thermal conductivity.

Nd:GSGG has been studied since almost four decades ago in terms of spectroscopic property [15, 16], thermal property[15–17], laser efficiency [18, 19] and so on. The interest mainly focuses on the emission at 1.06 μm; by codoping Cr3+ as ‘sensitizer’ in GSGG, it shows very high efficiency of transferring excitation [20] when pumped by flash lamp or solar. Nd:GSGG laser based on 4F3/2↔4I13/2 transition has been reported in Ref. [21], a self-Q-switched laser operated with wavelength of 1.32 μm, and the efficiency is 1 %. However, output laser at 1336.6 nm based on Nd:GSGG has never been reported to our knowledge.

This letter presents a tunable single-frequency ring Nd:GSGG laser at 1336.6 nm delivering a maximum pulse energy of 0.26 J at 10 Hz when it is pumped with laser diode (LD) energy of 5.68 J. The root-mean-square (RMS) of wavelength fluctuation in 1 h is 0.27 pm, and the beam quality M2 is 1.06 at the output energy of 0.16 J per pulse.

2 Experiment setup

The sketch of the experimental setup is shown in Fig. 1. The resonator is composed of two homemade laser (LH1 and LH2) heads, a quartz rotator (QR), two flat mirrors (M1 and M2), a thin film polarizer (TFP), two etalons (FP1 and FP2), a birefringent filter (BF), a Faraday rotator (FR) and half-wave plate (HW). M1 and M2 are high-reflection (HR) coated at 1336 nm and anti-reflection (AR) coated at 1060 and 1320 nm, so that the oscillation of 1.06 μm is suppressed. The specifications of the elements to select the desired wavelength and particular longitudinal mode are listed as the follows: The incident angle of 16-mm-thick BF is 57°, and the thickness of FP1 is 0.3 mm with a free spectral range (FSR) of 346.5 GHz and a finesse of 4.27, which combine to prohibit the neighboring laser wavelength of 1336.6 nm, the thickness of FP2 is 8 mm, the FSR of 13.0 GHz and the finesse of 4.27 allow to choose a single longitudinal mode and ensure the tunability of the laser. The FP1 is set between two laser heads. The TFP serves as the output coupler. The QR rotates the polarization by 90°, so that the thermal birefringence effect of the two laser head is compensated. The combination of the 22.5° FR, HW and the TFP keeps the laser propagate clockwise.

Fig. 1
figure 1

Schematic diagram of the Nd:GSGG ring laser. M1, M2: 17.3° dichroic mirror; M3: TFP at 1336 nm; LH1, LH2: laser head; QR: 90° quartz rotator; FR: 22.5° Faraday rotator; HW: half-wave plate; BF: 16-mm birefringent filter; FP1: 0.3-mm etalon; FP2: 8-mm etalon

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3 Results and discussion

Two Nd:GSGG rods (0.6 at.% doped) with a dimensions of Φ 3 mm × 82 mm are provided by Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. The end faces of the rods are AR-coated for 1336 and 1060 nm, and each of them is side-pumped by three commercial QCW 808 nm diode laser linear arrays, which are symmetrically positioned around the laser rod and provide pulses of 1 ms pulse width at a pulse repetition frequency (PRF) of 10 Hz. A water circulation system is used to stabilize the temperature of the LD arrays and the Nd:GSGG rods to 25 °C. The output average power was measured by a power meter (Ophir 30A-BB-18). The pulse energy as a function of LD pump energy was evaluated. The result is shown in Fig. 2. It is depicted that the threshold pump energy is 0.9 J per pulse, the maximum output pulse energy is 0.26 J at the LD pump pulse energy of 5.68 J, corresponding to an optical-to-optical conversion efficiency of 4.58 %, and the slope efficiency is about 7.5 %. With the increasing of the pump energy, a rollover occurs at the vicinity of the thermally critical unstable region of the resonator. It is induced that the thermal focal length of the ring cavity finally is about a fourth of the resonator length.

Fig. 2
figure 2

Output pulse energies at 1336.6 nm based on Nd:GSGG and Nd:GYSGG versus the incident LD pulse energy

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To compare the laser performances between the Nd:GYSGG and Nd:GSGG crystals, the output energy of Nd:GYSGG laser at 1336.6 nm was also measured under the same conditions, as shown in Fig. 2, the slope efficiency is about 4.3 %, and optical-to-optical conversion efficiency at the maximum output energy is 2.4 %. The results clearly reveal that it is favorable to achieve high pulse energy laser at 1336.6 nm based on Nd:GSGG crystal compared to Nd:GYSGG.

The pulse temporal characteristics of the FL at the pump pulse energy of 4.5 J were monitored by an InGaAs photodetector (Thorlabs PDA-10CF-EC) connected to a digital oscilloscope (Tektronix DPO 4104 B-L). The pulse train of 10 Hz is shown in Fig. 3a. An expanded single-pulse profile in temporal domain is shown in Fig. 3b. It can be seen from Fig. 3b that the relaxation oscillations converge to a steady state at first and restart in the middle of the pulse as is shown in Fig. 3b. The second relaxation oscillation may result from some disturbances. The pulse width of the output laser is about 900 μs with a pump pulse width of 1 ms. The difference can be attributed to the spontaneous lifetime of Nd3+ ion.

Fig. 3
figure 3

a Pulse trains for 1336.6-nm laser; b an expanded single-pulse profile

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The measurement of the wavelength characteristic was taken by a wavelength meter (WS-7, 350–1120 nm), whose absolute accuracy and linewidth accuracy are 0.1 and 0.3 pm, respectively. Since the measured range does not directly cover 1.3 μm, we deduced the FL wavelength and linewidth through measuring its second-harmonic generation (SHG). An LBO crystal (4 mm × 4 mm × 40 mm) was used to realize the SHG, and both end faces of the LBO were AR-coated at 1336 and 668 nm. The measurements of SH wavelength and linewidth exhibited 668.31483 nm and less than 0.1 pm, respectively. Correspondingly, the FL wavelength and linewidth can be estimated to be 1336.6296 nm and less than 0.85 pm or 154 MHz. As the optical length of the cavity is about 1270 mm, the separation of the longitudinal modes is about 236 MHz. It means that the FL laser operates in single longitudinal mode. Furthermore, the longitudinal mode characteristic is also measured by the inference pattern through an etalon of 6-mm thickness with reflectivity of 40 %. The etalon is set between two lenses with focal length of 100 and 200 mm, respectively. The beam goes through the lens with focal length of 100 mm, the etalon, and the lens with focal length of 200 mm in sequence. The distance between the first lens and the etalon is 80 mm, and the distance between the lenses is 300 mm. It is shown in Fig. 4 that there is only one set of homocentric circles. Thus, single longitudinal mode is deduced from the inference pattern.

Fig. 4
figure 4

Fabry–Perot interference pattern of the ring laser radiation

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To meet the requirement of Doppler cooling transition of 27Al+ optical clock, the FL laser wavelength is tuned by changing the incident angle of FP2. The angle is continuously changed from 0° to 0.5° with a step of 0.0025°, and the tuning property of SH wavelength is presented in Fig. 5. It can be seen from Fig. 5 that the SH tuning span is 12 pm from about 668.308 nm to about 668.320 nm, which corresponds to a FL tuning range of 24 pm from about 1336.616 nm to about 1336.640 nm, and the corresponding tuning range of the 167 nm laser is 3 pm varying from 167.0770 to 167.0800 nm.

Fig. 5
figure 5

SH wavelength as a function of the incident angle of the thick etalon

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The wavelength stability was measured in 1 h without feedback control loop. Figure 6 shows the measured wavelength stability of SHG. It can be seen that the RMS wavelength fluctuation is 0.14 pm, the peak-to-peak fluctuation is 0.54 pm, and correspondingly, the RMS of the wavelength fluctuation and the peak-to-peak fluctuation of the FL are 0.27 and 1.08 pm, respectively. However, the peak-to-peak fluctuation is not sufficiently low for the application of 27Al+ optical clock. Therefore, a piezoelectric transducer (PZT) actuator is needed to reduce the drift of the longitudinal mode.

Fig. 6
figure 6

Measured SH wavelength stability in 1 h

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The 90° QR inserted between the LH1 and LH2 compensates for the thermal-induced birefringence of the two laser rods significantly, which greatly benefits the beam quality. The beam quality was measured with a CinSquare Beam Quality M2 System HP (CINOGY Technologies GmbH CS300-HP). The M2 factors vary with the increase in the pump energy. At the maximum output energy of o.26 J, they are 1.51 and 1.40 along the x and y directions, respectively. With more pump energy, the beam quality turns better. Figure 7 shows the measured M2 factors to be 1.06 for both directions at the output energy of 0.16 J per pulse.

Fig. 7
figure 7

Measured M2 factors and far-field beam profile at 1336.6 nm

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4 Summary

In summary, a tunable laser around 1336.6 nm with an operation mode of the PRF of 10 Hz, pulse width of about 900 μs, and tuning range of 24 pm was demonstrated. The maximum pulse energy is 0.26 J, which is the highest comparing with previous reports. The RMS fluctuation is 0.27 pm in 1 h for the pump pulse energy of 4.5 J. For the application of 27Al+ optical clock, a further feedback control of wavelength is needed to reduce the peak-to-peak fluctuation, a master oscillator power amplifier system will be adopted to amplify the laser energy, and three stages cascaded SHG will be followed to generate tunable narrow-band laser around 167.0787 nm.