We developed a laser-diode pumped, 4.6-GHz repetition-rate, Yb:KYW Kerr-lens mode-locked femtosecond oscillator. A bow-tie ring cavity generates an output power of 14.6 mW with a spectrum width of 11 nm at 1046 nm. To the best of our knowledge, this is the highest-repetition frequency in the laser-diode pumped femtosecond Kerr-lens mode-locked laser.
©2012 Optical Society of America
Metrological applications of optical frequency combs have progressed in recent years . Broader-band spectrum, lower phase noise, and higher-repetition rate are favored in the mode-locked oscillator for further advancement of the optical frequency comb and its applications. Especially when applied to spectroscopy, a higher repetition rate is advantageous due to the following reasons: first, each longitudinal mode of the laser can be resolved with a commercially available spectrometer if the repetition rate of the mode-locked laser reaches about 4 GHz. Resolving each comb tooth with a grating spectrometer, broadband high-precision spectroscopy with an accuracy of comb linewidth can be easily achieved. Secondly, in the case of direct frequency comb spectroscopy, the spectroscopic signal repeats itself for every repetition frequency [2,3], and for this reason, the repetition rate has to be high enough compared to the target spectral structure. The Doppler broadening of atomic hydrogen is about 3.7 GHz at room temperature for a transition wavelength of 1 µm. Thus, at around this target wavelength, the Doppler broadened absorption spectrum of nearly all possible spectroscopic targets can be resolved easily when a frequency comb with a repetition rate higher than ~4 GHz is employed for spectroscopy. In addition, a higher-repetition-frequency comb has larger comb mode power, with which a single-frequency comb mode can be used as a narrow linewidth frequency-calibrated continuous wave (CW) laser. Thus, higher repetition-rate frequency combs could be applied for many applications such as broadband saturated absorption spectroscopy , human breath analysis , optical arbitrary waveform generations , ultra-stable microwave references , telecommunications , laser cooling [9,10], and astro-combs [11–13]. Assuming constant average power, the intracavity pulse energy would decrease at a higher repetition rate. Thus, higher pump power may be required to increase the intracavity average power to obtain sufficient peak intensity inside the gain crystal for Kerr-lens mode locking. For this reason, the achievable repetition rate is sometimes limited by the available pump power and it is often challenging to attain multi-GHz Kerr-lens mode locking. Multi-stage filtering cavities can be used to increase the effective repetition rate of the original oscillator up to a multi-GHz regime [12,13]. Multi-stage filtering cavities, however, have super-mode noise and less stability, and require an additional amplifier since considerable power is lost in the filtering. Dual comb spectroscopy can be used to perform broadband and comb-resolved spectroscopy without employing a high repetition rate oscillator . In this method, by measuring the heterodyne beat between two frequency combs with slightly different repetition frequencies, the optical comb structure is mapped onto a radio frequency spectrum. The single comb mode can be identified without an ultra-high resolution optical spectrometer or high repetition-rate oscillator. Although the method would be useful for characterizing the broadband spectroscopic signals of both phase and amplitude with very fast acquisition time, it requires a complicated setup with two frequency combs precisely phase-locked with each other. In order to obtain a high repetition rate oscillator, several methods have been investigated: Kerr-lens mode-locking of a Ti:sapphire oscillator, mode-locking by using a semiconductor saturable absorber mirror (SESAM), and harmonic mode-locking in a fiber laser. Ti:sapphire oscillators are widely used to obtain an octave-spanning spectrum. They operate with a lower phase noise  and achieve 10-GHz comb spacing . Mode-locking of 2-GHz  and 19.5-GHz  femtosecond fiber lasers and a 160-GHz solid-state laser  have been demonstrated by using SESAM, and harmonic mode-locking produces a 10-GHz repetition rate .
Ytterbium-doped potassium yttrium tungstate (Yb:KYW) is an interesting candidate as a gain medium for a high repetition rate oscillator. It has a higher nonlinear refractive index n2 than that of Ti:sapphire (Yb:KYW: 8.7 × 10−16 cm2/W, Ti:sapphire: 3.1 × 10−16 cm2/W ) and high thermal conductivity. High-efficiency and compact laser diodes can be used for pumping at an absorption peak of around 981 nm. The emission wavelength of a Yb:KYW laser is around 1 μm, and the output of the laser can be amplified by a ytterbium-doped fiber amplifier (YDFA) to high average power. Recently, a 2.8-GHz Yb:KYW  and 4.8-GHz Yb:KGW (ytterbium-doped potassium gadolinium tungstate)  mode-locked laser were demonstrated with the help of SESAM. The Kerr-lens mode-locking of the Yb:KYW oscillator was demonstrated at a repetition rate of 1 GHz  and used as a seed laser for a following chirped pulse amplifier system with ytterbium-doped gain fiber . 160-MHz Yb:KYW frequency comb with f-2f interferometer has been demonstrated . However, so far, a Kerr-lens mode-locked oscillator with a multi-GHz repetition rate with direct LD pumping has not been realized because the pumping power of the single-mode fiber-coupled LD is quite limited.
In this paper we design a 4.6-GHz, Kerr-lens mode-locked Yb:KYW laser with highly reflective mirrors and almost zero total group-velocity dispersion (GVD). Due to high cavity finesse and the resulting high intensity in the laser crystal, mode-locked operation was obtained at a relatively low pump power of 480 mW. High-finesse cavity would potentially introduce low phase and amplitude noise to the output pulse train. To the best of our knowledge, this is the highest repetition frequency of LD-pumped femtosecond Kerr-lens mode-locked lasers. Kerr-lens mode-locking is simpler compared with SESAM or harmonic mode-locking and expected to give broader spectrum and shorter pulses due to very fast time response of Kerr-effect. The compact setup with LD pumping and less phase noise with relatively short pulse duration make the Kerr-lens mode-locked Yb:KYW oscillator a promising candidate that may eventually substitute the widely used Ti:sapphire oscillator.
Conventional 1-GHz repetition rate Kerr-lens mode-locked oscillators consist of an output coupler with a reflectance of about 99.6%, and the total GVD in the cavity is set to have a largely negative value of about −1050 fs2 [24,25]. We found that it was difficult to achieve a repetition rate higher than 3 GHz with this conventional configuration of the cavity due to the low intracavity pulse energy. In this work, in order to obtain sufficiently high peak intensity for the Kerr-effect even at higher repetition rates, the following improvements have been applied: firstly we increased the intracavity power by improving the cavity finesse. Instead of using an output coupler, we closed the cavity with high reflective (HR) mirrors and a chirp-compensation mirror (CM). The HR mirrors have a reflectivity of over 99.9% at a wavelength of 1050 nm and an incidence angle of 10 degrees. The measured transmittance of the HR mirrors and CM are 0.025% and 0.03%, respectively. The transmitted beam from the CM is used as the output of this laser. CW operation produces an output power of 10 mW through the CM, leading to an intracavity power of 0.01/0.0003 = 33 W. Secondly, to obtain higher peak intensity, we set a considerably smaller total cavity GVD than the value commonly used in Kerr-lens or SESAM mode-locked lasers. The total GVD in the cavity is set to be about −250 fs2 assuming a crystal GVD of 400 fs2.
Figure 1 shows a schematic of the experimental setup. The bow-tie cavity consists of two concave mirrors (r = 20 mm) and two plane mirrors. The physical cavity length is 6.6 cm. The concave mirrors and one of the plane mirrors are HR-coated for the laser wavelength (1050 nm) and have a high-transmission coating for the pump wavelength (980 nm). In order to compensate for intracavity dispersion, chirped coating is applied on the last plane mirror. The 2-mm-thick, 5% Yb:KYW crystal on a copper mount is anti-reflection coated on both sides and cooled by a Peltier module. The pump source is a SMF coupled, FBG stabilized 980-nm diode laser with a maximum power of 750 mW. The pump beam is horizontally polarized and is collimated and focused by two lenses on the crystal. The eigen-spatial mode of the cavity is calculated by using an ABCD-matrix, and the waist radii at the crystal of the circulating beam and the pump beam are estimated to be 40 µm and 33 µm, respectively, which is suitable for soft-aperture Kerr-lens mode-locking. After optimizing the cavity alignment for CW operation, we searched for the best mirror position for the Kerr-lens mode locking by swinging one of the concave mirrors. In general, the output power, the spectrum, and the spatial mode fluctuated significantly when the mirror position was close to the optimum for the Kerr-lens mode locking. When mode-locked, the output beam shows a TEM00 spatial mode, and a jump in the output power and broadening of the spectrum are observed. In the ring cavity, clockwise and counter-clockwise oscillations are both possible for CW operation, and two output beams are observed from the output coupler with different propagation directions. When the laser is mode-locked, one of the output beams disappears, indicating that a single direction of oscillation is allowed inside the cavity for mode-locked operation. Once the mirror is fixed at the optimum position, mode locking can be initiated just by increasing the pump power. Figure 2 shows the laser output power versus pump power. The laser oscillation threshold is 70 mW. CW operation continues until the pump power reaches 480 mW, and mode locking is initiated automatically above this threshold. The sudden jump of the output power is due to the mode locking. Right after the mode locking, the output power is 8.4 mW, and increases linearly with the pump power. The maximum output power is 14.6 mW for a pump power of 750 mW. Currently, the output power is limited by the available pumping power from our LD, and even higher output power would be possible with a more powerful LD.
Figure 3 shows the optical spectrum of this laser measured by an optical spectrum analyzer (YOKOGAWA, AQ6373). The center wavelength is 1046 nm, and the spectrum width is 11 nm, which corresponds to a Fourier transform-limited pulse duration of 146 fs. Figure 4(a) shows the RF spectrum of the repetition rate measured by a fast photodetector (NewFocus, Model 1441-50, 18.5 ps of rise-time) and an RF spectrum analyzer (Rohde & Schwarz, FSV 30 GHz) with a resolution bandwidth (RBW) of 100 kHz. The inset shows the expanded trace of the fundamental peak with an RBW of 100 Hz.
Figure 4(b) shows the temporal profile of the pulse train measured by the same detector and a sampling scope (Tektronix, CSA8000B with a 50-GHz bandwidth). The temporal pulse profile in Fig. 4(b) reflects the time response function of the detection setup. If the laser were in multi-pulse mode-locking with pulse-to-pulse temporal separation below ~20 ps, a spectral interference should have been observed in Fig. 3, which is not the case here. Moreover, in Fig. 4(b), no multi-pulse structure can be seen at a pulse-to-pulse separation above 20 ps. This confirms that our laser is under stable single pulse operation.
Figure 5(a) shows the long-term stability of the repetition frequency measured by a universal frequency counter (Agilent, 53230A) with an average time of 1 second. The measured repetition rate was about 4.58 GHz and mode locking was sustained for hours. The repetition frequency fluctuated due to the temperature and air pressure changes. Figure 5(b) shows the short-term stability. The phase noise of the repetition frequency was measured by the RF spectrum analyzer. The value of the phase noise at the frequency region higher than 1 MHz was very close to the detection limit (below −130 dBc/Hz), which would be due to the high finesse of the cavity. The integrated timing jitter from 10 MHz to 1 kHz is 120 fs, supporting stable mode locking. The short-term stability indicates the low-noise comb structure that would be beneficial for precision laser control and comb applications.
3. Conclusions and future outlook
We demonstrated an LD-pumped 4.6-GHz femtosecond Kerr-lens mode-locked laser. With this very high repetition rate, one would be able to observe the comb tooth directly by using a commercially available optical spectrum analyzer, and the power contained in each comb mode can thus be fully characterized for the entire laser bandwidth. This offers a simple and promising way to perform broadband absorption spectroscopy with very high resolution limited by the comb linewidth. For applications where high average power is essential, our laser has sufficient power to seed a Yb-doped-fiber power amplifier, which can boost the average power up to several tens of watts . The spectrum of the laser shows 11 nm of bandwidth at 1046 nm, corresponding to a Fourier-transform-limited pulse duration of 146 fs. This high-repetition-rate laser is also useful for time-domain applications with higher signal to noise ratio. For frequency comb applications, the average power exceeding several watts would be required for spectral broadening in f-2f interferometer due to the high repetition rate of our oscillator. However a high-power amplification would induce AM-PM conversion, which causes broadening of the longitude modes. Our developed high repetition rate oscillator could be stabilized to optical frequency standards such as the cavity stabilized CW laser or a conventional low repetition rate frequency comb to avoid this problem. The direct multi-GHz frequency comb would be a simple and convenient tool for high precision broadband spectroscopy.
This research is supported by the Photon Frontier Network Program of MEXT, Japan.
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