Since the first realization of Kerr-lens mode locking (KLM) in 1991, passively mode-locked lasers have emerged as a powerful basis for a wide variety of applications [1]. In particular, passively mode-locked lasers play key roles in optical frequency combs, which provide equidistant frequency markers for applications including optical clocks, astro-combs, and low-noise microwave generation. One important parameter for these applications is the pulse repetition rate of the mode-locked lasers, and each application will require its own frequency range. For optical lattice clocks, repetition rates of 10–1000 MHz are preferred because of their accessibility to the radio frequency (RF) range [2]. In astronomical spectrograph calibration, a repetition rate of 5–50 GHz is required to resolve each longitudinal mode using an optical grating; this has enabled exploration of exoplanets [3]. Recent advances in electronic device technology require clocks that operate at more than 20 GHz for high-speed data communication and acquisition, e.g., for fifth-generation cellular mobile communications [4]. For these purposes, higher repetition rate optical frequency combs are required. In addition to working as frequency standards, multigigahertz (multi-GHz) mode-locked lasers are also attracting attention because of their potential for use in efficient material removal [5].

Several methods have been used to generate multi-GHz repetition rate pulses, including KLM, mode-locking using semiconductor saturable absorber mirrors (SESAMs) [6–9], electro-optic modulation (EOM) combs [10], microresonators [11,12], and repetition rate multiplication using a Fabry–Perot cavity [13]. In particular, KLM provides stable RF signals because of the ultrashort laser pulses produced using its passive mode-locking mechanism. To date, KLM has realized up to 15 GHz repetition frequencies with a pulse duration of 150 fs [14,15]. This repetition frequency corresponds to a cavity length of 20 mm, which is achieved by reducing the size of the conventional bow-tie cavity, as shown in Fig. 1(a). To increase the repetition rate above 20 GHz, the cavity length must be shorter than 15 mm. However, the cavity length is limited by both the sizes of the optical elements and the cavity optimization accuracy. In addition, the short ($<5\mathrm{mm}$) concave mirror radius makes it impossible to focus the pump beam through the tiny concave mirror.

 

Fig. 1. (a) Bow-tie ring cavity. OC, output coupler; CM, chirped mirror. (b) Proposed cavity geometry for high-repetition-rate KLM. DCM, dichroic chirped mirror.

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One way to shorten the cavity length is to design a new cavity geometry. While several cavity geometries have been proposed for high-repetition-rate KLM, the repetition frequencies of these lasers were limited up to 2.6 GHz [16–18]. Here, we propose a compact linear cavity geometry that is a half-cut model of the conventional bow-tie ring cavity, as shown in Fig. 1(b). The concave mirror is placed between two plane mirrors so that the two focal points appear at the edge of the cavity. The advantage of this cavity geometry is the good focusing of the pump beam because of the absence of optical elements on the pump beam trace. One may argue that the chromatic dispersion induced by the prism-like structure of the gain crystal could prevent the realization of ultrashort pulse generation. This drawback can be reduced with a smaller radius of the curvature of the mirror. In this work, we have tried to realize KLM using this new configuration with the small curvature radius mirror and have found that it works well, leading to $>20\mathrm{GHz}$ repetition rates.

The cavity configuration is described in detail as follows. To induce a strong Kerr-lens effect, 3 at. % $\mathrm{Yb}\text{:}{\mathrm{Y}}_2{\mathrm{O}}_3$ ceramic was used as a gain medium with a high nonlinear coefficient ($1.3\times {10}^{-15}{\mathrm{cm}}^2/\mathrm{W}$) [19]. The pump source was a wavelength-stabilized 976 nm laser diode coupled to a polarization-maintaining fiber, enabling tight pump beam focusing. One side of the gain medium was coated with a dichroic chirped mirror (DCM; $-250{\mathrm{fs}}^2$), while the other side was wedged at the Brewster angle. The wedged gain medium structure allows cavity length tuning so that the net cavity dispersion can be controlled. The concave mirror (radius $r=3.5\mathrm{mm}$) was dichroic-coated, and its angle compensated an astigmatism that was introduced by the Brewster-cut gain medium. The plane mirror was high-reflection coated for transmittance of 0.5% and was used as the output coupler.

KLM was achieved when the pump power was 1.0 W. The output power launched through the output coupler was 20 mW. The output beam was coupled into the single-mode fiber, and the optical spectrum was measured using an optical spectrum analyzer (AQ6373, Yokogawa) with resolution of 4 GHz, as shown in Fig. 2(a). The center wavelength was 1085 nm, and the full width at half-maximum (FWHM) spectral width was 11 nm. The corresponding Fourier-transform-limited pulse duration was 102 fs (assuming an envelope function of ${\mathrm{sech}}^2$). We assigned the peak at the wavelength of 1060 nm to the Kelly sideband. The inset in Fig. 2(a) shows the magnified optical spectrum from 1084 nm to 1085 nm. The individual modes are clearly separated. The visibility for each mode was $>95\%$. The spacing for each mode was 20.1 GHz, which means the pulse repetition rate is 20.1 GHz. Figure 2(b) shows the RF spectrum of the pulse train. A peak was observed at a frequency of 20.1 GHz, which corresponds to the measured mode spacing shown in Fig. 2(a).

 

Fig. 2. (a) Optical spectrum with resolution of 4 GHz. The inset shows the spectrum in the 1084–1085 nm range. (b) RF spectrum. The peak frequency of 20.1 GHz corresponds to the measured mode spacing in the inset of (a). RBW, resolution bandwidth. (c) Interferometric autocorrelation trace. The black lines are fitting curves, with the assumption that the pulses are shaped as a secant hyperbolic function. The FWHM pulse duration is estimated from these fittings to be 120 fs.

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The temporal profile of these pulses was characterized via interferometric autocorrelation without dispersion compensation outside the cavity. Figure 2(c) shows the autocorrelation trace and the fitting curve under the assumption that the envelope function was a secant hyperbolic function. From these fittings, the FWHM of the pulse was estimated to be 120 fs, which was close to the Fourier-transform-limited pulse duration of 102 fs.

Repetition frequency tuning was demonstrated by adjusting the output coupler position. We realized pulse repetition rates of 18.3, 20.1, 21.9, and 23.8 GHz at a pump power of 1.0 W. Figure 3 shows the spectral width and the pulse duration at FWHM as a function of repetition frequency. The spectral width was reduced when the repetition frequency increased. The repetition frequency of 23.8 GHz, which corresponds to a round trip cavity length of 12.5 mm, was achieved with a pulse duration of 140 fs.

 

Fig. 3. Measured pulse duration (orange) and spectral width (green) as functions of repetition frequency.

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In conclusion, we proposed a new cavity configuration for high-repetition-rate KLM. As a result, we realized KLM at repetition rates in the 18.3–23.8 GHz range. To the best of our knowledge, this repetition frequency of 23.8 GHz is the highest reported frequency to date in KLM lasers. Our results will enable precision clocks for spectroscopy, high-speed data communications, and other applications.