1. Introduction

The optical spectrum of a femtosecond mode-locked laser exhibits a comb-like structure, that is, the longitudinal modes are evenly spaced by a separation equal to the pulse repetition frequency (f_rep). The optical frequencies of such modes can be phase locked to a radio frequency (RF) standard or an optical frequency standard, and these frequency-stabilized mode-locked lasers are referred to as optical frequency combs (OFCs). OFCs have become invaluable tools in precision applications, such as with optical clocks [1], or frequency metrology [2] and spectroscopy [3].

OFCs offering a large mode spacing of more than several GHz could facilitate comb-resolved applications, since each comb tooth can simply be resolved by commercially-available small dispersive elements. Another one of their advantages, compared to low repetition rate OFCs, is the higher available power per mode. Potential applications of OFCs or high-repetition rate mode-locked lasers include nonlinear bio-imaging [4], low-noise microwave synthesis [5, 6], high-speed optical communication [7], calibration of astronomical spectrographs [8], line-by-line optical arbitrary waveform generation (OAWG) [9, 10], comb-resolved spectroscopy [11] and direct OFC spectroscopy [12]. Towards the application of calibrating spectrographs in astronomical observatories, the desirable comb mode-spacing is a frequency that is approximately three or four times that of the resolution, typically around 12 ~20 GHz [8]. In practice, the OFCs used have a mode spacing of several hundreds of MHz, and therefore require the use of multiple stages of filtering cavities, which makes the overall configuration complicated and difficult to operate over long periods of time. Typical repetition frequencies of femtosecond mode-locked lasers and OFCs are limited to less than one GHz, and spectrometers are unable to resolve the individual longitudinal modes.

The past ten years has seen progress towards extending the repetition frequency of femtosecond mode-locked lasers to GHz levels. These lasers include Kerr-lens mode-locked (KLM) sources that can reach up to 10 GHz in the case of a Ti:sapphire laser and an OFC [13, 14] and several GHz in the case of other lasers [15–17]. Saturable absorbers, such as semiconductor saturable absorber mirrors (SESAMs) assisted mode-locked lasers have been demonstrated to generate multi-GHz repetition rate pulses [18–24]. MIXSELs (mode-locked integrated external-cavity surface emitting lasers) have also been shown to be attractive sources, with their capacity to provide femtosecond pulses with repetition rates as high as 101.2 GHz [25]. KLM lasers, however, are more suitable for the above-mentioned OFC application, as they offer relatively short pulse durations (broad spectra) with low phase noise, thanks to their high speed response times and lossless configurations. Moreover, in combination with laser diode pumping and short cavity lengths (less than 3 cm), they have been shown to be robust and stable.

Ytterbium-doped rare earth oxides (Yb:Re₂O₃, Re = Sc, Y, Lu), especially Yb:Y₂O₃, are interesting gain medium candidates for femtosecond oscillators. Firstly, they have a relatively high thermal conductivity and a higher nonlinear refractive index n₂ than that of other Yb-doped gain media and Ti:sapphire crystals (Yb:Y₂O₃: 1.3 × 10⁻¹⁵ cm²/W [26] and Ti:sapphire: 3.1 × 10⁻¹⁶ cm²/W [27]). Secondly, affordable, high-efficiency and compact laser diodes (LDs) with an emission wavelength centered at 976 nm can be used as pump sources. Although Ti:sapphire laser technology is more mature in comparison, and has an enhanced performance in terms of ultra-short pulse duration and OFC applications, one of the drawbacks is the complicated pump laser system, such as for e. g. the 532-nm frequency-doubled Nd:YVO₄ laser. For these reasons, Ti:sapphire lasers are usually limited to applications in research fields. Finally, the emission wavelength of a Yb laser ranges between 1 and 1.1 μm, which makes it suitable for power amplification by a Yb-doped fiber amplifier (YDFA). While the fabrication of Yb:Re₂O₃ crystals is a difficult process, because of their elevated melting point, Yb:Re₂O₃ ceramics can easily be obtained [28]. Furthermore, the ceramic structure leads to a broader fluorescence spectrum, thus making Yb:Re₂O₃ ceramics convenient for the generation of broadband femtosecond pulses [29].

Single-mode-fiber coupled 976-nm LDs used to efficiently pump KLM lasers typically generate up to one-watt level of power, which restricts the achievable repetition frequency. To compensate for the lack of pump power, KLM Yb lasers with high-finesse cavities were developed, and repetition frequencies as high as 4.6 GHz and 6 GHz were achieved [15, 16]. For applications such as the calibration of spectrographs and OAWG, repetition rates exceeding 12 GHz are desirable in order to separate each longitudinal comb mode simply and clearly.

In this paper we describe a compact KLM Yb:Y₂O₃ ceramic laser cavity that produces pulses with a repetition rate of 15-GHz and a duration of 152 fs. The long-term operation capabilities are assessed as well, using a cavity stabilized CW laser and a RF standard to control two degrees of freedom of the comb.

2. 15-GHz Kerr-lens mode-locked laser

Figure 1(a) shows a schematic layout of the 15-GHz KLM laser cavity. Two concave mirrors (r = 5 mm) and two plane mirrors constitute the bow-tie ring cavity. The main deviation from our previous works [15, 16] was the use of concave mirrors with a smaller radius of curvature, in order to shorten the cavity length and increase the energy density at the lasing material. The net cavity length was set to 2 cm. Both concave mirrors were dichroic mirrors (DMs) coated for high-reflection (HR) at 1080 nm and high-transmission at 976 nm. One of the plane mirrors was HR coated for 1080 nm and mounted on a piezoelectric actuator (PZT) for repetition frequency locking. The other plane mirror is a chirp-compensation mirror (CM) with a group delay dispersion (GDD) of – 550 fs². The total GDD of the oscillator was calculated to be approximately – 400 fs², which allowed sufficient high peak powers to induce the Kerr effect. The CM, with a transmittance of 0.04%, worked as an output coupler. The 1-mm-thick, non-coated 3at.% Yb:Y₂O₃ ceramic (gain medium) was mounted on a copper plate with silver epoxy, and placed between the concave mirrors at Brewster’s angle (63°). The folding angles at the concave mirrors were adjusted to 17° to compensate for the astigmatism caused by the Brewster-placed ceramic. A LD was chosen as the pump source to ensure robust and long-term operation. The LD was coupled to a polarization-maintaining single-mode-fiber (PMF) and had a maximum output power of 1.1 W at the lasing wavelength of 976 nm that was stabilized by a fiber-Bragg-grating (FBG). The pump beam was collimated by a first achromatic lens (L1) of 25-mm focal length, then focused down into the gain ceramic by a second one (L2) of 50-mm focal length. The Gaussian spatial mode profile of the pump beam ensured the induction of stable Kerr-lens mode-locking. In addition, the calculated transverse cross-section of the pump beam at the lasing material was 12 μm and smaller than the one determined for the continuous wave (CW) lasing mode (~20 μm), which satisfied the necessary condition for soft-aperture Kerr-lens mode-locking. After optimization of the cavity alignment for CW operation, by increasing the pump power to more than 1 W and by adjusting the position of one of the concave mirrors, stable mode-locking was obtained and spectral broadening was observed. In the ring cavity, both clockwise and counter-clockwise beam propagations were possible for CW operation, and correspondingly two beams exited through the output coupler. In the CW regime, the laser threshold power was of 13 mW and operation in this mode was maintained until the pump power reached approximately 700 mW. Beyond this power, mode-locking was initiated automatically (self-start mode-locking). In the mode-locked regime, one of the output beams disappeared and the output power increased, indicating that the cavity only allowed a single beam propagation direction. In this regime, the cavity was optimized by broadening the optical spectrum and increasing the output power. This was achieved by improving the alignment of the cavity mirrors, the gain material and the focusing lens. A maximum output power of 60 mW was achieved at the maximum pump power of 1.1 W. The output pulse energy and the intracavity pulse energy were calculated to be 4 pJ and 10 nJ, respectively. Mode-locking was maintained until decreasing the pump power to ~550 mW.

 

Fig. 1 (a) Layout of the 15-GHz KLM laser. Pump LD: PMF-coupled LD operating at 1.1 W and at a wavelength of 976 nm, PMF: polarization-maintaining single-mode fiber, L1 and L2: collimating and focusing achromatic lenses with respective focal lengths of 25 mm and 50 mm, DM: dichroic concave mirror with a radius of curvature of 5 mm, HR: high-reflection coated mirror, CM chirped mirror (GDD = − 550 fs² at 1080nm), PZT: piezoelectric actuator, Gain medium: 3at.% 1-mm thick Yb:Y₂O₃ ceramic. (b) Optical spectra measured with an optical spectrum analyzer at a resolution of 2 nm and (inset) 16 pm. (c) RF spectra of the pulse train measured by a RF spectrum analyzer with resolution bandwidths (RBWs) of 3 MHz and 1 kHz (inset). (d) Fringe-resolved autocorrelation signal. The measured pulse duration was 152 fs (sech² fitting)

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Figure 1(b) shows the optical spectra measured using an optical spectrum analyzer (YOKOGAWA, AQ6373) with a resolution of 2 nm. The center wavelength was 1080 nm and the full-width half-maximum (FWHM) was 12 nm, which corresponds to a Fourier transform-limited pulse duration of 102 fs (sech² fitting). The inset in Fig. 1(b) is the optical spectrum of the output pulse observed over a span of 0.5 nm with a resolution of 16 pm (which corresponds to a frequency resolution of 4 GHz). The longitudinal modes were clearly resolved and were separated by a mode-spacing of 15 GHz. The power per longitudinal mode was found to be above 100 μW within the FWHM. Figure 1(c) shows the RF spectra of the repetition frequency measured with a fast photodetector (Discovery semiconductors, DSC10H with a bandwidth of 44 GHz) and a RF signal analyzer (Rohde & Schwarz, FSV 40 GHz). The figure represents the spectrum acquired over a frequency range of 0 to 40 GHz with a resolution bandwidth (RBW) of 3 MHz. Both the fundamental and second harmonic frequencies of the repetition rate are visible. The inset displays the fundamental peak measured with a RBW of 1 kHz. The average laser output power was insufficient to measure the pulse duration by autocorrelation, therefore a Yb-doped fiber amplifier (YDFA) and a compressor were used, to amplify the power and to compensate for the dispersion introduced by the amplifier, respectively. The pump source of the YDFA was a 976-nm multi-mode-fiber coupled LD and the gain medium was a 3-m long Yb-doped double-clad fiber. After the compressor, which consisted of a pair of transmission gratings (1000 grooves/mm), 300 mW of output power free of amplified spontaneous emission was obtained. Figure 1(d) shows the autocorrelation trace acquired using a fringe-resolved autocorrelator with a 150-μm thick beta barium borate crystal and a photomultiplier. The pulse duration was measured to be 152 fs. This value is longer than the estimated Fourier transform-limited pulse duration of 102 fs, due to a third order dispersion induced in the YDFA that cannot be compensated for by the grating compressor.

3. 15-GHz optical frequency comb

Two degrees of freedom of the 15-GHz KLM laser were stabilized: the repetition frequency and the optical frequency of the one mode. The schematic diagram of the experimental arrangement is shown in Fig. 2(a). The repetition frequency was locked to a Rb-clock referenced RF standard using a piezoelectric transducer and an analogue locking circuit (f_rep-locking circuit). The optical frequencies of the comb modes were stabilized by phase-locking the generated heterodyne beat signal between a single tooth and a CW laser centered at 1079 nm (f_beat). The CW laser was an external-cavity diode laser (ECDL) stabilized to a high-finesse, ultra-low expansion glass cavity with an optical frequency drift of 160 mHz/s over 16 hours of operation. The error signal produced by the digital phase-locked loop circuit (PLL circuit) was fed back to an acousto-optic modulator (AOM) in a double-pass configuration, used to shift the offset frequency of the comb. And the beat signal was phase locked to a reference frequency of 173 MHz. In order to increase the signal-to-noise ratio of the detected beat signal, a YDFA was placed after the AOM. The RF spectrum of the locked beat frequency shown in Fig. 2(b) was acquired with a RBW of 1 kHz. The phase noise integrated over the Fourier frequencies 10 Hz to 10 MHz was measured to be 0.61 rad. Although the PLL bandwidth was limited to approximately 100 kHz by the modulation bandwidth of the voltage-controlled oscillator (VCO) used for the AOM, a higher bandwidth (> MHz) should be possible by simply replacing the VCO to one that has a higher modulation bandwidth. Figure 2(c) shows the locked repetition (bottom) and beat (top) frequencies measured with frequency counters (Agilent, 53230A) over 360 seconds. The short-term frequency stability of the developed OFC was estimated to be less than 30 mHz from the root mean square (r.m.s.) obtained for the measurements of both f_rep (less than 30 mHz) and f_beat (less than 3 mHz). This value of stability was limited by the uncertainly of the Rb-clock itself, which is one part in 10¹². The long-term stability was dominated by the optical frequency drift of the ECDL. Over the course of several months, the long-term drift is expected to be maintained to less than a MHz with any typical ULE-cavity-stabilized ECDL. With respect to astronomical applications, the required optical frequency stability of a calibrating source is defined by a Doppler shift of 1 m/s in the absorption spectrum of a star, which corresponds to approximately 1 MHz. The developed OFC is therefore suitable for long-term operation as a calibration source for astronomical spectrographs. Phase-locking a low-repetition frequency (several hundred of MHz) OFC standard or an optical frequency standard (e.g. optical clock), would enable the realization of an absolute frequency controlled 15-GHz comb. In order to maintain the repetition frequency locked over longer periods of time, the oscillator could be temperature controlled, although this was not carried out.

 

Fig. 2 (a) Schematic diagram of the experimental configuration used to phase-lock f_rep and f_beat. HWP (QWP); half (quarter)-wave plate, PBS; polarization beam splitter, VCO; voltage-controlled oscillator, Amp.; RF amplifier, f_rep (f_beat) detector; 50-GHz (25-GHz) InGaAs photodetector. (b) Spectrum of the phase-locked beat signal between the 15-GHz OFC and the ECDL f_beat. (c) Long-term stability measurement of f_beat (top) and f_rep (bottom) using frequency counters with a gate time of 1 s.

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Another promising application of the 15-GHz OFC is OAWG. Since each comb tooth can simply be resolved by a grating, it is possible to modulate the phase and intensity of individual modes. In this way, the desired electric field within the spectrum bandwidth could be realized. In addition, the artificial waveform can be amplified by a YDFA.

4. Conclusion

We have demonstrated a 15-GHz mode-spacing OFC based on a Kerr-lens mode-locked Yb:Y₂O₃ ceramic laser pumped by a compact LD. Individual modes were clearly resolved with a commercial spectrometer. To the best of our knowledge, the mode-spacing of 15 GHz is the highest one achieved by a KLM laser based OFC. The pump LD provides sufficient power that the repetition rate could be increased by another factor of ~2. This would be achieved by further reducing the radius of curvature of the concave mirrors used in the oscillator. However, the smaller the radius of curvature, the more difficult the concave mirrors are to fabricate. The compact configuration, along with the LD as pump source, and the femtosecond pulse duration, make the KLM Yb:Y₂O₃ ceramic oscillator a promising candidate for OFC applications, which may eventually substitute the widely used Ti:sapphire oscillator. The LD-pumped large mode spacing OFC was evaluated to have sufficient long-term stability for precision applications such as the calibration of astronomical spectrographs.