1. Introduction

The development of ultrafast fiber lasers with pulse repetition rates in the gigahertz regime is of interest and has been driven primarily by the introduction of optical frequency combs and their applications in, for example, optical communications, nonlinear bioimaging, and the precision calibration of astronomical spectrograms in the search for Earth-like exoplanets [1–4]. For example, with the use of high-repetition-rate ultrafast lasers, bioimaging quality can be significantly upgraded through an increase in signal rate and imaging speed and a decrease in photobleaching and photodamage of fluorescent proteins [4]. Harmonic mode-locking techniques [5–7] and methods based on pulse repetition multiplication [8–10] are capable of producing pulse trains with extremely high pulse repetition frequencies (>100 GHz); however, fundamental mode-locking is more favorable for certain practical applications owing to its intrinsic low intensity and phase noise. During the past 15 years, ultrafast lasers with multi-gigahertz fundamental repetition rates have been realized based on laser gain mediums such as solid-state glasses/crystals [11–15], semiconductor disks [16–18], waveguides [19–21], and fibers [22–32]. Mayer et al. have recently achieved a fundamental repetition rate of 10 GHz in a solid-state Yb:CaGdAlO₄ laser delivering 166-fs pulses at an average output power of 1.2 W [11]. In 2013, an ultrafast waveguide laser operating with a repetition rate of 15.2 GHz at a wavelength of 1050 nm was experimentally realized by Lagatsky et al. [20]. Different benefits and trade-offs are associated with these lasers. Fiber lasers, regarded as a promising choice for realizing ultrafast pulses, can offer high beam quality, reliability and efficient heat dissipation in a compact size. To date, the highest pulse repetition rates among ultrafast fiber lasers have been reported to be 5 GHz [22] at a wavelength of 1.0 µm, 19.45 GHz [26] at a wavelength of 1.5 µm and 1.6 GHz [30] at a wavelength of 2.0 µm.

For stable operation of high-repetition-rate ultrafast fiber lasers, it is critical to choose appropriate system parameters. At higher pulse repetition rates, the tendency for Q-switched mode-locking will unavoidably increase [33,34]. The high peak power occurring during Q-switched instability damages the intracavity components (e.g., saturable absorber) before the power required to arrive at the threshold for stable continuous wave (CW) mode-locking is achieved. Thus, in 2016, the Q-switching instabilities in high-repetition-rate ultrafast fiber lasers have been studied [35]. It indicates that the selection of system parameters, saturation energy E_A, and modulation depth q₀ of the saturable absorber and the small-signal gain coefficient g₀ of the gain fiber becomes considerably strict for stable CW mode-locking. The parameter, g₀, which is determined by a highly rare-earth-doped fiber, always possesses a high value in practice in order to shorten the laser cavity. When the g₀ gradually decreases with a shortening of the laser cavity, a new pulse dynamic consisting of rectangular wave packets emerges [36]. To increase the pulse repetition rate to multi-gigahertz frequencies, the corresponding laser resonant cavity has to be shortened to a few centimeters. The system parameters in the ultrashort laser cavity are easily affected by ambient disturbances. For instance, an absolute cavity length change ∆l resulting from temperature perturbation will have a stronger impact on the laser performance than in a traditional ultrafast fiber laser with a meter-scale laser cavity. Thus, the changes in the performance of high-repetition-rate ultrafast fiber lasers owing to the effect of perturbations on the system parameters cannot be neglected. On the other hand, if system parameters could be controlled by using external measures, the laser performance would be flexibly and accurately tuned.

In this article, we introduce the dependence of repetition rate, laser wavelength, amplitude and phase noise characteristics on system parameters for high-repetition-rate ultrafast fiber lasers at wavelengths of 1.0, 1.5, and 2.0 µm, by controlling the temperature of the laser cavity and introducing a filter mechanism in the frequency domain. For 2.0-µm wavelength, we obtained a broader tuning range of 14 nm in optical spectra than for 1.0-µm wavelength. The phase noise is well suppressed, inducing a timing jitter of 940 fs, which is integrated from 10 Hz to 1 MHz. The efficiency of CW mode-locking in 1.0-µm fiber laser is significantly improved by employing an optimal reflectivity of 74% of the dielectric film at laser wavelength, and the average output power is significantly improved to 57 mW at a launched pump power of 213 mW. Finally, we propose a new method for tuning the wavelength and repetition rate in the 3-cm-long Er/Yb:glass fiber laser, thus achieving simultaneously tunable peak wavelength and repetition rate in certain ranges.

2. Resonator designs and operating characteristics

The schematic of the experimental setup of tunable, high-repetition-rate ultrafast fiber lasers operating at the wavelengths of 1.0 µm and 2.0 µm is shown in Fig. 1(a). For 1.0 µm, a 3-cm-long Yb:glass fiber (YGF) is pumped by a laser diode (LD) at a wavelength of 974 nm through a wavelength-division multiplexer (WDM). Further details on the glass fiber are described in [37]. To construct a robust laser cavity, the YGF was inserted and glued inside a ceramic ferrule with an inner diameter of 125 µm, both end facets of which were thereafter perpendicularly polished. One end of the YGF was butt-coupled to a fiber-type dielectric mirror, which was spliced to the common port of the WDM. Compared with a previous work with a maximum output average power of 0.8 mW [22], the dielectric mirror in the experiments is modified with a reflectivity of 74% at a wavelength of 1042 nm and a transmittance of 98% at a wavelength of 974 nm. The opposite end of the YGF was affixed to a semiconductor saturable absorber mirror (SESAM), which is capable of being sandwiched between the YGF and a fiber ferrule because of its compact size. The fiber ferrule here is made of copper for dissipation of heat on the SESAM to guarantee long-term stability in operation. The SESAM, with a chip area of 1.0 × 1.0 mm and thickness of 450 µm, has a modulation depth of 5%, non-saturable loss of 3%, recovery time of 1 ps, and saturation fluence of 40 µJ/cm² at 1040 nm (Batop GmbH). The schematic of the setup for the wavelength of 2 µm is shown in Fig. 1(a), where the optical components in the laser cavity are the same as in [30]. However, to realize a tunable wavelength/repetition rate and noise suppression at the wavelength of 2 µm, in this work, a temperature control (TC) is implemented on the Tm:glass fiber (TGF) for changing the system parameters. For both wavelengths of 1.0 µm and 2.0 µm, a thermoelectric cooler was employed for stabilizing and tuning the laser wavelength and repetition rate by providing a constant temperature to each gain fiber.

 

Fig. 1 Schematic setups of tunable, high-repetition-rate ultrafast lasers based on Yb:glass, Tm:glass, and Er/Yb:glass fibers as gain mediums. (a) Yb:glass and Tm:glass fiber oscillator structures, using a TC on each gain fiber for tuning laser wavelengths and repetition rates. (b) Er/Yb:glass fiber laser structure, using the proposed method to accomplish tuning by rotating alignment angles between the gain fiber and the SESAM. The inset in the left of (b) illustrates the geometric details of the tunable module. The photograph in the right shows the laser cavity of the Er/Yb:glass fiber oscillator, along with the tunable module. LD, laser diode; WDM, wavelength-division multiplexer; DF, dielectric film; YGF, Yb:glass fiber; TGF, Tm:glass fiber; EYGF, Er/Yb:glass fiber; SESAM, semiconductor saturable absorber mirror; TC, temperature control; and FOAS, fiber optics alignment station.

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Figure 1(b) shows a schematic diagram illustrating the design of a high-repetition-rate ultrafast fiber laser operating at the wavelength of 1.5 µm and the proposed method for tuning repetition rate and wavelength. A 3-cm-long Er-Yb:glass fiber (EYGF) with a gain coefficient of 5.2 dB/cm at 1535 nm acts as the gain medium [38]. The EYGF was pumped by a single-mode LD of wavelength 974 nm through a WDM, and the fiber was inserted into a size-matched ceramic ferrule. One end of the EYGF was butt-coupled to a fiber-type dielectric mirror, which has a high reflectivity of approximately 99% at a wavelength of 1550 nm. The opposite end of the EYGF was fixed on a 6-axis stage through a circular groove. Therefore, instead of being affixed to the SESAM, the EYGF can interact with the SESAM when the alignment angles between the facets of the EYGF and the SESAM are adjusted. The SESAM used for the wavelength of 1.5 µm was soldered onto a copper heat sink and subsequently mounted on a fixed bracket, with a modulation depth of 6%, non-saturable loss of 3%, relaxation time of 2 ps, and saturation fluence of 50 μJ/cm². A photograph of the configuration is shown in the right inset of Fig. 2(b).

 

Fig. 2 Average output power, autocorrelation, and tunable performance of ultrafast Yb-fiber oscillator with a repetition rate of 3 GHz: (a) Measured variation of the laser average output power with the launched pump power (974 nm); (b) Measured autocorrelation trace of mode-locked pulse (blue solid line) and Sech² fit trace (red dashed line); Tunable repetition rate (c) and spectra of wavelength (d) in mode-locked operation at different YGF temperatures controlled by TC of Fig. 1(a).

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The alignment angles can be rotated accurately and continuously. In the process, a high-pass filter (HPF) can be formed in the frequency domain with a deviation from the original angle between the facets of the EYGF and the SESAM, as shown in Fig. 1(b). The filter will thereafter enable the tuning of repetition rate and wavelength. The geometric illustration of the tunable module is presented in the left inset of Fig. 1(b). The deviation of the angle leads to a deviation x₁ when the light beam travels back to the facet of the fiber. The corresponding mathematical interpretation can simply be written as

In the above equations, apart from the parameters already defined in the left inset of Fig. 1(b), n₂ and n₂' represent the refractive index of the saturable absorber (SA) and its first derivative with respect to the frequency w, respectively. As can been seen from Eq. (2), the lower frequency results in a larger x₁ for n₂' > 0 and the increase in the angle of incidence θ can also cause a larger x₁. Namely, the components with lower frequencies are more likely to be blocked from being coupled back into the fiber, thus yielding the HPF. Aside from the SA layer with a thickness of d, an analogous process resulting in another similar HPF effect should occur in the Bragg mirror (consisting of a multilayer stack of alternate high and low index films) within the SESAM, which will dramatically aggravate the beam deviation and thus enhance the HPF effect.

In the above high-repetition-rate ultrafast fiber lasers, polarization controllers were employed to increase the pump coupling efficiency to the gain fiber and the signal-to-noise ratio of the fundamental repetition rate signal to some extent. The laser light was coupled out via each signal port of the WDM. The optical spectra of the output laser were measured using the optical spectrum analyzer Yokogawa AQ6370B for the wavelengths 1.0 µm and 1.5 µm, and the optical spectrum analyzer Yokogawa AQ6375 for the wavelength 2.0 µm. The pulse durations were measured using an autocorrelator (APE pulseCheck USB 50). The radio-frequency (RF) spectra and noise characteristics were detected using photodetectors with bandwidth >12.5 GHz and a signal analyzer (Rohde & Schwarz FSWP26).

3. High-repetition-rate ultrafast Yb³⁺-doped fiber laser with average output power of 57 mW and optical-to-optical efficiency of 27%

The measurements of the dependence of the output power of the oscillator of wavelength 1.0 µm on the launched pump power are shown in Fig. 2(a). The CW laser oscillation starts at a pump power of P ~15 mW. The launched pump power P was measured after the fiber-type dielectric mirror in the experiment. In the range 15 ≤ P ≤ 136 mW, the laser in Fig. 1(a) operates in a Q-switched mode-locking regime. Above the CW mode-locked threshold of 136 mW, self-started mode-locking of the oscillator is achieved and the output power increases linearly with an increase in the pump power. The slope efficiency of the ultrafast Yb-fiber oscillator with a repetition rate of 3 GHz at a peak wavelength of 1042 nm is 29%. The maximum output power is 57 mW for the Yb-laser at a launched pump power of 213 mW; the corresponding optical-to-optical efficiency is 27%. Compared with the previous work with a maximum average power of 0.8 mW [22], the output power of the oscillator herein is improved remarkably, benefiting from the optimal reflectivity of 74% of the dielectric film at the laser wavelength in this work. Correspondingly, Fig. 2(b) shows an autocorrelation trace of the CW mode-locked pulse at the launched pump power of 213 mW and its temporal width (full width at half maximum, FWHM) is observed to be 3.4 ps, assuming the intensity profile to be a hyperbolic secant.

As the TC in Fig. 1(a) increases the temperature from 10 °C to 28 °C, as depicted in Fig. 2(d), the peak wavelength of the CW mode-locked optical spectra continuously increases from 1040.1 nm to 1042.9 nm. In the process, the repetition rate shifts by 226 kHz, as shown in Fig. 2(c). The tuning process in the experiment is reproducible and reversible. For high-repetition-rate ultrafast lasers, the gain fiber length l is generally shortened to a few centimeters (e.g., ~3 cm in the experiment); thus, an absolute length change ∆l has a stronger impact on a short laser cavity than on a long cavity in a traditional ultrafast fiber laser.

4. High-repetition-rate ultrafast Tm³⁺-doped fiber laser with a low timing jitter of 940 fs

For the oscillator of wavelength 2.0 µm in Fig. 1(a), the pump threshold for an LD at a wavelength of 793 nm for self-starting CW mode-locking is 101.5 mW. In this work, we focus on the tuning performance of repetition rate, laser wavelength, amplitude and phase noise in the ultrashort laser cavity of wavelength 2.0 µm. For a fixed power of 102 mW, as depicted in Fig. 3(a), as the TC in Fig. 1(a) increases the temperature from 18°C to 32°C, the spectra of the photodiode signals gradually decrease by 294 kHz. Simultaneously, the peak wavelength of the optical spectra gradually shifts from 1974.1 nm to 1988.2 nm in the 1835–2085 nm wavelength interval, as shown in Fig. 3(b).

 

Fig. 3 Tuning characteristics and autocorrelation measurements for the high-repetition-rate ultrafast fiber laser of wavelength 2.0 µm: (a) Spectral variation of the photodiode signals in the 1.587–1.591 GHz region acquired using an RF spectrum analyzer at different TGF temperatures controlled by the TC; (b) Corresponding optical spectral variation in the 1835-2085 nm wavelength interval with the TDF temperatures; (c) Magnified view of the optical spectra at the TDF temperatures of 18 °C, 24 °C, and 32 °C. The left Inset shows the measured autocorrelation trace at a TDF temperature of 24 °C. In recording the data, the launched pump power at the wavelength of 793 nm was fixed at 102 mW. The right Inset shows output power of ultrafast oscillator as a function of the temperature.

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To observe the details of the optical spectra, the representative spectra at the TGF temperatures of 18 °C, 24 °C, and 32 °C in Fig. 3(b) are magnified in Fig. 3(c). It can be seen that the spectrum at the temperature of 18 °C extends from 1871.8 nm to 2060.7 nm, with an FWHM of ~26 nm and peak wavelength of 1988.2 nm. At 24 °C, the optical spectrum is narrower than that at 18 °C, extending from 1887.2 nm to 2042.2 nm with a narrower FWHM of ~19 nm and peak wavelength of 1980.1 nm. At 32 °C, the optical spectrum finally becomes much narrower and extends from 1892.1 nm to 2029.4 nm, with an FWHM of ~13 nm and peak wavelength of 1974.1 nm. It can be concluded that the FWHM of the mode-locked optical spectra becomes narrower with an increase in the temperature of the laser cavity. The inset of Fig. 3(c) is an autocorrelation trace of the laser pulse mode-locked at a temperature of 24 °C and its FWHM is observed to be ~1.0 ps, assuming the intensity profile to be a hyperbolic secant. In the measurement, the average power of the 1.6-GHz mode-locked pulses was amplified to 60 mW using a Tm-doped double-cladding fiber amplifier. For comparison, the transform-limited width of the pulse is calculated to be 217 fs from the optical spectrum of the emission line of wavelength 19 nm. The pulse broadening in the autocorrelation trace originates from the amplification process. As shown in the right inset of Fig. 3(c), the output power of the ultrafast oscillator gradually decreases from 6.18 mW to 5.79 mW as the TC increases the temperature from 10 °C to 28 °C.

Controlling the temperature helps to maintain a constant temperature on the laser cavity to prevent the fluctuation of ambient temperature, and optimizes the performance of the RIN and PN by flexibly tuning the temperature. We observe that, after scanning, the noise characteristics of the laser show the better performance at low temperatures. At the launched pump power of 102 mW, we tested all three PN and RIN traces illustrated in Fig. 4 at 11 °C, 12 °C, and 13 °C. As shown in Fig. 4(a), the values of PN gradually decrease from −50 dBc/Hz to −150 dBc/Hz with an increase in the offset frequency from 10 Hz to 10 MHz. The integrated timing jitter at 12 °C is measured to be 940 fs integrated from 10 Hz to 1 MHz. This is a remarkable value for ultrafast lasers with gigahertz repetition rates, because it is of the same order of magnitude as the value of 249 fs reported by Hakobyan [39] for full stabilization of an optical frequency comb based on a solid-state laser with a 1.05-GHz repetition rate. For the high-frequency range from 100 kHz to 10 MHz, the value of integrated timing jitter gradually increases with an increase in the temperature. The values of the timing jitter integrated in this range are 19.9 fs at 11 °C, 23.5 fs at 12 °C, and 28.3 fs at 13 °C. This increase is largely attributable to a decrease in the pulse energy in the process [40], which can be derived from the output power in the right inset of Fig. 3(c) and the repetition rate in Fig. 3(a). In addition, the corresponding RIN at the three temperatures is plotted in Fig. 4(b). The integration of RIN between 10 Hz and 10 MHz results in an integrated RIN of 0.023% at 11 °C, 0.027% at 12 °C and 0.030% at 13 °C.

 

Fig. 4 Noise characteristics of the high-repetition-rate Tm-doped oscillator: (a) The measurements of the phase noise (PN) at the TDF temperatures of 11 °C (blue trace), 12 °C (red trace), and 13 °C (green trace); (b) Corresponding relative intensity noise (RIN) curves at the TDF temperatures of 11 °C (blue trace), 12 °C (red trace), and 13 °C (green trace).

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5. Tunable wavelength and repetition rate achieved using the proposed tuning method in a 3-GHz Er³⁺/Yb³⁺-doped ultrafast fiber laser

For the ultrafast laser of wavelength 1.5 µm in Fig. 1(b), the pump threshold of an LD at a wavelength of 974 nm for self-starting CW mode-locking is 257 mW. At a pump power of 272 mW, in this case with an increase in θ from 0° to 0.1062° (the parameter θ is illustrated in section 2 and can be observed in the inset of Fig. 1 (b)), as shown in Fig. 5(a), the spectra of the photodiode signals continuously increase from 3.193320 GHz to 3.193380 GHz in the 3.19312–3.19360 GHz region, with a tunable range of 60 kHz. As expected, the peak wavelength of the optical spectra is continuously shifted to short wavelengths from 1591.4 nm to 1586.1 nm in the 1565–1615 nm wavelength interval. Notably, with an increase in the value of θ, the optical spectrum in the high-frequency (short wavelength) part retains its shape, whereas that at the low-frequency part is gradually cut off. This is experimental evidence for the existence of the HPF mentioned in section 2.

 

Fig. 5 Tuning characteristics and autocorrelation measurements for the high-repetition-rate ultrafast laser of wavelength 1.5 µm using the proposed tuning method: (a) Spectral variation of the photodiode signals in the 3.19312–3.19360 GHz region by rotating θ from 0° to 0.1062°; (b) Corresponding optical spectral variation in the 1565–1615 nm wavelength interval; (c) Magnified view of the optical spectra at θ = 0.0502°. The inset in the left shows the measured autocorrelation trace at θ = 0.0502°, and the inset in the right is the optical spectrum at a span of 0.4 nm, indicating a longitudinal mode spacing of approximately 0.027 nm, as expected for a laser operating at a repetition rate of 3.2 GHz.

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For the 3-GHz Er³⁺/Yb³⁺-doped ultrafast fiber laser, the longitudinal mode spacing is sufficiently large so that it can be easily observed using a spectrum analyzer. The optical spectrum at θ of 0.0502° in Fig. 5(b) is further magnified in Fig. 5(c). It shows a peak wavelength of 1590.2 nm and an FWHM of 4.1 nm. In particular, the longitudinal modes in the mode-locked spectrum can be observed, as shown in the right inset of Fig. 5(c), and the longitudinal mode spacing is 0.027 nm, which matches the cavity length of 3 cm. The left inset of Fig. 5(c) is an autocorrelation trace of the laser pulse mode-locked at a θ = 0; assuming the intensity profile to be a hyperbolic secant, its FWHM is 639 fs. For the optical spectrum of the emission line of wavelength 5 nm, the transform-limited width of the pulse is calculated to be 532 fs. The pulse broadening likely originates from the fiber pigtail of the WDM and fiber optical patch cord.

Similar to temperature controlling, rotating the alignment angle θ can also optimize the noise performance of the 1.5 µm fs fiber laser to a certain extent. Figure 6(a) shows the phase noise traces as a function of the offset frequency at the alignment angles θ of 0.0295°, 0.0502°, and 0.0649°. The quality of the PN declines with an increase in θ and the values of the integrated timing jitter integrated from 100 kHz to 10 MHz are 4.29 fs at θ = 0.0295°, 4.72 fs at θ = 0.0502°, and 5.70 fs at θ = 0.0649°. Correspondingly, the RIN traces at these angles are shown in Fig. 6(b), indicating the integrated RINs of 0.071% at θ = 0.0295°, 0.078% at θ = 0.0502°, and 0.094% at θ = 0.0649°, integrated from 10 Hz to 10 MHz.

 

Fig. 6 Noise characteristics of the high-repetition-rate ultrafast oscillator of wavelength 1.5 µm: (a) The measurements of the PN at θ of 0.0295° (blue), 0.0502° (red), and 0.0649° (green); (b) Corresponding RIN of the oscillator at θ of 0.0295° (blue), 0.0502° (red), and 0.0649° (green).

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6. Conclusion and outlook

Multi-gigahertz fundamental repetition rate, tunable repetition rate and wavelength, and ultrafast fiber lasers based on YGF, TGF, and EYGF as gain media were demonstrated and summarized. The laser wavelength is continuously tuned from 1040.1 nm to 1042.9 nm and the repetition rate is shifted by 226 kHz for an oscillator of wavelength 1.0 µm by changing the system parameters using a temperature control on the laser cavity. For the oscillator of wavelength 2.0 µm, a broad optical spectral tunable range of 14.1 nm from 1974.1 nm to 1988.2 nm was obtained. In particular, the average output power of the Yb-oscillator was 57 mW with an optical-to-optical efficiency of 27%, benefiting from the optimal reflectivity of 74% of the dielectric film at the laser wavelength. For the high-frequency range from 100 kHz to 10 MHz, the integrated timing jitter gradually increases with an increase in the temperature. Finally, to the best of our knowledge, for the first time, a new method for tuning wavelength and repetition rate was proposed and further applied to a femtosecond fiber laser of wavelength 1.5 µm. The peak wavelength could be tuned in the range 1591.4–1586.1 nm and the repetition rate was shifted by 60 kHz. The results of the ultrafast laser of wavelength 1.5 µm provide straightforward evidence for the existence of the HPF.

For the high-repetition-rate fiber lasers, the average output power is considerably lower than that of solid-state or waveguide lasers (>1 W) [11,21]. This is mainly because of the restriction of the maximum pump powers of a single-mode laser pump (e.g., a maximum of 250 mW for a commercial single-mode LD at a wavelength of 793 nm). Therefore, the development of highly-doped double-cladding fibers and pumping them using high-power multimode LDs would provide a promising approach to further increase the average power. Moreover, the pulse width for the high-repetition-rate ultrafast fiber lasers is expected to be further shortened. One method is the use of an intracavity dispersion compensating components (e.g., dispersion coatings on fiber-type dielectric mirrors [41]) providing sufficient negative group delay dispersion (GDD) to construct a laser cavity with a net negative GDD. The pulse duration when operating in the fundamental soliton regime is typically several hundreds of femtoseconds. Another way is to utilize a higher-order soliton compression outside the laser cavity during the amplification process, which generally enables pulse durations below 100 fs. We have already confirmed a nonlinear compression for high-repetition-rate ultrafast fiber lasers and obtained a pulse width of 30 fs, which will be stated in a separate paper.