206 MHz fully stabilized all-PM dispersion-managed figure-9 fiber laser comb

High-repetition-rate optical frequency combs are useful for precision spectroscopy because of their high power per comb mode, but conventional high-repetition-rate lasers do not have a broad enough spectrum. In this study, a fully stabilized polarization-maintaining figure-9 mode-locked fiber laser with a high repetition rate of 206 MHz and a broad spectrum was demonstrated by employing simultaneous control of cavity dispersion and length. The laser exhibited a 3 dB spectral bandwidth of 88 nm and a compressed pulse width of 66 fs. Additionally, fCEO and frep phase locking were implemented, resulting in low (0.21 rad) in-loop carrier-envelope-offset frequency phase noise. To the best of our knowledge, this is the widest spectrum bandwidth and shortest pulse duration directly obtained from an all-PM figure-9 fiber laser oscillator to date. The combination of high repetition rate and broad spectral range makes this system very useful for a wide range of applications, especially in the field of precision spectroscopy.

on an NALM fiber laser with a repetition rate exceeding 200 MHz has been reported, although no details of the laser design and optical characteristics were provided 16 .
In this work, we developed a stretched-pulse mode-locked Er-fiber laser with a repetition rate of 206 MHz and a 3 dB spectral width of 88 nm, by simultaneously shortening the cavity length and controlling the dispersion in a figure-9 Er-doped fiber laser.Also, a compressed pulse duration of as short as 66 fs was achieved.This spectral bandwidth and pulse duration are record values for all PM figure-9 fiber lasers, to the best of our knowledge.Moreover, by detecting and stabilizing f CEO and f rep of the oscillator, we constructed a fully stabilized optical frequency comb, and thanks to the characteristics of the NALM fiber laser and its broadband spectrum, the measured in-loop carrier-envelope-offset frequency SSB phase noise was suppressed to only 0.208 rad.

Figure-9 mode-locked fiber laser
Figure 1 shows a schematic diagram of the 206 MHz figure-9 Er-doped fiber laser oscillator.A 50 cm long section of PM erbium-doped fiber (PM-EDF; iXblue IXF-EDF-HD-PM) was used as a gain fiber.The fiber section other than the EDF was common PM-SMF, with a total length of 36 cm.The normal dispersion of the PM-EDF canceled out the anomalous dispersion of the PM-SMF, and the calculated net cavity dispersion value was + 0.0039 ps 2 , which was small enough to obtain stretch pulse mode-locking.As a pump source, two fibercoupled laser diodes (LDs) with a total maximum output power of 1.5 W and a center wavelength of 980 nm were used.The two collimators at the loop exit were rotated 90° to each other, and the output s-and p-polarized light components were combined at the polarization beam splitter/combiner (PBS).The free space section contained two PBSs, a Faraday rotator (FR), and two quarter-wave plates (QWP1 and QWP2).The modulation depth of the cavity could be optimized by adjusting the angle of QWP1.There were two output ports, called output port 1 and output port 2. The coupling ratio of output port 2, as well as the linear loss in the cavity, could be changed arbitrarily by adjusting the angle of QWP2.A PZT actuator was bonded to part of the PM-EDF to control the cavity length.First, the PZT was attached to the back side of the end mirror, but this caused too much crosstalk to f CEO , so it was then bonded to the fiber.The PZT connection to the back of the end mirror affected not only the cavity length but also the angle of the end mirror, resulting in an increase in linear loss in the cavity, which had a significant effect on f CEO .The entire optical system was built on an air-floating optical table to eliminate the effects of vibrations from the ground.Also, the laser cavity was temperature-stabilized with a water-cooled breadboard and covered by an acrylic enclosure with sound-absorbing sponges to suppress acoustic noise.The output pulse was analyzed with an autocorrelator (Femtochrome FR-103XL), an optical spectrum analyzer (Yokogawa, AQ6375B), and an RF spectral analyzer (Anritsu MS2840A).The output pulse was compressed by passing it through a dispersion compensation fiber (DCF) with a length of 55 cm and a β 2 of 79 ps 2 /km.The compressed pulse was analyzed with custom-made second harmonic frequency-resolved optical gating (SHG -FROG).

Fully stabilized optical frequency comb system
Figure 2 shows the whole setup of the optical frequency comb system, including an oscillator, f CEO detection optics, and phase stabilizing circuits.Of the two output ports, the output of port 1 was divided by a 50:50 coupler, and one output was used for f CEO detection, whereas the other one was used for applications.The output of port 2 was used for optical spectrum monitoring and f rep detection.The output power of the application port was 12 mW.f CEO detection was performed using the f-2f.interferometry method.The f CEO stabilization optics consisted of a PM-EDF amplifier, a highly nonlinear fiber (HNLF), a waveguide-type periodically poled lithium niobate (PPLN) second harmonic generator, and a polarization interferometer for temporal delay adjustment 17 .Phase detection circuits for f rep and f CEO consisted of a band pass filter (BPF), a low-noise RF amplifier, and a frequency mixer.As reference signals, a signal generator (Agilent 8648C) and a function generator (Tektronix AFG1062) were used for f rep and f CEO , respectively.The generated f CEO error signal was fed back to the oscillator LD current through a PID circuit (Vescent D2-125).The f rep signal was fed back to the PZT in the cavity through another

Output properties of figure-9 mode-locked fiber laser
The mode-locking was self-started by increasing the total output power of the two LDs to about 1.4 W. At this time, there was a CW peak in the spectrum, but when the pump power was reduced to about 1.0 W, the state changed to a single-pulse mode-locked state with no CW peaks.The angle of the two QWPs inside the cavity greatly affected the mode-locking condition, but once set to the optimum values, the waveplates did not need to be touched again to initiate mode-locking.Figure 3 shows the oscillation spectrum, autocorrelation trace, and radio frequency (RF) spectrum of the mode-locked output from output port 1.The average output power was about 30 mW from output port 1 and 0.5 mW from output port 2 when the pump power was 0.80 W. The measured pulse duration was 180 fs (assuming a Gaussian shape) (Fig. 3a), which was broadened at the output fiber.The spectrum showed the typical shape of stretched-pulse mode locking, and a 3 dB bandwidth of 88 nm was obtained, although the center of the spectrum was depressed (Fig. 3b).The RF spectra (Fig. 3c,d) showed SNRs above 70 dB and equally spaced beat notes of uniform amplitude, indicating that the oscillator was in a clean single-pulse mode-locking state.The repetition rate was variable between 205 and 209 MHz by adjusting a motor stage at the end mirror.Since the output pulses were mainly broadened by the patch fiber after output and had a linear chirp, they could be easily compressed by a DCF with normal dispersion.Figure 4 shows the temporal waveform and spectrum of the compressed pulse measured by SHG FROG, with a FROG error of 0.58%.The measured pulse duration was as short as 66 fs.To the best of our knowledge, this is the shortest pulse duration directly obtained from an NALM fiber laser.However, the transform-limited pulse duration calculated from the spectrum is 31 fs, which suggests that further shortening of the pulse is possible by compensating for higher-order dispersion and eliminating the additional nonlinearity in the DCF.

Properties of fully stabilized optical frequency comb
Figure 5 shows the spectrum and temporal pulse shape of the amplified output pulses measured by SHG-FROG.The spectrum was expanded to 110 nm due to the similariton effect during EDFA propagation.The pulses were optimally dispersion compensated by the cutback method, and the average output power, pulse duration, and peak power of the pulses were measured to be 440 mW, 44.5 fs, and 45 kW, respectively.By using 20 cm HNLF (γ = 21 W -1 km -1 , β 2 = 0.25 ps 2 /km), an octave-spanning spectrum from 1064 to 2128 nm was obtained (Fig. 6a).The f CEO signal was detected by a balanced detector by generating a second harmonic through a waveguide PPLN (NTT Electronics Corp., WH-1064) and using a polarization interferometer to adjust the time interval between the fundamental and SHG signals.Figure 6b shows the free-running f CEO signal.A free-run linewidth of 13 kHz and an SNR of 33 dB were obtained by Lorentz function fitting.The position of the f CEO can be adjusted from 3 to 100 MHz by pump LD current control.For the phase locking, a range of 20-40 MHz was selected to obtain the highest SNR.
Figure 7 shows the RF spectra and phase noise of the stabilized f CEO and f rep .The measured integrated phase noise of f CEO was 0.208 rad (1 Hz to 1 MHz), indicating that low-noise stabilization was achieved.The integrated timing jitter was calculated to be 0.17 fs.The control bandwidth of f CEO estimated from the servo bump was about 50 kHz, which was limited by the slow response of the pump modulation.By increasing the P-gain (Kp), the control bandwidth could be extended to about 150 kHz, but the integrated phase noise was degraded due to the large servo bump caused by the reduced phase margin.Additional fast-loss modulation, such as a graphene modulator, can be used to achieve a wider control bandwidth and lower noise 18 .The integrated phase noise of f rep was 2.1 mrad.However, in the case of locking to the RF reference, the phase noise is multiplied by the number of comb modes, N (≈ 10 6 ), so it is necessary to use a beat signal with an optical frequency reference such as a cavitystabilized CW laser instead of an RF reference to achieve more stable phase locking.A long-term operation test of the fully stabilized comb, including continuous measurements of f CEO and f rep using a frequency counter, was also

Discussion and conclusion
Table 1 shows a comparison of the performance of NALM Er-doped fiber lasers with repetition rates above 200 MHz 14,15,19,20 .The spectral bandwidth obtained in this study is the highest yet reported.This is also the second report of a fully stabilized NALM Er-doped fiber laser in an all-PM configuration with a high repetition rate.Ref. 19 reported the highest repetition rate and the shortest pulse duration by using a special optical component, but the fiber laser reported there was not an all-PM configuration, and the spectrum had a large modulation.To further enhance the repetition rate, it is necessary to reduce the length of the fiber section.The fibers utilized in this study include PM-EDF with normal dispersion and PM-SMF with anomalous dispersion.Their lengths were adjusted to approach zero dispersion.The primary limiting factor is the length of the EDF, which proves challenging to significantly shorten while maintaining sufficient gain.If a higher concentration PM-EDF were available, it is anticipated that further shortening of the cavity could be achieved.The free-space section has already been reduced to approximately 10 cm in this study, with additional shortening yielding minimal impact.Practical limitations also arise from the fusion splicer.The fusion splicer employed in this study necessitates a minimum length of about 7 cm at both ends.The combined length of the two collimators and the pigtail fibers at both ends of the WDM is a minimum of approximately 28 cm.To solve this problem, it is useful to directly connect the EDF to the WDM or package multiple elements, such as the collimator and WDM.Alternatively, placing the WDM outside the resonator presents another viable option.
In conclusion, we report the successful development of a fully-stabilized polarization-maintaining figure-9 fiber mode-locked laser comb with a repetition rate of 206 MHz and a wide spectrum.The 3 dB spectral bandwidth and compressed pulse width achieved were 88 nm and 66 fs, respectively.To the best of our knowledge, this represents the widest spectral bandwidth and shortest pulse duration directly obtained from an all-PM figure-9 laser oscillator.Additionally, phase locking of f CEO and f rep was performed, resulting in low (0.21 rad)

Figure 1 .
Figure 1.Setup of the all-PM figure-9 fiber laser oscillator.LD laser diode, PBC fiber type polarization beam combiner, WDM wavelength division multiplexer, PM-EDF polarization maintain Erbium-doped fiber, PZT piezoelectric actuator, PBS cube type polarization beam splitter, FR Faraday rotator, QWP quarter wave plate.

Figure 2 .
Figure 2. Setup of all-PMfigure-9 fiber laser-based fully stabilized optical frequency comb system.PID PID servo circuit, BPF band pass filter, ISO isolator, PBC fiber-type polarization beam combiner, HNLF high nonlinear fiber, PPLN in-line type periodically poled lithium niobate second harmonic generator, DCF dispersion compensation fiber.

Figure 3 .
Figure 3. Output characteristics of all-PM figure-9 fiber laser, (a) autocorrelation trace, (b) output spectra (blue line: log scale, red line: linear scale), (c) RF spectra of fundamental beat note, (d) RF spectrum of higher order beat notes up to 2 GHz.

Figure 4 .
Figure 4. (a) Pulse shape and (b) optical spectrum (blue line: log scale, red line: linear scale) of compressed output pulse measured by SHG FROG.

Figure 6 .
Figure 6.(a) Octave spanning supercontinuum spectrum after HNLF.(b) RF signal of free-run f CEO .The orange line shows a squared-Lorentzian fitting.

Figure 7 .
Figure 7. (a) RF spectrum of phase-locked f CEO with 1 Hz RBW.(b) In-loop SSB phase noise and integrated phase noise of phase-locked f CEO .(c) RF spectrum of phase-locked f rep with 1 Hz RBW.(d) In-loop SSB phase noise and integrated phase noise of phase-locked f rep .

Table 1 .
Comparison of NALM mode-locked Er fiber lasers with repetition rates above 200 MHz.