A femtosecond mode-locked laser (MLL), also known as an optical frequency comb, is widely used in high-precision metrology ranging from fundamental sciences to industrial applications since it can generate ultrashort pulse-width while millions of optical mode (ν_n = nf_rep + f_ceo, n = 0,1,2,3…), known as comb line, are simultaneously generated and defined with pulse repetition-rate (f_rep), and carrier-envelope offset frequency (f_ceo). The representative applications are such as low-noise microwave [1, 2], time/frequency standard [3], dimensional metrology [4, 5], photonic radar [6], and dual-comb spectroscopy [7].

In particular, dual-comb spectroscopy has a great advantage since it can combine the strength of broadband spectroscopy from the broadband optical spectrum and tunable laser spectroscopy from the delta-function-like narrow linewidth of each comb line. The broad optical bandwidth and short pulse characteristics enable the generation of mid-infrared (IR), which overlaps the fundamental absorption lines of most greenhouse gases, using nonlinear crystals and a single comb source via intrapulse difference frequency generation [8]. In mid-IR dual-comb spectroscopy, the coverable bandwidth with one-to-one mapping and the timing and power stability of the combs are very important [7].

For example, if the coverable bandwidth of the mid-IR comb is from 3 to 5 µm, the corresponding frequency is from 60 THz to 100 THz. In order to cover 40 THz, the required f_rep is 100 MHz when the repetition rate difference between each comb (∆f_rep) is 250 Hz. Since the coverable bandwidth scales as $f_{\text{rep}}^2$/∆f_rep, the higher f_rep is desirable. Timing stability is related to the resolution and accuracy of the measured spectral lines. Power stability is related to the frequency stability of the generated mid-IR combs. Therefore, a mode-locked laser >100 MHz f_rep with great timing and power stability is required for future mid-IR dual-comb spectroscopy.

As a strategy to achieve mode-locked lasers, real saturable absorbers such as semiconductor saturable absorber mirrors (SESAMs) [9] or artificial saturable absorbers such as nonlinear polarization rotation (NPR) [10] and nonlinear amplifying loop mirrors (NALMs) [11, 12] are widely used. Since the slow relaxation of a real saturable absorber often limits the noise performance and stability, an artificial saturable absorber-based approach is one solution for low-noise operation. For robust long-term operation, a polarization-maintaining (PM) fiber-based system has great advantages. It is challenging for NPR lasers to be PM-fiberized. Therefore, PM-NALM-based MLLs have attracted great attention and are widely used in outdoor experiments and satellite missions [13].

In this work, we built a polarization-maintaining (PM) fiber-based femtosecond mode-locked laser based on a NALM at a repetition rate of 111 MHz. A low-loss oscillator with near-zero dispersion, output coupling design to reduce amplified spontaneous emission noise, and pump power optimization help to generate ultralow relative intensity noise. We believe optimization of the cavity dispersion and the power is very important for low-noise NALM since the pulse shaping in NALM is based on the cavity dispersion and the power-dependent round trip transmission. The relative intensity noise (RIN) of the MLL is <−150 dB/Hz above 1 MHz Fourier frequency. The corresponding integrated root-mean-square (rms) RIN is 0.009% over 1 s. The long-term rms intensity fluctuation over 12 h is 0.17%. The peak-to-peak repetition rate fluctuation over 12 h is 1.2 kHz. The repetition-rate phase noise scaled at 10 GHz carrier frequency is −122 dBc/Hz at 10 kHz Fourier frequency.

An all- PM fiber-based NALM-based MLL is used for the experiment, as shown in Fig. 1.

Figure 1. All-fiber nonlinear amplifying loop mirror-based mode-locked laser. Er, erbium-doped gain fiber; WDM, wavelength division multiplexer; ϕ, non-reciprocal phase shifter; PD, photodetector; RIN, relative intensity noise.

A fiber loop is composed with a PM fiber coupler, a PM fiber-based non-reciprocal phase shifter, a PM Erbium-doped fiber and a PM wavelength division multiplexer. A non-reciprocal phase shifter is composed of a Faraday rotating mirror, a waveplate, and a Faraday rotating mirror in series. Pulses from one direction pass the fast axis of the waveplate, and pulses from the other direction pass the slow axis of the waveplate. Therefore, the phase delay is non-reciprocal in the phase shifter. A PM fiber mirror is used as an end mirror at the linear cavity. This all-PM-fiberized design of the laser is expected to have highly robust operation against vibration and shock [13–15]. In order to achieve a >100 MHz repetition rate, each component is tightly spliced. The net cavity dispersion is +0.004 ps² at 1,567 nm (center wavelength). The near-zero dispersion is promising for the broadband optical spectrum, and the corresponding short pulse width helps mid-infrared generation by high peak power [16, 17]. In addition, the near-zero dispersion improves the intensity noise by helping pulse shaping [18].

The MLL is pumped backward using a PM 976 nm diode laser. If the laser oscillator is an all-fiber system, it is difficult to perturb phase bias or nonlinear loop transmission by adjusting polarization or power ratio. To achieve self-starting operation without mechanical perturbation, the MLL is pumped with 900 mW for a considerable phase shift and the phase bias between the light in each direction in the fiber loop. However, high-power pumping is not necessarily helpful for noise performance and stability because it can induce too much phase shift that can degrade the stability by the inappropriate pulse shaping (i.e., round trip transmission). Therefore, pump power is adjusted to achieve stable conditions after the laser is mode-locked. The mode-locking is stable when the pump power is below 320 mW, and the mode-locking is not possible when the pump power is below 180 mW. The clockwise circulating power at the fiber loop is coupled out ~1.5 mW (30%) for the experiment. It can avoid the degradation of the intensity noise from the amplified spontaneous emission in the gain fiber [19]. In order to avoid the back reflection that can deteriorate mode-locking, the output port is spliced to a polarization-sensitive isolator. Then, the output is split and sent to an optical spectrum analyzer, a 1.2-GHz bandwidth photodetector for the RF measurement and the frequency measurement, and a 150-MHz bandwidth photodetector to monitor the intensity.

3.1. Performance of the All-fiber Nonlinear Amplifying Loop Mirror-based Mode-locked Laser

Figure 2 shows the performance of the all-fiber NALM-based mode-locked laser (MLL) at 300 mW pumping power. Figure 2(a) is the Radio frequency (RF) spectrum of the MLL at a fundamental repetition rate with a 1-MHz span. The repetition rate is 111.019 MHz. The signal-to-noise ratio (SNR) of the repetition rate with 1 kHz resolution bandwidth (RBW) is 70 dB without sideband peaks. Harmonics of the repetition rate in a 1 GHz span are displayed in Fig. 2(b). Since the net cavity dispersion is nearly zero, the optical spectrum is nearly Gaussian, as shown in Fig. 2(c). The 3-dB full-width half maximum (FWHM) bandwidth of the optical spectrum is 24 nm, and the expected transform-limited pulse width with Gaussian assumption is 150 fs.

Figure 2. Performance of the all-fiber nonlinear amplifying loop mirror-based mode-locked laser. (a) Radio frequency (RF) spectrum of repetition rate. (b) RF spectrum of mode-locked laser (MLL) with 1 GHz span. (c) Optical spectrum of MLL, the dashed red line denotes Gaussian fitting. (d) Relative intensity noise of MLL, detection background and integrated rms relative intensity noise (RIN).

Figure 2(d) shows the RIN power spectral density of the MLL. The photo-detected output (DC-coupled) is low-pass filtered with a 48-MHz BW low-pass filter. The relative intensity noise is <−150 dB/Hz at 1 MHz and <−130 dB/Hz at 1 kHz Fourier frequency, which significantly filters the pump RIN (typically, −120 dB/Hz at 1 kHz) and amplified spontaneous emission (ASE) noise in gain fiber. Above 1 kHz Fourier frequency, the roll-off of RIN is due to the slow time constant of excitation relaxations in Erbium. Below 100 Hz Fourier frequency, the 1/f dependence is observed. The dependence is from the flicker noise in the pump laser diode controller. The RIN level reaches close to the detection background. Integrated rms RIN is 0.009% [integration bandwidth: 1 Hz–10 MHz]. Since mid-infrared generation is a power-dependent process, we believe the demonstrated MLL with low RIN will be a robust seed source.

3.2. Pump Power Dependence on Optical Spectrum and Relative Intensity Noise

Figure 3 shows the pump power-dependent performance of the MLL. As the pump power increases, the center wavelength and bandwidth increase. The 3-dB FWHM bandwidth with 180 mW pump power [curve (i) in Fig. 3(a)] is 20 nm. We note that pump power higher than 340 mW does not guarantee single pulse operation, and pump power lower than 160 mW does not maintain mode-locking due to insufficient nonlinear phase shift.

Figure 3. Pump power-dependent performance of the mode-locked laser (MLL). (a) Optical spectra of the MLL from different pump power; (i) 180 mW, (ii) 200 mW, (iii) 220 mW, (iv) 240 mW, (v) 260 mW, (vi) 280 mW, (vii) 300 mW, and (viii) 320 mW. (b) Relative intensity noise (RIN) of the MLL from different pump power, (i) 180 mW, (ii) 200 mW, (iii) 220 mW, (iv) 240 mW, (v) 260 mW, (vi) 280 mW, (vii) 300 mW, (viii) 320 mW, and (ix) detection background.

It is noted that the center wavelength and bandwidth change less than 10%, while the RIN power spectral densities change more than 20 dB when the pump power changes. As pump power increases, the RIN is improved until 300 mW pumping. The integrated RMS RIN of 180 mW pumping is 0.015% [integration bandwidth: 1 Hz–10 MHz], which is 50% worse than 300 mW pumping [0.009%, integration bandwidth: 1 Hz–10 MHz]. The RIN gets worse when pumping higher than 320 mW, and the single pulse operation is no longer available after 340 mW pumping. This indicates that there is an optimized intracavity power for the stability of mode-locking and noise performance, as the nonlinear phase shift and pulse shaping are determined by the roundtrip transmission.

3.3. Repetition-rate Phase Noise of the Nonlinear Amplifying Loop Mirror Mode-locked Laser

Repetition-rate (f_rep) phase noise (i.e., timing jitter) is another important parameter of lasers for many applications. Moreover, repetition-rate phase noise is highly correlated to carrier-envelop offset (f_ceo) noise, and f_ceo noise is correlated to the accuracy of the spectroscopy.

We characterized the repetition-rate phase noise based on the microwave phase detector method [20]. In order to generate a single-frequency microwave, we used a 12-GHz high-speed photodiode, RF bandpass filters, and an RF amplifier. We launched 0.5 mW average power on the photodiode. The 8.1 GHz microwave (73^rd harmonics of the repetition rate) with −7 dBm is characterized by a commercial phase noise analyzer. The single side band (SSB) phase noise power spectral density (PSD) of 8.1 GHz scaled to 10 GHz carrier frequency is shown in Fig. 4. The phase noise at 10 kHz Fourier frequency is −122 dBc/Hz. Above 10 kHz Fourier frequency, the measurement is limited by photodetection.

Figure 4. Repetition-rate phase noise power spectral density of the mode-locked laser (MLL) scaled to 10 GHz carrier frequency. (i) Measured repetition rate phase noise. (ii) Noise floor of the phase noise analyzer.

3.4. Long-term Performance of the Nonlinear Amplifying Loop Mirror-based Mode-locked Laser

Figure 5 shows the long-term performance of the NALM-based MLL over 12 h. The repetition rate filtered by a 140-MHz BW low pass filter is monitored by a frequency counter. Over 12 h of measurement, the peak-to-peak repetition-rate drift is 1.2 kHz, as shown in Fig. 5(a).

Figure 5. Long-term performance of the nonlinear amplifying loop mirror (NALM)-based mode-locked laser (MLL). (a) Repetition-rate measurement over 12 h, (b) optical power monitoring over 12 h, and (c) Allan deviation from the repetition-rate measurement.

The optical power of the MLL is monitored with a high trans-impedance photodetector. The repetition rate is filtered out by the 48 MHz BW low-pass filter. The optical power is acquired every 1 s with a data acquisition board after a 3-Hz BW analog low pass filter. The root-mean-square deviation of the optical power is only 1 µW (0.17%) and 0.47 µW (0.078%) over 12 h and 1 h, respectively. The repetition rate and the optical power are measured simultaneously. In Figs. 5(a) and 5(b), the dominant fluctuation every 10–15 min is related to the period of air-conditioning.

The Allan deviation is evaluated from the measured repetition-rate data [21]. The Allan deviation starts 10⁻⁹ at 1 s and keeps increasing due to the linear drift of the system. Although the system is packaged in an aluminum box, further feedback control is required for better long-term stability for high-precision applications.

Optical spectra of the MLL are also monitored over 12 h. As shown in Fig. 6, mode-locking is maintained during the measurement. The center wavelength and bandwidth are slightly detuned from the original state. This is due to the linear drift over time.

Figure 6. Optical spectrum monitoring of the mode-locked laser (MLL). The gray lines denote a 6-dB grid.

We developed an all polarization maintaining fiber, nonlinear loop-mirror based mode-locked laser at 111-MHz repetition rate with low intensity noise and stable long-term performance. Since the NALM-based mode-locking is power dependent, the intensity noise with different pump power is investigated. We find that the lowest RIN is achieved with 300 mW pump power, showing <0.01% intensity fluctuation over 1 s and <0.17% over 12 h, respectively. In order to apply the low RIN MLL for precision spectroscopy, further feedback control is highly desirable for long-term performance. From the demonstrated system configuration, 50 MHz and 200 MHz comb sources will be studied for comb-based spectroscopy and mid-IR generation.

This study was supported by the National Research Council of Science and Technology [Project number: NK242G, 2023, Korea].

Development of Measurement Standards and Technology for Biomaterials and Medical Convergence funded by Korea Research Institute of Standards and Science (No. KRISS-2023-GP2023-0007).

The authors declare no conflicts of interest.

The data underlying the results presented in this paper are not publicly available at the time of publications, but can be obtained from the authors upon reasonable request.