1. Introduction

Nanosecond (ns) optical pulses have been used for LIDAR and remote sensing, precision micromachining, supercontinuum sources, and THz generation. Transform-limited ns pulses exhibit an ultranarrow bandwidth, which can be used to improve applications for optical spectroscopy [1] and quantum sensing and computing [2–4]. Fiber lasers, which are compact, robust, and maintenance-free, have been extensively developed to generate ns pulses. Among these approaches are Q-switched fiber lasers [5,6], electro-optic modulation of a narrow bandwidth laser [7,8], or gain medium [9], and passive mode locking using nonlinear polarization evolution [10,11], fast saturable absorbers [12,13], and nonlinear amplifying loop mirror (NALM) [14,15], but the output pulses are modestly [7,8] or highly [9–15] chirped. Recently, by substantially improving the peak power through a high-Q micro-resonator in an NALM architecture, transform-limited pulses with duration of 4.31 ns and an ultranarrow bandwidth of 104.9 MHz have been produced [16]. But the pulse energy from the oscillator is limited to 0.26 nJ [16].

Active mode locking (AML) has been another way to generate ns pulses in the fiber lasers [17–19]. In the AML scheme, when an electrically controlled modulators are used to introduce loss modulation, the modulation frequency is required to be precisely matched to the cavity round-trip frequency in order to produce stable shape of optical pulses [20]. In practice, environmental variations, e.g., temperature and vibration, always perturb the cavity, and the cavity round-trip frequency is inevitably detuned from the modulation frequency. So, the actively mode-locked fiber lasers without active control of either the modulation or the cavity round-trip frequency [17–19] cannot be operated reliably for an extended period of time. Regenerative mode locking [21,22], in which the modulation frequency is derived directly from the oscillator itself, is employed to generate stationary shape of pulses. Previously, fiber lasers using harmonically regenerative mode locking have focused on producing ultrashort pulses in the picosecond (ps) [23–25] and femtosecond [26,27] regimes.

Here, we report on the generation of transform-limited ns optical pulses with an ultranarrow bandwidth by using regenerative mode locking. In an Erbium (Er)-doped fiber laser, a narrow bandwidth fiber Bragg grating (FBG) and a bulk amplitude electro-optic modulator (EOM) are utilized to shape pulse evolution in a ring cavity. The fiber oscillator through regenerative mode locking delivers stationary shape of transform-limited pulses with duration of 2.05 ns, energy of 5 nJ, and a repetition rate of 9 MHz at 1.56 µm. Spectral characterization via high bandwidth optoelectronic devices shows that optical pulses exhibit an ultranarrow bandwidth of 220 MHz. Numerical simulation further shows that the shape of the FBG filter has a strong effect on the duration and bandwidth of output pulses.

2. Experimental setup of the regenerative mode locked fiber laser

Fig. 1 is the schematic of the regenerative mode locking Er-doped fiber oscillator. The oscillator mainly comprises passive and gain fiber, a narrow bandwidth FBG filter, an EOM, and a regenerative feedback loop. The gain medium is a 45 cm Er-doped fiber (ER30-4/125, Thorlabs) and co-pumped by 800 mW laser light at 980 nm, emitting from two fiber pigtailed diodes that are incoherently combined through a fiber polarization beam splitter (PBS). The pump light is coupled into the gain fiber through a wavelength division multiplexer. The FBG filter is combined with a fiber circulator to ensure that the laser beam propagates along one direction. The FBG from Teraxion is specified with a central wavelength of 1.56 µm, a reflectivity of 80%, and a full width at half-maximum (FWHM) bandwidth of 2.46 GHz. A segment of 10-meter long single-mode fiber (SMF-28, Corning) is used to extend the cavity length. Two fiber collimators are used for coupling the beam into free space and then back into the fiber, respectively. A half-wave plate (HWP), a quarter-wave plate (QWP), and a bulk PBS are combined to form a variable output coupler [26,28]. The amplitude EOM consists of a 137-mm long Lithium Tantalate crystal (M360-80-SE, Conoptics) with a half-wave-voltage of 268 V at 1.56 µm. The bulk EOM feathers low insertion loss and high-power handling capability over the waveguide counterpart, and it is also immune to the temperature variation. By combining two PBSs with one HWP and one QWP, the EOM is biased in the quadrature such that the light transmission intensity is linearly proportional to the modulation voltage. A sigma-cavity arm, using a PBS, a QWP and a motorized mirror, is integrated in the cavity so that the pulse repetition rate could be varied for some applications. Considering the total fiber length (20.5 meters), all the optical elements and free space, the frequency spacing of the cavity mode is 9.0 MHz. All the optical parts are sealed in a box for stable and reliable operation, and temperature stabilization of all the fiber parts will be necessarily added to uphold the long-term performance. Alternatively, polarization-maintenance fiber parts could be used to achieve the environmentally stable laser.

 

Fig. 1. Experimental setup of the regenerative mode locking Er-doped fiber oscillator. FBG, fiber Bragg grating; Er-doped single-mode (SM) gain fiber, EDFA, Erbium-doped fiber amplifier; WDM, wavelength division multiplexer coupler; HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; FC, fiber collimator; BS, beam sampler; PS, phase shifter; M, mirror; PD, photodiode; EOM, electro-optic modulator.

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To generate ultranarrow bandwidth pulses in the ns regime, a narrow bandwidth FBG filter has been used. In the AML scheme, a narrower spectral filter tends to pulse broadening while stronger amplitude modulation leads to pulse shortening, and both effects are well balanced to shape pulse evolution [29]. When the laser beam is circulating repeatedly inside the cavity, the stationary shape of optical pulses is produced accordingly. In the experiment, we have chosen a 2.46 GHz bandwidth FBG filter to generate pulses of 2 ns, but commercial FBG filters have a wide range of spectral widths. So, our design offers the flexibility that varies the pulse duration by replacing the FBG filter in the cavity. The FBG filters have been used in a number of fiber oscillators [30–36], but the focus has been put on the generation of ps pulses with narrow spectral widths. By contrast, our work is to produce ns pulses with an ultranarrow spectral width. Also, our simulation shows that, in addition to the bandwidth, the shape of the FBG filter has a strong effect on the duration and bandwidth of output pulses.

To initialize the mode locking and generate stable pulses, a regenerative feedback loop [21,22] is developed. The output pulses from the oscillator are sampled and detected by an ultrafast photodiode, and the signal is filtered through a 9.0 MHz bandpass filter (ZX75-12-S, Mini-Circuits) and boosted through RF amplifiers (ZFL-1000 and ZHL-1-2W, Mini-Circuits). A sinusoid modulation signal is thus produced and applied to the EOM. The RF phase can be tuned using an analog phase shifter (PS-B-0S, R&K) that provides a continuously variable phase shift of up to 360 degrees. In the feedback loop, the amplitude noise in the laser beam could be magnified and imparted to the modulation signal, leading to instability of mode locking in the oscillator. To suppress the noise in the feedback loop, the final RF amplifier operates in the saturated regime [37] such that the modulation signal is a sine wave with a constant amplitude. As such, the depth of amplitude modulation remains unchanged, and the modulation signal has been steadily applied to the laser beam. The saturated gain of the RF amplifier is 35.0 dBm, and the depth of amplitude modulation is 0.20 in the experiment.

To achieve steady-state mode locking, the laser cavity and feedback loop has been properly aligned. The RF phase in the feedback loop is adjusted to minimize the pulse duration. Also, the EOM is slightly tweaked to optimize the bias point and shorten the pulses further. Both alignments are iterated until the pulse duration is reached at its minimum. By these means, stationary shape of optical pulses from the oscillator have been produced. We estimate that the EDFA is 90% delivered to the output port and 10% compensated for various losses in the cavity and then seeded back to the EDFA. The fiber coupling loss is 20%, but the mode locking is not sensitive to this loss due to the saturating effect in the EDFA. The coupling efficiency will be further verified through numerical simulation. The fiber oscillator is self-started when the cavity is blocked and released, or the laser is turned off and on again. However, when the laser is turned on in the absence of regenerative feedback, no pulse has been formed in the laser cavity. So, the AML is the only mechanism for pulse formation in our experiment.

3. Characteristics of laser pulses and simulation result

The characteristic of pulses from the regeneratively mode locked oscillator is shown in Fig. 2. The optical pulses are sampled and measured through a 25 GHz high bandwidth photodiode and displayed in a 20 GHz bandwidth oscilloscope. Figure 2(a) is the trace of the optical pulse train with a repetition rate of 9.0 MHz. The optical pulses are also analyzed by using a RF spectrum analyzer, and Fig. 2(b) is the RF spectral measurement. It is illustrated that the spectral components are 9.0 MHz and its high harmonics. As any sideband has been suppressed to 70 dB below the main signal, it is clearly evident that there is no secondary pulse.

 

Fig. 2. Characteristics of optical pulses from the regenerative mode locking oscillator. 2(a), intensity trace of optical pulses; 2(b), RF spectrum of optical pulses; the stair is due to the change of the displayed average noise level in the RF spectrum analyzer; 2(c), temporal profile of optical pulses; the blue is the experimental data, and the red is the Gaussian fitting. 2(d), the blue is the normalized intensity of the RF spectrum, and the red is the Gaussian fitting. 2(d) is the same as 2(b) but the RF spectrum in 2(d) are acquired in a larger spectral range and exhibited in a linear scale.

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Figure 2(c) shows a single pulse within the pulse train. The temporal shape of pulses obtained from the oscillator exhibits a nearly perfect Gaussian profile, and the pulse duration is 2.05 ns (FWHM). The small discrepancy in the rising and falling edges arises from charge and discharge of the photodiode. Since the rise or fall time, integrated response of the detector and oscilloscope, is less than 25 ps, the duration measurement is accurate enough and the deviation is very tiny. A pulse energy of 5 nJ or an average power of 45 mW is obtained, corresponding to a peak power of 2.4 W. The nonlinear phase shift that the pulses accumulate during one round trip is < 0.01 rad, and the cavity length is significantly less than the nonlinear length (140 m) and the dispersion length (180 km). So, both nonlinear and dispersive effects are completely negligible during mode locking. The low peak power of optical pulses also implies the potential of power scaling if higher gain in the EDFA would be available.

To characterize ns pulses in the frequency domain, it is necessary to measure its optical spectrum. Using an optical spectrum analyzer, the laser beam is measured at 1560 nm and the signal-to-noise ratio is more than 30 dB over 100 nm range. However, transform-limited ns pulses typically exhibit a ultranarrow bandwidth of < 500 MHz, which is beyond the resolution of the state-of-the-art optical spectrum analyzers. To acquire the spectral width of transform-limited pulses in the ns regime, we utilize a technique of high-sensitive measurement of pulse envelope in the frequency domain. By combining high bandwidth optoelectronic measurement with RF spectral analysis, we are able to obtain the spectral envelope and thus bandwidth of ns optical pulses [16]. In the experiment, the ns pulses from the oscillator are measured by using a 25 GHz bandwidth photodiode, and the RF spectrum is obtained by using an RF analyzer. It has been shown in Fig. 2(d) that the envelop of the RF spectrum exhibits an approximately Gaussian profile, and the FWHM is fit to be 220 MHz. The time-bandwidth-product (TBP) is 0.45. So, the ns optical pulses from the oscillator are transform-limited. The ns pulses exhibit an ultranarrow bandwidth, which is 10 times smaller than the FBG bandwidth due to the pulse evolution in the cavity. As the spectral width is so narrow, our spectral measurement further suggests that the cavity dispersion plays no role in shaping pulse evolution for the mode locking. Compared with ultranarrow bandwidth pulses from a passively mode locked fiber laser [16], the duration and bandwidth in our experiment are approximately half and double, respectively, but the pulse energy has been improved by a factor of 18.

To understand the pulse generation in the cavity, we have simulated the pulse evolution following the master equation [38]. The model includes the effects due to saturated gain, amplitude modulation, spectral filtering, fiber coupling loss, FBG reflectivity, and output coupler, and the results show no difference with or without dispersive and nonlinear effects. In the AML models [29,38], a Gaussian spectral filter is approximated. Here, we have considered the influence of the FBG filter for three specific shapes as its bandwidth is as narrow as 2.46 GHz. Figure 3(a) are the temporal profiles of the simulated pulses when the spectral filter exhibits a Gaussian, super-Gaussian, or a mixed shape, respectively. The pulse duration and TBP due to the effect of a Gaussian filter are 3.61 ns and 0.44, respectively, consistent with the prediction of the AML models [29,38]. When a super-Gaussian filter is put into the cavity, the pulse duration and TBP are 1.63 ns and 0.48, respectively. So, a sharp-edged spectral filter leads to pulses with shorter duration and broader bandwidth. In the experiment, the FBG exhibits a mixture of Gaussian and super-Gaussian shapes (Fig. 3(b)), and when it is used for spectral filtering, the pulse duration and TBP are calculated to be 2.05 ns and 0.45, respectively, which are fit well to the experimental results. However, to ensure consistency of pulse duration between the simulation and the experimental results, Fig. 3(b) shows that the shape of the spectral filter in the simulation deviates slightly from the data that the vendor offered. To do so, we argue that the reflective index and period of the FBG is prone to the mechanical strain [39]; its specifications could have been slightly altered during the course of integration into the oscillator. As a result, we believe that our simulation is in a good agreement with the experimental results. Also, our simulation has clearly shown that, when the filter has a narrow bandwidth, its shape has a strong effect on the duration and bandwidth of output pulses, which provides an important guidance for precisely designing fiber lasers and engineering transform-limited pulses in the ns regime.

 

Fig. 3. Simulated pulses and profiles of the spectral filter. (a) the temporal profiles of the output pulses when the narrow bandwidth filter exhibits three specific shapes: M (mixture of Gaussian and super-Gaussian); S (super-Gaussian); and G (Gaussian); and (b) shape of the spectral filter: N (nominal data from the vendor); and F (fitting data).

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4. Conclusion

We have demonstrated a regeneratively mode-locked fiber laser for generating transform-limited ns pulses with an ultranarrow spectral width, employing a narrow FBG spectral filter and a bulk amplitude EOM to shape pulse evolution inside the cavity. To the best of our knowledge, it is the first demonstration of a regeneratively mode-locked laser generating transform-limited pulses in the ns regime. The numerical simulation shows that the shape of the narrow spectral filter has a strong effect on the duration and bandwidth of output pulses.