1. Introduction

Passively mode-locked lasers that work as practical ultra-low jitter photonic oscillators enable numerous of high precision microwave photonic applications, such as photonic analog-to-digital conversion [1,2], microwave signal extraction [3], as well as high precision timing synchronization [4]. In all those applications, the low-jitter laser oscillator with high fundamental repetition rate is desired. Gigahertz level repetition rate pulse trains can be routinely generated from mode-locked fiber lasers in recent years [5,6], which take full advantage of low-cost and easy to be operated. Hence, the accurate measurement and optimization of the timing jitter of high-repetition-rate mode-locked fiber lasers are crucial for extending ~GHz level mode-locked fiber lasers applications.

A diversity of techniques have been applied in mode-locked fiber lasers for the timing jitter reduction. In 2011, Y. Song et al. reduced the timing jitter of 80-MHz Yb:fiber lasers by the optimization of intra-cavity dispersions. The close-to-zero intra-cavity dispersion characterized the lowest rms timing jitter of 175 as (integrated from 40 MHz to 10 kHz). The timing jitter spectrum is 18 dB lower than the same laser working at normal intra-cavity dispersion regime [7]. K. Wu et al. reduced the timing jitter of 18.8 MHz Er:fiber lasers by the optimization of cavity loss. The rms timing jitter decreased by 24% at an optimal cavity loss (integrated from 20 kHz to 100 Hz) [8]. Another straightforward method is to use a narrow band intra-cavity filter to eliminate center frequency noise induced timing jitter. P. Qin et al. reduced the timing jitter of 161 MHz normal-dispersion Yb-fiber lasers by adding a 7-nm bandwidth filter in the cavity. As a result, ~10 dB reduction of timing jitter spectrum was achieved [9]. For Er-fiber lasers, a 9-nm bandpass filter brought ~20 dB jitter reduction at 10 kHz Fourier frequency, achieving 3.46 fs rms timing jitter (integrated from 10 MHz to 10 kHz) [10].

Aforementioned timing jitter characterization and optimization all concentrate on ~100 MHz level mode-locked fiber lasers. In our previous work, we measured the timing jitter of pulse trains emitted from ~GHz level repetition rate mode-locked Yb:fiber lasers by using BOC method. The rms timing jitter is 10 fs (integrated from 5 MHz to 30 kHz), which is 10-20 dB higher than that of reported ~GHz solid-state lasers and 100-MHz-level fiber lasers. Analytic model shows that the RIN induced timing jitter by self-steepening effect dominates the jitter performance below ~100 kHz, which is mainly because of the combined effects of high nonlinear phase shift per round trip in the laser cavity (~π rad) and the high fundamental repetition rate (~GHz level) [11]. This noise behavior is significantly different from that in ~GHz solid-state mode-locked lasers and 100-MHz-level fiber lasers, where amplified spontaneous emission (ASE) coupled timing jitter is a major contribution [7,12,13]. This theoretical analyzation suggested that the timing jitter could be reduced via RIN suppression in high-repetition-rate mode-locked fiber lasers below ~100 kHz.

In this work, we suppressed the RIN of the laser oscillators by feedback to the pump current, as to reduce the timing jitter of the pulse trains from 882 MHz mode-locked Yb-fiber lasers. In order to get a deeper understanding of RIN-to-timing jitter coupling mechanisms, we analysed both of the output voltage noise from the BOC and the fast PZT driving voltage noise in the slave laser to extend the BOC measurement dynamic range. In doing so, we obtained high precision and broadband timing jitter spectra in the Fourier frequency range from 100 Hz to 5 MHz. The measurements show a ~10 dB reduction from ~3 kHz to ~30 kHz with a unity-gain crossing point of 80 kHz, verifying the validity of our previous prediction in [11] that RIN induced jitter by self-steepening effect dominates the jitter performance below ~100 kHz in high-repetition-rate mode-locked fiber lasers. The rms timing jitter of the free-running lasers decreases from 1325 fs to 567 fs (integrated from 5 MHz to 100 Hz). Further comparison with analytical model shows that below ~3 kHz, the effect of RIN coupled jitter gradually vanishes, thus the reduction of timing jitter through RIN suppression in this frequency range is not obvious.

2. Active suppression of RIN

The two home-built 882 MHz Yb-doped NPE mode-locked fiber lasers have been demonstrated in [6,11]. The schematic of the experimental setup is shown in Fig. 1. Laser 1 is a σ cavity design with a fast PZT (Thorlabs, PA4CEW) mounted mirror, serving as the slave laser. Laser 2 is a ring cavity design. The RIN spectra of the mode-locked lasers are detected by a 10-MHz bandwidth photodetector. We stabilized the RIN using a proportional-integral (PI) servo [14]. The voltage signal from the photodiode which detects the laser’s intensity fluctuation was compared with a reference voltage source, generating the error signal for the PI servo. The output of the PI servo was fed back to the pump current. The current modulation input of the pump LD driver (Thorlabs, CLD1015) has a limited bandwidth of 250 kHz. The measured RIN spectra of laser 1 (laser 2) with and without the action of the PI servo are shown in Fig. 2. The PI servo suppresses RIN by ~10 dB in the frequency range from 100 Hz to ~30 kHz with a unity-gain crossing point of ~80 kHz. The integrated RIN of laser 1 (laser 2) decreases from 0.0098% (0.0082%) to 0.0065% (0.0074%) (integrated from 1 MHz to 100 Hz). The dash line in Fig. 2 indicates a measurement noise floor of 6.02 × 10^-16 1/Hz.

 

Fig. 1 Schematic of the experimental setup. λ/2: half wave plate; PBS: polarization beam splitter; PI servo: proportional-integral servo (Newfocus, LB1005).

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Fig. 2 (a) RIN spectra of laser 1. Curve (i) and (ii) are RIN spectrum without and with RIN suppression, respectively; curve (iii) and curve (iv) are integrated RIN spectrum without and with RIN suppression, respectively. (b) RIN spectra of laser 2. Curve (v) and (vi) are RIN spectrum without and with RIN suppression, respectively; curve (vii) and (viii) are integrated RIN spectrum without and with RIN suppression, respectively. Dash line: measurement noise floor.

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3. Measurement of timing jitter

The timing jitter spectra of the pulse trains emitted from 882 MHz mode-locked fiber lasers with and without RIN suppression were characterized with BOC technique (Fig. 1). The error signal from BOC was sent into a PI servo. The output of the PI servo was amplified and fed back to the fast PZT in slave laser, thus, achieving the low-bandwidth repetition rate locking between two lasers. After this procedure, the in-loop (IL) timing jitter spectrum can be obtained by analyzing the output voltage from BOC with RF analyzer (RIGOL, RSA3030) and FFT analyzer (Stanford research system, SR770). The resulting discrimination slope of IL BOC is 0.09 mV/fs, leading to a high measurement noise floor about 10^-5 fs²/Hz for the Fourier frequency range >100 kHz, as shown in dark gray curves in Figs. 3(a) and 3(b). To achieve high resolution timing jitter measurement and verify the validity of the IL BOC measurement result, we also conducted an out-of-loop (OOL) optics cross-correlator (OC). The timing jitter discrimination slope of OOL OC is 9.72 mV/fs leading to a measurement noise floor about 5 × 10^-10 fs²/Hz for the Fourier frequency range >2 MHz, as shown in gray curves in Figs. 3(a) and 3(b). More details about the BOC and OC measurement setup can be found in [11,15,16].

 

Fig. 3 (a) Measured timing jitter spectra with RIN suppression. Curve (i) and curve (ii) are measured by IL BOC and OOL OC, respectively. Inset: optical spectra of laser 1 and laser 2. (b) Measured timing jitter spectra without RIN suppression. Curve (iii) and curve (iv) are measured by IL BOC and OOL OC, respectively. Curve (v) and curve (vi) are IL BOC and OOL OC measurement noise floor, respectively.

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The timing jitter spectra with (without) RIN suppression measured by IL BOC and OOL OC are shown in Fig. 3. The inset in Fig. 3(a) shows the optical spectra of laser 1 and laser 2. The BOC locking bandwidth is 20 kHz which is the minimum locking bandwidth we can apply to achieve stable frequency synchronization between the two lasers. The IL and OOL jitter spectra overlap very well in the Fourier frequency range <100 kHz, which verify the validity of the measurement result. In the frequency range >100 kHz (2 MHz), the BOC (OC) measurement result is limited by the detection noise floor.

Given the limited phase-discrimination range of the error signal from BOC, we must establish low-bandwidth repetition rate locking between the two lasers by inputting this error signal into a PI servo. Then the timing jitter spectrum outside the locking bandwidth can be measured by analyzing the output voltage from BOC. However, the jitter spectrum inside the locking bandwidth cannot be characterized in this way. To this end, K. Jung et al. proposed a method by means of analyzing the input voltage signal to the PZT in the slave laser to retrieve the timing jitter spectrum inside BOC locking bandwidth, extending the BOC measurement dynamic range to mHz offset frequency and below [17]. As to analyze the timing jitter spectra with broader range, getting a deeper understanding of RIN-to-timing jitter coupling mechanisms, we also analyzed the fast PZT driving voltage signal in laser 1, which carries the frequency noise information between laser 1 and laser 2. The repetition rate of laser 1 changes as a function of the PZT driving voltage,$f_{\text{r}}=f_{\text{r0}}+\text{k}V$, where$f_r$is the resulting repetition rate,$f_{\text{r0}}$is the initial repetition rate without PZT driving voltage, and k is the gain coefficient (in Hz/v). Inside of the BOC locking bandwidth, the gain coefficient is a constant. We applied a known voltage to the PZT amplifier (Thorlabs, HVA200) and monitored the repetition rate changes. The calculated gain coefficient k is 2.7 kHz/V (the amplification factor of the PZT amplifier is 20). Thus, by sampling the fast PZT driving voltage signal using a FFT analyzer when stable repetition rate synchronization between the two lasers is achieved, we can obtain the frequency noise spectral density. Considering the definition of frequency noise spectral density $S_{\Delta f^2}(f)$(in Hz²/Hz), phase noise spectral density $S_{\Delta {\phi }^2}(f)$(in rad²/Hz) and timing jitter spectral density $S_{\Delta t^2}(f)$ (in fs²/Hz), we can obtain:

As shown in Fig. 4(a), the timing jitter spectrum with RIN suppression shows a ~10 dB reduction in the Fourier frequency range from ~3 kHz to ~30 kHz with a unity gain crossing point of 80 kHz. The noise peaking in the jitter spectrum past the unity-gain crossing point to ~400 kHz is due to the RIN servo bump, which brings an additional timing jitter of 0.26 fs. From 400 kHz to 5 MHz, the timing jitter spectra with and without RIN suppression overlap very well. Below ~3 kHz, the effect of the RIN suppression servo on timing jitter decays. The rms timing jitter integrated from 5 MHz to 100 Hz reduces from 1325 fs to 567 fs. For better comparison with other lasers or RF sources, we also calculated the rms timing jitter integrated from 10 MHz to 10 kHz. After RIN suppression, the rms timing jitter decreased from 6.22 fs to 2.52 fs (assuming the jitter spectra > 2 MHz offset frequency followed the −20 dB/dec slope). The experimental results are in good agreement with our previous theoretical analysis that the RIN induced jitter by self-steepening effect dominates the jitter performance below ~100 kHz.

 

Fig. 4 (a) Measured timing jitter spectra in the Fourier frequency range from 100 Hz to 5 MHz. The timing jitter spectra in the Fourier frequency range from 100 Hz to 20 kHz (inside the BOC locking bandwidth) and from 20 kHz to 5 MHz (outside the locking bandwidth) are obtained from the PZT driving voltage noise and the OC output voltage noise, respectively. Gray curves (curve (i) and (iii)) and red curves (curve (ii) and (iv)) are timing jitter spectra without and with RIN suppression, respectively. (b) Curve (v) and curve (vi) are calculated RIN coupled jitter spectrum by self-steepening effect without and with RIN suppression.

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4. Theoretical analysis of timing jitter

We further compared the experimental results with the well-established theoretical model in [18–20]. The RIN induced timing jitter by self-steepening effect can be expressed as:

5. Conclusion

In summary, we have demonstrated a simple technique to reduce timing jitter in 882 MHz mode-locked fiber lasers through active RIN suppression. The measurement based on BOC method shows a ~10 dB reduction of timing jitter in the frequency range from ~3 kHz to ~30 kHz with a unity-gain crossing point of 80 kHz due to the suppressed RIN coupled timing jitter by self-steepening effect. This method can be meaningful for the timing jitter optimization in other high-repetition-rate mode-locked fiber lasers. Moreover, the timing jitter reduction are especially pertinent for the high precision applications of high-repetition-rate mode-locked fiber lasers such as low noise microwave extraction and coherent pulse stacking.