Passively mode-locked lasers with ultralow timing jitter enable a number of high-precision applications, such as large-scale timing synchronization [1], and high spectral purity RF signal synthesis [2], as well as high-speed, high-resolution photonic analog to digital conversion [3]. Particularly, in the application of high spectral purity microwave signal synthesis, the pulse repetition rate is required to be the same, or the least fraction of the microwave frequency to be extracted. Therefore, gigahertz to multi-gigahertz repetition rate lasers are desirable, together with low noise or low jitter.

Gigahertz repetition rate solid-state lasers, like Ti:sapphire [4] and monolithic Er:glass [5], demonstrated very low noise. In contrast, mode-locked fiber lasers take the advantage of the direct diode pump, compactness, lower expense, and less alignment sensitivity at the cost of a higher amplified spontaneous emission (ASE) quantum-limited noise, due to their high nonlinearity and large chirp.

It was found that mode-locked fiber lasers at a lower repetition rate, for example, from 100 MHz to 250 MHz, had shown reasonably low timing jitter. However, a complicated multi-stage extra-cavity interleaver has to be applied to multiply the repetition rate for the extraction of multi-gigahertz RF signals [6]. High repetition rate (${\gt}{500}\;{\rm MHz}$) Er:fiber lasers mode-locked by semiconductor saturable absorber mirrors (SESAMs) usually show dozens of femtoseconds timing jitter [7]. Nonlinear polarization evolution (NPE) mode-locked Yb:fiber lasers have demonstrated 1 GHz repetition rate and delivered watt-level output power and tens of femtoseconds output pulses [8]. However, our previous investigation shows that the jitter was as high as 10 fs for the integration frequency band of 30 kHz–5 MHz [9,10]. This high timing jitter seemed to support the repetition rate square law [11], and our conclusion was that the nonlinear phase shift induced self-steepening should be responsible [10], although the relative intensity noise (RIN) was actively suppressed [12].

One of the alternatives is the micro-resonator combs, which directly generate tens to hundreds of GHz rate pulses. However, the timing jitter is not as low as that of mode-locked lasers. Kown et al. demonstrated that the timing jitter from a microring comb is a few femtoseconds, which is about an order of magnitude higher than that of a mode-locked fiber laser [13].

By careful review of our high repetition rate laser configuration (Fig. 1), we point out that such a structure is more like a solid-state laser with a fiber gain medium. This is because free-space components take almost half of the cavity length in such a short cavity (${\sim}30\;{\rm cm} $), and the fiber is only ${\sim}10\;{\rm cm} $ long and all doped. In this configuration, the holders for free-space components, specifically, the fiber collimators and the polarization beam splitter (PBSs), play a key role in cavity stability.

 

Fig. 1. (a) Schematic of 840 MHz repetition rate solid-state fiber laser, YDF, Yb-doped gain fiber; QWP, quarter-wave plate; HWP, half-wave plate; PBS, polarization beam splitter; FR, Faraday rotator; WPP, wedge plate pair (see Visualization 1). (b) Photograph of the bonded solid-state fiber laser cavity on a fused silica brick.

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In the previous version of the laser [10], the holders were all standard metal ones, and their contribution to laser noise was not investigated carefully. On the other hand, the zero non-gain fiber in this laser is coincidentally consistent with the empirical rule: shortening the non-gain fiber can minimize the timing jitter through the shortened pulse and the reduced excessive higher-order nonlinearity and nonlinear chirp [14]. Therefore, it is reasonable to deduce that the previously reported timing jitter might be overestimated because the real and intrinsic jitter of the laser was very much likely covered with the mechanical noise. Based on above considerations, we rebuilt the laser aiming at reducing the mechanical noise. We removed all metal holders and the baseplate. Instead, we adapted so-called “optical cubes” to integrate all components on a silica glass brick.

Bonding optical components on a baseplate has been proposed and demonstrated [15]. Before bonding, all components have to be aligned to form a cavity by optomechanics. The potential problem is that, after bonding, the freedom of realignment is lost. In the case of bonding agents deforming during the curing, there are no additional remedial measures to bring the alignment back.

The “optical cubes” are a concept that all optical components can be mounted on universal glass cubes (see Section 1 in Supplement 1). More remarkably, these cubes can offer some degree of online alignment through semi-ball joints [16]. A rotatable transmission thin wedge plate pair can also provide some degree of freedom for online beam steering [17]. Then all the optical components can be tightly bonded on a glass brick through cubes before precise alignment. This laser can be referred to as a “solid-state fiber laser” or “solid-state laser with fiber gain medium.” It is still considered a fiber laser because its mode-locking mechanism is NPE in fiber. We expect that in this way the mechanical noise is minimized so that the actual timing jitter can be revealed.

In this Letter, we report the ultralow timing jitter pulse train from such lasers characterized by the balanced optical cross correlation (BOC) technique. The timing jitter is 130 as for the integration frequency band of 10 kHz to 1 MHz. The result implies that high repetition rate fiber lasers do not necessarily come with high timing jitters. This fact refreshes the concept for high repetition rate fiber lasers.

The schematic of the laser is shown in Fig. 1(a), which is basically same as in [8]. The key components for alignment—the collimators and PBSs—are mounted on silica glass “cubes.” For compactness, all wave plate holders are made of thin ceramics with rotation gears. All these components are bonded on a $120 \;{\rm mm} \times 140 \;{\rm mm} \times 20\;{\rm mm} $ fused silica “brick” [Fig. 1(b)].

Two aforementioned novel online alignment mechanisms, the semi-ball joint and the wedge plate pair, were used to make the cavity aligned. In order to conveniently compare it with the previously reported timing jitter [9,10], in this work, the repetition rate of the laser was set to 840 MHz. The repetition rate can be promoted to 1 GHz, by shortening the intracavity free-space length [8]. A piezoelectric transducer (PZT, Thorlabs PK4FA2H3P2) was attached to a collimator holder for cavity length tuning and stabilization. A 1000 lines/mm grating pair was inserted for intracavity dispersion compensation in single-pass configuration.

Owing to the solid cube structure and the low expansion base board, the laser exhibits excellent stability. Figure 2 shows the repetition rate of the laser in free-running drifts within 1 kHz over 12 h in the laboratory environment ($23 \pm {1 ^ \circ}{\rm C}$).

 

Fig. 2. Free-running repetition rate drifts of the solid-state fiber laser over 12 h of continuous operation. Blue shading shows ${\pm}1\sigma$. Red shading shows the drift range.

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To evaluate the timing jitter with the BOC technique, two of these lasers with identical repetition rate were built. The average output power of these two lasers is ${\sim}510\;{\rm mW} $, and the measured pulse width is ${\sim}140\;{\rm fs} $. Meanwhile, shielding the acoustic noise (fan noise from instruments in the laboratory in particular) with an acryl cover with sound insulation foam attached is essential for the precision jitter measurement.

The configuration of the BOC measurement is shown in Fig. 3(a). The two laser beams in cross-polarization were combined at a PBS and directed to the BOC arrangement [18], in which a 5 mm long type II KTP crystal was used for sum frequency generation (SFG). The dichroic mirror DM2 returned the pulses to the SFG crystal to generate the second cross correlation pulse in reversed delay between the crossly polarized pulses. A balanced photodetector (Newfocus 1807FS) received these two cross correlation signals and created a timing error [Fig. 3(b)]. Considering the limited linear detection range of the BOC, the two lasers should be synchronized at low frequency by using that error signal as the phase discriminator. The error signal was sent to a proportional integral (PI) servo (Newport LB1005). Then, the correcting signal from the PI servo was amplified and fed back to the intracavity PZT in Laser B. So far, the loop for locking these two lasers was closed.

 

Fig. 3. (a) Experiment setup of BOC-based timing jitter measurement. DM1, dichroic mirror (AR at 1040 nm, 45° HR at 520 nm); DM2, dichroic mirror (0° HR at 1040 nm, AR at 520 nm); BPD, balanced photodetector. (b) Measured timing detection signal from BOC.

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The synchronization of these two solid-state fiber lasers was found much easier to achieve, in comparison with the lasers using optomechanic holders. It is obvious that the architecture makes the laser less sensitive to vibration and acoustic noise. Consequently, it is not necessary to increase the phase discrimination range by stretching the pulse from Laser B anymore [10]. In practice, the locking bandwidth of $5 \sim 6\;{\rm kHz} $ is sufficient for synchronizing these two lasers. In contrast, the locking bandwidth had to be as high as 30 kHz [10] for the lasers with optomechanic holders.

As long as the repetition rate locking is established, the residual timing jitter spectra density can be characterized through analyzing the error signal from the BOC using a RF analyzer and a fast Fourier transform (FFT) spectrum analyzer. The resulting timing error discrimination slope from BOC is ${1.6}\;{\rm mV/fs}$ [Fig. 3(b)], which exhibits a measurement floor of $2 \times {10^{- 8}} \;{{\rm fs}^2}/{\rm Hz}$. The calculated photodetection shot-noise limit [19] is $1.204 \times {10^{- 9}} \;{{\rm fs}^2}/{\rm Hz}$, which is well below the timing jitter spectra.

Figure 4 shows the measured RIN power spectral density (the measurement and analysis procedure can be reviewed in Section 2 in Supplement 1). The integrated rms RIN is 77.8 ppm (ranged from 100 Hz to 1 MHz), which is comparable to our previous work with an active RIN suppression [12]. There are dense spikes located at 100 Hz, 150 Hz, 200 Hz, and so on, which are considered the picking up of the harmonic frequencies of line power (AC 50 Hz). Well-insulated protection for the amplified photodetector or using uninterrupted power supply (UPS) might remove most harmonic peaks of line power.

 

Fig. 4. (i) Measured RIN spectrum of the free-running laser from 100 Hz to 1 MHz Fourier frequency, (ii) electronics noise floor, (iii) calculated shot-noise floor, and (iv) an integrated (100 Hz–1 MHz) RMS RIN noise of 77.8 ppm.

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Fig. 5. (i) Measured timing jitter spectrum with an integrated (10 kHz–1 MHz) RMS timing jitter of 130.07 as (magenta), (ii) equivalent single-sided phase noise spectral density of ${f_r}$, (iii) measured noise floor, and (iv) calculated shot-noise level.

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The timing jitter was evaluated outside the locking bandwidth, and the results were shown in Fig. 5. The timing jitter spectral density at 10 kHz offset frequency is $5.92 \times {10^{- 6}} \;{{\rm fs}^2}/{\rm Hz}$, which is similar to that of 80 MHz Yb-fiber laser [20]. Above 100 kHz offset frequency, the timing jitter spectral density ($2.72 \times {10^{- 8}} \;{{\rm fs}^2}/{\rm Hz}$ at 100 kHz) is close to the measurement floor, and the integrated rms timing jitter from 100 kHz to 1 MHz is 81.22 as, contributing more than 60% jitter in the integrated range. We can predict that, if a short SFG crystal is used, the synchronization performance between the lasers can be further improved, and the integrated jitter could be reduced to sub-100-as level.

The analysis of the measured timing jitter spectral density is shown in Fig. 6, which is based on the measured data of Fig. 5. The origin of the measured timing jitter can be found following the well-established analytic model of mode-locked lasers [11,21,22]. Above 1 MHz offset frequency, the measured timing jitter spectral density is limited by the measurement floor. From 80 kHz to 1 MHz offset frequency range, the curve slope is flat in the tail. We attribute it to the distortion for closing to the measurement floor. For 15 kHz–80 kHz offset frequency range, the measured jitter spectral density increases rapidly toward the lower offset frequency in the slope of 30 dB/dec. This rapid rising may be induced by RIN-coupled jitter via the self-steepening effect in laser. Then we use the same model in the previous work to calculate the RIN-coupled jitter, which can be express as

 

Fig. 6. (i) Measured timing jitter spectrum with 6 kHz locking bandwidth, following ${-}{20}\;{\rm dB/dec}$ slope and ${-}{30}\;{\rm dB/dec}$ slope in 6 kHz–15 kHz range and 15 kHz–80 kHz range, respectively, (ii) RIN-coupled jitter by self-steepening effect, (iii) measured noise floor, (iv) calculated shot-noise level, and (v) quantum limited jitter following ${-}{20}\;{\rm dB/dec}$.

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In summary, we have developed an NPE mode-locked 840 MHz “solid-state fiber laser” and characterized its timing jitter and stability in free-running mode. The timing jitter of the pulse train from such a laser is 130 as (integrated from 10 kHz–1 MHz offset frequency). This is, to the best of our knowledge, the lowest timing jitter ever reported for such high repetition rate NPE mode-locked fiber lasers. The drift of pulse repetition rate is ${\lt}{1}\;{\rm kHz}$ during the period of 12 h in free-running mode, which is impressively small, indicating its potential for long-term locking.

The ultralow timing jitter and ultrahigh stability impact the prejudice that high repetition rate fiber lasers come with high timing jitters. The ultralow timing jitter performance of such a high repetition rate laser paves the way for such lasers to apply in ultralow timing jitter microwave extraction, narrow linewidth frequency combs, and other precision metrology. Furthermore, the approach of constructing lasers with optical cubes could also be applied to other types of fiber and solid-state lasers.