Towards low timing phase noise operation in fiber lasers mode locked by graphene oxide and carbon nanotubes at 1 . 5 μ m

We investigate the timing phase noise of fiber lasers mode locked by graphene oxide (GO) and carbon nanotubes (CNTs), respectively, integrated in a linear cavity fiber laser in the reflecting operation. Due to the shorter decay time of the GO and CNTs, weaker slow saturable absorber effects are expected and mode-locked lasers based on these two saturable absorbers exhibit low excess timing phase noise coupled from the laser intensity noise. Compared with a reference laser mode locked by semiconductor saturable absorber mirror (SESAM), GO based laser obtains a timing phase noise reduction of 7 dB at 1 kHz and a timing jitter reduction of 45% experimentally whereas CNTs based laser obtains a timing phase noise reduction of 3 dB and a timing jitter reduction of 29%. 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For applications such as frequency metrology, optical sampling, clock distribution and optical sensing, laser timing phase noise and timing jitter are key parameters to achieve high precision [48].The timing phase noise model of mode-locked lasers has been developed [49][50][51] and experimental investigations of noise coupling have been reported [10,52].Modelocked lasers with low timing jitter have also demonstrated [53,54].However, the role of SAs on the timing phase noise of the mode-locked lasers has not been studied yet.Therefore it is meaningful to understand how different SAs affect the laser noise.
In this paper, from the view of timing phase noise of the mode-locked lasers, we investigate the noise properties of the fiber lasers operating at 1.5 µm mode locked by GO and single wall CNTs and compare them with a reference laser mode locked by SESAM (denoted as GO laser, CNT laser and SESAM laser, respectively).All three types of SAs share exactly the same linear laser cavity so that the influence of the laser cavity difference can be excluded as much as possible in the comparison.It is found that timing phase noises of three lasers are all dominated by the noise coupled from the laser relative intensity noise (RIN) due to the slow saturable absorber (SSA) effect, i.e., the laser RIN couples to the laser timing phase noise due to the time dependent response of the SA.Timing phase noise spectrum can be predicted through the measured laser RIN spectrum and noise conversion ratios.Moreover, compared with the SESAM laser, the GO laser and the CNT laser exhibit lower timing phase noise and timing jitter due to the smaller SA decay time and weaker SSA effect.7-dB improvement in the timing phase noise spectrum and 45% timing jitter reduction is observed in the GO laser.And a 3-dB improvement in the timing phase noise spectrum and 29% timing jitter reduction are observed in the CNT laser.This result indicates that SAs with smaller decay time have the potential to achieve mode locking with low timing phase noise.

Preparation of GO and CNT saturable absorbers
GO and single wall CNTs are embedded in PVA thin films for the experiments.The preparation of GO-PVA and CNT-PVA thin films are described as follows: GO sheets are fabricated by ultrasonic agitation after chemical oxidation of graphite and then dispersed in water.Single wall CNTs are dispersed in sodium dodecyl sulfate (SDS) aqueous solution by ultrasonic process.PVA is then added to the GO or CNT solutions, heated to 90 degrees and further mixed with CNT or GO by ultrasonic process.The prepared solutions are then poured into polystyrene cells.Part of the solution is adhered to the polystyrene cell wall due to the high viscosity to the cell wall.After evaporation process, GO-PVA or CNT-PVA thin films are formed and attached to the cell wall, which can be easily stripped off by tweezers.These SA thin films are then cut into small pieces and placed on the fiber end for experimental use.The thickness of GO-PVA and CNT-PVA thin films is between 35 ~50 μm characterized by the scanning electron microscope (SEM).The whole process is summarized in Fig. 1.The saturable absorption of the GO-PVA and CNT-PVA thin films is characterized by a homemade mode-locked laser operating at 1560 nm as shown in Fig. 2. It can be seen that GO-PVA thin film has a modulation depth of ~2% and a saturable fluence of 10.6 μJ/cm 2 .CNT-PVA thin film has a modulation depth of ~4.5% and a saturable fluence of 6.8 μJ/cm 2 .There are also ~20% non-saturable loss in each thin film which is probably due to the PVA absorption and scattering loss.As a reference, the saturable absorption of the SESAM (BATOP SAM-1550-9-2ps) is also measured.It has a modulation depth of ~6% and a saturable fluence of 40.2 μJ/cm 2 .The fitting curves based a two-level SA model are also plotted in Fig. 2. Two-photon absorption effect is considered for the SESAM in the fitting.

Experimental setup and laser optical properties
In order to compare the mode locking operation and the timing phase noise properties of different SAs, a fiber laser is designed as shown in Fig. 3(a).The laser has a linear cavity.The left cavity mirror is a partial reflection coating with 90% reflection at 1550 nm.The cavity consists of a 25-cm Erbium-doped fiber (EDF, Er 110 4/125) with normal dispersion of −8 ps/km•nm and ~135 cm standard single mode fiber with anomalous dispersion of 17 ps/km•nm.The net dispersion is ~21 fs/nm.The SAs are placed at the right side of the cavity.For GO-PVA and CNT-PVA thin films, they are embedded between a fiber end and a total reflection mirror coating (on another fiber end), shown in Fig. 3(b).For SESAM, it is directly butt coupled to the fiber end.976-nm pump is injected into the cavity through a 980/1550 wavelength division multiplexer (WDM) outside the cavity.Different SAs share the same laser cavity to exclude the influence of laser cavity difference and thus the laser output can actually reflect the role of these SAs on the mode locking operation and laser timing phase noise.The output of the laser is fed into the measurement equipment including optical spectrum analyzer (OSA), autocorrelator and signal source analyzer (R&S FSUP26) for the characterization of its optical and noise properties.Pump modulation technique is applied to measure the noise conversion from the pump RIN to the laser noise, which will be discussed in detail later.The general optical properties of three mode-locked lasers are summarized in Table 1.It can be observed that CNT laser has the lowest pump power and output power, which is consistent with its low saturation intensity.GO laser has a higher pump power and output power due to the higher saturation intensity.For comparison, SESAM laser has the highest output power due to the highest saturation intensity and the lowest non-saturable loss.

Laser noise properties
To compare the timing phase noise properties of the lasers, we first describe the noise coupling mechanisms from the pump to the lasers, shown in Fig. 4. Pump RIN directly couples to the laser RIN via the modulation of the gain media [10,52].This noise conversion ratio is denoted as r RIN .Laser RIN then couples to the laser phase noise via fiber nonlinearity and SSA effect, denoted as ∆r PN [51].SSA effect means the saturation of the absorber is not instant.Therefore the rising edge and the falling edge of the input pulse will experience different loss which leads to the tilting of the pulse shape and the shift of the pulse timing.Pump RIN can also directly couples to the laser phase noise via thermal effect and nonlinearity [55].The total noise conversion ratio from the pump RIN to the laser phase noise is denoted as r PN , including both the direct coupling (Pump RIN → Laser phase noise) and indirect coupling (Pump RIN → Laser RIN → Laser phase noise).In the experiment, r RIN and r PN are measured by using pump modulation technique.Through applying a weak modulation to the pump drive current, a spurious peak at the modulation frequency f M can be generated in the pump RIN spectrum.This pump RIN couples to the laser noise and generates spurious peaks at the same frequency f M in the laser RIN and phase noise spectra.By comparing the power difference of the spurious peaks between the laser noise spectrum and the pump RIN spectrum, r RIN and r PN at frequency f M are obtained.Then tuning the modulation frequency f M from 100 Hz to 80 kHz, the frequency dependence of r RIN and r PN can also be obtained.The noise conversion from the laser RIN to the laser phase noise (∆r PN ) can't be experimentally measured.Instead, we use theoretical model to estimate it.
For GO laser, the measured laser RIN and phase noise spectra are shown in Fig. 5(a).The pump RIN spectrum is shown in the inset.The corresponding noise conversion ratios are shown in Fig. 5(b).The calculated laser RIN and phase noise spectra in Fig. 5(a) are obtained using the following relations where S cal represents the calculated laser RIN or phase noise spectrum, S Pump-RIN is the pump RIN spectrum and r represents the measured noise conversion ratio r RIN or r PN .Very good agreement at low offset frequency can be found in Fig. 5(a).The deviation at high offset frequency is due to the noise floor of the measurement system.This result suggests that the measured noise conversion ratios are able to represent the noise properties in the laser operation.We have previously shown that SSA effect is the dominant effect causing laser RIN to laser phase noise coupling in a linear cavity when we refer to the absolute timing phase noise [52].Therefore we can use the theoretical model of SSA to estimate ∆r PN , given by [51] 2 2 ( ) ( ) where ∆S PN is the excess phase noise coupled from the laser RIN, f R is the repetition rate, f is the offset frequency, s is the saturation parameter defined as the ratio between input pulse energy and the SA saturation energy, ∆t is the pulse temporal shift due to the SSA effect.It can be seen that the material properties and the laser operation specifications have been included in the SSA model.The calculation of ∂∆t/∂s implements the differential equation governing the SSA, given by [56] ( ) where q is the instant SA absorption, q m is the modulation depth, τ A is the SA decay time, P(t) is the instant power of the pulse and E A is the SA saturation energy.The calculated pulse temporal shift ∆t with respect to s is shown in Fig. 6.For an easy comparison, the modulation depths for different SAs are all normalized to 1%.The temporal shift is proportional to the modulation depth for a given s.Using a homemade pump-probe system, the decay time of GO and CNT is measured, shown in Fig. 7.The laser source in the pump-probe system is a Ti:Sapphire mode-locked laser centered at 800 nm with a pulse width of 100 fs (Spectra-Physics Tsunami Series).The fast decay time of GO and CNT is measured to be 380 fs and 560 fs, respectively which is close to the measured values reported in other works [57,58].
The relaxation in the GO and CNT originates from two effects: the ultrafast intraband relaxation corresponding to a decay time of a few hundreds of femtosecond and the slower interband relaxation corresponding to a decay time of picosecond level.The decay time of SESAM is estimated to be 2 ps [59].It can be seen that, GO has the most flat curve due to its small decay time and SESAM has the sharpest curve due to its long decay time.This indicates that the laser RIN to phase noise conversion induced by SSA effect should be weakest in the GO laser and strongest in the SESAM laser.One may find that for a saturation parameter s near 3, the slope ∂∆t/∂s becomes zero which means an elimination of the noise conversion.
However, the actual value for s in many experimentally reported mode-locked lasers are far beyond this value (typically s > 6) due to the fact that SAs are usually deeply saturated in the mode locking operation [53,60].Moreover, even the mode locking is obtained for s = 3, the laser output power is sacrificed because s is defined as the ratio between pulse energy and SA saturation energy, and most probably the output bandwidth will also be reduced due to the lower pulse energy.For the SA with even longer decay time (i.e., sufficiently larger than the pulse width), the temporal shift will increase very weakly and the noise conversion reaches a constant value.It should also be mentioned that nanomaterials usually exhibit two decay timescales due to the fast intraband relaxation and slow interband relaxation [12,61].Although such a decay model with two time constants cannot be modelled using the form of differential equation in Eq. ( 4), we can still perform an approximate analysis.Using CNT as an example, its two decay time constants are τ 1 = 560 fs and τ 2 = 1.2 ps.The decay time can be expressed by where the coefficient 0.361 represents the strength of the slow interband relaxation.The equation can be re-written as Equation ( 6) means the strength of slow relaxation is comparable to the fast relaxation after 1.22 ps.Note that for most low-jitter mode-locked lasers, pulse width is much shorter than this time.Therefore, it can be inferred that the influence of slow decay time is negligible.
We use the following values for the calculation of ∆r PN in Eq. ( 7) for the GO laser: f R = 62.2 MHz, s = 17.1 and ∂∆t/∂s = 0.16 fs.It can be seen that the calculated ∆r PN nearly has identical trend compared with the measured r PN except for a 6-dB vertical shift in Fig. 5(b).The shift is attributed to the error in the estimation of material decay time and temporal shift.There is no other mechanism which leads to an f −2 dependence on the laser RIN.Therefore this result demonstrates that SSA effect is the dominant effect causing laser RIN to phase noise conversion in the GO laser.
( ) ( ) 20 lg 26.5 (dB) Similarly, the noise spectra and the noise conversion ratios for the CNT laser and the SESAM laser are also measured, shown in Fig. 8 and Fig. 9. Again, the laser RIN and phase noise can be estimated by using the measured pump RIN spectrum and the noise conversion ratios.Good agreement between the measured noise spectra and the calculated noise spectra can be observed.We use the following values for the calculation of ∆r PN in Eq. ( 8) for the CNT laser: f R = 62.2 MHz, s = 13 and ∂∆t/∂s = 0.16 fs.And the following values in Eq. ( 9) for the SESAM lasers: f R = 62.2 MHz, s = 6.5 and ∂∆t/∂s = 0.3 fs. ( ) ( ) 20lg 31.2 (dB)  As expected, due to the smallest material decay time of GO, the GO laser shows the lowest timing phase noise, lowest pump RIN to laser phase noise conversion ratio r PN and lowest ∆r PN induced by the SSA effect.In comparison, all these noise parameters in the CNT laser are higher than those in the GO laser, which is consistent with the fact that CNT has larger material decay time than GO.Moreover, due to the largest decay time in SESAM, the SESAM laser exhibits the highest noise properties among three lasers.For a more clear comparison on the timing phase noise of three lasers, the noise properties are summarized in Table 2.The minimum measureable timing jitter is ~11.4 fs at the repetition rate limited by the noise floor of the signal source analyzer and the shot noise.It can be seen that compared with the SESAM laser, the GO laser has a phase noise conversion 8.6 dB lower at 1 kHz, a phase noise 7 dB lower at 1 kHz and a timing jitter 45% reduced integrated from 100 Hz to 100 kHz while CNT laser has a phase noise conversion 4.3 dB lower, a phase noise 3 dB lower and a timing jitter 29% reduced.
However, it must also be clarified that our results do not reach the conclusion that SESAM is not a good SA compared with GO and CNT.In fact, from the view of optical properties the SESAM laser has the widest spectrum and the highest output power under the same laser cavity configuration, which benefits from its low non-saturable loss and high saturable fluence.Reducing the non-saturable loss and increasing the saturable fluence are still challenging in the preparation of GO and CNT SAs.But meanwhile, nanomaterials SAs such as graphene, GO and CNT have the advantages of broadband operation, i.e., a single SA can be used in a wide range of operation wavelength from visible to mid-IR while a SESAM can only be used for a specific wavelength.
It is worth mentioning that graphene in principle should give smaller phase noise conversion due to its very fast decay time and thus very weak SSA effect.Also, the fastest SA is the mode locking based on fiber nonlinearity, or NPE (nonlinear polarization evolution).
And it has been experimentally confirmed that the laser mode locked by NPE has much weaker SSA induced noise conversion in our previous work [52].

Conclusion
In conclusion, the timing phase noise properties of mode-locked lasers are characterized and compared when three different saturable absorbers GO, CNT and SESAM are utilized.Three saturable absorbers share exactly the same linear laser cavity so that the influence of the cavity difference is excluded and the laser output can actually reflect the role of these saturable absorbers on the laser timing phase noise.It is found that due to the smaller saturable absorber decay time and thus weaker excess phase noise conversion induced by the slow saturable absorber effect, both the GO laser and the CNT laser exhibit better timing phase noise and timing jitter compared with the SESAM laser.A timing phase noise reduction of 7 dB and a timing jitter reduction of 45% are achieved in the GO laser.And a timing phase noise reduction of 3 dB and a timing jitter reduction of 29% are achieved in the CNT laser.Moreover, the method presented in this paper can be applied to any other saturable absorbers to investigate their timing noise properties.Our finding suggests that saturable absorbers with fast decay time may have the potential for low-timing-phase-noise mode locking operation.

Fig. 1 .
Fig. 1. Preparation of GO-PVA and CNT-PVA thin film SAs (a) GO and CNT dispersed solution; (b) polystyrene cells filled with solutions; (c) thin film stripped off the cell wall after heating and evaporation process; (d) small piece of thin film SA on a fiber end.

Fig. 4 .
Fig. 4. Noise coupling from the pump to the laser and inside the laser.SSA: slow saturable absorber; RIN: relative intensity noise; PN: phase noise.

Fig. 5 .
Fig. 5. (a) Noise spectra of the GO laser.Inset: Pump RIN spectrum; (b) Measured noise conversion ratios and calculated excess phase noise conversion ∆r PN due to the SSA effect.

Fig. 8 .
Fig. 8. (a) Noise spectra of the CNT laser.Inset: Pump RIN spectrum; (b) Measured noise conversion ratios and calculated excess phase noise conversion ∆r PN due to the SSA effect.

Fig. 9 .
Fig. 9. (a) Noise spectra of the SESAM laser.Inset: Pump RIN spectrum; (b) Measured noise conversion ratios and calculated excess phase noise conversion ∆r PN due to the SSA effect