a pulsewidth measurement technology based on carbon

A pulsewidth measurement technology basedon carbon-nanotube saturable absorberPUSHAN XIAO,1 KAN WU,1,* DONG MAO,2,3 AND JIANPING CHEN1

1State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Institute forAdvanced Communication and Data Science, Department of Electronic Engineering, Shanghai Jiao TongUniversity, Shanghai 200240, China2Shaanxi Key Laboratory of Optical Information Technology, School of Science, NorthwesternPolytechnical University, Xi’an 710072, [email protected]*[email protected]

Abstract: We demonstrate a proof-of-concept saturable absorption based pulsewidth measure-ment (SAPM) by exploring the intensity dependent nonlinear transmission (i.e., saturableabsorption) of low-dimensional material (LDM) carbon nanotubes. A minimum pulse energyof 75 fJ is experimentally detected with an average-power-peak-power product (Pav · Ppk) of5.44 × 10−7 W2 near 1550 nm. A minimum detectable pulse energy of 10 fJ with a Pav ·

Ppk of 1.3 × 10−9 W2 is estimated with further optimization. The nanometer-level thicknessand femtosecond-level decay time of LDMs allow ultrafast light interaction on a very smallfootprint, which potentially supports chip-scale characterization of ultrafast pulses with minimumdistortion.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Autocorrelation (AC) is one of the key technologies to characterize ultrashort pulses. Autocor-relation based on second harmonic generation (SHG) has been a great success during the lastfew decades [1–6]. Moreover, technologies developed from SHG including frequency-resolvedoptical gating (FROG) [7–10] and spectral phase interferometry for direct electric-field recon-struction (SPIDER) [11–18], have enabled retrieval of pulse amplitude and phase informationsimultaneously. However, there are also some limitations caused either by technological orengineering issues [4, 5, 19]. For example, light at different wavelength may require phasematching by beam alignment to optimize the SHG efficiency in the SHG crystal. SHG crystal isdifficult to be integrated with current optical integration platforms (Si, Si3N4, III-V materials,etc.). The fabrication of high-quality SHG crystal may also be costly.Another autocorrelation technology based on two-photon absorption (TPA) effect in semi-

conductors has also been widely investigated [1, 20–30]. TPA effect allows very compactautocorrelator design [24, 25] and high detection sensitivity [21, 27]. TPA effect usually haspicosecond decay time in bulk semiconductors which may lead to limitation on the measurementof pulse width [27,29,30]. Hybrid integration between semiconductors and insulators (e.g., Si3N4or SiO2) is still challenging if the insulator waveguides are preferred to reduce the propagationloss of the pulses.

On the other hand, low dimensional materials (LDMs) including one-dimensional (1D) carbonnanotubes (CNTs) and various two-dimensional (2D) materials have shown abundant photonicand optoelectronic properties.Their saturable absorption(SA), i.e., intensity dependent nonlineartransmission, has been widely used for mode locking operation in pulsed lasers including carbonnanotube in [31, 32], graphene in [33–35], topological insulators in [36–39], transition metaldichalcogenides in [40–46], black phosphorus in [47–50] and MXene in [51], etc. Saturableabsorption also enables the materials to be a nonlinear medium for pulse interactions, which is a

#353203 https://doi.org/10.1364/OE.27.004188 Journal © 2019 Received 30 Nov 2018; revised 16 Jan 2019; accepted 16 Jan 2019; published 5 Feb 2019

Vol. 27, No. 4 | 18 Feb 2019 | OPTICS EXPRESS 4188

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key requirement for pulsewidth measurement technologies such as AC. Compared with TPA,most LDMs exhibit femtosecond-level decay time after photonic excitation which is promisingfor measuring ultrashort pulses with minimum distortion [30,52–54]. The atomic level thicknessof the LDMs also minimizes the potential pulse broadening caused by the optical dispersion inthe bulk materials, which is another advantage to achieve ultrashort pulse measurement [54–57].Moreover, hybrid integration between LDMs and planar waveguides or between LDMs andoptical fibers has been developed with simple procedures [54, 56–59]. Therefore, pulsewidthmeasurement based on the saturable absorption of LDMs may provide a new technical route forpulse characterization, which is potentially capable of measuring ultrashort pulses and compatiblewith various integrated or non-integrated photonic platforms.

Meanwhile, it is known that an ideal intensity AC requires the nonlinear medium to have aresponse proportional to the square of pulse intensity, which is unfortunately not the case ofsaturable absorption in LDMs. However, if there is still a nearly linear relation between theinput pulse width and the pulse width of measured trace, and the pulse width measurement erroris controlled within a reasonable range, e.g., less than 10%, we can still treat this LDM basedtechnology as a quasi-AC measurement considering its advantages mentioned above.In this paper, we propose and demonstrate a proof-of-concept quasi-autocorrelation technol-

ogy based on the saturable absorption of carbon nanotubes, called saturable absorption basedpulsewidth measurement(SAPM). Low saturation intensity of CNTs allows low input pulseintensity and relatively large modulation depth of CNTs allows better measurement result. Aminimum measurable pulse energy of 75 fJ is obtained limited by the system loss. The corre-sponding average-power-peak-power product (Pav · Ppk) is 5.44 × 10−7 W2 and the measurementtime resolution is 9.0 fs. By further optimizing the experimental setup, it is estimated thatthe specifications can be improved to 10 fJ for minimum pulse energy and 1.3 × 10−9 W2 forPav · Ppk . The measurement error of the pulse width is less than 6% due to the non-ideal ACmeasurement. We believe this work may pave the way to a new type of pulsewidth measurementtechnology which is capable of achieving pulse width measurement down to few-femtosecondlevel and is easy to be integrated to various photonic platforms.

2. Principle and simulation

An ideal AC measurement requires the nonlinear medium to have a response proportional to thesquare of input pulse intensity. On the other hand, it is known that an ideal AC measurementdoes not reflect the actual input pulse shape [60]. So from a more practical point of view, themost important function of an AC measurement is to obtain the input pulse width based on alinear relation given by the following equation:

τin = τAC/Ccon (1)

where τin is the input pulse width, τAC is the pulse width of the measured AC trace, and Ccon isa conversion coefficient. For ideal intensity AC, Ccon = 1.414 for Gaussian pulse and 1.543 forsoliton pulse [6]. As mentioned in the introduction section, saturable absorption of LDMs is notan ideal “intensity square” relation required by the intensity AC measurement. However, if therelation between the input pulse width and the pulse width measured by our proposed quasi-ACSAPM technology is still nearly linear, we can simply use a different coefficient Ccon in Eq.(1) to calculate the input pulse width. Moreover, in the following simulation and experimentinvestigation, readers will see that the actually measured SAPM trace based on LDM is verysimilar to an ideal AC trace based on SHG.

In the following part of this section, we will discuss the preparation of LDM carbon nanotubes,the characterization of their saturable absorption, the experimental setup of a CNT based SAPMsystem, and the modelling and simulation of such a SAPM system, respectively.

Vol. 27, No. 4 | 18 Feb 2019 | OPTICS EXPRESS 4189 Vol. 27, No. 4 | 18 Feb 2019 | OPTICS EXPRESS 4189

2.1. CNT preparation and characterization

A high-quality CNT thin film is the key component of our system. The single wall CNTs aresynthesized by the catalytic chemical vapor decomposition method and the diameters are from 1nm to 1.5 nm. Then CNTs are mixed with polyvinyl alcohol (PVA) to form thin films with thefollowing steps. Firstly, 0.5 mg·mL−1 CNT dispersion is prepared by dispersing filiform CNTsin deionized water using an ultrasonic cleaner for five hours. The dispersing agent used in theexperiment is sodium dodecyl benzenesulfonate. Secondly, the CNT dispersion is centrifuged at12000 g for several hours, and upper supernatant is collected to reduce unwanted scattering lossesfrom large-scale agglomeration. Thirdly, 10 wt% aqueous PVA solution and CNT dispersionare mixed at a volume ratio of 1 : 2 by a magnetic stirrer for three hours. Finally, the obtainedCNT-PVA mixture is dropped on a Petri dish for a two-day evaporation and a CNT-PVA thin filmis obtained. Figure 1(a) shows the transmission electron microscopy (TEM) image of CNTs andFig. 1(b) shows the image of the fabricated CNT-PVA thin film. The CNT-PVA thin film is thencut into small pieces and sandwiched between two fiber connectors to form a saturable absorberas shown in Fig. 1(c).

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The nonlinear saturable absorption property of the CNT is characterized by a standard two-armmeasurement as shown in Fig. 1(d). A passively Erbium-doped mode-locked laser (MLL) with arepetition rate of 37 MHz and a pulse width of 560 fs is used as an optical source with variableoutput power. After passing through a protective isolator (ISO), the pulses are divided by a99:1 coupler. 1 % power is directly measured by a power meter (denoted as power meter 1) asreference and 99 % output power propagates through the CNT saturable absorber and is detectedby another power meter (denoted as power meter 2). A 10 dB fixed attenuator (ATT) is addedbetween the CNT saturable absorber and the power meter 2 to maintain a suitable detection powerrange. Figure 1(e) shows the measured optical transmittance of the CNT saturable absorberunder different incident pulse intensity. The red curve in Fig. 1(e) is the fitting curve using the


following saturable absorption formula [40]:

T(I) = 1 − ∆T · exp(−I

Isat) − Ans − β · I (2)

where T is the transmittance, ∆T is the modulation depth, I is the incident optical intensity, Isatis the saturation intensity, Ans is the nonsaturable absorbance and β is the two-photon absorption(TPA) coefficient. From the data in Fig. 1(e), the tested CNT saturable absorber has a modulationdepth of 9.182 %, a nonsaturable absorbance of 35.12 %, a saturation intensity of 20.69 MW/cm2,and a TPA coefficient of 0.01928 cm2/MW. To avoid the ambiguity of the incident intensity in thetwo-photon absorption region, the proposed SAPM technology is working within the intensityregion from 0 to 40 MW/cm2 where the CNT transmittance monotonically increases with theincrease of optical intensity. The corresponding peak power is from 0 to 32 W in a standardsingle mode fiber (e.g., SMF-28) with a mode area of 80 µm2. Figure 1(f) shows the measuredtransmission spectrum of the CNT saturable absorber from 1500 nm to 1630 nm indicating theproposed CNT based SAPM can work in a wide spectral range.

2.2. Experimental setup, theory and simulation

The experimental setup of the proposed system with the CNT saturable absorber is shown inFig. 2(a). The all-fiber configuration is chosen to allow an alignment free system. A homemadepassively mode-locked laser with a repetition of 100 MHz and a center wavelength of 1560 nm isused as the optical pulsed source. An optical pulse from the MLL is divided by a polarizationbeam splitter (PBS). One of the split pulse is modulated by an electro-optic modulator (EOM)with a 1 kHz sinusoidal signal (denoted as R(t)) and the other pulse propagates through avariable time delay line (DL, General Photonics MDL-002). A tunable attenuator (ATT) isadded to balance the power of two paths. Two optical pulses are recombined by another PBS.Polarization-maintaining optical fiber devices are used to avoid the interference between twopaths. The output of the PBS (denoted as P(t)) passes through the CNT saturable absorber. Theoutput from the CNT saturable absorber (denoted as P1(t)) is detected by a photodetector (PD)and measured by a Lock-in Amplifier (LIA, Signal Recovery 7280) system. The setup is verysimilar to a conventional intensity AC system except that the nonlinear medium is CNT insteadof SHG crystal.

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Fig. 2. (a) Experimental setup of the CNT based SAPM. (b) Simulated transmittance changeof CNT saturable absorber with respect to different delay time.

The principle of the proposed SAPM can be explained as follows. When two split pulsescombine at PBS, the peak power of the combined output pulse is dependent on the time delaybetween two split pulses. The transmission of the CNT saturable absorber is dependent on thepeak power of the incident pulse. Therefore, the output power from the CNT saturable absorber


is monotonically determined by the time delay of two split pulses. By measuring the averageoutput photocurrent from the PD, the SAPM pulse profile can be obtained. The LIA and EOMare utilized to improve the measurement precision. Figure 2(b) shows an example of simulationresult of the dependence between the CNT transmission and the delay time with an input pulsefull width at half maximum (FWHM) of 1 ps.The theoretical analysis of the proposed system is performed as follows. The temporal pulse

power profile from the MLL is assumed Gaussian and given by:

Pin = P0 · exp(−t2

τ2 ) (3)

where τ is a measure of the pulse width and P0 is the peak power. The output pulse P(t) fromPBS can be described as:

P(t) = R(t) ·α1P0

2· exp

[−

t2

τ2

]+α2P0

2· exp

[−(t − tdelay)2

τ2

](4)

where R(t) is the 1-kHz modulation sinusoidal signal, α1 and α2 is the power transmission ofeach arm and tdelay is the time delay between two arms. The output instant power of the CNTsaturable absorber is then given by:

P1(t) = P(t) · T(I) (5)

where T(I) is the nonlinear transmission of the CNT saturable absorber in Eq. (2). Here a fastsaturable absorber model is used. The case of a slow saturable absorber model will be discussedin the Discussion section.

As mentioned previously, saturable absorption does not provide an ideal AC function, so it isimportant to understand how our quasi-AC SAPM technology is different from an ideal AC. Tocompare, we choose four different input pulse types, i.e., Gaussian pulse, soliton pulse (sech2

shape) and pulse with tale ringing caused by third order dispersion. The simulation results aresummarized in Fig. 3 shown below. All the pulses have a pulse width (FWHM) of 1 ps and anormalized peak power Pn of 1. Here the normalized peak power Pn is defined as the ratio ofpulse peak power over saturation power of CNT saturable absorber. And the saturation powerequals to Isat ·80 µm2 = 16.55 W for our CNT saturable absorber.

In Figs. 3(a)–3(c), the SAPM traces are shown in red dashed lines for Gaussian pulse, solitonpulse and pulse with tale ringing, respectively. The insets are the pulse shapes of the input pulses.For comparison, we also calculate the ideal AC traces generated by SHG based AC, shownin black solid lines. It can be seen that in all three cases, the traces generated by our SAPMtechnology match well with the AC traces by SHG based AC. In the pulse peak and wing regionof the traces, there do exist slight differences in three cases, shown in Figs. 3(d)–3(f). Thesedifferences are caused by the non-ideal AC nature of saturable absorption.

Moreover, it is known that Gaussian pulse and soliton pulse input can be separated by comparingthe fitting with Gaussian and soliton functions in the SHG AC trace. This can also be achievedby our technology. In Fig. 3(e), we also fit the soliton SAPM traces with a Gaussian function(green). It can be clearly seen that Gaussian fitting is different from both two traces in the wingregion.In Fig. 3, both SAPM traces and SHG AC traces are normalized by the corresponding Ccon

(in Eq. (1)) in time axis because Ccon for SAPM traces is different from Ccon for SHG ACtraces as discussed above. For example, for SHG AC trace with Gaussian/soliton pulse input, thecorresponding Ccon = 1.414/1.543. For SAPM trace with same Gaussian/soliton pulse input, thecorresponding Ccon = 1.365/1.779. This treatment is to allow a direct comparison of the traceshapes. The calculation of Ccon in the SAPM technology will be discussed later.


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Fig. 3. Simulated CNT based SAPM traces (red) and SHG AC traces (black) for an input of(a) Gaussian pulse, (b) soliton pulse, and (c) pulse with tale ringing. Insets in (a)-(c): Inputpulse shapes. (d)-(f) Zoomed views of wing region of the traces in (a)-(c). Insets in (d)-(f):Zoomed views of peak region of the traces.

A pulse pair input is also simulated to compare with SHG AC, shown in Fig. 4. The pulsewidth is 1 ps and the pulse spacing is 4 ps. Time axis is not normalized by Ccon this time becausethe pulse separation will be changed. It can be observed that 4 ps pulse spacing can be clearlyobserved and the ratio between the main peak and side peak is 2, which confirms the capabilityof our SAPM technology to detect pulse pair.

Then we investigate the conversion coefficientCcon in Eq. (1). Figure 5(a) shows the simulationresult of the relation between the input pulse width and the pulse width of the SAPM trace. Thepulse shape is Gaussian and the normalized peak power of input pulse is fixed to 1. A nearlylinear relation confirms our previous assumption that Eq. (1) is still held in our CNT based


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SAPM except for a different Ccon. The corresponding Ccon =1.365.

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Fig. 5. Simulation of (a) SAPM pulse width with respect to the input pulse width and(b) SAPM pulse width with respect to the input pulse peak power. (c) Three-dimensionalsimulation.

The situation when input pulses have different peak power is also studied. The simulationresult of the relation between normalized input peak power and SAPM pulse width is shown inFig. 5(b). The pulse shape is Gaussian and the input pulse width is fixed to 1. The normalizedpeak power is from 0.001 to 2 because the system is working on the monotonic region of CNTsaturable absorber to prevent data ambiguity (P0<32W or Pn < 1.93) as shown in Fig. 1(e).It can be seen that, due to the non-ideal AC nature of saturable absorption, the SAPM pulse

width increases with the increase of input peak power. This means for different input pulse peakpower, there will be a different conversion coefficient Ccon, which is not desired. However, it isnoted that the maximum change of Ccon is 0.17 when the normalized input peak power changesfrom 0.001 to 2. If we choose Ccon = 1.365 as a standard value (normalized peak power Pn = 1),the pulse measurement error induced by Ccon is less than 6% which is within a reasonable range.A more complete three-dimensional simulation result is shown in Fig. 5(c) to indicate the

dependence of SAPM pulse width on input pulse width and normalized peak power. The curvescorresponding to Figs. 5(a) and 5(b) are also denoted.

Lastly, it is worth mentioning that the value of Ccon is dependent on the nonlinear transmissionproperty of CNT (and other LDMs to be used). So a calibration procedure is needed to determinethe value of Ccon in the system.


3. Experimental results

3.1. SAPM pulse profile

A typical SAPM experimental result is shown as red circles in Fig. 6(a). The horizontal axis is thetime delay between two pulses and the vertical axis is the measured LIA signal amplitude. Eachdata point is averaged by 100 times to reduce the noise from the environmental perturbation. Theinput pulse has a bandwidth of ∼ 57.2 nm, a repetition rate of 100 MHz and a center wavelength of1560 nm. The red curve is the fitted SAPM pulse profile using a Gaussian shape. The pulse width(FWHM) of the SAPM trace is ∼ 11.94 ps based on the Gaussian fit. The pulse is broadened bythe fiber dispersion of the system. The calibration of the system will be discussed in the nextparagraph. The inset of Fig. 6(a) shows an AC trace measured by a standard SHG autocorrelator(Femtochrome FR-103 XL) with a pulse width (FWHM) of 1.03 ps. The pulse is not transformlimited due to the ∼ 1-meter long fiber pigtail from the laser. The pulse peak power at the inputport of the system is 23.635 W and the peak power entering the CNT saturable absorber is 0.345W (zero delay between two arms) due to dispersion induced pulse broadening and the systemloss of 7.71 dB. The corresponding normalized peak power is 0.02. The Fig. 6(b) shows theSAPM trace of a soliton pulse with hyperbolic secant profile and the inset of Fig. 6(b) is thecorresponding standard SHG AC trace.

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3.2. Influence of pulse width and peak power

The investigation on the influence of pulse width and peak power is also a calibration process forthe system. The value of conversion coefficient Ccon is dependent on the saturable absorption ofthe nanomaterials. The all fiber setup allows alignment free but also induces pulse broadening bythe dispersion, i.e., the group delay dispersion (GDD) with the units of ps/nm. So the calibrationprocess is to determine Ccon and GDD of the SAPM system. A pulse train with fixed peak powerand tunable pulse width is first generated. This pulse train is obtained by sending a pulse trainfrom a mode-locked laser to the single mode fiber with different length. Fiber dispersion willbroaden the pulse width. Meanwhile, the average power of the pulse train is adjusted so that thepeak power is fixed. Then the pulse train is measured both by a standard SHG autocorrelator andby our SAPM system. Figure 7(a) shows four typical measured SAPM traces and their fittingcurves for input pulses with four different pulse widths denoted on the figure. The traces arevertically offset to provide a clear view. Figure 7(b) summarizes the relation between the input


pulse width and measured SAPM pulse width using our system. A linear fit is then plotted in redin Fig. 7(b). The relation between the measured SAPM pulse widths τSAPM and the input pulsewidths τin is given by:

τin = (τSAPM − ∆τ)/1.217 (6)where ∆τ = 10.687 ps is the pulse broadening in the system and the conversion coefficient Ccon

= 1.217 assuming a Gaussian profile. The value of Ccon is close to the simulation result of 1.28at Pn = 0.01 (5% error) mentioned in Fig. 5(a). The corresponding GDD is given by ∆τ/∆λ =0.187 ps/nm which is identical to the value directly estimated by the 11-m fiber length in thesystem, given by 17 (ps/km·nm) · 11 (m) = 0.187 ps/nm.

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Fig. 7. (a) SAPM traces with different input pulse width. (b) Relationship of the measuredSAPM pulse width and the input pulse width. (c) SAPM traces with different input pulsepower. (d) SAPM pulse width with respect to the normalized peak power.

The influence of pulse peak power is also investigated when the input pulse peak power isincreased from 46.6 W to 127.3 W at system input port corresponding to a normalized peakpower Pn from 0.15 to 0.41 at the CNT saturable absorber. Four typical SAPM traces are shownin Fig. 7(c) with Pn denoted. Figure 7(d) summarizes the relation between measured pulse widthand normalized peak power. It can be seen that when the normalized peak power is increasedfrom 0.15 to 0.41 at the CNT saturable absorber, the measured SAPM pulse width is increasedby ∼ 2%. This pulse broadening is due to the nonlinear transmission of the CNT. The red curveis the linear fit which is consistent with the CNT saturable absorption described in Eq. (2) andthe simulation in Fig. 5(b).To briefly summarize, there are 2 steps for the system calibration: Firstly, determining the

conversion coefficient Ccon by comparing the input pulse widths (using SHG AC) and measured


pulse widths of our SAPM traces using a certain pulse train. This step is necessary because Ccon

is dependent on the nonlinear transmission property of LDM used. Secondly, determining thepulse broadening effect, i.e. group delay dispersion (ps/nm), caused by the fiber dispersion. Thisstep can be removed in the future by applying a free-space system.

3.3. Stability and sensitivity

The stability of the system output is also investigated as shown in Fig. 8. Figure 8(a) shows along-time SAPM traces (LIA signal train) obtained by measuring a known pulse 30 times whichindicates that the measurement results are stable under environmental disturbance. Four typicalmeasurement results with fitted pulse profiles are shown in Fig. 8(b). The data are verticallyoffset to give a clear view.Figure 8(c) summarizes the measured pulse width deviation for each measurement similar

to [1]. Blue circles represent the measured actual pulse width errors using SAPM technologyaccording to Eq. (6) for 30 measurements with reference to the pulse width measured by the SHGautocorrelator. Red square (9.0 fs) represents the root-mean-square (rms) error of the measuredpulse width. The error bar denotes the upper (21.6 fs) and lower (-17.6 fs) bound of the errors.The error histogram is shown in Fig. 8(d). The measurement error is mainly limited by the lossvariation (0.6 dB) and the delay accuracy (∼ 10 fs) of the tunable delay line.

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12

Data

0 500 1000 1500 2000 2500 3000

0.0

0.2

0.4

0.6

0.8

1.0

-20 -10 0 10 20

0

1

2

3

4

5

Time (ps) Delay time (ps)

(a) (b)

(d)(c)

Mea

sure

men

t er

ror

(fs)

Measurement time Measurement error (fs)

Num

ber

DataFitting

DataAverage

Nor

mal

ized

sig

nal

Nor

mal

ized

sig

nal

Fig. 8. (a) Long-time stability test of the SAPM. (b) Four typical SAPM traces and their fitfrom (a). (c) Measurement error of the pulse widths. (d) Histogram of the error.

The sensitivity of our system is also studied. A variable optical attenuator with negligibleexcess dispersion is inserted before the input port to adjust the input average power. Figure 9shows a typical SAPM trace with a minimum detectable input power of -21.26 dBm which in facthas exceeded the minimum measurable power of our SHG autocorrelator. The measured FWHM


-30 -20 -10 0 10 20 30

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Nor

mal

ized

sig

nal

Delay time (ps)

DataFitting

Fig. 9. SAPM measurement with a pulse energy of 75fJ (-21.26 dBm average power).

of SAPM pulse is 11.78 ps corresponding to an input pulse width (FWHM) of 895 fs accordingto Eq. (6). This calculated result has acceptable deviation (13.5%) in this low power conditioncompared with the actual input pulse width data in Fig. 6(a) (1029 fs (FWHM) measured athigh power with SHG autocorrelator) and the corresponding single pulse energy is 75 fJ with aPav · Ppk of 5.44 × 10−7 W2 for the system.

4. Discussion

In this section, we compare the properties of two current AC technologies SHG and TPA withour quasi-AC SAPM technology, shown in Table I.

Table 1. Property comparison among SHG, TPA and LDM based SAPM technologies

Technologies SHG TPA SAPM

Phase matching req. Yes No No

Integration No Yes Yes

Recovery time instant ps to ns sub ps to fs

Material thickness tens of µm to mm sub-µm to µm sub-nm to nm

Firstly, SHG technology requires phase matching whereas TPA and SAPM technologies don’twhich gives more flexibility in the beam alignment. Secondly, for integration, it is still challengingto integrate SHG crystal with current integration platform. TPA materials are compatible withsemiconductor platform (e.g., Si or InP [24, 25]) but hybrid integration with insulator platform(e.g. Si3N4 or SiO2) is challenging and lossy. LDMs used in SAPM are relatively easy to beintegrated to various platforms [54, 56, 57]. Thirdly, the recovery time of the nonlinear materialis an important measure of the minimum measurable pulse width. The recovery time is nearlyinstant for SHG but from tens of picoseconds to nanosecond for TPA [61–63] (e.g. 25ps in [22]and 25ns in [64]) and from tens of femtoseconds to sub-picosecond for LDMs [52–54] (e.g. <30fs for graphene [65], 280fs for CNT [66]). We simulate the influence of the recovery time forLDM saturable absorbers by using the slow saturable absorber model as follows [67]:

∂q∂t=

qm − qτR

− qP(t)EA

(7)


where q is the instant absorption, qm is the modulation depth, τR is the decay time, P(t) is theinstant pulse power and EA is the saturation energy. As shown in Fig. 10(a), for an input pulsewith of 1 ps the detected pulse width is broadened when the recovery time τR is increased. Fourtypical simulated SAPM traces are shown in Fig. 10(a) with recovery time denoted. Figure10(b) summarizes the relation between simulated pulse width and recovery time and the inset isan enlarge view. Here we define a normalized recovery time (NRT) given by NRT = τR/inputpulse width. It can be seen that when the recovery time is small compared with the input pulsewidth (NRT < 30%, corresponding to a recovery time less than 300 fs in this example), the pulsewidth calculated from the SAPM trace is slightly broadened, less than 10%, which is acceptable.The SAPM trace is well Gaussian fitted despite slightly pulse broadening (300 fs recovery timecase, NRT=0.3) as depicted in Fig. 10(c). When the recovery time is comparable or large thanthe input pulse width, the pulse broadening becomes serious. Moreover, the SAPM trace alsobecomes deformed from an ideal Gaussian shape, as shown in Fig. 10(d) (10 ps recovery timecase, NRT=10).

-6 -4 -2 0 2 4 6

0.0

0.2

0.4

0.6

0.8

1.0

-80 -60 -40 -20 0 20 40 60 80

0.0

0.2

0.4

0.6

0.8

1.0

-60 -40 -20 0 20 40 60

0

1

2

3

4

5

6

7

0 2 4 6 8 10

0

200

400

600

800

1000

0.0 0.1 0.2 0.30

4

8

12

Delay time (ps)

Nor

mal

ized

sig

nal

(a) (b)

(d)(c)

Nor

mal

ized

sig

nal

NRT

Mea

sure

men

t er

ror(

%)

Delay time (ps)Delay time (ps)

Nor

mal

ized

sig

nal

DataFitting

DataFitting

Recovery time τR

10 fs

100 fs

1 ps

10 ps

Recovery time τR

10ps

NRT=10

Recovery time τR300fs

NRT=0.3

DataFitting

Fig. 10. (a) Four typical simulated SAPM traces with different recovery time and their fit.(b) Relationship of the measurement error and NRT, inset: measurement error against NRTwhen error is less than 10%. (c) Simulated SAPM trace (purple circles) and Gaussian fit(red line) with NRT equals 10. (d) Simulated SAPM trace (purple circles) and Gaussian fit(red line) with NRT equals 0.3.

Lastly the material thickness is also important because a thinner material induces less dispersionand thus less pulse broadening. The typical thickness of these nonlinear materials is tens ofmicrons to few millimeters for SHG crystals, sub-micron to few microns for TPA materials [30]and sub-nanometer to few nanometers for LDMs. Therefore, LDM based SAPM technology hasadvantages in beam alignment, integration and thickness. Its material recovery time is between


SHG crystals and TPA materials.Table II summarizes the specifications achieved by current SHG and TPA AC technologies

as well as our LDM based SAPM technology. There are also other newly demonstratedpulsewidth measurement technologies including time-lens temporal imaging [68,69], FWM-X-SPIDER [16], transverse second harmonic generation (TSHG) in nanowires [4], third-harmonicgeneration (THG) in photonic crystal waveguide [70] and graphene photodetector [71, 72]. Theirspecifications are also provided in Table II.

Table 2. Different methods for pulse width measurementMethod Wavelength Pulse width Pav · Ppk Pulse energy Pulse width resolution Ref.

Commercial SHG 410∼1800 nm N/A 10−7 W2 N/A 5 fs [6]

Combination of FROG and spectral

interferometry SI859 nm 250 fs

6.72 × 10−19 W2

(calculation)42 zJ N/A [9]

X-SPIDER based on 1300∼1600 nm (prediction) up to 100 ps N/A 5 pJ N/A [16]

Si waveguide PD (TPA) 1500∼1600 nm (Calculation) 0.6 ps2 × 10−9 W2

(Calculation)6 fJ (calculation) N/A [22]

Si waveguide PD (TPA) 1100∼2200 nm (Prediction) 530 fs 10−6 W2 0.1 nJ (Calculation) ∼50 fs [20]

TPA in a GaAs PMT 1550 nm 1.56 ps 1.7 × 10−10 W2 N/A N/A [21]

TPA-PDs array integrated onto a Si PCW 1520∼1545 nm 4.5 ps 10−7 ∼ 10−6 W2 N/A 570 fs [24]

Rib waveguide with TPA-PD array 1300∼1630 nm N/A 10−6 ∼ 10−4 W2 N/A 57 fs [25]

TPA 800 nm 100 fs N/A 2 pJ 6 fs [27]

Transverse SHG in nanowire 1064 nm 200 fs N/A 2 fJ N/A [4]

THG in silicon PCW 1550∼1565 nm2.5 ps

for 100-mm deviceN/A N/A ∼ 53 fs [70]

Graphene heterostructure 1500∼1800 nm 250 fs 9.38 × 10−8 W2 17.9 fJ

3 ps

(improved

to sub-50 fs [72])

[71]

SAPM 1500∼1630 nm 135 fs 5.44 × 10−7 W2 75 fJ 9.4 fsThis

work

SAPM (potential of this work) Broadband few fs 1.3 × 10−9 W2 10 fJ sub-fs -

Here we analyze the potential performance of our LDM based SAPM system. For operationbandwidth, a broadband LDM can be chosen to cover a wide wavelength range [54, 56, 57]. Forminimum pulse width, the nanometer or sub-nanometer thickness and the ultrafast decay processof LDMs can support the measurement of pulse width down to few femtoseconds [52–54]. Forthe average-power-peak-power product and minimum measurable pulse energy, current systemis limited by the loss (7.71 dB) mainly introduced by the EOM. If a better EOM with lowinsertion loss is chosen, or even the LIA is removed if the whole system is well isolated fromthe noise, the allowable single pulse energy sensitivity can be ∼ 10 fJ and the Pav · Ppk can beimproved to 1.3× 10−9 W2 (corresponding to an average power of -21.26 dBm - 7.71 dB = -28.97dBm). Choosing a saturable absorber material with even lower saturation intensity and highermodulation depth may further improve the sensitivity of the system to several ∼ fJ. For pulsewidth resolution, a better tunable delay line with less loss variation and better delay accuracy canpotentially minimize the measurement error on the pulse width to sub-femtosecond level [1].Free-space system may also be considered to avoid the dispersion effect.

5. Conclusions

In conclusion, we have proposed and demonstrated a SAPM technology by using low dimensionalnanomaterials based saturable absorber. In a proof-of-concept experiment with carbon nanotube,the SAPM system has a minimum measurable single pulse energy of 75 fJ, an average-power-peak-power product Pav · Ppk of 5.44 × 10−7 W2, and a time resolution of 9.0 fs. By furtheroptimizing the experimental setup, it is estimated that the system can potentially support fJ levelpulse energy with fs pulse width. We believe this work may pave a new way for pulsewidth


measurement which is potentially capable of measuring ultrashort pulses with high sensitivityand resolution. Our technology is also compatible to various integration platforms and canbenefit the realization of a high-performance fully integrated pulsewidth measurement device.

Funding

National Natural Science Foundation of China (NSFC) (61505105,61875122); Open Fund ofIPOC (BUPT).

Acknowledgment

We appreciate the helpful suggestions from Prof. Supradeepa, Indian Institute of Science.

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a pulsewidth measurement technology based on carbon

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