1 Introduction

Graphene, a single layer of carbon atoms arranged in a honeycomb structure, has a universal linear optical absorption of 2.3 % spanning visible to far infrared light [1]. This universal interband absorption results from the linear dispersion near the Dirac point, where the conduction and the valence bands meet. However, when the distribution of electrons and holes are not symmetric about the Dirac point, i.e., Fermi level is either above (n-doping) or below (p-doping) the Dirac point, it has been observed that this linear absorption becomes non-universal at low photon energy due to state blocking [2]. This doping often originates from the contact of graphene with the substrate [3]. In addition to the doping induced by substrate, the Fermi level can be tuned by electric-field gating and the interband absorption is minimized when the Fermi level approaches half of the excitation photon energy [4]. Although the doping effect on the interband absorption was already observed at low excitation levels [2, 4], there has not been a study of the same effect in the nonlinear regime. The doping effects on the interband absorption at high excitation levels are of interest because the interband absorption can be saturated by a light pulse with high peak intensities [5, 6]. This saturable absorption has been used extensively to mode-lock lasers [7–16]; however, the effects of doping on the saturable absorption have, to the best of our knowledge, not been investigated. In this paper, we report the effect of chemical p-doping of graphene on its optical properties as a saturable absorber. We also discuss this controllability of saturable absorption and its importance in producing stable ultra-short pulse trains in lasers.

2 Preparation and characterization of graphene saturable absorbers

2.1 Growth and transfer of graphene

The graphene samples used in the experiment were grown on copper foils (Alfa Aesar #13382, 25 μm) by chemical vapor deposition (CVD) [17]. The total pressure in our CVD process was maintained at the level of 10 mTorr in order to obtain large domains of graphene [18]. The CVD process began with the annealing of the copper foils at 1000 °C with 5 sccm H2 flow for 30 minutes. While the copper foils were maintained at 1000 °C, graphene was grown with 1 sccm H2 and 1 sccm CH4 for 30 minutes, followed by a 5-minute phase of 1 sccm H2 and 10 sccm CH4 to fill gaps between domains [18]. Figure 1 shows the domain sizes and boundaries of our CVD graphene. After the growth, the graphene on copper foils was spin-coated with polymethyl methacrylate (PMMA) as a mechanical support during wet-transfer processes, in which the copper foils were etched by ferric chloride (0.5 M) solution, and the graphene was washed in deionized water several times before being transferred onto a microscope slide (VWR #48300-025).

Fig. 1
figure 1

A scanning electron microscope image of graphene domains and boundaries. Inset: disconnected graphene domains that are grown without a second step of high methane flow rates. The domain sizes (100–400 μm2) are much larger than the laser beam size in our experiments and are sufficient for most laser applications

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The transferred graphene was baked in a tube furnace at 300 °C for an hour with 50 sccm Ar flow, 5 sccm H2 flow (pressure ≈30 mTorr), reducing the doping that could result from adsorbates such water molecules or other contaminants [19, 20]. Moreover, we found that this heat treatment can prevent the delamination of the graphene from the substrates in the following doping step, which we hypothesized to be caused by the removal of water molecules between the graphene layer and the substrate. In this work, we use nitric acid of low concentration (≤0.8 wt%) to p-dope graphene [21] The acid was drop-cast on the graphene surface and, after 5 minutes, blown dry by nitrogen. Various doping levels were achieved by nitric acid of concentrations from 0.1 to 0.8 wt%.

2.2 Characterization of Fermi level in graphene

Fermi levels in graphene are often estimated from the gate voltage needed for obtaining the minimum electrical conductivity [22]. This method, however, brings complications of gate electrode implementation in transmissive samples. In this work, we quantified the Fermi levels by graphene’s infrared transmission spectra from 3000 nm to 900 nm with a spectrophotometer (Varian, Cary 500). The beam was 3 mm in diameter and at near-normal incidence to the graphene-substrate interface. A large beam size was used in order to average the spatial-dependent doping caused by the substrate and possibly by the dopants. The calibration of the transmission spectra were done by subtracting the spectrum of a blank microscope slide from all measurements.

The calculation of graphene’s transmissive spectrum begins with the optical conductivity (σ) of graphene as a function of optical frequency (ω), chemical potential (μ), and temperature (T) [1]:

$$ \sigma= \sigma_0 \biggl[ \frac{1}{2}+\frac{1}{72} \frac{(\hbar\omega)^2}{t^2} \biggr] \biggl( \tanh\frac{\hbar \omega+2\mu}{4k_BT}+\tanh\frac{\hbar\omega-2\mu}{4k_BT} \biggr), $$
(1)

where σ 0 is the optical conductivity of undoped graphene (μ=0), t is the hopping parameter connecting first nearest neighbors in the tight-binding model for graphene, k B is the Boltzmann constant, e is the electron charge, ħ is the reduced Plank constant, and T is the temperature of the sample. For the following discussion, we neglect the term (ħω/t)2 since 1/72×(ħω/t)2<3×10−3≪1/2 for the photon energies we work with (<1.2 eV).

At normal incidence, the transmittance \(\mathcal{T}\) of graphene at the interface of air (n=1) and glass (n≈1.5) is

$$ \mathcal{T} = \frac{4n_1n_2}{ ( n_1+n_2+\sigma/c\epsilon_0 )^2} \approx\mathcal{T}_0 \biggl[ 1- \frac{2\sigma}{c\epsilon_0 (n_1+n_2 )} \biggr], $$
(2)

where c is the speed of light in vacuum, ϵ 0 is the vacuum permittivity, and \(\mathcal{T}_{0}=4n_{1}n_{2} (n_{1}+n_{2} )^{-2}=0.96\) is the transmittance at the same interface without graphene. The change of transmittance due to the presence of graphene, including the two interfaces of a substrate, is then

$$ \Delta\mathcal{T}_{\mathrm{total}} = \bigl|\mathcal{T} \mathcal{T}_0-\mathcal{T}_0^2 \bigr|= \frac{2\sigma\mathcal{T}_0^2}{c \epsilon_0 (n_1+n_2 ) }. $$
(3)

Figure 2 shows the transmission spectra of graphene samples that are chemically p-doped to different levels. Due to spatial variations in the doping resulting from substrates and dopants, the curves in Fig. 2 possess a slow transition from occupied states to vacant states in the valence band. Assuming that the distribution of these spatial variations follows a normal distribution, which has a mean value of μ and a spread of Δμ, we can fit the data in Fig. 2 by averaging the optical conductivity σ (Eq. (1)) over this distribution. The chemical potentials found are shown next to the curves in Fig. 2. The deviations Δμ’s were found to be less than 0.09 eV, which we believe can be further reduced with a smaller beam size and/or atomically flat substrate surfaces.

Fig. 2
figure 2

Transmission spectra of doped graphene as a function of photon energy. The doping level can be controlled by nitric acid of different concentrations. Gray line: measurement; black line: fit. From top to bottom, the curves represent (S00) baked graphene, (S01) baked and doped by 0.1 wt% acid, (S02) baked and doped by 0.2 wt% acid, (S04) baked and doped by 0.4 wt% acid, (S08) baked and doped by 0.8 wt% acid. Linear optical absorption at low photon energy reduces as the p-doping level increases

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We have reproducibly observed that, as the concentration of nitric acid dopants increases, graphene becomes more p-doped. Furthermore, the optical absorption at low photon energies is reduced due to lack of electron population in the valence band. The baked sample (S00) shows nearly universal absorption at photon energies as low as 0.4 eV, which is limited by the spectral range of the spectrophotometer.

2.3 Raman spectra of graphene

In addition to optical absorption measurements, we examined the number of layers and defects of our graphene samples by their Raman spectra. Raman measurements were performed on a home-built Raman microscope in epi-illumination and detection geometry, with excitation provided by a 633 nm HeNe laser (spot size ≈1 μm, peak power <1 kW/cm2). The Raman scattered light is spectrally filtered with a 160 cm−1 cut-off filter (Semrock, LP02-633RU-25) and detected with a spectrometer with a 1200 g/mm (Newport, 53-*-220H) grating for single-peak measurements or a 600 g/mm grating (Newport, 53-*-350R) for measurements spanning the full relevant spectrum of graphene, and a liquid-nitrogen-cooled CCD camera (Princeton Instruments, Spec-10 2KB/LN).

The Raman spectrum of each sample was taken at five random locations. Peak positions and relative intensities were then extracted by fitting each peak to a Lorentzian distribution. We took the average of these values, combined with the statistical uncertainty of our spectrometer (<2 nm) to attain mean peak positions and relative intensities and uncertainties. The statistical uncertainty is likely due to the spatial variation in doping concentration.

The peak power was kept low so as not to damage the sample or remove dopants with thermal effects [23]. To confirm that our measurements were nonintrusive, an short measurement (<10 seconds) was made before and after the longer (60–300 seconds), higher SNR, measurements to confirm no change in the spectrum.

Figure 3 shows the Raman spectra of our graphene samples. The undoped, only baked sample showed low I(D)/I(G) ratio (<0.1) and single Lorenztian 2D peak with a FWHM of 35±3.5 cm−1. This suggests that our CVD-grown graphene is mostly defect-free and monolayer [24]. Our nitric-acid-doped graphene showed an upshift in the G band of 5±3 cm−1 and the 2D band of 4±2 cm−1, a peak narrowing in the FWHM of the G band of between 2 and 5 cm−1, and a decrease in the ratio I(2D)/I(G) from 2±0.1 to about 1.6±0.3 (from sample-a to sample-b). This agrees qualitatively with Raman measurements made on electrostatically doped graphene [25, 26] and graphene doped by organic molecules [27], although the G peak narrowing has not always been observed in chemically doped graphene.

Fig. 3
figure 3

(a) Representative Raman spectra of graphene samples used in the experiments. Sample-a: baked sample, E F <200 meV; sample-b: doped sample, E F ≈200 meV; sample-c: doped, E F ≈400 meV; sample-d: baked after doped to E F ≈400 meV. No significant changes of I(2D)/I(G) and I(D)/I(G) ratios were observed in samples-b, c, d, implying that nitric acid did not attack graphene and was removed by baking without damaging graphene. (b) All samples have small I(D)/I(G) ratios, which implies nearly defect-free graphene. (c) All samples have a I(2D)/I(G) ratio of about 2

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As we increased level of p-doping to −400 meV (sample-c), the G and 2D bands down-shifted about halfway towards their original positions, which to our knowledge, has not been observed in chemically doped graphene. However, doping graphene with nitric acid has not before been carefully studied, and the I(2D)/I(G) ratio, suggested to be an important measure of doping level, continued to decrease to about 1.5 as expected. We found no correlation between doping concentration and the I(D)/I(G) ratio, which is indicative of defects in graphene. We never found a mean I(D)/I(G) peak ratio above 0.12, and it should be noted that I(D) was intentionally over-estimated because of the background noise. When we later baked our samples at 100 °C for 1 hour to remove the adsorbents (sample-d), we found that the peak positions fully recovered and, in fact, downshifted by an additional 2±2 cm−1 for the 2D band and an additional 1.3±0.7 cm−1 for the G band. Furthermore, the I(2D)/I(G) peak ratio increased to about 2.6±0.3. All of these changes after baking imply pristine graphene. It is likely that baking after doping removed the adsorbates that had accumulated on the graphene sheet in the time between initial sample preparation of the undoped sample and its measurement in Raman. This would account for the seeming increase in purity after doping and baking.

3 Saturable absorption in graphene

3.1 Characterization of saturable absorption

The saturable absorption in graphene was characterized in a differential transmission setup with balanced detection, shown in Fig. 4. The optical elements used were carefully chosen so as to avoid any nonlinearities not resulting from the sample [28]. We used a soliton mode-locked Er:Yb:glass laser with a center wavelength of 1.56 μm, pulse width 210 fs, and 86 MHz repetition rate. The beam diameter on the sample was (4.4±0.6) μm. For each measurement, the peak intensity of the pulse was varied logarithmically from 3 to over 3000 MW/cm2, and the change of transmittance was recorded. Each sample was characterized at ten independent locations, and the fit parameters of all spots were averaged. Figure 5(a) shows one of these measurements.

Fig. 4
figure 4

Differential transmission setup for characterizing the saturable absorption of graphene. Isolator: optical Faraday isolator; PBS: polarization beam splitter cube, two used as a power attenuator; BS: beam splitter; PD1 and PD2: identical photodiodes for balanced detection; L1 and L2: focusing lenses; Sample: graphene on a microscope slide; Chopper: mechanical chopper used with lock-in amplifier to reject part of the laser noise

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Fig. 5
figure 5

(a) The change of transmittance caused by as-transferred graphene as a function of pulse peak intensity. The gray curves are ten individual measurements at different locations on the same sample; the black solid line is the resulting curve from the average of ten individual fits through the data. (b) Transmission transient of graphene. The slow component of the relaxation time is 1.1 ps; the fast component is not resolved due to the long pulse duration (∼210 fs)

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We also measured the relaxation time of photo-excited carriers in undoped graphene by a degenerate pump-probe setup with the aforementioned laser; the pump and probe beams were counter-propagating, polarized 90∘ with respect to each other, and mechanically chopped at two different frequencies around 1 kHz. The change of probe power due to the pump was measured by a lock-in amplifier at a frequency equal to the sum of the two chopping frequencies. The observed transmission transient of graphene is shown in Fig. 5(b).

3.2 Saturable absorption in as-transferred graphene

In graphene, photo-excited carriers relax within ∼200 fs via carrier-carrier scattering and carrier-phonon scattering [6, 29–31]. Our pump-probe measurements also showed that the fast relaxation in graphene contributes significantly to the saturable absorption (Fig. 5(b)). To find the macroscopic parameters of a graphene absorber (saturation intensity or fluence, saturable loss, and non-saturable loss), care needs to be taken in fitting a correct theoretical model to experimental saturable absorption curves. The saturation of an absorber can be described by the following equation [32]:

$$ \frac{\mathrm{d}q(t)}{\mathrm{d}t} = \frac{q_0-q(t)}{\tau_A}-\frac {q(t)I(t)}{F_{\mathrm{sat}, A}}, $$
(4)

where q(t) is the saturable loss, q 0 is the insertion loss, τ A is the relaxation time of the absorber, I(t) is the intensity of light, and F sat,A is the saturation fluence of the absorber. For simplicity, we first regard graphene as a fast saturable absorber (pulse width ≫τ A ). Given sech2-shaped pulses, the loss of absorber can be written as [33]

$$ q(S) = \frac{q_s}{\sqrt{S(1+S)}} \tanh^{-1} \biggl( \sqrt{\frac{S}{1+S}} \biggr)+q_{ns}, $$
(5)

where q s is the saturable loss, q ns is the nonsaturable loss, and S is the ratio of the pulse peak intensity to the saturation intensity of the graphene absorber. Figure 5(a) shows the nonlinear absorption curve of as-transferred and baked samples. Fitting Eq. (5) to the data, we found the saturation intensity to be (250±80) MW/cm2, the insertion loss (1.85±0.08) %, the saturable loss (0.85±0.04) %. It should be noted that the insertion loss here refers to the change of transmittance due to the presence of graphene on the air-glass interface, and it is lower than the optical absorption of free-standing graphene (πα=2.3 %). The insertion loss was comparable to the calculated change of transmittance \(\Delta\mathcal {T}_{\mathrm{total}}=1.7~\mbox{\%}\) in Eq. (3). The extra loss could be attributed to the light scattering from graphene or nongraphitic carbon produced incidentally by the CVD process [34].

From a full numerical solution to Eq. (4), assuming τ A =200 fs, sech2-shaped pulses with 210 fs (FWHM), we found that the saturation intensity was lower by a factor of 0.7 (I sat=175 MW/cm2, F sat=35 μJ/cm2), although in this regime, neither the saturation intensity nor fluence is a good macroscopic quantity of the absorber. One simply needs to refer to the pulse duration and the relaxation time of the absorber.

The saturation intensity we measured can be directly compared with the theoretical value calculated by Vasko [5]. For photon energies near 0.8 eV, the theoretical value is approximately 60 MW/cm2, and our measured value of (250±80) MW/cm2 agrees roughly within a factor of 4. The discrepancy between our measurement and the theoretical value could be due to the reduced carrier relaxation time (Fig. 5(b)) caused by the lattice defects around domain boundaries or by the interaction with the substrate, which could add additional relaxation pathways. Note that none of these effects can lower the measured saturation intensity.

Our result also agrees very well with Sun et al. [7], who measured the saturation intensity for 1.55 μm light to be 266 MW/cm2 for monolayer and bilayer graphene flakes dispersed in polymers, but we found a large discrepancy between our results and the values reported by Bao et al. [8–10], Tan et al. [11], and Zhang et al. [12–14], who found a saturation intensity value of 0.6–0.7 MW/cm2. Even though their measured saturation intensity seemingly agrees with the model they suggested [9], their model merely accounted for the carrier recombination in direct bandgap semiconductors such as gallium arsenide, but is likely not adequate to describe zero-bandgap graphene.

It may be argued that the saturation intensity depends on the pulse duration used for characterization, but from a full numerical solution to Eq. (4), we found that as the pulse duration increases from 200 fs to 10 ps, the saturation intensity decreases by a factor of at most 10, which could not explain this discrepancy.

According to Vasko’s calculation, the saturation intensity strongly increases with the photon energy due to the proportionality between the relaxation rate and the density of states to which carriers are excited. Several experiments have also shown that the saturation intensity for 800 nm light is above 1 GW/cm2: Dawlaty et al. observed saturable loss but could not reach the saturation intensity even at pulse peak intensities higher than 1 GW/cm2 (85 fs pulse duration) [29]; Xing et al. showed by z-scan measurements that the saturation intensity was near 4 GW/cm2 [6]; and Breusing et al. did not observe any saturation with pulse fluence as high as 0.7 mJ/cm2 (7 fs pulse duration) [31].

3.3 Saturable absorption in chemically-doped graphene

The transmission spectra of undoped and doped graphene are shown in Fig. 2. As the Fermi level was varied from close to the Dirac point to 0.4 eV below the Dirac point, the linear absorption at low photon energies decreased due to lack of electron population in the valence band. The corresponding saturation of optical absorption at 1.55 μm wavelength (0.8 eV) is shown in Fig. 6. As the doping level increased, the insertion loss of graphene decreased dramatically from 1.8 % to 1 %, which matched well with the measured linear absorption.

Fig. 6
figure 6

Transmission loss of doped graphene as a function of pulse peak intensity. For each doping level, one curve (dashed line) obtained by averaging the fit parameters of ten independent spots is shown. From top to bottom, the curves represent (S00) baked graphene, (S01) baked and doped by 0.1 wt% acid, (S02) baked and doped by 0.2 wt% acid, (S04) baked and doped by 0.4 wt% acid, (S08) baked and doped by 0.8 wt% acid. The three cones show the band structure of graphene at different doping levels. Upper cone: conduction band; Dark lower cone: electron-filled valence band; and light-colored area: hole-occupied states

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The nonsaturable loss, however, did not increase with the doping level, suggesting that doping with nitric acid does not cause more defects or introduce more scattering loss to the graphene. The saturation intensity also remained roughly the same in doped graphene, which could be understood from the fact that the density of states and carrier relaxation time are not modified by hole-doping.

This flexibility in designing the saturable absorbers is essential to successful continuous-wave mode-locking in solid-state lasers [35]. Given the parameters of a specific laser, suitable parameters of the saturable absorber can be chosen to prevent Q-switching. SESAMs have been used widely in solid-state laser mode-locking because of their design freedom. For graphene absorbers, one can exploit the doping effect to tailor the modulation depth in monolayer graphene, and if higher insertion loss is desired, stacked multilayer graphene can be used.

Even though the parameters of a saturable absorber can be tailored to specific values in order to prevent Q-switching, the allowed range of parameters is often quite limited, and the parameters of the laser such as gain cross section and pump power also need to be taken into account. In certain situations, using active feedback to suppress Q-switching can be favorable compared to designing absorbers. It has been demonstrated that the laser output power can be directly used to feedback-control the intracavity loss or gain [36, 37]. For graphene absorbers, it is possible to implement an external electric field to modulate the carrier density [4, 17], or essentially the Fermi level, so that the insertion loss can be controlled by electronics. The relation between the carrier density (n) and Fermi level (E F ) in graphene is given by

$$ n = \frac{1}{\pi} \biggl( \frac{E_F}{\hbar v_F} \biggr)^2, $$
(6)

where v F is the Fermi velocity (∼106 m/s). To achieve the maximal modulation of insertion loss in a laser with a center wavelength of 1.55 μm, the desired Fermi level is 0.4 eV below the Dirac point, corresponding to a carrier (hole) density of approximately 1013 cm−2. To achieve this level of carrier density in a normal electrical-gating configuration with 100 nm dielectric of ϵ≈4, one has to apply nearly 100 volts. Doping graphene with chemicals prior to applying electric fields can thus avoid the use of strong field and avoid dielectric breakdown. This predoping would be particularly important for applications in lasers with wavelengths in the near-infrared and visible regions, where the state-blocking is not trivial to achieve solely by electric-field gating.

3.4 Optical damage of graphene

The modulation depth and the saturation intensity of graphene are comparable to those of SESAMs [38]. However, the full modulation depth could not be exploited due to the onset of permanent damage for pulse peak intensities higher than 2 GW/cm2. We found that the damage resulted from the high peak power of the laser rather than from the heat due to the average power. This was confirmed by observing the damage with the laser under two conditions: (1) cw mode-locking regime and (2) continuous-wave regime. While the average power was the same in both regimes, the peak power was 50,000-times higher in the mode-locked regime. Despite the same average power, no damage was observed when the laser was operated in the continuous-wave regime. To further investigate the damage mechanism, the graphene sample was purged with argon, excluding the possibility of oxygen interacting with graphene under high pulse intensity. It was found that the damage threshold did not increase in this oxygen-free environment. We thus assume that the damage could have originated from the interaction of the high electric fields with graphene and possibly its residual surface contaminants or nongraphitic carbon left over from growth and transfer [34].

4 Summary

We showed that, in monolayer graphene, the modulation depth of its saturable absorption can be tuned by hole-doping. When applying graphene as a saturable absorber for ultrashort pulse generation, it can offer more design freedom that helps prevent Q-switching. Hole-doping does not noticeably affect the saturation intensity and the non-saturable loss in graphene. There might, however, be a stronger correlation between electron doping and the saturation intensity due to the decreased number of relaxation pathways, which will be the subject of a further study. For undoped graphene, we measured the saturation intensity to be (250±80) MW/cm2, and the previously reported values (<1 MW/cm2 at 1.55 μm wavelength) are, in our opinion, likely not correct. We also proposed that the insertion loss of graphene absorbers can be modulated by an electric field; therefore, negative feedback-control can be exploited to suppress Q-switching. We argued that for applications in lasers at telecommunication or shorter wavelengths, chemical predoping of graphene should be combined with electric-field gating to provide the maximal modulation. Saturable absorbers that are controlled electrically will likely push the development of compact solid-state mode-locked lasers with ultrahigh repetition rates.