Graphene based widely-tunable and singly-polarized pulse generation with random fiber lasers

Pulse generation often requires a stabilized cavity and its corresponding mode structure for initial phase-locking. Contrastingly, modeless cavity-free random lasers provide new possibilities for high quantum efficiency lasing that could potentially be widely tunable spectrally and temporally. Pulse generation in random lasers, however, has remained elusive since the discovery of modeless gain lasing. Here we report coherent pulse generation with modeless random lasers based on the unique polarization selectivity and broadband saturable absorption of monolayer graphene. Simultaneous temporal compression of cavity-free pulses are observed with such a polarization modulation, along with a broadly-tunable pulsewidth across two orders of magnitude down to 900 ps, a broadly-tunable repetition rate across three orders of magnitude up to 3 MHz, and a singly-polarized pulse train at 41 dB extinction ratio, about an order of magnitude larger than conventional pulsed fiber lasers. Moreover, our graphene-based pulse formation also demonstrates robust pulse-to-pulse stability and wide-wavelength operation due to the cavity-less feature. Such a graphene-based architecture not only provides a tunable pulsed random laser for fiber-optic sensing, speckle-free imaging, and laser-material processing, but also a new way for the non-random CW fiber lasers to generate widely tunable and singly-polarized pulses.

Here we report graphene-based pulse generation with cavity-free random fiber lasers, for the first time. By dynamically modulating the polarization via a polarization rotator (PR) and then transmitting through a designed graphene-coated D-shaped fiber (GDF), the continuous wave (CW) from the arbitrarily-polarized random fiber laser is transformed into coherent sub-nanosecond pulses even in the non-resonant single-pass configuration. The PR and the GDF hybrid waveguide serves simultaneously as the linearly polarized pulse generator (polarization modulation) and the pulse reshaper (saturable absorption). The pulses generated from the GDF not only inherit merits of the CW random fiber laser such as a high pump-power Stokes conversion efficiency, but also offer unique advantages such as a power-dependent singly-polarized output with polarization extinction ratios up to 41 dB, and wide tunability in both pulsewidths and repetition rates, across two and three orders of magnitude respectively.

Results
Architecture of the pulse generator. Figure 1(a) illustrates the concept of generating highly polarized pulses for a CW random fiber laser. Determined by the graphene's anisotropy, the loss on the TM-polarization is much higher than that on the TE-polarization 28,38 . When light transmits along the GDF, as shown schematically in the inset, it can be regarded as a x-polarization transmission filter. With the x-polarization periodically modulated by the PR, the transmission is a sinusoidal-like temporal wave after passing the GDF. Simultaneously, with Pauli blocking and self-phase modulation at high input powers 21,22,40 , the temporal width of sinusoidal-like wave can be dramatically compressed to form narrow pulses. In this process, the polarization rotation rate determines the pulse repetition rate while the saturable absorption efficiency determines the pulsewidth. Theoretical analysis is detailed in Supplementary Information Section S1.
With the finite element method (FEM), an example modeled E x -field distribution is shown in Fig. 1(b) with other polarization and fields shown in Supplementary Information Section S1. For the D-shaped fiber without (c) Optical micrograph of the graphene-coated D-shaped fiber. The boundary of the graphene coverage is illustrated with the white dashed line. By coupling 633 nm light into the fiber, the graphene-enhanced scattering is illustrated in the red scattering regions. Scale bar: 50 μ m. (d) Raman spectra of the CVD-grown graphene monolayer and the D-shaped silica fiber. The weak D-peak, the FWHM of the G-peak (32.5 cm −1 ) and 2D-peak (38.2 cm −1 ), and the G-to-2D peak ratio (0.36) means that the graphene film is of monolayer and uniformity.
Scientific RepoRts | 5:18526 | DOI: 10.1038/srep18526 graphene coverage, the x-polarized component and the y-polarized component have almost equal intensity. In comparison, with graphene cladding, the electromagnetic field distribution is pulled close to the graphene film and the x-polarized component is much stronger than the y-polarized component. With the graphene-based evanescent field enhancement, the transmitted CW random lasing field interacts slightly with the graphene film (detailed in Supplementary Information Section S1).
Graphene-coated D-shaped fiber. The D-shaped fiber was carefully polished with good uniformity and small surface roughness, with an insertion loss less than 10 dB over a polished length of 20 mm. Detailed fabrication process is shown in Supplementary Information Section S2. The fabrication of the GDF with a long length and a highly uniform surface is crucial to ensure effective light-graphene interaction and low scattering losses. Significantly, the polarization dependent loss (PDL) determines the initial polarization extinction ratio (PER) and the peak-to-noise ratio (PNR) of the generated pulses, while the absorption efficiency dominates how strongly the pulses could be modulated optically. Figure 1(c) shows an optical micrograph of the graphene cladded D-shaped fiber, under 633 nm transmission for clarity. In order to prepare high-quality graphene film and transfer it to the D-shaped fiber properly, monolayer CVD graphene was used 41 instead of exfoliated graphene. With the wet-transfer technique 36 , we successfully covered graphene over several centimeters of the D-shaped fiber surface with good flatness and uniformity, even when the fiber was polished down with 58 μ m depth (details in Supplementary Information Section S3). Figure 1(d) shows the Raman spectrum of the GDF, which verifies that the deposited graphene is of sufficient quality for our measurement. For a GDF with 1.67 cm length, the excess graphene loss is measured to be ~22 dB.

Random fiber lasing.
A high-power CW laser at 1455 nm serves as the pump for the random fiber laser.
After the accumulation of Rayleigh scatterings and Raman effects in a 50 km single mode fiber (SMF), a CW random fiber laser at 1550 nm is obtained. Random fiber lasers with other wavelengths are also achievable from their stimulated Raman scattering nature 42 . A fiber Bragg grating (FBG) serves as a mirror to reduce the lasing threshold 43 , and a WDM is used to filter off the pump component (detailed in Supplementary Information Section S4). Figure 2(a) shows the dependence of the laser power on the pump power. The lasing threshold is 0.88 W. When the pump power reaches 2.5 W, the output power of the random fiber laser measured after the WDM-2 is 160 mW. Considering the loss of the 50 km long system is over 10 dB, the pump-to-Stokes conversion efficiency of the random fiber laser is estimated conservatively to be above 60%, which could be even higher with short fiber lengths 42 .
Pulse generation and characteristics. The polarization output of the random fiber laser is next modulated periodically using the PR, with a rotation speed tunable from 1 kHz to 3 MHz, prior to launching into the GDF. The power-dependent polarization selectivity and saturable absorption of the GDF are shown in Fig. 2(b). With a broadband tunable laser with a low average power of 9.8 mW, the GDF has demonstrated its natural PDL as shown in the inset of Fig. 2(b). In the window of 1510 nm to 1570 nm, the transmission in the x-polarization was approximately − 22 dBm, while the transmission in the y-polarization was approximately − 57 dBm for a PER in excess of 34 dB. When the launched power of the GDF increases gradually, saturable absorption begins to occur along the GDF. Supplementary Information Section S5 details the saturable absorption and theoretical modeling. When the launched power of the x-polarized laser launched in the GDF increased from 1 mW to 2.9 W, the transmittance of the GDF increases from ~0.05% to ~3.4%. Contrastingly, for the y-polarized laser with launched power of 2.9 W, the transmission stays predominantly constant with only a 0.0002% increase, within the noise level and negligible. This indicates that much higher power is needed to use the y-polarized light to saturate the GDF. Such a polarization-dependent saturable absorption is determined compositely by the polarization dependent transmission of the waveguide, and the polarization dependent nonlinear response of graphene.
The polarization properties of the graphene based random fiber laser are shown in Fig. 2(c), illustrating the measured Stokes vectors before the PR, after the PR, and after the GDF. Details of the polarization selectivity are shown in Supplementary Information Section S6. Initially, the CW random fiber laser has a low polarization degree of less than 30%, with a random polarization state. The PR then polarizes it and rotates its polarization, with subsequent polarized transmission filtering by the GDF.
The intensity dynamics after the PR are measured by a real-time oscilloscope, comparing before and after the GDF. Under 2.8 MHz rotation, Fig. 2(d) shows the transmission with increasing powers up to 2.88 W where a constant CW transmission is observed before the GDF. In contrast, after the GDF, as shown in Fig. 2(e), the CW laser becomes a sinusoidal-like oscillation. With increasing launched powers from 13.8 mW to 2.88 W, the sinusoidal-like oscillation is compressed to be sub-ns pulses gradually, at a constant repetition rate. Figure 3(a) shows the progression of the generated pulses under increasing launched powers and a fixed 2.8 MHz repetition rate. The (left column) blue data points are the measured pulsewidths while the (right column) yellow curves are from the theoretical calculations, based on the theoretical analysis in Supplementary Information Section S1. With the launched power increasing from 13.8 mW to 2.88 W, the sinusoidal-like waveform with full width at half maximum (FWHM) more than 180 ns is compressed to be narrow pulses gradually. The pulse generation becomes obvious when the launched power higher than 2.2 W. At the launched power of 2.88 W, the duty cycle is lower than 0.3%, where the duty cycle means the value of the FWHM of a single pulse comparing the temporal period of the PR. Figure 3(b) demonstrates the ~900 ps pulse in detail. With the high power induced saturable absorption, the pulses are generated by compressing the sinusoidal-like waveform more than two orders of magnitude.
The correspondingly pulse spectra is shown in Fig. 3(c). At higher pulse energies based on the higher launched power, chirp and self-phase modulation is evident. At 13.4 mW initially, the 3-dB full-width half-maximum of the random fiber laser spectrum is ~0.1 nm, since the FBG performs as a narrow filter. At 2.88 W, the 3-dB spectral width increases to 0.96 nm and is dominated by the graphene pulse reshaping. Supplementary Information Section S7 also notes the 30-dB spectral width to illustrate the self-phase-modulation and chirp effects. Here the pulse compression and spectra broadening is modeled via the beam analysis and Fourier transform methods. The GDF formed pulses and details of the numerical modeling are illustrated in Supplementary Information Section S1. Figure 4(a) shows the dependence of the compressed-width and spectra for increasing the launched power of the GDF and at a fixed repetition rate, tuning over two orders of magnitude in the pulsewidth up to 2.88 W, with a fixed repetition of 2.8 MHz. With launched powers in excess of 2.88 W, we note that thermal damage of graphene starts to appear, limiting further compression currently. Moreover, considering the polarization-dependent saturable absorption of the GDF, the PER of the pulses is also power-controllable, as shown in inset of Fig. 1(a). With the launched power increasing from 1 mW to 2.88 W, the PER of the pulses increases gradually, due to stronger saturation in x-polarization. The PER reaches ~41 dB at ~2.88 W, one of the highest values observed for high power polarizers. Figure 4(b) shows the tuning of the repetition rate through the PR rotation rate, for a fixed launched power at 2.88 W, illustrated at 160 kHz, 560 kHz, and 3 MHz, for example. By increasing repetition rate, the sinusoidal-like pedestal is suppressed dramatically, and the pulse quality increases to 50.9%, at the launched power of 2.88 W and the repetition rate of 3 MHz. The time jitter of the pulse train generated by the PR and the GDF is mainly determined by the stability of the PR, whose temporal instability is lower than 0.1%. Hence, a higher repetition rate results in a lower time jitter. Figure 4(c) shows the pulsewidths versus the repetition rates, starting from 1 kHz to 3 MHz and with the pulsewidth depending exponentially on the repetition rate. A higher repetition rate also brings about narrower pulsewidth, as the pulses are compressed from the initial sinusoidal-like envelope formed by the GDF, based on its polarization selectivity. When the repetition rate increases, the width of the initial sinusoidal-like peaks becomes narrower. Hence, after compression, these faster sinusoidal-like peaks are transformed into even narrower pulses. Based on the numerical scaling, we note that the pulsewidth could reach sub-picosecond levels at a repetition rate above 6 MHz.

Tunability.
In addition, as the pulses are gradually compressed from the initial sinusoidal-like wave, a weak sinusoidal-like envelope is always persistent at the pulse pedestal, distinct from conventional cavity solitons or cavity mode-locking. Such a residual pedestal would deteriorate the pulse quality, which could be described as Q P = E FWHM /E 0 , here E FWHM is the energy in the full width at half maximum (FWHM) of the pulse, E 0 is the energy of the pulse integrated over its period 44 . However, by increasing launched power or repetition rate, the sinusoidal-like pedestal could be dramatically suppressed, so that the pulse quality could be improved, as shown in Fig. 4(d). Referring Supplementary S1, calculated curve suggests that the compressed pulses can have a Q P > 70%. However, limited by the background noise and instability of the PR, the measured pulse quality is relatively lower. In the experiment, the maximum measured Q P is 50.9%, with launched power 2.88 W and repetition rate 3 MHz.

Discussion
Distinct from conventional mode-locking lasers, pulse generated by the single-pass GDF configuration is compressed from sinusoidal-like envelope. To achieve short pulsewidth and acceptable pulse quality, relatively high launched power and fast PR is necessary. However, to generate pulses with cavity-free random fiber lasers, external methods are necessary. Fortunately, the GDF based pulse generation has exceptional properties, and could be further improved in the future, by optimizing the smoothness/uniformity of the GDF, the performance of the PR, and increasing the launched power or the modulation speed of polarization.
In addition, beyond the random fiber lasers, the graphene based pulse generator could also be widely applied on typical non-random CW lasers in common fiber systems, as the polarization selectivity and the saturable absorption of the GDF is unique and universal. Hence, it provides a new way for the non-random CW lasers to generate widely tunable and singly-polarized pulses. In summary, we have demonstrated a graphene based 900 ps and widely-tunable pulse generation, with up to 41 dB polarization extinction for random fiber lasers. The single-pass configuration affords unprecedented widely-tunable pulses over two orders of magnitude in pulsewidth and three orders of magnitude in repetition rate, drawing from the synergistic advantages of graphene photonics and random fiber lasers. This not only inspires exploration of the full potential of graphene-based fiber devices for ultrafast photonics, but also the realization of pulsed random fiber lasers towards sensing, imaging and laser-material processing applications.

Methods
Theoretical analysis and numerical simulations. The electric field distribution of the graphene-coated D-shaped fiber (GDF), the polarization-dependent transmission, and fast pulse generation were theoretically investigated and numerically simulated. To estimate the power density in the GDF, the field distribution of the graphene-coated D-shaped fiber was simulated by COMSOL (considering the index of graphene to be determined by its conductivity) by applying ε g,eq = −σ g,i /ωΔ + iσ g,r /ωΔ and ω 2 μ 0 ε = n 2 k 0 2 ; see Supplementary S1.1. Moreover, modulated by the graphene-coated D-shaped fiber, the CW light from the random fiber laser would be transformed into highly polarized pulses with power that varies with time.
GDF fabrication and characterization. The GDF samples were fabricated by following steps. Firstly, graphene was grown by using the CVD method on Cu foil. Secondly, after removing Cu by FeCl 3 solution, a soft and flexible PMMA/graphene was prepared. Thirdly, the PMMA/graphene hybrid was covered on the polished surface of a D-shaped fiber, which was carefully fabricated with the polished depth of 58 μ m and polished length ~20 mm. Finally, the PMMA was removed by acetone vapor. The D-shaped fiber and graphene were clearly identified and characterized using optical microscopes (OPM), scanning electronic microscopes (SEM), and a Raman spectrum analyzer. More details are shown in Figs S2 and S3.
Measurement and simulation of the polarization dependent saturable absorption. A polarization controller (PC) is used to adjust and fix the input polarization. The power launched into the graphene-coated D-shaped fiber can reach 3.5 W. The power meter with resolution of 0.1 dBm was used to detect the output power at 1550 nm. The transmittance could be calculated as P B /P A . Figure S5 in Supplementary Information shows the method and the results. GDF based polarization selectivity measurement. To verify the broadband polarization selectivity of the GDF, an experimental setup was built as shown in Supplementary Fig. S6. Light from 1510 nm to ~1570 nm was launched from a tunable fiber laser (81960A, Agilent, USA), and measured by a high resolution OSA (8163B, Agilent, USA) and a power meter. The output power of the laser is fixed at 9.8 mW. A polarizer was used to control the launched polarizations.