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Abstract
We demonstrate a 1.5 GHz harmonic mode-locked erbium-doped fiber laser by incorporating gold nanofilm as a saturable absorber (SA). The high-quality gold nanofilm SA fabricated by the physical vapor deposition method possesses a high modulation depth of 12.9% and a low saturation intensity of 1.69 MW/cm2 at 1.56 µm, facilitating the generation of harmonic mode-locking. The fundamental mode-locked operation was obtained at 1564.7 nm, with a pulse duration of 586 fs and a repetition rate of 34.235 MHz. At the pump power of 610 mW, 44th-order harmonic mode-locking with a repetition rate of 1.506 GHz was achieved, which is the highest yet reported in mode-locked fiber lasers using gold nanomaterials as SAs. Moreover, the gold nanofilm-based harmonic mode-locked fiber laser shows relatively high signal-to-noise ratios, high output power, and good stability. These results highlight the advantage of the gold nanofilm-based SA in realizing high repetition rate laser sources.
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1. Introduction
Passively mode-locked fiber lasers operating at gigahertz (GHz) repetition rate have been widely applied in telecommunication, data storage, optical surgery, material processing, and optical sensing [1–7]. To achieve a GHz repetition rate mode-locked fiber laser, one method is to shorten the cavity length. In this way, a ∼ 20 GHz repetition rate has been achieved within a 5 mm linear cavity [8]. However, such a technique usually poses challenges to the gain media and fiber components. Another method is to utilize the harmonic mode-locking (HML) technique, in which equidistant multiple pulses are formed in the cavity due to the long-range interaction between them [9], which can effectively increase the repetition rates. Both saturable absorption and Kerr nonlinearity are important in generating HML [10–12]. The nonlinear polarization rotation (NPR) technique has been used for implementing HML with GHz repetition rates [13,14]. However, this polarization-sensitive technique is prone to be influenced by external perturbations, which may cause the fluctuation of repetition rate and therefore is challenging for practical applications [15,16]. The saturable absorbers (SAs) fabricated from graphene and the related two-dimensional (2D) nanomaterials with high nonlinearity have been extensively studied, which show good performance in HML generation [11,17–22]. However, the fine-controlled material fabrication and the long-term stability of 2D materials may need further improvements for practical applications [23]. Furthermore, to obtain a higher repetition rate, an SA with even lower saturation intensity and higher modulation depth would be beneficial [24,25]. Therefore, an SA with easy fabrication, high-performance saturable absorption property, and high damage threshold for constructing GHz-level HML is highly desirable.
Gold nanofilms (or metasurfaces) based fiber devices can produce unprecedented nanoscale light manipulations, which have become an emerging light-coupling platform for both the nanoscience and fiber optics communities [26–29]. In the field of ultrafast photonics, gold nanofilms have emerged as promising SAs for ultrafast fiber laser generation. Zhang et al. reported gold metasurface-based SAs for the generation of all-fiber sub-picosecond soliton mode-locked lasers operating at 1.5 and 2 µm [30]. Gu et al. directly fabricated gold metasurface SA onto an optical fiber tip using a modified self-assembly nanosphere lithography technology, and demonstrated an all-fiber picosecond soliton mode-locked laser [31]. Hua et al. proposed a gold film metafiber for manipulating the spatial mode in fiber and demonstrated the direct generation of Q-switched cylindrical vector lasers [32]. These SAs are all based on fiber tip integration, which may suffer from certain drawbacks such as poor repeatability of nanostructures due to mechanical vibrations during the fabrication onto fiber tips, and the contaminations or even damage during the fiber connections. In contrast, side-polished fiber (SPF) based configuration features a longer interaction length along the polished surface, ensuring a significant accumulated nonlinear effect from the nanomaterials and thereby enhancing light-matter interaction [33]. Moreover, the optical damage threshold of an SA can be greatly improved by employing SPF-based integration [23,34]. The gold nanofilms deposited on SPF as SAs can be advantageous for realizing high power mode-locked fiber lasers. Very recently, we demonstrated high-performance saturable absorption property and high optical damage threshold of an all-fiber gold nanofilm SA and achieved bidirectional mode-locked fiber laser operating at 1.5 µm [35]. Compared to the integration with fiber tips, the SPF-based configuration has the advantage of ease and precise control in fabrication, high damage threshold, and high stability. However, HML based on such all-fiber gold nanofilm SAs has not been developed.
In this work, we demonstrate the fabrication of an all-fiber gold nanofilm-based SA, which was subsequently used for achieving harmonic mode-locked erbium-doped fiber lasers with a GHz-level repetition rate. The SA was fabricated by depositing a thin layer of gold onto an SPF using the physical vapor deposition (PVD) method. The smooth surface morphology of the gold nanofilm contributes to a high-performance saturable absorption of the fabricated SA. The SA exhibits a high modulation depth of 12.9% and a low saturation intensity of 1.69 MW/cm2, which are beneficial for stable HML generation. With the increase of pump power, HMLs were observed from the 7th to 44th-orders, centered around 1565 nm, accompanied by a notable repetition rate reaching up to 1.506 GHz. Besides, the harmonic mode-locked laser shows high signal-to-noise ratios (SNRs) and long-term stability. The results indicate that gold nanofilm could be a promising SA for realizing GHz-harmonic mode-locked fiber lasers.
2. Experiments and results
The all-fiber gold nanofilm SA was fabricated by depositing gold nanofilm on an SPF. The SPF was prepared from a piece of single-mode fiber (SMF, Corning, SMF28e) by the wheel side-polishing technique [36]. The length of the polishing surface is about 15 mm. Figure 1(a) shows the cross-section view of the optical microscopy image of the side-polished region, the distance between the fiber core and the polished surface is ∼6.4 µm. The gold nanofilm was deposited on the side-polished fiber via the PVD method, as shown in Fig. 1(b). The nanofilm consists of metallic gold and copper bilayers. Specifically, a 1.5 nm thick copper layer was first deposited on the polished surface of the SPF with a deposition rate of 0.9 Å/s as the seed layer. Then, an 8 nm thick gold film was grown on the copper layer with a deposition rate of 0.5 Å/s. The copper seed layer forms energetically favorable nucleation sites for the incoming gold atoms, facilitating a smoother surface morphology of the film [37–39]. The surface morphology of the gold nanofilm was characterized by atomic force microscopy (AFM), as shown in Fig. 1(c). Figures 1(d) and 1(e) show the typical surface height profile along the x-axis and the histogram of the surface-height of the film, respectively. The histogram shows a narrow and symmetric distribution, with a peak-to-valley height of only ∼2.2 nm. The root-mean-square (RMS) roughness of the film is 0.34 nm. The thicknesses of the copper and gold layers were characterized by AFM, as shown in Figs. 1(f)-1(i). The geometrical thickness of the copper seed layer and gold nanofilm are measured to be 1.58 ± 0.13 nm and 9.62 ± 0.18 nm, respectively. These results indicate the high quality of the prepared gold nanofilm, which contributes to the high-performance optical properties of the fabricated SA.
Fig. 1. (a) Cross-section view of the optical microscopy image of the prepared SPF. (b) Schematic diagram of the evaporation of gold nanofilm onto SPF. (c) 3D AFM image of the gold nanofilm. (d) Typical surface height along the x-axis and (e) histogram of the surface-height of the gold nanofilm. (f) Cross-sectional AFM image of the copper seed layer, and (g) the corresponding surface profile of step height at the film boundary. (h) Cross-sectional AFM image of the gold/copper nanofilm, and (i) the corresponding surface profile of step height at the film boundary.
Linear loss of the SA has an important influence on pulse dynamics in the fiber lasers [40]. Firstly, the linear loss of the fabricated device was measured with a 1570 nm fiber laser. The prepared SPF initially showed an insertion loss of 0.9 dB. After the depositing of the gold nanofilm, the all-fiber SA device showed an insertion loss of ∼5.5 dB. Then, the linear absorption spectra of the gold nanofilm-SPF SA (GFSA) were measured by using a super-continuum light source. As can be seen in Fig. 2(a), the GFSA exhibits broadband absorption ranging from 600 nm to 2400 nm, which originates from the localized surface plasmon resonance (LSPR) due to the presence of gold grains within the gold nanofilm [41–43]. The absorption peak near 1.5 µm contributes to strong light-matter interaction and greatly enhanced saturable absorption effect. Furthermore, the saturable absorption property of the GFSA was measured with the balanced twin-detector method using a 1563 nm (repetition rate: 50 MHz and pulse duration: 558 fs) femtosecond fiber laser as incident light. The measured transmittance as a function of the incident power is plotted in Fig. 2(b) with the dark squares, and the red curve corresponds to a fitting with a typical saturable absorption model [44–46]. The modulation depth (ΔT) is determined to be 12.9%, and the saturation intensity (Isat) is 1.69 MW/cm2. The SA with high modulation depth provides a wider operating range and lower threshold of the pump for mode-locking [47]. Besides, the low saturation intensity of the SA also contributes to a low threshold of mode-locking [48] and facilitates the HML generation [24]. Compared with the colloidal gold nanomaterials [49–51], our PVD-fabricated gold nanofilm SA shows more uniform morphology, repeatability, easy operations, and excellent saturable absorption properties. Furthermore, the optical damage threshold of the gold nanofilm SA was examined using a high power 1563 nm femtosecond fiber laser (repetition rate: 50 MHz, pulse duration: 78 fs, average power: 322 mW). No optical damage of the gold nanofilm SA occurred, indicating the optical damage threshold of the GFSA should be higher than 101 GW/cm2. This indicates that the gold nanofilm SA holds great promise in generating stable harmonic mode-locked fiber lasers.
Fig. 2. (a) Linear absorption spectra of the GFSA. (b) Measured (dark squares) and fitted (red curve) nonlinear transmittance of the GFSA.
The schematic of the gold nanofilm SA-based erbium-doped fiber laser is shown in Fig. 3. A 0.5 m long erbium-doped fiber (EDF, Liekki, Er80-8/125) serves as the gain medium. The group-velocity dispersion (GVD) of the gain fiber is −20 ps2/km at 1560 nm. The gain fiber is pumped by a 980 nm laser diode (LD) via a 980/1560 nm wavelength division multiplexing (WDM) coupler. An optical isolator (ISO) is used in the cavity to ensure unidirectional light propagation. The all-fiber GFSA in the cavity acts as an SA, which is critical for the formation of mode-locked pulses. A polarization controller (PC) is used to optimize the polarization state, which is beneficial for achieving the mode-locking operation. A 10 dB optical coupler (OC) is adopted to extract 10% of the laser for characterization. The fiber tails of all components are standard SMF with a GVD of −22 ps2/km at 1560 nm. The total length of the ring cavity is ∼6 m and the net GVD is −0.13 ps2. The output signal is measured by an optical spectrum analyzer (Yokogawa AQ6370D), a 4 GHz bandwidth oscilloscope (Keysight DSOS404A), a 12.5 GHz bandwidth photodetector (Newport 818-BB-51F), a scanning autocorrelator (Avesta, AA20DD), and a radio frequency (RF) spectrum analyzer (Agilent, E4405B).
Fig. 3. Schematic of the erbium-doped fiber laser cavity. WDM: wavelength-division multiplexing, EDF: erbium-doped fiber, ISO: isolator, PC: polarization controller, OC: optical coupler, and GFSA: gold nanofilm-SPF SA.
The cavity shows a self-started mode-locking threshold of 60 mW. Figure 4 shows the characterization of the fundamental mode-locked operation. The fundamental mode-locked optical spectrum is centered at 1564.7 nm, with a 3-dB bandwidth of 4.35 nm, as shown in Fig. 4(a). The Kelly sidebands can be observed on the spectrum, indicating that the mode-locked laser is operated in a traditional soliton regime. As shown in Fig. 4(b), the time interval between two adjacent pulses is about 29.2 ns, corresponding to the cavity length of 6 m, which indicates the pulse is operated at fundamental mode-locking (FML). The autocorrelation trace of the fundamental mode-locked pulse is shown in Fig. 4(c). The pulse duration is fitted (Sech2) to be 586 fs. The corresponding RF spectrum measured with 1 kHz resolution bandwidth (RBW) is displayed in Fig. 4(d), with a fundamental repetition rate of 34.235 MHz, which coincided with the cavity roundtrip time. The SNR is measured to be 41 dB. The flat RF spectrum with a 1.5 GHz span (RBW: 1 kHz) indicates low fluctuations of the mode-locked operation. The fundamental mode-locked operation could be maintained in the pump range of 60 to 90 mW.
Fig. 4. The characteristics of the fundamental mode-locked operation: (a) optical spectra, (b) oscilloscope pulse trains, (c) autocorrelation trace, and (d) RF spectra, inset: RF spectrum with a 1.5 GHz span.
As the pump power exceeded 90 mW, multiple pulses occurred owing to the peak power limitation effect and the soliton area theorem [10]. The ease in generating multiple pulses is also attributed to the low saturation intensity of the gold nanofilm SA [47,52]. In the experiment, multiple-pulse (2-6 pulses) operations instead of stable HMLs were observed in the pump range from 90 to 140 mW. Figure 5(a) shows the pulse trains of triple-pulse operation at the pump power of 100 mW. Typically, three pulses were generated in one roundtrip with short time intervals of ∼2 ns as shown in the top panel of Fig. 5(a). By slightly adjusting the polarization state of the PC, 3rd-order quasi-HML can be achieved, as shown in the bottom panel of Fig. 5(a). At this state, the energy of the three pulses is nearly the same. The position of the three solitons is relatively fixed, while the time intervals between the adjacent pulses are unequal, which are 7.69, 10.8, and 10.71 ns, respectively. Figure 5(b) shows the corresponding RF spectrum of the 3rd-order quasi-HML, the spectral modulation is the result of unequal time intervals between the solitons [53]. The optical spectrum is broadened compared to the FML, with the observation of a continuous-wave (CW) component, as shown in the black curve of Fig. 5(c).
Fig. 5. (a) Typical pulse trains of triple-pulse operation. (b) RF spectra of 3rd-order quasi-HML. (c) Optical spectra of 3rd-order quasi-HML (black) and 7th-order HML (red). (d) Pulse trains of 7th-order HML. (e) RF spectra of 7th-order HML, inset: RF spectrum with a 1.5 GHz span. (f) Autocorrelation trace of 7th-order HML.
When the pump power is increased to 150 mW, stable 7th-order HML operation could be realized. The formation of the HML results from the long-range interactions between pulses by means of the acoustic-wave effect, the dispersive wave effect, or the gain depletion and recovery mechanism [9,44,45,54]. Figure 5(d) shows the pulse trains of 7th-order HML with time intervals of 4.17 ns. The repetition rate of the 7th-order HML is 239.647 MHz, with a high SNR of 59.8 dB, as shown in Fig. 5(e). The inset shows the corresponding RF spectrum with a 1.5 GHz span. The supermode suppression ratio (SMSR), defined as the power difference between the principal mode and the second most dominant side mode, is measured to be 42.8 dB. The flatness of the RF spectrum and the low noise level indicate the stability of the harmonic mode-locked operation. The generated harmonic pulse duration is 597 fs with a Sech2 fitting, as shown in Fig. 5(f).
Further increasing the pump power while keeping the PC unadjusted, the order of the HML increased accordingly. Figure 6(a) shows the recorded pulse trains of fundamental mode-locking and the 10th, 16th, 25th, 35th, and 44th-order HML operations. At each harmonic order, the pulses are equally spaced with identical peak intensity and pulse width, indicating the stability of the operation. The corresponding RF spectra are shown in Fig. 6(b). With an increase in the pump power, the repetition rate increased to integral multiples of the fundamental repetition rate. Very slight frequency sidebands can be observed between the adjacent main RF peaks, indicating the low supermode noise of the harmonic mode-locked lasers, which might be attributed to the high modulation depth and low saturation intensity of the gold nanofilm SA. Significantly, as the pump power is increased to 610 mW, 44th-order HML could be realized, with a corresponding repetition frequency up to 1.506354 GHz. The SNR and SMSR are 37.4 dB and 28.5 dB, respectively. For passively harmonic mode-locked fiber lasers, variation of pulse repetition rate is typically obtained by changing pump power. Although a wide range of harmonic order tuning can also be achieved through polarization control under a fixed pump power in an NPR-based mode-locked fiber laser [55], in our case, only a slight adjustment of HML order can be realized by adjusting the polarization with a fixed pump power. A wide range adjustment of the PC, however, would result in instability of HML, which may switch to multi-pulse mode-locking, FML, or CW operations.
Fig. 6. Temporal profiles and RF spectra evolution with pump power. (a) Pulse trains and (b) RF spectra of fundamental mode-locking and the 10th, 16th, 25th, 35th, and 44th-order HML operations.
The relationship between harmonic order and pump power is shown in Fig. 7(a), where the harmonic order increases as the pump power increases. Correspondingly, the repetition rate increases from 34.235 MHz to 1.506354 GHz with the increase in pump power. This results in a pump harmonic efficiency of 2.69 MHz/mW. Figure 7(b) presents the dependence of the SNR and SMSR on the harmonic order. They both show an initial increase and then gradually saturated at ∼40 dB and ∼30 dB, respectively. This behavior is attributed to the competition between the harmonic and the fundamental mode-locking mechanisms [45,56]. As shown in Fig. 7(c), the output power increased linearly with pump power, resulting in a slope efficiency of 4.1%. Owing to the high damage optical threshold and stability of the gold nanofilm SA [34], the HML can operate stably with an output power of 23.34 mW. For high-order HML, a single pulse splits into multiple pulses under high pump powers [9,57–59]. The single pulse energy decreases with increasing harmonic order as shown in orange squares in Fig. 7(c). The single pulse energy is 27.5 pJ for the fundamental mode-locking, which decreases to 15.5 pJ for the 44th-order HML. Stable operation with such small pulse energies is enabled by the low saturation intensity of the gold nanofilm SA, which is the key feature enabling high repetition rate operation [24]. Figure 7(d) illustrates the variation of pulse duration as a function of the harmonic order. The pulse duration gradually increases from 586 fs to 623 fs, which is in accordance with the evolution of the single pulse energy.
Fig. 7. (a) The dependence of the harmonic order (blue dot) and repetition rate (orange box) on the pump power. (b) The dependence of the SNR (black) and SMSR (red) on the harmonic order. (c) Output power (blue) and single pulse energy (orange) as a function of pump power. (d) Pulse duration as a function of the harmonic order.
The long-term stability of the HMLs is of great significance in practical applications. The frequency and SMSR stabilities of the gold nanofilm-based harmonic mode-locked fiber laser were monitored for 1 hour. Figure 8 shows the frequency stability and SMSR stability of the 10th and 40th-order HML. Harmonic mode-locking operated stably during the monitored time. The fluctuations of both repetition rate and SMSR were small, indicating the good long-term stability of the gold nanofilm-based HML. Table 1 summarizes the nonlinear saturable absorption properties of various 2D and gold nanomaterials SAs and the related HML performances. The HML based on the MoSe2 SA realized the highest repetition rate with 3.27 GHz. However, our proposed all-fiber gold nanofilm SA exhibits a high optical damage threshold, high modulation depth, and low saturation intensity. Besides, compared with other HMLs operated at the same order, the laser with gold nanofilm SA exhibits a relatively high output power and short pulse duration. Significantly, the repetition rate of 1.506 GHz is the highest among the mode-locked fiber lasers using gold nanomaterials as SAs, to the best of our knowledge. We believe that further optimization of the laser cavity (such as adopting all-PM fiber, dispersion and nonlinearity management) will result in an improvement in the performance of HML based on the all-fiber gold nanofilm SA. It is worth noting that the proposed GFSA can also realize stable HML at 2 µm wavelength, owing to its broadband optical response and high-performance saturable absorption property. These findings suggest that the gold nanofilm could be a promising broadband SA for realizing high repetition rate harmonic mode-locked fiber lasers.
Fig. 8. Operation stability of the 10th and 40th-order HML. (a) RF spectra, and (b) repetition rate and SMSR of 10th-order HML as a function of monitored time. (c) RF spectra, and (d) repetition rate and SMSR of 40th-order HML as a function of monitored time.
Table 1. Performance comparison of different SAs and the related harmonic mode-locked fiber lasers
3. Discussion
Note that the saturable absorption property of an SPF-based SA can be tuned by varying the SPF geometry and film thickness [64–69]. Although the GFSA was fabricated with the same procedure in our previous article Ref. [35], distinct saturable absorption properties were produced. According to the two-energy-level saturable absorption model, the modulation depth and saturation intensity are associated with linear absorption [70]. The variations in the film thickness deposited on the SPF lead to differences in linear absorption arising from LSPR, and therefore the disparity in saturable absorption. Moreover, the interaction strength between the light field and the nanofilm can also be controlled by varying the polished length and polished depth. Therefore, the different parameter designs of SPF and film thickness result in the diversity in saturable absorption properties. However, the SA in our previous article of Ref. [35] did not work effectively for the HML operations. The too high modulation depth (26% in Ref. [35]) could lead to the generation of Q-switched mode-locking (QSML) or noise-like pulse (NLP) at elevated pump powers, which would disrupt the HML operation. To sustain stable HML and achieve a high repetition rate, the modulation depth should be optimized. Therefore, a thinner thickness of gold nanofilm with lower absorption was fabricated to obtain a reduced modulation depth. Consequently, the GFSA with a modulation depth of 12.9% and a saturation intensity of 1.69 MW/cm2 was implemented for a stable HML, which contributed to a notable repetition rate reaching up to 1.506 GHz. Overall, the impact of the SPF geometry and film thickness on the saturable absorption properties of an SA and their influence on different pulse regimes need a comprehensive investigation.
Harmonic mode-locking generation in anomalous dispersion cavities has been excessively studied and achieved impressive goals. In the net normal dispersion cavity, numerical research by Komarov et al. suggests that HML operation is available in the dissipative soliton resonance (DSR) regime [71], providing a method to obtain pulses with both high energy and high repetition rates. HML based on the NPR technique or real SAs such as semiconductor saturable absorber mirror (SESAM) and carbon nanotube (CNT) have been successfully demonstrated in cavities with net normal dispersion [72–75]. However, the repetition rates of HML in cavities with net normal dispersion were often restricted to tens or hundreds of megahertz. We believe that our proposed gold nanofilm SA, with its high modulation depth, low saturation intensity and high optical damage threshold, may also be effective for generating HML with optimized cavity parameters in net normal dispersion cavities, while systematical experimental studies need to be implemented in future work.
4. Conclusion
To summarize, we have fabricated an all-fiber gold-nanofilm-based SA with high stability and good saturable absorption properties. A high modulation depth of 12.9% and a low saturation intensity of 1.69 MW/cm2 were achieved, which facilitated the establishment of HML. With the gold nanofilm SA incorporated in an erbium-doped fiber laser, the fundamental mode-locked operation was achieved at 1564.7 nm, with a pulse duration of 586 fs and a repetition rate of 34.235 MHz. As the pump power gradually increased, stable 7th to 44th-order HML can be obtained. At the pump of 610 mW, an HML with a repetition rate as high as 1.506 GHz was achieved. The harmonic mode-locked operations exhibited relatively high SNR and good long-term stability. These results highlight the favorable nonlinear optical properties of the gold nanofilm, indicating promising potential for applications in high repetition rate lasers.
Funding
National Key Research and Development Program of China (2020YFB1805800); National Natural Science Foundation of China (62090063,62075082,U20A20210,61827821,U22A2085,62235014,62205121); the Opened Fund of the State Key Laboratory of Integrated Optoelectronics.
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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