1 Introduction

The development of optical devices based on optical fiber has been very rapid over the last few decades. It started with the optical amplifier using an erbium-doped fiber amplifier (EDFA) (Becker et al. 1999; Islam 2002; Zyskind et al. 1997) which supports the development of the existing optical network. On top of this, there has been interest in the studies of fiber lasers (Jarman 1996; Sirleto and Ferrara 2020) and also the generation of multiwavelength outputs (Ahmad et al. 2008; Han et al. 2005; Harun et al. 2006). Optical fiber is also useful as a medium for sensing external parameters such as refractive index (Bilro et al. 2011; Lim et al. 2012; Villatoro and Monzón-Hernández 2006). The current main interest is in the area of ultrashort pulse lasers which can find applications in optical sensing, biomedical applications, and optical communication (Fermann and Hartl 2013; Keller 2003; Meng et al. 2014). Generally, in short pulses, either the Q-switching or mode-locking approaches will be undertaken. Q-switching has the advantage of higher pulse energy but with broader durations in the region of microseconds. For a shorter duration of picoseconds to femtoseconds, the mode-locking technique will be the preferred choice.

The mode-locked pulses can be obtained either by passive or active means (Figueroa 1981; Ippen 1994). In the early days, active mode-locking is generally used in solid-state lasers and required precise control over the optical crystal to generate the ultra-short pulses. This approach has been superseded using passive elements in an optical fiber laser system. A saturable absorber (SA) is commonly implemented in the optical cavity to initiate mode-locked pulses (Fodil et al. 2016; Koo et al. 2016; Liu et al. 2014). Early reports are based on semiconductor saturable absorber mirrors (SESAM) which are made from semiconductor technology. The only disadvantages of SESAM are their complicated fabrication, cost-ineffectiveness and at times may not be able to withstand high circulating powers (Keller 2003; Keller et al. 1992, 1996).

As an alternative to SESAMs, there is a need to explore other SAs such as two-dimensional (2D) materials. There have been reports of using graphene (Ahmad et al. 2018; Luo et al. 2010; Peng and Yan 2021), single-walled carbon nanotube (Ahmed et al. 2014; Ismail et al. 2012), topological insulator (Tang et al. 2013), bismuthene (Guo et al. 2018), and black phosphorus (Razak et al. 2017; Ren et al. 2018). Fabrication of SAs using these 2D materials can be done using numerous methods such as embedding the material into a polymer host to form a thin film or by depositing these materials directly onto a tapered (Liu et al. 2014; Rosol et al. 2017) or D-shaped fibers (Duan et al. 2016; Nizamani et al. 2020). However, both fabrication methods require precise control in terms of the molecular/atomic layer numbers. Moreover, these materials themselves are easily oxidized and thus have a performance degradation with time (Wu et al. 2019). While real SAs make use of various material that offer non-linear optical absorption, artificial SAs generate laser pulses by manipulating the non-linear effect. Thus, artificial SAs have the advantage of having higher damage threshold as it can withstand high propagating power compared to the material based SAs. Thus, to generate high-power mode-locked pulses, an artificial SA is preferable. A high-performance SA is truly needed to improve the pulsed laser characteristic in terms of longer stability, shorter pulse width, and higher repetition rate.

Thus, graded index multimode fiber (GIMF) has gained a lot of attention among researchers to utilize it as an SA due to non-linear multimode interference (NL-MMI) properties, nonlinear optical properties, self-phase modulation (SPM) and cross-phase modulation (XPM). The simple geometry of single-mode fiber-graded index multimode fiber -single-mode fiber (SIMF–GIMF–SIMF) can act as an SA for generating mode-locked pulses demonstrated by Nazemosadat and Mafi (2013). In 2017, Wang et al. (2017) and Li et al. (2017) demonstrated ultra-short pulse laser based on the NL-MMI effect of the GIMF using erbium-doped (EDFL) cavity and thulium-doped fiber laser (TDFL) cavities respectively. There is also a report by Yang et al. (2018a) producing mode-locked pulses using SMF–GIMF–SMF with inner micro-cavity in erbium-doped fiber laser (EDFL). Also in 2018, Wang et al. (2018) provides an interesting demonstration of the tuneability of mode-locked pulses by the SMF–GIMF–SIMF SA by stretching the GIMF structure. There have been other reports using different combinations of SMF, GIMF, and SIMF (Pan et al. 2021; Tang et al. 2005; Yang et al. 2018a), but their output powers are generally low in the mW range. It will be interesting and important to investigate mode-locked pulses with higher output power.

For obtaining high-power mode-locked pulses in the 1.5 μm region, erbium ytterbium-doped fibers (EYDFs) are preferred instead of erbium-doped fibers (EDFs). This is due to the low absorption cross-section of EDF which is 2.1 × 10− 25 m2 at 980 nm (Ohishi et al. 1997). This will also promote a quenching effect if the EDF is pumped too high. Therefore, Ytterbium ions are co-doped with erbium in the silica host as ytterbium has a larger absorption cross section which is around 1.6 × 10− 24 m2 at a pumping wavelength of 915 nm (Ohishi et al. 1997). The pump energy absorbed by the ytterbium ions will be transferred non-radiatively to erbium ions which then produce lasing at the 1.5 μm region (Townsend et al. 1991). Thus, double-clad EYDFs (DC-EDYFs) were investigated extensively due to their excellent power scalability to obtain high power mode-locked pulses.

In this work, we demonstrate a GIMF–SIMF–GIMF structure as SA for generating mode-locked pulses in a DC-EYDF cavity. The use of the DC-EYDF in this work allows for power scaling of the fiber laser, whereby the gain medium can be cladding-pumped using high-power multimode laser diodes. The design of the SA is similar to that of Wu et al. (2019), however, their mode-locked pulses only generate a low output power of 10.75 mW due to the use of a single-mode erbium-doped fiber (EDF). Their design will have limitations for actual application due to the limited output power. In most industrial applications, high peak power is normally required in the mode-locked fiber laser.

As demonstrated in this report, the average output power is 322 mW with a peak power intensity of 15.4 GW/cm2, which is several times better than the early ones. Ultra-short pulses with a pulse duration of 2.32 ps and a repetition rate of 14.1 MHz were generated. The center wavelength of the mode-locked pulses was 1543 nm with signal to noise ratio (SNR) of 54.5 dB. This is the first report to the authors’ knowledge that GIMF–SIMF–GIMF-based SA in the EYDF cavity is capable of generating high-power mode-locked pulses.

2 Fabrication and characterization

Fabrication of the GIMF–SIMF–GIMF SA involves the use of a fiber fusion splicer. The structure of the SA is almost the same as Wu et al. (2019). The first GIMF(GIF625) was from Thorlabs having core and cladding diameters of 62.5 and 125 μm respectively. The second GIMF was also from Thorlabs (GIF50C) with a core and cladding diameter of 50 and 125 μm. The length of both GIMFs used to construct this SA was 20 cm and both were spliced with a piece of 395 μm SIMF in length. The SIMF has a core and cladding diameter of 105 and 125 μm respectively. The SA structure with its microscopic image was shown in Fig. 1.

Fig. 1
figure 1

Schematic of GIMF–SIMF–GIMF SA structure and its microscopic image capture

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The basic principle of SA also has been explained clearly by Wu et al. (2019). The phenomena of self-phase (SPM) and cross-phase modulation (XPM) can take place throughout the SA due to the construction of GIMF–SIMF–GIMF. From the reference (Wu et al. 2019), when the signal from the single-mode fiber travels into the GIMF, it will cause nonlinear multimode interference (NL-MMI). This will result in a periodic interference pattern formed throughout the fiber (Li et al. 2017; Nazemosadat and Mafi 2013; Wang et al. 2017). This is loosely called self-focusing or self-imaging. The main objective of this work, as explained earlier, is to use this device to generate high-power mode-locked pulses. One of the important parameters of an SA is to determine the modulation depth, saturation intensity, and also non-saturable loss. The parameters that affect the nonlinear properties of GIMF-based SAs are the length, the relative nonlinear coefficient γ, and the total number of propagating modes in the GIMF. As such, the modulation depth of these SAs can be optimized by changing the parameters of the GIMF used, such as the length and its properties (Nazemosadat and Mafi 2013).

To characterize the non-linear optical characteristic of the SA, the twin-balance detector technique was utilized as shown in Fig. 2.

Fig. 2
figure 2

Modulation depth experimental setup

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A mode-locked pulsed laser source from Menlo Systems with a pulse width of 100 fs, a repetition rate of 100 MHz, and a center wavelength of 1560 nm was used. The mode-locked pulsed laser was then connected to the variable optical attenuator (VOA). The output signal from the VOA was split equally by using a 3-dB coupler. The first output end was connected to a single-mode fiber (SMF) as a reference while the second output was connected to the SA. The output power readings from the reference SMF and the SA were measured simultaneously using two optical power meters. The attenuation of VOA was then increased from 0 to 30 dB and the output power measurement was measured for the interval at 1 dB attenuation. The data was then plotted as shown in Fig. 3.

Fig. 3
figure 3

Plot of non-linear absorption against pump power intensity

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The data obtained from the experiment was fitted by using Eq. 1 as below:

$$a\left(I\right)=\frac{{a}_{s}}{1+I/{I}_{sat}}+{a}_{ns}$$
(1)

where α, αs, I, αns, and Isat are absorption, saturable absorption, input intensity, non-saturable loss, and saturation intensity, respectively. Based on the plot in Fig. 3, the modulation depth of the SA was around 1.06% and the saturation intensity was 8.3 MW/cm2. The low modulation depth obtained in this work is comparable to other GIMF-based SAs (Wang et al. 2017; Yang et al. 2018a) and also to other 2D materials such as WS2 (Yan et al. 2015) and also Bi2Te3 (Lin et al. 2015). It is also worth noting that a modulation depth as low as 0.5% would still be suitable to generate mode-locked pulses, as discussed in Kartner et al. (1998). Additionally, Jeon et al. (2015) reported that an optical cavity with small net anomalous dispersion was found to be readily mode-locked using SA with small modulation depth.

The linear loss spectrum of the SA from 1500 to 1600 nm was obtained by using an amplified spontaneous emission (ASE) source shown in Fig. 4. The absorption of the SA at 1543 nm was measured to be 23.1%. The polarization-dependent loss (PDL) of SA was measured as 0.96 dB, which is not significant in contributing to the mode-locking (Jung et al. 2013).

Fig. 4
figure 4

Linear absorption spectrum of the SA

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3 Experimental setup

The erbium–ytterbium doped fiber laser (EYDFL) used consists of a ring laser cavity schematically shown in Fig. 5. To achieve ultrashort pulses, the GIMF–SIMF–GIMF SA was inserted into the EYDFL cavity to produce ultrashort pulses. A pair of 915 nm laser diodes with a maximum rated power of 9 W each was used to pump the gain medium through a (2 + 1) × 1 pump combiner. It is noted that in this work, the LDs are only driven to half of their rated power as a safety precaution. This is to reduce overheating, which is to avoid damage to the LDs. The output fiber of the pump combiner was a double-clad fiber with an 8 µm core and 125 µm cladding.

Fig. 5
figure 5

Experimental setup of the EYDFL cavity

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DC-EYDF has a core and cladding diameter of 10 and 125 μm respectively and is used as the active fiber. Although the absorption coefficient is lower at 915 nm compared to 980 nm, the absorption spectrum at around 915 nm is broader compared to the narrow peak at 980 nm, which eliminates the need for wavelength stabilization of the LDs. Furthermore, pumping off-peak of the Yb3+ absorption allows the absorption distribution over a longer fiber length and helps to suppress the 1 μm parasitic effects. This may be suitable for higher power scaling of EYDF lasers in the 1.5 μm region (Creeden et al. 2016). To construct the DC-EYDF ring cavity, the output of the gain medium was connected to a 70:30 single-mode fiber (SMF-28) coupler. Due to the different sizes and structures between all those fibers, there would be some splicing loss, especially between the pump combiners and the input part of the gain medium. There was also some splicing loss between the output part of the gain medium and the input port of the coupler. The 30% port of the coupler was tapped out for optical analysis. In the meantime, the polarization-independent isolator (PI-ISO) was connected to the coupler’s 70% port. This was to ensure the signal only propagates in one direction inside the cavity. The output of the PI-ISO was then connected to a polarization controller (PC) to adjust the polarization state of the signal. Lastly, the output of the PC was connected to the signal port of the pump combiners.

A length of 10.7 m of single-mode fibers (SMF-28) and 4 m long DC-EYDF make up the cavity in Fig. 5. The total length of this cavity is 14.7 m. The group velocity dispersion (GVD) can be calculated using the equation GVD = λ2Dλ/2πc where c is the speed of light, λ is the center wavelength and Dλ is the material dispersion. The value of Dλ for the gain medium is −16.65 ps nm− 1 km− 1. The value of Dλ for the SMF-28 is 15.78 psnm− 1 km− 1. The calculated GVD for the DC-EYDF is 0.021 ps2m− 1 while for the SMF-28 the value is -0.0199 ps2m− 1. Total net cavity dispersion can be obtained by utilizing the equation, GVDcavity=LEYDFGVDEYDF+ LSMF−28SGVDSMF−28 S. thus, the calculated value of the total net cavity dispersion is -0.129 ps2 which indicated mode-locked operation is in the anomalous dispersion regime.

4 Results and discussion

Initially, the SA was not included in the DC-EYDF laser cavity. Continuous-wave lasing starts to occur at the pump power of 2 W without the insertion of any saturable absorber. The laser only operates in a continuous wave (CW) state even though pump power and beam polarization states were adjusted. This rules out the possibility of self-mode locking due to nonlinear polarization rotation. Upon inserting the SA into the optical cavity, optical soliton was observed using OSA with pump power and PC being adjusted. The mode-locked pulsed laser starts at a high pump power level. To measure the power threshold of the mode-locked pulses, pump power was increased and then decreased slowly until the appearance of the pulses. The observed cavity’s threshold pump power for the generation of mode-locked pulses was 2.4 W. Mode-locked pulses were obtained at higher pump power due to the high cavity loss and high saturation intensity of the SA. With a high saturation intensity, it can be said that the mode-locking threshold would be high (Li et al. 2019; Yang et al. 2018b).

Figure 6 shows the optical characteristic of mode-locked pulses upon inserting the SIMF–GIMF–SIMF saturable absorber in the laser cavity at an average output power of 72.3 mW when pumped at 2.4 W. The center wavelength of the optical spectrum measured was 1543 nm with a 3dB bandwidth of 1.2 nm with the SA. The mode-locked laser experienced a blueshift from 1550 nm without the SA to compensate for the additional loss induced by the SA. Kelly’s sideband’s existence in the optical spectrum indicates that the mode-locked pulsed laser was operating in an anomalous dispersion region. This is shown in Fig. 6a.

An oscilloscope pulse train is shown in Fig. 6b with a fundamental frequency of 14.1 MHz. Figure 6c shows the autocorrelation (AC) pulse trace of the mode-locked with a full width at half maximum (FWHM) of 3.58 ps. By taking the convolution factor of the sech2 function (0.648), the actual pulse width is 2.32 ps. The autocorrelation trace observed shows slight bumps on both sides of the pulse due to the noise floor of the detection system (Li et al. 2012). For the case of a bound soliton, the side peaks have an intensity of about half of the central peak and they are normally very distinct, which is not in this case. In the AC trace given in Fig. 6c, the intensities of the side bumps were insignificant. Thus, this excludes the possibility of bound soliton operation of the mode-locked pulses (Luo et al. 2017). The time-bandwidth product (TBP) was calculated using the equation of TBP= (ΔλΔτ)c/λ2 whereby c is the speed of light, Δτ is the minimum pulse width, λ is the center wavelength, and Δλ is the 3-dB bandwidth. The value obtained is 0.35 which is slightly higher than the theoretical value of 0.315, this indicates that the pulses are slightly chirped. Figure 6d shows a narrow peak obtained at a fundamental frequency of 14.1 MHz with signal to noise ratio (SNR) of 54.5 dB. This indicates that mode-locked pulses are very stable. The inset in Fig. 6d shows the radio frequency spectrum with a wide frequency span of 250 MHz at a pump power of 2.4 W. For Fig. 6e, the radio frequency spectrum was measured at pump power of 8 W with a wide frequency span of 250 MHz.

Fig. 6
figure 6

Optical characteristics of mode-locked pulses showing, a the optical spectrum with and without the SA, b the oscilloscope pulse train, c the autocorrelation trace, d the RF spectrum with the inset showing wide range spectrum at 2.4 W pump power and e the RF spectrum with inset showing wide range spectrum at 8 W pump power

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Figure 7 shows the graph of output power against pump power. A linear plot was obtained with a slope efficiency of 4.37%. The pump power threshold for mode-locking occurs at 2.4 W with an average output power of 72.3 mW. The maximum average output power that can be reached is 322 mW when 8 W was pumped into the cavity without destabilizing the mode-locked pulses. Maximum average output power, pulse energy, and peak power obtained from the mode-locked pulses generated were 322 mW, 22.8 nJ, and 9.84 kW respectively. By taking into consideration the core diameter of a single-mode fiber of 9 µm, the calculated peak power intensity is 15.4 GW/cm2.

Fig. 7
figure 7

Graph of output power against pump power

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To investigate the stability of mode-locked pulses generated, the RF spectrum of mode-locked pulses was measured at the minimum pump power of 2.4 W and maximum pump power of 8 W. The RF spectrum was observed for 50 minutes. Figure 8 shows the RF spectrum of mode-locked pulses measured every 10 min. Both Fig. 8a, b are RF spectrum at a pump power of 2.4 W and 8 W respectively. The standard deviation (STD) is calculated by considering the SNRs from the RF spectrum at 10, 20, 30, 40 and 50 min. The STD is then obtained using the standard deviation function in Microsoft Excel by taking the values at 10, 20, 30, 40 and 50 min. For the case of 2.4 W, the SNR together with the STD obtained is 54.5 ± 1.6 dB as given in Fig. 8a. For 8W, the SNR and the STD is 54.5 ± 1.9 dB and is given in Fig. 8b. Since there is only a slight change in the SNR values, the mode-locked pulses are considered stable.

Fig. 8
figure 8

RF spectrum for mode-locked pulses measured for 50 min at intervals of 10, 20, 30, 40 and 50 at pump power of a 2.4 W with SNR value of 54.5 ± 1.6 dB, and (b) 8 W with SNR value of 54.5 ± 1.9 dB

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Figure 9 shows the optical spectrum of the mode-locked pulses obtained by the GIMF–SIMF–GIMF SA with pump powers of 2.4 W and 8 W. The existence of Kelly’s sidebands has been maintained throughout increasing pump power. When the pump power is increased, the center wavelength of the spectrum remains constant at 1543 nm. The intensity of the spectrum at 8 W pump power is higher than at 2.4 W pump power. As shown in the figure, Kelly’s sidebands, 1st, 2nd, and 3rd pairs are present at both pump power. This indicates the absence of the bound soliton state.

Fig. 9
figure 9

: Optical spectrum at pump power of 2.4 and 8 W

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Table 1 shows the comparison of this work with others using different structures of GIMF-based SAs in the 1.5-micron region. In this work, the output signal has a shorter center wavelength compared to others. The fundamental frequency generated in this work is lower than Wu et al. (2019) and Yang et al. (2018a), except Wang et al. (2017). The value of the fundamental frequency depends on the total cavity length which consists of the lengths of the gain medium, SMF, and SA itself. As our SA has a relatively lowest modulation depth compared to other SAs, the pulse width obtained from this mode-locked laser becomes broader. The 3-dB bandwidth of the optical spectrum also is relatively narrow. According to Jeon et al. (2015), a saturable absorber with a larger modulation depth will generate a narrower output pulse and broader optical spectrum. Small variations in modulation depth have little effect on spectral width and pulse duration in the anomalous dispersion regime, as discussed by Jeon et al. (2015) and Lee et al. (2020). Theoretically, even lasers with a modulation depth of just 0.5% can perform as an SA for mode-locked operations (Kurtner et al. 1998). The modulation depth of GIMF–SIMF–GIMF SA in our work can be further improved by optimizing the length of the GIMF (Nazemosadat and Mafi 2013).

Table 1 Performance of mode-locked pulsed laser using GIMF-based SAs in the 1.5-micron region
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Overall, this work produces a mode-locked pulsed laser with the highest maximum average output power compared to others. This is due to the ability of DC-EYDF as a gain medium which reduces the quenching problems that occur in the EDF (Ainslie 1991; Bentahar and Kandouci 2015). By co-doping Yb3+ ions with Er3+ ions in the silica host, a larger absorption cross-section can be obtained (Wang et al. 2020). This leads to a higher number of ions undergoing population inversion giving a higher output power (Li et al. 2007). The geometry structure of GIMF–SIMF–GIMF SA enables operation at a much higher power level compared to SA which exploits non-linear polarization rotation and other real SA-based materials. As a result, this approach offers a better option to generate mode-locked pulses with high output power, which can find many industrial applications.

5 Conclusion

This work demonstrates the ability of the GIMF–SIMF–GIMF structure as an SA to produce a high-power ultrashort pulsed laser. Mode-locked pulses obtained in the laser cavity have a pulse duration of 2.32 ps with a center wavelength of 1543 nm. The fundamental frequency was 14.1 MHz with an SNR of 54.5 dB. The maximum average output power obtained was 322 mW when 8 W of pump power was pumped into the laser cavity. The pulse energy and peak power obtained from the mode-locked pulses were 22.8 nJ and 9.84 kW respectively. The calculated peak power intensity was 15.4 GW/cm2. With the benefits of a high damage threshold, high immunity to the external environment perturbations and durability, the proposed GIMF–SIMF–GIMF SA structure will find new opportunities in generating high-power ultrashort pulses for industrial applications.