**4. Dissipative soliton dynamics of 2 μm fiber lasers**

**Figure 9.** Laser spectrum of the mode-locked pulse [56].

both average power and pulse energy increase near linearly with pump power, and the maximum output power and pulse energy are 263 mW and 12.07 nJ, respectively. **Figure 8** shows the pulse duration versus pump power measured with an autocorrelator. The pulse duration displays a linear increase with pump power, indicating that the pulse was highly chirped. Large chirp is a typical characteristic of DSs for supporting high pulse energy. The laser spectrum, as shown in **Figure 9** [56], locates at 1928.2 nm and has FWHM (full width at half maximum) bandwidth of 2.65 nm. The comparatively narrow spectrum width can be attributed to the high chirp-induced decrease of the pulse peak power. The spectrum shape is very similar

**Figure 10(a)** shows the pulse train of the mode-locked fiber laser measured at the maximum output level. The pulse train has repetition rate of ~21.8 MHz, consistent with the total

**Figure 8.** Pulse duration (autocorrelated trace) of the mode-locked fiber laser versus launched pump power [56].

to that of another recent report about DS fiber laser at the 1 μm regime [57].

120 High Power Laser Systems

The repetition rate of a passively mode-locked fiber laser is usually limited by the total cavity fiber length, and the pulsing repetition rate is generally of several MHz to tens of MHz. However, high-repetition-rate laser pulses are required in some application areas, including biological imaging [58], optical communication [59], and so on. If the high-repetition-rate laser pulses also have high pulse energy, then they are more preferred [60]. There are many ways to generate high-repetition-rate laser pulses from fiber lasers, but the most efficient one may be passive harmonic mode-locking. With harmonic mode-locking, the pulsing frequency will be highly multiplied just through increasing the intracavity light intensity to get higher-order harmonics. However, the single pulse energy usually decreases with increasing harmonic order. The pulse energy of harmonically mode-locked fiber lasers is limited by either pulsing instability or energy storage capability of fibers [61, 62]. In the 2 μm region, passively harmonic mode-locked fiber lasers, especially high-pulse-energy ones, are seldom reported.

Here, based on the CGFML and through appropriate designing the cavity dispersion map and adjusting the cavity gain, we experimentally realize multiple orders of harmonic modelocking of 2 μm Tm-doped fiber laser (TDFLs) with a SESAM. To achieve high pulse energy, we design this laser to operate in the DS state and adopt a linear laser cavity. We observe stable harmonic mode-locking up to the fourth order, and the pulse energy of all these harmonic pulses is larger than 3 nJ, with the highest one being 12.37 nJ of the fundamental frequency pulsing. Besides harmonic mode-locking, we also observe soliton molecule mode-locking state of this 2 μm DS mode-locked fiber laser.

The laser system we adopted for the passively harmonic mode-locked 2 μm DS fiber laser has a simple configuration, as shown in **Figure 11**. It is mainly consisted of 1.1 m length of standard SMF (β2 = −67 ps2 /km), 0.11 m length of thulium-doped fiber (β2 = −12 ps2 /km), and 3.5 m length of DCF (β2 = 93 ps2 /km). The total cavity net dispersion is estimated to be ~ 0.25 ps2 . A commercial 2 μm SESAM was adopted as the modulator, which has a modulation depth of 25% and relaxation time of 10 ps. A 1.1 W 1550 nm CW Er/Yb-codoped fiber laser was used as the pump source, and a WDM was adopted to launch the pump light into the cavity. The DCF was directly butt coupled to the SESAM. A 0.3-m-long SMF with one end perpendicularly cleaved was employed as the output coupler, and the ~4% fiber facet Fresnel reflection finishes the laser cavity together with the SESAM.

First, we stimulated the laser to operate in the fundamental frequency mode-locking state. This was achieved through increasing the pump power to over a threshold value (here is 456 mW) and at the same time carefully adjusting the position of the SESAM. Once attained, the fundamental frequency mode-locking state could be sustained up to the maximum available pump power (1.1 W). This mode-locking state has a pulse frequency of 21.7 MHz, rightly consistent with the total cavity length of 4.71 m. At the maximum pump level, the average output power was 268 mW, giving a single pulse energy of 12.37 nJ for the fundamental frequency mode-locking.

After accomplishing the fundamental frequency mode-locking, we carefully tuned both the pump power and the SESAM position to achieve higher-order harmonic mode-locking. Here, harmonic mode-locking transition was obtained through changing the intracavity gain, and different light intensity leaded to different pulse dynamics [64]. Harmonic mode-locking from the first to the fourth order was consecutively observed, as presented in **Figure 12** [63]. Compared to the fundamental mode-locking, the pump power had to be increased to over 708 mW to achieve the higher-order harmonic mode-locking. This clearly indicates that more gain is required for sustaining high-order harmonic mode-locking than the fundamental frequency mode-locking. RF spectrum of different harmonic orders at their maximum output powers is shown in **Figure 13**. No clear supermode noise was observed for the fundamental

and the fourth harmonics, but certain supermode noises were present for the second and the

**Figure 12.** DS pulse trains for (a) fundamental HML at 21.7 MHz, (b) second-order HML at 43.4 MHz, (c) third-order

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Here, the harmonic transfer was achieved through changing the light intensity, which is different from those based on polarization variation [61, 62]. By tuning the SESAM, we change the light spot size incident on the SESAM and therefore change the light intensity and thus nonlinear phase shift. In addition, the cavity loss is also altered through tuning the SESAM. At the appropriate pump level, careful balancing nonlinearity and dispersion, and gain and loss,

third harmonics. The SNR for the fourth harmonic mode-locking state is ~38 dB.

finally leads to different harmonic mode-locking states.

HML at 65.1 MHz, and (d) fourth-order HML at 86.8 MHz [63].

**Figure 11.** Schematic of the passively mode-locked thulium-doped fiber laser. WDM, wavelength division multiplexer; SMF, single-mode fiber; TDF, thulium-doped fiber; DCF, dispersion-compensating fiber; SESAM, semiconductor saturable absorber mirror [63].

The laser system we adopted for the passively harmonic mode-locked 2 μm DS fiber laser has a simple configuration, as shown in **Figure 11**. It is mainly consisted of 1.1 m length of stan-

commercial 2 μm SESAM was adopted as the modulator, which has a modulation depth of 25% and relaxation time of 10 ps. A 1.1 W 1550 nm CW Er/Yb-codoped fiber laser was used as the pump source, and a WDM was adopted to launch the pump light into the cavity. The DCF was directly butt coupled to the SESAM. A 0.3-m-long SMF with one end perpendicularly cleaved was employed as the output coupler, and the ~4% fiber facet Fresnel reflection

First, we stimulated the laser to operate in the fundamental frequency mode-locking state. This was achieved through increasing the pump power to over a threshold value (here is 456 mW) and at the same time carefully adjusting the position of the SESAM. Once attained, the fundamental frequency mode-locking state could be sustained up to the maximum available pump power (1.1 W). This mode-locking state has a pulse frequency of 21.7 MHz, rightly consistent with the total cavity length of 4.71 m. At the maximum pump level, the average output power was 268 mW, giving a single pulse energy of 12.37 nJ for the fundamental fre-

After accomplishing the fundamental frequency mode-locking, we carefully tuned both the pump power and the SESAM position to achieve higher-order harmonic mode-locking. Here, harmonic mode-locking transition was obtained through changing the intracavity gain, and different light intensity leaded to different pulse dynamics [64]. Harmonic mode-locking from the first to the fourth order was consecutively observed, as presented in **Figure 12** [63]. Compared to the fundamental mode-locking, the pump power had to be increased to over 708 mW to achieve the higher-order harmonic mode-locking. This clearly indicates that more gain is required for sustaining high-order harmonic mode-locking than the fundamental frequency mode-locking. RF spectrum of different harmonic orders at their maximum output powers is shown in **Figure 13**. No clear supermode noise was observed for the fundamental

**Figure 11.** Schematic of the passively mode-locked thulium-doped fiber laser. WDM, wavelength division multiplexer; SMF, single-mode fiber; TDF, thulium-doped fiber; DCF, dispersion-compensating fiber; SESAM, semiconductor

/km), 0.11 m length of thulium-doped fiber (β2 = −12 ps2

/km). The total cavity net dispersion is estimated to be ~ 0.25 ps2

/km), and 3.5 m

. A

dard SMF (β2 = −67 ps2

122 High Power Laser Systems

quency mode-locking.

saturable absorber mirror [63].

length of DCF (β2 = 93 ps2

finishes the laser cavity together with the SESAM.

**Figure 12.** DS pulse trains for (a) fundamental HML at 21.7 MHz, (b) second-order HML at 43.4 MHz, (c) third-order HML at 65.1 MHz, and (d) fourth-order HML at 86.8 MHz [63].

and the fourth harmonics, but certain supermode noises were present for the second and the third harmonics. The SNR for the fourth harmonic mode-locking state is ~38 dB.

Here, the harmonic transfer was achieved through changing the light intensity, which is different from those based on polarization variation [61, 62]. By tuning the SESAM, we change the light spot size incident on the SESAM and therefore change the light intensity and thus nonlinear phase shift. In addition, the cavity loss is also altered through tuning the SESAM. At the appropriate pump level, careful balancing nonlinearity and dispersion, and gain and loss, finally leads to different harmonic mode-locking states.

**Figure 13.** RF spectrum of the fiber laser for the (a) first-, (b) second-, (c) third-, and (d) fourth-order harmonics [63].

In each harmonic mode-locking state, we increased the pump power to the maximum available level, measured the maximum output power, and calculated the corresponding maximum pulse energy, and the results are shown in **Figure 14**. The highest single pulse energy is 12.37 nJ, achieved with the first-order harmonics. With increasing harmonic order, the pulse energy decreases significantly due to that more pulses (every round trip) need to share the laser power. For the fourth-order harmonics, the maximum single pulse energy is 3.29 nJ. We have also observed the sixth- and eighth-order harmonics mode-locking, but they were not stable. This is probably because that the available pump power (thus gain) is not high enough to balance the loss. Therefore, if higher pump power is provided, higher-order 2 μm HML DSs are expected.

the AC traces of all these harmonics have similar shape and width and the AC of the fundamental mode-locking pulse is present in **Figure 15(b)**. As shown, the AC trace has a FWHM width

**Figure 15.** (a) Spectra of the first- to fourth-order harmonic mode-locking solitons and (b) autocorrelation trace of the

**Figure 14.** Maximum single pulse energy and average output power of the 2 μm harmonic mode-locked fiber laser at

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the first-order harmonics (fundamental mode-locking), the time-bandwidth product (TBP) of the pulse is calculated to be close to 8, indicating that the pulse was moderately chirped.

Under every stable mode-locking state, carefully tuning the SESAM can lead to another novel multi-soliton state, the soliton molecule mode-locking. **Figure 16** shows two typical kinds of soliton molecules, doublet and the triplet soliton molecules. Soliton molecule is formed through soliton splitting and strong interaction between separated solitons. The total energy of a soliton molecule entity is proportional to the number of single-soliton constituents [67], but the single-soliton's energy is actually decreased. Under, respectively, maximum pump powers (624 and 660 mW), the output powers of the doublet and the triplet soliton molecules

pulse shape is assumed. For

of 46.37 ps, corresponding to pulse width of ~30 ps when a sech2

several harmonic orders [63].

first-order harmonics [63].

**Figure 15(a)** shows the laser spectrum of the fundamental pulsing and the successive three high-order harmonics measured at their maximum output levels. All these spectra are similar and have a near-triangle shape and center wavelength of 1929 nm. With increasing harmonic order, spectral width tends to narrow a little bit, which is consistent with the theoretical predictions [65] and experimental results [62, 66]. For the first harmonics, the FWHM width is 3.26 nm, while for the fourth harmonics, the FWHM width is decreased to ~2.5 nm. To get more insight of the pulsing characteristics, we measured autocorrelation (AC) traces of both the fundamental mode-locked DSs and high-order harmonics with an autocorrelator. We found that Developing High-Energy Dissipative Soliton 2 μm Tm3+-Doped Fiber Lasers http://dx.doi.org/10.5772/intechopen.75037 125

**Figure 14.** Maximum single pulse energy and average output power of the 2 μm harmonic mode-locked fiber laser at several harmonic orders [63].

**Figure 15.** (a) Spectra of the first- to fourth-order harmonic mode-locking solitons and (b) autocorrelation trace of the first-order harmonics [63].

In each harmonic mode-locking state, we increased the pump power to the maximum available level, measured the maximum output power, and calculated the corresponding maximum pulse energy, and the results are shown in **Figure 14**. The highest single pulse energy is 12.37 nJ, achieved with the first-order harmonics. With increasing harmonic order, the pulse energy decreases significantly due to that more pulses (every round trip) need to share the laser power. For the fourth-order harmonics, the maximum single pulse energy is 3.29 nJ. We have also observed the sixth- and eighth-order harmonics mode-locking, but they were not stable. This is probably because that the available pump power (thus gain) is not high enough to balance the loss. Therefore, if higher pump power is provided, higher-order 2 μm HML

**Figure 13.** RF spectrum of the fiber laser for the (a) first-, (b) second-, (c) third-, and (d) fourth-order harmonics [63].

**Figure 15(a)** shows the laser spectrum of the fundamental pulsing and the successive three high-order harmonics measured at their maximum output levels. All these spectra are similar and have a near-triangle shape and center wavelength of 1929 nm. With increasing harmonic order, spectral width tends to narrow a little bit, which is consistent with the theoretical predictions [65] and experimental results [62, 66]. For the first harmonics, the FWHM width is 3.26 nm, while for the fourth harmonics, the FWHM width is decreased to ~2.5 nm. To get more insight of the pulsing characteristics, we measured autocorrelation (AC) traces of both the fundamental mode-locked DSs and high-order harmonics with an autocorrelator. We found that

DSs are expected.

124 High Power Laser Systems

the AC traces of all these harmonics have similar shape and width and the AC of the fundamental mode-locking pulse is present in **Figure 15(b)**. As shown, the AC trace has a FWHM width of 46.37 ps, corresponding to pulse width of ~30 ps when a sech2 pulse shape is assumed. For the first-order harmonics (fundamental mode-locking), the time-bandwidth product (TBP) of the pulse is calculated to be close to 8, indicating that the pulse was moderately chirped.

Under every stable mode-locking state, carefully tuning the SESAM can lead to another novel multi-soliton state, the soliton molecule mode-locking. **Figure 16** shows two typical kinds of soliton molecules, doublet and the triplet soliton molecules. Soliton molecule is formed through soliton splitting and strong interaction between separated solitons. The total energy of a soliton molecule entity is proportional to the number of single-soliton constituents [67], but the single-soliton's energy is actually decreased. Under, respectively, maximum pump powers (624 and 660 mW), the output powers of the doublet and the triplet soliton molecules

Here, through combining the CGFML and multilayer MoS2

a linear cavity incorporated with the multilayer MoS2

in **Figure 17(a)**. The spectral position of the E2g

~408 cm − 1 for A1g) shows that the MoS2

the transmittance of the multilayer MoS2

here, T(I) is the transmission, α0

MoS2 sheets coated on a gold mirror [6].

bility of layered MoS2

be scaled to over 15 nJ.

The multilayer MoS2

and the MoS2

model of [57]

of the MoS2

, we show that mode-locking capa-

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1 and 127

, non-

SA at the 2 μm

modulator, fundamental mode-locking

and A1g modes (~383 cm−1 for E2g

sample has a thickness of approximately four

on the gold mirror is shown in **Figure 17(b)** [6].

is the modulation depth, I is the input intensity, Isat is the satura-

sheets can be definitely extended to the 2 μm wavelength region. With

Developing High-Energy Dissipative Soliton 2 μm Tm3+-Doped Fiber Lasers

was synthesized with the liquid-phase exfoliation method (LPE) [6],

nanosheet was transferred onto a gold mirror acting as SA. Raman spectrum

on the mirror was detected with a spectrometer, and the results are shown

1

in the DS regime for 2 μm Tm3+ fiber lasers is achieved. At the same time, through elongating the total fiber length, thus decreasing the mode-locking repetition rate, the pulse energy can

layers [82]. With a self-constructed 1940 nm ~800 ps fiber laser as the probe source, the reflection method was used to measure the saturable absorption of the sample, and

The nonlinear optical parameters were obtained by using a simple saturable absorption

T(I) = 1 − α0 × exp(−I/Isat) − αns (4)

saturable loss αns, and saturation intensity Isat were 13.6%, 16.7%, and 23.1 MW cm−2, respectively. The modulation depth is comparable to that measured in the 1 μm region [57, 77] but larger

wavelength region is efficient for suppressing wave breaking in mode-locking operation [83].

**Figure 17.** (a) Raman spectrum of the adopted multilayer MoS2 sheets and (b) nonlinear absorption of the multilayer

tion intensity, and αns is the non-saturable absorbance. The measured modulation depth α0

than that in the 1.5 μm region [79, 80]. This large modulation depth of the MoS2

**Figure 16.** Experimentally measured doublet (a) and triplet (b) soliton molecule pulse trains [63].

are 72 and 95 mW, respectively, corresponding to soliton molecule energies of 3.32 and 4.38 nJ. While their single-soliton energies are 1.66 and 1.46 nJ, respectively.
