**3. High-energy dissipative soliton 2 μm fiber lasers**

To verify the simulation results, we carried out a corresponding experimental observation of 2 μm DS mode-locking with short GFs. These GFs are highly thulium doped, and the net cavity dispersion is kept normal through adjusting the length of the DCF and SMF. Experimental setup is schematically shown in **Figure 1(b)** [53]. The pump source is a 1550-nm-CW Er/ Yb-codoped fiber laser with maximum output of 1 W. The pump light is delivered into the gain fiber (with absorption of ~1.2 dB/cm at 1550 nm) by wavelength-division-multiplexing (WDM) couplers with a coupling efficiency of 95%. The parameters of these three kinds of fibers are the same as used in the simulation. Total cavity dispersion is kept at a net normal value of ~0.04 ps2 . On the output end, the perpendicularly cleaved fiber facet is employed for both laser feedback (~4% Fresnel reflection) and the output coupler (~96% output coupling ratio). The right side fiber end is directly butt coupled to the SESAM with a reflectance of ~85% at 1900 nm, a modulation depth of ~25%, and a saturation fluence of ~35 mJ/cm2 .

Short lengths of single-cladding Tm-doped fiber (tens of centimeters) are chosen as the GF. Under stable mode-locking operation, maximum pulse energies with different GF lengths are shown in **Figure 4(b)** [53]. The experimental results clearly follow the trend of the simulation prediction; that is, the pulse energy increases quickly as the length of GF decreases. When the GF length is shortened to ~15 cm, pulse energy of ~5 nJ is achieved, and detailed laser characteristics are shown in the following.

As shown in the insets, in the case of 1 and 1.5 μm, the GFs (Yb-doped or Er-doped) have normal dispersion and introduce positive phase shift, which can be compensated (even if the shift is large) by the negative phase shift provided by the SMF. However, it is quite different in the 2 μm wavelength regime, where the GF (Tm-doped) has anomalous dispersion and, thus, negative phase shift. To achieve soliton mode-locking, normally dispersive fibers (DCF and SMF) are thus required to be integrated into the cavity. However, too large normal dispersion value (long fibers) will induce large phase shift and consequently pulse splitting. Therefore, small net normal dispersion (caused both by DCF and SMF) places a tolerant phase shift region for the GF (purple area). A longer GF will induce much more significant phase shift (red-dashed arrow) than that incurred by the DCF or SMF (yellow- or green-dashed arrow). In the phase limitation range, shorter GF (red arrow) has a larger slope and hence can achieve higher pulse energy. On the contrary, longer GF (orange arrow), due to its smaller slope, has to sacrifice a large part of amplitude to reduce its phase shift under the tolerable level. Therefore, short GF should be adopted to achieve high energy pulses from a cavity in

Based on the above analysis, we propose the condensed GF (shortened to a small length while providing adequate gain at the same time) to scale the pulse energy of DSs in the 2 μm and mid-infrared spectral regions. Within the phase limitation range, a condensed GF has a large

To verify the advantages of CGFML in the 2 μm regime, we carry out simulations in a semiconductor saturable absorber mirror (SESAM) mode-locked fiber laser (**Figure 1** [53]). The simulated maximum output pulse energies with various GF lengths are indicated in **Figure 4(a)** [53]. It is clear that decreasing the GF length will dramatically increase the pulse energy. Shortening the GF to 0.2 m, as high as 11 nJ pulses, is achieved, which is much higher than the pulse energy of tradition solitons (usually less than 1 nJ). This thus confirms that CGFML is an effective route for generating high-energy soliton pulses in laser systems with anomalous dispersion GFs (shortening the anomalous dispersion GF as much as possible).

To verify the simulation results, we carried out a corresponding experimental observation of 2 μm DS mode-locking with short GFs. These GFs are highly thulium doped, and the net cavity dispersion is kept normal through adjusting the length of the DCF and SMF. Experimental setup is schematically shown in **Figure 1(b)** [53]. The pump source is a 1550-nm-CW Er/ Yb-codoped fiber laser with maximum output of 1 W. The pump light is delivered into the gain fiber (with absorption of ~1.2 dB/cm at 1550 nm) by wavelength-division-multiplexing (WDM) couplers with a coupling efficiency of 95%. The parameters of these three kinds of fibers are the same as used in the simulation. Total cavity dispersion is kept at a net normal

both laser feedback (~4% Fresnel reflection) and the output coupler (~96% output coupling ratio). The right side fiber end is directly butt coupled to the SESAM with a reflectance of

~85% at 1900 nm, a modulation depth of ~25%, and a saturation fluence of ~35 mJ/cm2

. On the output end, the perpendicularly cleaved fiber facet is employed for

.

slope (**Figure 3** [53]) and thereby can provide high pulse energy.

**3. High-energy dissipative soliton 2 μm fiber lasers**

the 2 μm spectral region.

116 High Power Laser Systems

value of ~0.04 ps2

With the 15 cm GF, stable CW mode-locking is self-started when pump power is increased to ~650 mW. Owing to the large output coupling ratio suppressing the intermediate transitions between the CW laser operation and the CW mode-locking regime [55], no Q-switching or Q-switched mode-locking is observed. The stable CW mode-locked operation maintains when pump power is increased up to the maximum 1 W available pump power. The maximum average output power of this 2 μm DS fiber laser is 158 mW. **Figure 5(a)** [53] shows the 2 μm DS pulse train at the maximum output. The repetition rate is ~32 MHz, giving a pulse energy of ~4.9 nJ.

The laser spectrum, detected with a spectrometer (0.1 nm resolution), is shown in **Figure 5(b)**. The center wavelength is 1918 nm and the 3 dB bandwidth is 15 nm. Steep spectral edges indicate the typical characteristics of DSs [31, 32]. The radio-frequency (RF) spectrum (**Figure 5(c)**) has a signal-to-noise ratio of ~52 dB, showing that the mode-locking state is very stable. We also use an autocorrelator to measure the pulse characteristics at the maximum output, and the pulse shape (autocorrelation (AC) trace) directly outputted from the laser cavity is indicated in **Figure 5(d)**. The autocorrelation trace is fitted well by a Gaussian curve, giving a pulse duration of 16 ps. Therefore, the time-bandwidth product of the 2 μm DS pulse is calculated to be 18, which is highly chirped. For compressing this chirped pulse, we couple the output pulse directly into a ~25 m length of SMF-28 fiber. After dispersion compensation, the pulse is compressed to 579 fs (**Figure 5(e)**), and the time-bandwidth product reduces to 0.7.

This CGFML model can be readily extended to beyond 2 μm, e.g., mid-infrared fiber lasers to scale DS energy. According to this model, to achieve high-energy DSs, the GF length should

**Figure 4.** Simulated (circle dots) (a) and measured (asterisk dots) (b) maximum pulse energy under different lengths of GF under the pump power of 1 W. The curves are exponential fittings [53].

The experimental system is illustrated in **Figure 6** [56]. Pump light from a continuous-wave (CW) Er/Yb-codoped fiber laser with maximum output of ~1 W centered at 1550 nm was coupled into the fiber through a 1550/1900 nm WDM. The laser cavity includes two pieces of SMF-28 fibers, 12 cm length of single-mode Tm-doped silica fiber (5 μm core and 0.24 NA) and 1.5 m DCF. The DCF was butt coupled to the SESAM, whose reflection combined with the ~4% Fresnel reflection of the perpendicularly cleaved output fiber end completed the laser cavity. The dispersions of the thulium fiber, the SMF-28 fiber, and the DCF at 1920 nm were—

**Figure 6.** Schematic of the thulium-doped fiber laser passively mode-locked by a semiconductor saturable absorber mirror (SESAM). EYFL, erbium/ytterbium-codoped fiber laser; WDM, wavelength division multiplexer; SMF, single-

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

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When we increased the pump power to 456 mW and at the same time carefully adjusted the SESAM, stable mode-locking was observed and could maintain up to the maximum pump power (1.09 W). Under different pump levels, the average output power was measured, and the pulse energy could be estimated based on the pulsing repetition rate. As shown in **Figure 7**,

**Figure 7.** Average output power and pulse energy of the mode-locked fiber laser versus launched pump power [56].

SESAM had a relaxation time of 10 ps and a modulation depth of 25%.

mode fiber; TDF, thulium-doped fiber; DCF, dispersion-compensating fiber [56].

/km, respectively [52], giving a total net cavity dispersion of ~0.004 ps2

. The

119

12, −67, and 93 ps2

**Figure 5.** The laser pulse train (a), laser spectrum (b), and RF spectrum (c) of the mode-locked Tm-doped fiber laser and the autocorrelation traces of the pulse before (d) and after (e) dispersion compensation [53].

be as short as possible to keep phase shift within the phase limitation range while providing enough gain at the same time. To this end, the GF should be highly doped (short length with enough gain), so that gain can decouple from dispersion and suppress phase shift. This can efficiently avoid the pulses' evolution to conventional solitons during amplification in the GF. This CGFML model can also be applied for ring laser cavities. In a ring cavity, the pulse passes every element only once during one cycle, leading to less phase shift accumulation. Therefore, a ring cavity has the potential to accommodate a larger phase limitation range and thus has a higher pulse energy generating possibility.

**Scaling pulse energy.** Based on the above condensed-gain model [53], we went to probe the upper limit of the pulse energy of 2 μm DS fiber lasers. In order to increase the pulse energy, we slightly increased the cavity fiber length, and therefore the pulse repetition rate will decrease and the pulse energy will be enhanced. In addition, we optimize the cavity parameters and manage the intracavity dispersion to scale the pulse energy of DS fiber laser in the 2 μm region. Here, we shorten the gain fiber to an optimal length and at the same time use a short piece of optimized single-mode fiber to compensate the dispersion.

Developing High-Energy Dissipative Soliton 2 μm Tm3+-Doped Fiber Lasers http://dx.doi.org/10.5772/intechopen.75037 119

**Figure 6.** Schematic of the thulium-doped fiber laser passively mode-locked by a semiconductor saturable absorber mirror (SESAM). EYFL, erbium/ytterbium-codoped fiber laser; WDM, wavelength division multiplexer; SMF, singlemode fiber; TDF, thulium-doped fiber; DCF, dispersion-compensating fiber [56].

The experimental system is illustrated in **Figure 6** [56]. Pump light from a continuous-wave (CW) Er/Yb-codoped fiber laser with maximum output of ~1 W centered at 1550 nm was coupled into the fiber through a 1550/1900 nm WDM. The laser cavity includes two pieces of SMF-28 fibers, 12 cm length of single-mode Tm-doped silica fiber (5 μm core and 0.24 NA) and 1.5 m DCF. The DCF was butt coupled to the SESAM, whose reflection combined with the ~4% Fresnel reflection of the perpendicularly cleaved output fiber end completed the laser cavity. The dispersions of the thulium fiber, the SMF-28 fiber, and the DCF at 1920 nm were— 12, −67, and 93 ps2 /km, respectively [52], giving a total net cavity dispersion of ~0.004 ps2 . The SESAM had a relaxation time of 10 ps and a modulation depth of 25%.

When we increased the pump power to 456 mW and at the same time carefully adjusted the SESAM, stable mode-locking was observed and could maintain up to the maximum pump power (1.09 W). Under different pump levels, the average output power was measured, and the pulse energy could be estimated based on the pulsing repetition rate. As shown in **Figure 7**,

be as short as possible to keep phase shift within the phase limitation range while providing enough gain at the same time. To this end, the GF should be highly doped (short length with enough gain), so that gain can decouple from dispersion and suppress phase shift. This can efficiently avoid the pulses' evolution to conventional solitons during amplification in the GF. This CGFML model can also be applied for ring laser cavities. In a ring cavity, the pulse passes every element only once during one cycle, leading to less phase shift accumulation. Therefore, a ring cavity has the potential to accommodate a larger phase limitation range and

**Figure 5.** The laser pulse train (a), laser spectrum (b), and RF spectrum (c) of the mode-locked Tm-doped fiber laser and

the autocorrelation traces of the pulse before (d) and after (e) dispersion compensation [53].

**Scaling pulse energy.** Based on the above condensed-gain model [53], we went to probe the upper limit of the pulse energy of 2 μm DS fiber lasers. In order to increase the pulse energy, we slightly increased the cavity fiber length, and therefore the pulse repetition rate will decrease and the pulse energy will be enhanced. In addition, we optimize the cavity parameters and manage the intracavity dispersion to scale the pulse energy of DS fiber laser in the 2 μm region. Here, we shorten the gain fiber to an optimal length and at the same time

use a short piece of optimized single-mode fiber to compensate the dispersion.

thus has a higher pulse energy generating possibility.

118 High Power Laser Systems

**Figure 7.** Average output power and pulse energy of the mode-locked fiber laser versus launched pump power [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 to that of another recent report about DS fiber laser at the 1 μm regime [57].

**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

cavity length of 4.7 m. **Figure 10(b)** displays the autocorrelation trace of the pulse, giving

**Figure 10.** Dissipative soliton: (a) pulse train on oscilloscope and (b) autocorrelation trace of the single pulse at the

2.65 nm, the pulse has a time-bandwidth product (TBWP) of ~9.3, indicating the presence

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

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

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

pulse shape is assumed. Based on the spectral width of

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

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121

a FWHM width of 43.5 ps if sech2

ones, are seldom reported.

state of this 2 μm DS mode-locked fiber laser.

of large chirp.

maximum output level [56].

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

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

**Figure 10.** Dissipative soliton: (a) pulse train on oscilloscope and (b) autocorrelation trace of the single pulse at the maximum output level [56].

cavity length of 4.7 m. **Figure 10(b)** displays the autocorrelation trace of the pulse, giving a FWHM width of 43.5 ps if sech2 pulse shape is assumed. Based on the spectral width of 2.65 nm, the pulse has a time-bandwidth product (TBWP) of ~9.3, indicating the presence of large chirp.
