1. Introduction

Q-switched all-fiber lasers are of great interest because of their flexibility, large accumulated one-trip gain, high beam quality and intense power confined in mode field diameters of only a few micrometers. In addition, all-fiber lasers are alignment-free and have low cavity losses that are essential for efficient Q-switching performance. Q-switching in all-fiber lasers has been achieved by applying a mechanical force on highly dispersive fiber Bragg gratings (FBG). The mechanical force or vibration could be provided by piezoelectric actuators [1], acousto-optics modulators [2,3], or magnetostrictive transducers [4]. Modulation of the Q factor can also be realized in passive approaches using semiconductor saturable-absorber mirrors [5,6] and solid-state saturable-absorber fibers [7–14].

The advantages of the solid-state saturable-absorber Q-switch (SAQS) fibers are their ability to hold enormous gain excited in the gain fiber from lasing and their high damage threshold for high-power Q-switched pulses. The saturable absorber Q-switching criterion, considering level degeneracy and mode-field-area (MFA) mismatch [13] is:

Only a few SAQS fibers have been demonstrated in the literature, and most are for ytterbium-doped fiber lasers [7–11]. Recently, we reported a few techniques to enable the self-Q-switching mechanism in all-fiber erbium lasers [12–14]. In spite of the success of the self-Q-switching methods, its efficiency and structural simplicity could be overshadowed by the use of a natural SAQS that has an inherently high σ_a. Here we propose and demonstrate a passively Q-switched erbium all-fiber laser using a thulium-doped SAQS fiber. Thulium-doped fiber is the first SAQS fiber material (except for erbium itself) demonstrated for an erbium all-fiber laser.

The energy transition ³H₆-³F₄ of Tm³⁺ has a very broad emission wavelength range, from 1.6 to 2.1 μm, and an absorption band from 1.5 to 1.9 μm. Tm³⁺ silicate fibers co-doped with aluminum, germanium, and Zinc modifiers have exhibited varying emission and absorption cross sections. The reported absorption cross section at 1.6 μm was about 3.5-4.5 × 10⁻²¹ cm² in Al/Ge co-doped fibers [15] and about 8 × 10⁻²¹ cm² in Zn-boro-silicate fibers [16]. These values were larger than the emission cross sections of Er³⁺ doped fiber at 1.6 μm, σ_e~1 × 10⁻²¹ cm², suggesting a possible realization of a passively Q-switched erbium fiber laser using a thulium saturable-absorber fiber.

A thulium fiber (model Tm134) employed in the experiment was obtained from the manufacturer CorActive. The core glass host was alumino-phospho silicate. The fiber had a small core diameter of 3 μm and a core aperture number (NA) of 0.18. A large mode-field diameter (MFD) of about 10 μm and a weak confinement factor of 0.17 at 1570 nm were estimated. The thulium fiber was originally designed for single-mode guiding of wavelengths as short as 1210 nm and 790 nm. Figure 1 shows the absorption spectrum of the Tm134 fiber and the normalized σ_a(λ), which is the absorption spectrum divided by the numerically calculated confinement factor, Γ(λ), and further normalized by the peak value at 1210 nm. The spectrum of the thulium fiber shows an absorption band in the ³H₆-³F₄ transition that is relatively strong compared to the peak absorption at 1210 nm. This absorption strength (³H₆-³F₄) was found stronger than the values reported in the literature.

 

Fig. 1 The absorption spectrum of the thulium fiber (model Tm134, the left y axis). The normalized σ_a(λ) is the absorption spectrum divided by the estimated confinement factor Γ(λ) and normalized by the peak value at 1210 nm (the right y axis).

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As the wavelength decreases from 1.6 to 1.57 μm, the σ_a of the SAQS Tm fiber decreases by a factor of 1.7 and the σ_g of the Er gain fiber increases by a factor of 2.6, leading to an increasingly unfavorable Q-switching condition. According to the σ_a values in the literature and the Q-switching criteria, an erbium laser should not be Q-switched with a thulium fiber at wavelengths at or shorter than 1570 nm. Nevertheless, as demonstrated in the later experiment, erbium lasers were efficiently Q-switched with thulium fibers at 1570 nm, indicating higher-than-expected σ_a values for the employed thulium fibers. The σ_a of a bulk crystal could be measured in a bleaching experiment with a best-fit curve of the modified Avizonis-Grotbeck’s equation [17]. Since light power is partially confined in the fiber core, we further modified Avizonis-Grotbeck’s equation to consider the confinement factor of fiber samples in the bleaching experiment. The σ_a of a Tm SAQS fiber was determined to be 1.44 × 10⁻²⁰ cm² at 1570 nm.

2. Experiments of saturable absorber Q-switching and bleaching

The schematic diagram of a passively Q-switched all-fiber erbium laser using a thulium SAQS fiber is shown in Fig. 2 .

 

Fig. 2 The schematic diagram of a passively Q-switched all-fiber erbium laser using a thulium SAQS fiber.

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The laser cavity was simple, consisting of two FBGs, one erbium fiber and one thulium fiber. One 980/1570 nm WDM was located outside the cavity to couple the pump input and pulse output. The FBGs had a high reflectivity (HR) near 100% and a low reflectivity (LR) about 20% at 1570nm. The erbium gain fiber (model Er80-8/125) was manufactured by nLight to the following specifications: a core diameter of 8 μm, a MFD of 9.5 μm, and an absorption loss of 34.6 dB⋅m⁻¹ at 1570 nm. The gain fiber was 40 cm long. The thulium fiber (Tm134 by Coractive) was a 1.8 meter long with an initial absorption loss of 6 dB at 1570 nm. In spite of the disadvantage of a large MFA in the Tm134 fiber, sequentially Q-switched pulses were successfully produced. The pulse had a stable pulse energy of 9 μJ and pulse width of 420 ns at repetition rates in the range 0.1-2 kHz, as shown in Fig. 3 . The pulse repetition rate was proportional to the pump power, and limited to 6 kHz by the maximum power of the LD, about 230 mW.

 

Fig. 3 (a) The output characteristics of the thulium-Q-switched erbium laser: pulse energy, pulse width (FWHM) and pulse repetition rate relative to pump power. (b) A steady pulse shape at repetition rates 0.2-2 kHz. (c) A pulse train at a repetition rate of 1 kHz.

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When the repetition rate, R_p, was larger than about 2 kHz, the pulse energy started to decrease because the SAQS could not fully recover in time after a pulse and less gain population was excited before the next pulsing. It indicates that the relaxation lifetime (³F₄) of the thulium fiber should be near and less than 0.5 ms that was the inversion of the largest R_p before the degrading of pulse energy. The estimated lifetime is consistent with the reported lifetime range of 0.3-0.6 ms [15,18]. The stability of thulium Q-switch was evaluated by the standard deviation of the repetition rate with a constant CW pump. By sampling of a thousand times on an oscilloscope, the deviation of the repetition rate were about ± 3.4% at 1 kHz, and slowly increased to ± 4.6% at 6 kHz. Furthermore, a long-term (110 hours) operation with a constant pump power of 100 mW (R_p~1 kHz) was tested for observing the photodarkening in Tm fiber reported in the literature [19]. The average output power started initially at 9.1 mW, decreased with time in the early 40 hours and became stabilized at 8 mW afterward as shown in Fig. 4 . The R_p remained stably at 1 kHz, thereby indicating a near 11% degradation of pulse energy by photodarkening.

 

Fig. 4 Degradation of the average output power by photo-darkening in a 110-hour operation of the Tm-Q-switched erbium fiber laser with a constant 918-nm pump power of 100 mW. The pulse width of 420 ns and the pulse repetition rate of 1 kHz were stable in the period.

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Observing the Q-switching performances with various ratios of p_gA_a/(p_aA_g) could help reveal the σ_a value of the thulium fiber. An erbium fiber (model Er110-4/125 by nLight) and a thulium-holmium co-doped fiber (model TH512 by CorActive) were tested in the experiment. The characteristics of the fibers and the performances at a pulse repetition rate of 1 kHz are listed in Table 1 . Because of the relatively small p_gA_a/(p_aA_g), the case using Er80 and TH512 fibers had the best Q-switching performance. It should be noted that multi-peak and distorted pulse shapes were observed in the cases using the TH512 fiber. The physics of these complex shapes was not clear and was attributed to the interaction between Tm³⁺ and Ho³⁺ dopants because they were not found in the cases using the Tm134 fiber. On the other hand, the case using the Er110 and Tm134 fibers had the lowest Q-switching efficiency, indicating operation near the critical condition. An educated guess, by σ_a ~[p_gA_a/(p_aA_g)] × (1.5σ_g) near the Q-switching criterion, suggested that the σ_a of thulium should be larger than and close to 11.8 × 10⁻²⁰ cm² at 1570 nm. This estimated σ_a value was larger by a factor of 4.5 and 2.5 than the previously reported data [15,16].

Table 1. Saturable-absorber Q-switching performances of erbium lasers using a Tm fiber and a Tm-Ho co-doped fiber. The factor Δτ_pw is the pulse FWHM, and E_p is the pulse energy. The factors p_g (for erbium) and p_a (for thulium) are 1.5 and 1.2 at 1570 nm.

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To determine the precise σ_a value, a Tm134 fiber with an initial absorption loss of about 2 dB was tested in a bleaching experiment, as illustrated in Fig. 5(a) . The input pulse source was the Q-switched laser using the Er80 and TH512 fibers as indicated in Table 1. The pulse repetition rate was set to be 0.5 kHz, providing an average power of 8 mW. Because of the low repetition rate, full recovery of the absorption population of the thulium fiber from every pulse bleaching was expected. A manual attenuator and a power splitter were employed to control and monitor the incident pulse energy upon the thulium fiber. The fusion loss between the bare fiber and the thulium fiber was measured by a 1570-nm CW signal to be 0.9 dB. Therefore, the true pulse energy, E_i, that entered the tested sample could be estimated and modulated in a range of 0.6-10 μJ. The E_i and the corresponding internal transmission were obtained as shown in Fig. 5(b). The modified Avizonis-Grotbeck’s equation has been used to determine the σ_a and the excited-state absorption cross section, σ_ESA, of bulk saturable absorbers [17]. To include the effect of power confinement in the fiber core, we redefine the parameters and further modify the equation to be:

 

Fig. 5 (a) Bleaching experiment for measuring the absorption cross section of thulium fiber. (b) Experimental bleaching data of a thulium fiber (Tm134), and the best-fit theoretical matching curve. The best-fit curve of the modified Avizonis-Grotbeck’s equation was obtained with the following parameters: initial absorption loss = 1.83 dB (~66% transmission), σ_a = 1.44 × 10⁻²⁰ cm², σ_ESA = 0, α = 0, λ = 1570 nm, p_a = 1.2, Γ = 0.17 and the core diameter d_c = 3 μm.

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With a lack of excited-state absorption of 1.57 μm from the ³F₄ level of Tm³⁺, σ_ESA is negligible. The σ_a of Tm³⁺ was determined to be 1.44 × 10⁻²⁰ cm² with a best-fit numerical solution of Eq. (2) to the experimental data. The parameters for the best-fit bleaching curve were consistent with the sample characteristics.

4. Conclusion

We have demonstrated passively Q-switched all-fiber erbium lasers at 1570 nm using Tm-doped and Tm-Ho co-doped SAQS fibers. With a Tm-doped fiber, sequentially Q-switched pulses at repetition rates of 0.1-6 kHz were stably achieved using CW 980-nm pump powers of 60-230 mW. By use of a Tm-Ho co-doped fiber with a mode-field area of 8.6 μm, Q-switched pulses with pulse energy of 15.7 μJ and pulse width of 120 ns were obtained. Because of relatively larger cross-section ratios, σ_a/σ_g at 1.57-1.6 μm, better Q-switching performances were expected at higher wavelengths. We also modified the Avizonis-Grotbeck’s equation to consider the power confinement factor of the fiber core in the bleaching experiment. The absorption cross section of Tm was identified to be about 1.44 × 10⁻²⁰ cm² at 1570 nm by the best fit of a theoretical curve to the experimental data.