1. Introduction

A pulsed fiber laser could provide high peak power density with good flexibility that is useful for applications of medicine, nonlinear optics and efficient pumping of fiber lasers. Q-switched fiber lasers could be achieved using the conventional bulk Q-switches, such as acousto-optic modulators (AOM) [1,2] and solid-state saturable absorbers [3,4]. A bulk Q-switch aligned in a fiber resonator generally comes with complexities of alignment, packaging and maintenance, and large losses of signal coupling into and out of the fiber cores. The internal Fresnel reflection caused by the air gaps between the bulk and the fibers could also lead to undesired wavelength competitions and noise by amplified spontaneous emission (ASE), especially in a high-gain Q-switched resonator. All-fiber Q-switched lasers with no air gap in the resonators have recently attracted the attention of researchers because of the relative small cavity loss and negligible internal Fresnel reflection that favor Q-switching operations in high-gain fiber resonators.

Sequential Q-switching in an all-fiber laser could be achieved actively using a piezoelectric transducer (PZT) [5–7] and passively by a fiber-type saturable absorber Q-switch (SAQS) [8–17]. Passive Q-switching using a SAQS fiber is of particular interest because of the relative advantages of holding up very large roundtrip gain before Q-switching and no extra electric driving circuit required. Nevertheless, the drawback is the eligibility of a SAQS fiber that is restricted to a certain laser medium in a limited wavelength range where the absorption cross section (σ_a) of the SAQS is larger than the emission cross section (σ_e) of the laser gain medium. This threshold criterion of saturable-absorber Q switching results in a difficulty in finding suitable SAQS fiber materials, especially for a laser medium that has a very large σ_e at the desired Q-switching wavelength.

Most SAQS fibers to date are silicate fibers doped with rare earth ions, such as Tm³⁺ for erbium fiber lasers 1.57-1.6 μm [9], Ho³⁺ for thulium fiber lasers at 2 μm [10], and Tm³⁺, Sm³⁺, Ho³⁺, bismuth (not rare earth) for ytterbium fiber lasers at the wavelengths of 1055-1090, 1085, 1050-1160 and 1125 nm, respectively, where the Yb³⁺ fiber has a relatively small σ_e [11–14]. Recently, we demonstrated all-fiber erbium lasers passively Q-switched with erbium fibers, using a mode-filed-area (MFA) mismatch method [15,16] that successfully enhanced the photon density through the SAQS fiber and thereby eased the SAQS threshold criterion. These methods are applicable to the 3-level laser media that can also serve as 2-level saturable absorbers, such as a 915-nm pumped Yb³⁺ fiber lasing at 976 nm.

The excited state manifolds (²F_5/2) and the ground state manifolds (²F_7/2) of an Yb³⁺-doped fiber provide an absorption band from 0.9 to 0.98 μm and a very broad emission band from 0.97 to 1.18 μm. Both the absorption and emission cross sections (σ_a and σ_e) overlap at 970 to 980 nm and equally reach a peak value of about 2.6 pm² at 976 nm. A 976-nm pulsed ytterbium laser is useful in serving as an efficient pump source for a gain-switched ytterbium laser at 1 to 1.1 μm or for an up-conversion green erbium laser at 540 nm. However, because of the uniquely high σ_e of Yb³⁺ at 976 nm and lack of efficient pump sources, an ytterbium laser has never been neither actively nor passively Q-switched at this emission wavelength. Here, for the first time, we demonstrate a 915-nm CW-pumped passively Q-switched ytterbium all-fiber laser at 976 nm using the MFA mismatch method. In the design, each Q-switching action by the ytterbium SAQS fiber located in a 1064-nm intracavity would lead to an instant gain-switched pulse of 1064-nm that resets the SAQS back to the initial value for the next Q-switching. Such an intra-cavity employed for shortening the relaxation time of the SAQS was first suggested by Dvoyrin et al. [14]. A set of four rate equations is established to simulate such self-balancing correlation between the Q- and gain-switched photons and the populations of the gain and the SAQS fibers. Ideally, the laser with suitable fiber Bragg gratings (FBG) could produce pulses at most Yb³⁺ emission band between 0.97 to 1.18 μm.

2. Experiments

Figure 1 depicts the schematic design of a passively Q- and gain-switched ytterbium all-fiber laser system. The laser was CW-pumped by a 915-nm laser diode (LD) through a 915/976-nm WDM coupler that protected the LD from the 976-nm pulses leaked out of the high-reflectivity (HR) FBG. The 976-nm resonator consisted of a HR FBG, a FBG of 11%R, a large-core ytterbium gain fiber with a calculated fundamental mode field diameter (MFD) of 7 μm and an ytterbium SAQS fiber with a relatively small MFD of 3.5 μm. The gain fiber was 30 cm long with absorption strength of 75 dB at 976 nm. The SAQS fiber was 110 cm long with 976-nm absorption strength of 36 dB. A 915/976-nm WDM was located between the gain fiber and the SAQS to prevent the SAQS from the 915-nm pump. The SAQS was also the gain medium in the 1064-nm intracavity formed with a HR FBG and a FBG of 80%R. The resonator lengths of 976 and 1064 nm were about 10 and 3 meters, respectively. The output 976-nm and 1064-nm pulses were separated by a 976/1064-nm WDM and detected by two InGaAs photo-detectors that were connected to an oscilloscope.

 

Fig. 1 Schematic design of a self-balancing passively Q- and gain-switched all-Yb³⁺ all-fiber laser.

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The MFA ratio of 976 nm between the gain fiber and the SAQS was about 4, which caused a calculable transmission loss near 2 dB and an enhanced photon density in the SAQS. When the laser reached the threshold, the enhanced photon density induced a quick bleaching of the SAQS, followed by a passively Q-switched 976-nm pulse. Figure 2 illustrates the correlation of the lasing and absorption between the manifolds in ²F_5/2 and ²F_7/2 of the gain fiber and the SAQS. Because of negligible σ_e at 0.9-0.97 μm and σ_a at 1-1.1 μm, an Yb³⁺ resonator is considered a quasi-three-level laser at 976 nm and quasi-four-level laser at 1064 nm.

 

Fig. 2 The manifolds of the ²F_5/2 and ²F_7/2 levels of Yb³⁺ fibers, and the correlation between the gain fiber Q-switched at 976 nm and the SAQS fiber gain-switched at 1064 nm (or 1 to 1.1 μm).

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When the SAQS was fully saturated in a Q-switching action, half of the total population of the SAQS (N_aT) was lifted to the excited state ²F_5/2 (N_a2 = N_aT/2). Therefore, a Q switching by the SAQS in the 976-nm resonator was actually a gain switching in the 1064-nm intracavity. A gain-switched pulse would quickly deplete the N_a2 and re-initialize the SAQS for the next Q- and gain-switching cycle. Evidently, the pulse repetition rate, R_rp, of 976 nm (or 1064 nm) was no longer restricted to the recovering rate of N_a (i.e., 1/τ₂, τ₂: relaxation lifetime of Yb) but proportional to the applied pump power. In the experiment, the maximum R_rp was about 9 kHz limited by the maximum pump power of about 105 mW.

Figure 3 shows sequential Q- and gain-switched pulses at R_rp ~9 kHz that were detected and simultaneously monitored by a two-channel oscilloscope. The wavelengths of the two outputs were verified to be individually 976 nm and 1064 nm by an Oriel Cornerstone monochromator. The time spacing between the Q- and gain-switched pulses, ΔT_s, was 1.1 μs with a standard deviation of 0.04 μs. The pulse of 976 nm had a full width at half maximum (FWHM) of 280 ns, an estimated energy of 2.8 μJ and a peak power of 10 W. Correspondingly, the pulse of 1064 nm had a pulse width of 430 ns, an energy of 1.1 μJ and a peak power of 2.6 W. Figure 4 presents the measured output characteristics of the 976- and 1064-nm pulses, the R_rp, and ΔT_s, relative to the applied 915-nm CW pump power from 72 to 105 mW.

 

Fig. 3 (a) Sequentially saturable absorber Q-switched pulses (signal above) and gain-switched pulses simultaneously detected and monitored on an oscilloscope. (b) Single pulsing of 976 and 1064 nm observed in a minor scale. The time spacing between the 976- and 1064-nm pulses was 1.1 μs with a standard deviation of 0.04 μs.

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Fig. 4 (a) Normalized 976-nm pulse repetition rate, pulse energy and width relative to the applied CW pump power. (b) Normalized time spacing (ΔT_s) between the pulses of 976 and 1064 nm, 1064-nm pulse energy and width relative to the CW pump power.

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The system performance was increasingly improved with the increased pump power. It is reasonable that the relatively high pump rate contributed more gain population over the threshold before the Q-switched pulse surged (as shown in Fig. 5 . below by simulation), thereby giving rise to better Q-switching efficiency and higher 976-nm pulse energy. An efficient Q switching indicated a nearly 100% bleached SAQS that suggested the achievable maximum gain population of 1064 nm, N_a2 = N_aT/2, and a converging 1064-nm pulse energy, as 1.1 μJ at the maximum pump shown in Fig. 4(b). For σ_e ~3 × 10⁻²¹ cm² at 1064 nm, the maximum gain-switched roundtrip gain was about 4 dB, sufficient for creating a 1064-nm pulse that ensured the depletion of N_a2 for next cycles. Evidently, the efficiencies of Q and gain switching are essential for the repeatability and stability of pulsing cycle and pulse characteristics. In a long-term operation (48 hours) with a constant pump power of 100 mW, the pulse energy and duration was stable and showed no degradation with time.

 

Fig. 5 (a) Normalized N_a, N_g and output Q-switched pulses of 976 nm and gain-switched pulses of 1064 nm. N_a is normalized by N_aT, N_g by the threshold N_gth, and the pulses by the maximum peak power (i.e., the first Q-switched pulse power). (b) The performance in a minor time scale. The pulses of 976 and 1064 nm have energies of 2.7 and 1.2 μJ and pulse widths of 135 and 348 ns, respectively.

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3. Modeling and simulation

A set of four rate equations Eq. (1-4) are modified based on Siegman’s three rate equations [17] for modeling the interaction between the Q- and gain-switched photon numbers, n₁ and n₂ (correspondingly at λ₁ and λ₂), the gain population of the gain fiber, N_g, and the absorption population of the SAQS, N_a, as shown below:

The coupling coefficients K_g and K_a are defined to be σ_e1/(A_gt₁) and σ_a1/(A_at₁), respectively, where σ_e1 and σ_a1, respectively, are the emission and absorption cross sections at λ₁, A_g and A_a are the fundamental mode-field areas in the gain and SAQS fibers, respectively, and t₁ is the one-way-trip transmit time of the Q-switched resonator. The coupling coefficient K_g2 is σ_e2/(A_g2t₂), where σ_e2 is the σ_e at λ₂, A_g2 is the mode-field area of λ₂ in the SAQS fiber, and t₂ is the one-way-trip transmit time of the gain-switched resonator. The factors α₁ and α₂ are the non-saturable cavity losses in the resonators of λ₁ and λ₂, respectively, R_p is the pump rate of N_g, and τ₂ is the relaxation lifetime of the excited state ²F_5/2 (~0.8 ms for Yb fiber). N_gT and N_aT are the total Yb³⁺ populations in the gain and SAQS fibers, respectively, and p_g and p_a are (1 + σ_a1/σ_e1) and (1 + σ_e1/σ_a1), respectively. N_g and N_a are the factors for Q switching, defined to be N_g2-(σ_a1/σ_e1)N_g1 and N_a1-(σ_e1/σ_e1)N_a2, respectively. The gain population, N_gs, in the gain-switched resonator of λ₂ has a time-independent relation with N_a as

For λ₁ and λ₂ being 976 and 1064 nm, p_g and p_a are 2, σ_e2 is about 3 × 10⁻²¹ cm², and σ_a2 is negligible. Thus, N_gs is simplified to be N_a2, N_a to (N_a1-N_a2), and N_g to (N_g2-N_g1). The time developments of n₁, n₂, N_g, N_a, and N_gs can be solved iteratively in each time step of the time loop. Using the parameters employed in the experiment, Fig. 5 shows the simulation result of sequentially Q- and gain-switched pulses at repetition rate of 9 kHz where N_a is normalized by N_aT, N_g by the threshold N_gth, and the pulses by the maximum peak power (i.e., the first Q-switched pulse power). The absorption population of the SAQS, N_a, starts from the initial value N_aT for the first Q-switched pulse and is iteratively re-initialized by gain-switched pulses to 0.8 N_aT (i.e., N_a2 = 0.1 × N_aT and N_a1 = 0.9 × N_aT) for the next Q switching. As shown in Fig. 5(b), the SAQS is completely bleached by each Q-switched pulse, indicating a fully switched gain population of 1064 nm, N_gs = N_aT/2. Thus, the extraction efficiency of N_gs by a 1064-nm pulse is about 80%. The pulse widths of 976 and 1064 nm, respectively, are 135 and 348 ns that deviate from the measured 280 and 430 ns, especially for the 976-nm pulses. This deviation might be attributed to the non-uniformity of n₁ along the 976-nm resonator that is not taken into account in Eq. (1-4) and is basically caused by the enormous two-trip gain (~60 dB) in the gain fiber and the equally large absorption loss in the SAQS at the beginning of the Q switching. Aside from the deviation of pulse widths, the time spacing of 1.17 μs between the 976- and 1064-nm pulses and the corresponding pulse energies of 2.7 and 1.2 μJ are in good agreement with the experimental results.

4. Conclusion

We have demonstrated a passively Q- and gain-switched all-Yb³⁺ all-fiber laser at 976 and 1064 nm using the MFA-mismatch method. To the best of our knowledge, this is the first Q-switched ytterbium fiber laser demonstrated at 976 nm. With CW 915-nm pump power of 105 mW, a Q-switched pulse with an energy of 2.8 μJ and a width of 280 ns followed by a gain-switched pulse with 1.1-μJ and a 430-ns width was achieved at a repetition rate of 9 kHz. In addition, the rate equations of the Q- and gain-switched photon numbers and the populations of the gain and SAQS fibers were established to simulate the self-balancing mechanism and the pulse characteristics that were in good agreement with the experimental results. The rate equations and system simulation are helpful in providing understanding and further optimization of the laser system.