1. Introduction

Telecom industry had resulted in development of mature fiber technology and reliable and cost effective components, which makes suitably designed fiber lasers real contenders to conventional solid-state lasers. Rare-earth doped fibers exploiting the three-level and four-level transitions in Er³⁺, Nd³⁺, Pr³⁺ and Yb³⁺ are now used in many applications, including fiber lasers and optical amplifiers. For these sources, especially those operated in mode-locked or Q-switched regime, it is important to know the process that governs the transient emission buildup, including the population inversion dynamics, the effect of spontaneous emission and the nature of the laser transition. The broad fluorescence spectrum makes different fiber gain media particularly attractive for tunable and ultra short pulse sources. Cw operation for a Nd:glass fiber laser was reported over a tuning range of 30 nm [1] and more recently over 50 nm [2]. For Er-doped fiber lasers, tuning over 35 nm was achieved in an actively mode-locked system [3] and over 50 nm in a passively mode-locked fiber soliton laser [4].

Ytterbium-doped silica fiber having broad gain bandwidth, high optical conversion efficiency, and large saturation optical flux offers an almost ideal gain medium for the generation and the amplification of wavelength-tunable ultra short optical pulses. The broad gain spectrum of Yb fiber attracted many researchers; particularly emission and cross section were measured in [5]. For fiber lasers doped with ytterbium, which exhibits a particularly wide fluorescence spectrum, a tuning range of ~100 nm was demonstrated [6]. An additional interesting feature of Yb-doped fiber lasers is that under certain conditions those lasers can operate in the 977 nm spectral band, which make them very attractive as a master source for frequency doubling to achieve 488 nm and thus to substitute the bulky and inefficient Ar-ion lasers [7]. Therefore, the vast wavelength range of 980 to 1100 nm can be achieved with Yb-fiber lasers. Such broad wavelength tunability, however, requires knowledge of the mechanisms of the laser transition and dynamics. Earlier it was shown that in glasses doped with erbium and neodymium as active ions, the laser transition changes its property over the gain bandwidth [2, 8, 9]. This feature alters the oscillation dynamics of the lasers that in turn may strongly affect the characteristics of the pulsed operation. In particular, it was shown that notable transient effects in lasers that take the form of well-known relaxation oscillations have a characteristic period and damping decay time strongly dependent on the operation wavelength. Experiments performed with the rare-earth-doped fiber lasers clearly demonstrate the different wavelength dependence behavior of the transient oscillations depending on the nature of the laser transition. A close inspection of the frequency of relaxation oscillations ω_relax across the gain bandwidth resulted in some interesting features being observed [2, 8, 9]. The slopes of the linear dependencies of ${{\mathrm{\omega }}^2}_{\text{relax}}$ vs. (r–1) were found to change noticeably with wavelength for the three-level transition relaxation oscillations; here r is a normalized pumping rate. In contrast, the linear dependence was wavelength independent for the four-level transition relaxation oscillations, as expected. The origin of the wavelength dependence of ${{\mathrm{\omega }}^2}_{\text{relax}}$ for three-level systems was understood from the small-signal analytic solution of the rate equations, taking into account the thermal level population [2]:

The symbols used in this equation are defined as follows: N is total number of active ions, c, σ are the speed of light and laser transition cross section, η=l/[L+l (n-1)], where L, l are the total cavity length and the length of the gain medium, respectively, n is the refractive index, f ^l is the fractional thermal occupation of the lower laser level and τ_c, τ_s are the cavity and laser transition lifetimes.

From this equation it is clear that the wavelength-dependent term in parentheses disappears for lasers operating on transitions with a negligible population on the terminal level (f^l =0). An important consequence of this feature (not observed in four-level systems) is that the relaxation oscillation frequency depends directly on the absorption at the signal wavelength (σf^l ≠0) as a result of the finite thermal population of the ground level. Therefore the wavelength dependence of the relaxation oscillations provides a method to distinguish three- and four-level transitions, and this can be useful in spectroscopic studies as well as in determining the parameters of the laser transition [9–11].

2. Experimental results

In this article we use this method to identify the mechanism of the laser transitions in ytterbium fiber laser. The measurements show that the transient buildup of the emission in the long-wavelength tail of the Yb-fiber gain spectrum (λ>1060 nm) reveals the 4-level nature of the laser transition contrary to the operation at shorter wavelengths. This feature modifies strongly the properties of the Yb-fiber laser, affects laser operation in a pulsed mode, e.g. Q-switching, and should be accounted for when constructing a pulse laser.

The linear cavity (see Fig. 1) containing a piece of Yb³⁺-doped fiber as the gain medium was defined by a fiber loop mirror acting also as a 15% output coupler and a 1/1200 mm^-1 reflection grating in a Littrow configuration. An intracavity antireflection coated lens was used to collimate the beam from the single-mode fiber onto the diffraction grating. Optical pumping for 980 nm region lasing was provided by a 915 nm diode laser through dichroic fiber combiner supplying up to 100 mW in the gain fiber. The tunable operation in the 1030–1105 nm wavelength range exploits a 980 nm pump diode with an appropriate fiber combiner. 1-kHz chopper placed in the open section of the cavity was used to observe the transient evolution of the laser emission towards its stationary state.

 

Fig. 1. Experimental setup. For 980 nm spectral range, a 915 nm pump was used with 30 cm Yb-fiber and three wavelength-division multiplexers (WDM) 1: 915/980, 2: 910/1024, 3: 920/1050. For 1030–1100 nm range, 142 cm-long Yb-fiber was pumped with 980 nm single-mode pigtailed diode laser through the cascade of three fiber WDMs 1: 980/1100, 2: 980/1030, 3: 980/1050.

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A signal/pump wavelength-selective coupler and output coupler were made of fiber with a cutoff wavelength of 920 nm. Depending on the operating spectral range, the fiber was pumped through a different kind of fiber multiplexers (see Fig. 1) to achieve high extinction in a broad wavelength range. We have observed that external reflections may severely affect the dynamics of ytterbium fiber laser. Few pump multiplexers were then used in series to exclude any optical coupling between pump laser diode and fiber laser cavity.

When the doped fiber length was short enough (~30 cm) to ensure at least 50% population inversion along all fiber, the laser was operating straight at 980 nm even without any wavelength selective elements. Pump through power in this instance was around 10 mW (for 100 mW of launched power at 915 nm). When the doped fiber length was increased to 142 cm, so that 980 nm radiation was re-absorbed inside the fiber, the central lasing wavelength was shifted towards 1040 nm. It should be noted that the cavity length, L, and the total number of active ions in the cavity, N, affect the absolute value of the relaxation oscillation frequency, as seen from Eq. (1). However, although ω_relax changes with the length of the ytterbium fiber placed as an active medium, the nature of the laser transition (3- or 4- level transition) depends only on population of the terminal level (f^l ) and obviously not on the amount of the gain fiber.

Yb³⁺-doped fiber had a core diameter of 3.0 µm and showed absorption of 3.1 dB/m at 810 nm. The relaxation oscillation frequency ω_relax was determined from the repetition period of the small-amplitude strongly damped nearly sinusoidal oscillations (see Fig. 2).

 

Fig. 2. Typical transient oscillations from an Yb³⁺-doped fiber laser. Pumping rate normalized to the threshold pumping rate is r–1=0.12 and lasing wavelength is λ=1053 nm.

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The wavelength-resolved relaxation oscillations measured at room temperature were analyzed over the whole gain spectrum of ytterbium fiber. Figures 3 and 4 show a plot of (ω_relax/2π)² vs. (r–1), where r is the pumping rate normalized to the threshold pumping rate, around 980 and 1030–1105 nm, respectively, taking the lasing wavelength as a parameter. Although, we always observed linear dependencies for (ω_relax/2π)² vs. (r–1), as it is expected from analysis based on rate equations; the relaxation oscillations originating at the four-level (λ>1060 nm) and three-level (λ<1060 nm) transitions exhibited different wavelength dependencies.

 

Fig. 3. (ω_relax/2π)² versus normalized pumping rate (r–l) around 980 nm with the lasing wavelength as a parameter.

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Fig. 4. (ω _relax/2π)² against normalized pumping rate (r-l) for 1030–1105 nm spectral range.

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Figure 5 presents spectral dependence of the relaxation oscillation parameter (ω_relax/2π)²/(r–1), i.e., the slope of the linear dependencies of (ω_relax/2π)² vs. (r–1). As seen from the Fig., this slope changes noticeably with wavelength for the three-level transition. It, however, was fairly wavelength independent for λ>1060 nm demonstrating the four-level nature of laser transition at the long-wavelength tail of the ytterbium gain spectrum [8, 9]. Particularly, the strong decrease in the frequency of the relaxation oscillations was observed at long wavelength resulting in a slow laser dynamics. It is also evident from the Fig. 5 that the individual absorption transitions originated from Stark sublevels with different equilibrium populations have pronounced correlation with transient dynamics. We can deduce from the absorption spectrum that the lasing transitions for λ>1060 nm becomes four-level owing to negligible population of the ground level at room temperature.

 

Fig. 5. Wavelength dependence of the relaxation oscillation parameter (ω_relax/2π)²/(r-l) derived from the plots presented in Fig. 4 and of the Yb³⁺-ϕiβερ αττενυατιoν.

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3. Summary

In summary, the relaxation oscillations in the tunable ytterbium fiber laser were studied at room temperature in a wide spectral range. The measurements revealed remarkable wavelength dependence of the oscillator dynamics that reflects the change in the character of the laser transition. Particularly, the laser transition at the long-wavelength edge of the gain spectrum (λ>1060 nm) functions as a four-level system contrary to the short-wavelength operation, where transition corresponds to three-level behavior. This phenomenon significantly alters the transient dynamics and should be accounted in pulsed lasers especially in broad gain spectrum tunable lasers.