1. Introduction

Because of their outstanding thermo-optical properties, ytterbium-doped single-mode double clad fiber lasers exhibit nowadays better performances than conventional bulk solid-state lasers in various regimes. For instance, several kW-class fiber laser have been reported in the continuous wave mode [1–2], 4.1 mJ at several tens of kHz of repetition rate was demonstrated in a Q-switched regime [3] and the millijoule level at 50 kHz repetition rate for 800 fs pulse [4] was recently achieved in a fiber chirped pulse amplification scheme. However, most of the reported performances of these high power fiber laser systems exploit the quasi-four-level system in the 1020 nm–1100 nm spectral range, whereas relatively few papers report on the exploitation of the 970 nm–980 nm zero line laser transition [5–9]. The small number of experimental work in the latter spectral range is easily explained by the obvious difficulty to achieve efficient laser operation on the zero-line transition of ytterbium ions embedded in a silica host around 977 nm.

Two severe drawbacks are responsible for the strong difficulties arising when trying to obtain efficient ytterbium-doped fiber laser operation at 977 nm. First of all, in a three-level laser scheme, ground state absorption (GSA) imposes a transparency inversion at the laser wavelength of 977 nm close to 50% (for comparison an inversion of 5% is sufficient to reach the transparency in the four-level system lasing around 1030 nm). Sufficiently intense pumping and fine fiber transverse geometry management is then required to invert half of the total population all along the fiber in order to reach the laser oscillation threshold.

The second major drawback of high power ytterbium-doped three-level fiber laser is the gain competition between the three-level and the four-level laser scheme operation. In fact, considering the limited overlap between the pump radiation and the doped core in a clad pumped fiber laser scheme, efficient pump absorption requires typical fiber length of several meters. With such a long fiber, the gain experienced on the three-level transition at 977 nm is several orders of magnitude smaller than on the four-level laser transition (with negligible reabsorption), leading to spurious laser oscillation in the 1030nm–1080 nm spectral range. To obtain efficient three-level laser operation, it is then necessary to invert the gain ratio by use of intra-cavity wavelength-selective elements.

To overcome these difficulties, it was first proposed to use core-pumped fiber laser architecture, in order to maximize the pump intensity in the doped core and to reduce the fiber length [5–7]. But, in such a scheme, the pump source must deliver a diffraction limited beam and is thus limited to few hundreds of mW. So far, the maximum output power reported in this configuration was limited to 655 mW [7].

Another strategy was the development of specific double clad fibers with smaller clad to core area ratio compared to conventional geometry together with a high clad numerical aperture (NA) [8,9]. As a consequence, powerful laser diodes can be used to increase the pump intensity in the doped core and keep the fiber short. The best results, published by K.H. Yllä Jarkko and al in 2003, were based on the use of a jacketed air-clad fiber with doped core and clad diameters of 9 µm and 30 µm, respectively (NA_clad=0.6). But due to the restricted inner cladding area of ~700 µm² of this fiber, the launched pump power was limited to a few watts leading to a maximum output power of 3.5 W at 977 nm [9].

Even though theoretical limits of the three-level fiber laser have been reviewed in details in the past [10–11], we highlight in this paper that outstanding recent progress of the ytterbium-doped fiber technology have a direct impact on the expected performances of fiber lasers in this spectral range. In particular, the potential of ultra-large core ytterbium-doped rod-type photonic crystal fiber (PCF) for high power continuous wave laser operation at 977 nm is investigated.

In the first part of this paper, we review fundamentals of the three-level fiber laser theory, highlighting critical parameters which have to be considered for their fine understanding and optimization. We then report on performances of a high power fiber laser, which generates up to 94 W at the laser wavelength of 977 nm with a slope efficiency of 48% with respect to the incident pump power at 915 nm. In conclusion, we stress through numerical simulations that this experimental demonstration, the highest output power in a diffraction limited beam ever reported at this wavelength, is intrinsically linked to the extreme opto-geometrical parameters of the rod-type photonic crystal fiber used in these experiments.

2. Theoretical background of a three-level ytterbium-doped fiber laser

In this section, we rapidly review the theoretical basis of three-level ytterbium-doped fiber lasers. Based on spectroscopic considerations, we first introduce the notion of transparency at the laser wavelength in a three-level laser scheme, with associated stiff constraints on the fiber geometry and on the pumping rate. In a second part, we discuss qualitatively the problem of gain competition between the four-level and the three-level system laser operation. These two points will then be analyzed in the context of our experimental conditions in section 4.

2.1 Transparency population inversion and transparency pump intensity

 

Fig. 1. (a) The three-level atomic system and (b) emission and absorption cross section of ytterbium in silica host [12].

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In Fig. 1(a), we present the three-level atomic system of ytterbium in a silica host. The laser emission at 977 nm corresponds to a transition between the lowest level of the excited ²F_5/2 manifold and the lowest level of the fundamental ²F_7/2 manifold while the absorption of the pump at 915 nm corresponds to a transition between the lowest level of the fundamental ²F_7/2 manifold and the upper level of the excited ²F_5/2 manifold. As shown on Fig. 1(b), ytterbium ions exhibit a strong emission cross section around 977 nm, associated with a broad absorption band around 915 nm. However, the large emission cross section at 977 nm is nearly equal to the absorption at the same laser wavelength (σ _eL=σ _aL=2.7 10^-20 cm² [12]). In fact, the latter scheme consists in a genuine three-level system implying stiff constraints on the pumping rate as well as on the amplifying medium geometry if operated in a laser configuration. In particular, in the absence of optical pumping, ytterbium-doped silica absorbs any signal in the 977 nm spectral range. Even though stimulated emission occurs, it will be annihilated by the corresponding absorption.

In order to reach the lasing threshold, it is then necessary to operate under strong pumping rate in a regime for which the amplifying medium becomes transparent to the laser radiation: emission outperforms absorption leading to a potential gain. The pumping intensity required to reach the transparency at the laser wavelength of 977 nm (denoted I_ptransL) and the corresponding inverted population ratio (denoted n_2trpL) are given by [13]:

Here, h is Planck’s constant, υ _p is the pump frequency, τ_fluo is the fluorescence lifetime of ytterbium ion in a silica host, σ _eL, σ _aL, σ _eP, σ _aP are the emission and absorption cross sections for the signal and the pump radiations, respectively. Considering a pump wavelength at 915 nm, a fluorescence lifetime of 0.9 ms, and cross section values [12] of σ _eL=σ _aL=2.7 10^-20 cm², σ _eP=5.3 10^-22 cm² and σ _aP=0.8 10^-20 cm², we find an inverted population ratio at the laser wavelength transparency of n_2trpL=0.5, and a transparency pump intensity of I_ptransL~30 kW/cm². In a fiber amplifier or laser, the pump intensity has to be greater than I_ptransL all along the fiber to invert approximately half the ion population and consequently bleach the reabsorption of the laser medium at 977 nm. Transparency conditions at the laser wavelength of 977 nm then leads to straight conditions on the required pumping level as well as on the fiber transverse geometry and length:

- First, the available pump power must be large compared to the transparency pump power P_ptransL, given by the product I_PtransL * S_g, where S_g is the pump clad area, to obtain a satisfying three-level laser efficiency.

- Second, for a fixed available pump power, local pump intensity can be increased above I_ptransL by decreasing the inner cladding surface S_g. However, this parameter is in practice not adjustable as it is imposed by the laser diode brightness. For the experiments reported in this paper, we use a laser diode emitting at 915 nm, delivering 230 W coupled on a 400 µm fiber (NA=0.22).

- Third, for fixed pump power and inner cladding surface, the fiber length value has to be limited to conserve a residual pump power at the fiber end above the limit fixed by the transparency pump power P_ptransL.

2.2 Gain competition between the 1030 nm and the 977 nm laser transitions

We now consider the problem of the competition between the three and four-level laser operation, as it constitutes a major issue for efficient operation on the three-level scheme. It is well known [10] that before reaching the lasing threshold at 977 nm, pumping at 915 nm induces a high gain at longer wavelengths with a weak re-absorption in the 1030 nm–1080 nm spectral range (see Fig. 1(b)). Because of the large gain in the 1030 nm spectral range, ASE noise severely degrades the slope efficiency of the three-level fiber laser. More detrimentally, it leads to spurious laser oscillation in the 1030 nm–1080 nm spectral range. To quantify this competition between the gain build-up around 977 nm and the one at longer wavelengths in double clad fiber laser, one can use the simple equation proposed by Nilsson et al [10]:

Here, G₁₀₃₀, G₉₇₇ and α are respectively the gain at 977 nm, the gain at 1030 nm, the pump absorption (in dB) and β the clad to core area ratio. From this expression, one can easily see that for fixed inner cladding (see section 2.1) and pump absorption, the detrimental gain at 1030 nm rapidly increases with the decrease of the core diameter indicating the intrinsic need for large core sizes.

3. High power three-level ytterbium-doped rod-type photonic crystal fiber laser experiments and results

In this third section, we report on our experimental results. We first present the state of the art, ultra-large core photonic crystal rod-type fiber used in these experiments. The experimental laser configuration we use is then described. Finally, we report on laser performances obtained with up to 94 W demonstrated in continuous wave regime over 6 nm around 977 nm.

3.1 Rod-type 80 µm core diameter photonic crystal fiber

The key element of our high power three-level fiber laser is a state of the art Yb doped ultralarge core single mode rod-type fiber, shown on Fig. 2:

 

Fig. 2. Center region of the rod-type photonic crystal fiber used in these experiments.

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As shown on Fig. 2, this photonic crystal fiber delivers a nearly diffraction-limited beam from an 80 µm diameter (NA_core ~0.01), providing a measured mode field diameter of 70 µm which is significantly higher than conventional LMA fibers. The inner cladding has a diameter of 200 µm and a very large numerical aperture (NA_clad > 0.7) defined by the surrounding air filled microstructure. In cladding-pumped configuration, this fiber exhibits a small signal pump absorption as high as α_p=10 dB/m at 915 nm. The extreme optogeometrical parameters of the rod-type fibre lead to a clad to core surface ratio of ~6.25 comparable with the fiber used in [8] but with a pump clad area of 31400 µm², that is two orders of magnitude larger, allowing the use of commercially available high power fibercoupled laser diode.

3.2 High power three-level fiber laser setup:

The high power three-level laser setup is depicted on Fig. 3:

 

Fig. 3. Experimental set-up of the high power clad pumped three-level fiber laser. DC RTF : double clad rod-type fiber.

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The rod-type fiber, whose geometry is described in Fig. 2, was end-pumped through a dichroïc mirror M₁ by a 230 W fiber coupled laser diode emitting at 915 nm (clad diameter of 400 µm, clad NA=0.22). This first mirror is highly reflective at the laser wavelength of 977 nm as well as 1030 nm. Because of the gain competition between these two laser transitions introduced in section 2.2, wavelength selective elements have to be implemented in the laser cavity to favor the three-level laser operation (mirrors characteristics are included in Fig. 3). Thus, dichroïc mirror M₂ is highly reflective at the laser wavelength 977 nm for a normal incidence and closes the three-level fiber laser cavity while introducing losses > 30 dB at 1030 nm. Unfortunately, these losses are not sufficient to prevent from parasitic lasing in the 1030 nm spectral range. Hence, another mirror M₃, introducing also losses > 30 dB at 1030 nm, was then added in the laser cavity. With a total radiation extinction in excess of 60 dB at 1030 nm, the laser spontaneously oscillates around 977 nm. The output coupler is simply achieved by the 4% Fresnel reflection of the cleaved fiber end. Mirror M₄ is highly reflective at wavelength above 950 nm and delivers the 977 nm laser beam without reflecting the remaining pump. This residual pump power is further re-injected in the clad of the photonic crytal fiber by mirror M₅, which is highly reflective at the pump wavelength for normal incidence.

3.3 Experimental results:

The output power curve of the three-level fiber laser is given in Fig. 4:

 

Fig. 4. Output characteristic of the laser. The laser threshold is reached for 18 W of pump power and the slope efficiency is 48%. The near field beam profile at maximum output power is displayed in inset.

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The laser threshold is reached for 18 W of pump power at 915 nm. At the maximum available pump power (230 W) the laser produces up to 94 W of continuous wave radiation at 977 nm. The slope efficiency is 48%, with respect to the diode pump power. This relatively low efficiency can be partially explained by incomplete pump absorption. Furthermore, the fiber used in these experiments was cleaved at both ends. An improved fiber end preparation process (polishing) should limit intra-cavity losses, increase the pump light coupling, and then lead to a higher laser efficiency. Due to the avoidance of polymer coating, no thermo-optical nor thermo-mechanical problems were observed up to the maximum output power. The near field intensity profile of the output beam from the 80 µm core rod-type fiber, measured at full output power, is shown on the inset of Fig. 4. It is power-independent, and characterized by a near diffraction limited beam quality M² < 1.2. No roll-off is observed in the laser characteristic, and these performances are only limited by the available pump power.

The laser output spectrum, measured at full output power with an optical spectrum analyzer with a resolution of 0.07 nm, is shown on Fig. 5:

As shown on the spectrum displayed on Fig. 5, the laser spontaneously oscillates on a 6 nm spectral range centered at 977 nm. Due to the efficient spectral filtering of the combined action of mirrors M₂ and M₃, the parasitic emission at 1030 nm is 35 dB below the laser peak signal at 977 nm. However, more than 98% of the spectral power density is contained within the 975 nm–980 nm spectral range. A narrower laser linewidth could be easily obtained by using an intra-cavity narrow bandwidth filter. The inset in the Fig. 5 shows the laser output spectrum as well as the amplified spontaneous emission (ASE) spectrum obtained by suppressing the M₂ retroaction, both in linear scale.

 

Fig. 5. High resolution laser output spectrum in dB. Inset: Laser (line) and ASE (dash) spectrum in linear scale

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4. Analysis and discussion

Here, we analyze the results reported in section 3 through numerical simulations. We first analyze the longitudinal evolution of residual pump power to determine the maximal fiber length which satisfies the conditions of transparency at the laser wavelength of 977 nm, in our pumping conditions. We then numerically consider our experimental setup including the pump reinjection. Finally, we discuss the gain competition between 977 nm and 1030 nm wavelength, to highlight the major fact that performances reported in this paper are intrinsically linked to the extreme opto-geometric parameters of rod-type PCF.

4.1 Pump absorption, fiber length limitation, and residual pump power recycling investigation

Considering the determined transparency pump intensity I_ptransL=30 kW/cm² (see section 2.1) and the rod-type PCF inner cladding surface of 31400 µm², the pump power needs to exceed the critical power of 11 W at 915 nm all along the fiber in order to bleach the re-absorption at 977 nm. In our experimental conditions where 230 W of pump power is injected in the fiber and 11 W of remaining power is released at the fiber end, the corresponding single pass pump absorption of 13 dB will set the upper limit of the fiber length, that we denote L_{abs(13 dB)}. It is important to notice that a direct evaluation of L_{abs(13 dB)} by use of the small signal pump absorption α_p will clearly lead to an under-estimated value of about 1.3 m because of the effect of pump absorption saturation effect. When pumped at 915 nm, ytterbium exhibits a saturation pump intensity I_psat=35 kW/cm² [13], corresponding in our experimental conditions to a pump power of 11 W in the cladding. As I_psat and I_ptransL are nearly equal, the pump absorption is here saturated all along the fiber. The dynamics of our system have been simulated by numerically solving the laser rate equations [13]. Local inversion density and photon density along the fiber are calculated in an iterative way, assuming cross sections values of Fig. 1(b) [12], an ytterbium doping concentration N_TOT=2.5 10^-19 cm^-3 and the geometrical parameters of the fiber given in Fig. 2. In Fig. 6, we have plotted the longitudinal residual pump power and the evolution of the inverted population ratio n₂, for a pump power of 230 W.

 

Fig. 6. Residual pump power (lower graph) and density of inverted population n₂ (upper graph) as a function of the fiber length for a launched pump power of 230 W. The transparency pump power P_trpL, the transparency inversion ratio n_2trpL, and the fiber length for 13 dB of pump absorption L_{abs(13 dB)} are added (blue dotted line). The experimental measurements of residual pump power for different length of rod-type fibers are also displayed (blue triangle).

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As shown on the lower graph of Fig. 6, for a launched pump power of 230 W, the fiber length has to be limited to L_{abs(13 dB)} ~200 cm to keep the residual pump power beyond the P_trL limit. For a fiber length shorter than L_{abs(13 dB)}, the inverted population ratio is kept beyond the n_2trpL limit, and re-absorption at 977 nm is consequently completely bleached all along the fiber.

To validate these calculations, we also made experimental measurements of residual pump power for four different lengths of rod-type fibers (respectively 57 cm, 77 cm, 101 cm and 123 cm). These experimental data are added on the graph (blue triangles), with a very good agreement with the theoretical predictions. Notice that pump absorption saturation effect is clearly visible here, as we estimate that pump absorption under this high pumping rate is reduced to 6 dB/m (for a small signal pump absorption of α_p=10 dB/m).

Because of the rigid silica outer cladding of 1.2 mm diameter, rod-type fibers can not be coiled nor bended and the estimated optimal length of 2 m is in practice not compatible with a compact laser setup. To reduce the fiber length without detrimental effect on the laser efficiency, it is possible to recycle the un-absorbed pump power in a double pass pump architecture.

The effect of residual pump power recycling is here numerically analyzed with the fiber dimension considered experimentally (see section 3), i.e. a fiber length L=1.23 m.

 

Fig. 7. Simulated co- and contra-propagating residual pump power (lower graph) and population inverstion ratio n₂ (upper graph) as a function of the location in the fiber for a launched pump power of 230 W. The transparency pump power P_trpL, the transparency inversion ratio n_2trpL, (blue dotted line) and the population inversion ratio for a single pump pass (red dotted line) are also added.

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We have plotted on Fig. 7 (lower graph) the calculated residual pump power as a function of the fiber length for a pump power of 230 W. The calculated residual pump power at the fiber end after one pump pass is ~65 W, which is in good agreement with experimental measurement (63 W, see Fig. 6). We have then simulated a second pass of this residual pump power in the inner cladding of the fiber. After two pump passes, the unabsorbed pump power is as low as 20 W, corresponding to a total pump absorption of more than 93% (~11 dB). The upper graph of Fig. 7 shows the longitudinal dependences of the inverted population ratio n₂ for the two configurations (single pass and double pass of the pump radiation). It varies from 0.8 to 0.7 (respectively 0.8 to 0.65) in a double pass configuration (respectively for a single pass configuration). Both configurations lead to a complete bleaching of the laser medium reabsorption well above the inversion ratio transparency limit n_2trpL. In conclusion, a 123 cm long fiber pumped with 230 W both enables the complete bleaching at the laser wavelength of 977 nm, as well as the efficient pump absorption.

4.2 Investigation of gain competition between 1030 nm and 977 nm laser transitions

In this section, we quantify the gain competition between 977 nm and 1030 nm laser transitions in the laser configuration investigated experimentally.

In the fiber laser depicted in Fig. 3, the saturated gain at 977 nm is fixed by the round trip losses at the laser wavelength. Considering the experimental cavity parameters (mirrors reflectivity of 100% and 4% at the laser wavelength 977 nm), they can be evaluated to ~14.6 dB. A single pass gain at 977 nm is therefore G₉₇₇=7.3 dB. The gain experienced by the 1030 nm radiation given by equation (4) with a pump absorption α=11 dB and a clad to core area ratio β=6.25 is >51 dB. These results are consistent with the necessity to introduce intracavity losses > 60 dB (given by mirrors M₂ and M₃) in our fiber laser setup to discriminate the 977 nm laser operation from the spurious operation at 1030 nm.

We now discuss the influence of the fiber core diameter on the gain competition between 977 nm and 1030 nm laser transitions. In fact, as mentioned earlier, for a pump absorption of 11 dB and a double pass scheme, the fiber length necessary to achieve 11 dB absorption L_{abs(11 dB)} increases rapidly with decreasing core diameter. Accordingly, as illustrated on Fig. 8, the gain experienced by the four-level laser transition at 1030 nm also increases with decreasing core diameter and may reach levels where the insertion of the corresponding losses is not anymore possible in practice.

More precisely, we have considered a fixed inner cladding diameter of 200 µm and determined numerically the value of L_{abs(11 dB)} in double pass scheme for a fiber core diameter varying from 10 µm to 80 µm. We have also calculated in the same core diameter range the required losses at 1030 nm using Eq. (3).

 

Fig. 8. Simulation 11 dB absorption fiber length L_{abs(11 dB)} (upper graph) in double pump pass configuration and required losses at 1030 nm (lower graph) with respect to the fiber core diameter and technology.

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As shown on the bottom curve of Fig. 8, for a 30 µm core diameter fiber, which represents a typical value for a state of the art non-PCF large mode area (LMA) fiber, the required fiber length for 11 dB absorption in a double pump pass scheme is about 8 m. In this case, the gain experienced by the 1030 nm radiation is about 300 dB (lower graph), which can not be compensated by any wavelength selective elements. However, we can reasonably consider filters able to suppress up 60 dB before spurious lasing around 1030 nm. Furthermore, even with a theoretical complete suppression of Rayleigh backscattering on the fiber ends or optics, a strong amplified spontaneous emission (ASE) in this spectral range will definitely degrade the slope efficiency of the three-level fiber laser. Considering an upper limit of 60 dB of gain at 1030 nm, efficient 977 nm laser operation imposes a minimal fiber core of about 70 µm and therefore a corresponding fiber length of L_{abs(11 dB)}=2.10 m. Thus, we highlight here the major fact that considering actual fiber as well as laser diodes technology, the power level experimentally demonstrated in this paper is intrinsically linked to the use of the rod-type photonic crystal fiber technology.

5. Conclusion

In conclusion, we have experimentally demonstrated and theoretically analyzed the possible applications of ultra-large core fiber photonic crystal fiber for high power operation at 977 nm. First, we have demonstrated a high power, clad pumped rod-type fiber laser operating in a continuous wave regime on the three-level laser transition at 977 nm. The average power of 94 W obtained is, to our knowledge, the highest power ever generated at this wavelength in a nearly diffraction limited beam. The slope efficiency was as high as 48% with respect to the pump power. To our knowledge, this performance represents the highest power achieved from a single-mode solid-state laser operating at this wavelength. Then, we have introduced and numerically investigated the critical phenomenons which have to be considered to understand and design such a laser: transparency pump power, pump absorption saturation and gain competition between the three and four-level laser operation. We conclude this work by highlighting that the performances reported in this work are directly linked to the used technology of ultra-large core rod-type PCF. However, the analysis proposed in this paper also provides the theoretical background necessary to design fiber lasers to be operated as a three-level system for different given output power.

Recently, more than 710W was achieved from a 1.2 m long rod-type fiber operating at 1030 nm and pumped at 976 nm with a record power extraction of about 500 W/m [14]. These values clearly show the power scalability of rod-type fiber based laser setup, and that performances reported on this paper should be improved by use of higher level pump diodes. Furthermore, these results open new ways for efficient frequency conversion in the blue region from fiber laser sources as well as for high pumping level.