Two-wavelength passively Q-switched ytterbium doped fiber laser

doi:10.1364/OE.16.011858

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Two-wavelength passively Q-switched ytterbium doped fiber laser

Lei Pan, Ilya Utkin, and Robert Fedosejevs »View Author Affiliations

Optics Express, Vol. 16, Issue 16, pp. 11858-11870 (2008)
http://dx.doi.org/10.1364/OE.16.011858

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– Abstract
1. Introduction
2. Experimental setup
3. Experimental results
4. Theoretical analysis and discussions
5. Summary
– References and links

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Abstract

A high power passively Q-switched dual wavelength Yb fiber laser using a Cr⁴⁺:YAG saturable absorber has been realized. Two wavelengths centered at 1040 nm and 1070 nm are generated directly from the cladding pumped Yb doped fiber laser. The pulse trains exhibit regions of stability and instability dependent on the pump power. At a pump power of 7.8 W, 1040 nm and 1070 nm pulses are generated alternatively, with pulse durations of 105 ns, pulse-repetition rates of 32 KHz and average pulse energies of 56 μJ and 47 μJ, respectively. A theoretical model is developed to simulate the two-wavelength Q-switched operation, which gives qualitative agreement with the experimental observations.

1. Introduction

Recently there has been considerable interest in studying Yb doped fiber lasers because of their beneficial properties for a number of applications. With a small quantum defect, Yb doped fiber lasers are suitable for high power operation with reduced thermal loading. The relatively long upper-state lifetime of Yb enables more efficient pumping from a given diode pump source and storage of a large amount of energy which is of benefit for Q-switching operation. A number of actively and passively Q-switched double-clad Yb fiber lasers have been reported to date [1-6

J. A. Alvarez-Chavez, H. L. Offerhaus, J. Nilsson, P. W. Turner, W. A. Clarkson, and D. J. Richardson,“High-energy, high-power ytterbium-doped Q-switched fiber laser,” Opt. Lett. 25, 37–39 (2000). [CrossRef]

]. The emission spectrum of Yb is also broad which allows wide wavelength tuning or multi-wavelength lasing. Recently a few multi or two-wavelength Yb doped fiber lasers have been demonstrated, with different configurations for the wavelength selection and stabilization. These include the use of spatial mode beating in multimode fiber [7

R. Chi, K. Lu, and S. Chen, “Multi-wavelength Yb-doped fiber ring laser,” Microwave Opt. Technol. Lett. 36, 170–172 (2003). [CrossRef]

], a few-mode fiber Bragg grating (FBG) together with polarization control working as a filter [8

X. Feng, Y. Liu, S. Fu, S. Yuan, and X. Dong, “Switchable dual-wavelength ytterbium-doped fiber laser based on a few-mode fiber grating,” IEEE Photon. Technol. Lett. 16, 762–764 (2004). [CrossRef]

], dual frequency generation using the birefringence of a polarization-maintaining (PM) FBG [9

W. Guan and J. R. Marciante, “Dual-frequency operation in a short-cavity Ytterbium-doped fiber laser,” IEEE Photon. Technol. Lett. 19, 261–263 (2007). [CrossRef]

], dual wavelength operation using a FBG stabilized by four wave mixing [10

L. R. Chen and X. J. Gu, “Dual-wavelength Yb-doped fiber laser stabilized through four-wave mixing,” Opt. Express 15, 5083–5088 (2007),http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-5083. [CrossRef] [PubMed]

], and a Mach–Zehnder interferometer (MZI) operating as a comb filter [11

C. Tu, W. Guo, Y. Li, S. Zhang, and F. Lu, “Stable multiwavelength and passively mode-locked Yb-doped fiber laser based on nonlinear polarization rotation,” Opt. Commun. 280, 448–452 (2007). [CrossRef]

]. All the above lasers operated in the CW region. In many cases, pulsed lasers operating at high peak power are of interest for applications such as laser micromaching and laser sensing. Hu et. al. [12

S. L. Hu, J. Yu, C. Q. Gao, G. H. Wei, and F. Y. Lü, “Dual-wavelength stable nanosecond pulses generation from cladding-pumped fiber laser,” Chin. Opt. Lett. 4, 655–657 (2006).

] reported a dual wavelength nanosecond Yb doped fiber laser based on the mechanism of stimulated Brillouin scattering (SBS) induced self-Q-switching. The two wavelengths 1109.6 nm and 1127.6 nm were reportedly due to the birefringence in the fiber and the pulse energy was relatively low (~nJ) in this case. In this paper we present a high power multi-μJ two-wavelength passively Q-switched Yb fiber laser based on a Cr⁴⁺:YAG saturable absorber (SA). The two wavelengths centered at 1040 nm and 1070 nm were generated without using any spectral control mechanism and arise from the natural peaks in the net gain curve. A theoretical model is developed and the resultant simulations could explain the two-wavelength operation reasonably well.

2. Experimental setup

The laser configuration is shown in Fig. 1. A Yb doped single-mode double-clad fiber with a length of ~1.9 m was used as a gain medium. The fiber core/inner cladding diameters (numerical aperture NA) were 10/125 μm (0.08/0.46). Cladding absorption at 976 nm was approximately 6.5 dB/meter. The pump laser was a fiber coupled diode laser with a center wavelength of 976 nm. The Pump light was coupled into the active fiber by two collimating lenses L1, L2 and a dichroic mirror (DM) with >96% transmission at 976 nm and >99% reflectance at 1030-1100 nm. End-caps were put onto both ends of the fiber to avoid unnecessary reflection and damage. A broadband high-reflection (HR) mirror at the left side and a mirror with 4% reflection on the right side were used as a rear mirror and an output coupler, respectively. Lenses 3 and 4 were used to focus the laser through the SA (T₀=30% at 1064 nm) with a focal spot diameter of ~15 μm. A diffraction grating (1180 g/mm) was used for spectral separation of the laser output. To detect the dynamics of the two wavelength output two fast photodiodes were placed at a distance of ~2 m from the grating where the spectrum displayed two well separated peaks. Each photodiode was centered on the corresponding peak and connected to a two channel digital oscilloscope.

Fig. 1. Experiment setup; HR-high reflection mirror; SA - saturable absorber T₀=30%; Yb DC fiber - Yb doped single-mode double-clad fiber; DM - dichroic mirror; L1, L2, L3 and L4 are focusing or imaging lenses; LD - fiber coupled pump laser diode; BS - beam splitter; PD1, PD2 – photodiodes; OC – output coupling mirror 4% reflection; the arrow (→) marks the direction convention for distance x in the theoretical simulation.

3. Experimental results

The gain and absorption spectra of Yb fiber are shown in Fig. 2. During operation two output wavelength components were observed as shown in Fig. 3. The dependency of the average output power at 1040 nm and 1070 nm and the total output power on pump power was measured with a power meter and is shown in Fig. 4. Two-wavelength emissions appeared when the pump power was 3.5 W or higher; below this power, only one output wavelength at 1040 nm existed. The spectral positions of two-wavelength peaks were stable with pump power, with a minor shift of the short wavelength peak from 1040 nm to 1042 nm when the pump power increased up to 9.9 W. A total output power of 4.2 W was obtained at a pump power of 9.9 W, with a slope efficiency of 44%. The ratio of average power at the two wavelengths was determined by measuring the two beams in the first diffraction order from the grating. As can be seen in the figure, the 1040 nm power at first increased with the pump power; reached a maximum at a pump power of 7.8 W and then decreased. The 1070 nm output increased steadily with the pump power.

Fig. 2. Absorption and emission cross section of Yb doped fiber, provided by the fiber manufacturer LIEKKI.

Fig. 3. Laser output spectrum measured by a compact spectrometer (Ocean-Optics with resolution ~1.5 nm) at a pump power of 7.8 W; the low peak height at 1070 nm is due to the rapidly decreasing responsivity of the silicon based spectrometer CCD at this wavelength.

Fig. 4. Dependences of total average power, 1070 nm, and 1040 nm power on pump power.

At a pump power of 4.5 W, the pulse trains for both wavelengths exhibited a period-doubled behavior; a big-small 1040 nm pulse pattern was accompanied with a big-small 1070 nm pulse pattern, as shown in Fig. 5(a). The average powers for 1040 nm and 1070 nm were 1.4 W and 0.4 W; and pulse durations (Fig. 5(b)) were about 100 ns and 300 ns, respectively. At this pump power, the 1040 nm emission dominates in the wavelength competition, experiencing higher gain, and achieving higher pulse energy and shorter pulse duration. As also can be seen in Fig. 5(b), the 1070 nm pulse was ~500 ns later than 1040 nm pulse.

With an increase in pump power, the output at 1070 nm increased significantly; the big-small and big-small pulse patterns became unstable and changed to big-small small-big patterns for the two wavelengths respectively: a strong 1040 nm pulse was accompanied with a weak 1070 nm pulse, and vice versa. At a pump power of 7.8 W, the weak pulse almost disappeared in the pattern and the two-wavelength pulses appeared alternatively. The 1040 nm pulse train still exhibited period-doubled shape and the 1070 nm pulse train was stable, as shown in Fig. 6(a). Average outputs of 1.8 W and 1.5 W have been obtained for 1040 nm and 1070 nm, with a pulse repetition rate of 32 KHz and average pulse energies of 56 μJ and 47 μJ. Considering their same pulse durations of 105 ns, the peak powers of two wavelengths pulses were 533 W and 448 W, respectively. At this pump power, the two wavelengths achieved a balance in competition in gain and dominated alternatively with every second pulse. With further increase in the pump power, the output at 1070 nm increased further and the pulse pattern became more complicated. A new stable pattern was formed at a pump power of ~9.9 W; in this case period-2 for 1040 nm and period-6 for 1070 nm output was observed, as shown in Fig. 6(b). The dual wavelength operation also depended on fiber length;longer fibers would lase primarily around 1070 nm while shorter fibers would lase around 1040 nm. However similar behavior was observed for fibers with approximate lengths from ~1.6 m to ~2.0 m.

Fig. 5. Synchronized (a) pulse trains and (b) pulse shapes of the output at the two wavelengths for a pump power of 4.5 W, the dashed line marks the peak of 1040 nm pulse. The intensity of 1070 nm pulse has been amplified for convenience of viewing.

Fig. 6. Synchronized pulse trains at a pump power of (a) 7.8 W (b) 9.9 W.

4. Theoretical analysis and discussions

Yb doped fiber lasers have a very broad emission spectrum from approximately 970 nm to 1200 nm. In the case of homogenous broadened medium, the wavelength with the highest net gain will build up the quickest and deplete the inversion number thus suppressing the gain for other wavelengths. However Q-switching is not a static process; the gain for each wavelength is changing with time as well as the position along the fiber. To understand this behaviour, we have theoretically simulated the Q-switched operation using a multi-wavelength model. For Yb doped double clad fiber, the equations are [13

Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber laser,” Appl. Opt. 45, 2058–2071 (2006). [CrossRef] [PubMed]

N_{0} = N_{1} + N_{2}

(1)

\frac{{\partial N}_{2} (x, t)}{\partial t} = \frac{Γ_{p} λ_{p}}{{hcA}_{co}} [σ_{αp} N_{1} (x, t) - σ_{ep} N_{2} (x, t)] {P_{p}}^{-} (x, t)

+ \sum_{k} \frac{Γ_{k} λ_{k}}{{hcA}_{co}} [σ_{αk} N_{1} (x, t) - σ_{ek} N_{2} (x, t)] ({P_{k}}^{+} (x, t) + {P_{k}}^{-} (x, t)) - \frac{N_{2} (x, t)}{τ}

(2)

- \frac{{\partial P}_{p}^{-} (x, t)}{\partial x} + \frac{1}{v_{p}} \frac{{\partial P}_{p}^{-} (x, t)}{\partial t} = Γ_{p} [σ_{ep} N_{2} (x, t) - σ_{αp} N_{1} (x, t)] {P_{p}}^{-} (x, t) - α_{p} . {P_{p}}^{-} (x, t)

(3)

\pm \frac{{\partial P}_{k}^{\pm} (x, t)}{\partial x} + \frac{1}{v_{k}} \frac{{\partial P}_{k}^{\pm} (x, t)}{\partial t} = Γ_{k} [σ_{ek} N_{2} (x, t) - σ_{αk} N_{1} (x, t)] {P_{k}}^{\pm} (x, t) - α_{k} {∙ P}_{k}^{\pm} (x, t) + {2 Γ}_{k} σ_{ek} N_{2} (x, t) \frac{{hc}^{2}}{λ_{k}^{3}} {Δλ}_{k}

(4)

where N₀ is the total Yb dopant concentration (Provided by LIEKKI); N₁and N₂ are ground and excited number densities. P_p ^- represents the backward propagating pump power.P_k ^±are the forward and backward propagating laser radiation. k is a spectral index allowing multiple simultaneous wavelengths to grow and interact within the laser cavity. To simulate the behaviour observed experimentally only the two wavelengths at 1040 nm and 1070 nm were chosen and retained in order to explore the system dynamics. σ_αp, σ_ep, σ_αk, σ_ek are the absorption and emission cross sections of Yb ion at pump wavelength and each emission wavelength, respectively (shown in Fig. 2). The pump (emission) and fiber core overlap factors Γ_p(s) were calculated with Gaussian shape assumption for signal waves. For the spontaneous emission bandwidth we have used Δλ_k=30 nm for each of the two components.The fiber refractive index was set as n=1.5 and the pump and emission group velocities v_p and v_k were both set to c/n, where c is the speed of light in vacuum. h is the plank constant, τ is the lifetime of Yb, and α_p(k) is the fiber attenuation at pump (emission) wavelength.

For Cr⁴⁺:YAG SA, we have used a point model [14

Y. M. Huo and P. K. Cheo, “Modeling of passively Q-switched Er³⁺/Yb³⁺-codoped clad-pumped fiber lasers,” IEEE J. Sel. Top Quantum Electron. 11, 658–665 (2005). [CrossRef]

N^{sa} = N_{1}^{sa} (t) + N_{2}^{sa} (t)

(5)

T_{k} (t) = \exp [- {2 L}_{sa} (σ_{gska} N_{1}^{sa} + σ_{esak} N_{2}^{sa})]

(6)

\frac{{dN}_{2}^{sa}}{dt} = \sum_{k} \frac{P_{k}^{+} (0, t) + P_{k}^{-} (0, t)}{2} \frac{λ_{k}}{A_{sa} hc} σ_{gsak} N_{1}^{sa} - \frac{N_{1}^{sa}}{τ_{sa}}

(7)

where N^sa is the total ion doping, N₁ ^sa and N₂ ^sa are the ground and excited level number intensities; T_k(t) is the instantaneous two way transmission of the SA, and σ_gsa, σ_esa are the ground-state and excited-state-absorption cross sections, respectively. L_sa is the thickness of the SA (~4.5 mm). Asa is the focal spot area on the SA; τ_sa is the lifetime of the excited state. N^sa was calculated based on L_sa, initial transmission T₀=30% and σ_gsa=4.3×10^-18 cm² [15

X. Y. Zhang, S. Z. Zhao, Q. P. Wang, Q. D. Zhang, L. K. Sun, and S. J. Zhang, “Optimization of Cr-doped saturable-absorber -switched lasers,” IEEE J. Quantum Electron. 33, 2286–2294 (1997). [CrossRef]

] at 1064 nm. T0 was measured to be 26% at 1040 nm and 35% at 1070 nm, so σ_gsa can be estimated at the two wavelengths. For the ratio of σ_gsa/σ_esa, we have used 6 and 4 for 1040nm and 1070 nm as approximate values [16

H. Ridderbusch and T. Graf, “Saturation of 1047- and 1064nm absorption in Cr⁴⁺:YAG crystals,” IEEE J.Quantum Electron. 43, 168–173 (2007). [CrossRef]

]. Because the SA is relatively thick and the focused beam was not uniform in the SA; the positions far from the focal spot may not be well saturated and thus would contribute towards the non-saturable loss rather than acting as a saturable absorber. In the simulation we have used L_sa=3.5 mm and an averaged focal spot diameter d_sa=70 μm to represent the central region of SA where the saturation is expected. The above equations are solved under the boundary conditions given by:

P_{p}^{-} (L) = P_{0}

(8)

P_{k}^{-} (L, t) = P_{k}^{+} (L, t) R_{oc}

(9)

P_{k}^{+} (0, t) = P_{k}^{-} (0, t) {(1 - η)}^{2} T_{k} (t)

(10)

where P₀ is the pump power, L is the fiber length, R_oc=0.04 is the reflectivity of the output coupler, η is the loss at the high reflector end ( ~15% one way) due to the non-saturable loss of the saturable absorber, Fresnel reflection from the end-cap, coating loss and lens coupling loss, etc.. The values of parameters used in simulation are shown in Table 1.

Table 1. Values of parameters in simulation

Parameters	Values	Parameters	Values
N₀	9.0×10¹⁹/cm³	τ	850 μs [17 Y. Sintov, O. Katz, Y. Glick, S. Acco, Y. Nafcha, A. Englander, and R. Lavi, “Extractable energy from ytterbium-doped high-energy pulsed fiber amplifiers and lasers,” J. Opt. Soc. Am. B 23, 218–230 (2006). [CrossRef] ]
σ_e1040	5.86×10^-21cm²	σ_e1070	2.47×10^-21cm²
σ_α1040	3.34×10^-22cm²	σ_α1070	2.51×10^-23cm²
Γ₁₀₄₀	0.811	Γ₁₀₇₀	0.799
α_P(k)	0.005 m^-1	Γ_p	0.064
N_sa	6.2×10¹⁷/cm³	τ_sa	4μs [15 X. Y. Zhang, S. Z. Zhao, Q. P. Wang, Q. D. Zhang, L. K. Sun, and S. J. Zhang, “Optimization of Cr-doped saturable-absorber -switched lasers,” IEEE J. Quantum Electron. 33, 2286–2294 (1997). [CrossRef] ]
σ_gsa1040	4.8×10¹⁸ cm²	σ_gsa1070	3.8×10¹⁸ cm²

The simulation results show that the two emission wavelengths can co-exist in the Q-switched operation; the ratio of the power between two wavelengths depended on the fiber length and pump power; long fibers and higher pump will favour 1070 nm radiation. We have fixed the fiber length L=190 cm and investigated the Q-switching characteristics at different pump powers, which are shown in Fig. 7(a-f). At a pump power of 5 W, the 1040 nm dominates in the output, achieving much higher peak power (~560 W compared with ~5 W).With an increase of pump power to 8 W, the 1070 nm wavelengths observes higher gain and starts to induce instabilities to the pulse train: An alternative big-small pulse pattern starts to be evident. At a pump power of 11 W, the weak pulse almost disappears in the big-small pattern, and the two wavelengths appear alternatively, which is similar to the experimental results shown in Fig. 6(a). With further increase to a pump power to 18 W, the pulse intensities return to constant values; the 1070 nm wavelength dominates the output and achieves higher peak power (~580 W compared with ~115 W for 1040 nm). The time delay of 1070 nm pulse to 1040 nm pulse is shown in Fig. 7(b) and 7(f). The output at 1040 nm precedes the output at 1070 nm similar to that in Fig. 5(b).

Fig. 7. Simulated Q-switched pulse trains and shapes at different pump powers P₀, fiber length L= 190 cm; (b) the dashed line marks the peak of 1040 nm pulse; (f) t₁ to t₆ mark different times through the pulse at a pump power of 18 W, which are explained in Fig. 8. Note each plot uses different vertical scale.

Since the Yb ion inversion number is changing with time and position in the fiber, we can define a position averaged inversion number density as:

{\underline{N}}_{2} (t) = \int_{0}^{L} \frac{N_{2} (x, t) dx}{L}

(11)

The two-way signal gain (loss) for each wavelength with fiber and SA at an instantaneous time can be estimated as:

gk (t) = 2 . L . Γ_{k} . [σ_{ek .} {\underline{N}}_{2} (t) - σ_{αk} . (N_{0} - {\underline{N}}_{2} (t))] - \ln [\frac{1}{T_{k} (t)}]

(12)

With a relatively larger σ_e, there is higher gain at 1040 nm when N̲₂(t) is higher; also with much smaller σ_α, the lasing threshold for1070 nm is lower: N̲₂ ^th ₁₀₇₀<N̲₂ ^th ₁₀₄₀. Thus there exists a critical value N̲₂ ^c above which g_1040nm>g_1070nm and below which g_1070nm> g_1040nm. At an early stage of each pulse when N̲₂(t) is its maximum (N̲₂ 0), g_1040nm> g_1070nm; the 1040 nm wavelength pulse can build up and bleach the SA more quickly, and lead to emission at 1040 nm early in time. With the decrease of N̲₂(t) throughout the pulse to N̲₂ ^c, higher gain is observed at 1070 nm sometime later during the pulse. With lower threshold, the 1070 nm wavelength continues to see gain even after the 1040 nm wavelength is no longer amplified.Thus the 1070 nm pulse can deplete N̲₂(t) to a deeper final level N̲₂ ^f, which explains why the 1070 nm pulse could lase well after 1040nm pulse, as shown in Fig. 5(b) and Fig. 7(b, f). Fig. 8 shows an example of how the inversion number along the length of fiber changes during the stages discussed above for a pump power of 18 W; the times t₁ to t₆ are defined in Fig. 7(f). As shown in the figure, the gain drops below threshold at t₃ and t₄ for 1040 nm and 1070 nm wavelengths respectively. In the period of time from t₅ to t₆ the 1070 nm laser pulse continues to deplete the inversion number after the 1040 nm pulse has finished. If we increase the fiber length without changing other parameters, the overall inversion number will be distributed over a longer fiber. Thus N̲₂ ⁰ will decrease and the 1070 nm emission will dominate sooner. If the fiber is long enough then N̲₂ ⁰ drops below N̲₂ ^th ₁₀₄₀, and the 1040 nm emission will completely disappear.

Fig. 8. Inversion number distribution along fiber at different times which are shown in Fig.7(f); t₁ and t₆ are the times when the inversion number is maximum and minimum; t₃ and t₄ mark the peaks of the two pulses when the inversion number drops to threshold for 1040 nm and 1070 nm wavelengths respectively; t₂ is the time when the gain at 1070 nm becomes higher than at 1040 nm; t₅ marks 10% intensity tail of the 1040 nm pulse.

The situation is further complicated by the recovery time and spectral characteristics of the saturable absorber. At a low pump power, the pulse repetition rate is low and the time period between pulses is long; so the saturable absorber recovers to its thermal equilibrium state between pulses. Thus N̲₂ ⁰ is high to overcome the large initial absorption in the saturable absorber and the 1040 nm wavelength dominates in each pulse. At a high pump power, the pulse separation time and the recovery time for saturable absorber is short, thus N̲₂ ⁰ is lower in order to reach the switching threshold, and emission at 1070 nm wavelength will become stronger. The 1040 nm (1070 nm) pulse will dominate only when the pump power is very low (high). For a medium pump power, the two wavelengths both see net gain; they dominate in the output alternatively and big-small pulse patterns are observed. Fig. 9 shows the dynamics of g₁₀₄₀(t), g₁₀₇₀(t), N̲₂(t) and N̲₂ ^sa with the 1040 nm and 1070 nm output pulses at a pump power of 11W. As can be seen in the figure, after a stronger 1070 nm pulse, the inversion number is depleted to a deeper level. It takes longer time for the pump to restore the inversion number. At the same time the saturable absorber has more time to recover and N̲₂ ^sa reaches a lower value for the start of the next pulse. Thus N̲₂ ⁰ will be higher for the next pulse and the 1040 nm wavelength will dominate. After the strong 1040 nm pulse the inversion number is not depleted so deeply and the time to buildup to the next pulse time is shorter, thus 1070 nm will dominate in turn for next pulse. So the two wavelengths dominate alternatively as shown in Fig. 6(a) and Fig. 7(d). In the figures, there is a longer time period between pulses after a 1070 nm pulse compared to after a 1040 nm pulse, which also agrees with the above explanation. Figure 10 shows an expanded view of the details of the changes in g₁₀₄₀(t),g₁₀₇₀(t) within the time duration of the pulses themselves. As depicted in Fig. 9 g₁₀₄₀(t) becomes higher than g₁₀₇₀(t) sometime preceding the pulses and then drops below g₁₀₇₀(t) sometimes during the pulse. For the 1070 nm dominated case shown in Fig. 10(a), the 1070 nm output overcomes 1040 nm output all the time during the pulse, although g₁₀₄₀(t) is slightly higher than g₁₀₇₀(t) during a relatively short period.

Fig. 9. Simulated dynamics of g₁₀₄₀(t), g₁₀₇₀(t), N̲₂(t) and N̲₂ ^sa with 1040 nm or 1070 nm pulses at a pump power of 11 W. The pulse train is also shown in Fig. 7(d). Cavity linear loss (~3.56) includes output coupler loss, cavity loss η, and fiber attenuation α_k.

Fig. 10. Expanded views in time of g₁₀₄₀(t) and g₁₀₇₀(t) for the pulses P1 and P2 shown in Fig. 9.The vertical dashed lines mark the time when g₁₀₇₀(t) becomes higher than g₁₀₄₀(t) during the pulses.

Fig. 11. Yb energy levels [21

K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Appl. Phys. 91, 576–581 (2002). [CrossRef]

]; 974nm represents pump absorption transition; 1040nm and 1068nm represent two lasing transitions in this experiment.

The above modeling and discussion can explain the coexistence of the two peak wavelengths, with longer fibers and higher pump powers favoring 1070 nm output, as well, the pulse instabilities such as the two wavelengths lasing alternatively in the pulse train.However we have not reproduced all the pulse patterns in the experiment, such as big-small and big-small pattern for the two wavelengths respectively in Fig. 5(a) and period-6 behaviors in Fig. 6(b). In a passive Q-switched laser, pulse instabilities due to nonlinear dynamics have been reported and investigated recently [18-20

J. J. Zayhowski and C. Dill III, “Diode-pumped passively Q-switched picosecond microchip lasers,” Opt.Lett. 19, 1427–1429 (1994). [CrossRef] [PubMed]

]. In [19

D. Y. Tang, S. P. Ng, L. J. Qin, and X. L. Meng, “Deterministic chaos in a diode-pumped NdYAG laser passively Q switched by a Cr⁴⁺ :YAG crystal,” Opt. Lett. 28, 325–327 (2003). [CrossRef] [PubMed]

], a period-doubled route to chaotic pulse trains have been observed in a passively Q-switched Nd:YAG laser operating under specific cavity configurations and pump powers. The nonlinear behavior arose from including the rapid relaxation between levels in the lower manifold. In the modeling, in addition to the two-level model for the Nd ion that was conventionally used, the authors included splitting of the ground level with a relaxation lifetime of ~30 ns (compared to an upper level lifetime of ~230 μs). The period-doubling to chaotic pulse shapes could be observed in the simulation under certain pump conditions. Fig. 11 shows the Yb ion energy levels in a fiber involved in the lasing output around 1050 nm. The upper and lower manifolds include three and four stark shifted levels, respectively. The 1040 nm and 1070 nm output radiation correspond to transitions from the bottom of upper level to two different sublevels of the lower manifold.Due to the strong broadening of Yb ions in glass at room temperature, the transitions between the sublevels are not fully resolved [22

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium- doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997). [CrossRef]

]. A complete simulation of two wavelength operation would require a more advanced model, in which transitions between the sublevels should be considered, and will be the subject of future work.

5. Summary

A high power two-wavelength passively Q-switched Yb doped fiber laser has been demonstrated with a very simple cavity configuration. Single transverse mode output at 1040 nm and 1070 nm was obtained with tens of micro-joule pulse energies and hundred nanosecond pulse durations. The two-wavelength generation can be achieved for particular configurations where the effective net gains seen by both wavelengths are comparable and is dependent on fiber length, pump power and cavity Q. A theoretical simulation model qualitatively explains the dynamics of the two wavelengths behavior observed in the experiment indicating that longer fibers and higher pump powers favor 1070 nm laser output and reproduces the pulse pattern where two wavelength pulses alternate at an intermediate pump power. A more advanced model will be required to obtain more quantitative agreement with the details observed in the experiment.

Acknowledgments

Financial support from MPB Technologies Inc. and the Natural Sciences and Engineering Research Council is gratefully acknowledged.

References and links

1.	J. A. Alvarez-Chavez, H. L. Offerhaus, J. Nilsson, P. W. Turner, W. A. Clarkson, and D. J. Richardson,“High-energy, high-power ytterbium-doped Q-switched fiber laser,” Opt. Lett. 25, 37–39 (2000). [CrossRef]
2.	C. C. Ranaud, H. L. Offerhaus, J. A. Alvarez-Chavez, C. J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, “Characteristics of Q-switched cladding-pumped ytterbium- doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron. 37, 199–206 (2001). [CrossRef]
3.	A. Piper, A. Malinowski, K. Furusawa, and D. J. Richardson, “High-power, high- brightness, mJ Q-switched ytterbium-doped fibre laser,” Electron. Lett. 40, 928–929 (2004). [CrossRef]
4.	M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr⁴⁺:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764–766 (2006). [CrossRef]
5.	J. Y. Huang, H. C. Liang, K. W. Su, and Y. F. Chen, “High power passively Q-switched ytterbium fiber laser with Cr⁴⁺:YAG as a saturable absorber,” Opt. Express 15, 473–479 (2007),http://www.opticsexpress.org/abstract.cfm?uri=OE-15-2-473 [CrossRef] [PubMed]
6.	L. Pan, I. Utkin, and R. Fedosejevs, “Passively Q-switched ytterbium doped double-clad fiber laser with a Cr⁴⁺:YAG saturable absorber,” IEEE Photon. Technol. Lett. 19, 1979–1981 (2007). [CrossRef]
7.	R. Chi, K. Lu, and S. Chen, “Multi-wavelength Yb-doped fiber ring laser,” Microwave Opt. Technol. Lett. 36, 170–172 (2003). [CrossRef]
8.	X. Feng, Y. Liu, S. Fu, S. Yuan, and X. Dong, “Switchable dual-wavelength ytterbium-doped fiber laser based on a few-mode fiber grating,” IEEE Photon. Technol. Lett. 16, 762–764 (2004). [CrossRef]
9.	W. Guan and J. R. Marciante, “Dual-frequency operation in a short-cavity Ytterbium-doped fiber laser,” IEEE Photon. Technol. Lett. 19, 261–263 (2007). [CrossRef]
10.	L. R. Chen and X. J. Gu, “Dual-wavelength Yb-doped fiber laser stabilized through four-wave mixing,” Opt. Express 15, 5083–5088 (2007),http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-5083. [CrossRef] [PubMed]
11.	C. Tu, W. Guo, Y. Li, S. Zhang, and F. Lu, “Stable multiwavelength and passively mode-locked Yb-doped fiber laser based on nonlinear polarization rotation,” Opt. Commun. 280, 448–452 (2007). [CrossRef]
12.	S. L. Hu, J. Yu, C. Q. Gao, G. H. Wei, and F. Y. Lü, “Dual-wavelength stable nanosecond pulses generation from cladding-pumped fiber laser,” Chin. Opt. Lett. 4, 655–657 (2006).
13.	Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber laser,” Appl. Opt. 45, 2058–2071 (2006). [CrossRef] [PubMed]
14.	Y. M. Huo and P. K. Cheo, “Modeling of passively Q-switched Er³⁺/Yb³⁺-codoped clad-pumped fiber lasers,” IEEE J. Sel. Top Quantum Electron. 11, 658–665 (2005). [CrossRef]
15.	X. Y. Zhang, S. Z. Zhao, Q. P. Wang, Q. D. Zhang, L. K. Sun, and S. J. Zhang, “Optimization of Cr-doped saturable-absorber -switched lasers,” IEEE J. Quantum Electron. 33, 2286–2294 (1997). [CrossRef]
16.	H. Ridderbusch and T. Graf, “Saturation of 1047- and 1064nm absorption in Cr⁴⁺:YAG crystals,” IEEE J.Quantum Electron. 43, 168–173 (2007). [CrossRef]
17.	Y. Sintov, O. Katz, Y. Glick, S. Acco, Y. Nafcha, A. Englander, and R. Lavi, “Extractable energy from ytterbium-doped high-energy pulsed fiber amplifiers and lasers,” J. Opt. Soc. Am. B 23, 218–230 (2006). [CrossRef]
18.	J. J. Zayhowski and C. Dill III, “Diode-pumped passively Q-switched picosecond microchip lasers,” Opt.Lett. 19, 1427–1429 (1994). [CrossRef] [PubMed]
19.	D. Y. Tang, S. P. Ng, L. J. Qin, and X. L. Meng, “Deterministic chaos in a diode-pumped NdYAG laser passively Q switched by a Cr⁴⁺ :YAG crystal,” Opt. Lett. 28, 325–327 (2003). [CrossRef] [PubMed]
20.	M. D. Wei, C. H. Chen, and K. C. Tu, “Spatial and temporal instabilities in a passively Q-switched Nd:YAG laser with a Cr⁴⁺:YAG saturable absorber,” Opt. Express 12, 3972–3980 (2004),http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-17-3972. [CrossRef] [PubMed]
21.	K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Appl. Phys. 91, 576–581 (2002). [CrossRef]
22.	R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium- doped fiber amplifiers,” IEEE J. Quantum Electron. 33, 1049–1056 (1997). [CrossRef]

OCIS Codes
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3540) Lasers and laser optics : Lasers, Q-switched

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: May 19, 2008
Revised Manuscript: July 10, 2008
Manuscript Accepted: July 10, 2008
Published: July 24, 2008

Citation
Lei Pan, Ilya Utkin, and Robert Fedosejevs, "Two-wavelength passively Q-switched ytterbium doped fiber laser," Opt. Express 16, 11858-11870 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11858

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References

J. A. Alvarez-Chavez, H. L. Offerhaus, J. Nilsson, P. W. Turner, W. A. Clarkson, and D. J. Richardson, "High-energy, high-power ytterbium-doped Q-switched fiber laser," Opt. Lett. 25, 37-39 (2000). [CrossRef]
C. C. Ranaud, H. L. Offerhaus, J. A. Alvarez-Chavez, C. J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium- doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001). [CrossRef]
A. Piper, A. Malinowski, K. Furusawa, D. J. Richardson, "High-power, high- brightness, mJ Q-switched ytterbium-doped fibre laser," Electron. Lett. 40, 928-929 (2004). [CrossRef]
M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, "Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 18, 764-766 (2006). [CrossRef]
J. Y. Huang, H. C. Liang, K. W. Su, and Y. F. Chen, "High power passively Q-switched ytterbium fiber laser with Cr4+:YAG as a saturable absorber," Opt. Express 15, 473-479 (2007). [CrossRef] [PubMed]
L. Pan, I. Utkin, and R. Fedosejevs, "Passively Q-switched ytterbium doped double-clad fiber laser with a Cr4+:YAG saturable absorber," IEEE Photon. Technol. Lett. 19, 1979-1981 (2007). [CrossRef]
R. Chi, K. Lu, and S. Chen, "Multi-wavelength Yb-doped fiber ring laser," Microwave Opt. Technol. Lett. 36, 170-172 (2003). [CrossRef]
X. Feng, Y. Liu, S. Fu, S. Yuan, and X. Dong, "Switchable dual-wavelength ytterbium-doped fiber laser based on a few-mode fiber grating," IEEE Photon. Technol. Lett. 16, 762-764 (2004). [CrossRef]
W. Guan and J. R. Marciante, "Dual-frequency operation in a short-cavity Ytterbium-doped fiber laser," IEEE Photon. Technol. Lett. 19, 261-263 (2007). [CrossRef]
L. R. Chen and X. J. Gu, "Dual-wavelength Yb-doped fiber laser stabilized through four-wave mixing," Opt. Express 15, 5083-5088 (2007). [CrossRef] [PubMed]
C. Tu, W. Guo, Y. Li, S. Zhang, and F. Lu, "Stable multiwavelength and passively mode-locked Yb-doped fiber laser based on nonlinear polarization rotation," Opt. Commun. 280, 448-452 (2007). [CrossRef]
S. L. Hu, J. Yu, C. Q. Gao, G. H. Wei, and F. Y. Lü, "Dual-wavelength stable nanosecond pulses generation from cladding-pumped fiber laser," Chin. Opt. Lett. 4, 655-657 (2006).
Y. Wang and C. Q. Xu, "Modeling and optimization of Q-switched double-clad fiber laser," Appl. Opt. 45, 2058-2071 (2006). [CrossRef] [PubMed]
Y. M. Huo and P. K. Cheo, "Modeling of passively Q-switched Er3+/Yb3+-codoped clad-pumped fiber lasers," IEEE J. Sel. Top Quantum Electron. 11, 658-665 (2005). [CrossRef]
X. Y. Zhang, S. Z. Zhao, Q. P. Wang, Q. D. Zhang, L. K. Sun, and S. J. Zhang, "Optimization of Cr-doped saturable-absorber -switched lasers," IEEE J. Quantum Electron. 33, 2286-2294 (1997). [CrossRef]
H. Ridderbusch and T. Graf, "Saturation of 1047- and 1064nm absorption in Cr4+:YAG crystals," IEEE J. Quantum Electron. 43, 168-173 (2007). [CrossRef]
Y. Sintov, O. Katz, Y. Glick, S. Acco, Y. Nafcha, A. Englander, and R. Lavi, "Extractable energy from ytterbium-doped high-energy pulsed fiber amplifiers and lasers," J. Opt. Soc. Am. B 23, 218-230 (2006). [CrossRef]
J. J. Zayhowski and C. DillIII, "Diode-pumped passively Q-switched picosecond microchip lasers," Opt. Lett. 19, 1427-1429 (1994). [CrossRef] [PubMed]
D. Y. Tang, S. P. Ng, L. J. Qin, and X. L. Meng, "Deterministic chaos in a diode-pumped NdYAG laser passively Q switched by a Cr4+:YAG crystal," Opt. Lett. 28, 325-327 (2003). [CrossRef] [PubMed]
M. D. Wei, C. H. Chen, and K. C. Tu, "Spatial and temporal instabilities in a passively Q-switched Nd:YAG laser with a Cr4+:YAG saturable absorber," Opt. Express 12, 3972-3980 (2004). [CrossRef] [PubMed]
K. Lu and N. K. Dutta, "Spectroscopic properties of Yb-doped silica glass," J. Appl. Phys. 91, 576-581 (2002). [CrossRef]
R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium- doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997). [CrossRef]

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