Theoretical modeling and analysis of a passively Q-switched Er-dopedfiber laser with Tm-doped fiber saturable absorber

Mengmeng Tao a,n, Xisheng Ye a,b,nn, Zhenbao Wang a, Yong Wu a, Ping Wang a,Pengling Yang a, Guobin Feng a

a State Key Laboratory of Laser Interaction with Matter, Northwest Institute of Nuclear Technology, Xi0an 710024, PR Chinab Research Center of Space Laser Information Technology, Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences, Shanghai 201800, PR China

a r t i c l e i n f o

Article history:Received 10 December 2013Accepted 6 January 2014Available online 21 January 2014

Keywords:Rate equation theoryEr-doped fiber laserPassive Q-switchingTm-doped fiberFiber saturable absorber

a b s t r a c t

A theoretical model concerning the 3H6-3F4 transition of Tm ions for passive Q-switching of an Er-doped

fiber laser is built. Related population transitions of the passive Q-switching mechanism are simulated anddescribed. Effects of pump power, output reflectivity and cavity length on the laser performance areinvestigated and analyzed. Numerical results indicate that pump power and output reflectivity are majorfactors affecting the laser output, while the cavity length mainly determines the pulse duration. Besides,high repetition rate operation is achievable with 3H6-

3F4 transition of Tm ions at the expense of theoutput pulse energy.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Tm-doped fiber has been widely studied for amplifications inoptical communications and high power fiber lasers/amplifiers.Utilizing the 3H4-

3F4 transition of Tm ions, S-band amplificationwith Tm-doped fiber is obtained [1]. The signal gain could be ashigh as 11.3 dB at 1470 nm [2], which is applicable for WDMtelecommunication. The 3F4-3H6 transition is usually studied forhigh power output around 2 μm [3–5]. And, the maximum outputhas exceeded 1 kW from a single fiber [6].

Beside these applications concerning the emission bands ofTm-doped fiber, applications related to its absorption bands havealso been explored. In 2003, P. Adel and his coworkers reported,for the first time, the passive Q-switching of an Yb-doped fiberlaser with Tm-codoping as the saturable absorber [7]. Inside thecavity, the 3F4-3F2,3 transition of Tm ions is excited as thistransition corresponds to the emission band of Yb ions. And,repetition rate of this laser system is up to 140 kHz due to therelatively fast decay from 3F2,3 to 3F4. Later, in 2010, T. Tsai researchgroup proposed and demonstrated the passive Q-switching of anEr-doped fiber laser with Tm-doped fiber as the saturable absorber[8]. Several months later, A.S. Kurkov realized passive Q-switchingof a double-clad GTWave Er-doped fiber laser with only 6 cm long

heavily Tm-doped fiber [9]. As for passive Q-switching of Er-dopedfiber lasers, the 3H6-

3F4 transition of Tm ions is involved.However, as the lifetime of 3F4 is much longer compared withthat of 3F2,3, the achieved repetition rate is much smaller, 2 kHz inRef. [9] and 6 kHz in Ref. [8].

In this paper, a theoretical model of Tm-doped fiber saturableabsorber (FSA) in passive Q-switching of an Er-doped fiber laser isestablished based on the rate equation theory. Effects of the pumppower, output reflectivity and laser cavity lengths on the outputperformance of the passively Q-switched Er-doped fiber laser,including the repetition rate, pulse duration and peak power, areinvestigated and analyzed. The simulation results show that highrepetition rate operation of an Er-doped fiber laser is also achiev-able with 3H6-

3F4 transition of Tm ions.

2. Theoretical modeling

Here, we consider a linear cavity with two pieces of fibersclosed inside of the laser cavity, Er-doped fiber as the gain mediumand Tm-doped fiber as the saturable absorber, as shown in Fig. 1.The 980 nm pump is launched into the cavity through a 980/1550 nm WDM. The pulsed laser output is extracted from thepartially reflective cavity mirror (PR) port.

Simplified energy levels and related energy transitions of Erions and Tm ions are shown in Fig. 2.

As the lifetime of the 4I11/2 energy level (200 μs) is negligiblecompared with that of the 4I13/2 energy level (10 ms), the popula-tion density of the 4I11/2 energy level, N3, is usually taken as

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Optics Communications

0030-4018/$ - see front matter & 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.optcom.2014.01.015

n Corresponding author.nn Corresponding author at: Research Center of Space Laser Information Technol-

ogy, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences,Shanghai 201800, PR China.

E-mail addresses: tonylemon@hotmail.com (M. Tao), yxschx@yeah.net (X. Ye).

Optics Communications 319 (2014) 128–132

zero [10]. Thus, the rate equation of this laser system could bewritten as

dϕdt

¼ ϕ

τr½sesN2�sasðNEr�N2Þ�l

�

þ½ses_saN5�sas_saðNTm�N5Þ�lsa�½δ� lnðR1R2Þ��þβN2

dN2

dt¼WpðNEr�N2Þ�

N2

τ2�cϕ½sesN2�sasðNEr�N2Þ�

dN5

dt¼ �½ses_saN5�sas_saðNTm�N5Þ�cϕ�

N5

τ5; ð1Þ

where ϕ is the photon density inside of the cavity, and c is thevelocity of light in vacuum. NEr and NTm are the total populationdensities of Er ions and Tm ions, respectively. And, N2 and N5 arethe population densities of 4I13/2 and 3F4 energy levels, as illu-strated in Fig. 2. ses and sas are the emission cross-section andabsorption cross-section of the gain fiber at 1550 nm, while ses_sa

and sas_sa are the emission cross-section and absorption cross-section of the FSA at 1550 nm. δ represents the intrinsic loss of thelaser cavity, and β is the spontaneous emission coefficient thatinitiates the laser oscillation. R1 and R2 are, respectively, thereflectivities of the HR mirror and the PR mirror. Wp is the pumprate, which is related to the pump power P by

Wp¼ λpsap

AhcP: ð2Þ

Here, λp is the wavelength of the pump, which is 980 nm. sap isthe absorption cross-section of the gain fiber at 980 nm. A is theeffective doping area of the gain fiber, and h is Planck0s constant.

Pump

Output

PR HR

WDM

Er-doped Fiber

Tm-doped Fiber

Fig. 1. Schematic diagram of the laser system. HR: highly reflective cavity mirror at1550 nm; PR: partially reflective cavity mirror at 1550 nm.

Fig. 2. Simplified energy levels and related energy transitions of Er ions andTm ions.

Fig. 3. Temporal evolution of the 4I13/2 and 3F4 energy levels and the formation of a laser pulse. (a) Normalized population of the 4I13/2 energy level; (b) normalizedpopulation of the 3F4 energy level; (c) normalized lasing intensity. The part inside the dashed circle in (b) shows the saturation of the Tm-doped fiber.

Table 1Parameters used in the simulation.

Parameters Values Parameters Values Parameters Values

A 63.6�10�12 m2 R1 1 R2 TBDa

l 9 m lsa 0.2 m lp TBDNEr 1.81�1025 m�3 NTm 5�1025 m�3 n 1.5sap 3.1�10�25 m2 ses 3.6�10�25 m2 sas 3.6�10�26 m2

ses_sa 4.92�10�25 m2 sas_sa 2.46�10�24 m2 β 1�10�7 s�1

τ2 10 ms τ5 334.7 μs α 0.01

a TBD: to be determined.

M. Tao et al. / Optics Communications 319 (2014) 128–132 129

τ2 and τ5 are the lifetime of 4I13/2 and 3F4, and τr is the round-trip time of the cavity, expressed as

τr ¼ 2nLc

; ð3Þ

with L¼ lþ lsaþ lp. Here, l, lsa and lp are the lengths of the gain fiber,the FSA and the passive fiber inside of the cavity, respectively.

3. Simulation results and analysis

Numerical calculation is carried out with the parameters listedin Table 1 [3,11–14].

3.1. Population transition

Typical population transition is investigated with 100 mWpump power, 50% output reflectivity and a passive fiber lengthof 10 m. The temporal evolution of 4I13/2 and 3F4 is shown in Fig. 3.

As can be seen, with 980 nm pump, population of the 4I13/2energy level increases, generating 1550 nm laser photons through4I13/2-4I15/2 transition. And, part of these laser photons areabsorbed by the 3H6 energy level of Tm ions. This absorptionpopulates the 3F4 energy level while it introduces a huge lossinside of the cavity, making the system below the lasing threshold.When a considerable amount of population has been accumulatedat the 3F4 energy level, the absorption ability of the 3H6 energylevel gets saturated. Soon, with persistent 980 nm pumping, lasing

threshold is reached, generating a pulse signal. At the same time,decay rate of the 3F4 energy level suppresses the absorption, andthe population at the 3F4 energy level decreases. When thepopulation falls to a certain level, the absorption dominates againtill the 3F4 energy level gets saturated. Thus, sequential pulses areobtained. The saturation of the Tm ions can be clearly observed inFig. 3(b) as indicated with a dashed circle.

In Fig. 3(b), compared with the build-up process of the 3F4 energylevel, the decay process is much slower, indicating that the repetitionrate is mainly limited by the long lifetime of the 3F4 energy level.

Fig. 4 depicts a laser pulse train with correlated passive modula-tion amplitude of the Tm-doped FSA. As can be found, the modula-tion depth of the Tm-doped FSA is about 15%, much higher than thatin Ref. [7]. This 15% loss modulation depth induces the passiveQ-switching operation of the Er-doped fiber laser.

The pulse repetition rate in Fig. 4 is about 66.6 kHz, demon-strating that the 3H6-

3F4 transition is also capable of generatinghigh repetition rate laser pulses.

3.2. Pump power

Fig. 5 gives the output characteristics of the passive Q-switchedEr-doped fiber laser with different pump powers. In Fig. 5(a), therepetition rate and the pulse duration both increase with thepump power, while the pulse energy decreases. And, as a result,the peak power also decreases with the pump as shown in Fig. 5(b). Changing trends of these parameters are consistent with thoseexperimental results in Ref. [8].

Theoretically, with the increase of the pump power, the 3F4energy level needs less time to get into saturation and more timeto get out, resulting in higher repetition rate and longer pulseduration. As for the pulse energy, as stated in Ref. [8], the pulseenergy decreases because the population of the 3H6 energy level isnot fully recovered and less gain population is excited to the 4I13/2energy level. To validate this statement, the recovery ratio of the3H6 energy level and the relative gain population of the 4I13/2energy level at different pump powers are given in Fig. 6.

As can be seen in Fig. 6(a), the recovery ratio of the 3H6 energylevel and the relative gain population of the 4I13/2 energy levelboth decrease with the pump power. Fig. 6(b) gives the temporalevolution of the relative gain population of the 4I13/2 energy leveland recovery population of the 3H6 energy level at 60 mW and90 mW, respectively. These simulation results demonstrate that,with the increase of the pump power, the population of the 3H6

energy level could not get fully recovered, and the gain populationexcited to the 4I13/2 energy level also shrinks, leading to thedeterioration of the pulse energy.

Fig. 4. Laser pulse train (lower curve) and correlated absorption of the Tm-dopedFSA (upper curve).

Fig. 5. Output characteristics of the passive Q-switched Er-doped fiber laser with different pump powers. (a) Repetition rate, pulse energy and pulse duration at differentpump powers; (b) peak power at different pump powers. The simulation is performed with a cavity length of 10.2 m and a 30% output reflectivity.

M. Tao et al. / Optics Communications 319 (2014) 128–132130

3.3. Output reflectivity

Output reflectivity is another important factor that imposesdirect influence on the laser performance. The simulation resultswith different output reflectivities are presented in Fig. 7. As canbe found, the repetition rate and the pulse duration rise with theincrease of the output reflectivity, while the peak power falls.

With higher output reflectivity, the photon density inside of thecavity increases. Thus, the Tm-doped fiber could be saturatedmore easily, leading to a higher repetition rate.

The pulse duration is mainly related to the lifetime of thephoton density inside of the cavity. And, from Eq. (1), the photondensity can be expressed as

dϕdt

¼ �½δ� lnðR2Þ�τr

ϕþφðϕÞ; ð4Þ

whereφðϕÞ ¼ ϕ

τr½sesN2�sasðNEr�N2Þ�lþ½ses_saN5�sas_saðNTm�N5Þ�lsa

� �þβN2:

Further, we have

ϕpe� tτr =½δ� lnðR2 Þ�: ð5Þ

Then, the lifetime of the photon density τϕ is derived as

τϕ � τrδ� ln ðR2Þ

; ð6Þ

which explains the increase of the pulse duration with the outputreflectivity.

In Ref. [15], the peak power P of passively Q-switched lasers isderived as

Pp½ ln ð1=R2Þþγ� ln ð1=R2Þ

τr; ð7Þ

where γ depends on the original transmission of the Tm-doped FSAand the dissipative optical loss of the cavity. Obviously, the relation-ship between the repetition rate and the output reflectivity in Fig. 7follows a similar trend with Eq. (7).

3.4. Cavity length

The output also varies with the cavity length as shown in Fig. 8.The variation of the cavity length is realized with the increase ofthe passive fiber length, while the lengths of the Er-doped fiberand the Tm-doped fiber keep constant.

In Fig. 8, it can be found that the pulse duration increasesalmost linearly with the cavity length with a slope of 10.9 ns/m.With Eqs. (3) and (6), the pulse duration can be written as

τϕ �2nL

c½δ� ln ðR2Þ�: ð8Þ

Fig. 6. Recovery ratio of the 3H6 energy level and relative gain population of the 4I13/2 energy level of the 4I13/2 energy level at different pump powers. (a) Recovery ratio andrelative gain population curves; (b) temporal evolution of the recovery ratio and the relative gain population at certain pump powers.

Fig. 7. Output characteristics of the passive Q-switched Er-doped fiber laser withdifferent output reflectivities. The simulation is performed with a cavity length of10.2 m and a pump power of 60 mW.

Fig. 8. Output characteristics of the passive Q-switched Er-doped fiber laser withdifferent cavity lengths. The cavity length is varied by increasing the length of thepassive fiber. The simulation is performed with a pump power of 60 mW and a 30%output reflectivity.

M. Tao et al. / Optics Communications 319 (2014) 128–132 131

Taking related parameters in Table 1 into Eq. (8), we obtainτϕ � 8:24L (ns), which is quite close to the 10.9 ns/m slope.

For the repetition rate, we have [16]

RR� κ

τϕ; ð9Þ

where κ is, here, a constant. And, this explains the decay of therepetition rate in Fig. 8. And, the same explanation also fits thepeak power since, in Eq. (7), the peak power is also inverselyproportional to the cavity length.

The modeling and simulations above can be used for designand optimization of Tm-doped FSA based passive Q-switchedEr-doped fiber lasers. Pump power and output reflectivity aremajor elements that determine the output of the laser system.And, the cavity length mainly affects the pulse duration, as thevariations of the repetition rate and the peak power are not thatsensitive to the cavity length compared with the pump power andthe output reflectivity. For instance, if laser pulses with high peakpower and narrow pulse duration are desired, a relative low pumpfor a cavity design with a small output reflectivity and a shortcavity length might be a good choice. However, if a high repetitionrate is also required, then, tradeoffs are expected.

4. Conclusions

The passive Q-switching of an Er-doped fiber laser with Tm-doped FSA is studied numerically. The saturation induced passiveQ-switching mechanism of the Tm ions with 3H6-

3F4 transition issimulated and described. Simulations with different pump powers,output reflectivities and cavity lengths are taken to investigate andanalyze their impacts on the laser performance. Numerical resultsindicate that pump power and output reflectivity are global factorsaffecting the laser output, while the cavity length mainly deter-mines the pulse duration. In addition, simulation demonstratesthat high repetition rate operation is also achievable with 3H6-

3F4

transition of Tm ions at the expense of the output pulse energy.This theoretical modeling and analysis is helpful in the design andoptimization of FSA based passive Q-switched fiber lasers.

Acknowledgments

The authors would like to express their gratitude to Fei Wang,Yongsheng Zhang, Chenghua Wei and Ke Huang from the State KeyLaboratory of Laser Interaction with Matter for their generous helpduring the program writing and manuscript preparation.

References

[1] T. Kasamatsu, Y. Yano, T. Ono, IEEE Photonics Technol. Lett. 13 (5) (2001) 433.[2] P.R. Watekar, S. Ju, W. Han, IEEE Photonics Technol. Lett. 19 (19) (2007) 1478.[3] S.D. Jackson, T.A. King, J. Lightwave Technol. 17 (5) (1999) 948.[4] R.A. Hayward, W.A. Clarkson, P.W. Turner, Electron. Lett. 36 (2000) 711.[5] T.S. McComb, M.C. Richardson, M.Bass, High-power Fiber Lasers and Ampli-

fiers in Handbook of Optics: Volume V - Atmospheric Optics, Modulators, FiberOptics, X-Ray and Neutron Optics, McGraw-Hill, 2010.

[6] T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, G. Rines, P. Moulton, 1-kW,all-glass Tm:fiber laser, in: Fiber Lasers VII: Technology, Systems and Applica-tions of SPIE Photonics West 2010, Conference 7580, Session 16, 2010.

[7] P. Adel, M. Auerbach, C. Fallnich, Opt. Express 11 (21) (2003) 2730.[8] T. Tsai, Y. Fang, S. Huang, Opt. Express 18 (10) (2010) 10049.[9] A.S. Kurkov, Y.E. Sadovnikova, A.V. Marakulin, E.M. Sholokhov, Laser Phys. Lett.

7 (11) (2010) 795.[10] Paul-HenriBarret, Michael Palmer, High-Power and Femtosecond Lasers:

Properties, Materials and Applications, Nova Science Publishers, New York,2009 (Chap. 8).

[11] C.E. Preda, G. Ravet, P. Megret, Opt. Lett. 37 (4) (2012) 629.[12] J. Li, K. Duan, Y. Wang, W. Zhao, J. Zhu, Y. Guo, X. Lin, J. Mod. Opt. 55 (3) (2008)

447.[13] M. Tao, X. Ye, P. Wang, T. Yu, Z. Wang, P. Yang, G. Feng, Laser Phys. 23 (2013)

105104.[14] S.D. Agger, J.H. Povlsen, Opt. Express 14 (1) (2006) 50.[15] X. Zhang, S. Zhao, Q. Wang, B. Ozygus, H. Weber, J. Opt. Soc. Am. B 17 (7)

(2000) 1166.[16] J. Liu, B. Ozygus, S. Yang, J. Erhard, U. Seeling, A. Ding, H. Weber, J. Opt. Soc. Am.

B 20 (2003) 652.

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