Characterization of an ytterbium-doped double-clad fiber laser passively mode-locked by nonlinear polarization rotation

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DOI: 10.1007/s00340-003-1302-8 Lasers and Optics

b. ortac¸¹ a. hideur¹ m. brunel¹ t. chartier^1,u^,∗

m. salhi² h. leblond² f. sanchez²

Characterization of an ytterbium-doped

double-clad fiber laser passively mode-locked by nonlinear polarization rotation

1Groupe d’Optique et d’Optronique, CORIA UMR 6614, Universit´e de Rouen, Avenue de l’universit´e BP 12, 76801 Saint Etienne du Rouvray Cedex, France

2Laboratoire POMA, UMR 6136, Universit´e d’Angers, 2 Bd. Lavoisier, 49045 Angers Cedex 01, France

Received: 18 April 2003/Revised version: 14 July 2003 Published online: 8 October 2003 • © Springer-Verlag 2003 ABSTRACTThe properties of an ytterbium-doped double-clad fiber laser, passively mode-locked by nonlinear polarization rotation are investigated in this work. Cartographies of mode- locking regime versus halfwave plates orientations are presented for several values of the total cavity dispersion and for different pump powers. Bistability between the continuous and the mode-locking regimes is pointed out. The effect of the total group velocity dispersion is described with a master mode- locking equation.

PACS42.55.Wd; 42.65.Re

1 Introduction

In contrast with other solid-state lasers, passively mode-locked fiber lasers offer a number of advan- tages, including compactness, freedom from misalignment or diffraction-limited beam. The use of the polarization additive pulse mode-locking [1] as the mode-locking mechanism is very attractive because of its simplicity. Basically, this technique works as follows. The nonlinear polarization rotation, induced by the optical Kerr effect along the fiber, associated with an intracavity polarizer acts like a fast saturable absorber that ensures passive mode-locking (PML). The response time of the saturable absorber is the response time of the Kerr effect, i.e. few femtoseconds [2]. In general, the polarizer is fixed and two polarization controllers at each side of the polarizer are adjusted to obtain PML. During the last decade, a large number of passively mode-locked fiber lasers have been realized using this technique. To achieve ultrashort-pulse operation (a few tens of femtoseconds), most of these devices use dispersion management to balance the group-velocity dispersion of the fiber. For fiber lasers operating around 1550 nm, the dispersion of the amplifying Er-doped fiber can be compensated by a portion of fiber with opposite dispersion [3]. For systems operating around 1060 nm (Nd- or Yb-doped fibers), the dispersion of the amplifying doped fiber must be compensated by bulk elements (such as gratings [4] or prisms [5])

u Fax: +33-2/9637-0199, E-mail: Thierry.Chartier@enssat.fr

∗Present address: Laboratoire d’Optronique UMR 6082, ENSSAT, 6 rue de K´erampont, 22300 Lannion, France

or, more recently, by microstuctured fibers [6]. With the recent development of double-clad fibers, these devices can now be designed to support high powers [7–9]. In some of these lasers, the influence of the amount of path-averaged dispersion of the cavity has been experimentally investigated [3, 10].

Important results are the observation of the soliton regime when the total dispersion of the cavity is in the anomalous dispersion regime, and the stretched-pulse regime when the cavity is in the normal dispersion regime [10]. Although there is a large number of results, no systematic study of the influence of the polarization controllers is done. In a previous paper, a simplified experimental configuration involving a polarizer placed between two halfwave plates was considered.

It reported, for the first time to the best current knowledge, an experimental cartography of the PML regions versus the orientation of the two phase plates [11].

From the theoretical point of view, the PML regime is gen- erally modelled with a Ginzburg–Landau equation that takes into account gain, dispersion and Kerr effect. This approach has been used to study the effect of dispersion on the perfor- mances of passively mode-locked fiber lasers [3]. Recently proposed was the theoretical modelling of PML in an Yb- doped double-clad fiber laser [12]. The model in this work is sufficiently general to take into account explicitly the experimental orientation angles of the two halfwave plates. This allows comparison of theoretical and experimental cartographies of the PML regime.

The aim of this paper is to fully characterize the mode- locking regime of the laser, not only versus the orientation of the phase plates, but also against the pump power and the total cavity dispersion. A comparison with the theoretical model is also performed. In Sect. 2 the experimental setup for polarization additive pulse mode-locking of an ytterbium-doped double-clad fiber laser is presented. In addition to the polarizer and to the two halfwave plates, the setup includes a dispersion delay line allowing to vary the total cavity dispersion.

The influence of the cavity dispersion on the mode-locking regions is investigated in Sect. 3. It is shown that, for the parameters used in the experiment, these regions do not strongly vary when the dispersion is changed in a wide range above and below the zero dispersion point. It is also shown that below a particular value of dispersion, no mode-locking regime is possible. Further study is taken in Sect. 4 on the influence of the pump power. For the pumping powers achievable in

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this experiment, the mode-locking regions slowly increase above a threshold pumping value. In Sect. 5 large bistability domains between the PML regime and the continuous wave (cw) regime is demonstrated versus the orientation angles of the phase plates. Theoretical results are presented in Sect. 6.

A comparison is made with the results of a previously reported model [12] to the experimental data. It is shown that there is a good agreement in the positive group velocity dispersion case whereas significant discrepancies appear in the negative case.

2 The experimental setup

The complete description of the laser is presented in Fig. 1. The amplifying medium is a diode-pumped Yb- doped double-clad fiber amplifier manufactured by Keopsys (Lannion, France). The laser diode is coupled into the fiber using the V-groove technique. The pumping laser diode operates at 975 nm. Its maximum output power is 3.7 W. The doped fiber length is 4 m, which allows a complete absorption of the pump power. The core diameter is 7µm, while the in- ner cladding is a square whose dimensions are 125×125µm². Two undoped single mode fibers are spliced at both ends of the double-clad fiber leading to a total fiber length of about 8.8 m.

Passive mode-locking is achieved by the polarization additive pulse mode-locking (PAPM) technique [1]. This technique requires a polarizer and two polarization controllers in the cavity. It is self-starting in a unidirectional cavity. In this experiment the halfwave plates no. 1 and no. 2 were used instead of polarization controllers. This allows only two degrees of freedom corresponding to the orientation angles of the phase plates. The bulk polarization-dependent optical isolator inserted in the cavity plays the double-role of an isolator which ensures the unidirectional operation and a polarizer re- quired for the PAPM. A partially reflecting mirror is used to ensure an output coupling of about 90%.

The second-order group-velocity dispersionβ^F2of the fiber has been evaluated using the side-bands technique [13, 14].

It was found that the average dispersion per unit length of the fiber isβ2^F= +0.026 ps²/maround 1050 nm. The grating- based dispersion delay line (DDL) ensures partial or total compensation of the dispersion of the fiber. The DDL is composed of a pair of two identical holographic gratings (1200 lines/mm) blazed at λ=1060 nm with a diffraction

Pump 975 nm Yb-doped

double-clad fiber V-groove

λ/2 n° 1 λ/2 n° 3 λ

Optical Isolator

Grating 1 Grating 2 M

Output

/2 n° 2

FIGURE 1 Schematic representation of the laser

efficiency of 95% for the TM incident polarization. The halfwave plate no. 3 allows injection of the appropriate TM polarization in the DDL. SettingL anddas the fiber length and the distance between the two gratings of the DDL respectively and neglecting other sources of dispersion, the total cavity dispersion is given by

β2^T=β^F2L+2β2^Gd, (1)

whereβ^G2 is the second-order dispersion introduced by a single pass in the grating pair per unit of length. Using ba- sic calculations [2] this dispersion has been evaluated to be β2^G= −4 ps²/mat 1050 nm. From relation (1) it is found that the distanced=2.86 cm allows exact compensation of the second-order dispersion of the fiber, and therefore the second- order dispersion of the cavity vanishes. It should be noted in this case, that the dispersion of the cavity is dominated by its third-order term. Indeed, third-order dispersion of the DDL cannot balance the third-order dispersion of the fiber since they have the same sign.

The PAPM technique is very sensitive to the orientation of the halfwave plates no. 1 and no. 2. It has already been reported on mode-locking, Q-switching and cw operation in a similar laser with no DDL [11]. The different regimes could be chosen by an appropriate orientation of the two halfwave plates. In these previous experiments, the absence of DDL prevented the study of these regimes versus the total dispersion of the cavity.

3 Mode-locking regimes versus dispersion

In [11] the different operating regimes of the laser versus the anglesθ1andθ2were studied, corresponding to the orientation angles of the halfwave plates no. 1 and no. 2 in an arbitrary reference axis system. Practically, for a given pump power, a value forθ1 was fixed and the particular values of θ2 measured for which a change in the operating regime oc- curred. With a variation of 90^◦inθ1andθ2it was possible to represent a cartography in the plane(θ1, θ2)of the different operating regimes. More recently, a theoretical investigation of the PML regime of this laser was carried out [12]. In particular, it is possible to predict 4 zones of PML in the plane (θ1, θ2). This corresponded to a rather good agreement with the experiments.

In this paper, the procedure to obtain the cartography of PML is slightly different. This is motivated by the fact that large regions of bistability exist between the PML regime and the cw regime (see Sect. 5). Then, to be sure to determine the regions where the PML regime is stable, apply the following method. First determine the location of the 4 zones of PML by varyingθ1 andθ2. Then, starting from the center of each zone, vary slowly bothθ1andθ2to find the boundary with the cw regime. For each zone, obtain the PML domain by link- ing the different points of coordinates(θ1, θ2). An example of cartography is given in Fig. 2 forβ^T2 = −0.01 ps²(d=3 cm) and a pump power of 2.25 W. Note that the 4 zones of PML, named A, B, C and D, are clearly identified. It must be men- tioned that, sometimes, at the boundary between PML and cw, some very thin regions of unstable pulsing occurs. For simplicity, these regions are not represented and will be assimi- lated to PML in the following. The approximative distance (in

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-10 0 10 20 30 40 50 60 70 80 -20

-10 0 10 20 30 40 50 60 70 80 90

Angle ₁ 45 °

22.5 ° 45 °

22.5 °

PML CW

B

C

Angle2

D A

(deg.)

FIGURE 2 Cartography forβ2^T= −0.01 ps²and 2.25 W of pump power

degrees) between each zone are quoted on the figure. The periodicity of 90^◦ of the pattern represented in Fig. 2 has been verified versus the anglesθ1andθ2. For each zone of PML, the characteristics of the pulse train are similar to those already reported by Hideur et al. [9, 13], i.e. a repetition rate of 18 MHz, a pulse duration of about 700 fs, a spectral width of few nanometers around 1050 nm and a pulse energy around 15 nJ.

Since the experimental configuration allows control of the total dispersion of the cavity through the DDL, cartographies were plotted for different values of β₂^T by varying the dis- tancedbetween the gratings. The results are summarized in Fig. 3 fromd=1 cm(β^T₂ = +0.15 ps², normal regime of dispersion) tod=5 cm(β^T2 = −0.17 ps², anomalous dispersion regime). Note that the largest positive total cavity dispersion is limited by the total dispersion of the doped fiber (this situation occurs when there is no gratings). The interesting point is the fact that the 4 zones of PML remain approximatively unchanged whenβ2^T≥ −0.09 ps². Below this value, the PML

-10 0 10 20 30 40 50 60 70 80 90

0 10 20 30 40 50 60 70 80 90

2T= + 0.15 ps² 2T= + 0.08 ps² 2T= 0.01 ps² 2T= 0.09 ps² 2T= 0.17 ps²

A B

C

D

Angle ₁(deg.) Angle2(deg.)

FIGURE 3 Cartographies versus dispersion for 2.25 W of pump power

regime becomes more and more difficult to obtain. For example, forβ2^T= −0.17 ps², only one zone can be obtained (zone C). For values of β^T2 <−0.21 ps² (d=5.5 cm), the mode-locking regime does not occur for any value of(θ1, θ2). It should be noted that, while the domains of PML slightly change with dispersion whenβ^T2 ≥ −0.09 ps², the nature of PML strongly depends on the regime of dispersion. Indeed, forβ2^T>0, PML occurs in the stretched-pulse regime (with significant pulse duration variations within a round-trip) and forβ2^T<0, PML is in the soliton regime. This point has been already investigated [10, 13] and is not the subject of this paper.

In summary, PML is possible in the Yb-doped double- clad fiber laser with a total dispersion of the cavity ranging from β2^T= +0.22 ps² (no DDL inserted [11, 12]) to β2^T=

−0.21 ps². Four zones of PML are well identified in the plane (θ1, θ2)with a periodicity of 90^◦.

4 Mode-locking regimes versus pump power In the previous experiment the pump power was fixed to the particular value of 2.25 W. It is of importance to study the cartography of mode-locking versus the pump power. To do this, fix the value ofθ1to 20^◦and the total cavity dispersionβ2^T= −0.01 ps². For this configuration it can potentially reach the zone A and B of mode-locking by vary- ingθ2. Then, using the same procedure used previously, for different values of the pump power (from 1.25 Wto 2.75 W) the boundary of appearance of the PML regime as a function ofθ2is found. The results are represented in Fig. 4. Starting from the laser threshold (about 1.2 W), the laser is continuous for any value ofθ2. From about 1.3 W, the threshold of mode-locking is reached and the laser spontaneously delivers a regular train of mode-locked pulses. In agreement with the results of Fig. 3, two separate zones of PML exist versusθ2. Above the mode-locking threshold, the width of the two regions slightly increase when the pump power increases. An interesting question is to know if the mode-locking threshold remains unchanged when the pump power is decreased from

1,25 1,50 1,75 2,00 2,25 2,50 2,75 0

10 20 30 40 50 60 70 80 90

Pump power (W)

PML CW

Angle2(deg.)

FIGURE 4 Cartography versus pump power for β2^T= −0.01 ps² and θ1=20^◦

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a value allowing the PML to occur. The experiment shows that the PML threshold does not vary significantly.

A series of experiments shows that the evolution of the PML regions versus the pump power is qualitatively the same for any orientation of the phase plate no. 1, provided that PML is possible. The same results are also obtained for other values of the total cavity dispersion.

5 Bistability

During the experiment, it was observed that, under certain conditions, the PML regime can switch towards the cw regime, for example when an obstacle is inserted into the cavity and then removed. The mode-locking regime can be restored if an external perturbation is applied. This observation suggests the existence of bistability domains between the PML regime and the cw regime. To investigate this phe- nomenon, attention is focused on region A of the PML cartography. The experimental conditions areβ2^T= −0.09 ps²(d= 4 cm) and a pump power of 2.25 W. Two different methods are used to determine the zone A. The first one is the procedure described previously: starting from the center of the region A, search for the boundary where the cw regime ap- pears. This procedure leads to the curve A1 of Fig. 5. The second method consists of starting from points where the laser operates in the cw regime and to find the position of appearance of the PML regime. This obtains the curve A2 of Fig. 5.

In the grey zone of Fig. 5, the PML regime is stable while the cw is unstable, in the shaded zone both PML and cw regimes are stable and in the white zone, the cw regime is stable and the PML regime is unstable. Therefore, there ex- ists a large domain of bistability versus the orientation angles of the phase plates. It has been verified that for any point in the shaded zone, the PML regime can be switched towards the cw regime by simply inserting a hand inside the cavity and then removing it. Finally, similar results are obtained by considering regions B, C, or D instead of region A of the cartography.

6 Comparison with theory

Several theoretical approaches have been used to describe the PML regime in rare-earth doped fiber lasers. The

-10 0 10 20 30 40 50

0 10 20 30 40

A1 A2

PML CW or ML (bistability) CW

Angle ₁(deg.) Angle2(deg.)

FIGURE 5 Illustration of bistability in zone A for β2^T= −0.09 ps²and 2.25 W of pump power

most commonly used is the master equation proposed by Haus et al. [15]. It takes into account the dispersion, the Kerr effect and the gain. However, this model does not include the effect of polarization controllers. In a recent paper, a unidirectional fiber ring cavity containing a polarizer placed between two halfwave plates as shown in Fig. 6 was considered [12]. Start- ing from two coupled nonlinear Schrödinger equations for the electric field components in the framework of the eigenaxis of the fiber moving at the group velocity, the system has been reduced to only one equation for the amplitude of the electric field just after the polarizer where the polarization is well de- fined. The model takes into account the gain, the optical Kerr effect, the birefringence of the fiber, the group velocity dispersion and also the orientation of the eigenaxis of the fiber at each side of the polarizer. Full details of the calculation are given by Leblond et al. [12]. The resulting equation for the electric field amplitudeFis of the complex Ginzburg–Landau (CGL) type and, for a large number of round trips in the cavity, is written as

i∂F

∂z =ig1F+ β2

2 +i ∂²F

∂t² +(Dr+iDi)F|F|² , (2) where β2 =β^T2/(L+d) is the group-velocity dispersion (GVD) coefficient,=g0/ω²g is the gain filtering,ωg is the spectral gain bandwidth andg0is the gain coefficient. In order to compensate losses,g0must satisfy the equation

g₀=−1 2L ln

β²|Q|²

, (3)

whereβis the transmission coefficient of the polarizer, and Q=cos(θ+−θ−)cosK L−i cos(θ++θ−)sinK L. (4) θ+andθ−are the angles between the eigenaxis of the fiber and the passing axis of the polarizer respectively after and before the latter.g1is the excess of linear gain.

The effective nonlinear self-phase modulationDrand effective nonlinear gain (or absorption) Di are the real and imaginary parts ofDdefined as

D=−P

Q L , (5)

Polarizer

FIGURE 6 Schematic representation of the unidirectional ring cavity investigated theoretically and definition of the anglesθ+andθ−

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where P=γ

e^2g⁰^L−1 2g0

Q+A−1

2 sin 2θ+[sin(θ++θ−)cosK L

−i sin(θ+−θ−)sinK L]

+B 2sin 2θ+

sinθ+cosθ−e^{−iK L} e^(2g⁰^+4iK)L−1 2g₀+4iK +cosθ+sinθ−e^{iK L}e^(2g⁰^−4iK)L−1

2g0−4iK

, (6)

Kis the birefringent parameter,γis the nonlinear coefficient, A=2/3andB=1/3. For numerical simulations the following values for the parameters are used: K=1.5 m⁻¹ [12], L=9 m,γ=3×10⁻³W⁻¹m⁻¹,ωg=10¹³s⁻¹andβ=0.9.

The global GVDβ2is varied.

The CGL (2) admits a stable analytical short pulse solution [16]. In the case of anomalous dispersion, this solution is stable [17] and corresponds to the mode-locking operation [18]. In the case of normal dispersion, a criterion for mode-locking operation can also be given [12]. The stability analysis of these solutions can be summarized in a cartography versus the anglesθ+andθ−. Such a representation can be directly compared with the experimental data of Fig. 3.

Although (2) is valid for positive and negative GVD, the stability condition is different depending on the sign of the GVD [12, 17, 18].

When the total dispersion of the cavity β2^T is positive, i.e. has the same sign as the dispersionβ2^Fof the Yb-doped fiber, the model works very well. Theoretical results in this case are represented in Fig. 7. Note that the cartographies are represented as a function of half of the value of the angles in order to compare with the experiment where a rota- tionθof the halfwave plates corresponds to a rotation 2θof the polarisation. A good agreement with the data of Fig. 3 is obtained. Indeed, four different regions of PML are obtained. The distances between the regions are the same as that

0 45 90

0 45

90 ps

ps

(deg.) (deg.)

FIGURE 7 Theoretical cartographies versus dispersion for the positive case

measured experimentally. In addition, the PML regions vary slightly when the dispersion is reduced. In the case of negative total dispersionβ^T2, theoretic rings are obtained instead of the experimentally observed simple closed domains [18].

Therefore this is not represented in the corresponding theoretical cartographies: the model is not valid in this case. The theory uses a perturbative approach equivalent to the assump- tion that the dispersion is averaged over one round trip. The stability condition of the localized solution of the CGL (2) depends strongly on the sign of the GVD coefficientβ2 (as an example, the excess of linear gaing1must have opposite signs in the two cases). Therefore the reason for which the averaged model is not valid forβ^T2 <0seems to be the following one: the condition for stable pulse formation in the doped fiber is structurally different from the same condition written for the averaged model. A more realistic approach, using a numerical simulation of a periodic medium with al- ternatively positive and negative dispersion, is currently under investigation.

It should be noted that no stable PML is obtained theoretically when the total cavity dispersion is below about +0.04 ps². This is due to the fact that the compression of the pulses due to the nonlinear gainDicannot be compensated by the dispersion which is too small. This problem can be solved by including higher order dispersion terms in the propagation equation. However, no analytical solutions can be found in this situation.

7 Conclusion

In summary the mode-locking properties of an ytterbium doped double-clad fiber laser has been character- ized. Pulse generation is obtained through polarization additive pulse mode-locking in a unidirectional cavity containing a polarizer placed between two halfwave plates. A dispersion delay line has been used in order to vary the total cavity dispersion. Cartographies of the mode-locked regime as a function of the total cavity dispersion show that the regions of mode- locking do not vary significantly for positive values ofβ2. The PML is lost for large negative values of the total dispersion. For a given position of the phase plates, it has been shown that the PML regions slightly increase versus the pump power above the mode-locking threshold. Large bistability domains between the continuous regime and the PML regime have been pointed out as functions of the orientation angles of the two halfwave plates. The experimental data concern- ing the PML properties versus the total cavity dispersion have been compared with theoretical results obtained from a master equation which explicitly involves the orientation of the two phase plates. It has been shown that a good agreement can be obtained in the normal dispersion regime (β2positive) while significant discrepancies occur in the anomalous dispersion regime. The results therefore validate the model for positive values ofβ2. In the negative case, the model which assumes an average of the dispersion over one round trip is not valid. This suggests consideration of the more realistic case of a periodic sequence of media with positive and negative GVD. This is currently under investigation and requires fully numerical studies.

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REFERENCES

1 K. Tamura, H.A. Haus, E.P. Ippen: Electron. Lett.28, 2226 (1992) 2 G.P. Agrawal:Nonlinear fiber optics, 2nd. ed. (Academic Press, San

Diego, 1995)

3 H.A. Haus, K. Tamura, L.E. Nelson, E.P. Ippen: IEEE J. Quant. Elect.

QE-31, 591 (1995)

4 L. Lefort, J.H.V. Price, D.J. Richardson, G.J. Spühler, R. Pashotta, U. Keller, A.R. Fry, J. Weston: Opt. Lett.27, 291 (2002)

5 V. Cautaerts, D.J. Richardson, R. Paschotta, D.C. Hanna: Opt. Lett.22, 316 (1997)

6 H. Lim, F. Ö. Ilday, F.W. Wise: Optics Express,10, 1497 (2002) 7 M. Hofer, M.E. Fermann, L. Goldberg: IEEE Photon. Tech. Lett.10,

1247 (1998)

8 P. Adel, M. Auerbach, C. Fallnich, S. Unger, H.R. Müller: Opt. Comm.

211, 283 (2002)

9 A. Hideur, T. Chartier, M. Brunel, S. Louis, C. Özkul, F. Sanchez: Appl.

Phys. Lett.79, 3389 (2001)

10 K. Tamura, L.E. Nelson, H.A. Haus, E.P. Ippen: Appl. Phys. Lett.64, 149 (1994)

11 A. Hideur, T. Chartier, M. Brunel, M. Salhi, C. Özkul, F. Sanchez: Optics Comm.198, 141 (2001)

12 H. Leblond, M. Salhi, A. Hideur, T. Chartier, M. Brunel, F. Sanchez:

Phys. Rev. A65, 063 811 (2002)

13 A. Hideur, T. Chartier, C. Özkul, M. Brunel, F. Sanchez: Appl. Phys. B 74, 121 (2002)

14 M.L. Dennis, N. Duling: IEEE Jour. Quant. Electron.QE-30, 1469 (1994) 15 H.A. Haus, J.G. Fujimoto, E.P. Ippen: J. Opt. Soc. Am. B8, 2068 (1991) 16 N.N. Akhmediev, V.V. Afanasjev: Phys. Rev. E53, 1190 (1996) 17 N.N. Akhmediev, A. Ankiewicz:Solitons, nonlinear pulses and beams,

(Chapman Hall, London, 1997)

18 M. Salhi, H. Leblond, F. Sanchez: Phys. Rev. A67, 013 802 (2003)