Double-clad fiber laser design for particle image velocimetry and material science applications

Review

Double-clad fiber laser design for particle image velocimetry and material science applications

Driss Mgharaz ^a,

, Nawal Rouchdi ^b , Abdelkader Boulezhar ^b , Marc Brunel ^a

a

UMR 6614 CORIA CNRS, Avenue de l’Universite´, BP 12, 76801 Saint-Etienne du Rouvray Cedex, France

b

Universite´ Hassan II Ain Chock, B.P. 5366 Maarif, Casablanca 20100, Maroc

a r t i c l e i n f o

Article history:

Received 8 March 2010 Received in revised form 19 August 2010 Accepted 28 August 2010 Available online 6 October 2010 Keywords:

Double-clad ring fiber laser Q-switching

PIV Laser marking

a b s t r a c t

We have developed models to design actively Q-switched Yb-doped Double-Clad fiber lasers in various configurations. Based on these simulations, we present the design of two specific cavities: the first one is able to emit a pair of sub-nanosecond pulses separated by more than 500 ns for Particle Imagery Velocimetry applications. The time delay between the pulses can be adjusted by proper choice of the length of an un-doped fiber inserted in the cavity. The second cavity designed allows to emit long 150 ns pulses exceeding a few millijoules per pulse. Applications concern in this case materials science and combustion. In all cases, the rise time of the EOM is an essential parameter.

& 2010 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . 1

2. Theoretical model for the design of Q-switched DC fiber laser . . . 2

2.1. Configuration . . . 2

2.2. Rate equations . . . 2

2.3. Validation of the simulator . . . 3

3. Laser design for PIV . . . 3

4. Laser design for combustion or material science . . . 5

5. Conclusion . . . 6

References . . . 6

1. Introduction

In the last decade, double-clad (DC) fibers have shown their potentiality for the development of low-cost, compact, high power fiber lasers [1–3]. A wide range of operating regimes have been demonstrated from Continuous Wave operation to Q-switched, or mode-locked regimes [4]. In the same time, much attention has been devoted to the development of numerical simulations, which have proven their ability to describe quantita- tively the behaviors observed experimentally. It is now possible to simulate precisely DC fiber laser cavities and to design specific cavities for specific applications [5,6].

Of main interest is the development of Q-switched DC fiber lasers that are able to emit a pair of nanosecond pulses separated

by more than 500 ns. The main application of such laser systems is the Particle Image Velocimetry (PIV) technique [5,7]. PIV is commonly involved in flow measurements (fluid mechanics and turbulent flow characterizations, combustion). It requires a double- pulse laser. Commercial systems are the association of two synchronized Nd-doped lasers. An anamorphous optics allows the generation of laser sheets that are used in velocimetry measure- ments. A limitation of these systems is the relative alignment of the two cavities. When laser sheets are created for flow measurements, the non-superposition of both sheets induces limitations to the precision of the technique. The design of a system that would be able to emit a pair of pulses issued from the same cavity would be particularly attractive. DC fiber lasers offer this alternative and we will show that they can solve the problem [8].

A second domain of application concerns the emission of long nanosecond pulses in such a way that their peak power remains relatively low while their energy is important. Scientific and industrial applications are coherent anti-Stokes Raman Contents lists available at ScienceDirect

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Optics and Lasers in Engineering

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2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.optlaseng.2010.08.015

n

Corresponding author. Tel.: + 33 0 2 32 95 37 33; fax: +33 0 2 32 91 04 85.

E-mail address: driss.mgharaz@coria.fr (D. Mgharaz).

spectroscopy [9], emission spectroscopy of laser ablation [10], texturing [11], and coloring surface [12] in the domain of metal surface treatments. For example, this last application requires long Q-switched pulse laser varying from 150 to 500 ns, with higher energy between 3 and 6 mJ [13–15]. Q-switched diode- pumped Nd:YAG lasers are traditionally used. We will show in the present study the potentiality of Q-switched DC fiber lasers.

The two applications considered in this paper are quite opposite as the first one requires short multi-pulse emission, while the second requires long energetic pulses. These applications have been chosen deliberately to show the high potentiality of DC fiber lasers in various domains. Section 2 will present the model developed, and the cavity that will be under consideration. Section 3 will present the design of a cavity for PIV applications, while Section 4 will present the design of a laser emitting long 150 ns pulses.

2. Theoretical model for the design of Q-switched DC fiber laser

2.1. Configuration

The configuration that we consider is presented in Fig. 1 a ytterbium-doped DC fiber is inserted into a ring cavity. The DC fiber is pumped with a laser diode. Other elements are a wavelength division multiplexer (WDM), an optical isolator, an electro-optic modulator, and a 90/10 output coupler. Pump light issued from the laser diode is injected into the cavity ring through the WDM coupler.

The EOM ensures Q-switching of the cavity. The optical isolator ensures unidirectional oscillation. This element is very important because it eliminates backward stimulated brillouin scattering that could modify dramatically the pulse emission. An un-doped optical fiber is inserted to adjust the ISL of the cavity. The output pulses are extracted with the 90/10 coupler.

2.2. Rate equations

This laser system can be described numerically using the traveling wave model. We integrate numerically the equations describing the spatial and temporal evolutions of the pump and signal light intensities, and the populations of a two level system.

Equations set, boundary, and initial conditions are well known and full details can be found in some previous works [1–3, 16].

Finally, the rate equations in the ytterbium-doped optical fiber are given by

@N

=@t ¼ s

bhu

A

= G

cI

þ s

½hu

A

= G

I

N

s

hu

A

= G

I

þ s

hu

A

= G

I

þ ð1= t

Þ

N

ðaÞ

N

¼ N

N

ðbÞ

The Yb ions are described by two level-atoms. N

(x,t) and N

(x,t) are the population densities in the two energy levels. They are functions of position and time. N

is the total ytterbium ion density. It is uniform along the fiber axis. A

¼ G

/hu

A

and A

¼ G

/hu

A

are constant terms. u

and u

are the frequencies of the pump and signal light. s

and s

are the absorption and emission cross sections at the pump frequency, respectively, while s

and s

are the absorption and emission cross sections at the signal frequency. G

and G

are the pump power and the signal power filling factors, and t

is the relaxation time for the transition b - a. The propagation equations for the pump and signal lights in the doped fiber are given by

ð@=@xÞ þ ð1= n

Þð@=@tÞ þ a

I

¼ ð s

N

s

N

Þ G

I

ðcÞ

ð@=@xÞ þ ð1= n

Þð@=@tÞ þ a

I

¼ ð s

N

s

N

Þ G

I

þ2 G

s

D u

N

ðdÞ where I

and I

are the intensities of the pump and signal lights, respectively, v

and v

are the group velocities of the pump and signal lights in the fiber. We neglect the chromatic dispersion effect; thus, v

and v

are independent of wavelength, and we take v

¼v

¼v, where v ¼c/n. Here c is the velocity of light in vacuum, n the refractive index of the fiber. a

and a

are the attenuation constants for the pump and signal lights.

Along the un-doped fiber, we can simply write

ðð@=@xÞ þ ð1= n

Þð@=@tÞ þ a

ÞI

¼ 0 ðeÞ

ðð@=@xÞ þ ð1= n

Þð@=@tÞ þ a

ÞI

¼ 0 ðfÞ

We have developed this computational model: the ring cavity is divided longitudinally into a number of equally sized cells in which the population densities in the two energy levels and the pump and the signal light intensities are assumed to be uniform.

The pump and the signal lights propagate from cell to cell in accordance with difference equations based on theoretical equations [3,16,17]. The localized losses arising from the EOM, isolator, WDM, and 90/10 couplers are incorporated as losses at the exit of the fiber. Numerically, we divide the fiber into segments whose width is D x, and the time step is D t ¼ D x/v.

During the simulation, D x is decreased until no obvious difference in results is observed. We found that by dividing the fiber into 240 segments for a 6 m-cavity length (i.e. 40 segments for 1 m-cavity length), as demonstrated by other work [16], we obtain accurate results for the fiber lengths considered. In the simulations, the fiber segment length D x is set to be 0.025 m, and the correspond- ing time step D t is about 0.12 ns, which is short enough to ensure high resolution for Q-switching simulations.

Fig. 1.

Set-up of the ytterbium-doped FC fiber ring laser designed.

D. Mgharaz et al. / Optics and Lasers in Engineering 49 (2011) 1–7

2

2.3. Validation of the simulator

A key issue is to test the accuracy of the simulator. To best of our knowledge, a similar simulator does not exist to describe a Q-switched, unidirectional, Yb-doped fiber laser cavity, emitting at 1.08 m m. A direct comparison of our results with existing results is thus not possible. However, a similar simulator has been developed to describe a unidirectional fiber laser cavity, in the case of an Er-doped fiber emitting at 1.55 m m. In order to validate our simulator, we have thus adapted our simulator to the case of an Er-doped fiber. We have considered the cavity described in Ref. [17]. Using parameters identical to those considered in this publication, we have calculated the pulses predicted with our simulator. We could then compare them to those observed experimentally, and predicted with the simulator of the corresponding reference. Fig. 2 shows the pulse predicted with our simulator. It has to be compared with the calculated and measured pulses presented in Fig. 3 (a–1) and (a–2) of Adachi’s work [17]. This case corresponds to a 25 m-cavity length and a 100 ns-rise time for the modulator. Similar comparisons can be done with other cases of this references [17]. These figures show that both simulators give very similar results, in good accordance with experimental results: the multi-peak regime, the temporal spacing between adjacent peaks, the number of peaks y are well-described.

3. Laser design for PIV

In all cases described here, we will consider the following parameters for the ytterbium-doped fiber: a ytterbium dopant concentration of 1 10

m

, core and cladding diameters of 16 and 400 m m, pump and signal wavelengths of 0.94 and 1.08 m m (which correspond to the frequencies u

¼3.19 10

Hz and u

¼2.78 10

Hz, respectively). The absorption and emission cross sections for the pump are s

¼3 10

m

and

s

¼5 10

m

, while the absorption and emission cross sections for the signal are s

¼1.4 10

m

and

s

¼2.5 10

m

. The relaxation time for the EOM is t

¼1 ms, and the bandwidth of spontaneous emission D u

is 5.14 10

Hz.

The pump power injected into the optical fiber is 10 W. In the different cases considered in this paper, the fiber lengths will be comprised between 6 and 110 m. Consequently, the length of the other elements can be neglected (their length is much shorter than 6 m) and the attenuation in the fiber can be neglected (attenuation would be significant for fiber lengths

longer than hundreds of meters). The switching response of the electro-optical modulator is approximated by a linear response

T

¼

t ðT

= t

Þ, 0r t o t

T

, t

r t ot

0, t Z t

*

ðgÞ

where T

is the EOM transmissivity, t

the modulator rise time, and t

the electro-optic modulator opening time. t is the switching

Validation of the simulator: typical output pulse predicted in the case of an

Er-doped fiber laser (to be compared with

Fig. 3.

Temporal evolution of output pulses for three different values of the rise

time: a—1000 ns, b—500 ns, and c—100 ns.

time, T

the maximum transmission and is assumed to be 100%.

We divide the cavity length in equal slices of the smallest length D x to have a more precision in our calculations. Then, we repeat the calculations at given repetition frequency.

Previous works have studied the influence of the rise time in the laser operation regime, and in the temporal output pulse shaping [16–18]. Its value affects very significantly the pulse width and the pulse energy.

To present the output pulse power P

, we can express an effective average power throughout the ytterbium-doped region as [19]

P

¼ I

p ðD

=2Þ

G

, i ¼ s,p ðhÞ

where D

is the core diameter.

The output energy E

is determined by the following expression:

E

¼ D t X

P

ðiÞ

where D t is the time step determined by D x/v

This influence of the rise time is illustrated in Fig. 3; we have calculated the pulses emitted by the laser for three values of

t

: 1000, 500, and 100 ns, respectively. Fig. 3 shows the temporal profile of the output pulses. The Yb-doped fiber length is 6 m, but there is no un-doped fiber in this preliminary stage. The EOM opening time is 1 m s. From these pulse shapes, we see that the pulse is composed of multiple peaks. Such shapes are clearly confirmed by experiments [17,20]. This phenomenon is explained in some previous works by the contribution of amplified spontaneous emission (ASE) in output pulse formation [18,19].

In our case, this phenomenon is presented by the last term in equation (d) that described the injected ASE in output pulse at lasing wavelength. When the modulator is still switched off, the ASE signal grows slowly through the fiber, exhibiting a

‘‘triangular-profile’’ between both extremities of the Yb-doped fiber. When the modulator starts to open, the ASE pulse starts to travel around the ring cavity, being amplified periodically after each round trip in the Yb-doped fiber, until the population inversion is depleted. As the initial profile of the ASE exhibits a triangular-profile, the rear of the ASE pulse is less amplified than the front. Consequently the ASE pulse becomes rapidly like a peak.

Finally, the global output pulse is a sequence of the partially extracted pulses traveling around the cavity, and is composed of multiple peaks [17]. ASE is thus a very important factor that influences the multi-peak regime. It appears in equation (d) through the term 2 G

s

D u

N

. The coefficient of ASE has to be determined rigorously for proper description of our cavity. We use in this paper the exact values of Ref. [16]. The interval between two adjacent peaks is 29 ns in all cases. This value corresponds to the theoretical round trip time (with our 6 m ring cavity). The global envelope of the multi-peak pulses is more or less wide (depending on the rise time value). A small rise time leads to a long pulse composed of a wide number of peaks, while a longer rise time leads to shorter pulses composed of only a few peaks. In addition the shorter the rise time, the shorter the peaks durations. The rise time appears as a very important factor. We can see from Fig. 3(c) that it seems possible to isolate two identical peaks by reducing the opening time of the EOM, and thus elaborate a bi-pulse fiber laser. Unfortunately the separation between adjacent peaks (29 ns) is too small for PIV applications.

For PIV, two nanosecond pulses are required, whose energies exceed the microjoule, while the time interval between the two pulses must be more than 500 ns. This last limitation is due to the acquisition time of standard cameras classically used in PIV experiments. This point can however be solved using longer

fibers; this latter will enlarge the cavity round trip time. Let us indeed verify the importance of length cavity by changing of length fibers.

We consider now a 30 m length cavity. The EOM rise time is 100 ns in this case. Other parameters are not modified. Fig. 4 shows the temporal profile of the pulse emitted in this case. After comparison with previous cases plotted in Fig. 1, the main difference is the temporal spacing between two successive peaks; it is now 145 ns (which corresponds to the round trip time of the 30 m length ring cavity). The full width half maximum (FWHM) and energy of the first peak are, respectively, 600 ps and 0.2 mJ. It is thus possible to emit pulses with higher time separation. Note however that the Yb-doped fiber length cannot be increased indefinitely when its length exceeds 35 m, the final part of the fiber becomes unpumped (with our 10 W pumping scheme) which induces high losses.

A solution is then to splice an un-doped fiber at the end of the amplifying medium, as is described in previous section.

Based on these conclusions, next steps consist to isolate two peaks with same energies and separated by a temporal spacing exceeding 500 ns. After several optimization steps that are not detailed here, we consider finally the following configuration:

a 80 m un-doped fiber introduced onto the cavity. The role of the un-doped fiber is to increase the temporal interval between the multiple peaks without increasing the pulse duration. The total cavity length is 110 m. The EOM has a rise time of 10 ns to generate very short pulses, as previously mentioned, and an opening time of 1.8 m s. Fig. 5 shows the output pulses emitted by our fiber ring cavity at a 30 kHz-repetition frequency. Fig. 5 shows clearly the emission of a pair of pulses separated by approxi- mately 532 ns (which corresponds to the round trip time of our 110 m ring cavity). The FWHM and the energy of each pulse are (185 ps; 0.15 mJ) and (115 ps; 0.14 mJ), respectively. The two pulses are not rigorously identical. But the main parameter for PIV experiments is the relative energy between both pulses. In our case there is only 6% difference between both pulses.

This data demonstrate the possibility to design a Q-switched DC fiber laser for PIV applications. The main advantage of this system is the unicity of the cavity and the elimination of any alignment between both pulses. The spatial alignment is indeed ensured since the two pulses provide from the same laser cavity.

Combined to the low-cost of this device, it offers an important range of applications to DC fiber lasers.

It is interesting to better understand the intracavity bi-pulse formation. For this purpose, Fig. 6 shows the longitudinal

Temporal evolution of the output pulse produced by the laser cavity of 30 m with a 100 ns-rise time of the EOM.

D. Mgharaz et al. / Optics and Lasers in Engineering 49 (2011) 1–7

4

evolution of excited state population N

and signal power P

within the doped fiber at three different times.

Fig. 6(a) shows first the initial condition (t

¼0), i.e. the state of the system when the transmissivity of the EOM just begins to increase (to reach 100%). We can observe that the pump power decreases slowly along the fiber. But it does not lead to an intense excited state population N

all along the fiber. After a few meters, excited state population N

decreases indeed rapidly to let place to the formation of a signal power through ASE mechanism. The power of this signal exhibits its higher value at the end of the doped fiber.

Fig. 6(b) shows then the profiles of the signal P

(in blue dashed line) and the excited state population N

(in black solid line) along the doped fiber at time t

¼435 ns. We can observe the formation of the first pulse within the doped fiber. Note that 435 ns is exactly the time necessary to the ASE previously mentioned at the end of the doped fiber to go through the un-doped fiber and reach the doped fiber after one round trip.

This ASE activates stimulated emission in the doped fiber and the pulse power increases rapidly, which is accompanied by an instantaneous decay of the excited state population.

Fig. 6(c) shows finally the P

profile (in blue dashed line) and the N

profile (in black solid line) along the doped fiber at time t

¼950 ns during formation of the second pulse within the doped fiber. This second pulse is in fact the part of the first pulse that has not been evacuated from the cavity, and that propagates through the doped fiber after a second roundtrip.

The pulse activates there stimulated emission from the population inversion still present into the doped fiber. Pulse amplification is accompanied by an instantaneous decay of the excited state population.

In conclusion, we have designed a ring cavity able to emit a pair of sub-nanosecond pulses for PIV applications. These results confirm that it is possible to replace the classical Nd:YAG laser.

A second laser design will be now described. It concerns the emission of long, energetic pulses.

4. Laser design for combustion or material science

PIV requires the emission of a pair of short energetic pulses.

This condition on the pulse shortness is imposed by image formation in a flow which requires the acquisition of a fixed

image. Any long pulse leads to the acquisition of a blurred image of the flow under investigation. On the opposite side, many applications in combustion or material science require the emission of long energetic pulses whose peak power remains moderate. For example, an external stretching of nanosecond laser pulses has been applied in coherent anti-Stokes Raman spectroscopy (CARS) experiments to increase signal-to-noise ratio and to improve the precision of temperatures and concentrations determinations [9,10]. Emission spectroscopy of laser ablation plume to in situ analysis of solid surface can be improved using long nanosecond laser pulses (150 ns). The long nanosecond pulse not only suppresses the disadvantageous broadening and defor- mation of spectral line profiles usually observed when short

Evolution of P

and of the N

population along the fiber during the formation of the first and second pulses at different times after the opening time of the electro-optic modulator: 0 ns (a), 435 ns (b), and 950 ns (c).

Fig. 5.

Pair of sub-nanoseconds pulses produced by a laser cavity of 110 m with a

10 ns-rise time for PIV application.

nanosecond pulses are used, but also greatly suppresses the material removal from analyte surfaces [10]. The texturing [11]

and coloring surface [12] processes are industrial applications, which require long Q-switched laser pulses varying from 150 to 500 ns, with a pulse energy between 3 and 6 mJ [13–15].

In many domains, Nd:YAG lasers are traditionally used (Q-switched Nd:YAG laser pumped by diode). However, these lasers can be replaced by a Q-switched rare-earth doped fiber laser. Q-switched fiber laser with special core designs can be realized to obtain both high energy emission and monomode oscillation for high spatial beam quality [21–24]. In large-mode area fibers, the core size is indeed increased to emit energetic pulses. Single mode operation is obtained through judicious design of the inner cladding. In this section, we will thus consider a Yb-doped fiber with a 30 m m core and a 300 m m inner cladding.

Numerical aperture of this large-mode area fiber is small (0.0125) to ensure spatial monomode oscillation. The length of the pulse needs now to be optimized through efficient cavity design.

Fig. 3(c) shows the way to produce long pulses with a Q-switched DC fiber laser. We observe in this case a global envelope exceed- ing 200 ns. Pulses are unfortunately composed of a wide number of intense peaks, but it seems possible to optimize the parameters of the cavity to enlarge each of these peaks and obtain then a global pulse with a smooth envelope exceeding 200 ns. The duration of the peaks can indeed be increased by the combination of 2 factors: a short cavity to reduce the interval between the peaks, and a relatively high rise time of the EOM (typically hundreds of nanoseconds) to enlarge the peaks.

We consider finally the ring cavity described in Fig. 1. The Yb-doped optical fiber is a large-mode area fiber. We do not need any un-doped fiber for this application. Eqs. (c) and (d) which give the pump and signal evolution in this fiber can thus be eliminated in the theoretical model. The length of the Yb-doped fiber is 3.5 m.

The Yb-dopant concentration is 2 10

m

. The fiber is pumped by a 14 W laser diode at 940 nm. The EOM parameters are: a rise time of 380 ns, and an opening time of 5 m s. Note that both important parameters (cavity length and EOM rise time) have been modified as previously mentioned. Finally, we extract 10% of the signal that propagates in the cavity by the 90/10 coupler.

Fig. 7 shows the pulse predicted in this case. As expected, we obtain a long envelope where the multi-peak nature is highly smoothed. In this case, the parameters of the cavity are such that the initial ASE signal exhibits low differences between both extremities of the fiber. When the modulator is switched on, the

ASE signal is progressively amplified. Due to its initial profile, it does not lead to intense peaks but to slow ripples. Experimen- tally, effects as dispersion would attenuate these ripples. Note however, that such ripples can be observed experimentally [25].

The pulse length is 150 ns at full width half time, and the pulse energy is 4.8 mJ. It is thus possible to develop Q-switched DC fiber lasers that can emit 150 ns pulses exceeding the millijoule per pulse. Fig. 8 shows the evolution of the signal power P

inside the cavity at different times during the pulse formation. The big difference with previous paragraph is the progressive buildup of the global pulse during a wide number of cavity round-trips, contrarily to previous case where the bi-pulse was due to only two round-trips. The small discontinuities observed in the P

profiles are due to the initial difference in the ASE signal observed at the beginning and the end of the doped fiber at initial time t ¼0 (just before the EOM is opened).

5. Conclusion

We have developed models to design actively Q-switched Yb-doped DC fiber lasers in various configurations. It has been possible to design two cavities : the first one is able to emit a pair of sub-nanosecond pulses separated by more than 500 ns for PIV applications. This time interval can be adjusted by proper choice of the length of an un-doped fiber inserted in the cavity.

The second cavity designed allows to emit long 150 ns pulses exceeding a few millijoules per pulse. Applications concern in this case materials science and combustion. In all cases, the rise time of the EOM is an essential parameter. Our results show that Yb-Doped DC fiber lasers are very good candidates to replace the Nd:YAG lasers that are traditionally used in these applications.

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Fig. 7.

Long and energetic output pulse issued from a double-clad ytterbium- doped fiber laser cavity.

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