Diffraction limited polarized emission from a multimode Yb-doped fiber amplifier after nonlinear beam cleanup L. Lombarda , A. Brignona , J.P. Huignarda , E. Lalliera , G. Lucas-Leclinb , P. Georgesb , G. Pauliatb , G. Roosenb a

Thales Research and Technology - France, Domaine de Corbeville, 91404 Orsay, France; b Laboratoire Charles Fabry de l’Institut d’Optique, du CNRS, et de l’Universit´ e Paris Sud, Centre universitaire, Bat 503 91403 Orsay, France ABSTRACT

The multimode and depolarized output beam of a highly multimode diode-pumped Yb-doped fiber amplifier is converted to a diffraction limited, linearly polarized beam by a self-referencing two wave mixing process in an infrared sensitive photorefractive crystal (Rh : BaT iO3 ). Up to 11.6W singlemode output is achieved with a 78% multimode to singlemode photorefractive conversion efficiency. Keywords: Fiber optics amplifiers and oscillators, Photorefractive nonlinear optics, Two-wave mixing, phase conjugation

1. INTRODUCTION The performances and the technology of fiber lasers capable of delivery high power has progressed very rapidly since early demonstrations more than ten years ago. Over the past two years, the level of CW power which can be produced at one micron wavelength with a good beam quality has increased from 100W 1 to nearly 1kW .2 In the ns pulse regime, output energies of a few mJ 3 are demonstrated. These lasers exhibit intrinsic advantages in comparison with classical solid state technology: fiber lasers can be made more compact, efficient, reliable and cost effective. These qualities are of major interest in industrial applications, for optronic systems or material processing. It also provide very attractive coherent sources for scientific instrumentation, active imaging or atmospheric remote sensing. This breakthrough in the performances has been driven by the following technological advances: • The development of high power diodes for pumping the double-clad fiber amplifiers • The emergence of large mode area fibers (LMA) which are doped with Yb or Er. To realize high power fiber lasers, it is required to use large core area: it is the only practical way to reduce both the susceptibility of the fiber to optical damage and also the appearance of detrimental nonlinear effects (Brillouin, Kerr, Raman...) which would limit the output power of the source and disturb the spectral qualities. The high numerical aperture of the double clad also permits to efficiently collect the pumping power issued from the low brightness diodes. In order to realize large core fiber, the numerical aperture N A has to be decreased. This conclusion appears from the following simple formalism: a step q 2 − n2 = 2π · R · N A fulfills index fiber is single mode when the normalized parameter V = 2π · R n c c c g λ λ the condition V < 2.4. Rc is the core radius; nc , ng are respectively the core and clad index of refraction. Thus, increasing Rc require fiber N A to be decreased: Low core-cladding ∆n index difference is required in order to maintain single mode operation. Therefore, the recent availability of low N A, large mode area (LMA) fibers with ≈ 20 to 30µm and N A of ≈ 0.06 has made possible remarkable achievements and performances. CW output powers of the order of 800W to 1kW with beam qualities M 2 ≈ 1.3 to 1.7 using ≈ 20 to ≈ 30µm core Yb-LMA fibers lasers2, 4 have been measured recently by several Universities (Michigan, Southampton, Jena). Single frequency MOPA have also been achieved.5 It is now expected from these excellent results that, by carefully controlling the guiding properties of the fundamental mode of the LMA fibers will permit to optimize the output power while being not affected by fiber bending and thermal, mechanical perturbations. However, for a further increase of the current LMA fiber laser Further author information: (Send correspondence to L. Lombard) L. Lombard: E-mail: [email protected], Telephone: +33 (0)1 69 33 91 80

Figure 1. Multimode amplifier with beam reshaping by two wave mixing in a nonlinear photorefractive crystal. SM: Singlemode input beam. MM: Amplified multimode beam. Output: Reshaped beam.

Figure 2. Multimode amplifier with phase conjugating mirror. The phase conjugation occurs in a nonlinear medium. SM: Singlemode input beam. MM: Amplified multimode beam. Output: Singlemode beam after a two pass amplification and a phase conjugation.

performances, in particular in the pulsed regime, it will be required to switch to very large mode area fibers (VLMA). Fulfilling the condition on V is no more possible: this would lead to weak guiding in the core and eventually makes very low N A fibers extremely sensitive to bending losses. Therefore, there will be a need for step index fiber amplifiers with large enough N A and doped core diameters in the range of 50µm to 500µm. They would permit to deliver output energies beyond several 100mJ with 10ns pulse duration. This level of performances would replace classical solid state lasers in optronic equipments or for material processing by more compact and efficient fiber sources. Such a very large mode area will inevitably support many propagation modes thus leading to a reduced beam quality due to mode coupling, after several meters of beam propagation. The resulting large value of the M 2 factor (M 2 À 1) will provide a significant beam divergence and a complex speckle structure due to interference between the modes. In view of recovering a nearly diffraction limited beam quality (M 2 ≈ 1)in such a fiber, new techniques have been invastigated, as maintaining a single-transverse mode propagation in multimode fiber amplifiers.6 We propose at THALES TRT to implement a nonlinear mode conversion technique. In other words, the multimode beam issued from the very large core fiber amplifier is transformed into a Gaussian beam. Two original approaches are proposed: first, the beam cleanup method based on nonlinear two wave mixing, second optical phase conjugation. These ideas which are issued from the research works at TRT on nonlinear wave mixing techniques applied to beam correction and manipulation are shown in figures 1 and 2. According to figure 1, the multimode pump beam transfers its intensity (and not the phase) to a single mode probe beam after two beams interaction in a nonlinear media which exhibits a photoinduced index modulation (third order nonlinearity). In figure 2, the output multimode beam is reflected by a nonlinear mirror which generates the phase conjugate replica of the complex incident wavefront. After double pass through the amplifier, a nearly diffraction limited beam can be recovered. According to our previous experiences at TH-TRT on these subjects we propose to analyze and validate these concepts with multimode amplifiers at limited output power levels. Single mode, single frequency and polarized beam emission is demonstrated with preliminary experiments using respectively a photorefractive crystal for beam clan-up and stimulated Brillouin scattering for phase conjugation.

The first original approach, firstly proposed in Ref. 7, consists in correcting the beam profile after the multimode amplifier by a nonlinear beam cleanup method. The photorefractive two-wave mixing beam cleanup interaction has been validated in previous works in visible light8, 9 after a depolarizer,10 and at 1064nm after an aberrator.7, 11 Here we propose and demonstrate an improved version of this technique applied to a diode pumped multimode Yb-doped fiber amplifier. We will also introduce the second technique, that is still under progress.

2. PRINCIPLE OF TWO-WAVE MIXING BEAM CLEANUP Diffusion-type photorefractive materials allow energy transfer between two coherent beams by interferenceinduced index grating.12 The photorefractive effect is a phenomenon in which the local index of refraction is changed by the spatial variation of light intensity. It arises from optically-generated charge carriers which migrate when the crystal is exposed to a spatially varying pattern of illumination. In case of diffusion-type photorefractive crystals such as BaT iO3 , the charge carriers are mostly generated where light is intense and then diffuse all over the crystal, leaving charge defects. This space-charge separation gives rise to a strong space-charge field that induces refractive index change by Pockel’s effect. In case of an interference pattern between two coherent beams in the medium, the induced refraction index pattern acts as a volume diffraction grating. This is the two-wave mixing interaction: the two beams diffract on this grating along each other. Furthermore, the index pattern is shifted by a quarter wave in the direction defined by the crystal c-axis orientation (see Figure 3). In this direction the diffraction is phase-matched and S gets cumulatively diffracted along R. Thus the intensity of S is transferred to R. This effect is shown on Figure 3 and expressed in the coupled equations (1,2) where IR , IS are beam intensities, Γ is the photorefractive gain coefficient (cm−1 ) and α is the absorption coefficient (cm−1 ). dIS dz dIR dz

IS IR − αIS IS + IR IS IR = Γ − αIR IS + IR = −Γ

(1) (2)

Figure 3. Two wave mixing process in a photorefractive crystal. IR (z), IS (z): intensities of beams R and S along the propagation. Continuous lines: maxima of the interference pattern. Dashed lines: maxima of the shifted index pattern.

After a propagation in a crystal with a thickness d, beam R experiences an intensity gain G given by (3) where β is the reference to signal intensity ratio (4). G = β

=

IR (d) β+1 = · e(Γ−α)d IR (0) β + eΓd IS (0) IR (0)

(3) (4)

The wavefront of the two beams are unaffected in the interaction: S transfers its energy and not its phase to R. This remarkable property allows the two-wave mixing beam cleanup. As shown on Figure 3, a low-power singlemode beam R is mixed with a coherent high power multimode beam S, so that the index grating diffracts the high-power beam S along the singlemode beam R with the phase characteristics of R. The intense and aberrated beam S is diffracted to a singlemode intense beam R. In other words, photorefractive two-wave mixing acts as a nonlinear spatial mode converter.7

3. A Rh : BaTiO3 PHOTOREFRACTIVE CRYSTAL FOR 1µm BEAM CLEANUP The crystal used in the experiment is a Rh : BaT iO3 crystal∗ . This crystal has a ”roof shape” to prevent any parasitic oscillation arising from beam fanning.13 The 8 × 8mm2 input and output faces are antireflection coated and are cut at 45◦ from the crystal c-axis. This c-axis lies in the horizontal plane, plane of the incident polarizations, in order to access large photorefractive gains. The crystal thickness is 3mm. The ∗

from D. Rytz, FEE GmbH, Germany. Rh doping concentration is 1000 ppm in the melt.

Figure 4. Measured photorefractive gain in a two wave mixing experiment as a function on incident beams intensity ratio.

photorefractive gain, defined as G in equation 3, was measured in a simple two-wave mixing experiment as a function of the input power ratio β (see Figure 4). The maximum measured gain Gmax is 2000, which corresponds to a photorefractive gain coefficient Γ of 24.6cm−1 . With the crystal used in this experiment, both beam polarizations must be in the same plane as the crystal c-axis in order to access maximum efficiency.

4. EXPERIMENTAL SETUP In this paper, the technique is applied to a diode pumped multimode-Yb-doped-fiber amplifier as shown in Figure 6. A CW master oscillator (Nd:YAG NPRO laser, 500mW @1.06µm, spatially and spectrally singlemode) is amplified in a multimode fiber amplifier. The amplifier uses a double clad fiber † with a 55µm diameter (N A = 0.19) Yb-doped signal core (6500mol ppm Y b2 O3 ) and a 340/400µm diameter (N A = 0.38) D-shaped pump core. A picture of the fiber is shown on Figure 5. The 3.5m long fiber absorbs a power of 60W of the 940nm pumping diode. The amplified signal beam S has a power of 18W , is depolarized and bears many transverse modes as seen on picture in Figure 6. All the speckle grains have a different elliptical polarization but are coherent with each other. A 55µm core diameter fiber has been used in this experiment but the approach is scalable to significantly larger core diameters. To treat its two polarizations, S is split into its two linear components S1 (horizontal polarization) and S2 (vertical polarization, changed to horizontal polarization by a half-waveplate, see Figure 6). The powers of S1 and S2 are 8.3W and 6.6W respectively. A diffraction-limited reference beam R is created Figure 5. Fibre used in the experiment, by spatially selecting a small part of one of S1 bright speckle with a Yb-doped signal core (55µm diamgrains with a dot mirror. This mirror is a 1mm diameter gold eter, 0.19N A) and a D-shaped pump core spot coated on a high transmission plate. The reflected bright (400µm diameter, 0.39N A). speckle grain is spatially filtered with a lens-pinhole system. This 110mW reference beam R is horizontally polarized, diffraction limited and coherent with S. S1 and S2 are then mixed with the reference beam R in the photorefractive crystal. In the crystal plane, R is a 1.5mm diameter diverging beam normal to the crystal surface, and S1 and S2 are 1 × 1.5mm2 elliptical converging beams with a 40◦ incidence angle. The angle between S1 and S1 is 1.5◦ . Here, S1 and S2 spots are smaller than R and they overlap and amplify respectively the upper and lower halves of R. S1 and S2 could as well be the same size as R and overlap the whole beam. The two-wave-mixing process in the photorefractive crystal then occurs as follows: the intensity fringes between R and S1 are converted into a π2 -shifted index grating by the crystal. This grating diffracts S1 along R and adds coherently the diffracted S1 to R. As a result, R is amplified by S1 . The same process †

from the Institute for Physical High Technology (IPHT), Jena, Germany

Figure 6. Experimental setup of an Yb-doped multimode fiber amplifier with spatial beam converter. The amplified depolarized multimode signal beam S is split into its two linear polarizations and combined with an extracted singlemode beam R in a Rh:BaTiO3 crystal and converted to singlemode. DM : dichroic mirror to separate 940nm and 1064nm beams. L1, L2, L3: lenses. M 1, M 2, M 3: mirrors. λ/2: half-wave plate P BS: Polarizing Beam Splitters M : spot mirror of the size of one speckle grain of S. F S: spatial filtering device. Signal and amplified reference spot shapes are shown in squares. An arrow in the crystal indicated the c-axis orientation.

occurs between R and S2 . The remarkable property of this two-wave-mixing interaction is that it amplifies R intensity profile in the crystal but leaves R phase profile unchanged: S transfers only its intensity and not its phase to R. In this self referencing interferometer, the interference pattern is very stable. The reference R is in phase with the signals S1 and S2 , even when the temperature fluctuates in the fiber. In an early version,14 the reference beam R was taken directly on the oscillator before the amplifier. The phase fluctuations between R and S, induced by thermal and mechanical fluctuations in the fiber, had to be compensated because of the relatively slow photorefractive response. In the present paper, the self referencing interferometer gets rid of this problem because R, S1 and S2 are always in phase and no active phase stabilization is required.

5. EXPERIMENTAL RESULTS Under these conditions, we obtain after the spatial beam converter an amplified R output power of 11.6W with 110mW reference power and 14.9W total signal power IS = IS1 + IS2 before the crystal. The power of S is IS = 18W at the spatial beam converter input, before M1 on Figure 6. Behind the crystal, the total signal is depleted to 2.7W . Figure 7 shows R power IR vs time as it is amplified by S1 alone, by S2 alone, and by both S1 and S2 . The rise time is 2 to 3s and the two-wave-mixing power efficiencies are respectively 77%, 82% and 78%. Taking into account the 81% transmission between the output fiber signal S and S1 + S2 before the crystal leads to a total power efficiency of 63% for the whole spatial beam converter. Of course most of these losses could be reduced by optimizing the optical elements transmission with appropriate coatings. The M 2 parameter has been measured for the different beams with the second order moment method. The results are shown in Figure 8. The reference R is diffraction limited, the 11.6W output beam is almost diffraction limited with M 2 = 1.2 while S1 is multimode with M 2 = 7.4. Amplified R is less diverging than R because of the additional converging thermal lens due to residual absorption in the crystal. Figure 9 shows the intensity profiles of the waists in the far field.

Figure 7. Power evolution of R after the crystal (a) with S1 on, (b) with S2 on, and (c) with both S1 and S2 on. The rise time (from 10 to 90% of the full power) is around 2-3s. The base level is the power lewel of beam R: 110mW .

Figure 8. Measure of the M 2 parameter for the different beams. The experimental points are represented by the symbols, and the solid lines are the corresponding fitted curves.

After a constant illumination at 1.06µm, we have noticed a decrease of the two-wave-mixing efficiency in the Rh : BaT iO3 crystal: in Figure 7, a slight decrease is visible on the 11.6W curve. As observed in reference 15, depoled horizontal lines appear in the crystal with a spatial period of ≈ 190µm. Applying a 200mW green beam on the whole surface for several hours repoles the crystal and recovers the efficiency. This effect is similar to the one reported in 15.

6. SCALABILITY Note that this beam correcting setup can be seen as a ”black box” that converts any coherent depolarized multimode beam to a diffraction limited, linearly polarized beam with the spectral characteristics of the beam emitted by the oscillator. The input beam can be highly multimode or aberrated, since the angular acceptance of the crystal is several degrees and its surface is 1cm2 (equivalent to a M 2 > 1000). The required coherence length for the multimode signal is several mm or more, corresponding to the interaction length in the photorefractive crystal. Furthermore, the concept is applicable to pulsed operation since the very large core fiber could sustain high peak power.

7. SBS PHASE CONJUGATION An all-fiber system would be attractive in comparision with the semi-bulk architecture described earlier. This idea makes the Stimulated Brillouin Scattering (SBS) phase conjugation technique (cf. Figure 2) quite interesting: a first multimode fiber is used for amplification, whereas a second multimode fiber is the

Figure 9. Beam profiles: (a) signal S1 at the fiber output, (b) extracted singlemode 110mW reference beam R, (c) singlemode 11.6W amplified R.

Figure 10. Experimental setup for testing the phase conjugation: We compare the returning beams after a double pass in a 70mm multimode fiber with a Brillouin phase conjugating mirror or a simple mirror.

SBS phase conjugator. The technique is schemed on Figure 2. The clean oscillator beam is amplified by a first pass in the aberrating multimode fiber amplifier. Its disturbed beam phase map is then reversed by the phase conjugating mirror. This is a pre-compensation for a second pass: After a second pass in the multimode amplifier, the twice-amplified beam is clean again. A non-reciprocal element allows the extraction of the clean and nearly diffraction limited amplified beam. The Brillouin effect is a nonlinear interaction between the optical wave and the phonons in the medium. A resulting acoustic wave propagates in the fibre and acts as a Bragg mirror that reflects the optical wave with a frequency shift (called the Stokes wave). The effect is known to be armful in the telecommunication field but in this approach, SBS allows the realization of phase conjugating mirrors with multimode fibers. For a preliminary demonstration of the principle, a simple experiment shown on figure 10 is used. The aberrator is a 7cm multimode fiber with a 50µm step index core diameter and a 0.2 numerical aperture. Note that the aberrated beam after a single pass was still polarized. A Brillouin phase conjugating mirror is made with a 2m step index fiber with the same characteristics as the aberrator. The oscillator is an injected Q-switched laser that delivers mJ-level 20ns pulses with full coherence. Figure 11 compares beam profiles without and with the SBS phase conjugator: the figure shows the beam profile after a double pass in the aberrator and a reflection on (11a) a simple mirror and (11b) a Brillouin phase conjugating mirror. The beam parameter M 2 is measured to be improved from 3.6 to 1.1. The nonlinear mirror reflectivity was 50% at an incident energy of 150µJ and can in the steady state nearly reach 100%. For longer Brillouin fibers, phase mismatch due to Brillouin shift can prevent perfect phase conjugation to occur. In various conditions we observed for long fibers either random non-conjugated Stokes waves or beam cleanup. Further theoretical and experimental investigations are under progress to determine optimal parameters and operating conditions both in the CW and pulsed regime.

8. CONCLUSION In conclusion, we have experimentally demonstrated that the beam issued from a multimode Yb-doped fiber amplifier can be efficiently converted into a linearly polarized and nearly diffraction limited beam. This original MOPA architecture involves a nonlinear photorefractive mode converter allowing beam cleanup by a self-referencing two wave mixing interaction. The emitted beam has the spatial and spectral qualities of the oscillator. The achieved output power with the components used in this experiment is 11.6W with 78% photorefractive efficiency. The important feature is that the concept can be extended to very large

Figure 11. Beam intensity profiles after a double pass in a 70mm multimode fiber with (a) a simple mirror (M 2 = 3.6) and (b) a Brillouin phase conjugating mirror (M 2 = 1.1).

core fiber amplifiers which will support very high powers in the CW or pulsed regimes. Rh : BaT iO3 has been used for proof of concept but alternative crystals or nonlinear mechanisms can also be appropriate for reliable operation at the high power levels required in industrial applications. Moreover, a phase conjugating mirror using a Brillouin fiber has also been investigated with preliminary experiments. It is observed that in pulsed operation phase conjugation occurs with good reflectivity. For longer fibers, theoretical and experimental works are still ongoing in order to determine optimal conditions for phase conjugation with good fidelity and good reflectivity to occur.

REFERENCES 1. V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. Yeh, and E. Zucker, “110W fibre laser,” Electron. Lett. 35, p. 1158, 1999. 2. A. Liem et al., “1.3kW Yb-doped fiber laser with excellent beam quality,” Postdedline Paper, CLEO , p. CPD2, 2004. 3. A. Piper, A.Malinowski, K.Furusawa, and D.J.Richardson, “1.2mJ, 37ns single-moded pulses at 10kHz repetition rate from a Q-switched ytterbium fiber laser,” proceedings, CLEO , p. CMK3, 2004. 4. J. Limpert, A. Liem, H. Zellmer, and A. Tunnermann, “500W continuous wave fibre laser with excellent beam quality,” Electron. Lett 39, p. 645, 2003. 5. Y. Jeong et al., “Single-frequency, polarized ytterbium-doped fiber MOPA source with 264W output power,” Postdedline Paper, CLEO , p. CPD2, 2004. 6. F. Di-Teodoro, J. Koplow, S. Moore, and D. Kliner, “Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier,” Opt. Lett. 27, p. 518, 2002. 7. A. Brignon, J. Huignard, and E. Lallier, “Multimode to single-mode conversion of a Yb-doped fiber amplifier with a photorefractive Rh:BaTiO3 crystal,” App. Phys. B Lasers and Optics 72, p. 789, 2001. 8. A. Chiou and P. Yeh, “Beam cleanup using photorefractive two-wave mixing,” Opt. Lett. 10, p. 621, 1985. 9. L. Mager, G. Pauliat, D. Rytz, M. Garrett, and G. Roosen, “Wavefront correction of nanosecond pulses at 532 nm by photorefractive two wave mixing,” Non Linear Optics 135, 1995. 10. J. E. Heebner, R. S. Bennink, R. W. Boyd, and R. A. Fisher, “Conversion of unpolarized light to polarized light with greater than 50% efficiency by photorefractive two-beam coupling,” Opt. Lett. 25, p. 257, 2000. 11. A. Brignon, J. Huignard, M. Garrett, and I. Mnushkina, “Spatial beam cleanup of a Nd:YAG laser operating at 1.06µm with two-wave mixing in Rh : BaT iO3 ,” Applied Optics-LP 36, p. 7788, 1997. 12. P. Yeh, “Two-wave Mixing in Nonlinear Media,” J. of Quantum Electronics 25, p. 484, 1989. 13. N. Huot, J. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06µm in CW and nanosecond regimes using photorefractive Rh : BaT iO3 ,” Opt. Com. 140, p. 296, 1997. 14. L. Lombard, A. Brignon, J. Huignard, E. Lallier, G. Lucas-Leclin, P. Georges, G. Pauliat, and G. Roosen, “Diode-pumped Yb-doped large-core fiber amplifier with a multimode-to-singlemode photorefractive converter,” proceedings, CLEO , 2003. 15. R. S. Cudney and M. Kaczmarek, “Light-induced removal of 180◦ ferroelectric domains in Rh : BaT iO3 ,” Opt. Express 7, p. 323, 2000.