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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 16494–16503
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Parameter space for the collective laser coupling in the laser fusion driver based on the concept of fiber amplification network

Zhihua Huang, Honghuan Lin, Dangpeng Xu, Mingzhong Li, Jianjun Wang, Ying Deng, Rui Zhang, Yongliang Zhang, Xiaocheng Tian, and Xiaofeng Wei  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 16494-16503 (2013)
http://dx.doi.org/10.1364/OE.21.016494


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Abstract

Collective laser coupling of the fiber array in the inertial confinement fusion (ICF) laser driver based on the concept of fiber amplification network (FAN) is researched. The feasible parameter space is given for laser coupling of the fundamental, second and third harmonic waves by neglecting the influence of the frequency conversion on the beam quality under the assumption of beam quality factor conservation. Third harmonic laser coupling is preferred due to its lower output energy requirement from a single fiber amplifier. For coplanar fiber array, the energy requirement is around 0.4J with an effective mode field diameter of around 500μm while maintaining the fundamental mode operation which is more than one order of magnitude higher than what can be achieved with state-of-the-art technology. Novel waveguide structure needs to be developed to enlarge the fundamental mode size while mitigating the catastrophic self-focusing effect.

© 2013 OSA

1. Introduction

The history of the research of the laser driven inertial confinement fusion (ICF) is almost as long as that of the laser technology. The output energy, peak power and intensity of the laser beam have been enhanced profoundly in the last few decades due to the construction of the large-scale laser drivers such as NIF [1

1. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. 46, 3276–3303 (2007) [CrossRef] [PubMed] .

], LMJ [2

2. C. Lion, “The LMJ program: An overview,”J. Phys. Conf. Ser. 244, 012003 (2010) [CrossRef] .

] and SG-III [3

3. W. Zheng, X. Zhang, X. Wei, F. Jing, Z. Sui, K. Zheng, X. Yuan, X. Jiang, J. Su, H. Zhou, M. Li, J. Wang, D. Hu, S. He, Y. Xiang, Z. Peng, B. Feng, L. Guo, X. Li, Q. Zhu, H. Yu, Y. You, D. Fan, and W. Zhang, “Status of the SG-III solid-state laser facility,”J. Phys. Conf. Ser. 112, 032009 (2008) [CrossRef] .

]. Large aperture Nd:Glass bulk medium is applied in these facilities which can produce nanosecond-pulse with energy of around twenty kilo-joules per beamlet at fundamental harmonic wavelength (1ω). Therefore, only around 200 beamlets are required to generate pulse energy as high as 2MJ at third harmonic wavelength (3ω) which was thought to be enough for the indirect drive central ignition method [4

4. J. A. Paisner, S. A. Kumpan, W. H. Lowdermilk, J. D. Boyes, and M. S. Sorem, “Conceptual design of the national ignition facility,” Proceedings of Solid State Lasers for Application to Inertial Confinement Fusion , 2633: 2–12 (1995) [CrossRef] .

] but proven to be too optimistic [5

5. National Research Council, “An Assessment of the Prospects for Inertial Fusion Energy” (National Academies Press, Washington D. C., 2013).

]. However, direct drive or other ignition modes may also be feasible at this energy level [5

5. National Research Council, “An Assessment of the Prospects for Inertial Fusion Energy” (National Academies Press, Washington D. C., 2013).

].

A disadvantage of current Xenon lamp pumped bulk laser driver is that its energy conversion efficiency is too low which results in high thermal load and very low repetition rate. Replacing the pump source to laser diode while keeping the laser amplifiers unchanged is one option which guides the design of LIFE [6

6. W. R. Meier, T. M. Anklam, A. C. Erlandson, R. R. Miles, A. J. Simon, R. Sawicki, and E. Storm, “Integrated process modeling for the laser inertial fusion energy (LIFE) generation system,”J. Phys. Conf. Ser. 244, 032035 (2010) [CrossRef] .

]. The fiber amplification network (FAN) proposed by G. Mourou et al. [7

7. C. Labaune, D. Hulin, A. Galvanauskas, and G. A. Mourou, “On the feasibility of a fiber-based inertial fusion laser driver,” Opt. Commun. 281, 4075–4080 (2008) [CrossRef] .

, 8

8. G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photon. 7, 258–261 (2013) [CrossRef] .

] provides us a promising alternative which takes advantage of the rapid development of the fiber laser technology. In the last few years, the output energy of from the single-mode photonic crystal fiber has been enhanced to larger than 4.3mJ for 1ns pulse [9

9. C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100 mu m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006) [CrossRef] .

] while the output energy from the multimode fiber has reached 33mJ for 10ns pulse [10

10. C. Zheng, H. Zhang, P. Yan, and M. Gong, “Low repetition rate broadband high energy and peak power nanosecond pulsed Yb-doped fiber amplifier,” Opt. Laser Technol. 49, 284–287 (2013) [CrossRef] .

]. However, due to the megajoule-class energy requirement in the ICF laser driver, millions of fiber amplifiers are still required in the FAN configuration which makes laser coupling a difficult problem. The requirements of output capabilities from a single fiber amplifier are prior issues to be confirmed in order to assess the feasibility of this concept and guide the research of fiber amplifiers based on this concept.

In this work, the feasible parameter space for the collective laser coupling of the laser fusion driver based on the FAN concept is researched. Beam quality factor conservation law is applied by neglecting the influence of the frequency conversion on the beam quality. The output beam from each fiber amplifier is assumed to be diffraction-limited with a lower limit of center-to-center pitch.

2. Collective laser coupling

Collective laser coupling means that a number of fiber sources (fiber array) use the same laser coupling optics, as is shown in Fig. 1. The integration level is higher in collective laser coupling while the output beam quality of the fiber array is degraded compared to that of a single fiber source. Frequency conversion unit is omitted in this configuration.

Fig. 1 Configuration of collective laser coupling optics.

2.1. Integrated parameters for the ICF laser driver

Part of the integrated parameters for the ICF laser driver are given in table 1 which follow the design of NIF [1

1. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. 46, 3276–3303 (2007) [CrossRef] [PubMed] .

] and LMJ [2

2. C. Lion, “The LMJ program: An overview,”J. Phys. Conf. Ser. 244, 012003 (2010) [CrossRef] .

] while replacing indirect drive method with direct drive method. For comparison, laser energy requirements at the fundamental harmonic (1ω), second harmonic (2ω) and (3ω) are assumed. The chamber opening proportion ζ determines the area that can be used for laser coupling, and therefore the average energy fluence through the coupling area for given laser energy which is shown in Fig. 2(left). ζ is approximately 0.1 for NIF [1

1. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. 46, 3276–3303 (2007) [CrossRef] [PubMed] .

]. ζ = 0.3 is chosen here to accommodate numerous fiber sources which is almost the upper limit of the opening proportion considering the mechanical stability of the chamber.

Table 1. Part of the integrated parameters for the ICF laser driver

table-icon
View This Table
Fig. 2 (Left) variation of average energy fluence with the chamber opening proportion, (right) variation of the output pulse energy with the mode field diameter for the in-core fluence of 200J/cm2.

Another important parameter is the output energy fluence EF from a single circular core fiber. In the large aperture Nd:glass laser system, the saturation fluence Js is around 4.5J/cm2. The output energy fluence at fundamental harmonic wave is approximately 20J/cm2 which is 4 ∼ 5 times of Js[4

4. J. A. Paisner, S. A. Kumpan, W. H. Lowdermilk, J. D. Boyes, and M. S. Sorem, “Conceptual design of the national ignition facility,” Proceedings of Solid State Lasers for Application to Inertial Confinement Fusion , 2633: 2–12 (1995) [CrossRef] .

]. In Ytterbium-doped fibers, Js at 1053nm is around 50J/cm2[11

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

]. The extracted energy fluence can be as large as 10 times of Js [12

12. C. Renaud, H. Offerhaus, J. Alvarez-Chavez, J. Nilsson, W. Clarkson, P. Turner, D. Richardson, and A. Grudinin, “Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron. 37, 199–206 (2001) [CrossRef] .

] in small mode area fiber amplifiers. However, based on the experimental demonstrations of large mode area fiber (LMAF) amplifiers, the output energy fluence of around 200J/cm2 (4Js) for 10ns pulse is expectable. Therefore, JF = 200J/cm2 is used in this paper to estimate the output pulse energy for a given mode filed diameter (MFD). The variation of output pulse energy with the MFD is shown in Fig. 2 (right).

2.2. Arrangement of the fiber array

Two kinds of typical two-dimensional coplanar arrangement of the fiber array is shown Fig. 3, i.e. the rectangular and hexagonal arrangements. The number of rings k is chosen to describe the scale of the fiber array. The relation between k and the total number of fiber sources is as follows:
NF={4k2rectangular3k(k1)+1hexagonal
(1)
The relation between the diagonal of the fiber array DB and the center-to-center pitch Λ is given as
DB={(m1)2Λ+DFrectangular(m1)Λ+DFhexagonal
(2)
where m is the number of fiber sources across the diagonal. The relation between m and k is
m={2krectangular2k1hexagonal
(3)

Fig. 3 (Left) rectangular and (right) hexagonal arrangement of the fiber array.

3. Beam quality factor conservation

As is shown in Fig. 4, the beam parameter product (BPP) is defined as the product of the beam waist radius w and half divergence angle θ defined by the second order intensity moment within which over 86.5% energy is enclosed [13

13. N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications, 2nd ed. (Springer, 2005).

]
BPP=w×θ
(5)
For diffraction-limited beam, the minimum of beam parameter product BPP0 is
BPP0=λ/π
(6)
where λ is the central wavelength. For λ = 1053nm, BPP0 = 0.335mm · mrad. Beam quality factor M2 of an arbitrary beam is defined as the ratio of its BPP to BPP0, therefore, M2 equals to 1.0 for the diffraction-limited Gaussian beam. Generally, beam quality becomes worse for larger M2. In the context of laser coupling, worse beam quality means that the focused spot size is larger for given beam aperture and focusing lens. In the LMFA, M2 is larger for higher order modes [14

14. H. Yoda, P. Polynkin, and M. Mansuripur, “Beam Quality Factor of Higher Order Modes in a Step-Index Fiber,” J. Lightwave Technol. 24, 1350 (2006) [CrossRef] .

].

Fig. 4 Conservation of the beam parameter product in the focusing process.

The conservation law of the beam quality factor says that M2 is a constant in an ABCD-optical system where only free space propagation and parabolic phase element (ideal lens) are involved [13

13. N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications, 2nd ed. (Springer, 2005).

]. In the laser-driven ICF, incoherent beam combining is an advantage to realize uniform laser intensity distribution on the target. For an incoherent fiber array, the summation of all the beams can be viewed as a single beam which also must follow the conservation law if incoherent condition is assumed. For simplicity, the impact of the frequency conversion to M2 factor is neglected (BPP varies because the wavelength is different). This is close to be true if the combined near field intensity distribution is flattened which results in an equal nonlinear phase shift across the lateral section. Only a frequency conversion efficiency is assumed for the calculation of the effective energy at the fundamental harmonic wavelength. The maximum 1-D M2 (along the longest diagnoal) is applied to guarantee high coupling efficiency althought 2-D arrangement is assumed for analysis.

4. Analyzing procedure of the collective laser coupling

Fig. 5 Analyzing procedure of the collective laser coupling under the beam quality factor conservation condition (notations are explained in the text).

5. Results

Fig. 6 For laser coupling of 2MJ@3ω, (a) 3-dimensional and (b) contour plot of Λ/Λlim, variation of the number of (c) fiber arrays and (d) fiber sources.

Fig. 7 For laser coupling of (top) 4MJ@1ω and (bottom) 3MJ@2ω, (a)(c) are the contour plot of Λ/Λlim, (b)(d) are the variation of number of fiber arrays NB with beam quality factor MB2.

6. Conclusions and discussions

Acknowledgments

This study was funded by China Academy of Engineering Physics (grant no. 2012B0401060 and 2011B0401063).

References and links

1.

C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt. 46, 3276–3303 (2007) [CrossRef] [PubMed] .

2.

C. Lion, “The LMJ program: An overview,”J. Phys. Conf. Ser. 244, 012003 (2010) [CrossRef] .

3.

W. Zheng, X. Zhang, X. Wei, F. Jing, Z. Sui, K. Zheng, X. Yuan, X. Jiang, J. Su, H. Zhou, M. Li, J. Wang, D. Hu, S. He, Y. Xiang, Z. Peng, B. Feng, L. Guo, X. Li, Q. Zhu, H. Yu, Y. You, D. Fan, and W. Zhang, “Status of the SG-III solid-state laser facility,”J. Phys. Conf. Ser. 112, 032009 (2008) [CrossRef] .

4.

J. A. Paisner, S. A. Kumpan, W. H. Lowdermilk, J. D. Boyes, and M. S. Sorem, “Conceptual design of the national ignition facility,” Proceedings of Solid State Lasers for Application to Inertial Confinement Fusion , 2633: 2–12 (1995) [CrossRef] .

5.

National Research Council, “An Assessment of the Prospects for Inertial Fusion Energy” (National Academies Press, Washington D. C., 2013).

6.

W. R. Meier, T. M. Anklam, A. C. Erlandson, R. R. Miles, A. J. Simon, R. Sawicki, and E. Storm, “Integrated process modeling for the laser inertial fusion energy (LIFE) generation system,”J. Phys. Conf. Ser. 244, 032035 (2010) [CrossRef] .

7.

C. Labaune, D. Hulin, A. Galvanauskas, and G. A. Mourou, “On the feasibility of a fiber-based inertial fusion laser driver,” Opt. Commun. 281, 4075–4080 (2008) [CrossRef] .

8.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photon. 7, 258–261 (2013) [CrossRef] .

9.

C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100 mu m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006) [CrossRef] .

10.

C. Zheng, H. Zhang, P. Yan, and M. Gong, “Low repetition rate broadband high energy and peak power nanosecond pulsed Yb-doped fiber amplifier,” Opt. Laser Technol. 49, 284–287 (2013) [CrossRef] .

11.

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

12.

C. Renaud, H. Offerhaus, J. Alvarez-Chavez, J. Nilsson, W. Clarkson, P. Turner, D. Richardson, and A. Grudinin, “Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron. 37, 199–206 (2001) [CrossRef] .

13.

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications, 2nd ed. (Springer, 2005).

14.

H. Yoda, P. Polynkin, and M. Mansuripur, “Beam Quality Factor of Higher Order Modes in a Step-Index Fiber,” J. Lightwave Technol. 24, 1350 (2006) [CrossRef] .

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(080.2468) Geometric optics : First-order optics
(140.3298) Lasers and laser optics : Laser beam combining
(060.3510) Fiber optics and optical communications : Lasers, fiber

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 22, 2013
Revised Manuscript: June 11, 2013
Manuscript Accepted: June 11, 2013
Published: July 2, 2013

Citation
Zhihua Huang, Honghuan Lin, Dangpeng Xu, Mingzhong Li, Jianjun Wang, Ying Deng, Rui Zhang, Yongliang Zhang, Xiaocheng Tian, and Xiaofeng Wei, "Parameter space for the collective laser coupling in the laser fusion driver based on the concept of fiber amplification network," Opt. Express 21, 16494-16503 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-14-16494


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References

  1. C. A. Haynam, P. J. Wegner, J. M. Auerbach, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, E. Moses, J. R. Murray, M. C. Nostrand, C. D. Orth, R. Patterson, R. A. Sacks, M. J. Shaw, M. Spaeth, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. Van Wonterghem, “National Ignition Facility laser performance status,” Appl. Opt.46, 3276–3303 (2007). [CrossRef] [PubMed]
  2. C. Lion, “The LMJ program: An overview,”J. Phys. Conf. Ser.244, 012003 (2010). [CrossRef]
  3. W. Zheng, X. Zhang, X. Wei, F. Jing, Z. Sui, K. Zheng, X. Yuan, X. Jiang, J. Su, H. Zhou, M. Li, J. Wang, D. Hu, S. He, Y. Xiang, Z. Peng, B. Feng, L. Guo, X. Li, Q. Zhu, H. Yu, Y. You, D. Fan, and W. Zhang, “Status of the SG-III solid-state laser facility,”J. Phys. Conf. Ser.112, 032009 (2008). [CrossRef]
  4. J. A. Paisner, S. A. Kumpan, W. H. Lowdermilk, J. D. Boyes, and M. S. Sorem, “Conceptual design of the national ignition facility,” Proceedings of Solid State Lasers for Application to Inertial Confinement Fusion, 2633: 2–12 (1995). [CrossRef]
  5. National Research Council, “An Assessment of the Prospects for Inertial Fusion Energy” (National Academies Press, Washington D. C., 2013).
  6. W. R. Meier, T. M. Anklam, A. C. Erlandson, R. R. Miles, A. J. Simon, R. Sawicki, and E. Storm, “Integrated process modeling for the laser inertial fusion energy (LIFE) generation system,”J. Phys. Conf. Ser.244, 032035 (2010). [CrossRef]
  7. C. Labaune, D. Hulin, A. Galvanauskas, and G. A. Mourou, “On the feasibility of a fiber-based inertial fusion laser driver,” Opt. Commun.281, 4075–4080 (2008). [CrossRef]
  8. G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photon.7, 258–261 (2013). [CrossRef]
  9. C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, single-transverse-mode operation of a 100 mu m core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett.89, 111119 (2006). [CrossRef]
  10. C. Zheng, H. Zhang, P. Yan, and M. Gong, “Low repetition rate broadband high energy and peak power nanosecond pulsed Yb-doped fiber amplifier,” Opt. Laser Technol.49, 284–287 (2013). [CrossRef]
  11. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-Doped Fiber Amplifiers,” IEEE J. Quantum Electron.33, 1049–1056 (1997). [CrossRef]
  12. C. Renaud, H. Offerhaus, J. Alvarez-Chavez, J. Nilsson, W. Clarkson, P. Turner, D. Richardson, and A. Grudinin, “Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron.37, 199–206 (2001). [CrossRef]
  13. N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications, 2nd ed. (Springer, 2005).
  14. H. Yoda, P. Polynkin, and M. Mansuripur, “Beam Quality Factor of Higher Order Modes in a Step-Index Fiber,” J. Lightwave Technol.24, 1350 (2006). [CrossRef]

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