Abstract

Coherent and incoherent combination of Gaussian beams employing a lens array distributed on the spherical chamber is theoretically analyzed. The output field of each source in the array is coupled through an individual optical system whose local optical axis coincides with the radial direction of the chamber. The resulting intensity profile near the origin is derived. The intensity profile and power in the bucket on the target for rectangular and hexagonal arrangement are numerically calculated. The influences of the center-to-center separation and the ring number of the focusing lens array are given. The synthetic intensity profile of incoherent combination changes little for a lens array scale much smaller than the chamber size. In contrast, the synthetic intensity profile of coherent combination shows an interference pattern with a sharp central peak and sidelobes.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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. M. H. Key, “Status of and prospects for the fast ignition inertial fusion concept,” Phys. Plasmas 14, 055502 (2007).
    [CrossRef]
  9. R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
    [CrossRef]
  10. F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
    [CrossRef]

2010 (1)

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

2008 (2)

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]

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33, 354–356 (2008).
[CrossRef]

2007 (4)

M. H. Key, “Status of and prospects for the fast ignition inertial fusion concept,” Phys. Plasmas 14, 055502 (2007).
[CrossRef]

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

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]

2006 (1)

2005 (1)

T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” Proc. SPIE 5709, 157–164 (2005).
[CrossRef]

2000 (1)

Anderson, K. S.

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Auerbach, J. M.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Betti, R.

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Bowers, M. W.

Cheung, E. C.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33, 354–356 (2008).
[CrossRef]

Di Teodoro, F.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Dixit, S. N.

Erbert, G. V.

Fan, T. Y.

T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” Proc. SPIE 5709, 157–164 (2005).
[CrossRef]

Galvanauskas, A.

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]

Goodno, G. D.

Haynam, C. A.

Heestand, G. M.

Hemmat, M. K.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Henesian, M. A.

Hermann, M. R.

Ho, J. G.

Hulin, D.

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]

Jancaitis, K. S.

Key, M. H.

M. H. Key, “Status of and prospects for the fast ignition inertial fusion concept,” Phys. Plasmas 14, 055502 (2007).
[CrossRef]

Komine, H.

Labaune, C.

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]

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Lü, B.

Ma, H.

Manes, K. R.

Marshall, C. D.

McNaught, S. J.

Mehta, N. C.

Menapace, J.

Morais, J.

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

Moses, E.

Mourou, G. A.

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]

Murray, J. R.

Nostrand, M. C.

Orth, C. D.

Patterson, R.

Perkins, L. J.

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Rice, R. R.

Rothenberg, J.

Sacks, R. A.

Sanchez, A.

T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” Proc. SPIE 5709, 157–164 (2005).
[CrossRef]

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Shaw, M. J.

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Solodov, A. A.

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Spaeth, M.

Sutton, S. B.

Theobald, W.

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Thielen, P.

Van Wonterghem, B. M.

Weber, M.

Wegner, P. J.

White, R. K.

Wickham, M.

Widmayer, C. C.

Williams, W. H.

Yang, S. T.

Zhou, C. D.

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Lett. (2)

Phys. Plasmas (1)

M. H. Key, “Status of and prospects for the fast ignition inertial fusion concept,” Phys. Plasmas 14, 055502 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, and A. A. Solodov, “Shock ignition of thermonuclear fuel with high areal density,” Phys. Rev. Lett. 98, 155001 (2007).
[CrossRef]

Proc. SPIE (2)

F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “100 micron core, Yb-doped, single-transverse-mode and single-polarization rod-type photonic crystal fiber amplifier,” Proc. SPIE 7580, 758006 (2010).
[CrossRef]

T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” Proc. SPIE 5709, 157–164 (2005).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Laser coupling optical system for an individual source.

Fig. 2.
Fig. 2.

Rectangular (a) and hexagonal (b) arrangement of the lens array on the spherical chamber.

Fig. 3.
Fig. 3.

Intensity distributions for the rectangular arrangement. (a) Λ=5mm; (b) Λ=10mm; (c) Λ=20mm; (d) Λ=30mm.

Fig. 4.
Fig. 4.

Intensity distributions for the hexagonal arrangement. (a) Λ=5mm; (b) Λ=10mm; (c) Λ=20mm; (d) Λ=30mm.

Fig. 5.
Fig. 5.

Intensity distributions of coherent combination for rectangular (a) and hexagonal (b) arrangements with increasing ring number.

Fig. 6.
Fig. 6.

Power in the bucket of rectangular (a) and hexagonal (b) arrangements for n=3.

Fig. 7.
Fig. 7.

Peak intensities versus M for rectangular (a) and hexagonal (b) arrangements with Λ=5mm. Circle denotes the peak intensity for incoherent combination, while triangle denotes the peak intensity for coherent combination. Solid line denotes the quadratic curve, while dashed line denotes the linear curve.

Tables (1)

Tables Icon

Table 1. Parameters of the Laser Coupling System for Different RF

Equations (15)

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(x,y,z)=(ρsinθcosφ,ρsinθsinφ,ρcosθ).
wL=w01+(L/z0)2,
E1(x1,y1)=E0exp[ik2q1(x12+y12)],
[ABCD]=[1L201][101/f1][1L101]=[1L2/fL2+L1(1L2/f)1/f1L1/f],
E2(x2,y2)=E0AB/q1exp[ik2q2(x22+y22)],
q2=Aq1+BCq1+D=q2R+iq2I,
q2R=f2(L1+L2)+L2(L12+z02)f(L12+2L1L2+z02)f22L1f+L12+zF2,
q2I=zFf2f22L1f+L12+zF2.
w2=λ|q2|2πq2I=λπzF[(L1+L2L1L2f)2+(z0L2zFf)2].
f=L2L12λ+L1L2λ+z02λ±πλL12w22zF+πλw22zF3L22zF2λ2πw22zF+L12λ+2L1L2λ+L22λ+zF2λ.
E2(x,y,z)E0AB/q1exp[ik2q2(x2+y2)]exp(ikz).
x=zsinθ+cosθ(xcosφ+ysinφ),y=ycosφxsinφ,z=zcosθ+sinθ(xcosφ+ysinφ).
M={4n2rectangular3n(n1)+1hexagonal.
I2incoherent(x,y,z)=i=1M|E2i(x,y,z;θi,φi)|2.
I2coherent(x,y,z)=|i=1ME2i(x,y,z;θi,φi)|2.

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