Abstract

A high-aspect-ratio line focus is required on a plane target in x-ray laser experiments for obtaining a high gain-length product. Inherent wave-front aberrations in line-focusing optics, which consist of a cylindrical lens and a spherical lens, are discussed with respect to beam diameter. The nonuniformity of the linewidth that is due to the aberrations is also calculated by the ABCD matrix method. A deformable mirror of a continuous plate type with a diameter of 185 mm provides an adequate wave-front distribution for compensating for the wave-front aberration. The wave-front control by the deformable mirror realizes a fine linewidth of 25 µm and 18.2 mm long, corresponding to the aspect ratio of 728. The linewidth is three times the diffraction limit. The intensity distribution along the line focus is also improved.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).
  2. I. N. Ross, J. Boon, R. Corbett, A. Damerell, P. Gottfeldt, C. Hooker, M. H. Key, G. Kiehn, C. Lewis, O. Willi, “Design and performance of a new line focus geometry for x-ray laser experiments,” Appl. Opt. 26, 1584–1588 (1987).
    [CrossRef] [PubMed]
  3. D. M. Villeneuve, G. D. Enright, H. A. Baldis, “Novel laser line focus geometry applied to x-ray lasers,” Opt. Commun. 81, 54–58 (1991).
    [CrossRef]
  4. W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.
  5. R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, 1991), Chap. 6.5, pp. 194–204.
  6. J. W. Hardy, J. E. Lefebvre, C. L. Koliopoulos, “Real-time atmospheric compensation,” J. Opt. Soc. Am. 67, 360–369 (1977).
    [CrossRef]
  7. R. P. Grosso, M. Yellin, “The membrane mirror as an adaptive optical element,” J. Opt. Soc. Am. 67, 399–406 (1977).
    [CrossRef]
  8. N. C. Mehta, C. W. Allen, “Remote alignment of segmented mirrors with far-field optimization,” Appl. Opt. 31, 6510–6518 (1985).
    [CrossRef]
  9. J. D. Downie, J. W. Goodman, “Optimal wavefront control for adaptive segmented mirrors,” Appl. Opt. 28, 5326–5332 (1989).
    [CrossRef] [PubMed]
  10. M. A. Ealey, J. F. Washeda, “Continuous facesheet low voltage deformable mirrors,” Opt. Eng. 29, 1191–1198 (1990).
    [CrossRef]
  11. J. H. Everson, R. E. Aldrich, N. P. Albertinetti, “Discrete deformable mirror,” Opt. Eng. 20, 316–319 (1981).
    [CrossRef]
  12. M. V. Klein, Optics (Wiley, New York, 1970), Chap. 3, pp. 84–105.
  13. M. A. Ealey, P. A. Davis, “Standard SELECT electrostrictive lead magnesium niobate actuators for active and adaptive optical components,” Opt. Eng. 29, 1373–1382 (1990).
    [CrossRef]
  14. A. Menikoff, “Actuator influence functions of active mirrors,” Appl. Opt. 30, 833–838 (1991).
    [CrossRef] [PubMed]
  15. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 9, pp. 464–466.
  16. R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
    [CrossRef] [PubMed]
  17. C. Yamanaka, “Inertial confinement fusion research at ILE Osaka,” Nucl. Fusion 25, 1343–1349 (1985).
    [CrossRef]

1994

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

1991

A. Menikoff, “Actuator influence functions of active mirrors,” Appl. Opt. 30, 833–838 (1991).
[CrossRef] [PubMed]

D. M. Villeneuve, G. D. Enright, H. A. Baldis, “Novel laser line focus geometry applied to x-ray lasers,” Opt. Commun. 81, 54–58 (1991).
[CrossRef]

1990

M. A. Ealey, J. F. Washeda, “Continuous facesheet low voltage deformable mirrors,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

M. A. Ealey, P. A. Davis, “Standard SELECT electrostrictive lead magnesium niobate actuators for active and adaptive optical components,” Opt. Eng. 29, 1373–1382 (1990).
[CrossRef]

1989

1987

1985

N. C. Mehta, C. W. Allen, “Remote alignment of segmented mirrors with far-field optimization,” Appl. Opt. 31, 6510–6518 (1985).
[CrossRef]

C. Yamanaka, “Inertial confinement fusion research at ILE Osaka,” Nucl. Fusion 25, 1343–1349 (1985).
[CrossRef]

1981

J. H. Everson, R. E. Aldrich, N. P. Albertinetti, “Discrete deformable mirror,” Opt. Eng. 20, 316–319 (1981).
[CrossRef]

1977

Albertinetti, N. P.

J. H. Everson, R. E. Aldrich, N. P. Albertinetti, “Discrete deformable mirror,” Opt. Eng. 20, 316–319 (1981).
[CrossRef]

Aldrich, R. E.

J. H. Everson, R. E. Aldrich, N. P. Albertinetti, “Discrete deformable mirror,” Opt. Eng. 20, 316–319 (1981).
[CrossRef]

Allen, C. W.

Baldis, H. A.

D. M. Villeneuve, G. D. Enright, H. A. Baldis, “Novel laser line focus geometry applied to x-ray lasers,” Opt. Commun. 81, 54–58 (1991).
[CrossRef]

Bann, R.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

Boon, J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 9, pp. 464–466.

Chen, B.

W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.

Chen, W.

W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.

Corbett, R.

Daido, H.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Damerell, A.

Danson, C.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

Davis, P. A.

M. A. Ealey, P. A. Davis, “Standard SELECT electrostrictive lead magnesium niobate actuators for active and adaptive optical components,” Opt. Eng. 29, 1373–1382 (1990).
[CrossRef]

Downie, J. D.

Ealey, M. A.

M. A. Ealey, J. F. Washeda, “Continuous facesheet low voltage deformable mirrors,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

M. A. Ealey, P. A. Davis, “Standard SELECT electrostrictive lead magnesium niobate actuators for active and adaptive optical components,” Opt. Eng. 29, 1373–1382 (1990).
[CrossRef]

Enright, G. D.

D. M. Villeneuve, G. D. Enright, H. A. Baldis, “Novel laser line focus geometry applied to x-ray lasers,” Opt. Commun. 81, 54–58 (1991).
[CrossRef]

Everson, J. H.

J. H. Everson, R. E. Aldrich, N. P. Albertinetti, “Discrete deformable mirror,” Opt. Eng. 20, 316–319 (1981).
[CrossRef]

Exley, J.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

Goodman, J. W.

Gottfeldt, P.

Grosso, R. P.

Hardy, J. W.

Hooker, C.

Kato, Y.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Key, M. H.

Kiehn, G.

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 3, pp. 84–105.

Kodama, R.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Koliopoulos, C. L.

Lefebvre, J. E.

Lewis, C.

Lewis, C. L. S.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

MacPhee, A.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Mao, C.

W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.

Mehta, N. C.

Menikoff, A.

Murai, K.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Neely, D.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Pepler, D.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

Ross, I.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

Ross, I. N.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, 1991), Chap. 6.5, pp. 194–204.

Villeneuve, D. M.

D. M. Villeneuve, G. D. Enright, H. A. Baldis, “Novel laser line focus geometry applied to x-ray lasers,” Opt. Commun. 81, 54–58 (1991).
[CrossRef]

Wang, S.

W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.

Washeda, J. F.

M. A. Ealey, J. F. Washeda, “Continuous facesheet low voltage deformable mirrors,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

Watson, I.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

Willi, O.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 9, pp. 464–466.

Xu, A.

W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.

Yamanaka, C.

C. Yamanaka, “Inertial confinement fusion research at ILE Osaka,” Nucl. Fusion 25, 1343–1349 (1985).
[CrossRef]

Yellin, M.

Yuan, G.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Appl. Opt.

J. Opt. Soc. Am.

Nucl. Fusion

C. Yamanaka, “Inertial confinement fusion research at ILE Osaka,” Nucl. Fusion 25, 1343–1349 (1985).
[CrossRef]

Opt. Commun.

D. M. Villeneuve, G. D. Enright, H. A. Baldis, “Novel laser line focus geometry applied to x-ray lasers,” Opt. Commun. 81, 54–58 (1991).
[CrossRef]

Opt. Eng.

M. A. Ealey, J. F. Washeda, “Continuous facesheet low voltage deformable mirrors,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

J. H. Everson, R. E. Aldrich, N. P. Albertinetti, “Discrete deformable mirror,” Opt. Eng. 20, 316–319 (1981).
[CrossRef]

M. A. Ealey, P. A. Davis, “Standard SELECT electrostrictive lead magnesium niobate actuators for active and adaptive optical components,” Opt. Eng. 29, 1373–1382 (1990).
[CrossRef]

Phys. Rev. Lett.

R. Kodama, D. Neely, Y. Kato, H. Daido, K. Murai, G. Yuan, A. MacPhee, C. L. S. Lewis, “Generation of small-divergence soft x-ray laser by plasma waveguiding with a curved target,” Phys. Rev. Lett. 73, 3215–3218 (1994).
[CrossRef] [PubMed]

Other

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), Chap. 9, pp. 464–466.

C. Danson, R. Bann, J. Exley, D. Pepler, I. Ross, I. Watson, “The generation of line foci using random phase plates,” in X-Ray Lasers, Inst. Phys. Conf. Series116, 81–84 (1990).

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 3, pp. 84–105.

W. Chen, S. Wang, C. Mao, B. Chen, A. Xu, “Cylinder lens array line focus system for x-ray laser experiments,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper CWF42.

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, 1991), Chap. 6.5, pp. 194–204.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Geometric optics consideration of the inherent wave-front aberration in conventional line-focusing optics: (a) the top-view and side-view images of line-focus geometry, (b) spot diagram at the in foci and out foci and the best focus.

Fig. 2
Fig. 2

Relation between the central width of the line focus and the laser beam diameter by the calculation (solid curve) and the measurement (circles) when both sides of the line focus have the minimum width: The inserted images are the central line-focus pattern 5 mm in length of a 18.2-mm line focus in the case of several beam diameters.

Fig. 3
Fig. 3

Required wave-front compensation of peak-to-valley (P–V) values by a deformable mirror with respect to the beam diameter for generating a uniform line focus.

Fig. 4
Fig. 4

Surface shape of the deformable mirror during each process of the fabrication (λ = 633 nm) and the point-spread function (PSF): (a) surface shape of the polished substrate, (b) surface shape after the adhesion of actuators, (c) surface shape after the best control to obtain a plane surface.

Fig. 5
Fig. 5

Influence function of the deformable mirror by the experiment and the calculation by the finite-element method.

Fig. 6
Fig. 6

Optical setup for improving the line-focus pattern. PMN, lead, magnesium, and niobate.

Fig. 7
Fig. 7

Experimental results of improving the line focus: (a) nonuniform line-focus pattern before wave-front control, (b) uniform-line focus pattern after wave-front control by a deformable mirror.

Fig. 8
Fig. 8

One-dimensional profile scanned across the line focus before (left) and after (right) wave-front control.

Fig. 9
Fig. 9

Controlled wave front for improving the line-focus pattern.

Tables (1)

Tables Icon

Table 1 Lower-Order Zernike Coefficients by the Expansion of the Wave Front by Zernike Circle Polynomials

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Δf=fy-fs=-fs2fcy+fs-l.
dc=Δf1+14Dfs21/2-1.
Wc=fsdcDfs2+Δf+dcfs-lΔf-ldc.
Wpv=2Ry-4Ry2-D21/2,
Fi=A expBri2,

Metrics