Abstract

Efficient amplification of coherent short-wavelength pulses along a plasma gain column requires traveling-wave excitation with the sweep velocity matched to the signal group velocity. Through simulations incorporating the gain dynamics of the system, we show that the group velocity is not constant but increases monotonically along the line focus due to strong saturation. We demonstrate a line-focusing configuration that results in traveling wave excitation with the sweep velocity well matched to the spatially varying group velocity. Moreover, we show through numerical simulations that the improved velocity matching yields a significant improvement in signal amplification.

© 2014 Optical Society of America

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  1. D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
    [CrossRef]
  2. B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
    [CrossRef]
  3. J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
    [CrossRef]
  4. P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
    [CrossRef]
  5. R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
    [CrossRef]
  6. S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
    [CrossRef]
  7. J. Nilsen, “Analysis of a picosecond-laser-driven Ne-like Ti x-ray laser,” Phys. Rev. A 55, 3271–3274 (1997).
    [CrossRef]
  8. B. A. Reagan, K. A. Wernsing, A. H. Curtis, F. J. Furch, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “Demonstration of a 100  Hz repetition rate gain-saturated diode-pumped table-top soft x-ray laser,” Opt. Lett. 37, 3624–3626 (2012).
    [CrossRef]
  9. M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
    [CrossRef]
  10. R. Tommasini and E. Fill, “Excitation-velocity and group-velocity mismatch in amplified spontaneous emission lasers: a discussion on the transient gain x-ray lasers,” Phys. Rev. A 62, 034701 (2000).
    [CrossRef]
  11. R. Tommasini and E. Fill, “Effective traveling-wave excitation below the speed of light,” Opt. Lett. 26, 689–691 (2001).
    [CrossRef]
  12. I. N. Ross and E. M. Hodgson, “Some optical designs for the generation of high quality line foci,” J. Phys. E 18, 169–173 (1985).
    [CrossRef]
  13. L. W. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett. 26, 293–295 (1971).
    [CrossRef]
  14. J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
    [CrossRef]
  15. G. J. Pert, “Collisional-cross-relaxation effects in amplified-spontaneous-emission lasers,” Phys. Rev. A 50, 4412–4414 (1994).
    [CrossRef]
  16. F. Strati and G. J. Tallents, “Analytical modeling of group-velocity effects in saturated soft-x-ray lasers pumped with a picosecond traveling-wave excitation,” Phys. Rev. A 64, 013807 (2001).
    [CrossRef]
  17. G. J. Pert, “Output characteristics of amplified-stimulated-emission lasers,” J. Opt. Soc. Am. B 11, 1425–1435 (1994).
    [CrossRef]
  18. J. C. Chanteloup, E. Salmon, C. Sauteret, A. Migus, Ph. Zeitoun, A. Klisnick, M. Carillon, S. Hubert, D. Ros, P. Nickles, and M. Kalachnikov, “Pulse-front control of 15-TW pulses with a tilted compressor, and application to the subpicosecond traveling-wave pumping of a soft-x-ray laser,” J. Opt. Soc. Am. B 17, 151–157 (2000).
    [CrossRef]

2012 (1)

2005 (1)

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

2001 (2)

R. Tommasini and E. Fill, “Effective traveling-wave excitation below the speed of light,” Opt. Lett. 26, 689–691 (2001).
[CrossRef]

F. Strati and G. J. Tallents, “Analytical modeling of group-velocity effects in saturated soft-x-ray lasers pumped with a picosecond traveling-wave excitation,” Phys. Rev. A 64, 013807 (2001).
[CrossRef]

2000 (2)

1998 (1)

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

1997 (2)

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

J. Nilsen, “Analysis of a picosecond-laser-driven Ne-like Ti x-ray laser,” Phys. Rev. A 55, 3271–3274 (1997).
[CrossRef]

1996 (1)

S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
[CrossRef]

1994 (2)

G. J. Pert, “Output characteristics of amplified-stimulated-emission lasers,” J. Opt. Soc. Am. B 11, 1425–1435 (1994).
[CrossRef]

G. J. Pert, “Collisional-cross-relaxation effects in amplified-spontaneous-emission lasers,” Phys. Rev. A 50, 4412–4414 (1994).
[CrossRef]

1993 (1)

J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
[CrossRef]

1992 (1)

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

1987 (1)

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

1985 (2)

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

I. N. Ross and E. M. Hodgson, “Some optical designs for the generation of high quality line foci,” J. Phys. E 18, 169–173 (1985).
[CrossRef]

1971 (1)

L. W. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett. 26, 293–295 (1971).
[CrossRef]

Batson, P. J.

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

Behjat, A.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Carillon, M.

Casperson, L. W.

L. W. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett. 26, 293–295 (1971).
[CrossRef]

Ceglio, N. M.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Chanteloup, J. C.

Curtis, A. H.

Da Silva, L. B.

J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
[CrossRef]

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

Danson, C.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Demir, A.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Dunn, J.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

Eckart, M. J.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Fill, E.

R. Tommasini and E. Fill, “Effective traveling-wave excitation below the speed of light,” Opt. Lett. 26, 689–691 (2001).
[CrossRef]

R. Tommasini and E. Fill, “Excitation-velocity and group-velocity mismatch in amplified spontaneous emission lasers: a discussion on the transient gain x-ray lasers,” Phys. Rev. A 62, 034701 (2000).
[CrossRef]

Furch, F. J.

Hagelstein, P. L.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Hazi, A. U.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Healy, S. B.

S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
[CrossRef]

Hodgson, E. M.

I. N. Ross and E. M. Hodgson, “Some optical designs for the generation of high quality line foci,” J. Phys. E 18, 169–173 (1985).
[CrossRef]

Hubert, S.

Janulewicz, K. A.

S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
[CrossRef]

Kalachnikov, M.

Kalachnikov, M. P.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Keane, C. J.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

Keenan, R.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

Klisnick, A.

Koch, J. A.

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

Lewis, C. L. S.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

London, R. A.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

Luther, B. M.

MacGowan, A. J.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

MacGowan, B. J.

J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
[CrossRef]

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

Matthews, D. L.

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Maxon, S.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

Medecki, H.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Menoni, C. S.

Migus, A.

Moreno, J. C.

J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
[CrossRef]

Mrowka, S.

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

Neely, D.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Nickles, P.

Nickles, P. V.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Nilsen, J.

J. Nilsen, “Analysis of a picosecond-laser-driven Ne-like Ti x-ray laser,” Phys. Rev. A 55, 3271–3274 (1997).
[CrossRef]

J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
[CrossRef]

Patel, D.

Patel, P. K.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

Pert, G. J.

S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
[CrossRef]

G. J. Pert, “Collisional-cross-relaxation effects in amplified-spontaneous-emission lasers,” Phys. Rev. A 50, 4412–4414 (1994).
[CrossRef]

G. J. Pert, “Output characteristics of amplified-stimulated-emission lasers,” J. Opt. Soc. Am. B 11, 1425–1435 (1994).
[CrossRef]

Plowes, J. A.

S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
[CrossRef]

Price, D. F.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

Reagan, B. A.

Rocca, J. J.

Ros, D.

Rosen, M. D.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Ross, I. N.

I. N. Ross and E. M. Hodgson, “Some optical designs for the generation of high quality line foci,” J. Phys. E 18, 169–173 (1985).
[CrossRef]

Salmon, E.

Sandner, W.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Sauteret, C.

Schnrer, M.

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Schnurer, M.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Scofield, J. H.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

Shlyaptsev, V. N.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Smith, R. F.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

Strati, F.

F. Strati and G. J. Tallents, “Analytical modeling of group-velocity effects in saturated soft-x-ray lasers pumped with a picosecond traveling-wave excitation,” Phys. Rev. A 64, 013807 (2001).
[CrossRef]

Tallents, G. J.

F. Strati and G. J. Tallents, “Analytical modeling of group-velocity effects in saturated soft-x-ray lasers pumped with a picosecond traveling-wave excitation,” Phys. Rev. A 64, 013807 (2001).
[CrossRef]

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Tommasini, R.

R. Tommasini and E. Fill, “Effective traveling-wave excitation below the speed of light,” Opt. Lett. 26, 689–691 (2001).
[CrossRef]

R. Tommasini and E. Fill, “Excitation-velocity and group-velocity mismatch in amplified spontaneous emission lasers: a discussion on the transient gain x-ray lasers,” Phys. Rev. A 62, 034701 (2000).
[CrossRef]

Trebes, J. E.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Underwood, J. H.

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

Warwick, P. J.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Wernsing, K. A.

Whelan, D. A.

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

Whitten, B. L.

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

Will, I.

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Wolfrum, E.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

Yariv, A.

L. W. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett. 26, 293–295 (1971).
[CrossRef]

Zeitoun, Ph.

Zhang, J.

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. E (1)

I. N. Ross and E. M. Hodgson, “Some optical designs for the generation of high quality line foci,” J. Phys. E 18, 169–173 (1985).
[CrossRef]

Opt. Commun. (1)

S. B. Healy, K. A. Janulewicz, J. A. Plowes, and G. J. Pert, “Transient high gains at 196 produced by picosecond heating of a preformed germanium plasma,” Opt. Commun. 132, 442–448(1996).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (6)

G. J. Pert, “Collisional-cross-relaxation effects in amplified-spontaneous-emission lasers,” Phys. Rev. A 50, 4412–4414 (1994).
[CrossRef]

F. Strati and G. J. Tallents, “Analytical modeling of group-velocity effects in saturated soft-x-ray lasers pumped with a picosecond traveling-wave excitation,” Phys. Rev. A 64, 013807 (2001).
[CrossRef]

M. P. Kalachnikov, P. V. Nickles, M. Schnurer, W. Sandner, V. N. Shlyaptsev, C. Danson, D. Neely, E. Wolfrum, J. Zhang, A. Behjat, A. Demir, G. J. Tallents, P. J. Warwick, and C. L. S. Lewis, “Saturated operation of a transient collisional x-ray laser,” Phys. Rev. A 57, 4778–4783 (1998).
[CrossRef]

R. Tommasini and E. Fill, “Excitation-velocity and group-velocity mismatch in amplified spontaneous emission lasers: a discussion on the transient gain x-ray lasers,” Phys. Rev. A 62, 034701 (2000).
[CrossRef]

J. Nilsen, “Analysis of a picosecond-laser-driven Ne-like Ti x-ray laser,” Phys. Rev. A 55, 3271–3274 (1997).
[CrossRef]

J. Nilsen, B. J. MacGowan, L. B. Da Silva, and J. C. Moreno, “Prepulse technique for producing low-Z Ne-like x-ray lasers,” Phys. Rev. A 48, 4682–4685 (1993).
[CrossRef]

Phys. Rev. Lett. (6)

P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnrer, I. Will, and W. Sandner, “Short pulse X-ray laser at 32.6  nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V. N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9  nm,” Phys. Rev. Lett. 94, 103901 (2005).
[CrossRef]

D. L. Matthews, P. L. Hagelstein, M. D. Rosen, M. J. Eckart, N. M. Ceglio, A. U. Hazi, H. Medecki, J. E. Trebes, B. L. Whitten, and A. J. MacGowan, “Demonstration of a soft x-ray amplifier,” Phys. Rev. Lett. 54, 110–113 (1985).
[CrossRef]

B. J. MacGowan, S. Maxon, P. L. Hagelstein, C. J. Keane, R. A. London, D. L. Matthews, M. D. Rosen, J. H. Scofield, and D. A. Whelan, “Demonstration of soft x-ray amplification in nickel-like ions,” Phys. Rev. Lett. 59, 2157–2160 (1987).
[CrossRef]

L. W. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett. 26, 293–295 (1971).
[CrossRef]

J. A. Koch, B. J. MacGowan, L. B. Da Silva, D. L. Matthews, J. H. Underwood, P. J. Batson, and S. Mrowka, “Observation of gain-narrowing and saturation behavior in Se x-ray laser line profiles,” Phys. Rev. Lett. 68, 3291–3294 (1992).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

ASE pulse propagation velocity, vg, as a function of distance along line focus for saturating gain having a small-signal value of 100cm1.

Fig. 2.
Fig. 2.

(a) OPL obtained from both analytic solution and ray-tracing. (b) Monotonic increase of traveling-wave velocity.

Fig. 3.
Fig. 3.

(a) vTW(x) variation with respect to variation of the initial pulse-front tilt (tanγ). (b) vTW(x) slope variation caused by variation of astigmatic distance q.

Fig. 4.
Fig. 4.

Evolution of group velocities (vg) with respect to different slopes of TWE velocity.

Fig. 5.
Fig. 5.

Amplification characteristics subject to mismatch delay-induced g0 reduction and saturation effect.

Fig. 6.
Fig. 6.

Schematic of the conventional “Ross” focusing system for an incidence angle θ0.

Fig. 7.
Fig. 7.

Analytic and measured results of OPL(x) for the “Ross” focusing scheme. Experimentally measured OPLs are marked as squares.

Fig. 8.
Fig. 8.

Numerical simulation of vg with decreasing traveling-wave velocity. (a) Negative slope of vTW(x) and the results of vg(x). (b) Signal amplification and gain variations.

Fig. 9.
Fig. 9.

“Ross” focusing scheme modified by adding one convex cylindrical mirror. (a) Distribution of laser fluence on the 8 mm (FWHM) line focus. (b) Distribution of integrated energy over a width of 40 μm. (c) Modified “Ross” focusing scheme with slope of vTW reversed to become positive.

Fig. 10.
Fig. 10.

Numerical simulation of the modified “Ross” focusing scheme, showing reduced velocity mismatch and enhanced efficiency on ASE amplification.

Fig. 11.
Fig. 11.

Line focus induced by combination of a (positive) spherical and a (negative) cylindrical lens. (a) Side view of the lens group, showing a high-quality line focus located at the sagittal focus denoted by Fs. (b) Top view of lens group revealing a tangential focus located at Ft. (c) Schematic drawing supporting the analytic formula of vTW(x) along the line focus, where O denotes the origin of the coordinate of the line focus and P is the position on the line focus at which the arbitrary ray ξ converges, thus setting the displacement of OP equal to x.

Equations (17)

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vgc=11+cg(0)ln2/(π3/2ΔνD),
vgc=11+cG(0)/(2πΔνh),
zI(ν,z)=G(ν,z)I(ν,z)+E(ν,z)=G(ν,z)[I(ν,z)+I0f(0)],
G(ν,z)=g(0,z)1+I¯(z)/Isφ(ν)
ift(z)mis0,g(0,z)=g0(0,z)exp[t(z)misτ],withI¯(z)=I(ν)φ(ν)dν,1vg(z)=1c+G(0,z)2πΔνh,t(z)mis=0z[1/vg(z)1/ve(z)]dz.
vTW(x)=c/[ftq2tanγ(q2+x2)3/2xq2+x2],
t=Rsinβ0sinθ0,h=Rsinβ0sinρ0=Rsinβ0sin(θ02β0).
OPL(α)=TW(α)+LQ¯(α)+QP¯(α),
dOPL(α)dαdαdx=cvTW(x).
TW(α)=tanαtanγf.
LQ¯(α)=hcosρ+R2h2+h2cos2ρ,ρ=θ02β0α.
LQ¯(α)=Rsin(β+ρ)sin(2β+ρ),β=β(α).
Rsin(ρ(α)+2β(α))=txsinβ(α).
1ft=1f1+1f2df1f2,
q=ft+H22H2¯f2=ftf2f1.
MN¯=sinθfttanγ,SP¯=ftq2+x2,sinθ=xq2+x2,dOPL(x)dx=d(MN¯+SP¯)dx=cvTW(x),
vTW(x)=c/[ftq2tanγ(q2+x2)3/2xq2+x2].

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