Abstract

The Linford formula for the intensity output from a medium undergoing amplified spontaneous emission is generalized to the case when the gain coefficient is position dependent. The generalized Linford formula is of particular interest in the field of x-ray lasers, because it provides a better tool for fitting the experimental data to infer the parameters of the medium and affords more insight into the appropriate pumping scheme.

© 2000 Optical Society of America

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  1. G. J. Linford, E. R. Peressini, W. R. Sooy, and M. L. Spaeth, “Very long lasers,” Appl. Opt. 13, 379–390 (1974).
    [CrossRef] [PubMed]
  2. R. Tommasini and J. E. Balmer, “Amplified spontaneous emission and maximum gain–length product revised for general line shapes,” J. Opt. Soc. Am. B 16, 538–545 (1999).
    [CrossRef]
  3. L. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett. 26, 293–295 (1971).
    [CrossRef]
  4. P. V. Nickles, V. N. Shlyaptsev, M. Kalachnikov, M. Schnurer, I. Will, and W. Sandner, “Short pulse x-ray laser 32.6 nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
    [CrossRef]
  5. 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]
  6. P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
    [CrossRef]
  7. J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
    [CrossRef]
  8. J. Dunn, J. Nilsen, A. L. Osterheld, Y. Li, and V. N. Shlyaptsev, “Demonstration of transient gain x-ray lasers near 20 nm for nickellike yttrium, zirconium, niobium, and molybdenum,” Opt. Lett. 24, 101–103 (1999).
    [CrossRef]
  9. 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, 34701 (2000).
    [CrossRef]
  10. J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
    [CrossRef]
  11. S. Insam, R. Tommasini, and E. Fill, “Vuv laser in the Lyman band of molecular hydrogen pumped by fs titanium-sapphire laser pulses,” IEEE J. Sel. Top. Quantum Electron. 5, 1510–1514 (1999).
    [CrossRef]
  12. R. A. London, “Beam optics of exploding foil plasma x-ray lasers,” Phys. Fluids 31, 184–192 (1988).
    [CrossRef]
  13. R. C. Elton, X-Ray Lasers (Academic, San Diego, Calif., 1990).

2000

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, 34701 (2000).
[CrossRef]

1999

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

S. Insam, R. Tommasini, and E. Fill, “Vuv laser in the Lyman band of molecular hydrogen pumped by fs titanium-sapphire laser pulses,” IEEE J. Sel. Top. Quantum Electron. 5, 1510–1514 (1999).
[CrossRef]

R. Tommasini and J. E. Balmer, “Amplified spontaneous emission and maximum gain–length product revised for general line shapes,” J. Opt. Soc. Am. B 16, 538–545 (1999).
[CrossRef]

J. Dunn, J. Nilsen, A. L. Osterheld, Y. Li, and V. N. Shlyaptsev, “Demonstration of transient gain x-ray lasers near 20 nm for nickellike yttrium, zirconium, niobium, and molybdenum,” Opt. Lett. 24, 101–103 (1999).
[CrossRef]

1998

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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]

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

1997

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

1988

R. A. London, “Beam optics of exploding foil plasma x-ray lasers,” Phys. Fluids 31, 184–192 (1988).
[CrossRef]

1974

1971

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

Balmer, J. E.

Behjat, A.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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]

Casperson, L.

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

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[CrossRef]

Dunn, J.

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

J. Dunn, J. Nilsen, A. L. Osterheld, Y. Li, and V. N. Shlyaptsev, “Demonstration of transient gain x-ray lasers near 20 nm for nickellike yttrium, zirconium, niobium, and molybdenum,” Opt. Lett. 24, 101–103 (1999).
[CrossRef]

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

Fill, E.

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, 34701 (2000).
[CrossRef]

S. Insam, R. Tommasini, and E. Fill, “Vuv laser in the Lyman band of molecular hydrogen pumped by fs titanium-sapphire laser pulses,” IEEE J. Sel. Top. Quantum Electron. 5, 1510–1514 (1999).
[CrossRef]

Insam, S.

S. Insam, R. Tommasini, and E. Fill, “Vuv laser in the Lyman band of molecular hydrogen pumped by fs titanium-sapphire laser pulses,” IEEE J. Sel. Top. Quantum Electron. 5, 1510–1514 (1999).
[CrossRef]

Kalachnikov, M.

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

Kalachnikov, M. P.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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]

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]

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[CrossRef]

Li, Y.

Li, Y. L.

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

Linford, G. J.

London, R. A.

R. A. London, “Beam optics of exploding foil plasma x-ray lasers,” Phys. Fluids 31, 184–192 (1988).
[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]

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[CrossRef]

Nickles, P. V.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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. Schnurer, I. Will, and W. Sandner, “Short pulse x-ray laser 32.6 nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Nilsen, J.

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

J. Dunn, J. Nilsen, A. L. Osterheld, Y. Li, and V. N. Shlyaptsev, “Demonstration of transient gain x-ray lasers near 20 nm for nickellike yttrium, zirconium, niobium, and molybdenum,” Opt. Lett. 24, 101–103 (1999).
[CrossRef]

Osterheld, A. L.

J. Dunn, J. Nilsen, A. L. Osterheld, Y. Li, and V. N. Shlyaptsev, “Demonstration of transient gain x-ray lasers near 20 nm for nickellike yttrium, zirconium, niobium, and molybdenum,” Opt. Lett. 24, 101–103 (1999).
[CrossRef]

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

Peressini, E. R.

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. Schnurer, I. Will, and W. Sandner, “Short pulse x-ray laser 32.6 nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Schnurer, M.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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. Schnurer, I. Will, and W. Sandner, “Short pulse x-ray laser 32.6 nm based on transient gain in Ne-like titanium,” Phys. Rev. Lett. 78, 2748–2751 (1997).
[CrossRef]

Shepherd, R.

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

Shlyaptsev, V. N.

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

J. Dunn, J. Nilsen, A. L. Osterheld, Y. Li, and V. N. Shlyaptsev, “Demonstration of transient gain x-ray lasers near 20 nm for nickellike yttrium, zirconium, niobium, and molybdenum,” Opt. Lett. 24, 101–103 (1999).
[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]

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

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

Sooy, W. R.

Spaeth, M. L.

Stewart, R. E.

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

Tallents, G. J.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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, “Excitation velocity and group velocity mismatch in amplified spontaneous emission lasers: a discussion on the transient gain x-ray lasers,” Phys. Rev. A 62, 34701 (2000).
[CrossRef]

R. Tommasini and J. E. Balmer, “Amplified spontaneous emission and maximum gain–length product revised for general line shapes,” J. Opt. Soc. Am. B 16, 538–545 (1999).
[CrossRef]

S. Insam, R. Tommasini, and E. Fill, “Vuv laser in the Lyman band of molecular hydrogen pumped by fs titanium-sapphire laser pulses,” IEEE J. Sel. Top. Quantum Electron. 5, 1510–1514 (1999).
[CrossRef]

Warwick, P. J.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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]

White, W. E.

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

Will, I.

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

Wolfrum, E.

P. J. Warwick, C. L. S. Lewis, M. P. Kalachnikov, P. V. Nickles, M. Schnurer, A. Behjat, A. Demir, G. J. Tallents, D. Neely, and E. Wolfrum, “Observation of high transient gain in the germanium x-ray laser at 19.6 nm,” J. Opt. Soc. Am. B 15, 1808–1814 (1998).
[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]

Yariv, A.

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

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]

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

J. Dunn, A. L. Osterheld, Y. L. Li, J. Nilsen, and V. N. Shlyaptsev, “Transient collisional excitation x-ray lasers with 1-ps tabletop drivers,” IEEE J. Sel. Top. Quantum Electron. 5, 1441–1446 (1999).
[CrossRef]

S. Insam, R. Tommasini, and E. Fill, “Vuv laser in the Lyman band of molecular hydrogen pumped by fs titanium-sapphire laser pulses,” IEEE J. Sel. Top. Quantum Electron. 5, 1510–1514 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Fluids

R. A. London, “Beam optics of exploding foil plasma x-ray lasers,” Phys. Fluids 31, 184–192 (1988).
[CrossRef]

Phys. Rev. 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]

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, 34701 (2000).
[CrossRef]

Phys. Rev. Lett.

J. Dunn, A. L. Osterheld, R. Shepherd, W. E. White, V. N. Shlyaptsev, and R. E. Stewart, “Demonstration of x-ray amplification in transient gain nickel-like palladium scheme,” Phys. Rev. Lett. 80, 2825–2828 (1998).
[CrossRef]

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

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

Other

R. C. Elton, X-Ray Lasers (Academic, San Diego, Calif., 1990).

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Figures (3)

Fig. 1
Fig. 1

Effects of a semicircular excitation profile along the line focus on the emitted intensity. The average gain along the whole line focus is held the same for all curves. Excitation of constant intensity, thus reproducing the standard Linford formula (g0=5 cm-1), is represented by the dashed curve. A semicircular excitation profile is shown that produces gain decaying to 0.6 of its peak (ge=0.6g0) (curve a), 0.3 of its peak (ge=0.3g0) (curve b), and 0.0 of its peak (ge=0.0g0) (curve c) at the edges of the gain column. The average gain is held to be the same for all curves. As expected, the effect is to produce steeper (with respect to standard Linford behavior) growth for lengths of less than L0/2, when the gain coefficient attains its peak, and then to induce saturationlike behavior at greater lengths in the emitted intensity.

Fig. 2
Fig. 2

Effects of a semicircular excitation profile along the line focus on the linewidth of the emitted radiation. The average gain along the whole line focus is held the same for all curves. Excitation of constant intensity (g0=5 cm-1) yields the curve represented by the dashed curve. Linewidths of the emitted radiation generated by a semicircular excitation profile producing gain decaying to 0.6 of its peak (ge=0.6g0) (curve a), 0.3 of its peak (ge=0.3g0) (curve b), and 0.0 of its peak (ge=0.0g0) (curve c) at the edges of the gain column. The average gain is held to be the same for all curves.

Fig. 3
Fig. 3

Fit to the intensity output from the femtosecond-laser-pumped H2 laser emitting at 160-nm,11 including (solid curve) and not including (dashed curve) the semicircular profile of the excitation intensity along the line focus (ge=0.7g0). Fit parameters are g0=5.5 cm-1 and τ0=40 ps (g0=5.3 cm-1 and τ0=40 ps in the dashed-curve case).

Equations (31)

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I(ν, z)z=g(ν, z)I(ν, z)+J(ν, z),
I(ν, L)=0LdzJ(ν, z)expzLdzg(ν, z),
g(ν, z)=g0(z)S(ν)/S0,
I(L)=π-k/2 ΔνstΔνsp×0LdzJ0(z)exp[X(z, L)]3/20LdzJ0(z)[X(z, L)+1]exp[X(z, L)]1/2,
I(L)=π-k/2 J0g0 ΔνstΔνsp [exp(g0L)-1]3/2[g0L exp(g0L)]1/2.
Δνase(L)
=ln(2)k/2Δνst×0LdzJ0(z)exp[X(z, L)]1/20LdzJ0(z)[X(z, L)+1]exp[X(z, L)]1/2.
Δνase(L)=ln(2)k/2Δνstexp(g0L)-1g0L exp(g0L).
g(ν, t)=S(ν)S0 exp-Δtτ0,
vp/c={1+cg[ln(2)/π3]1/2Δν-1}-1,
Δt(z)=z(1/vp-1/vex).
I(L)=dνSsp(ν)F(ν, L),
F(ν, L)0LdzJ0(z)expS(ν)S0X(z, L),
J(ν, z)Ssp(ν)J0(z),
I(L)=Ssp(ν0)dνF(ν, L),
H(ν, L)q(L)exp[-ln(2)(ν-ν0)2/Δνase(L)2],
H(ν0, L)=F(ν0, L),
2ν2H(ν0, L)=2ν2F(ν0, L)+f(L);
limL0Δνase(L)=Δνst.
q(L)=0LdzJ0(z)exp[X(z, L)].
Δνase2(L)=C q(L)Cf(L)+0LdzJ0(z)X(z, L)exp[X(z, L)],
C-2 ln(2)S0d2S(ν0)dν2-1.
f(L)=q(L)/C,
Δνase(L)=C0LdzJ0(z)exp[X(z, L)]1/20LdzJ0(z)[X(z, L)+1]exp[X(z, L)]1/2.
I(L)=Ssp(ν0)πCln(2)×0LdzJ0(z)exp[X(z, L)]3/20LdzJ0(z)[X(z, L)+1]exp[X(z, L)]1/2.
S(ν)=SG(ν)exp[-ln(2)(ν-ν0)2/Δνst2]Δνstπ,
S(ν)=SL(ν)1Δνstπ 1+(ν-ν0)2Δνst2-1,
C=ln(2)kΔνst2,
Δνase(L)=ln(2)k/2Δνst×0LdzJ0(z)exp[X(z, L)]1/20LdzJ0(z)[X(z, L)1+]exp[X(z, L)]1/2,
I(L)=π-k/2 ΔνstΔνsp×0LdzJ0(z)exp[X(z, L)]3/20LdzJ0(z)[X(z, L)-1]exp[X(z, L)]1/2,
Ssp(ν0)=1Δνsp ln(2)1-kπ1+k.

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