Abstract

It is shown that the statistics of the intensity distribution in the output beam of a collisional X-ray laser, analysed in terms of the degree of freedom or equivalently the number of the coherence modes in the beam cross-section, has non-Gaussian character. The non-Gaussian character seems to be caused by the small-scale plasma/medium fluctuations. It was assumed that these overlap the modal structure imposed by the geometry of the medium and considered as equivalent to a large-scale inhomogeneity. Thus, the fluctuations decide about the character of the output beam transverse coherence. It is also shown that the relevant to this model compound statistics of the intensity fluctuations in the output beam is well described by the m-m-distribution, a specific form of the K-distribution. The deviation from the Gaussian statistics was confirmed by the field correlation function at the laser exit plane, retrieved from the experimental data.

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2010 (1)

K. A. Janulewicz and C. M. Kim, “Role of the precursor in a triple-pulse pumping scheme of a nickel-like silver soft-x-ray laser in the grazing-incidence-pumping geometry,” Phys. Rev. E82, 056405 (2010)
[CrossRef]

2008 (1)

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

2006 (3)

G. J. Pert, “Optimizing the performance of nickel-like collisionally pumped x-ray lasers,” Phys. Rev. A73, 033809 (2006)
[CrossRef]

Y. Liu, Y. Wang, M. A. Larotonda, B. M. Luther, J. J. Rocca, and D. T. Attwood, “Spatial coherence measurements of a 13.2 nm transient nickel-like cadmium soft X-ray laser pumped at grazing incidence,” Opt. Express14, 12872–9 (2006)
[CrossRef] [PubMed]

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

2001 (1)

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser bem propagating through turbulent media,” Opt. Eng.40, 1554 (2001)
[CrossRef]

1999 (1)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999)
[CrossRef]

1996 (1)

P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and X-ray laser transverse coherence,” Phys. Rev. A53, R23 (1996)
[CrossRef] [PubMed]

1995 (1)

R. P. Ratowsky and R. A. London, “Propagation of mutual coherence in refratctive x-ray lasers using a WKB method,” Phys. Rev. A51, 2361 (1995)
[CrossRef] [PubMed]

1994 (1)

1993 (1)

P. Amendt, R. London, and M. Strauss, “Optimization of single-stage- x-ray laser coherence,” Phys. Rev. A47, 4348 (1993)
[CrossRef] [PubMed]

1992 (1)

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

1990 (1)

R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett.65, 563 (1990)
[CrossRef] [PubMed]

1989 (2)

G. Hazak and A. Bar-Shalom, “Mode-selecting effects and coherence in hot-plasma x-ray lasers,” Phys. Rev. A40, 7055 (1989)
[CrossRef] [PubMed]

G. J. Pert, “Two-dimensional hydrodynamic models of laser-produced plasmas,” J. Plasma Physics41 (part 2), 263 (1989)
[CrossRef]

1984 (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng.23, 453 (1984)
[CrossRef]

1983 (1)

1982 (3)

V. S. Rao Gudimetla and J. Fred Holmes, “Probability density function of the intensity for a laser-generated speckle field after propagation through the turbulent atmosphere,” J. Opt. Soc. Am.72, 1213 (1982)
[CrossRef]

R. G. Evans, A.J. Bennett, and G.J. Pert, “Rayleigh-Taylor instabilities in laser accelerated targets,” Phys. Rev. Lett.49, 1639 (1982)
[CrossRef]

P. D. Drummond and J. H. Eberly, “Transverse coherence and scaling in four dimensional simulations of superfluorescence,” Phys. Rev. A25, 3446 (1982)
[CrossRef]

1978 (1)

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett.40, 546 (1978)
[CrossRef]

1973 (1)

R. Barakat, “The brightness distribution of the sum of two coherent speckle patterns,” Opt. Commun.8, 14–16 (1973)
[CrossRef]

1971 (1)

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

Al-Habash, M. A.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser bem propagating through turbulent media,” Opt. Eng.40, 1554 (2001)
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999)
[CrossRef]

Amendt, P.

P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and X-ray laser transverse coherence,” Phys. Rev. A53, R23 (1996)
[CrossRef] [PubMed]

P. Amendt, R. London, and M. Strauss, “Optimization of single-stage- x-ray laser coherence,” Phys. Rev. A47, 4348 (1993)
[CrossRef] [PubMed]

Andrews, L. C.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser bem propagating through turbulent media,” Opt. Eng.40, 1554 (2001)
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999)
[CrossRef]

Attwood, D. T.

Barakat, R.

R. Barakat, “The brightness distribution of the sum of two coherent speckle patterns,” Opt. Commun.8, 14–16 (1973)
[CrossRef]

Barbee, T. W.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Bar-Shalom, A.

G. Hazak and A. Bar-Shalom, “Mode-selecting effects and coherence in hot-plasma x-ray lasers,” Phys. Rev. A40, 7055 (1989)
[CrossRef] [PubMed]

Bennett, A.J.

R. G. Evans, A.J. Bennett, and G.J. Pert, “Rayleigh-Taylor instabilities in laser accelerated targets,” Phys. Rev. Lett.49, 1639 (1982)
[CrossRef]

Carter, M. R.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Casperson, L.

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

Cassou, K.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Choi, I. W.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Crosignani, B.

Da Silva, L. B.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Drummond, P. D.

P. D. Drummond and J. H. Eberly, “Transverse coherence and scaling in four dimensional simulations of superfluorescence,” Phys. Rev. A25, 3446 (1982)
[CrossRef]

Eberly, J. H.

P. D. Drummond and J. H. Eberly, “Transverse coherence and scaling in four dimensional simulations of superfluorescence,” Phys. Rev. A25, 3446 (1982)
[CrossRef]

Evans, R. G.

R. G. Evans, A.J. Bennett, and G.J. Pert, “Rayleigh-Taylor instabilities in laser accelerated targets,” Phys. Rev. Lett.49, 1639 (1982)
[CrossRef]

Feit, M. D.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Fred Holmes, J.

Gilbaud, O.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics, chapt.9.1, (A Wiley-Interscience Publication, John Wiley and Sons, Inc., 1985)

J. W. Goodman, “Statistical properties of laser speckle patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed., (Springer Verlag, 2nd. edition, 1984)

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, (Roberts & Company Publishers, Englewood, Colorado2006)

Hafz, N

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Hazak, G.

G. Hazak and A. Bar-Shalom, “Mode-selecting effects and coherence in hot-plasma x-ray lasers,” Phys. Rev. A40, 7055 (1989)
[CrossRef] [PubMed]

Hong, K.-H.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999)
[CrossRef]

Jakeman, E.

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng.23, 453 (1984)
[CrossRef]

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett.40, 546 (1978)
[CrossRef]

Jamelot, G.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Janulewicz, K. A.

K. A. Janulewicz and C. M. Kim, “Role of the precursor in a triple-pulse pumping scheme of a nickel-like silver soft-x-ray laser in the grazing-incidence-pumping geometry,” Phys. Rev. E82, 056405 (2010)
[CrossRef]

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Jeong, T. M.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Joyeux, D.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Kang, H. C.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Kazamias, S.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Kim, C. M.

K. A. Janulewicz and C. M. Kim, “Role of the precursor in a triple-pulse pumping scheme of a nickel-like silver soft-x-ray laser in the grazing-incidence-pumping geometry,” Phys. Rev. E82, 056405 (2010)
[CrossRef]

Kim, C.-M

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Kim, H. T.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Klisnick, A.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Ko, D.-K.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Koch, J. A.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Larotonda, M. A.

Lee, J.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Lee, S. G.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Liu, Y.

London, R.

P. Amendt, R. London, and M. Strauss, “Optimization of single-stage- x-ray laser coherence,” Phys. Rev. A47, 4348 (1993)
[CrossRef] [PubMed]

London, R. A.

P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and X-ray laser transverse coherence,” Phys. Rev. A53, R23 (1996)
[CrossRef] [PubMed]

R. P. Ratowsky and R. A. London, “Propagation of mutual coherence in refratctive x-ray lasers using a WKB method,” Phys. Rev. A51, 2361 (1995)
[CrossRef] [PubMed]

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett.65, 563 (1990)
[CrossRef] [PubMed]

Luther, B. M.

MacGowan, B. J.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995)

Matthews, D. L.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Mrowka, S.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Nakagami, M.

M. Nakagami, “The m-distribution - a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, 1960), p.6–36

Nickles, P. V.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Noh, Y.-C.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Nugent, K. A.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Pert, G. J.

G. J. Pert, “Optimizing the performance of nickel-like collisionally pumped x-ray lasers,” Phys. Rev. A73, 033809 (2006)
[CrossRef]

G. J. Pert, “Output characteristics of amplified-stimulated-emission lasers,” J. Opt. Soc. Am. B11, 1425 (1994)
[CrossRef]

G. J. Pert, “Two-dimensional hydrodynamic models of laser-produced plasmas,” J. Plasma Physics41 (part 2), 263 (1989)
[CrossRef]

Pert, G.J.

R. G. Evans, A.J. Bennett, and G.J. Pert, “Rayleigh-Taylor instabilities in laser accelerated targets,” Phys. Rev. Lett.49, 1639 (1982)
[CrossRef]

Phalippou, D.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Phillips, R. L.

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser bem propagating through turbulent media,” Opt. Eng.40, 1554 (2001)
[CrossRef]

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999)
[CrossRef]

Pusey, P. N.

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett.40, 546 (1978)
[CrossRef]

Rao Gudimetla, V. S.

Ratowsky, R. P.

R. P. Ratowsky and R. A. London, “Propagation of mutual coherence in refratctive x-ray lasers using a WKB method,” Phys. Rev. A51, 2361 (1995)
[CrossRef] [PubMed]

Rocca, J. J.

Ros, D.

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

Rosen, M. D.

R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett.65, 563 (1990)
[CrossRef] [PubMed]

Sandner, W.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Stone, G. F.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Strauss, M.

P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and X-ray laser transverse coherence,” Phys. Rev. A53, R23 (1996)
[CrossRef] [PubMed]

P. Amendt, R. London, and M. Strauss, “Optimization of single-stage- x-ray laser coherence,” Phys. Rev. A47, 4348 (1993)
[CrossRef] [PubMed]

R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett.65, 563 (1990)
[CrossRef] [PubMed]

Sung, J. H.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Trebes, J. E.

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Tümmler, J.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Wang, Y.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995)

Yariv, A.

B. Crosignani and A. Yariv, “Statistical properties of modal noise in fiber-laser systems,” J. Opt. Soc. Am.73, 1022 (1983)
[CrossRef]

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

Yu, T. J.

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

Europhys. Lett. (1)

O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006)
[CrossRef]

J. Opt. Soc. Am (1)

L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999)
[CrossRef]

J. Opt. Soc. Am B (1)

H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008)
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (1)

J. Plasma Physics (1)

G. J. Pert, “Two-dimensional hydrodynamic models of laser-produced plasmas,” J. Plasma Physics41 (part 2), 263 (1989)
[CrossRef]

Opt. Commun. (1)

R. Barakat, “The brightness distribution of the sum of two coherent speckle patterns,” Opt. Commun.8, 14–16 (1973)
[CrossRef]

Opt. Eng. (2)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng.23, 453 (1984)
[CrossRef]

M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser bem propagating through turbulent media,” Opt. Eng.40, 1554 (2001)
[CrossRef]

Opt. Express (1)

Phys. Rev. A (6)

P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and X-ray laser transverse coherence,” Phys. Rev. A53, R23 (1996)
[CrossRef] [PubMed]

G. J. Pert, “Optimizing the performance of nickel-like collisionally pumped x-ray lasers,” Phys. Rev. A73, 033809 (2006)
[CrossRef]

P. D. Drummond and J. H. Eberly, “Transverse coherence and scaling in four dimensional simulations of superfluorescence,” Phys. Rev. A25, 3446 (1982)
[CrossRef]

G. Hazak and A. Bar-Shalom, “Mode-selecting effects and coherence in hot-plasma x-ray lasers,” Phys. Rev. A40, 7055 (1989)
[CrossRef] [PubMed]

P. Amendt, R. London, and M. Strauss, “Optimization of single-stage- x-ray laser coherence,” Phys. Rev. A47, 4348 (1993)
[CrossRef] [PubMed]

R. P. Ratowsky and R. A. London, “Propagation of mutual coherence in refratctive x-ray lasers using a WKB method,” Phys. Rev. A51, 2361 (1995)
[CrossRef] [PubMed]

Phys. Rev. E (1)

K. A. Janulewicz and C. M. Kim, “Role of the precursor in a triple-pulse pumping scheme of a nickel-like silver soft-x-ray laser in the grazing-incidence-pumping geometry,” Phys. Rev. E82, 056405 (2010)
[CrossRef]

Phys. Rev. Lett. (5)

E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett.40, 546 (1978)
[CrossRef]

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

R. G. Evans, A.J. Bennett, and G.J. Pert, “Rayleigh-Taylor instabilities in laser accelerated targets,” Phys. Rev. Lett.49, 1639 (1982)
[CrossRef]

R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett.65, 563 (1990)
[CrossRef] [PubMed]

J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992)
[CrossRef] [PubMed]

Other (5)

J. W. Goodman, Statistical Optics, chapt.9.1, (A Wiley-Interscience Publication, John Wiley and Sons, Inc., 1985)

J. W. Goodman, “Statistical properties of laser speckle patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed., (Springer Verlag, 2nd. edition, 1984)

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, (Roberts & Company Publishers, Englewood, Colorado2006)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995)

M. Nakagami, “The m-distribution - a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, 1960), p.6–36

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Figures (3)

Fig. 1
Fig. 1

a) The far-field image of an X-ray laser shot in a double-pulse GRIP geometry and b) the corresponding probability density distribution. The speckle image corresponds to the analysis area.

Fig. 2
Fig. 2

a) The contour plot of the 2D correlation function (CFf ) of the field at the laser exit reconstructed by the Fourier transform of the intensity autocorrelation function in the far-field (speckle pattern); the saturation in the central part of the image is introduced deliberately to show details of the low-level part of CFf at a very high dynamics of the figure; b) cross-sections of the reconstructed correlation function along x and y axes.

Fig. 3
Fig. 3

Fit of the histogram presented in Fig. 1(b) applying K-distribution in its specific form (m-m distribution) given by Eq. (3). M1=3.2, M2=62. The dashed-line-curve is an m distribution with M=3.23.

Equations (3)

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

p M ( E / E ¯ ) = M M ( E / E ¯ ) M 1 exp ( M E / E ¯ ) / [ Γ ( M ) E ¯ ]
p M M ( E / E ¯ ) = 2 ( M 1 M 2 ) ( M 1 + M 2 ) / 2 E Γ ( M 1 ) Γ ( M 2 ) ( E E ) ( M 1 + M 2 2 ) / 2 × K | M 2 M 1 | ( 2 M 1 M 2 E E )
σ E E = Γ ( M 1 ) Γ ( 2 + M 1 ) Γ ( M 2 ) Γ ( 2 + M 2 ) Γ 2 ( 1 + M 1 ) Γ 2 ( 1 + M 2 ) 1

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