Abstract

Optical signals generated by multiple sinusoidal temporal phase modulations (multi-FMs) applied to a monochromatic field are studied from the viewpoint of their optical spectrum and temporal modulations arising from spectral impairments. Statistical analysis based on the central limit theorem shows that the signals’ optical spectrum converges to a normal distribution as the number of modulations increases, allowing one to predict the frequency range containing a given fraction of the total energy with the associated cumulative density function. The conversion of frequency modulation to amplitude modulation is analyzed and simulated for arbitrary multi-FM signals. These developments are of theoretical and practical importance for high-energy laser systems, where optical pulses are phase modulated in the front end to smooth out the on-target beam profile and prevent potentially catastrophic damage to optical components.

© 2014 Optical Society of America

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2013 (1)

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

2012 (1)

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

2011 (2)

2010 (1)

2009 (1)

2008 (2)

S. Hocquet, D. Penninckx, E. Bordenave, C. Gouédard, and Y. Jaouën, “FM-to-AM conversion in high-power lasers,” Appl. Opt. 47, 3338–3349 (2008).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (1)

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Mégajoule (LMJ) project dedicated to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

2004 (1)

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

1989 (2)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

J. R. Murray, J. R. Smith, R. B. Ehrlich, D. T. Kyrazis, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, “Experimental observation and suppression of transverse stimulated Brillouin scattering in large optical components,” J. Opt. Soc. Am. B 6, 2402–2411 (1989).
[CrossRef]

Amendt, P.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
[CrossRef]

Anderson, K. S.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

Auerbach, J. M.

Balonek, G.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Beck, N.

Begishev, I. A.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Berger, R. L.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
[CrossRef]

Betti, R.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Bittle, W.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Bittle, W. A.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

Bordenave, E.

Bourgade, J. L.

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Mégajoule (LMJ) project dedicated to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

Bowers, M. W.

Browning, D. F.

P. J. Wisoff, M. W. Bowers, G. V. Erbert, D. F. Browning, and D. R. Jedlovec, “NIF injection laser system,” in Optical Engineering at the Lawrence Livermore National Laboratory II: The National Ignition Facility, M. A. Lane and C. R. Wuest, eds. (SPIE, 2004), Vol. 5341, pp. 146–155.

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed. (SPIE, 1999), Vol. 3492, pp. 51–61.

Cao, H.

Cavailler, C.

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Mégajoule (LMJ) project dedicated to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

Collett, D.

D. Collett, Modelling Binary Data, 2nd ed. (Chapman & Hall/CRC, 2003).

Collins, T. J. B.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

Consentino, A.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Couch, L. W.

L. W. Couch, Digital and Analog Communication Systems, 8th ed. (Prentice-Hall, 2012).

Craxton, R. S.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Cuffney, R.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Delettrez, J. A.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Di Nicola, J.-M.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

Dixit, S. N.

Dorrer, C.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

Edgell, D. H.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Ehrlich, R. B.

Erbert, G. V.

Fan, D.

Fleurot, N.

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R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
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Glebov, V. Y.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
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J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
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J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
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Gleyze, J.-F.

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T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
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R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
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Gouédard, C.

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J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

Haan, S. W.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
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J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
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Hammel, B. A.

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
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Harding, D. R.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
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R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
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Heestand, G. M.

Henesian, M. A.

Hermann, M. R.

Hill, E.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
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J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Hocquet, S.

Jacobs-Perkins, D. W.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
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Jedlovec, D. R.

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Kauffman, R. L.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
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Kelly, J. H.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Kessler, T.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
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Kessler, T. J.

Kilkenny, J. D.

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

Knauer, J. P.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

Kruschwitz, B. E.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Kyrazis, D. T.

Lacroix, G.

Landen, O. L.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
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Lawrence, G. N.

Letzring, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
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Li, C. K.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Li, L.

Lin, Y.

Lindl, J. D.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
[CrossRef]

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

Lu, X.

Luce, J.

Ma, W.

Manes, K. R.

Marozas, J. A.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Marshall, C. D.

Marshall, F. J.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

McCrory, R. L.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

McKenty, P. W.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Mehta, N. C.

Menapace, J.

Meyerhofer, D. D.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Moore, M.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Moses, E.

Munro, D.

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
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Murray, J. R.

Nostrand, M. C.

Okishev, A. V.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

Orth, C. D.

Patterson, R.

Penninckx, D.

Petrasso, R. D.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Radha, P. B.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Regan, S. P.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Remington, B. A.

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

Roides, R.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

Roides, R. G.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Rothenberg, J. E.

J. E. Rothenberg, “Comparison of beam-smoothing methods for direct-drive inertial confinement fusion,” J. Opt. Soc. Am. B 14, 1664–1671 (1997).
[CrossRef]

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed. (SPIE, 1999), Vol. 3492, pp. 51–61.

Sacks, R. A.

Sangster, T. C.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Séguin, F. H.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Seka, W.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Shaw, M. J.

Short, R. W.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Shvarts, D.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Shvydky, A.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

Skupsky, S.

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Smalyuk, V. A.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Smith, J. R.

Soures, J. M.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

Spaeth, M.

Stoeckl, C.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Suter, L. J.

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
[CrossRef]

Sutton, S. B.

Thompson, C. E.

Van Wonterghem, B. M.

Verdon, C. P.

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

Vidal, S.

Videau, L.

Waxer, L. J.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Weber, S. V.

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

Wegner, P. J.

Weiland, T. L.

White, R. K.

Widmayer, C. C.

Wilcox, R. B.

J. R. Murray, J. R. Smith, R. B. Ehrlich, D. T. Kyrazis, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, “Experimental observation and suppression of transverse stimulated Brillouin scattering in large optical components,” J. Opt. Soc. Am. B 6, 2402–2411 (1989).
[CrossRef]

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed. (SPIE, 1999), Vol. 3492, pp. 51–61.

Williams, W. H.

Wisoff, P. J.

P. J. Wisoff, M. W. Bowers, G. V. Erbert, D. F. Browning, and D. R. Jedlovec, “NIF injection laser system,” in Optical Engineering at the Lawrence Livermore National Laboratory II: The National Ignition Facility, M. A. Lane and C. R. Wuest, eds. (SPIE, 2004), Vol. 5341, pp. 146–155.

Yaakobi, B.

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Yang, S. T.

Yin, X.

Zhu, J.

Zuegel, J. D.

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

Appl. Opt. (5)

Fusion Eng. Des. (1)

N. Fleurot, C. Cavailler, and J. L. Bourgade, “The Laser Mégajoule (LMJ) project dedicated to inertial confinement fusion: development and construction status,” Fusion Eng. Des. 74, 147–154 (2005).
[CrossRef]

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

C. Dorrer, R. Roides, R. Cuffney, A. V. Okishev, W. A. Bittle, G. Balonek, A. Consentino, E. Hill, and J. D. Zuegel, “Fiber front end with multiple phase modulations and high-bandwidth pulse shaping for high-energy laser-beam smoothing,” IEEE J. Sel. Top. Quantum Electron. 19, 3500112 (2013).
[CrossRef]

J. Appl. Phys. (1)

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys. 66, 3456–3462 (1989).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Lett. (2)

Phys. Plasmas (4)

J. D. Kilkenny, S. G. Glendinning, S. W. Haan, B. A. Hammel, J. D. Lindl, D. Munro, B. A. Remington, S. V. Weber, J. P. Knauer, and C. P. Verdon, “A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion,” Phys. Plasmas 1, 1379–1389 (1994).
[CrossRef]

T. J. B. Collins, J. A. Marozas, K. S. Anderson, R. Betti, R. S. Craxton, J. A. Delettrez, V. N. Goncharov, D. R. Harding, F. J. Marshall, R. L. McCrory, D. D. Meyerhofer, P. W. McKenty, P. B. Radha, A. Shvydky, S. Skupsky, and J. D. Zuegel, “A polar-drive-ignition design for the National Ignition Facility,” Phys. Plasmas 19, 056308 (2012).
[CrossRef]

J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on the National Ignition Facility,” Phys. Plasmas 11, 339–491 (2004).
[CrossRef]

R. L. McCrory, D. D. Meyerhofer, R. Betti, R. S. Craxton, J. A. Delettrez, D. H. Edgell, V. Y. Glebov, V. N. Goncharov, D. R. Harding, D. W. Jacobs-Perkins, J. P. Knauer, F. J. Marshall, P. W. McKenty, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, R. W. Short, S. Skupsky, V. A. Smalyuk, J. M. Soures, C. Stoeckl, B. Yaakobi, D. Shvarts, J. A. Frenje, C. K. Li, R. D. Petrasso, and F. H. Séguin, “Progress in direct-drive inertial confinement fusion research,” Phys. Plasmas 15, 055503 (2008).
[CrossRef]

Other (8)

P. J. Wisoff, M. W. Bowers, G. V. Erbert, D. F. Browning, and D. R. Jedlovec, “NIF injection laser system,” in Optical Engineering at the Lawrence Livermore National Laboratory II: The National Ignition Facility, M. A. Lane and C. R. Wuest, eds. (SPIE, 2004), Vol. 5341, pp. 146–155.

J. H. Kelly, A. Shvydky, J. A. Marozas, M. J. Guardalben, B. E. Kruschwitz, L. J. Waxer, C. Dorrer, E. Hill, A. V. Okishev, and J.-M. Di Nicola, “Simulations of the propagation of multiple-FM smoothing by spectral dispersion on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020D.

B. E. Kruschwitz, J. H. Kelly, C. Dorrer, A. V. Okishev, L. J. Waxer, G. Balonek, I. A. Begishev, W. Bittle, A. Consentino, R. Cuffney, E. Hill, J. A. Marozas, M. Moore, R. G. Roides, and J. D. Zuegel, “Commissioning of a multiple-frequency modulation smoothing by spectral dispersion demonstration system on OMEGA EP,” in High Power Lasers for Fusion Research II, A. A. S. Awwal, ed. (SPIE, 2013), Vol. 8602, paper 86020E.

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed. (SPIE, 1999), Vol. 3492, pp. 51–61.

“Multiple-FM smoothing by spectral dispersion—an augmented laser speckle smoothing scheme,” LLE Review Quarterly Report, Laboratory for Laser Energetics, LLE Document No.  (University of Rochester, Rochester, NY, 2008), Vol. 114, pp. 73–80.

L. W. Couch, Digital and Analog Communication Systems, 8th ed. (Prentice-Hall, 2012).

J. W. Goodman, Statistical Optics (Wiley, 2000).

D. Collett, Modelling Binary Data, 2nd ed. (Chapman & Hall/CRC, 2003).

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Figures (12)

Fig. 1.
Fig. 1.

(a) Phase modulations used for simulations with parameters given in Table 1 (f1, f2, and f3 plotted in blue, green, and red, respectively). (b) Optical spectrum resulting from these phase modulations applied to a monochromatic field (black solid line) and Gaussian spectrum with identical rms bandwidth (red-dashed line).

Fig. 2.
Fig. 2.

Cumulative density function of the spectrum shown in Fig. 1(b) (black solid line) and of the Gaussian function with identical rms bandwidth (red-dashed line). The inset is a close-up on the tail of the cumulative density functions at high frequencies, where a horizontal dashed line has been added to show the frequency values at which the two functions reach 0.99.

Fig. 3.
Fig. 3.

Statistics for the ratio ρ of the bandwidths containing 98% of the energy calculated from the spectral density of a multi-FM spectrum and directly calculated from the modulation parameters (frequencies and indices) assuming a normal spectral density. The upper and lower rows correspond to the average value and standard deviation, respectively, determined as a function of the number of modulation frequencies and standard deviation of the modulation index. The statistics are calculated over 1000 random draws of the modulation parameters.

Fig. 4.
Fig. 4.

Temporal power after linear spectral amplitude modulation corresponding to l=0.44/(100GHz).

Fig. 5.
Fig. 5.

(a) PV and rms AM versus magnitude of the linear spectral amplitude modulation. (b) PV AM at the frequencies fj versus magnitude of the linear spectral amplitude modulation. The lines correspond to the simulations and the markers correspond to the analytical derivation.

Fig. 6.
Fig. 6.

Temporal power after quadratic spectral phase corresponding to φ2=1.01ps2.

Fig. 7.
Fig. 7.

(a) PV and rms AM versus magnitude of the quadratic spectral phase modulation. (b) PV AM at the frequencies fj versus magnitude of the quadratic spectral phase modulation. The lines correspond to the simulations and the markers correspond to the analytical derivation.

Fig. 8.
Fig. 8.

(a) PV and rms AM versus magnitude of the linear spectral amplitude for φ2=1.01ps2. (b) PV AM at the frequencies fj versus magnitude of the linear spectral amplitude for φ2=1.01ps2. The lines correspond to the simulations and the markers correspond to the analytical derivation.

Fig. 9.
Fig. 9.

Temporal power after quadratic spectral amplitude modulation corresponding to q=0.44/(100GHz)2.

Fig. 10.
Fig. 10.

(a) PV and rms AM versus magnitude of the quadratic spectral amplitude modulation. (b)–(d) PV AM at the frequencies 2fj, fj+fk, and fjfk versus magnitude of the quadratic spectral amplitude modulation. The lines correspond to the simulations and the markers correspond to the analytical derivation.

Fig. 11.
Fig. 11.

Temporal power after cubic spectral phase modulation corresponding to φ3=4.8ps3.

Fig. 12.
Fig. 12.

(a) PV and rms AM versus magnitude of the cubic spectral phase modulation. The lower and higher bounds for the PV AM are shown with black and gray markers, respectively. (b)–(d) PV AM at the frequencies 2fj, fj+fk, and fjfk versus magnitude of the cubic spectral phase modulation. The lines correspond to the simulations and the markers correspond to the analytical derivation.

Tables (1)

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Table 1. Characteristics of the Phase Modulations Used for Simulations in Sections 4 and 5a

Equations (53)

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E(t)=exp[ijmjcos(Ωjt)].
τ(ω)=1+lω,
τ(ω)=1+qω2,
τ(ω)=exp(iφ2ω2/2),
τ(ω)=exp(iφ3ω3/6).
BW98%=2(m+1)Ω.
BWrms(m,Ω)=ω2S(ω,m,Ω)dω/S(ω,m,Ω)dω,
BWrms(m,Ω)=|Et(t)|2dt/|E(t)|2dt.
BWrms(m,Ω)=mΩ/2.
BWrms({mj,Ωj})=[jmjΩjsin(Ωjt)]2dt,
BWrms({mj,Ωj})=j,kmjmkΩjΩksin(Ωjt)sin(Ωkt)dt.
BWrms({mj,Ωj})=jmj2Ωj2/2.
τ(ω)=1+lω1+l2ω.
E=E+il2Et.
E(t)=E(t)[1+l2jmjΩjsin(Ωjt)],
P(t)=1+ljmjΩjsin(Ωjt).
PV(Ωj)=2lmjΩj.
PV=2ljmjΩj,
rms=ljmj2Ωj2/2.
τ(ω)=exp(iφ2ω2/2)1+iφ2ω2/2,
E=Eiφ222Et2.
E(t)=E(t){1φ22jmjΩj2cos(Ωjt)+iφ22[mjΩjsin(Ωjt)]2}.
P(t)=1φ2jmjΩj2cos(Ωjt).
PV(Ωj)=2φ2mjΩj2.
PV=2φ2jmjΩj2,
rms=φ2jmj2Ωj4/2.
PV(Ωj)=2mjΩj(φ2Ωj)2+l2.
PV=2jmjΩj(φ2Ωj)2+l2.
rms=jmj2Ωj2(φ2Ωj)2+l2]/2.
τ(ω)=1+qω21+q2ω2,
E=Eq22Et2.
E(t)=E(t){1+q2[jmjΩjsin(Ωjt)]2+iq2jmjΩj2cos(Ωjt)},
P(t)=1+q[jmjΩjsin(Ωjt)]2.
1+q2jmj2Ωj2.
PV=q(jmjΩj)2/(1+q2jmj2Ωj2).
rms=qjmj4Ωj4/8+j,kmj2mk2Ωj2Ωk2(1+q2jmj2Ωj2).
PV(2Ωj)=qmj2Ωj2/(1+q2jmj2Ωj2)
PV(Ωj±Ωk)=2qmjmkΩjΩk/(1+q2jmj2Ωj2).
τ(ω)=exp(iφ3ω3/6)1+iφ3ω3/6.
E=E+φ363Et3.
P(t)=1φ3jmjΩjsin(Ωjt)jmjΩj2cos(Ωjt).
φ3mjΩjsin(Ωjt)mjΩj2cos(Ωjt)=φ3mj2Ωj3sin(2Ωjt)/2.
PV(2Ωj)=φ3mj2Ωj3.
φ3mjmkΩjΩk[Ωksin(Ωjt)cos(Ωkt)+Ωjsin(Ωkt)cos(Ωjt)],
φ3mjmkΩjΩk{(Ωj+Ωk)sin[(Ωj+Ωk)t]+(ΩkΩj)sin[(ΩjΩk)t]}/2.
PV(Ωj±Ωk)=φ3mjmkΩjΩk(Ωj±Ωk),
rms2=φ32[jmjΩjsin(Ωjt)]2[jmjΩj2cos(Ωjt)]2dt.
rms2=φ32jmj2Ωj2sin2(Ωjt)jmj2Ωj4cos2(Ωjt)dt
rms2=φ32[jmj4Ωj6sin2(Ωjt)cos2(Ωjt)+jkmj2mk2Ωj2Ωk4sin2(Ωjt)cos2(Ωkt)]dt.
rms=φ32jmj4Ωj6/2+jkmj2mk2Ωj2Ωk4.
PVPVmin=φ3jmjΩjjmjΩj2.
PVPVmax=PVmin+φ3j>kmjmkΩjΩk(ΩjΩk).
P(t)=1+ljmjΩjsin(Ωjt)φ2jmjΩj2cos(Ωjt)+q[jmjΩjsin(Ωjt)]2φ3jmjΩjsin(Ωjt)jmjΩj2cos(Ωjt),

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