Abstract

Resonant three-wave interactions appear in many fields of physics e.g. nonlinear optics, plasma physics, acoustics and hydrodynamics. A general theory of autoresonant three-wave mixing in a nonuniform media is derived analytically and demonstrated numerically. It is shown that due to the medium nonuniformity, a stable phase-locked evolution is automatically established. For a weak nonuniformity, the efficiency of the energy conversion between the interacting waves can reach almost 100%. One of the potential applications of our theory is the design of highly-efficient optical parametric amplifiers.

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    [CrossRef]
  2. V. I. Veksler, “A new method of acceleration of relativistic particles,” J. Phys. USSR9, 153–158 (1945).
  3. E. M. McMillan, “The synchrotron - a proposed high energy particle accelerator,” Phys. Rev.68, 143–144 (1945).
    [CrossRef]
  4. G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009).
    [CrossRef] [PubMed]
  10. A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett.103, 123901 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  18. O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008).
    [CrossRef]
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    [CrossRef]
  20. O. Yaakobi and L. Friedland, “Multidimensional, autoresonant three-wave interactions,” Phys. Plasmas15, 102104 (2008).
    [CrossRef]
  21. O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
    [CrossRef]
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    [CrossRef]
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2010 (6)

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant propagation of incoherent light-waves,” Optics Express, 18, 17709–17718 (2010).
[CrossRef] [PubMed]

S. Trendafilov, V. Khudik, M. Tokman, and G. Shvets, “Hamiltonian description of non-reciprocal light propagation in nonlinear chiral fibers,” Physica B405, 3003–3006 (2010).
[CrossRef]

T. Chapman, S. Huller, P. E. Masson-Laborde, W. Rozmus, and D. Pesme, “Spatially autoresonant stimulated Raman scattering in inhomogeneous plasmas in the kinetic regime,” Phys. Plasmas17, 122317 (2010).
[CrossRef]

O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
[CrossRef]

S. Richard, “Second-harmonic generation in tapered optical fibers,” J. Opt. Soc. Am. B27, 1504–1512 (2010).
[CrossRef]

2009 (3)

L. Friedland, “Autoresonance in nonlinear systems,” Scholarpedia4, 5473 (2009).
[CrossRef]

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009).
[CrossRef] [PubMed]

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett.103, 123901 (2009).
[CrossRef] [PubMed]

2008 (4)

O. Yaakobi and L. Friedland, “Multidimensional, autoresonant three-wave interactions,” Phys. Plasmas15, 102104 (2008).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B,25, 1402–1413 (2008).
[CrossRef]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A78, 063821 (2008).
[CrossRef]

O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008).
[CrossRef]

2007 (1)

S. Longhi, “Third-harmonic generation in quasi-phase-matched χ(2) media with missing second harmonic,” Optics Letters32, 1791–1793 (2007).
[CrossRef] [PubMed]

2002 (1)

I. Y. Dodin, G. M. Fraiman, V. M. Malkin, and N. J. Fisch, “Amplification of short laser pulses by Raman backscattering in capillary plasmas,” JETP95, 625–638 (2002).
[CrossRef]

2001 (1)

G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B,18, 534–539 (2001).
[CrossRef]

1995 (2)

A. P. Mayer, “Surface acoustic waves in nonlinear elastic media,” Phys. Rep.256, 237–366 (1995).
[CrossRef]

K. Trulsen and C. C. Mei, “Modulation of three resonating gravity-capillary waves by a long gravity wave,” J. Fluid Mech.290, 345–376 (1995).
[CrossRef]

1994 (1)

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron.30, 1596–1604 (1994).
[CrossRef]

1992 (1)

L. Friedland, “Autoresonant three-wave interactions,” Phys. Rev. Lett.69, 1749–1752 (1992).
[CrossRef] [PubMed]

1990 (1)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron.26, 1265–1276 (1990).
[CrossRef]

1945 (2)

V. I. Veksler, “A new method of acceleration of relativistic particles,” J. Phys. USSR9, 153–158 (1945).

E. M. McMillan, “The synchrotron - a proposed high energy particle accelerator,” Phys. Rev.68, 143–144 (1945).
[CrossRef]

Afeyan, B.

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B,25, 1402–1413 (2008).
[CrossRef]

Andresen, G. B.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Arie, A.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009).
[CrossRef] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A78, 063821 (2008).
[CrossRef]

Ashkezari, M. D.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Baquero-Ruiz, M.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Barak, A.

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant propagation of incoherent light-waves,” Optics Express, 18, 17709–17718 (2010).
[CrossRef] [PubMed]

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett.103, 123901 (2009).
[CrossRef] [PubMed]

Bertsche, W.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Bowe, P. D.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Boyd, R. B.

R. B. Boyd, Nonlinear Optics (Third Edition, AP2007).

Butler, E.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Cesar, C. L.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Chapman, S.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Chapman, T.

T. Chapman, S. Huller, P. E. Masson-Laborde, W. Rozmus, and D. Pesme, “Spatially autoresonant stimulated Raman scattering in inhomogeneous plasmas in the kinetic regime,” Phys. Plasmas17, 122317 (2010).
[CrossRef]

Charbonneau-Lefort, M.

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B,25, 1402–1413 (2008).
[CrossRef]

Charlton, M.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Charman, A. E.

O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008).
[CrossRef]

Deller, A.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Dodin, I. Y.

I. Y. Dodin, G. M. Fraiman, V. M. Malkin, and N. J. Fisch, “Amplification of short laser pulses by Raman backscattering in capillary plasmas,” JETP95, 625–638 (2002).
[CrossRef]

Eriksson, S.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Fajans, J.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Fejer, M. M.

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B,25, 1402–1413 (2008).
[CrossRef]

G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B,18, 534–539 (2001).
[CrossRef]

Fisch, N. J.

I. Y. Dodin, G. M. Fraiman, V. M. Malkin, and N. J. Fisch, “Amplification of short laser pulses by Raman backscattering in capillary plasmas,” JETP95, 625–638 (2002).
[CrossRef]

Fraiman, G. M.

I. Y. Dodin, G. M. Fraiman, V. M. Malkin, and N. J. Fisch, “Amplification of short laser pulses by Raman backscattering in capillary plasmas,” JETP95, 625–638 (2002).
[CrossRef]

Friedland, L.

O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
[CrossRef]

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant propagation of incoherent light-waves,” Optics Express, 18, 17709–17718 (2010).
[CrossRef] [PubMed]

L. Friedland, “Autoresonance in nonlinear systems,” Scholarpedia4, 5473 (2009).
[CrossRef]

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Richard, S.

Robicheaux, F.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Rozmus, W.

T. Chapman, S. Huller, P. E. Masson-Laborde, W. Rozmus, and D. Pesme, “Spatially autoresonant stimulated Raman scattering in inhomogeneous plasmas in the kinetic regime,” Phys. Plasmas17, 122317 (2010).
[CrossRef]

Sarid, E.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron.30, 1596–1604 (1994).
[CrossRef]

Segev, M.

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant propagation of incoherent light-waves,” Optics Express, 18, 17709–17718 (2010).
[CrossRef] [PubMed]

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett.103, 123901 (2009).
[CrossRef] [PubMed]

Seif el Nasr, S.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Shvets, G.

S. Trendafilov, V. Khudik, M. Tokman, and G. Shvets, “Hamiltonian description of non-reciprocal light propagation in nonlinear chiral fibers,” Physica B405, 3003–3006 (2010).
[CrossRef]

Silberberg, Y.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009).
[CrossRef] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A78, 063821 (2008).
[CrossRef]

Silveira, D. M.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

So, C.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Storey, J. W.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Suchowski, H.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009).
[CrossRef] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A78, 063821 (2008).
[CrossRef]

Suhara, T.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron.26, 1265–1276 (1990).
[CrossRef]

Thompson, R. I.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Tokman, M.

S. Trendafilov, V. Khudik, M. Tokman, and G. Shvets, “Hamiltonian description of non-reciprocal light propagation in nonlinear chiral fibers,” Physica B405, 3003–3006 (2010).
[CrossRef]

Trendafilov, S.

S. Trendafilov, V. Khudik, M. Tokman, and G. Shvets, “Hamiltonian description of non-reciprocal light propagation in nonlinear chiral fibers,” Physica B405, 3003–3006 (2010).
[CrossRef]

Trulsen, K.

K. Trulsen and C. C. Mei, “Modulation of three resonating gravity-capillary waves by a long gravity wave,” J. Fluid Mech.290, 345–376 (1995).
[CrossRef]

van der Werf, D. P.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Veksler, V. I.

V. I. Veksler, “A new method of acceleration of relativistic particles,” J. Phys. USSR9, 153–158 (1945).

Wurtele, J. S.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008).
[CrossRef]

Yaakobi, O.

O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
[CrossRef]

O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008).
[CrossRef]

O. Yaakobi and L. Friedland, “Multidimensional, autoresonant three-wave interactions,” Phys. Plasmas15, 102104 (2008).
[CrossRef]

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron.30, 1596–1604 (1994).
[CrossRef]

Yamazaki, Y.

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron.26, 1265–1276 (1990).
[CrossRef]

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron.30, 1596–1604 (1994).
[CrossRef]

J. Fluid Mech. (1)

K. Trulsen and C. C. Mei, “Modulation of three resonating gravity-capillary waves by a long gravity wave,” J. Fluid Mech.290, 345–376 (1995).
[CrossRef]

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

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

G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B,18, 534–539 (2001).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B,25, 1402–1413 (2008).
[CrossRef]

J. Phys. USSR (1)

V. I. Veksler, “A new method of acceleration of relativistic particles,” J. Phys. USSR9, 153–158 (1945).

JETP (1)

I. Y. Dodin, G. M. Fraiman, V. M. Malkin, and N. J. Fisch, “Amplification of short laser pulses by Raman backscattering in capillary plasmas,” JETP95, 625–638 (2002).
[CrossRef]

Nature (1)

G. B. Andresen, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, C. L. Cesar, S. Chapman, M. Charlton, A. Deller, S. Eriksson, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, A. Gutierrez, J. S. Hangst, W. N. Hardy, M. E. Hayden, A. J. Humphries, R. Hydomako, M. J. Jenkins, S. Jonsell, L. V. Jorgensen, L. Kurchaninov, N. Madsen, S. Menary, P. Nolan, K. Olchanski, A. Olin, A. Povilus, P. Pusa, F. Robicheaux, E. Sarid, S. Seif el Nasr, D. M. Silveira, C. So, J. W. Storey, R. I. Thompson, D. P. van der Werf, J. S. Wurtele, and Y. Yamazaki, “Trapped antihydrogen,” Nature468, 673–676 (2010).
[CrossRef] [PubMed]

Optics Express (2)

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Optics Express17, 12731–12740 (2009).
[CrossRef] [PubMed]

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant propagation of incoherent light-waves,” Optics Express, 18, 17709–17718 (2010).
[CrossRef] [PubMed]

Optics Letters (1)

S. Longhi, “Third-harmonic generation in quasi-phase-matched χ(2) media with missing second harmonic,” Optics Letters32, 1791–1793 (2007).
[CrossRef] [PubMed]

Phys. Plasmas (3)

O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, “Spatially autoresonant stimulated Raman scattering in nonuniform plasmas,” Phys. Plasmas15, 032105 (2008).
[CrossRef]

T. Chapman, S. Huller, P. E. Masson-Laborde, W. Rozmus, and D. Pesme, “Spatially autoresonant stimulated Raman scattering in inhomogeneous plasmas in the kinetic regime,” Phys. Plasmas17, 122317 (2010).
[CrossRef]

O. Yaakobi and L. Friedland, “Multidimensional, autoresonant three-wave interactions,” Phys. Plasmas15, 102104 (2008).
[CrossRef]

Phys. Rep. (1)

A. P. Mayer, “Surface acoustic waves in nonlinear elastic media,” Phys. Rep.256, 237–366 (1995).
[CrossRef]

Phys. Rev. (1)

E. M. McMillan, “The synchrotron - a proposed high energy particle accelerator,” Phys. Rev.68, 143–144 (1945).
[CrossRef]

Phys. Rev. A (2)

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A78, 063821 (2008).
[CrossRef]

O. Yaakobi and L. Friedland, “Autoresonant four-wave mixing in optical fibers,” Phys. Rev. A82, 023820 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett.103, 123901 (2009).
[CrossRef] [PubMed]

L. Friedland, “Autoresonant three-wave interactions,” Phys. Rev. Lett.69, 1749–1752 (1992).
[CrossRef] [PubMed]

Physica B (1)

S. Trendafilov, V. Khudik, M. Tokman, and G. Shvets, “Hamiltonian description of non-reciprocal light propagation in nonlinear chiral fibers,” Physica B405, 3003–3006 (2010).
[CrossRef]

Scholarpedia (1)

L. Friedland, “Autoresonance in nonlinear systems,” Scholarpedia4, 5473 (2009).
[CrossRef]

Other (2)

W. L. Kruer, The Physics of Laser Plasma Interactions (reprint ed.Westview Press, Boulder, CO, 2001).

R. B. Boyd, Nonlinear Optics (Third Edition, AP2007).

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Figures (3)

Fig. 1
Fig. 1

Phase-locked evolution of (a) wave envelopes B j 2 and (b) phase mismatch Φ versus normalized distance |α|ξ for a spatial nonuniformity rate α = 0.01. In (a), the idler, signal and pump are denoted by (1) green, (2) blue and (3) red respectively. The black curves represent the value of the analytical expressions Eqs. (16)(17). Note that the curves of the signal and idler are almost overlapping.

Fig. 2
Fig. 2

Evolution of (a) wave envelopes B j 2 and (b) phase mismatch Φ for large value of nonuniformity rate α = 1. Due to the large value of α, the initial phase-locking is lost prior to reaching the point |α|ξ = −2. Note that the curves of the signal and idler (blue and green, respectively) are almost overlapping.

Fig. 3
Fig. 3

Stability function Ω2 versus |α|ξ for different values of the initial signal amplitude B2,0 (blue: 0.01, red: 0.05, green: 0.1). The black curve represents the value of the analytical expression Eq. (24). Satisfying the criterion |α| < Ω2 continuously is required for the stability of phase-locking. The inset (b) is a zoom of (a) at the location of the minimum of Ω2 near |α|ξ = −2. Note that all the curves are almost overlapping.

Equations (30)

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d A j d z = i η j A m * A 3 e i 0 z Δ k ( z ) d z ; j , m = 1 , 2 ; j m ,
d A 3 d z = i η 3 A 1 A 2 e + i 0 z Δ k ( z ) d z .
d a j d ζ = i a m * a 3 e i l 0 ζ Δ k ( ζ ) d ζ ; j , m = 1 , 2 ; j m ,
d a 3 d ζ = i a 1 a 2 e + i l 0 ζ Δ k ( ζ ) d ζ .
d B j d ζ = ε j B m B n sin Φ ; j , m , n = 1 3 ; j m n ,
d Φ d ζ = l Δ k + Q cos Φ ,
d B 1 d ζ = B 2 B 3 sin Φ ,
B 1 2 B 2 2 = B 1 , 0 2 B 2 , 0 2 , B 1 2 + B 3 2 = B 1 , 0 2 + B 3 , 0 2 .
d B 1 d ξ = B 2 B 3 sin Φ ,
d Φ d ξ = α ξ + Q cos Φ .
d B 1 d ξ = B 2 , 0 sin Φ , d Φ d ξ = α ξ + B 2 , 0 B 1 cos Φ .
d B 1 d ξ = B 2 sin Φ , B 2 2 = B 1 2 , + B 2 , 0 2
d Φ d ξ = α ξ + ( B 2 B 1 + B 1 B 2 ) cos Φ .
α ξ + s Q ^ = 0 ,
sin Φ ^ = 1 B ^ 1 B ^ 3 d B ^ 1 d ξ ,
B ^ 3 = | α | ξ + ( | α | ξ ) 2 + 12 6 , | α | ξ > 2 .
B ^ 2 2 B ^ 1 2 = 1 [ | α | ξ + ( | α | ξ ) 2 + 12 6 ] 2 , | α | ξ > 2 .
d Φ d ξ = s ( | α | ξ + Q ^ ) + s Q ^ δ B 1 ,
Q ^ | α | ξ .
d ( δ Φ ) d ξ = s Q ^ δ B 1 .
d ( δ B 1 ) d ξ = s D sin δ Φ + | α | Q ^ ,
H ( δ B 1 , δ Φ , ξ ) = s [ Q ^ 2 ( δ B 1 ) 2 + V eff ( δ Φ , ξ ) ] ,
| α | < Ω 2 ,
Ω 2 2 | α | ξ ( | α | ξ ) 2 + 12 3 + ( | α | ξ ) 2 3 + 4 .
l = [ ( c ε 0 8 π 2 ) n 1 , avg n 2 , avg n 3 , 0 λ 1 λ 2 d eff 2 I 3 , 0 ] 1 / 2 ,
α = l 2 L ( Δ k fin Δ k ini ) ,
ξ = l Δ k α = L l Δ k ( Δ k fin Δ k ini ) ,
| α | ξ = l Δ k sign ( Δ k fin Δ k ini ) .
| Δ k ini | , | Δ k fin | > 2 l .
| Δ k fin Δ k ini | L < Ω min 2 l 2 .

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