Abstract

The mechanisms of nonlinear phase-locking of a large fiber amplifier array are analyzed. The preference is given to the most suitable configuration for a coherent coupling of thousands of fundamental spatial mode fiber beams into a single smooth beam ready for chirped pulse compression. It is shown that a Michelson phase-conjugating configuration with double passage through an array of fiber amplifiers has the definite advantage compared to a one-way fiber array coupled in a Mach–Zehnder configuration. Regardless of the amount of synchronized fiber amplifiers, the Michelson phase-conjugating interferometer is expected to do a perfect compensation of the phase-piston errors and collimation of backwardly amplified fiber beams on an entrance/output beam splitter. In both configurations, the nonlinear transformation of the stretched pulse envelope, due to gain saturation, is capable of randomizing the position of chirp inside an envelope; thus it may reduce the visibility of the interference pattern at an output beam splitter. Certain advantages are inherent to the sech-form temporal envelope because of the exponential precursor and self-similar propagation in gain medium. The Gaussian envelope is significantly compressed in a deep gain saturation regime, and the frequency chirp position inside pulse envelope is more deformed.

© 2014 Optical Society of America

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2013 (1)

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7, 258–261 (2013).
[CrossRef]

2012 (4)

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Impact of spectral phase mismatch on femtosecond coherent beam combining systems,” Opt. Lett. 37, 650–652 (2012).
[CrossRef]

L. A. Siiman, W.-Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20, 18097–18116 (2012).
[CrossRef]

2011 (3)

2010 (4)

2009 (2)

2008 (2)

A. Yu. Okulov, “3D-vortex labyrinths in the near field of solid-state microchip laser,” J. Mod. Opt. 55, 241–259 (2008).
[CrossRef]

A. Yu. Okulov, “Optical and sound helical structures in a Mandelstam–Brillouin mirror,” J. Exp. Theor. Phys. Lett. 88, 487–491 (2008).
[CrossRef]

2006 (1)

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78, 309–371 (2006).
[CrossRef]

2002 (1)

T. Tajima and G. A. Mourou, “Zettawatt-exawatt lasers and their applications in ultrastrong-field physics,” Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

1998 (1)

M. W. Bowers and R. W. Boyd, “Phase locking via Brillouin-enhanced four-wave-mixing phase conjugation,” IEEE J. Quantum Electron. 34, 634–644 (1998).
[CrossRef]

1993 (1)

A. Yu. Okulov, “Scaling of diode-array-pumped solid-state lasers via self-imaging,” Opt. Commun. 99, 350–354 (1993).
[CrossRef]

1992 (1)

1991 (1)

A. Yu. Okulov, “The effect of roughness of optical elements on the transverse structure of a light field in a nonlinear Talbot cavity,” J. Mod. Opt. 38, 1887–1890 (1991).
[CrossRef]

1988 (1)

A. Yu. Okulov and A. N. Oraevsky, “Compensation of self-focusing distortions in quasiresonant amplification of a light pulse,” Sov. J. Quantum Electron. 18, 233–237 (1988).
[CrossRef]

1986 (1)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

1983 (1)

I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Accuracy of reproduction of time structure of the exciting radiation in stimulated scattering of light,” J. Exp. Theor. Phys. 57, 270–274 (1983).

1980 (2)

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

1978 (1)

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14, 650–660 (1978).
[CrossRef]

1975 (1)

1966 (2)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–310 (1966).

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

1965 (1)

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845–850 (1965).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Alpmann, C.

Ambartsumyan, R. V.

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

Babin, A.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Basov, N. G.

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845–850 (1965).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser system,” USSR PatentN 1088620 (Author’s certificate, December22, 1983; filed October 23, 1980).

Belenov, E. M.

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845–850 (1965).

Bellanger, C.

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–310 (1966).

Bourderionnet, J.

Bourdon, P.

Bowers, M. W.

M. W. Bowers and R. W. Boyd, “Phase locking via Brillouin-enhanced four-wave-mixing phase conjugation,” IEEE J. Quantum Electron. 34, 634–644 (1998).
[CrossRef]

Boyd, R. W.

M. W. Bowers and R. W. Boyd, “Phase locking via Brillouin-enhanced four-wave-mixing phase conjugation,” IEEE J. Quantum Electron. 34, 634–644 (1998).
[CrossRef]

R. W. Boyd, Nonlinear Optic, 3rd ed. (Academic, 2007).

Brignon, A.

Brocklesby, B.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7, 258–261 (2013).
[CrossRef]

Bulanov, S. V.

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78, 309–371 (2006).
[CrossRef]

Carroll, D. L.

Carstens, H.

Chang, W.

Chang, W.-Z.

Daniault, L.

Davidson, N.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Denz, C.

Druon, F.

Eidam, T.

Fadeev, S.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Fridman, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Friesem, A. A.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Galvanauskas, A.

Georges, P.

Ginzburg, V. N.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Giuliano, C. R.

Goodno, G. D.

Goular, D.

Hadrich, S.

Hanna, M.

Jansen, F.

Jauregui, C.

Johnson, R.

Khazanov, E. A.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Khizhnyak, A. I.

S. G. Odulov, M. S. Soskin, and A. I. Khizhnyak, Optical Oscillators With Degenerate Four-Wave Mixing (Dynamic Grating Lasers) (Harwood Academic, 1991).

Klenke, A.

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Kluwer Academic, 1987).

Kryukov, P. G.

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

Letokhov, V. S.

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845–850 (1965).

Limpert, J.

Lombard, L.

Lozhkarev, V. V.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Luchinin, G.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Mikhailov, S. I.

I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Accuracy of reproduction of time structure of the exciting radiation in stimulated scattering of light,” J. Exp. Theor. Phys. 57, 270–274 (1983).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser system,” USSR PatentN 1088620 (Author’s certificate, December22, 1983; filed October 23, 1980).

Mironov, A. B.

I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Accuracy of reproduction of time structure of the exciting radiation in stimulated scattering of light,” J. Exp. Theor. Phys. 57, 270–274 (1983).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser system,” USSR PatentN 1088620 (Author’s certificate, December22, 1983; filed October 23, 1980).

Mironov, S. Yu.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Mottay, E.

Mourou, G.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7, 258–261 (2013).
[CrossRef]

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Mourou, G. A.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78, 309–371 (2006).
[CrossRef]

T. Tajima and G. A. Mourou, “Zettawatt-exawatt lasers and their applications in ultrastrong-field physics,” Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

Moyer, R. H.

Nixon, M.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Novikov, E.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Odulov, S. G.

S. G. Odulov, M. S. Soskin, and A. I. Khizhnyak, Optical Oscillators With Degenerate Four-Wave Mixing (Dynamic Grating Lasers) (Harwood Academic, 1991).

Okulov, A. Yu.

A. Yu. Okulov, “Phase-conjugation of the isolated optical vortex using a flat surfaces,” J. Opt. Soc. Am. B 27, 2424–2427 (2010).
[CrossRef]

A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 013837 (2009).
[CrossRef]

A. Yu. Okulov, “3D-vortex labyrinths in the near field of solid-state microchip laser,” J. Mod. Opt. 55, 241–259 (2008).
[CrossRef]

A. Yu. Okulov, “Optical and sound helical structures in a Mandelstam–Brillouin mirror,” J. Exp. Theor. Phys. Lett. 88, 487–491 (2008).
[CrossRef]

A. Yu. Okulov, “Scaling of diode-array-pumped solid-state lasers via self-imaging,” Opt. Commun. 99, 350–354 (1993).
[CrossRef]

A. Yu. Okulov, “The effect of roughness of optical elements on the transverse structure of a light field in a nonlinear Talbot cavity,” J. Mod. Opt. 38, 1887–1890 (1991).
[CrossRef]

A. Yu. Okulov and A. N. Oraevsky, “Compensation of self-focusing distortions in quasiresonant amplification of a light pulse,” Sov. J. Quantum Electron. 18, 233–237 (1988).
[CrossRef]

I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Accuracy of reproduction of time structure of the exciting radiation in stimulated scattering of light,” J. Exp. Theor. Phys. 57, 270–274 (1983).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser system,” USSR PatentN 1088620 (Author’s certificate, December22, 1983; filed October 23, 1980).

A. Yu. Okulov and A. N. Oraevsky, “Spatiotemporal dynamics of a wave packet in nonlinear medium and discrete maps,” in Proceedings Lebedev Physics Institute (in Russian), N. G. Basov, ed., (Nauka, 1988), Vol. 187, pp. 202–222.

Oraevsky, A. N.

A. Yu. Okulov and A. N. Oraevsky, “Compensation of self-focusing distortions in quasiresonant amplification of a light pulse,” Sov. J. Quantum Electron. 18, 233–237 (1988).
[CrossRef]

A. Yu. Okulov and A. N. Oraevsky, “Spatiotemporal dynamics of a wave packet in nonlinear medium and discrete maps,” in Proceedings Lebedev Physics Institute (in Russian), N. G. Basov, ed., (Nauka, 1988), Vol. 187, pp. 202–222.

Pepper, D. M.

D. M. Pepper, “Phase conjugate optics,” Ph.D. thesis (Caltech, 1980), p. 37 ( http://thesis.library.caltech.edu/4044/ ).

Pfeifer, S. J.

Pilipetsky, N. F.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).

Primot, J.

Rockwell, D. A.

Ronen, E.

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Rothenberg, J. E.

Rothhardt, J.

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Kluwer Academic, 1987).

Seise, E.

Sergeev, A. M.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Shaykin, A.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Shih, C. C.

Shkunov, V. V.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).

Siegman, A. E.

Siiman, L. A.

Soskin, M. S.

S. G. Odulov, M. S. Soskin, and A. I. Khizhnyak, Optical Oscillators With Degenerate Four-Wave Mixing (Dynamic Grating Lasers) (Harwood Academic, 1991).

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Stutzki, F.

Sziklas, E. A.

Tajima, T.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7, 258–261 (2013).
[CrossRef]

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78, 309–371 (2006).
[CrossRef]

T. Tajima and G. A. Mourou, “Zettawatt-exawatt lasers and their applications in ultrastrong-field physics,” Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–310 (1966).

Tatarskii, V. I.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Kluwer Academic, 1987).

Tunnermann, A.

Winful, H. G.

Woerdemann, M.

Wu, T.

Yakovlev, I. V.

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

Yariv, A.

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14, 650–660 (1978).
[CrossRef]

Zaouter, Y.

Zeldovich, B. Y.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).

Zhou, T.

Zubarev, I. G.

I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Accuracy of reproduction of time structure of the exciting radiation in stimulated scattering of light,” J. Exp. Theor. Phys. 57, 270–274 (1983).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser system,” USSR PatentN 1088620 (Author’s certificate, December22, 1983; filed October 23, 1980).

Zuev, V. S.

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

M. W. Bowers and R. W. Boyd, “Phase locking via Brillouin-enhanced four-wave-mixing phase conjugation,” IEEE J. Quantum Electron. 34, 634–644 (1998).
[CrossRef]

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. 14, 650–660 (1978).
[CrossRef]

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

S. Yu. Mironov, V. V. Lozhkarev, V. N. Ginzburg, I. V. Yakovlev, G. Luchinin, A. Shaykin, E. A. Khazanov, A. Babin, E. Novikov, S. Fadeev, A. M. Sergeev, and G. A. Mourou, “Second-harmonic generation of super powerful femtosecond pulses under strong influence of cubic nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 18, 7 (2012).
[CrossRef]

J. Exp. Theor. Phys. (3)

R. V. Ambartsumyan, N. G. Basov, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, “Nonlinear amplification of light pulses,” J. Exp. Theor. Phys. 23, 16–22 (1966).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser interferometer with wavefront reversing mirrors,” J. Exp. Theor. Phys. 52, 847–851 (1980).

I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Accuracy of reproduction of time structure of the exciting radiation in stimulated scattering of light,” J. Exp. Theor. Phys. 57, 270–274 (1983).

J. Exp. Theor. Phys. Lett. (3)

A. Yu. Okulov, “Optical and sound helical structures in a Mandelstam–Brillouin mirror,” J. Exp. Theor. Phys. Lett. 88, 487–491 (2008).
[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–310 (1966).

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Phase fluctuations of the Stockes wave produced as a result of stimulated scattering of light,” J. Exp. Theor. Phys. Lett. 31, 645–649 (1980).

J. Mod. Opt. (2)

A. Yu. Okulov, “3D-vortex labyrinths in the near field of solid-state microchip laser,” J. Mod. Opt. 55, 241–259 (2008).
[CrossRef]

A. Yu. Okulov, “The effect of roughness of optical elements on the transverse structure of a light field in a nonlinear Talbot cavity,” J. Mod. Opt. 38, 1887–1890 (1991).
[CrossRef]

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

Nat. Photonics (1)

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nat. Photonics 7, 258–261 (2013).
[CrossRef]

Opt. Commun. (2)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

A. Yu. Okulov, “Scaling of diode-array-pumped solid-state lasers via self-imaging,” Opt. Commun. 99, 350–354 (1993).
[CrossRef]

Opt. Express (8)

G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18, 25403–25414 (2010).
[CrossRef]

T. Wu, W. Chang, A. Galvanauskas, and H. G. Winful, “Dynamical, bidirectional model for coherent beam combining in passive fiber laser arrays,” Opt. Express 18, 25873–25886 (2010).
[CrossRef]

E. Seise, A. Klenke, J. Limpert, and A. Tunnermann, “Coherent addition of fiber-amplified ultrashort laser pulses,” Opt. Express 18, 27827–27835 (2010).
[CrossRef]

T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hadrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tunnermann, “Fiber chirped-pulse amplification system emitting 3.8  GW peak power,” Opt. Express 19, 255–260 (2011).
[CrossRef]

J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Express 19, 17053–17058 (2011).
[CrossRef]

E. Seise, A. Klenke, J. Limpert, and A. Tunnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19, 25379–25387 (2011).
[CrossRef]

M. Woerdemann, C. Alpmann, and C. Denz, “Self-pumped phase conjugation of light beams carrying orbital angular momentum,” Opt. Express 17, 22791–22799 (2009).
[CrossRef]

L. A. Siiman, W.-Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20, 18097–18116 (2012).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

A. Yu. Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 013837 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

M. Nixon, M. Fridman, E. Ronen, A. A. Friesem, and N. Davidson, “Controlling synchronization in large laser networks,” Phys. Rev. Lett. 108, 214101 (2012).
[CrossRef]

Phys. Rev. ST Accel. Beams (1)

T. Tajima and G. A. Mourou, “Zettawatt-exawatt lasers and their applications in ultrastrong-field physics,” Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

G. A. Mourou, T. Tajima, and S. V. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78, 309–371 (2006).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. Yu. Okulov and A. N. Oraevsky, “Compensation of self-focusing distortions in quasiresonant amplification of a light pulse,” Sov. J. Quantum Electron. 18, 233–237 (1988).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

N. G. Basov, E. M. Belenov, and V. S. Letokhov, “Diffraction synchronization of lasers,” Sov. Phys. Tech. Phys. 10, 845–850 (1965).

Other (9)

A. Brignon, ed., Coherent Laser Beam Combining (Wiley, 2013), pp. 498.

N. G. Basov, I. G. Zubarev, A. B. Mironov, S. I. Mikhailov, and A. Yu. Okulov, “Laser system,” USSR PatentN 1088620 (Author’s certificate, December22, 1983; filed October 23, 1980).

D. M. Pepper, “Phase conjugate optics,” Ph.D. thesis (Caltech, 1980), p. 37 ( http://thesis.library.caltech.edu/4044/ ).

A. Yu. Okulov and A. N. Oraevsky, “Spatiotemporal dynamics of a wave packet in nonlinear medium and discrete maps,” in Proceedings Lebedev Physics Institute (in Russian), N. G. Basov, ed., (Nauka, 1988), Vol. 187, pp. 202–222.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

S. G. Odulov, M. S. Soskin, and A. I. Khizhnyak, Optical Oscillators With Degenerate Four-Wave Mixing (Dynamic Grating Lasers) (Harwood Academic, 1991).

R. W. Boyd, Nonlinear Optic, 3rd ed. (Academic, 2007).

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Kluwer Academic, 1987).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Chirped pulse amplification and compression in Mach–Zehnder configuration. MO, master oscillator; CPA, chirped pulse amplifying array; BSfiber [1], entrance beam-splitter tree, which may be both free space and fiber array; M, ordinary retro-mirrors; BST, free-space output binary BS tree [9,11]; λ3T, target of volume λ3. (b) Chirped pulse amplification and compression in Michelson configuration. PCM, degenerate four-wave mixing (DFWM) phase-conjugating mirror; λ(t)/2, Pockels time-dependent chirp preserving decoupler; BST, free-space entrance binary BS tree dividing MO beam into Nf=2Nex amplified beams. Backward phase-conjugated amplified emission is combined into a single beam by this Michelson BST.

Fig. 2.
Fig. 2.

Phase conjugation of sech(t) and Gaussian chirped pulses in degenerate four-wave χ3 mirror. Reflectivity RPCM(t)LPCM2γPC2I2(z=0,t)θGs,Se2 is proportional to the square of intensity (1–3, gradually increased, arb.units). (a) sech4(t/τSe); (b) exp[4τ2/2τGa2].

Fig. 3.
Fig. 3.

Principle of phase locking of the CPA fiber array with phase-piston errors Δϕmn having parameters of a 64 fiber array [9] with pD100μm. Inside Fresnel zone zfrD2/λ, the interference of overlapping Gaussian beams produces speckle pattern [30], which is randomly spaced set of field zeros. This random field, composed of vortex–antivortex pairs [34], passes into degenerate four-wave mixing PC mirror (DFWM PCM). Each vortex produces a helical interference pattern with its phase-conjugated replica [35]. The phase-conjugated field EbGa,Se(z,τ,r⃗) propagates backward along curvilinear helical waveguides with λ/2 modulation and recovers phase-piston errors Δϕmn. This ensures optimal collection of a reflected and backwardly amplified field at the entrance/output beam splitter BST. Each speckle inhomogeneity is considered here as a tilted-plate-emitting plane wave with wave vector K⃗pq. K⃗X,Y is deflection of K⃗pq from normal K⃗Z.

Fig. 4.
Fig. 4.

Spectrum distortion of 2πδνSe(τ)=θSe(τ)/τ the chirped backward pulse Ebsech3((tz/vg)/τSe) with the exponential precursor in the backward amplifier before the compressor; (a) and (b) correspond to the weak gain saturation [G=2, 2.5, 3, 3.5, 4(1–5)]; (c) and (d) stand for deep saturation regime [G=6, 7, 8, 9, 10(1–5)]. The shift of the pulse maximum along the precursor, i.e., to negative t corresponds to superluminal propagation with envelope speed V>c due to saturation of the resonant transition.

Fig. 5.
Fig. 5.

Spectrum distortion 2πδνGs(τ)=θGs(τ)/τ of the chirped backward Gaussian pulse Ebexp[3(tz/vg)2/2τGa] in backward amplifier before compressor; (a) and (b) correspond to weak gain saturation [G=2, 2.5, 3, 3.5, 4(1–5)]; (c) and (d) stand for deep saturation regime [G=6, 6.1, 6.2, 6.3, 6.4(1–5)]. The shift of the Gaussian pulse maximum along precursor and temporal steepening corresponds to subluminal propagation with envelope speed V<c.

Equations (35)

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EGs,Se(z,t,r⃗)Eo·exp(r2/2D2)·fGs,Se(τ)·exp[iθGs,Se(τ)]·exp(iωt+ikzz),θGs,Se(τ)kn2·Lstr·|EGs,Se(z,t,r=0)|2,fGs(τ)=exp[τ2/2τGs2],fSe(τ)=sech[τ/τSe],
θGs,Se(τ)B(r⃗=0,τ)=2πn2λ0Lstr|EGs,Se(z,τ,r=0)|2dz,n2=3χ(3)8n0,
iEGs,Se(z,τ)z=β2·2EGs,Se(z,τ)2τγ|EGs,Se(z,τ)|2×EGs,Se(z,τ),Aeff=[|EGs,Se|2d2r⃗]2|EGs,Se|4d2r⃗,
iEGs,Se(z,τ)z=β2·2EGs,Se(z,τ)2τ.
EGs,Se(z,τ)=EGs,Se(z=0,ω)2πexp[i2βω2ziωτ]dω,
EGs(z=0,ω)=exp[τ2/2τGs2]exp[iωτ]dτ=τGsπ2exp[ω2τGs2/4],ESe(z=0,ω)=sech[τ/τSe]exp[iωτ]dτ=πτSe2sech(πωτSe2).
EGs(z,ω)=(2πτGs)1/2exp[ω2τGs2/4+iω2βz/2],ESe(z,ω)sech[πω(τSeβωz)/2].
EGs(Lstr,ω)exp[τ22τGs2]exp[iωτ+iθGs(τ)]dτ,ESe(Lstr,ω)sech[τ/τSe]exp[iωτ+iθSe(τ)]dτ.
EGs(z,ω)τGs2π2kn2·Lstr2EGa(0,τ=0)/τ2×exp[ω2τGs2/4]×exp[i2βω2z+ikn2·Lstr·|EGa(0,τ=0)|2+iπ/4],
ESe(z,ω)τGs2π2kn2·Lstr2ESe(0,τ=0)/τ2×sech(πωτSe2)×exp[i2βω2z+ikn2·Lstr·|ESe(0,τ=0)|2+iπ/4].
Emn(z,t,r⃗)Emno·exp[(r⃗r⃗mn)2/2D2],EGs,Se(z,τ)·exp(iωt+ikzz+iΔϕmn).
Ef(z,t,r⃗)exp[iωt+ikzz]·EGs,Se(z,τ)m,nEmno·exp[(r⃗r⃗mn)2/2D2+iΔϕmn],
Ef(z,t,r⃗)z+n0cEft+i2kp2Ef=iγSBSωp4cn0ρ0QEb,
Eb(z,t,r⃗)zn0cEbti2ks2Eb=iγSBSωs4cn0ρ0EfQ*,
vacQ(z,t,r⃗)z+Qt+ΓQ2=EfEb*iγSBS(kp+ks)216πωac,
EGs,SePC(z,t,r⃗)z=i2k·2EGs,SePCiγPC2|EGs,SePC|2·EGs,SePC,
EGs,SePC(z,t,r⃗)=E1+E2+Ef+Eb,
EbGs,Se(z,t,r⃗)z=iγPC2E1E2f2(τ)EfGs,Se*(z,t,r⃗),RPCM(t)=|Eb(z=0,t)|2|Ef(z=0,t)|2=f4(τ)·LPCM2γPC2E1·E2,KPCM=|EfEb*d2r⃗|2|Ef|2d2r⃗·|Eb|2d2r⃗1,
Ef(z,t,r⃗)exp[iωt+ikzz+iθGs,Se(τ)]·fGs,Se(τ)MaM·exp[iK⃗Mr⃗],
Eb(z,t,r⃗)exp[iωtikzz+iθGs,Se(τ)]·fGs,Se(τ)MaM*·exp[iK⃗Mr⃗].
Ispeckle(z,t,r⃗)=|Ef(z,t,r⃗)+Eb(z,t,r⃗)|2.
Ef,b(z,t,r⃗)z±nrcEf,bt+i2kp2Ef,b=σYbN(z,t)2Ef,b+ikn2|Ef+Eb|2·Ef,b,
N(z,t)t=σYbN(z,t)·|Ef+Eb|2+N0(z)N(z,t)T1,
Ef,b(z,t)z±nrcEf,b(z,t)t=σYbN0(z)Ef,b(z,t)2×exp[2σYbt|Ef,b|2dτ]ikn2|Ef,b(z,t)|2Ef,b(z,t),
Eb(z,t)=Eb(Lf,t)·exp[ikn2z|Eb(z,t)|2dz]1[1exp[σYbLfzN0(z)dz]exp[2σYbtz/vg|Eb(z,τ)|2dτ]].
EbSe(z=0,τ)=Eb(Lf)sech3(τ/τSe)·exp[ikn2Lf|Eb(τ)sech3(τ/τSe)|2dz]1[1exp[σYbN0Lf]exp[2σYbEb6(Lf)[8+4sech2(τ/τSe)+3sech4(τ/τSe)]tanh(τ/τSe)]]
EbGa(z=0,τ)=Eb(Lf)exp(3τ2/τGa2)·exp[ikn2Lf|Eb(τ)exp(3τ2/τGa2)|2dz]1[1exp[σYbN0Lf]exp[σYbπEb6(Lf)[erf(6τ/τGa)]]],
FOM12(ω)=Pcomb(ω)Pidle(ω)Pcomb(ω)+Pidle(ω)=|E1(ω)+E2(ω)·exp(iΔΦ1,2(ω))|2|E1(ω)|2+|E2(ω)|2,
FOM12(ω)=|E1(ω)+E2(ω)·exp(iΔΦ1,2(ω))|2|E1(ω)|2+|E2(ω)|2=±2P0(ω)cos[ΔΦ1,2(ω)]2P0(ω)=±cos[ΔΦ1,2(ω)].
FOM12=C·s(ω)FOM12(ω)dω=±C·s(ω)cos[ΔΦ1,2(ω)]dω,C=1/s(ω)d(ω),
Eb(z=BS,ω)=1NfnNfE0(ω)exp[iΦn(ω)]=E0(ω0)s(ω)NfnNfexp[iΦn(ω)].
I(ω)=Eb(ω)Eb*(ω)=|E0(ω)|2s(ω)Nf[Nf+n,mnNfnNfcos[iΦmn(ω)]],
FOM=(I(ω)(Nf·s(ω)I(ω)))dωNf·s(ω)dω=CNf×s(ω)[(2Nf)+2Nfn,mnNfnNfcos[iΦmn(ω)]]dω,
FOM=[2Nf1]+2Nf2n,mnNfnNf·FOMnm.
FOMlarge[2Nf1]+2[11Nf]·FOM12.

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