Abstract

We have proposed a new method of enhancing the efficiency of pulsed anti-Stokes stimulated Raman generation by using quasi-phase matching in a stack of alternating layers with different Raman properties. We have derived a system of coupled differential equations describing a multifrequency stimulated Raman process with interacting waves propagating in both the forward and the backward direction. We show that the efficiency of anti-Stokes generation can reach 20–30%. We also show that an optimized layered structure can perform for a broad range of pump parameters, such as pulse duration, intensity, and Fresnel number.

© 2005 Optical Society of America

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  6. V. G. Bespalov, D. I. Staselko, and A. M. Dukhovnyi, "The study of radiation coherence at SRS in compressed hydrogen," Sov. Tech. Phys. Lett. 5, 518 (1979).
  7. R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. R. Chu, M. Kanefsky, and J. Falk, "Numerical study of transient stimulated Brillouin scattering," J. Appl. Phys. 71, 4653-4658 (1992).
    [CrossRef]
  20. W. K. Bischel and M. J. Dyer, "Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transmission in H2," J. Opt. Soc. Am. B 3, 677-682 (1986).
    [CrossRef]
  21. P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
    [CrossRef]
  22. Yu. A. Ilynsky and V. D. Taranuhin, "About optical Stark effect at stimulated Raman scattering in gases," Quantum Electron. 1, 1500-1506 (1974).
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    [CrossRef]

2004

N. S. Makarov and V. G. Bespalov, "Backward and forward quasi-phase-matched multiwave SRS in nonlinear periodical structures," in Nonresonant Laser-Matter Interaction (NLMI-II), M. N. Libenson, ed., Proc. SPIE 5506, 87-94 (2004).
[CrossRef]

2003

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

2002

N. S. Makarov and V. G. Bespalov, "Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering," Opt. Commun. 203, 413-420 (2002).
[CrossRef]

2001

1999

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

R. G. Zaporozhchenko, S. Ya. Kilin, V. G. Bespalov, and D. I. Stasel'ko, "Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium," Opt. Spectrosc. 86, 632-639 (1999).

R. Urschel, U. Bäder, A. Borsutzky, and R. Wallenstein, "Spectral properties and conversion efficiency of 355-nm-pumped pulsed optical parametric oscillators of β-barium borate with noncollinear phase matching," J. Opt. Soc. Am. B 16, 565-579 (1999).
[CrossRef]

M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, "Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides," Opt. Lett. 24, 1157-1159 (1999).
[CrossRef]

1992

R. Chu, M. Kanefsky, and J. Falk, "Numerical study of transient stimulated Brillouin scattering," J. Appl. Phys. 71, 4653-4658 (1992).
[CrossRef]

1991

J. J. Ottusch, M. S. Mangir, and D. A. Rockwell, "Efficient anti-Stokes Raman conversion by four-wave mixing in gases," J. Opt. Soc. Am. B 8, 68-77 (1991).
[CrossRef]

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

1986

W. K. Bischel and M. J. Dyer, "Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transmission in H2," J. Opt. Soc. Am. B 3, 677-682 (1986).
[CrossRef]

A. P. Hickman, J. A. Paisner, and W. K. Bischel, "Theory of multiwave propagation and frequency conversion in a Raman medium," Phys. Rev. A 33, 1788-1797 (1986).
[CrossRef] [PubMed]

1982

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

1979

V. G. Bespalov, D. I. Staselko, and A. M. Dukhovnyi, "The study of radiation coherence at SRS in compressed hydrogen," Sov. Tech. Phys. Lett. 5, 518 (1979).

1974

Yu. A. Ilynsky and V. D. Taranuhin, "About optical Stark effect at stimulated Raman scattering in gases," Quantum Electron. 1, 1500-1506 (1974).

1969

M. Maier, W. Kaiser, and J. A. Giordmaine, "Backward stimulated Raman scattering," Phys. Rev. 177, 580-599 (1969).
[CrossRef]

1963

R. W. Minck, R. W. Terhune, and W. G. Rado, "Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H2,D2 and CH4," Appl. Phys. Lett. 3, 181-184 (1963).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Andreev, R. B.

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

Aquila, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Attwood, D. T.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Bäder, U.

Basiev, T. T.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Bespalov, V. G.

N. S. Makarov and V. G. Bespalov, "Backward and forward quasi-phase-matched multiwave SRS in nonlinear periodical structures," in Nonresonant Laser-Matter Interaction (NLMI-II), M. N. Libenson, ed., Proc. SPIE 5506, 87-94 (2004).
[CrossRef]

N. S. Makarov and V. G. Bespalov, "Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering," Opt. Commun. 203, 413-420 (2002).
[CrossRef]

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

R. G. Zaporozhchenko, S. Ya. Kilin, V. G. Bespalov, and D. I. Stasel'ko, "Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium," Opt. Spectrosc. 86, 632-639 (1999).

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

V. G. Bespalov, D. I. Staselko, and A. M. Dukhovnyi, "The study of radiation coherence at SRS in compressed hydrogen," Sov. Tech. Phys. Lett. 5, 518 (1979).

Bischel, W. K.

A. P. Hickman, J. A. Paisner, and W. K. Bischel, "Theory of multiwave propagation and frequency conversion in a Raman medium," Phys. Rev. A 33, 1788-1797 (1986).
[CrossRef] [PubMed]

Bischel , W. K.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Borsutzky, A.

Brener, I.

Chou, M. H.

Christov, I. P.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Chu, R.

R. Chu, M. Kanefsky, and J. Falk, "Numerical study of transient stimulated Brillouin scattering," J. Appl. Phys. 71, 4653-4658 (1992).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Dukhovnyi, A. M.

V. G. Bespalov, D. I. Staselko, and A. M. Dukhovnyi, "The study of radiation coherence at SRS in compressed hydrogen," Sov. Tech. Phys. Lett. 5, 518 (1979).

Dyer, M. J.

Falk, J.

R. Chu, M. Kanefsky, and J. Falk, "Numerical study of transient stimulated Brillouin scattering," J. Appl. Phys. 71, 4653-4658 (1992).
[CrossRef]

Fejer, M. M.

Gibson, E. A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Giordmaine, J. A.

M. Maier, W. Kaiser, and J. A. Giordmaine, "Backward stimulated Raman scattering," Phys. Rev. 177, 580-599 (1969).
[CrossRef]

Gorbunov, V. A.

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

Gulidov, S. S.

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

Gullikson, E.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Hickman, A. P.

A. P. Hickman, J. A. Paisner, and W. K. Bischel, "Theory of multiwave propagation and frequency conversion in a Raman medium," Phys. Rev. A 33, 1788-1797 (1986).
[CrossRef] [PubMed]

Ilynsky , Yu. A.

Yu. A. Ilynsky and V. D. Taranuhin, "About optical Stark effect at stimulated Raman scattering in gases," Quantum Electron. 1, 1500-1506 (1974).

Kaiser, W.

M. Maier, W. Kaiser, and J. A. Giordmaine, "Backward stimulated Raman scattering," Phys. Rev. 177, 580-599 (1969).
[CrossRef]

Kanefsky, M.

R. Chu, M. Kanefsky, and J. Falk, "Numerical study of transient stimulated Brillouin scattering," J. Appl. Phys. 71, 4653-4658 (1992).
[CrossRef]

Kapteyn, H. C.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Kilin, S. Ya.

R. G. Zaporozhchenko, S. Ya. Kilin, V. G. Bespalov, and D. I. Stasel'ko, "Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium," Opt. Spectrosc. 86, 632-639 (1999).

Kozlov, S. A.

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

Krylov, V. N.

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

Kulkov, A. M.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Maier, M.

M. Maier, W. Kaiser, and J. A. Giordmaine, "Backward stimulated Raman scattering," Phys. Rev. 177, 580-599 (1969).
[CrossRef]

Makarov , N. S.

N. S. Makarov and V. G. Bespalov, "Backward and forward quasi-phase-matched multiwave SRS in nonlinear periodical structures," in Nonresonant Laser-Matter Interaction (NLMI-II), M. N. Libenson, ed., Proc. SPIE 5506, 87-94 (2004).
[CrossRef]

N. S. Makarov and V. G. Bespalov, "Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering," Opt. Commun. 203, 413-420 (2002).
[CrossRef]

Mangir, M. S.

Matsuo, S.

Mikhailov, V. N.

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

Minck, R. W.

R. W. Minck, R. W. Terhune, and W. G. Rado, "Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H2,D2 and CH4," Appl. Phys. Lett. 3, 181-184 (1963).
[CrossRef]

Misawa, H.

Murnane, M. M.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Osiko, O. O.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Ottusch, J. J.

Oukrainski, A. O.

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

Paisner, J. A.

A. P. Hickman, J. A. Paisner, and W. K. Bischel, "Theory of multiwave propagation and frequency conversion in a Raman medium," Phys. Rev. A 33, 1788-1797 (1986).
[CrossRef] [PubMed]

Paperni, S. B.

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

Parameswaran, K. R.

Parfenov, V. A.

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

Paul, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Rado, W. G.

R. W. Minck, R. W. Terhune, and W. G. Rado, "Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H2,D2 and CH4," Appl. Phys. Lett. 3, 181-184 (1963).
[CrossRef]

Rockwell, D. A.

Sazonov, S. V.

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

Serebryakov, V. A.

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

Shpolyanskiy, Yu. A.

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

Staselko, D. I.

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

V. G. Bespalov, D. I. Staselko, and A. M. Dukhovnyi, "The study of radiation coherence at SRS in compressed hydrogen," Sov. Tech. Phys. Lett. 5, 518 (1979).

Stasel'ko, D. I.

R. G. Zaporozhchenko, S. Ya. Kilin, V. G. Bespalov, and D. I. Stasel'ko, "Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium," Opt. Spectrosc. 86, 632-639 (1999).

Sun, H.-B.

Taranuhin, V. D.

Yu. A. Ilynsky and V. D. Taranuhin, "About optical Stark effect at stimulated Raman scattering in gases," Quantum Electron. 1, 1500-1506 (1974).

Terhune, R. W.

R. W. Minck, R. W. Terhune, and W. G. Rado, "Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H2,D2 and CH4," Appl. Phys. Lett. 3, 181-184 (1963).
[CrossRef]

Tobey, R.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Urschel, R.

Voitsekhovskii, V. N.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Wagner, N.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Wallenstein, R.

Xu, Y.

Yakobson, V. E.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Ye, J.-Y.

Zaporozhchenko, R. G.

R. G. Zaporozhchenko, S. Ya. Kilin, V. G. Bespalov, and D. I. Stasel'ko, "Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium," Opt. Spectrosc. 86, 632-639 (1999).

Zverev, P. G.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Appl. Phys. Lett.

R. W. Minck, R. W. Terhune, and W. G. Rado, "Laser-stimulated Raman effect and resonant four-photon interactions in gaseous H2,D2 and CH4," Appl. Phys. Lett. 3, 181-184 (1963).
[CrossRef]

J. Appl. Phys.

R. Chu, M. Kanefsky, and J. Falk, "Numerical study of transient stimulated Brillouin scattering," J. Appl. Phys. 71, 4653-4658 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

N. S. Makarov and V. G. Bespalov, "Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering," Opt. Commun. 203, 413-420 (2002).
[CrossRef]

Opt. Lett.

Opt. Mater.

P. G. Zverev, T. T. Basiev, O. O. Osiko, A. M. Kulkov, V. N. Voitsekhovskii, and V. E. Yakobson, "Physical, chemical and optical properties of barium nitrate Raman crystal," Opt. Mater. 11, 315-334 (1999).
[CrossRef]

Opt. Spectrosc.

R. G. Zaporozhchenko, S. Ya. Kilin, V. G. Bespalov, and D. I. Stasel'ko, "Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium," Opt. Spectrosc. 86, 632-639 (1999).

V. G. Bespalov, V. N. Krylov, V. N. Mikhailov, V. A. Parfenov, and D. I. Staselko, "Generation of tunable radiation with high spectral brightness on the basis of oscillatory and rotary SRS in gases," Opt. Spectrosc. 70, 332-336 (1991).

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

M. Maier, W. Kaiser, and J. A. Giordmaine, "Backward stimulated Raman scattering," Phys. Rev. 177, 580-599 (1969).
[CrossRef]

Phys. Rev. A

A. P. Hickman, J. A. Paisner, and W. K. Bischel, "Theory of multiwave propagation and frequency conversion in a Raman medium," Phys. Rev. A 33, 1788-1797 (1986).
[CrossRef] [PubMed]

Phys. Vib.

S. A. Kozlov, A. O. Oukrainski, Yu. A. Shpolyanskiy, V. G. Bespalov, and S. V. Sazonov, "Spectral evolution of propagating extremely short pulses," Phys. Vib. 7, 19-27 (1999).

Proc. SPIE

N. S. Makarov and V. G. Bespalov, "Backward and forward quasi-phase-matched multiwave SRS in nonlinear periodical structures," in Nonresonant Laser-Matter Interaction (NLMI-II), M. N. Libenson, ed., Proc. SPIE 5506, 87-94 (2004).
[CrossRef]

Quantum Electron.

R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, and V. A. Serebryakov, "About the role of parametric effects at high-order SRS components generation in gases," Quantum Electron. 9, 56-60 (1982).

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Science

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, I. P. Christov, D. T. Attwood, E. Gullikson, A. Aquila, M. M. Murnane, and H. C. Kapteyn, "Generation of coherent soft x-rays in the water window using quasi phase-matched harmonic generation," Science 302, 95-98 (2003).
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Figures (11)

Fig. 1
Fig. 1

Illustration of optimal layer lengths for maximization of anti-Stokes generation efficiency. The example here is for the fifth active and passive layers in hydrogen. The black curve corresponds to anti-Stokes efficiency at the beginning of the sixth active layer, and the gray curve corresponds to anti-Stokes efficiency at the end of the fifth active layer (without the fifth passive layer). (a) Zoomed changes of efficiency after the passive layer and (b) efficiency in the active and passive layers.

Fig. 2
Fig. 2

Comparison of anti-Stokes intensity growth for a QPM condition, phase matching, and simple focusing in compressed hydrogen (white layers, active; gray layers, passive) 1, QPM (Δ=3.84 rad/cm); 2, simple focusing in compressed hydrogen (Δ=3.84 rad/cm); 3, phase matching (Δ=0.025 rad/cm).

Fig. 3
Fig. 3

Influence of the dispersion of the steady-state Raman gain coefficient on multifrequency SRS in hydrogen. (a) Results without the dispersion and (b) results with the dispersion. 1, pump; 2, first Stokes; 3, first anti-Stokes; 4, second Stokes. The plots are analogous to barium nitrate.

Fig. 4
Fig. 4

Dependencies of the lengths of (a) active and (b) passive layers of an optimal layered structure, providing the effective generation of quasi-phase-matched anti-Stokes SRS radiation in hydrogen (I0+=0.2 GW/cm2, I-1+=0.01 GW/cm2) on the layer’s ordinal number (the comparison of a unidirectional assumption with a bidirectional one). The gray curves correspond to a forward SRS approximation and the black curves correspond to a simultaneous forward and backward SRS.

Fig. 5
Fig. 5

Dependence of the optimum ratio of the input Stokes intensity to the input pump intensity on the steady-state Raman gain coefficient.

Fig. 6
Fig. 6

Dependence of the critical pump wave intensity on wave mismatching and the steady-state Raman gain coefficient.

Fig. 7
Fig. 7

Diffraction influence on anti-Stokes SRS generation efficiency: (a) hydrogen and (b) barium nitrate.

Fig. 8
Fig. 8

Influence of beam focusing on anti-Stokes SRS generation efficiency: (a) hydrogen and (b) barium nitrate. Positive values of dL correspond to the case of the beam-waist position in front of the medium, and negative values of dL correspond to the case of the beam-waist position within and behind the medium.

Fig. 9
Fig. 9

Influence of the pump (a) intensity and (b) duration on anti-Stokes generation efficiency.

Fig. 10
Fig. 10

Influence of the (a) Stokes seed intensity and (b) duration of the anti-Stokes generation efficiency.

Fig. 11
Fig. 11

Influence of the pump wavelength on anti-Stokes generation efficiency in a fixed QPM structure.

Equations (38)

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2z2+2x2+2y2-1c2 2t2ε(z, x, y, t)-μ0 2PLNt2
=μ0 2PNLt2,
ε(z, x, y, t)=12 jEj+ exp[i(ωjt-kj+z)]+jEj- exp[i(ωjt-kj-z)]+c.c.
kj-=-kj+=-ωjn(ωj)c,
PLN=12 jPLN+j exp[i(ωjt-kj+z)]+12 jPLN-j exp[i(ωjt-kj-z)]+c.c.,
1c2Ej±+μ0PLN±j=n2(ωj)c2Ej±,
2z2+2x2+2y2-1c2 2t2ε(z, x, y, t)-μ0 2PLNt2c.c.+j exp[i(ωjt-kj+z)]×-ikj+z+n(ωj)c t+12 2x2+2y2Ej++j exp[i(ωjt-kj-z)]-ikj-z-n(ωj)c t+12 2x2+2y2Ej-.
PNL=ε0χ(3)Qε;2Qt2+2T2 Qt+ων2Q=γνε2,
PNLRES=12 jPjNR++12 jPjNR-+c.c.,
Q=12q exp[i(ωνt-kνz)]+c.c.,
kν=k0+-k-1+,
PjNR+=ε0χ(3)2[Ej+1+q* exp(izΔj+11)+Ej-1+q exp(-izΔj1)]exp[i(ωjt-kj+z)]+ε0χ(3)2[Ej+1-q* exp(izΔj+12)+Ej-1-q exp(-izΔj3)]exp[i(ωjt-kj+z)],
PjNR-=ε0χ(3)2[Ej+1+q* exp(izΔj+13)+Ej-1+q exp(-izΔj2)]exp[i(ωjt-kj-z)]+ε0χ(3)2[Ej+1-q* exp(izΔj+14)+Ej-1-q exp(-izΔj4)]exp[i(ωjt-kj-z)],
Δj+11=kj+1+-kj+-kνΔj+12=kj+1--kj+-kνΔj+13=kj+1+-kj--kνΔj+14=kj+1--kj--kν 
Δ11=Δ.
qt 1+1iωνT2exp[i(ωνt-kνz)]+qT2 
×exp[i(ωνt-kνz)]=γνε2iων.
z+n(ωj)c t+i2kj+ 2x2+2y2Ej+
=kj+χ(3)4n(ωj)2iEj+1+q* exp(izΔj+11)+kj+χ(3)4n(ωj)2i[Ej+1-q* exp(izΔj+12)
+Ej-1-q exp(-izΔj3)+Ej-1+q exp(-izΔj1)]
-z+n(ωj)c t+i2kj+ 2x2+2y2Ej-
=kj+χ(3)4n(ωj)2iEj+1-q* exp(izΔj+14)+kj+χ(3)4n(ωj)2j[Ej+1+q* exp(izΔj+13)
+Ej-1+q exp(-izΔj2)+Ej-1-q exp(-izΔj4)],
qt 1+1iωνT2=-qT2+γν4iων jEj+Ej-1+* exp(izΔj1)+γν4iων jEj-Ej-1+* exp(izΔj2)+jEj+Ej-1-* exp(izΔj3)+jEj-Ej-1-* exp(izΔj4).
g0+=ω-1χ(3)T2γν4n2ε0c2ων;E(new)=ε0cn21/2E,
q(new)=q(old) 2ωνε0cnT2γν,
z+n(ωj)c t+i2kj+ 2x2+2y2Ej+=gj+ωj2ω-1i[Ej+1+q* exp(izΔj+11)+Ej-1+q exp(-izΔj1)]+gj+ωj2ω-1i[Ej+1-q* exp(izΔj+12)+Ej-1-q exp(-izΔj3)]
-z+n(ωj)c t+i2kj+ 2x2+2y2Ej-=gj-ωj2ω-1i[Ej+1-q* exp(izΔj+14)+Ej-1-q exp(-izΔj4)]+gj-ωj2ω-1i[Ej+1+q* exp(izΔj+13)+Ej-1+q exp(izΔj2)],
qt=1iT2 -iq+jEj+Ej-1+* exp(izΔj1)+jEj-Ej-1-* exp(izΔj4)+jEj-Ej-1+* exp(izΔj2)+jEj+Ej-1-* exp(izΔj3).
z+n(ω0)c tE0=ig2 ω0ω-1(q+E-1++q-E-1-),
z+n(ω-1)c tE-1+=ig2q+*E0,
-z+n(ω-1)c tE-1-=ig2q-*E0,
q±t=1T2(-q±+iE-1±*E0).
q(t+Δt, z)=ΔtiT2 -iq(t, z)+jEj+(t, z)Ej-1+*(t, z)exp(izΔj1)+jEj-(t, z)Ej-1-*(t, z)exp(izΔj4)+ΔtiT2 jEj-(t, z)Ej-1+*(t, z)×exp(izΔj2)+jEj+(t, z)×Ej-1-*(t, z)exp(izΔj3)+q(t, z),
Ej±(t+Δt, z)=C2jEj±(t, z)+C3j gj±ωj2ω-1iq*(t, z)×[Ej+1-(t, z)exp(izΔj+12,4)+Ej+1+(t, z)exp(izΔj+11,3)]+C3j gj±ωj2ω-1iq(t, z)×[Ej-1+(t, z)exp(-izΔj1,2)+Ej-1-(t, z)exp(-izΔj3,4)]+C1jEj±(t+Δt, z±Δz),
C1j=cΔtcΔt+n(ωj)Δz,C2j=n(ωj)ΔzcΔt+n(ωj)Δz,C3j=cΔtΔzcΔt+n(ωj)Δz.
gj±=A±λjB±-1λj+122,j<0;g0±=g1±=g-1±;gj±=A±λjB±-1λj-122,j>1;g0+=g,
dL=Fπ2R4π2R4+F2λ2;r0=FλR(π2R4+F2λ2)1/2.

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