Abstract

Based on the dressed state formalism, we obtain the adiabatic criterion of the sum frequency conversion. We show that this constraint restricts the energy conversion between the two dressed fields, which are superpositions of the signal field and the sum frequency field. We also show that the evolution of the populations of the dressed fields, which in turn describes the conversion of light photons from the seed frequency to the sum frequency during propagation through the nonlinear crystal. Take the quasiphased matched (QPM) scheme as an example, we calculate the expected bandwidth of the frequency conversion process, and its dependence on the length of the crystal. We demonstrate that the evolutionary patterns of the sum frequency field’s energy are similar to the Fresnel diffraction of a light field. We finally show that the expected bandwidth can be also deduced from the evolution of the adiabaticity of the dressed fileds.

© 2010 OSA

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  1. M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
    [CrossRef] [PubMed]
  2. M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30(1), 34–35 (1994).
    [CrossRef]
  3. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
    [CrossRef]
  4. H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
    [CrossRef] [PubMed]
  5. M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
    [CrossRef] [PubMed]
  6. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22(17), 1341–1343 (1997).
    [CrossRef] [PubMed]
  7. G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping,” J. Opt. Soc. Am. B 17(2), 304–318 (2000).
    [CrossRef]
  8. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007).
    [CrossRef]
  9. G. Imeshev, M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B 18(4), 534–539 (2001).
    [CrossRef]
  10. M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Optical parametric amplifiers using chirped quasi-phasematching gratings. I. Practical design formulas,” J. Opt. Soc. Am. B 25(4), 463–480 (2008).
    [CrossRef]
  11. L. D. Allen, and J. H. Eberly, Optical Resonance and Two Level Atoms (Wiley, New York, 1975)
  12. H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion,” Phys. Rev. A 78(6), 063821 (2008).
    [CrossRef]
  13. H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 12731–12740 (2009).
    [CrossRef] [PubMed]
  14. M. Shapiro, and P. Brumer, Principles of the Quantum Control of Molecular Processes (Wiley, New York, 2003)
  15. L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
    [CrossRef]
  16. A. Massiah, Quantum Mechanics (North Holland, Amsterdam, 1962), Vol. II.
  17. J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72(1), 56–59 (1994).
    [CrossRef] [PubMed]
  18. J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [CrossRef]

2009 (1)

2008 (3)

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Optical parametric amplifiers using chirped quasi-phasematching gratings. I. Practical design formulas,” J. Opt. Soc. Am. B 25(4), 463–480 (2008).
[CrossRef]

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion,” Phys. Rev. A 78(6), 063821 (2008).
[CrossRef]

2007 (1)

D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007).
[CrossRef]

2005 (1)

H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
[CrossRef] [PubMed]

2004 (1)

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

2002 (1)

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

2001 (1)

2000 (1)

1997 (1)

1994 (3)

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72(1), 56–59 (1994).
[CrossRef] [PubMed]

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30(1), 34–35 (1994).
[CrossRef]

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
[CrossRef]

1962 (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Afeyan, B.

Arbore, M. A.

Arie, A.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 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. A 78(6), 063821 (2008).
[CrossRef]

Armstrong, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Bergmann, K.

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

Bloembergen, N.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bortz, M. L.

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30(1), 34–35 (1994).
[CrossRef]

Carrasco, S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Charbonneau-Lefort, M.

Chou, M. H.

Ducuing, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Eberly, J. H.

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72(1), 56–59 (1994).
[CrossRef] [PubMed]

Fejer, M.

Fejer, M. M.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

M. Charbonneau-Lefort, B. Afeyan, and M. M. Fejer, “Optical parametric amplifiers using chirped quasi-phasematching gratings. I. Practical design formulas,” J. Opt. Soc. Am. B 25(4), 463–480 (2008).
[CrossRef]

D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007).
[CrossRef]

G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping,” J. Opt. Soc. Am. B 17(2), 304–318 (2000).
[CrossRef]

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22(17), 1341–1343 (1997).
[CrossRef] [PubMed]

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30(1), 34–35 (1994).
[CrossRef]

Fermann, M.

Fujimura, M.

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30(1), 34–35 (1994).
[CrossRef]

Galvanauskas, A.

Guo, H.

H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
[CrossRef] [PubMed]

Haïdar, R.

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Haq, H. R.

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72(1), 56–59 (1994).
[CrossRef] [PubMed]

Harter, D.

Hum, D. S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007).
[CrossRef]

Imeshev, G.

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
[CrossRef]

Kupecek, Ph.

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Lemasson, Ph.

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
[CrossRef]

Nasr, M. B.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Oron, D.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 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. A 78(6), 063821 (2008).
[CrossRef]

Pershan, P.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Pons, M. L.

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72(1), 56–59 (1994).
[CrossRef] [PubMed]

Prabhudesai, V.

Qin, Y.

H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
[CrossRef] [PubMed]

Rickes, T.

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

Rosencher, E.

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Saleh, B. E. A.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
[CrossRef]

Sergienko, A. V.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Shore, B. W.

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

Silberberg, Y.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 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. A 78(6), 063821 (2008).
[CrossRef]

Suchowski, H.

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17(15), 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. A 78(6), 063821 (2008).
[CrossRef]

Tang, S. H.

H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
[CrossRef] [PubMed]

Teich, M. C.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Torner, L.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Torres, J. P.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

Vitanov, N. V.

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
[CrossRef]

Yatsenko, L. P.

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

Zhu, Y. Y.

H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
[CrossRef] [PubMed]

C. R. Phys. (1)

D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007).
[CrossRef]

Electron. Lett. (1)

M. L. Bortz, M. Fujimura, and M. M. Fejer, “Increased acceptance bandwidth for quasi-phasematched second harmonic generation in LiNbO3 waveguides,” Electron. Lett. 30(1), 34–35 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phasematched second-harmonic generation,” IEEE J. Quantum Electron. 30(7), 1596–1604 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nature (1)

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Opt. Commun. (1)

L. P. Yatsenko, N. V. Vitanov, B. W. Shore, T. Rickes, and K. Bergmann, “Creation of coherent superpositions using Stark-chirped rapid adiabatic passage,” Opt. Commun. 204(1-6), 413–423 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Phys. Rev. A (1)

H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical Representation of Sum Frequency Generation and Adiabatic Frequency Conversion,” Phys. Rev. A 78(6), 063821 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

H. Guo, S. H. Tang, Y. Qin, and Y. Y. Zhu, “Nonlinear frequency conversion with quasi-phase-mismatch effect,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(6), 066615 (2005).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100(18), 183601 (2008).
[CrossRef] [PubMed]

J. H. Eberly, M. L. Pons, and H. R. Haq, “Dressed-field pulses in an absorbing medium,” Phys. Rev. Lett. 72(1), 56–59 (1994).
[CrossRef] [PubMed]

Other (3)

A. Massiah, Quantum Mechanics (North Holland, Amsterdam, 1962), Vol. II.

M. Shapiro, and P. Brumer, Principles of the Quantum Control of Molecular Processes (Wiley, New York, 2003)

L. D. Allen, and J. H. Eberly, Optical Resonance and Two Level Atoms (Wiley, New York, 1975)

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Figures (5)

Fig. 1
Fig. 1

| 2 θ ' ( z ) / ( λ 1 λ 3 ) | varies with the propagation distance z. The two dotted lines divide the z axis into two regions, with one being called as diabatic region (I) and another one as adiabatic region ( II ). The dashed line corresponds to the position z d of the energy conversion between the two dressed fields. The crystal’s length is 9 m m , and it’s central point corresponds to the origin z = 0 . The parameters are chosen as: | q | = 4 / mm , D g = 8 / m m 2 , Δ K 0 = 2 / m m , δ ν δ Ω = 2 /mm .

Fig. 2
Fig. 2

Numerical results for the energy conversion between he signal field and the sum frequency field. The solid line and dashed line correspond to the energy of the signal field and the sum frequency field, respectively. The two dotted lines devide the z axis into two regions, the diabatic region (I) and the diabatic region ( II ). The parameters are same as that shown in Fig. 1.

Fig. 3
Fig. 3

The relation between energy conversion of the two dressed fields and the diabatic process. (a) Numerical results for the energy evolution of the dressed fields. The solid line shows the energy evolution | B ˜ 1 | 2 , while the dashed line corresponds to | B ˜ 3 | 2 . (b) cos 2 [ θ ] , sin 2 [ θ ] and sin [ 2 θ ] are denoted with the solid line attached with △, ○and □ respectively. The two dotted lines divide the z axis into two regions, the diabatic region (I) and the diabatic region ( II ). The parameters are same as that shown in Fig. 1.

Fig. 4
Fig. 4

Numerical results for the intensity of the sum frequency field. The traces show the intensity of the sum frequency field as a function of the frequency variation δ ν δ Ω . Each panel corresponds to a different length of the crystal, l = 0.5 m m , 2.5 m m , and 6 m m . The parameters are chosen as: | q | = 2 .5 / mm , D g = 8 / m m 2 , Δ K 0 = 2 / m m .

Fig. 5
Fig. 5

The adiabatic and diabatic process during the light propagation accompanied by the energy transfer. (a) The solid line corresponds to the energy evolution of the sum frequency field | A 3 | 2 with δ ν δ Ω , while the dashed line denotes that of the signal field | A 1 | 2 with δ ν δ Ω . (b) The variation for | 2 θ ' / ( λ 1 λ 3 ) | with δ ν δ Ω . (c) The energy transfer between the two dressed fields with δ ν δ Ω . The parameters are chosen as: | q | = 2 .5 / mm , D g = 8 / m m 2 , Δ K 0 = 2 / m m , l = 8 m m .

Equations (9)

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{ d A 1 d z = i q A 3 e i Δ k z d A 3 d z = i q * A 1 e + i Δ k z ,
i d d z B ˜ ( z ) = G a B ˜ ( z ) ,
| θ ' | ( λ 1 λ 3 ) / 2 ,
i d d z ( B ˜ 1 ( z ) B ˜ 3 ( z ) ) = ( λ 1 0 0 λ 3 ) ( B ˜ 1 ( z ) B ˜ 3 ( z ) ) .
{ A 1 ( z ) = A 10 e i Δ k z 2 [ cos ( ϕ ( z ) ) i Δ k 2 λ sin ( ϕ ( z ) ) ] A 3 ( z ) = i A 10 | q | λ e i Δ k z 2 sin ( ϕ ( z ) )
χ ( 2 ) ( ω ) = d m E x p [ i φ ( z ) ] .
| 2 θ ' ( z ) / ( λ 1 λ 3 ) | = | 4 | q | D g / [ 4 | q | 2 + Δ K ( z ) 2 ] 3 / 2 | 1.
{ | B ˜ 1 ( ω 1 , ω 3 , z ) | 2 = cos 2 θ | A 1 ( ω 1 , z ) | 2 + sin 2 θ | A 3 ( ω 3 , z ) | 2 1 2 sin 2 θ [ A 1 ( ω 1 , z ) A 3 * ( ω 3 , z ) e i Δ k z + A 1 * ( ω 1 , z ) A 3 ( ω 3 , z ) e i Δ k z ] | B ˜ 3 ( ω 1 , ω 3 , z ) | 2 = sin 2 θ | A 1 ( ω 1 , z ) | 2 + cos 2 θ | A 3 ( ω 3 , z ) | 2 + 1 2 sin 2 θ [ A 1 ( ω 1 , z ) A 3 * ( ω 3 , z ) e i Δ k z + A 1 * ( ω 1 , z ) A 3 ( ω 3 , z ) e i Δ k z ] ,
| A 1 ( ω 1 , z d ) | 2 + | A 3 ( ω 3 , z d ) | 2 = A 1 ( ω 1 , z d ) A 3 * ( ω 3 , z d ) + A 1 * ( ω 1 , z d ) A 3 ( ω 3 , z d ) .

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