Abstract

We obtain theoretically the phonon-polariton spectrum in nonlinear dielectric medium with the third-order Kerr-type nonlinearity. We investigate the dependence of number of the polariton spectrum branches on the intensity of electromagnetic field and demonstrate that the appearance of new branches located in the polariton spectrum gap is caused by the influence of dispersion of the third-order dielectric susceptibility at the intensive electromagnetic field in the medium. The modulation instability of new spectrum branch waves leads to the appearance of the cnoidal waves or solitons. These new nonlinear waves one can use for designing optical devices such as the nonlinear optical filter converter.

© 2013 Optical Society of America

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  1. K. B. Tolpygo, “Physical properties of the salt lattice constructed from deforming ions,” JETP 20, 497–509 (1950) (in Russian).
  2. K. Huang, “On the interaction between the radiation field and ionic crystals,” Proc Roy. Soc. A 208, 352–365 (1951).
    [CrossRef]
  3. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer, 1984).
  4. E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier, 2004).
  5. D. N. Klyshko, Quantum and Nonlinear Optics (Nauka, 1980) (in Russian).
  6. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  7. I. V. Dzedolik, Polaritons in Optical Fibers and Dielectric Resonators (DIP, 2007) (in Russian).
  8. S. Baher and M. G. Cottam, “Theory of nonlinear s-polarized phonon-polaritons in multilayered structures,” J. Sci. Islamic Repub. Iran 15, 171–177 (2004).
  9. H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
    [CrossRef]
  10. Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
    [CrossRef]
  11. I. V. Dzedolik, “Period variation of polariton waves in optical fiber,” J. Opt. A 11, 094012 (2009).
    [CrossRef]
  12. I. V. Dzedolik and S. N. Lapayeva, “Mass of polaritons in different dielectric media,” J. Opt. 13, 015204 (2011).
    [CrossRef]
  13. I. V. Dzedolik and O. S. Karakchieva, “Polaritons in nonlinear medium: generation, propagation, and interaction,” in 2011 International Nonlinear Photonics Workshop (IEEE, 2011).
  14. G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
    [CrossRef]
  15. N. A. Kudryashov, P. N. Ryabov, and D. I. Sinelshchikov, “Nonlinear waves in media with fifth order dispersion,” Opt. Lett. A 375, 2051–2055 (2011).
    [CrossRef]
  16. E. Gaizauskas, A. Savickas, and K. Staliunas, “Radiation from band-gap solitons,” Opt. Commun. 285, 2166–2170 (2012).
    [CrossRef]
  17. A. Scott, Active and Nonlinear Wave Propagation in Electronics (Wiley, 1970).
  18. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  19. R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, 1969).

2012 (2)

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

E. Gaizauskas, A. Savickas, and K. Staliunas, “Radiation from band-gap solitons,” Opt. Commun. 285, 2166–2170 (2012).
[CrossRef]

2011 (2)

N. A. Kudryashov, P. N. Ryabov, and D. I. Sinelshchikov, “Nonlinear waves in media with fifth order dispersion,” Opt. Lett. A 375, 2051–2055 (2011).
[CrossRef]

I. V. Dzedolik and S. N. Lapayeva, “Mass of polaritons in different dielectric media,” J. Opt. 13, 015204 (2011).
[CrossRef]

2009 (3)

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

I. V. Dzedolik, “Period variation of polariton waves in optical fiber,” J. Opt. A 11, 094012 (2009).
[CrossRef]

2004 (1)

S. Baher and M. G. Cottam, “Theory of nonlinear s-polarized phonon-polaritons in multilayered structures,” J. Sci. Islamic Repub. Iran 15, 171–177 (2004).

1951 (1)

K. Huang, “On the interaction between the radiation field and ionic crystals,” Proc Roy. Soc. A 208, 352–365 (1951).
[CrossRef]

1950 (1)

K. B. Tolpygo, “Physical properties of the salt lattice constructed from deforming ions,” JETP 20, 497–509 (1950) (in Russian).

Agranovich, V. M.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer, 1984).

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Albuquerque, E. L.

E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier, 2004).

Baher, S.

S. Baher and M. G. Cottam, “Theory of nonlinear s-polarized phonon-polaritons in multilayered structures,” J. Sci. Islamic Repub. Iran 15, 171–177 (2004).

Buchler, B. C.

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

Campbell, G.

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

Cottam, M. G.

S. Baher and M. G. Cottam, “Theory of nonlinear s-polarized phonon-polaritons in multilayered structures,” J. Sci. Islamic Repub. Iran 15, 171–177 (2004).

E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier, 2004).

Dzedolik, I. V.

I. V. Dzedolik and S. N. Lapayeva, “Mass of polaritons in different dielectric media,” J. Opt. 13, 015204 (2011).
[CrossRef]

I. V. Dzedolik, “Period variation of polariton waves in optical fiber,” J. Opt. A 11, 094012 (2009).
[CrossRef]

I. V. Dzedolik and O. S. Karakchieva, “Polaritons in nonlinear medium: generation, propagation, and interaction,” in 2011 International Nonlinear Photonics Workshop (IEEE, 2011).

I. V. Dzedolik, Polaritons in Optical Fibers and Dielectric Resonators (DIP, 2007) (in Russian).

Gaizauskas, E.

E. Gaizauskas, A. Savickas, and K. Staliunas, “Radiation from band-gap solitons,” Opt. Commun. 285, 2166–2170 (2012).
[CrossRef]

Ginzburg, V. L.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer, 1984).

Hosseini, M.

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

Huang, C.-P.

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

Huang, K.

K. Huang, “On the interaction between the radiation field and ionic crystals,” Proc Roy. Soc. A 208, 352–365 (1951).
[CrossRef]

Inoue, H.

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Karakchieva, O. S.

I. V. Dzedolik and O. S. Karakchieva, “Polaritons in nonlinear medium: generation, propagation, and interaction,” in 2011 International Nonlinear Photonics Workshop (IEEE, 2011).

Katayma, K.

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Klyshko, D. N.

D. N. Klyshko, Quantum and Nonlinear Optics (Nauka, 1980) (in Russian).

Kudryashov, N. A.

N. A. Kudryashov, P. N. Ryabov, and D. I. Sinelshchikov, “Nonlinear waves in media with fifth order dispersion,” Opt. Lett. A 375, 2051–2055 (2011).
[CrossRef]

Lam, P. K.

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

Lapayeva, S. N.

I. V. Dzedolik and S. N. Lapayeva, “Mass of polaritons in different dielectric media,” J. Opt. 13, 015204 (2011).
[CrossRef]

Nelson, K.

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Pantell, R. H.

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, 1969).

Puthoff, H. E.

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, 1969).

Qi, Z.

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

Ryabov, P. N.

N. A. Kudryashov, P. N. Ryabov, and D. I. Sinelshchikov, “Nonlinear waves in media with fifth order dispersion,” Opt. Lett. A 375, 2051–2055 (2011).
[CrossRef]

Savickas, A.

E. Gaizauskas, A. Savickas, and K. Staliunas, “Radiation from band-gap solitons,” Opt. Commun. 285, 2166–2170 (2012).
[CrossRef]

Scott, A.

A. Scott, Active and Nonlinear Wave Propagation in Electronics (Wiley, 1970).

Shen, Q.

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Shen, Z.-Q.

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

Sinelshchikov, D. I.

N. A. Kudryashov, P. N. Ryabov, and D. I. Sinelshchikov, “Nonlinear waves in media with fifth order dispersion,” Opt. Lett. A 375, 2051–2055 (2011).
[CrossRef]

Sparkes, B. M.

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

Staliunas, K.

E. Gaizauskas, A. Savickas, and K. Staliunas, “Radiation from band-gap solitons,” Opt. Commun. 285, 2166–2170 (2012).
[CrossRef]

Tolpygo, K. B.

K. B. Tolpygo, “Physical properties of the salt lattice constructed from deforming ions,” JETP 20, 497–509 (1950) (in Russian).

Toyoda, T.

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Zhu, S.-N.

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

Zhu, Y.-Y.

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

J. Appl. Phys. (2)

H. Inoue, K. Katayma, Q. Shen, T. Toyoda, and K. Nelson, “Terahertz reflection response measurement using a phonon-polariton wave,” J. Appl. Phys. 105, 054902 (2009).
[CrossRef]

Z. Qi, Z.-Q. Shen, C.-P. Huang, S.-N. Zhu, and Y.-Y. Zhu, “Phonon-polaritons in a nonaxial aligned piezoelectric superlattice,” J. Appl. Phys. 105, 074102 (2009).
[CrossRef]

J. Opt. (1)

I. V. Dzedolik and S. N. Lapayeva, “Mass of polaritons in different dielectric media,” J. Opt. 13, 015204 (2011).
[CrossRef]

J. Opt. A (1)

I. V. Dzedolik, “Period variation of polariton waves in optical fiber,” J. Opt. A 11, 094012 (2009).
[CrossRef]

J. Sci. Islamic Repub. Iran (1)

S. Baher and M. G. Cottam, “Theory of nonlinear s-polarized phonon-polaritons in multilayered structures,” J. Sci. Islamic Repub. Iran 15, 171–177 (2004).

JETP (1)

K. B. Tolpygo, “Physical properties of the salt lattice constructed from deforming ions,” JETP 20, 497–509 (1950) (in Russian).

New J. Phys. (1)

G. Campbell, M. Hosseini, B. M. Sparkes, P. K. Lam, and B. C. Buchler, “Time- and frequency-domain polariton interference,” New J. Phys. 14, 033022 (2012).
[CrossRef]

Opt. Commun. (1)

E. Gaizauskas, A. Savickas, and K. Staliunas, “Radiation from band-gap solitons,” Opt. Commun. 285, 2166–2170 (2012).
[CrossRef]

Opt. Lett. A (1)

N. A. Kudryashov, P. N. Ryabov, and D. I. Sinelshchikov, “Nonlinear waves in media with fifth order dispersion,” Opt. Lett. A 375, 2051–2055 (2011).
[CrossRef]

Proc Roy. Soc. A (1)

K. Huang, “On the interaction between the radiation field and ionic crystals,” Proc Roy. Soc. A 208, 352–365 (1951).
[CrossRef]

Other (9)

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer, 1984).

E. L. Albuquerque and M. G. Cottam, Polaritons in Periodic and Quasiperiodic Structures (Elsevier, 2004).

D. N. Klyshko, Quantum and Nonlinear Optics (Nauka, 1980) (in Russian).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

I. V. Dzedolik, Polaritons in Optical Fibers and Dielectric Resonators (DIP, 2007) (in Russian).

I. V. Dzedolik and O. S. Karakchieva, “Polaritons in nonlinear medium: generation, propagation, and interaction,” in 2011 International Nonlinear Photonics Workshop (IEEE, 2011).

A. Scott, Active and Nonlinear Wave Propagation in Electronics (Wiley, 1970).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, 1969).

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Figures (3)

Fig. 1.
Fig. 1.

Polariton spectra in the nonlinear medium with the dispersion of the third-order susceptibility χ3: (a) at 4πχ31Ea20 and (b) 4πχ31Ea2=105; Γ=0. Here ω¯=ω/Ω and k¯=ck/Ω are dimensionless. The solid lines are the branches of the polariton spectrum; the dashed horizontal lines are the edges of the polariton spectrum gaps.

Fig. 2.
Fig. 2.

Dependence of the normalized perturbing frequency Ω¯j=Ωj/Ω on the real part of normalized perturbing wavevector K¯=cRe(K)/Ω.

Fig. 3.
Fig. 3.

Dependence of the real part ReΩj and the imaginary part ImΩj of the perturbing wave frequency on the normalized electromagnetic field density I¯=4πχ31Ea2 at K¯=1.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

meffd2Rdt2+meffΓdRdt+RUR=eeff(E+1cdRdt×B),
md2rdt2+mΓdrdt+rUr=e(E+1cdrdt×B),
×B=c1(E˙+4πP˙),×E=c1B˙,
P=χ1Eaexp(iωt)+χ20EaEa+χ22EaEaexp(i2ωt)+χ31Ea2Eaexp(iωt)+χ33Ea2Eaexp(i3ωt),
(k2c2εω2)Ea=k(kEa).
k2c2ω2[1+4πχ1(ω)+4πχ31(ω)Ea2]=0.
2Ez2ε1c22Et24πχ31c22|E|2Et2=0,
(2z2ε˜c22t2+ω2ε˜c2k2)u2Ea(kz+ωεc2t)w=0,2(kz+ωε˜c2t)u+Ea(2z2εc22t2)w=0,
(Ω2ε˜c2K2+ω2ε˜c2k2)(Ω2εc2K2)4(Ωωε˜c2kK)(Ωωεc2kK)=0.
Ω4a1Ω2+a2Ω+a3=0,
2ez2+ε1ω2c2e+4πχ31ω2c2|e|2eε1c2(2et2i2ωet)4πχ31c2(e2|e|2t2+2|e|2tet+|e|22et2i2ωe|e|2ti2ω|e|2et)=0.
2ez2+ε¯e+χ¯|e|2e=0,
e=Bcn{K(k˜)[χ¯(α2/4+C)1/2]1/2z,k˜},
e=|α|sch(ε¯z).

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