Abstract

We predict the existence of a new type of spatiotemporal soliton (so-called light bullets) in two-dimensional self-induced-transparency media with refractive-index modulation in the direction transverse to that of pulse propagation. These self-localized guided modes are found in an approximate analytical form. Their existence and stability are confirmed by numerical simulations, and they may have advantageous properties for signal transmission.

© 2002 Optical Society of America

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  1. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15, 1282–1284 (1990).
    [CrossRef] [PubMed]
  2. K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275–3278 (1993).
    [CrossRef] [PubMed]
  3. D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
    [CrossRef]
  4. D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
    [CrossRef]
  5. A. Desyatnikov, A. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
    [CrossRef]
  6. B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
    [CrossRef]
  7. D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
    [CrossRef]
  8. H. He and P. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
    [CrossRef]
  9. K. V. Kheruntsyan and P. D. Drummond, “Three-dimensional quantum solitons with parametric coupling,” Phys. Rev. A 58, 2488–2499 (1998).
    [CrossRef]
  10. K. V. Kheruntsyan and P. D. Drummond, “Multidimensional parametric quantum solitons,” Phys. Rev. A 58, R2676–R2679 (1998).
    [CrossRef]
  11. D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
    [CrossRef]
  12. G. Gottwald, R. Grimshaw, and B. A. Malomed, “Stable two-dimensional parametric solitons in fluid systems,” Phys. Lett. A 248, 208–218 (1998).
    [CrossRef]
  13. M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
    [CrossRef] [PubMed]
  14. M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
    [CrossRef]
  15. X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
    [CrossRef]
  16. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
    [CrossRef]
  17. G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in a resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
    [CrossRef]
  18. A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
    [CrossRef]
  19. P. D. Drummond, “Formation and stability of vee simultons,” Opt. Commun. 49, 219–223 (1984).
    [CrossRef]
  20. A somewhat similar situation was considered by S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–328 (2000), who predicted that parabolic transverse modulation of the RI allows for stabilization of LBs in a Kerr medium.
    [CrossRef]
  21. M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
    [CrossRef] [PubMed]
  22. M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
    [CrossRef]
  23. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992).
  24. See, e.g., L. Levi, Applied Optics (Wiley, New York, 1980), Chap. 13.
  25. See the numerical scheme proposed in P. D. Drummond, “Central partial difference propagation algorithms,” Comput. Phys. Commun. 29, 211–225 (1983).
    [CrossRef]
  26. These bullets can be guided in the presence of a different refractive-index modulation given by n(x)=1−½C2 (−1+ ½ sech 2 Θ1 +½sech 2 Θ2 +tanh Θ1 tanh Θ2), with C, Θ1, and Θ2 as defined in Ref. 13.
  27. As an example of another type of 2D guided-LB mode, one can find a family of LBs that correspond to α=∞ in Eq. (2d). Their velocity, given by the expression v=α2 /(α2 +1), takes the maximum possible value, v=1. These solutions are obtained by substitution of a plane wave (in z) ansatz E (τ, z, x)=E (τ, x)exp (−ikz), P (τ, z, x)=P (τ, x)× exp (−ikz), and W(τ, z, x)=W(τ, x), with an arbitrary real constant k, into Eqs. (1). The equation for the field then becomes −iE xx +n2 E τ +ikE +i(1−n2)E −P =0, with the equations for P and W given by Eqs. (1b) and (1c). If the RI in the medium is modulated as n2 (x)=1−β2 [tanh 2 (βx)−sech 2 (βx)]+kβ, the LB solution to Eqs. (1) can be approximated by Eq. (2), with Θ(τ, z) replaced by τ+Θ0. Thus these solutions are localized in τ and x, but at a fixed τ they are not localized in z.
  28. A guided LB similar to that in Eq. (2) can be found in a 3D SIT medium embedded in a cylindrical waveguiding structure. The medium is described by Eqs. (1), with E xx → E rr +(1/r)E r, where r≡x2 +y2 is the transverse radial coordinate. Searching for an axisymmetric solution of these 3D equations, we arrive at an approximation of the same form as Eqs. (2) but with x replaced by r, and a corresponding cylindrical RI modulation:n2 (r)=1−ββ[1−2 sech 2 (βr)]−tanh (βr) r, for |βr|≪1. Comparison with results of simulations of the cylindrically symmetric 3D equations by use of the analytical approximation as an initial ansatz again shows good agreement (with a deviation of <2%). In practice, however, such 3D guided-LB and waveguiding structures are probably much harder to realize than their 2D counterparts.
  29. G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
    [CrossRef]
  30. See J. P. Dowling, H. Everitt, and E. Yablonovitch, “Photonic band-gap bibliography,” http://home.earthlink.net/~jpdowling/pbgbib.html.
  31. C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
    [CrossRef]
  32. R. E. Slusher, “Self-induced transparency, experiment,” in Progress in Optics, by E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 76–85.

2000

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

A somewhat similar situation was considered by S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–328 (2000), who predicted that parabolic transverse modulation of the RI allows for stabilization of LBs in a Kerr medium.
[CrossRef]

1999

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

1998

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
[CrossRef]

H. He and P. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

K. V. Kheruntsyan and P. D. Drummond, “Three-dimensional quantum solitons with parametric coupling,” Phys. Rev. A 58, 2488–2499 (1998).
[CrossRef]

K. V. Kheruntsyan and P. D. Drummond, “Multidimensional parametric quantum solitons,” Phys. Rev. A 58, R2676–R2679 (1998).
[CrossRef]

D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
[CrossRef]

G. Gottwald, R. Grimshaw, and B. A. Malomed, “Stable two-dimensional parametric solitons in fluid systems,” Phys. Lett. A 248, 208–218 (1998).
[CrossRef]

1997

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

1993

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275–3278 (1993).
[CrossRef] [PubMed]

1992

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
[CrossRef]

1990

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15, 1282–1284 (1990).
[CrossRef] [PubMed]

A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
[CrossRef]

1984

P. D. Drummond, “Formation and stability of vee simultons,” Opt. Commun. 49, 219–223 (1984).
[CrossRef]

1983

See the numerical scheme proposed in P. D. Drummond, “Central partial difference propagation algorithms,” Comput. Phys. Commun. 29, 211–225 (1983).
[CrossRef]

1971

G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in a resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
[CrossRef]

1967

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Agrawal, G. P.

A somewhat similar situation was considered by S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–328 (2000), who predicted that parabolic transverse modulation of the RI allows for stabilization of LBs in a Kerr medium.
[CrossRef]

Anderson, D.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Basharov, A. M.

A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
[CrossRef]

Berntson, A.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Blaauboer, M.

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

Boggs, B.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Desyatnikov, A.

A. Desyatnikov, A. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

Dörring, J.

D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

Drummond, P.

H. He and P. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Drummond, P. D.

K. V. Kheruntsyan and P. D. Drummond, “Three-dimensional quantum solitons with parametric coupling,” Phys. Rev. A 58, 2488–2499 (1998).
[CrossRef]

K. V. Kheruntsyan and P. D. Drummond, “Multidimensional parametric quantum solitons,” Phys. Rev. A 58, R2676–R2679 (1998).
[CrossRef]

P. D. Drummond, “Formation and stability of vee simultons,” Opt. Commun. 49, 219–223 (1984).
[CrossRef]

See the numerical scheme proposed in P. D. Drummond, “Central partial difference propagation algorithms,” Comput. Phys. Commun. 29, 211–225 (1983).
[CrossRef]

Elyutin, S. O.

A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
[CrossRef]

Firth, W. J.

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

Frantzeskakis, D. J.

D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
[CrossRef]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Gottwald, G.

G. Gottwald, R. Grimshaw, and B. A. Malomed, “Stable two-dimensional parametric solitons in fluid systems,” Phys. Lett. A 248, 208–218 (1998).
[CrossRef]

Greiner, C.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Grimshaw, R.

G. Gottwald, R. Grimshaw, and B. A. Malomed, “Stable two-dimensional parametric solitons in fluid systems,” Phys. Lett. A 248, 208–218 (1998).
[CrossRef]

Hahn, E. L.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Hayata, K.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275–3278 (1993).
[CrossRef] [PubMed]

He, H.

H. He and P. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Hizanidis, K.

D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
[CrossRef]

Jahnke, F.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Kheruntsyan, K. V.

K. V. Kheruntsyan and P. D. Drummond, “Multidimensional parametric quantum solitons,” Phys. Rev. A 58, R2676–R2679 (1998).
[CrossRef]

K. V. Kheruntsyan and P. D. Drummond, “Three-dimensional quantum solitons with parametric coupling,” Phys. Rev. A 58, 2488–2499 (1998).
[CrossRef]

Khitrova, G.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Kimura, Y.

M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
[CrossRef]

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

Kira, M.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Koch, S. W.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Koshiba, M.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275–3278 (1993).
[CrossRef] [PubMed]

Kubota, H.

M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
[CrossRef]

Kurizki, G.

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

Kurokawa, K.

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

Lamb, G. L.

G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in a resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
[CrossRef]

Lisak, M.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

Loftus, T.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Maimistov, A.

A. Desyatnikov, A. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

Maimistov, A. A.

A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
[CrossRef]

Malomed, B. A.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

G. Gottwald, R. Grimshaw, and B. A. Malomed, “Stable two-dimensional parametric solitons in fluid systems,” Phys. Lett. A 248, 208–218 (1998).
[CrossRef]

D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
[CrossRef]

McCall, S. L.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
[CrossRef]

Mossberg, T. W.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
[CrossRef]

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

Polymilis, C.

D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
[CrossRef]

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

Raghavan, S.

A somewhat similar situation was considered by S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–328 (2000), who predicted that parabolic transverse modulation of the RI allows for stabilization of LBs in a Kerr medium.
[CrossRef]

Silberberg, Y.

Sklyarov, Yu. M.

A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

Suzuki, K.

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
[CrossRef]

Torner, L.

D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
[CrossRef]

Wang, T.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Wise, F. W.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

Comput. Phys. Commun.

See the numerical scheme proposed in P. D. Drummond, “Central partial difference propagation algorithms,” Comput. Phys. Commun. 29, 211–225 (1983).
[CrossRef]

Opt. Commun.

P. D. Drummond, “Formation and stability of vee simultons,” Opt. Commun. 49, 219–223 (1984).
[CrossRef]

A somewhat similar situation was considered by S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–328 (2000), who predicted that parabolic transverse modulation of the RI allows for stabilization of LBs in a Kerr medium.
[CrossRef]

D. V. Skryabin and W. J. Firth, “Generation and stability of optical bullets in quadratic nonlinear media,” Opt. Commun. 148, 79–84 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, J. Dörring, and L. Torner, “Elliptical light bullets,” Opt. Commun. 159, 129–138 (1999).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, “Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152, 365–370 (1998).
[CrossRef]

Opt. Lett.

Phys. Lett. A

D. J. Frantzeskakis, K. Hizanidis, B. A. Malomed, and C. Polymilis, “Stable anti-dark light bullets supported by the third-order dispersion,” Phys. Lett. A 248, 203–207 (1998).
[CrossRef]

G. Gottwald, R. Grimshaw, and B. A. Malomed, “Stable two-dimensional parametric solitons in fluid systems,” Phys. Lett. A 248, 208–218 (1998).
[CrossRef]

Phys. Rep.

A. A. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, “Present state of self-induced transparency theory,” Phys. Rep. 191, 1–108 (1990).
[CrossRef]

Phys. Rev. A

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

M. Nakazawa, K. Suzuki, Y. Kimura, and H. Kubota, “Coherent pi-pulse propagation with pulse breakup in an erbium-doped fiber waveguide amplifier,” Phys. Rev. A 45, R2682–R2685 (1992).
[CrossRef]

K. V. Kheruntsyan and P. D. Drummond, “Three-dimensional quantum solitons with parametric coupling,” Phys. Rev. A 58, 2488–2499 (1998).
[CrossRef]

K. V. Kheruntsyan and P. D. Drummond, “Multidimensional parametric quantum solitons,” Phys. Rev. A 58, R2676–R2679 (1998).
[CrossRef]

Phys. Rev. E

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

H. He and P. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. A. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E 61, 3107–3113 (2000).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997).
[CrossRef]

Phys. Rev. Lett.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275–3278 (1993).
[CrossRef] [PubMed]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys.

G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in a resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
[CrossRef]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Other

See J. P. Dowling, H. Everitt, and E. Yablonovitch, “Photonic band-gap bibliography,” http://home.earthlink.net/~jpdowling/pbgbib.html.

R. E. Slusher, “Self-induced transparency, experiment,” in Progress in Optics, by E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 76–85.

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992).

See, e.g., L. Levi, Applied Optics (Wiley, New York, 1980), Chap. 13.

These bullets can be guided in the presence of a different refractive-index modulation given by n(x)=1−½C2 (−1+ ½ sech 2 Θ1 +½sech 2 Θ2 +tanh Θ1 tanh Θ2), with C, Θ1, and Θ2 as defined in Ref. 13.

As an example of another type of 2D guided-LB mode, one can find a family of LBs that correspond to α=∞ in Eq. (2d). Their velocity, given by the expression v=α2 /(α2 +1), takes the maximum possible value, v=1. These solutions are obtained by substitution of a plane wave (in z) ansatz E (τ, z, x)=E (τ, x)exp (−ikz), P (τ, z, x)=P (τ, x)× exp (−ikz), and W(τ, z, x)=W(τ, x), with an arbitrary real constant k, into Eqs. (1). The equation for the field then becomes −iE xx +n2 E τ +ikE +i(1−n2)E −P =0, with the equations for P and W given by Eqs. (1b) and (1c). If the RI in the medium is modulated as n2 (x)=1−β2 [tanh 2 (βx)−sech 2 (βx)]+kβ, the LB solution to Eqs. (1) can be approximated by Eq. (2), with Θ(τ, z) replaced by τ+Θ0. Thus these solutions are localized in τ and x, but at a fixed τ they are not localized in z.

A guided LB similar to that in Eq. (2) can be found in a 3D SIT medium embedded in a cylindrical waveguiding structure. The medium is described by Eqs. (1), with E xx → E rr +(1/r)E r, where r≡x2 +y2 is the transverse radial coordinate. Searching for an axisymmetric solution of these 3D equations, we arrive at an approximation of the same form as Eqs. (2) but with x replaced by r, and a corresponding cylindrical RI modulation:n2 (r)=1−ββ[1−2 sech 2 (βr)]−tanh (βr) r, for |βr|≪1. Comparison with results of simulations of the cylindrically symmetric 3D equations by use of the analytical approximation as an initial ansatz again shows good agreement (with a deviation of <2%). In practice, however, such 3D guided-LB and waveguiding structures are probably much harder to realize than their 2D counterparts.

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Figures (2)

Fig. 1
Fig. 1

Profile of the guiding structure that corresponds to the modulated refractive index [Eq. (2e)] with β=0.5.

Fig. 2
Fig. 2

Electric field inside the 2D light bullet, |E|, in a SIT medium with a transversely modulated refractive index in accordance with Eq. (2e) as a function of time τ and transverse coordinate x after propagation a distance z=1000. Parameters used are α=1, β=0.5, ϕ=0, and Θ0=1000.

Equations (11)

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-iExx+n2Eτ+Ez+i(1-n2)E-P=0,
Pτ-EW=0,
Wτ+½(E*P+P*E)=0,
E=±2α sech Θ(τ, z)sech(βx)exp(iϕ),
P=±2 sech Θ(τ, z)tanh Θ(τ, z)sech(βx)exp(iϕ),
W=[1-4 sech2 Θ(τ, z)tanh2 Θ(τ, z)sech2(βx)]1/2,
Θ(τ, z)α(τ-z)-z/α+Θ0
n2(x)=1-β2[1-2 sech2(βx)]|x|xmax1|x|xmax.
-iExx+n2Eτ+ikE+i(1-n2)E-P=0,
n2(x)=1-β2[tanh2(βx)-sech2(βx)]+kβ,
n2(r)=1-ββ[1-2 sech2(βr)]-tanh(βr)r,

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