Abstract

Reflectionless transmission of light waves with unitary transmittance is shown to occur in a certain class of gain-grating structures and phase-conjugation mirrors in the unstable (above-threshold) regime. Such structures are synthesized by means of the Darboux method developed in the context of supersymmetric relativistic quantum mechanics. Transparency is associated to superluminal pulse transmission.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  2. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  3. I. Kay and H. E. Moses, J. Appl. Phys. 27, 1503 (1956).
    [CrossRef]
  4. A. A. Sukhorukov, Opt. Lett. 35, 989 (2010).
    [CrossRef] [PubMed]
  5. H. Kogelnik and C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
    [CrossRef]
  6. J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quant. Electron. 37, 165 (2001).
    [CrossRef]
  7. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).
  8. Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
    [CrossRef]
  9. R.A.Fisher, ed., Optical Phase Conjugation (Academic, 1983).
  10. N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
    [CrossRef]
  11. S. Longhi, Phys. Rev. Lett. 105, 013903 (2010).
    [CrossRef] [PubMed]
  12. M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
    [CrossRef]
  13. According to the inverse scattering theory, the potential corresponds to a radiationless (fundamental soliton) initial condition q(x,0) of the self-focusing nonlinear Schrödinger equation ∂τq=i∂x2q+2i|q|2q (see ).

2010

2002

N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
[CrossRef]

2001

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quant. Electron. 37, 165 (2001).
[CrossRef]

1998

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

1990

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

1974

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).

1972

H. Kogelnik and C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

1956

I. Kay and H. E. Moses, J. Appl. Phys. 27, 1503 (1956).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).

Blaauboer, M.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Debergh, N.

N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
[CrossRef]

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quant. Electron. 37, 165 (2001).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Hosomatsu, H.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

Inoue, T.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

Iwaoka, H.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

Kaup, D. J.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).

Kay, I.

I. Kay and H. E. Moses, J. Appl. Phys. 27, 1503 (1956).
[CrossRef]

Kofman, A. G.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Kogelnik, H.

H. Kogelnik and C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Kozhekin, A. E.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Kurizki, G.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Lenstra, D.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Lodder, A.

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Longhi, S.

S. Longhi, Phys. Rev. Lett. 105, 013903 (2010).
[CrossRef] [PubMed]

Luo, Y.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

Moses, H. E.

I. Kay and H. E. Moses, J. Appl. Phys. 27, 1503 (1956).
[CrossRef]

Nakano, Y.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

Newell, A. C.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).

Pecheritsin, A. A.

N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
[CrossRef]

Samsonov, B. F.

N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
[CrossRef]

Segur, H.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).

Shank, C. V.

H. Kogelnik and C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Skaar, J.

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quant. Electron. 37, 165 (2001).
[CrossRef]

Sukhorukov, A. A.

Tada, K.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

Van den Bossche, B.

N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quant. Electron. 37, 165 (2001).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Appl. Phys. Lett.

Y. Luo, Y. Nakano, K. Tada, T. Inoue, H. Hosomatsu, and H. Iwaoka, Appl. Phys. Lett. 56, 1620 (1990).
[CrossRef]

IEEE J. Quant. Electron.

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quant. Electron. 37, 165 (2001).
[CrossRef]

J. Appl. Phys.

I. Kay and H. E. Moses, J. Appl. Phys. 27, 1503 (1956).
[CrossRef]

H. Kogelnik and C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

J. Phys. A

N. Debergh, A. A. Pecheritsin, B. F. Samsonov, and B. Van den Bossche, J. Phys. A 35, 3279 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Blaauboer, A. G. Kofman, A. E. Kozhekin, G. Kurizki, D. Lenstra, and A. Lodder, Phys. Rev. A 57, 4905 (1998).
[CrossRef]

Phys. Rev. Lett.

S. Longhi, Phys. Rev. Lett. 105, 013903 (2010).
[CrossRef] [PubMed]

Stud. Appl. Math.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249 (1974).

Other

R.A.Fisher, ed., Optical Phase Conjugation (Academic, 1983).

According to the inverse scattering theory, the potential corresponds to a radiationless (fundamental soliton) initial condition q(x,0) of the self-focusing nonlinear Schrödinger equation ∂τq=i∂x2q+2i|q|2q (see ).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

(a) Schematic of Bragg scattering in a gain grating. (b) Schematic of a PC mirror, comprising a nonlinear cubic medium (nonlinear polarization P NL = ϵ 0 χ ( 3 ) E 3 ) pumped by two strong fields of envelopes E 1 ( x ) and E 2 ( x ) counterpropagating normal to the x axis of the probe ( ψ 1 ) and phase-conjugate ( ψ 2 * ) fields.

Fig. 2
Fig. 2

Pulse propagation in the transparent gain grating [Eq. (3)] for σ = 2 . (a) Amplitude of the forward-propagating field ψ 1 ( x , τ ) at time τ = 0 (solid curve) and grating profile q ( x ) (dashed curve). (b) Evolution of the field intensity | ψ 1 | 2 + | ψ 2 | 2 in the ( x , τ ) plane. The gain grating is switched off at τ > 11 . The arrows show the unstable mode, which splits after the grating switches off. (c) Intensity profile of the forward-propagating field | ψ 1 | 2 at τ = 16 (solid curve) and corresponding profile that one would observe in absence of the grating (dashed curve).

Equations (10)

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

i ψ τ = ( γ x + V ( x ) ) ψ H ψ ,
γ = i ( 1 0 0 1 ) , V ( x ) = i ( 0 q ( x ) q * ( x ) 0 ) ,
q ( x ) = σ cosh ( σ x ) .
ψ + ( x , δ ) = ( i δ ( σ / 2 ) tanh ( σ x ) σ / [ 2 cosh ( σ x ) ] ) exp ( i δ x ) ,
ψ ( x , δ ) = ( σ / [ 2 cosh ( σ x ) ] i δ + ( σ / 2 ) tanh ( σ x ) ) exp ( i δ x ) .
ψ ( 1 ) ( x ) = 1 cosh ( σ x ) ( exp ( σ x / 2 ) exp ( σ x / 2 ) ) ,
ψ ( 2 ) ( x ) = 1 cosh ( σ x ) ( exp ( σ x / 2 ) exp ( σ x / 2 ) ) .
t ( δ ) = i δ σ / 2 i δ + σ / 2 .
τ t ( δ ) = Im ( ln t ) δ = σ δ 2 + ( σ / 2 ) 2 .
φ ( x , τ ) = d δ G + ( δ ) exp ( i δ x 0 ) ψ + ( x , δ ) exp ( i δ τ ) ,

Metrics