Abstract

Light wave propagation in third-order nonlinear media with applied external electric field is investigated. Interplay between the nonlinear electro-optic and all-optical effects is examined theoretically. Energy exchange between the orthogonal light polarizations, the cross polarization conversion, results. The assisting external field acts as either the effect-enhancing or functionality-controlling parameter. Various materials such as silica glass, silicon, other bulk and quantum well semiconductors, organic materials, and particle-doped nanostructures are referred to as possible candidates for device implementations. Numerical estimates of achievable parameters in a selected suitable material are discussed.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
    [CrossRef]
  2. M. M. Fejer, “Nonlinear optical frequency conversion,” Physics Today 47, 25–32 (1994).
    [CrossRef]
  3. M. Cada, “Nonlinear optical devices,” Optica Pura i Aplicada 38, 1–11 (2005).
  4. R. Ramaswami and K. N. Sivarajan, Optical networks (Morgan Kaufman, New York, 2002).
  5. G. P. Agrawal, Nonlinear fiber optics (Academic Press, New York, 2001).
  6. R. P. Khare, Fiber optics and optoelectronics (Oxford University Press, London, 2004).
  7. M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. 87, 11101–11102 (2005).
    [CrossRef]
  8. E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. 6, 1094–1110 (2000).
    [CrossRef]
  9. K. L. Sala, “Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions,” Phys. Rev. A. 29, 1944–1954 (1984).
    [CrossRef]
  10. P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-matched optical fibers,” J. Opt. Soc. Am. B 14, 3170–3179 (1997).
    [CrossRef]
  11. J. Kerr, Phil. Mag. J. Sci., ser. Fourth50, (1875).
  12. R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent fibers,” Opt. Lett. 7, 512–516 (1982).
    [CrossRef] [PubMed]
  13. M. Horowitz and Y. Silberberg, “Nonlinear filtering by use of intensity-dependent polarization rotation in birefringent fibers,” Opt. Lett. 22, 1760–1764 (1997).
    [CrossRef]
  14. J. M. Dziedzic, R.H. Stolen, and A. Ashkin, “Optical Kerr effect in long fibers,” Appl. Opt. 20, 1403–1411 (1981).
    [CrossRef] [PubMed]
  15. B. Nickolaus, D. Grischkowsky, and A.C. Balant, “Optical pulse reshaping based on the nonlinear birefringence of single-mode optical fibers,” Opt. Lett. 8, 189–193 (1983).
    [CrossRef]
  16. H.G. Winful and A. Hu,“Intensity discrimination with twisted birefingent optical fibers,” Opt. Lett. 11, 668–672 (1986).
    [CrossRef] [PubMed]
  17. M. Hofer, M.E. Fermann, M.E. Haberl, M.H. Ober, and A.J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett. 16, 502–506 (1991).
    [CrossRef] [PubMed]
  18. H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200–208 (1994).
    [CrossRef]
  19. F. Torrens, “Molecular polarizability of semiconductor clusters and nanostructures,” Ninth Foresight Conference on Molecular Nanotechnology, November 2001.
  20. A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. 117, 401–409 (2005).
    [CrossRef]
  21. S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
    [CrossRef]
  22. A. Yariv, Optical electronics in modern communications (Oxford ser. Elec. Comp. Eng., London, 1997).
  23. R. W. Boyd, Nonlinear optics (Academic Press, New York, 1992).
  24. C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. 23, 177–179 (1987).
    [CrossRef]
  25. E. Infeld and G. Rowlands, Nonlinear waves, solitons and chaos (Cambridge University Press, London, 2000).
  26. S. Brandt and H. D. Dahmen: The picture book of quantum mechanics (Springer Verlag, New York, 1995).
  27. M. J. Weber, Handbook of optical materials (CRC Press, Washington D.C., 2003).
  28. J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
    [CrossRef]
  29. Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
    [CrossRef]
  30. G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
    [CrossRef]
  31. H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett,  88, 331091–331093 (2006).
    [CrossRef]
  32. Q. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerene-containing polyurethane films at telecommunication wavelengths,” Opt. Lett.,  30, 3057–3059 (2005).
  33. M. Qasymeh, M. Cada, and S. Ponomarenko, “Quadratic electro-optic Kerr effect: Applications to photonic devices,” sub. IEEE J. Quantum Electron. (2007).
  34. M. Qasymeh and M. Cada, “Re-configurable all-optical devices based on electrically controlled cross-polarization wave conversion,” ISDRS, College Park, MD, USA (2007).
  35. M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007).

2006 (1)

H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett,  88, 331091–331093 (2006).
[CrossRef]

2005 (4)

Q. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerene-containing polyurethane films at telecommunication wavelengths,” Opt. Lett.,  30, 3057–3059 (2005).

M. Cada, “Nonlinear optical devices,” Optica Pura i Aplicada 38, 1–11 (2005).

M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. 87, 11101–11102 (2005).
[CrossRef]

A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. 117, 401–409 (2005).
[CrossRef]

2004 (1)

J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
[CrossRef]

2002 (1)

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

2001 (1)

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

2000 (2)

E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. 6, 1094–1110 (2000).
[CrossRef]

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

1997 (2)

1994 (2)

H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200–208 (1994).
[CrossRef]

M. M. Fejer, “Nonlinear optical frequency conversion,” Physics Today 47, 25–32 (1994).
[CrossRef]

1992 (1)

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

1991 (1)

1987 (1)

C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. 23, 177–179 (1987).
[CrossRef]

1986 (1)

1984 (1)

K. L. Sala, “Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions,” Phys. Rev. A. 29, 1944–1954 (1984).
[CrossRef]

1983 (1)

1982 (1)

1981 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, New York, 2001).

Artemyev, M. V.

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

Ashkin, A.

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Balant, A.C.

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Botineau, J.

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Academic Press, New York, 1992).

Brandt, S.

S. Brandt and H. D. Dahmen: The picture book of quantum mechanics (Springer Verlag, New York, 1995).

Cada, M.

M. Cada, “Nonlinear optical devices,” Optica Pura i Aplicada 38, 1–11 (2005).

M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. 87, 11101–11102 (2005).
[CrossRef]

M. Qasymeh, M. Cada, and S. Ponomarenko, “Quadratic electro-optic Kerr effect: Applications to photonic devices,” sub. IEEE J. Quantum Electron. (2007).

M. Qasymeh and M. Cada, “Re-configurable all-optical devices based on electrically controlled cross-polarization wave conversion,” ISDRS, College Park, MD, USA (2007).

M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007).

Cazzanelli, M.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Chen, Q.

Dahmen, H. D.

S. Brandt and H. D. Dahmen: The picture book of quantum mechanics (Springer Verlag, New York, 1995).

Delplancke, J.-L.

J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
[CrossRef]

Dziedzic, J. M.

Fejer, M. M.

M. M. Fejer, “Nonlinear optical frequency conversion,” Physics Today 47, 25–32 (1994).
[CrossRef]

Fermann, M.E.

Franzo, G.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Gaburro, Z.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Garmire, E.

E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. 6, 1094–1110 (2000).
[CrossRef]

Gish, S. K.

A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. 117, 401–409 (2005).
[CrossRef]

Gomes, M. J. M.

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

Grischkowsky, D.

Haberl, M.E.

Hallemeier, P. F.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Haus, H. A.

H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200–208 (1994).
[CrossRef]

Hofer, M.

Horowitz, M.

Hsu, H.

C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. 23, 177–179 (1987).
[CrossRef]

Hu, A.

Iacona, F.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Infeld, E.

E. Infeld and G. Rowlands, Nonlinear waves, solitons and chaos (Cambridge University Press, London, 2000).

Ippen, E.P.

H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200–208 (1994).
[CrossRef]

Kazansky, P. G.

Kerr, J.

J. Kerr, Phil. Mag. J. Sci., ser. Fourth50, (1875).

Khare, R. P.

R. P. Khare, Fiber optics and optoelectronics (Oxford University Press, London, 2004).

Kissa, K. M.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Koyama, T.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Kuang, L.

Lafaw, D. A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Lion, Y.

J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
[CrossRef]

Loicq, J.

J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
[CrossRef]

Maak, D.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

McBrien, G. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Murphy, E. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Nagata, H.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Nickolaus, B.

Ober, M.H.

Ohtsuka, S.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Pavesi, L.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Pistora, J.

M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007).

Ponomarenko, S.

M. Qasymeh, M. Cada, and S. Ponomarenko, “Quadratic electro-optic Kerr effect: Applications to photonic devices,” sub. IEEE J. Quantum Electron. (2007).

M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007).

Prakash, G. V.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Priolo, F.

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

Pruneri, V.

Qasymeh, M.

M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007).

M. Qasymeh and M. Cada, “Re-configurable all-optical devices based on electrically controlled cross-polarization wave conversion,” ISDRS, College Park, MD, USA (2007).

M. Qasymeh, M. Cada, and S. Ponomarenko, “Quadratic electro-optic Kerr effect: Applications to photonic devices,” sub. IEEE J. Quantum Electron. (2007).

Rajagopalan, H.

H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett,  88, 331091–331093 (2006).
[CrossRef]

Rakovich, Y. P.

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

Ramaswami, R.

R. Ramaswami and K. N. Sivarajan, Optical networks (Morgan Kaufman, New York, 2002).

Renotte, Y.

J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
[CrossRef]

Rolo, A. G.

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

Rowlands, G.

E. Infeld and G. Rowlands, Nonlinear waves, solitons and chaos (Cambridge University Press, London, 2000).

Sala, K. L.

K. L. Sala, “Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions,” Phys. Rev. A. 29, 1944–1954 (1984).
[CrossRef]

Sargent, E. H.

Schmidt, A.J.

Shang, C. C.

C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. 23, 177–179 (1987).
[CrossRef]

Silberberg, Y.

Sivarajan, K. N.

R. Ramaswami and K. N. Sivarajan, Optical networks (Morgan Kaufman, New York, 2002).

Stolen, R. H.

Stolen, R.H.

Tamura, K.

H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200–208 (1994).
[CrossRef]

Tanaka, S.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Thakur, M.

H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett,  88, 331091–331093 (2006).
[CrossRef]

Torrens, F.

F. Torrens, “Molecular polarizability of semiconductor clusters and nanostructures,” Ninth Foresight Conference on Molecular Nanotechnology, November 2001.

Tsunemoto, K.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Vasilevskiy, M. I.

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

Vippa, P.

H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett,  88, 331091–331093 (2006).
[CrossRef]

Wadehra, A.

A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. 117, 401–409 (2005).
[CrossRef]

Wang, Z. Y.

Weber, M. J.

M. J. Weber, Handbook of optical materials (CRC Press, Washington D.C., 2003).

Winful, H.G.

Wooten, E. L.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Yariv, A.

A. Yariv, Optical electronics in modern communications (Oxford ser. Elec. Comp. Eng., London, 1997).

Yi-Yan, A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett (1)

H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett,  88, 331091–331093 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. 87, 11101–11102 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200–208 (1994).
[CrossRef]

C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. 23, 177–179 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. 6, 1094–1110 (2000).
[CrossRef]

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

J. Appl. Phys. (1)

G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. 91, 4607–4615 (2002).
[CrossRef]

J. Chem. Sci. (1)

A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. 117, 401–409 (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

New J. Phys. (1)

J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. 6, 1–13 (2004).
[CrossRef]

Opt. Lett. (6)

Optica Pura i Aplicada (1)

M. Cada, “Nonlinear optical devices,” Optica Pura i Aplicada 38, 1–11 (2005).

Phys. Rev. A. (1)

K. L. Sala, “Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions,” Phys. Rev. A. 29, 1944–1954 (1984).
[CrossRef]

Phys. Stat. Sol. (1)

Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. 224, 319–324 (2001).
[CrossRef]

Physics Today (1)

M. M. Fejer, “Nonlinear optical frequency conversion,” Physics Today 47, 25–32 (1994).
[CrossRef]

Other (13)

R. Ramaswami and K. N. Sivarajan, Optical networks (Morgan Kaufman, New York, 2002).

G. P. Agrawal, Nonlinear fiber optics (Academic Press, New York, 2001).

R. P. Khare, Fiber optics and optoelectronics (Oxford University Press, London, 2004).

J. Kerr, Phil. Mag. J. Sci., ser. Fourth50, (1875).

M. Qasymeh, M. Cada, and S. Ponomarenko, “Quadratic electro-optic Kerr effect: Applications to photonic devices,” sub. IEEE J. Quantum Electron. (2007).

M. Qasymeh and M. Cada, “Re-configurable all-optical devices based on electrically controlled cross-polarization wave conversion,” ISDRS, College Park, MD, USA (2007).

M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007).

E. Infeld and G. Rowlands, Nonlinear waves, solitons and chaos (Cambridge University Press, London, 2000).

S. Brandt and H. D. Dahmen: The picture book of quantum mechanics (Springer Verlag, New York, 1995).

M. J. Weber, Handbook of optical materials (CRC Press, Washington D.C., 2003).

F. Torrens, “Molecular polarizability of semiconductor clusters and nanostructures,” Ninth Foresight Conference on Molecular Nanotechnology, November 2001.

A. Yariv, Optical electronics in modern communications (Oxford ser. Elec. Comp. Eng., London, 1997).

R. W. Boyd, Nonlinear optics (Academic Press, New York, 1992).

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 (3)

Fig. 1.
Fig. 1.

The power percentage in the x-component versus distance. Constant total power and initial power percentage. The external electric fields are E ext (1)<E ext (2)<E ext (3).

Fig. 2.
Fig. 2.

The power percentage in the x-component versus distance. Constant external field and total optical power. The initial power percentages are P I%(1)<P I%(2)<P I%(3)<P I%(4).

Fig. 3.
Fig. 3.

The power percentage in the x-component versus distance. Constant external field and initial power percentage. The total launched optical powers are P T(1)<P T(2)<P T(3)<P T(4).

Equations (78)

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

× H = ( ε 0 E + P ) t
× E = μ 0 H t .
P = ε 0 ( χ ( 1 ) E + χ ( 2 ) EE + χ ( 3 ) EEE . . . ) = ε 0 χ ( 1 ) E + P NL ,
× × E = μ 0 ε 2 E t 2 μ 0 2 P NL t 2 ,
P i NL = ε 0 ( χ ixxx E x E x E x + χ ixxy E x E x E y + . . . . +
χ izzy E z E z E y + χ izzz E z E z E z ) = ε 0 xyz χ ijkl E j E k E l ,
χ yyzz = χ zzyy = χ zzxx = χ xxzz = χ xxyy = χ yyxx
χ yzyz = χ zyzy = χ zxzx = χ xzxz = χ xyxy = χ yxyx
χ yzzy = χ zyyz = χ zxxz = χ xzzx = χ xyyx = χ yxxy
χ xxxx = χ xxyy + χ xyxy + χ xyyx
χ yyyy = χ xxzz + χ xzxz + χ xzzx
χ zzzz = χ yyzz + χ yzyz + χ yzzy
χ xxxx = χ yyyy = χ zzzz
P x NL = ε 0 χ E x ( E x 2 + E y 2 + E z 2 )
P y NL = ε 0 χ E y ( E x 2 + E y 2 + E z 2 )
P z NL = ε 0 χ E z ( E x 2 + E y 2 + E z 2 ) ,
E x , y , z = 1 2 e x , y , z γ + 1 2 e x , y , z * r *
P x NL = ε 0 χ [ 1 8 e x e 2 γ 3 + 1 4 ( e x 2 + 1 2 e 2 ) E ext γ 2 + ( 1 4 e x e 2
+ 1 8 e x * e 2 + 3 8 e x E ext 2 ) γ + 1 2 e x e x * E ext + 1 4 e 2 E ext + 1 8 E ext 3 ]
P y , z NL = ε 0 χ [ 1 8 e y , z e 2 γ 3 + 1 4 e y , z e x E ext γ 2 + ( 1 4 e y , z e 2
+ 1 8 e y , z * e 2 + 1 8 e y , z E ext 2 ) γ + 1 4 ( e y , z e x * + e y , z * e x ) E ext ] ,
P x NL = ε 0 χ ( 1 4 e x e 2 + 1 8 e x * e 2 + 3 8 e x E ext 2 ) γ = ε 0 χ [ 3 8 e x e 2
1 8 e x e y e y * ( 1 e x * e y e x e y * ) 1 8 e x e z e z * ( 1 e x * e z e x e z * ) + 3 8 e x E ext 2 ] γ
P y , z NL = ε 0 χ ( 1 4 e y , z e 2 + 1 8 e y , z * e 2 + 1 8 e y , z E ext 2 ) γ
= ε 0 χ [ 3 8 e y , z e 2 1 8 e y , z e x e x * ( 1 e y , z * e x e y , z e x * )
1 8 e y , z e z , y e z , y * ( 1 e y , z * e z , y e y , z e z , y * ) + 1 8 e y , z E ext 2 ] γ .
e x * e y e x e y * e x * e z e x e z * e y , z * e x e y , z e x * e y , z * e z , y e y , z e z , y * 1 .
P x NL = ε 0 χ 3 8 ( e 2 + E ext 2 ) e x γ
P y , z NL = ε 0 χ 3 8 ( e 2 + 1 3 E ext 2 ) e y , z γ .
E z = E = j k 2 ε P NL .
e x ( z ) e x ( z ) = j k n L 2 χ 3 8 ( e 2 + E ext 2 )
e y , z ( z ) e y , z ( z ) = j k n L 2 χ 3 8 ( e 2 + 1 3 E ext 2 ) .
E x = e x ( 0 ) e j ω t e j k 0 ( n L + n NL I + n EXT E ext 2 ) z
E y , z = e y , z ( 0 ) e j ω t e j k 0 ( n L + n NL I + 1 3 n EXT E ext 2 ) Z ,
n NL · I = 3 χ Z 0 4 n L 2 · n L 2 Z 0 e 2 .
n EXT = 3 χ 8 n L = n L 2 Z 0 n NL ,
Δ n = n EXT E ext 2 = 3 8 n L χ E ext 2 = n L 2 Z 0 n NL E ext 2 .
L π = λ 0 Z 0 n L n NL E ext 2 ,
χ y y z z = χ z z y y = χ z z x x = χ x x z z = χ x x y y = χ y y x x
χ y z y z = χ z y z y = χ z x z x = χ x z x z = χ x y x y = χ y x y x
χ y z z y = χ z y y z = χ z x x z = χ x z z x = χ x y y x = χ y x x y
χ x x x x = χ y y y y = χ z z z z
P x NL = ε 0 χ E x [ E x 2 + φ ( E y 2 + E z 2 ) ]
P y NL = ε 0 χ E y [ ( E x 2 + φ ( E y 2 + E z 2 ) ]
P z NL = ε 0 χ E z [ ( E x 2 + φ ( E y 2 + E z 2 ) ] ,
P x NL = ε 0 χ 3 8 [ e x 2 + φ ( e y 2 + e z 2 ) + E ext 2 ] e x γ
P y , z NL = ε 0 χ 3 8 [ e x 2 + φ ( e y 2 + e z 2 ) + 1 3 E ext 2 ] e y , z γ .
I = n L 2 Z 0 [ e x 2 + φ ( e y 2 + e z 2 ) ] .
P x NL = ε 0 χ ( 1 4 e x e 2 + 1 8 e x * e 2 + 3 8 e x E ext 2 ) = ε 0 χ [ 3 8 e x e x 2
+ 3 8 e x e y 2 1 8 e x e y 2 ( 1 e x * e y e x e y * ) + 3 8 e x E ext 2 ] ,
e x e x = j k 0 n L χ 3 8 [ e x 2 + e y 2 + E ext 2 + 1 3 e y 2 ( e x * e y e x e y * 1 ) ] .
e x * e y e x e y * 1 = e j 2 ϕ z 1 = 2 j e j ϕ z sin ( ϕ z ) ,
l n e x = j k 0 n L χ 3 8 { ( e x 2 + e y 2 + E ext 2 ) dz
+ j 2 3 e y 2 e j ϕ z sin ( ϕ z ) dz } ,
ln e x = j k 0 n L χ 3 8 { [ e x 2 + e y 2 + E ext 2 ] z
+ j 1 3 e y 2 [ j z 1 2 ϕ ( e j 2 ϕ z 1 ) ] } .
1 2 ϕ ( e j 2 ϕ z 1 ) = 1 2 ϕ [ cos ( 2 ϕ z ) 1 + j sin ( 2 ϕ z ) ]
= 1 2 ϕ [ cos ( 2 ϕ z ) 1 ] + j z sin c ( 2 ϕ z ) .
e x = e j k 0 n L χ 3 8 { e x 2 + e y 2 + E ext 2 1 3 e y 2 [ 1 sin c ( 2 ϕ z ) ] } z
× e k 0 n L χ 1 8 e y 2 · 1 cos ( 2 ϕ z ) 2 ϕ
e y = e j k 0 n L χ 3 8 { e y 2 + e x 2 + 1 3 E ext 2 1 3 e x 2 [ 1 sin c ( 2 ϕ z ) ] } z
× e k 0 n L χ 1 8 e x 2 · 1 cos ( 2 ϕ z ) 2 ϕ .
p x i + 1 = n L 2 Z 0 e x i 2 = p x i · e 1 2 E ext 2 e y i 2 [ 1 cos ( 2 ϕ z ) ]
p y i + 1 = n L 2 Z 0 e y i 2 = p y i · e 1 2 E ext 2 e x i 2 [ 1 cos ( 2 ϕ z ) ] .
p x i + 1 = p x i · e f · p y i
p y i + 1 = p y i · e f · p x i ,
f ( z , E ext ) = Z 0 n L E ext 2 [ 1 cos ( 2 ϕ z ) ] .
p x i + 1 p x i = p x i · ( e f · p y i 1 )
p y i + 1 p y i = p y i · ( e f · p x i 1 ) ,
d ( p x ) = p x · d ( f · p y )
d ( p y ) = p y · d ( f · p x ) .
p x = p x 0 · e f · p y
p y = p y 0 · e f · p x .
p x = 1 f · ln [ p x N e f · p T + p y N ]
p y = 1 f · ln [ p y N e f · p T + p x N ] ,
p x = 1 f ln [ 1 + 2 sinh ( f p T 2 ) p x N e f p T 2 ]
p y = 1 f ln [ 1 2 sinh ( f p T 2 ) p y N e f p T 2 ] .
f = 2 Z 0 n L E ext 2 , z = λ n L χ E ext 2 .

Metrics