Abstract

We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.

© 2008 Optical Society of America

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  1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
    [Crossref]
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    [Crossref]
  3. J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
    [Crossref]
  4. P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
    [Crossref]
  5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [Crossref]
  6. N. Bloembergen and Y. R. Shen, “Quantum-Theoretical Comparison of Nonlinear Susceptibilities in Parametric Media, Lasers, and Raman Lasers,” Phys. Rev. 133, A37–A49 (1964).
    [Crossref]
  7. G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
    [Crossref]
  8. G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
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  9. J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
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  11. Günter Steinmeyer, “Laser physics: Terahertz meets attoscience,” Nature Physics 2, 305–306 (2006).
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    [Crossref]
  13. B. Ferguson and X.-Cheng Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
    [Crossref]
  14. E. Mueller, “Terahertz radiation sources for imaging and sensing applications,” Photonics Spectra 40, 60 (2006).
  15. E. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
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    [Crossref] [PubMed]
  17. G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
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  22. K. Sakoda and K. Ohtaka, “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
    [Crossref]
  23. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, New Jersey, 1984).
  24. J. D. Joannopoulos, R. D. Meade, and J. N Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).
  25. C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
    [Crossref] [PubMed]
  26. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
    [Crossref]
  27. M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced Photonic Band-Gap Confinement via Van Hove Saddle Point Singularities,” Phys. Rev. Lett. 96, 033904 (2006).
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  28. G. Chang, C. J. Divin, J. Yang, M. A. Musheinish, S. L. Williamson, A. Galvanauskas, and T. B. Norris, “GaP waveguide emitters for high power broadband THz generation pumped by Yb-doped fiber lasers,” Opt. Express 15, 16308–16315 (2007).
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    [Crossref]
  30. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  31. R. W. Boyd, Nonlinear Optics (Academic Press, 2002).
  32. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
    [Crossref] [PubMed]

2007 (3)

2006 (6)

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref] [PubMed]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced Photonic Band-Gap Confinement via Van Hove Saddle Point Singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[Crossref] [PubMed]

Yuri Kivshar, “Spatial solitons: Bending light at will,” Nature Physics 2, 729–730 (2006).
[Crossref]

Günter Steinmeyer, “Laser physics: Terahertz meets attoscience,” Nature Physics 2, 305–306 (2006).
[Crossref]

E. Mueller, “Terahertz radiation sources for imaging and sensing applications,” Photonics Spectra 40, 60 (2006).

2005 (1)

2004 (1)

M. Soljačić and J. D. Joannopoulos, “Enhancement of non-linear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

2003 (1)

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

2002 (2)

B. Ferguson and X.-Cheng Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
[Crossref]

2001 (3)

J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
[Crossref]

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

1996 (2)

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwells equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[Crossref]

K. Sakoda and K. Ohtaka, “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[Crossref]

1984 (1)

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

1964 (1)

N. Bloembergen and Y. R. Shen, “Quantum-Theoretical Comparison of Nonlinear Susceptibilities in Parametric Media, Lasers, and Raman Lasers,” Phys. Rev. 133, A37–A49 (1964).
[Crossref]

1962 (5)

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
[Crossref]

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[Crossref]

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

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
[Crossref]

1946 (1)

E. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Agrawal, G. P.

G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
[Crossref]

Armstrong, J. A.

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

Auston, D. H.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Baida, F. I.

Bass, M.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

Bermel, P.

Bertolotti, M.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Bloembergen, N.

N. Bloembergen and Y. R. Shen, “Quantum-Theoretical Comparison of Nonlinear Susceptibilities in Parametric Media, Lasers, and Raman Lasers,” Phys. Rev. 133, A37–A49 (1964).
[Crossref]

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

Bloemer, M. J.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Bowden, C. M.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2002).

Bravo-Abad, J.

Burr, G.

Centini, M.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Chang, G.

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

DAguanno, G.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Divin, C. J.

Ducuing, J.

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

Dudley, J. M.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nature Phys. 3, 597–603 (2007).
[Crossref]

Dumeige, Y.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Eckardt, G.

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

Farjadpour, A.

Ferguson, B.

B. Ferguson and X.-Cheng Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

Finot, C.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nature Phys. 3, 597–603 (2007).
[Crossref]

Franken, P. A.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
[Crossref]

Galvanauskas, A.

Giordmaine, J. A.

J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
[Crossref]

Hasegawa, A.

G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
[Crossref]

Haus, H. A.

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

Haus, J. W.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Hellwarth, R. W.

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

Hill, A. E.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
[Crossref]

Ibanescu, M.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced Photonic Band-Gap Confinement via Van Hove Saddle Point Singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[Crossref] [PubMed]

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref] [PubMed]

Joannopoulos, J. D.

J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express 15, 16161–16176 (2007).
[Crossref] [PubMed]

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref] [PubMed]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced Photonic Band-Gap Confinement via Van Hove Saddle Point Singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[Crossref] [PubMed]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

M. Soljačić and J. D. Joannopoulos, “Enhancement of non-linear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

Johnson, S. G.

Kimura, T.

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

Kivshar, Y.

G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
[Crossref]

Kivshar, Yuri

Yuri Kivshar, “Spatial solitons: Bending light at will,” Nature Physics 2, 729–730 (2006).
[Crossref]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Laroche, T.

Levenson, J. A.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Luo, C.

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref] [PubMed]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[Crossref]

McClung, F. J.

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

Millot, G.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nature Phys. 3, 597–603 (2007).
[Crossref]

Mueller, E.

E. Mueller, “Terahertz radiation sources for imaging and sensing applications,” Photonics Spectra 40, 60 (2006).

Müller, M.

J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
[Crossref]

Musheinish, M. A.

Nisenhoff, M.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[Crossref]

Nishizawa, J.-ichi

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

Norris, T. B.

Ohtaka, K.

K. Sakoda and K. Ohtaka, “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[Crossref]

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwells equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[Crossref]

Pershan, P. S.

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

Peters, C. W.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
[Crossref]

Purcell, E.

E. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Reed, E. J.

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref] [PubMed]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced Photonic Band-Gap Confinement via Van Hove Saddle Point Singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[Crossref] [PubMed]

Richardson, D. J.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nature Phys. 3, 597–603 (2007).
[Crossref]

Rodriguez, A.

Roundy, D.

Saito, K.

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

Sakoda, K.

K. Sakoda and K. Ohtaka, “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[Crossref]

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwells equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[Crossref]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[Crossref]

Scalora, M.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Schwartz, S. E.

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

Shen, Y. R.

N. Bloembergen and Y. R. Shen, “Quantum-Theoretical Comparison of Nonlinear Susceptibilities in Parametric Media, Lasers, and Raman Lasers,” Phys. Rev. 133, A37–A49 (1964).
[Crossref]

Sibilia, C.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Soljacic, M.

Squier, J.

J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
[Crossref]

Steinmeyer, Günter

Günter Steinmeyer, “Laser physics: Terahertz meets attoscience,” Nature Physics 2, 305–306 (2006).
[Crossref]

Suto, K.

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 1995).

Tanabe, T.

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[Crossref]

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Van Labeke, D.

Vidakovic, P.

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Wabnitz, S.

G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
[Crossref]

Weiner, D.

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

Weinreich, G.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
[Crossref]

Williamson, S. L.

Winn, J. N

J. D. Joannopoulos, R. D. Meade, and J. N Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

Woodbury, E. J

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

Yang, J.

Zhang, X.-Cheng

B. Ferguson and X.-Cheng Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

IEEE J. Sel. Top. In Quantum Electron. (1)

G. P. Agrawal, A. Hasegawa, Y. Kivshar, and S. Wabnitz, “Introduction to the Special Issue on Nonlinear Optics,” IEEE J. Sel. Top. In Quantum Electron. 8, 405–407 (2002).
[Crossref]

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

J. Phys. D: Applied Physics (1)

T. Tanabe, K. Suto, J.-ichi Nishizawa, K. Saito, and T. Kimura, “Frequency-tunable terahertz wave generation via excitation of phonon-polaritons in GaP,” J. Phys. D: Applied Physics 36, 953–957 (2003).
[Crossref]

Nature Materials (2)

B. Ferguson and X.-Cheng Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of non-linear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

Nature Phys. (1)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nature Phys. 3, 597–603 (2007).
[Crossref]

Nature Physics (2)

Yuri Kivshar, “Spatial solitons: Bending light at will,” Nature Physics 2, 729–730 (2006).
[Crossref]

Günter Steinmeyer, “Laser physics: Terahertz meets attoscience,” Nature Physics 2, 305–306 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Photonics Spectra (1)

E. Mueller, “Terahertz radiation sources for imaging and sensing applications,” Photonics Spectra 40, 60 (2006).

Phys. Rev. (3)

E. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

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

N. Bloembergen and Y. R. Shen, “Quantum-Theoretical Comparison of Nonlinear Susceptibilities in Parametric Media, Lasers, and Raman Lasers,” Phys. Rev. 133, A37–A49 (1964).
[Crossref]

Phys. Rev. B (2)

K. Sakoda and K. Ohtaka, “Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwells equations and their applications,” Phys. Rev. B 54, 5732–5741 (1996).
[Crossref]

K. Sakoda and K. Ohtaka, “Sum-frequency generation in a two-dimensional photonic lattice,” Phys. Rev. B 54, 5742–5749 (1996).
[Crossref]

Phys. Rev. E. (1)

G. DAguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidakovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E. 64, 016609 (2001).
[Crossref]

Phys. Rev. Lett. (8)

G. Eckardt, R. W. Hellwarth, F. J. McClung, S. E. Schwartz, D. Weiner, and E. J Woodbury, “Stimulated Raman Scattering From Organic Liquids,” Phys. Rev. Lett. 9, 455 (1962).
[Crossref]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 6, 118–119 (1961).
[Crossref]

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Optical Mixing,” Phys. Rev. Lett. 8, 18–18 (1962).
[Crossref]

J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
[Crossref]

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8, 21–22 (1962).
[Crossref]

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler Radiation Emitted by an Oscillating Dipole Moving inside a Photonic Band-Gap Crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref] [PubMed]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced Photonic Band-Gap Confinement via Van Hove Saddle Point Singularities,” Phys. Rev. Lett. 96, 033904 (2006).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

J. Squier and M. Müller, “High resolution nonlinear microscopy: a review of sources and methods for achieving optimal imaging,” Rev. Sci. Instrum. 72, 2855–2867 (2001).
[Crossref]

Other (4)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 1995).

R. W. Boyd, Nonlinear Optics (Academic Press, 2002).

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

J. D. Joannopoulos, R. D. Meade, and J. N Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

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Figures (8)

Fig. 1.
Fig. 1.

(Color online) Color contour plot of the dielectric function ε(x,y) of the 2D PhC srtucture: (a) 1a×1a cell, and (b) 5a×5a cell, showing the optical beam through the central waveguide.

Fig. 2.
Fig. 2.

(Color online) (a) Projected band diagram of the first three bands. (b) Color contour plot of the second band, showing the saddle point where the band is narrowest.

Fig. 3.
Fig. 3.

(Color online) Color contour plot of w k y = 0 ( x , y ) .

Fig. 4.
Fig. 4.

(Color online) Periodically poled PhC structure. The red portions correspond to the original orientation of the nonlinear crystal when χ(2) is positive, while in the blue portions, the crystal’s orientation is flipped resulting in a negative χ(2).

Fig. 5.
Fig. 5.

(Color online) Overlap integral �� poled one period as a function of ky for modes at the narrowest portion (kx =0.1559(2π/a)) of the second band.

Fig. 6.
Fig. 6.

(Color online) CMT calculations: (a) Color contour plot of the unnormalized terahertz energy density ε(x,y)|E(x,y,t)|2 at t=1010(a/c), in a 2D box of size 1a×80a. (b) A zoom-in version of the plot in Fig. a, showing more details of the interval y∈±[8a,19a]. Note that the optical beam was originally sent through the waveguide at y=0

Fig. 7.
Fig. 7.

(Color online) FDTD calculation for the terahertz emitted energy in the PhC structure (not normalized to the bulk).

Fig. 8.
Fig. 8.

(Color online) FDTD calculations: (a) Color contour plot of the terahertz energy density ε(x,y)|E(x,y,t)|2 at t=1010(a/c), in a 2D box of size 1a×80a. (b) A zoom-in version of the plot in Fig. a, showing more details of the interval y∈±[8a,19a]. Note that the optical beam was originally sent through the waveguide at y=0.

Equations (35)

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

E ( r , t ) = v a v ( t ) E v ( r ) d 3 r ε ( r ) 2 E v ( r ) 2
d a v d t = i ω v a v ( Γ rad v + Γ abs v Γ g v ) a v + κ v s + v
κ v s + v = d 3 r J ( r , t ) · E v * ( r ) d 3 r ε ( r ) 2 E v ( r ) 2
d d t ( a v ( t ) Ξ ( t ) ) = Ξ ( t ) κ v s + v
a v ( t ) = a v ( t o ) e i ω v ( t t o ) e ( Γ rad v + Γ abs v Γ g v ) ( t t o )
+ t o t d t all space d 3 r J ( r , t ) · E v * ( r ) d 3 r ε ( r ) 2 E v ( r ) 2 e i ω v ( t t ) e ( Γ rad v + Γ abs v Γ g v ) ( t t )
E ( r , t ) = v E v ( r ) d 3 r ε ( r ) 2 E v ( r ) 2 a v ( t o ) e i ω v ( t t o ) e ( Γ ras v + Γ abs v Γ g v ) ( t t o ) +
v E v ( r ) d 3 r ε ( r ) 2 E v ( r ) 2 t o t d t all space d 3 r J ( r , t ) · E v * ( r ) e i ω v ( t t ) e ( Γ rad v + Γ abs v Γ g v ) ( t t )
A S · d a = A { Real [ E ( r , t ) ] × Real [ H ( r , t ) ] } · d a
a v = i ω s p · E v * ( r o ) i ( ω v ω s ) + ( Γ rad v + Γ abs v ) e i ω s t d 3 r ε ( r ) 2 E v ( r ) 2
𝒫 = v Γ rad v ( ω v ω s ) 2 + ( Γ v ) 2 2 ( ω s ) 2 p · E v * ( r o ) 2 d 3 r ε ( r ) 2 E v ( r ) 2
𝒫 = 4 π ( ω s ) 2 p 2 ε ( r o ) v ε ( r o ) p ̂ · E v * ( r o ) 2 δ ( ω v ω s ) d 3 r ε ( r ) E v ( r ) 2
𝒫 = 4 π ( ω s ) 2 p 2 ε ( r o ) g ( ω s , r o )
g ( ω s , r o ) = v ε ( r o ) E v ( r o ) 2 δ ( ω v ω s ) d 3 r ε ( r ) E v ( r ) 2
J ( r , t ) = j o e i ω s t δ ( r v t )
E ( r , t ) = v E v ( r ) d 3 r ε ( r ) 2 E v ( r ) 2 t d t e i ω s t j o · E v * ( v t ) e i ω v ( t t )
E ( r , t ) = n k σ E n k σ ( r ) d 3 r ε ( r ) 2 E n k σ ( r ) 2 G j o · e n k , G * t d t e i ω s t e i ( k + G ) · v t e i ω n k σ ( t t )
E ( r , t ) = n k σ E n k σ ( r ) d 3 r ε ( r ) 2 E n k σ ( r ) 2 G i [ j o · ( e n k , G ) * ] ω n k σ [ ω s + ( k + G ) · v ] e i [ ω s + ( k + G ) · v ] t
J T H z ( x , y ; t ) = z ̂ e i k x s x y 2 2 ζ 2 e i ω s t ( t 500 a c ) 2 2 τ 2
J T H z ( x , y ; t ) = J space T H z ( x , y ) · 𝓕 ( t )
J space T H z ( x , y ) = z ̂ e i k x s x y 2 2 ζ 2
𝓕 ( t ) = e i ω s t ( t 500 a c ) 2 2 τ 2
w k y ( x , y ) ε ( x , y ) E n = 2 ; ( k x = 0.1559 ( 2 π a ) , k y ; σ = T M ) ( x , y ) 2
𝒪 n k all space d 3 r J space T H z ( r ) · E n k * ( r )
𝒪 all space poled ( k y ) all space d 3 r q ( x ) J space T H z ( r ) · E n = 2 ; ( k x s , k y ) * ( r )
= all space d 3 r q ( x ) e i k x s x y 2 2 ζ 2 z ̂ . E n = 2 ; ( k x s , k y ) * ( r )
𝒥 t ( k y ) e i ω ( n = 2 ; k x s , k y ) t 0 t d t 𝓕 ( t ) e i ω ( n = 2 , k x s , k y ) t
= e i ω ( n = 2 ; k x s , k y ) t 0 t d t e i ( ω s ω ( n = 2 ; k x s , k y ) ) t ( t 500 a c ) 2 2 τ 2
E n k ( r ) = e i k · r u n k ( r )
𝒪 all space poled ( k y ) = all space d 3 r q ( x ) e i k y y y 2 2 ζ 2 z ̂ · u n = 2 ; ( k x s , k y ) * ( r )
𝒪 all space poled ( k y ) = 𝒩 x · 𝒪 one period poled ( k y )
𝒪 one period poled ( k y ) = a 2 a 2 d x a 2 a 2 d y q ( x ) e i k y y y 2 2 ζ 2 z ̂ · u n = 2 ; ( k x s , k y ) * ( r )
E ( r , t ) = k y E n = 2 ; ( k x s , k y ) ( r ) 𝒩 x 𝒩 y 2 𝒩 x · 𝒪 one period poled ( k y ) 𝓘 t ( k y )
E ( r , t ) = a 𝒩 y 2 π 0.5 ( 2 π a ) 0.5 ( 2 π a ) d k y E n = 2 ; ( k x s , k y ) ( r ) 𝒩 x 𝒩 y 2 𝒩 x · 𝒪 one period poled ( k y ) 𝓘 t ( k y )
= a π · π a π a d k y E n = 2 ; ( k x s , k y ) ( r ) 𝒪 one period poled ( k y ) 𝓘 t ( k y )

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