Abstract

We show that general-form optical cavities are able to perform the temporal differentiation of optical signals. Analytical relationships to account for the scattering losses for such a cavity’s characteristics are deduced on the basis of temporal coupled-mode theory. A compact nanocavity-aided differentiator based on a ridge photonic crystal waveguide is designed.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Kulishov, D. Krcmarík, and R. Slavík, Opt. Lett. 32, 2978 (2007).
    [CrossRef]
  2. Y. Park, J. Azaña, and R. Slavík, Opt. Lett. 32, 710 (2007).
    [CrossRef]
  3. F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, Opt. Express 16, 15880 (2008).
    [CrossRef]
  4. D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, Opt. Lett. 36, 3509 (2011).
    [CrossRef]
  5. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
    [CrossRef]
  6. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
  7. M. Li, D. Janner, J. Yao, and V. Pruneri, Opt. Express 17, 19798 (2009).
    [CrossRef]
  8. H.-C. Liu and A. Yariv, Opt. Express 20, 9249 (2012).
    [CrossRef]
  9. S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
    [CrossRef]
  10. C. Sauvan, G. Lecamp, P. Lalanne, and J. Hugonin, Opt. Express 13, 245 (2005).
    [CrossRef]
  11. Q. Quan and M. Loncar, Opt. Express 19, 18529 (2011).
    [CrossRef]
  12. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  13. R. Ashrafi and J. Azaña, Opt. Express 20, 2626 (2012).
    [CrossRef]
  14. R. Ashrafi, M. H. Asghari, and J. Azaña, IEEE Photon. J. 3, 353 (2011).
    [CrossRef]
  15. R. Slavík, Y. Park, M. Kulishov, and J. Azaña, Opt. Lett. 34, 3116 (2009).
    [CrossRef]
  16. L. M. Rivas, S. Boudreau, Y. Park, R. Slavík, S. Larochelle, A. Carballar, and J. Azaña, Opt. Lett. 34, 1792 (2009).
    [CrossRef]

2012

2011

2009

2008

2007

2005

1999

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

1995

Asghari, M. H.

R. Ashrafi, M. H. Asghari, and J. Azaña, IEEE Photon. J. 3, 353 (2011).
[CrossRef]

Ashrafi, R.

R. Ashrafi and J. Azaña, Opt. Express 20, 2626 (2012).
[CrossRef]

R. Ashrafi, M. H. Asghari, and J. Azaña, IEEE Photon. J. 3, 353 (2011).
[CrossRef]

Azaña, J.

Boudreau, S.

Bykov, D. A.

Carballar, A.

Chen, J. C.

Devenyi, A.

Doskolovich, L. L.

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
[CrossRef]

Hagness, S. C.

Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Hugonin, J.

Janner, D.

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Krcmarík, D.

Kulishov, M.

Lalanne, P.

Larochelle, S.

Lecamp, G.

Li, M.

Liu, F.

Liu, H.-C.

Loncar, M.

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Meade, R. D.

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Park, Y.

Pruneri, V.

Qiang, L.

Qiu, M.

Quan, Q.

Rivas, L. M.

Sauvan, C.

Slavík, R.

Soifer, V. A.

Su, Y.

Taflove,

Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

Wang, T.

Winn, J. N.

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Yao, J.

Yariv, A.

Ye, T.

Zhang, Z.

IEEE J. Quantum Electron.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999).
[CrossRef]

IEEE Photon. J.

R. Ashrafi, M. H. Asghari, and J. Azaña, IEEE Photon. J. 3, 353 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

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.

Schematic representation of a resonator with two input/output channels. The losses in the channels are characterized by the decay time τw (τw=τ1+τ2). Scattering losses within the resonator are characterized by the magnitude τr. The complex amplitudes sl±, l=1,2 determine the resonator’s incoming and outgoing energy. |A|2 characterizes the energy contained within the resonator.

Fig. 2.
Fig. 2.

Q factor as a function of the number of PhC layers in the resonator’s mirrors. The top inset depicts the designed nanoresonator’s structure. The bottom inset shows the energy density distribution within the resonator.

Fig. 3.
Fig. 3.

Coefficients En and the differentiation results for a pulse with the envelope defined by exp(x2/(2σ2)). (a) The first eight coefficients of En for an 25ps pulse, (b) the differentiation result for the 25ps pulse obtained with the resonator designed (rms=46%), (c), (d) differentiation results for an 50ps pulse (rms=29%), and (e), (f) differentiation results for an 100ps pulse (rms=4%).

Equations (7)

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

dAdt=iω0AAτrl=12Aτll=122τlsl+,
sl=sl++2τlA.
R(ω)=s1s1+=i(ωω0)1τri(ωω0)+1τ,
R(ω0)=ττr,R(n)(ω0)=(1)nn!τn(1+ττr),n>0.
En=Ω2π02π/Ω(τn(1+ττr)cos(n)(Ωt))2dt,n>0.
E0=τ2τr,En=τ+τr2τrτnΩn,n>0.
E1n1En1τΩτ2Ω2+ττr(1τΩ).

Metrics