Abstract

We present a method to fully characterize linear photonic devices that change their properties on ultrashort time scales. When we feed the device with a broadband input pulse and detect the resulting output field for a sufficient number of arrival times of the input, the device response to any other input with smaller bandwidth can be extracted numerically, without the need for additional measurements. Our approach is based on the formalism of linear time-varying systems, and we experimentally demonstrate its feasibility for the example of an ultrafast nanophotonic switch.

© 2009 Optical Society of America

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  1. S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
    [CrossRef]
  2. P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
    [CrossRef]
  3. X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
    [CrossRef]
  4. M. Waldow, T. Plötzing, M. Gottheil, M. Först, J. Bolten, T. Wahlbrink, and H. Kurz, Opt. Express 16, 7693 (2008).
    [CrossRef] [PubMed]
  5. S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
    [CrossRef]
  6. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
    [CrossRef]
  7. T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
    [CrossRef]
  8. D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, Opt. Lett. 33, 147 (2008).
    [CrossRef] [PubMed]
  9. A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
    [CrossRef]
  10. C. Dorrer and I. Kang, Opt. Lett. 27, 1315 (2002).
    [CrossRef]
  11. F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
    [CrossRef]
  12. Y. Park, T.-J. Ahn, and J. Azaña, Opt. Express 17, 1734 (2009).
    [CrossRef] [PubMed]
  13. M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).
  14. In this work, the Fourier transform and its inverse are defined by Ff(ω)=∫dtf(t)exp(iωt) and f(t)=∫dωFf(ω)exp(−iωt)/2π, respectively.
  15. R. D. Nelson, D. E. Leaird, and A. M. Weiner, Opt. Express 11, 1763 (2003).
    [CrossRef] [PubMed]
  16. L. Lepetit, G. Chriaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995).
    [CrossRef]
  17. R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer, 2002).
    [CrossRef]

2009 (2)

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Y. Park, T.-J. Ahn, and J. Azaña, Opt. Express 17, 1734 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (3)

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

2005 (1)

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

2003 (1)

2002 (3)

C. Dorrer and I. Kang, Opt. Lett. 27, 1315 (2002).
[CrossRef]

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
[CrossRef]

1995 (1)

Ahn, T.-J.

Akimov, A. V.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Azaña, J.

Balaban, P.

M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).

Beggs, D. M.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, Opt. Lett. 33, 147 (2008).
[CrossRef] [PubMed]

Birkedal, D.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Bolten, J.

Burresi, M.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Chriaux, G.

Dijkhuis, J. I.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Ding, C.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Dorrer, C.

Euser, T. G.

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Först, M.

Gérard, J.-M.

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Golubev, V. G.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Gomez-Iglesias, A.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Gong, Q.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Gottheil, M.

Harding, P. J.

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Hu, X.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Hvam, J. M.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Jeruchim, M. C.

M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).

Jiang, P.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Joffre, M.

Kampfrath, T.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Kang, I.

Kaplyanskii, A. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Kerst, R.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Krauss, T. F.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, Opt. Lett. 33, 147 (2008).
[CrossRef] [PubMed]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Kuipers, L.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Kurdyukov, D. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Kurz, H.

Leaird, D. E.

Leonard, S. W.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
[CrossRef]

Lepetit, L.

Lipson, M.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Mazurenko, D. A.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Miller, A.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Mørk, J.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Nelson, R. D.

Nowicki-Bringuier, Y.-R.

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

O'Brien, D.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

O'Faolain, L.

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, Opt. Lett. 33, 147 (2008).
[CrossRef] [PubMed]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

Park, Y.

Pevtsov, A. B.

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

Plötzing, T.

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Romstad, F. P.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Schilling, J.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
[CrossRef]

Shanmugan, K. S.

M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).

Trebino, R.

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer, 2002).
[CrossRef]

van Driel, H. M.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
[CrossRef]

van Oosten, D.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

Vos, W. L.

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

Wahlbrink, T.

Waldow, M.

Wehrspohn, R. B.

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
[CrossRef]

Weiner, A. M.

White, T. P.

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, Opt. Lett. 33, 147 (2008).
[CrossRef] [PubMed]

Xu, Q.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Yang, H.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Appl. Phys. Lett. (4)

D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, A. A. Kaplyanskii, D. A. Kurdyukov, and A. B. Pevtsov, Appl. Phys. Lett. 86, 041114 (2005).
[CrossRef]

T. Kampfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, Appl. Phys. Lett. 94, 241119 (2009).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, Appl. Phys. Lett. 90, 261107 (2007).
[CrossRef]

P. J. Harding, T. G. Euser, Y.-R. Nowicki-Bringuier, J.-M. Gérard, and W. L. Vos, Appl. Phys. Lett. 91, 111103 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

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

Nat. Photonics (2)

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (1)

S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66, 161102 (2002).
[CrossRef]

Other (3)

M. C. Jeruchim, P. Balaban, and K. S. Shanmugan, Simulation of Communication Systems: Modeling, Methodology and Techniques (Kluwer, 2000).

In this work, the Fourier transform and its inverse are defined by Ff(ω)=∫dtf(t)exp(iωt) and f(t)=∫dωFf(ω)exp(−iωt)/2π, respectively.

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer, 2002).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of an abstract black-box system that produces an output signal E o as a response to an input signal E i . An external stimulus like an intense pump laser pulse arriving at time τ makes the optical properties of the device time dependent. In the characterization experiment, a broadband probe pulse E i enters the device at time 0, and the resulting output field E o is detected via interference with a reference pulse.

Fig. 2
Fig. 2

(a) Intensity spectra of the 180 fs broadband and 1.9 ps narrowband input pulse E i and E i , respectively, used in this work. (b) Output spectra | F 1 E o ( ω , 10 ps ) | 2 resulting from the broadband input of (a) at 10 ps before and after arrival of the pump pulse, respectively.

Fig. 3
Fig. 3

(a) Intensity spectra of the output pulses resulting from the broadband input of Fig. 2a as a function of the pump–probe delay τ. (b) Phase of F 1 E o ( ω , τ ) for selected wavelengths marked as dashed lines in (a).

Fig. 4
Fig. 4

(a) Device response to the narrowband input pulse shown in Fig. 2a as extracted from the the data in Figs. 2a, 3 by virtue of Eq. (2). (b) Device output measured. Note the excellent agreement of both figures.

Equations (2)

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E o ( t ) = d t T ( t , t ) E i ( t ) .
F 12 E o ( ω , Ω ) = F 12 E o ( ω , Ω ) F E i ( ω Ω ) F E i ( ω Ω ) ,

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