Abstract

An ultrafast pump-probe experiment is performed on wavelength-scale, silicon-based, optical microcavities that confine light in three dimensions with resonant wavelengths near 1.5 µm, and lifetimes on the order of 20 ps. A below-bandgap probe pulse tuned to overlap the cavity resonant frequency is used to inject electromagnetic energy into the cavity, and an above-bandgap pump pulse is used to generate free carriers in the silicon, thus altering the real and imaginary components of the cavity’s refractive index, and hence its resonant frequency and lifetime. When the pump pulse injects a carrier density of ~5×1017 cm-3 before the resonant probe pulse strikes the sample, the emitted radiation from the cavity is blue-shifted by 16 times the bare cavity linewidth, and the new linewidth is 3.5 times wider than the original. When the pump pulse injects carriers, and thus suddenly perturbs the cavity properties after the probe pulse has injected energy into the cavity, we show that the emitted radiation is not simply a superposition of Lorentzians centred at the initial and perturbed cavity frequencies. Under these conditions, a simple model and the experimental results show that the power spectrum of radiation emitted by the stored electromagnetic energy when the cavity frequency is perturbed during ring-down consists of a series of coherent oscillations between the original and perturbed cavity frequencies, accompanied by a gradual decrease and broadening of the original cavity line, and the emergence of the new cavity resonance. The modified cavity lifetime is shown to have a significant impact on the evolution of the emission as a function of the pump-probe delay.

© 2007 Optical Society of America

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  1. B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
    [CrossRef]
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    [CrossRef]
  3. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-928 (2003).
    [CrossRef] [PubMed]
  4. T. J. Johnson, M. Borselli, and O. Painter, "Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator," Opt. Express 14, 817-831 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, "Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs," Phys. Rev. Lett. 97, 023903 (2006).
    [CrossRef] [PubMed]
  16. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  19. A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, "Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode SOI waveguide," J. Lightwave Technol. 15, 505-518 (1997).
    [CrossRef]
  20. R. Graham, "Squeezing and frequency changes in harmonic oscillations," J. Mod. Opt. 34, 873-879 (1987).
    [CrossRef]
  21. C. Aslangul, "Sudden expansion or squeezing of a harmonic oscillator," Am. J. Phys. 63, 1021-1025 (1995).
    [CrossRef]

2007 (3)

M. G. Banaee, A. G. Pattantyus-Abraham,M.W. McCutcheon, G.W. Rieger, and J. F. Young, "Efficient coupling of photonic crystal microcavity modes to a ridge waveguide," Appl. Phys. Lett. 90, 193106 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity," Nat. Photon. 1, 49-52 (2007).
[CrossRef]

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vuˇckovi’c, "Ultrafast nonlinear optical tuning of photonic crystal cavities," Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

2006 (3)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, "Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs," Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

T. J. Johnson, M. Borselli, and O. Painter, "Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator," Opt. Express 14, 817-831 (2006).
[CrossRef] [PubMed]

2005 (5)

P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13, 801-820 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Fr’ed’erick, P. J. Poole, G. C. Aers, and R. L. Williams, "Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities," Appl. Phys. Lett. 87, 221110 (2005).
[CrossRef]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

2004 (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431,1081-1084 (2004).
[CrossRef] [PubMed]

2003 (3)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-928 (2003).
[CrossRef] [PubMed]

A. R. Cowan, and J. F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

1997 (1)

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, "Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode SOI waveguide," J. Lightwave Technol. 15, 505-518 (1997).
[CrossRef]

1995 (1)

C. Aslangul, "Sudden expansion or squeezing of a harmonic oscillator," Am. J. Phys. 63, 1021-1025 (1995).
[CrossRef]

1987 (1)

R. Graham, "Squeezing and frequency changes in harmonic oscillations," J. Mod. Opt. 34, 873-879 (1987).
[CrossRef]

1974 (1)

F. Bassani, G. Iadonisi, and B. Preziosi, "Electronic impurity levels in semiconductors," Rep. Prog. Phys. 37, 1099-1210 (1974).
[CrossRef]

Am. J. Phys. (1)

C. Aslangul, "Sudden expansion or squeezing of a harmonic oscillator," Am. J. Phys. 63, 1021-1025 (1995).
[CrossRef]

Appl. Phys. Lett. (5)

M. W. McCutcheon, G. W. Rieger, I. W. Cheung, J. F. Young, D. Dalacu, S. Fr’ed’erick, P. J. Poole, G. C. Aers, and R. L. Williams, "Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities," Appl. Phys. Lett. 87, 221110 (2005).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. G. Banaee, A. G. Pattantyus-Abraham,M.W. McCutcheon, G.W. Rieger, and J. F. Young, "Efficient coupling of photonic crystal microcavity modes to a ridge waveguide," Appl. Phys. Lett. 90, 193106 (2007).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vuˇckovi’c, "Ultrafast nonlinear optical tuning of photonic crystal cavities," Appl. Phys. Lett. 90, 091118 (2007).
[CrossRef]

J. Lightwave Technol. (1)

A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, "Silicon electro-optic modulator based on a three terminal device integrated in a low-loss single-mode SOI waveguide," J. Lightwave Technol. 15, 505-518 (1997).
[CrossRef]

J. Mod. Opt. (1)

R. Graham, "Squeezing and frequency changes in harmonic oscillations," J. Mod. Opt. 34, 873-879 (1987).
[CrossRef]

Nat. Mater. (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Nat. Photon. (1)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity," Nat. Photon. 1, 49-52 (2007).
[CrossRef]

Nature (3)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431,1081-1084 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-928 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Rev. E (1)

A. R. Cowan, and J. F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, "Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs," Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

F. Bassani, G. Iadonisi, and B. Preziosi, "Electronic impurity levels in semiconductors," Rep. Prog. Phys. 37, 1099-1210 (1974).
[CrossRef]

Other (2)

M. Soljaˇci´c, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601(R) (2002).

M. Notomi, and S. Mitsugi, "Wavelength conversion via dynamic refractive index tuning of a cavity," Phys. Rev. A 73, 051803(R) (2006).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Optical set-up of the pump-probe resonant scattering experiment. The two beams propagate colinearly after beamsplitter 1 (BS1), with a relative delay controlled by the delay line on the pump beam path. The resonantly scattered radiation is collected in reflection and detected in the cross polarization by a Fourier transform (FT) spectrometer. A scanning electron microscope image of the L3-microcavity is shown in the inset. The scalebar denotes 1 µm.

Fig. 2.
Fig. 2.

Example of a raw resonant scattering spectrum, showing the sharp mode feature superimposed on the non-resonant laser line-shape. The data of Figs. 3 and 4 are obtained by normalizing the raw spectrum by a similar spectrum for which the mode is temperature-tuned to a different frequency. This normalization procedure removes the Fabry Perot fringes evident in the spectrum and results in an essentially background-free probe of the mode.

Fig. 3.
Fig. 3.

Resonant scattering spectra from a microcavity for a wide range of delay times between the pump and the probe beams. The spectra are offset so that their non-resonant backgrounds intercept the vertical axis at the corresponding pump-probe delay, τ=t0 -tp . The red spectrum in the lower plot shows the bare mode spectrum with the pump off. The bare mode and the two spectra at negative delays are not fully resolved, and so appear broader than the numbers quoted in the text.

Fig. 4.
Fig. 4.

(a) Experimental spectra of a high-Q mode dynamically perturbed by a population of free carriers. The data are normalized by a reference spectrum of the non-resonantly scattered laser line-shape. (b) Normalized spectra from simulations of a perturbed harmonic oscillator in which the perturbation of ω and G occurs instantaneously (blue traces), as in Eq. 1, and linearly over a 500 fs time width (red traces). The dashed black line in both plots indicates the e -1 lifetime of 17 ps of the mode (at ω1) before the dynamic perturbation.

Fig. 5.
Fig. 5.

Simulation of a dynamically perturbed mode with no change in damping, and a new mode frequency that does not relax with time. The unperturbed mode frequency and Q are the same as in Fig. 4(b). The dashed red line is explained in the caption to Fig. 4.

Equations (1)

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P ( t ) = e i ω 1 t Γ 1 t ( θ ( t ) θ ( t t p ) ) + e i ω 1 t p Γ 1 t p e i ω 2 ( t t p ) Γ 2 ( t t p ) θ ( t t p ) ,

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