Abstract

We show the first experimental demonstration of multiple heterostructure photonic crystal cavities being coupled together to form a chain of coupled resonators with up to ten cavities. This system allows us to engineer the group velocity of light over a wide range. Devices were fabricated using 193 nm deep UV lithography and standard silicon processing technology. Structures were analysed using both coupled resonator and photonic bandstructure theory, and we highlight the discrepancies arising from subtle imperfections of the fabricated structure.

© 2007 Optical Society of America

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References

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  1. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya and T. Tanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
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    [CrossRef]
  3. T. A. T. Uesugi, B. S. Song and S. Noda, "Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic Crystal slab," Opt. Express 14, 377-386 (2006).
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    [CrossRef]
  5. M. Yanik and S. Fan, "Stopping Light All Optically," Phys. Rev. Lett. 92, 083901 (2004).
    [CrossRef] [PubMed]
  6. T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
    [CrossRef]
  7. T. Asano, B. Song and S. Noda, "Analysis of the experimental Q factors (1 million) of photonic crystal nanocavities," Opt. Express 14, 1996-2002 (2006).
    [CrossRef] [PubMed]
  8. A. Melloni, F. Moricheti and M. Matinelli, "Linear and nonlinear pulse propogation in coupled resonator slowwave optical structures," Opt. Quantum Electron. 35, 365-379 (2003).
    [CrossRef]
  9. J. B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparency media and coupled resonators : comparative analysis," J. Opt. Soc. Am. B 22, 1062-1074 (2005).
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    [CrossRef] [PubMed]
  12. M. Settle, M. Salib, A. Michaeli and T. Krauss, "Low loss silicon on insulator photonic crystal waveguides made by 193nm optical lithography," Opt. Express 14, 2440-2445 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]

2006

2005

J. B. Khurgin, "Optical buffers based on slow light in electromagnetically induced transparency media and coupled resonators : comparative analysis," J. Opt. Soc. Am. B 22, 1062-1074 (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

M. Yanik and S. Fan, "Stopping Light All Optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

2003

A. Melloni, F. Moricheti and M. Matinelli, "Linear and nonlinear pulse propogation in coupled resonator slowwave optical structures," Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

2001

1999

Akahane, Y.

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

Asano, T.

T. Asano, B. Song and S. Noda, "Analysis of the experimental Q factors (1 million) of photonic crystal nanocavities," Opt. Express 14, 1996-2002 (2006).
[CrossRef] [PubMed]

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

Chai, Y.

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

Fan, S.

M. Povinelli and S. Fan, "Radiation loss of coupled-resonator waveguides in photonic-crystal slabs," Appl. Phys. Lett. 89, 191114 (2006).
[CrossRef]

M. Yanik and S. Fan, "Stopping Light All Optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Joannopoulos, J.

Johnson, S.

Karle, T.

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

Khurgin, J. B.

Krauss, T.

M. Settle, M. Salib, A. Michaeli and T. Krauss, "Low loss silicon on insulator photonic crystal waveguides made by 193nm optical lithography," Opt. Express 14, 2440-2445 (2006).
[CrossRef] [PubMed]

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

Kuramochi, E.

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

Lee, R. K.

Matinelli, M.

A. Melloni, F. Moricheti and M. Matinelli, "Linear and nonlinear pulse propogation in coupled resonator slowwave optical structures," Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

Melloni, A.

A. Melloni, F. Moricheti and M. Matinelli, "Linear and nonlinear pulse propogation in coupled resonator slowwave optical structures," Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

Michaeli, A.

Mitsugi, S.

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

Morgan, C.

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

Moricheti, F.

A. Melloni, F. Moricheti and M. Matinelli, "Linear and nonlinear pulse propogation in coupled resonator slowwave optical structures," Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

Noda, S.

Notomi, M.

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

Povinelli, M.

M. Povinelli and S. Fan, "Radiation loss of coupled-resonator waveguides in photonic-crystal slabs," Appl. Phys. Lett. 89, 191114 (2006).
[CrossRef]

Salib, M.

Scherer, A.

Settle, M.

Shinya, A.

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

Song, B.

Song, B. S.

Tanabe, T.

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

Uesugi, T. A. T.

White, I.

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

Xu, Y.

Yanik, M.

M. Yanik and S. Fan, "Stopping Light All Optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Yariv, A.

Appl. Phys. Lett.

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

M. Povinelli and S. Fan, "Radiation loss of coupled-resonator waveguides in photonic-crystal slabs," Appl. Phys. Lett. 89, 191114 (2006).
[CrossRef]

IEEE J. Lightwave Technol.

T. Karle, Y. Chai, C. Morgan, I. White and T. Krauss, "Observation of Pulse Compression in Photonic Crystal Coupled Cavity Waveguides," IEEE J. Lightwave Technol. 22, 514-519 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

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

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

A. Melloni, F. Moricheti and M. Matinelli, "Linear and nonlinear pulse propogation in coupled resonator slowwave optical structures," Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

Phys. Rev. Lett.

M. Yanik and S. Fan, "Stopping Light All Optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Other

A. Yariv. "Optical Electronics in Modern Communications" (Fifth Edition). Oxford University Press, USA, 1997.

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Figures (4)

Fig. 1.
Fig. 1.

Scanning electron micrograph image of a chain of 10 coupled heterostructure cavities. The dashed markers below the photonic crystal structure indicate the positions of the lattice shifts that give rise to the heterostucture nanocavities. The electric field profile of the confined cavity modes is shown below for 3 of the cavities.

Fig. 2.
Fig. 2.

Left: Experimental transmission spectra for (a) 2 cavity (b) 3 cavity and (c) 10 cavity CRS devices. Arrows indicate the observed 1nm bandwidth. Right: Finite difference time domain (FDTD) calculations of the response of different coupled heterostructure nanocav-ity systems. (d) Mode splitting observed in 2 coupled cavity, (e) 3 cavity and (f) 10 cavity systems. The bandwidth becomes populated with the additional cavity modes of the chain in the 3 and 10 cavity case. We experimentally observe a small increase in bandwidth for longer chains which we associate with inhomogeneous broadening, caused by small variations in the size of individual cavities. The observed broadening suggests that it will be difficult to achieve a bandwidth below 0.5 nm in such a coupled system. Fabrications tolerances also account for variation in mode amplitudes and positions.

Fig. 3.
Fig. 3.

Band structure of aW1 photonic crystal waveguide alongside a coupled heterostruc-ture waveguide. The defect state associated with the CRS is isolated from the bottom of the waveguide mode. Inset: Close up of the defect state shows that it has a very low group velocity and exhibits very low dispersion for most of the bandwidth of the state. Please note that the bandstructure is simplified and only shows the CRS band for one period of π/d (0.43 < k [2π/a] < 0.5); in reality, the CRS band repeats with a period of π/d and extends all the way to k = 0, thus highlighting the fact that the device operates above the light line.

Fig. 4.
Fig. 4.

For the ideal case where losses are negligible, the relationship between the bandwidth of the defect state B, slowing factor S and the individual cavity Q-factor is calculated.

Equations (5)

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

1 Q meas = 1 Q + 1 Q .
cos ( βd ) = sin ( kd ) t .
B = 2 FSR π sin 1 ( t ) .
Q = m π 1 t 2 t 2 .
v g = c n 0 t 2 sin 2 ( kd ) cos ( kd ) .

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