Abstract

We extend the control range of the Q factor of a ring cavity that consists of a photonic crystal. The control range, which determines the storage time (high Q) and efficiency of input and output (low Q) of light, is required to be wide for the random-access memory of an optical pulse train. The conventional photonic-crystal ring cavity with a directional coupler and a hexagonal-shape ring waveguide has a very narrow range. We replace these components by a directional coupler having flat dispersion and a circularly curved ring waveguide. We experimentally varied the Q factor by thermal modulation of the device and achieved a control range between 1.9×103 and 1.7×104.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, and M. Itoh, “Short photonic-crystal directional coupling optical switch of extended optical bandwidth using flat dispersion,” Jpn. J. Appl. Phys. 50, 032201 (2011).
[CrossRef]

2008 (2)

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, T. Yatagai, and M. Itoh, “Development of curved two-dimensional photonic crystal waveguides,” Opt. Commun. 281, 5788–5792 (2008).
[CrossRef]

M. David, F. Monifi, A. Ghaffari, and M. S. Abrishamian, “Heterostructure wavelength division demultiplexers using photonic crystal ring resonators,” Opt. Commun. 281, 4028–4032 (2008).
[CrossRef]

2007 (3)

2006 (1)

2005 (1)

N. Yamamoto, Y. Watanabe, and K. Komori, “Design of photonic crystal directional coupler with high extinction ratio and small coupling length,” Jpn. J. Appl. Phys. 44, 2575–2578 (2005).
[CrossRef]

2004 (3)

2003 (1)

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]

2002 (1)

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[CrossRef]

1999 (1)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

1998 (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

1997 (1)

1996 (1)

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1982 (1)

Abrishamian, M. S.

M. David, F. Monifi, A. Ghaffari, and M. S. Abrishamian, “Heterostructure wavelength division demultiplexers using photonic crystal ring resonators,” Opt. Commun. 281, 4028–4032 (2008).
[CrossRef]

Akahane, Y.

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]

Asakawa, K.

Asano, T.

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]

Cai, J.

Chodorow, M.

Choi, Y.-S.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Chu, S. T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

David, M.

M. David, F. Monifi, A. Ghaffari, and M. S. Abrishamian, “Heterostructure wavelength division demultiplexers using photonic crystal ring resonators,” Opt. Commun. 281, 4028–4032 (2008).
[CrossRef]

Dietrich, E.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Eiselt, M.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Furuya, K.

K. Furuya, N. Yamamoto, Y. Watanabe, and K. Komori, “Novel ring waveguide device in a 2D photonic crystal slab: transmittance simulated by finite-difference time-domain analysis,” Jpn. J. Appl. Phys. 43, 1995–2001 (2004).
[CrossRef]

Ghaffari, A.

M. David, F. Monifi, A. Ghaffari, and M. S. Abrishamian, “Heterostructure wavelength division demultiplexers using photonic crystal ring resonators,” Opt. Commun. 281, 4028–4032 (2008).
[CrossRef]

Goldring, D.

Greene, W.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Grosskopf, G.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Hagness, S. C.

Haus, H. A.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Ho, S. T.

Ikeda, N.

Ippen, E. P.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Itoh, M.

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, and M. Itoh, “Short photonic-crystal directional coupling optical switch of extended optical bandwidth using flat dispersion,” Jpn. J. Appl. Phys. 50, 032201 (2011).
[CrossRef]

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, T. Yatagai, and M. Itoh, “Development of curved two-dimensional photonic crystal waveguides,” Opt. Commun. 281, 5788–5792 (2008).
[CrossRef]

Jeong, S.-H.

S.-H. Jeong, J. Sugisaka, N. Yamamoto, M. Okano, and K. Komori, “Resonant characteristics in a two-dimensional photonic crystal ring resonator with a triangular lattice of air holes,” Jpn. J. Appl. Phys. 46, L534–L536 (2007).
[CrossRef]

S.-H. Jeong, N. Yamamoto, J. Sugisaka, M. Okano, and K. Komori, “GaAs-based two-dimensional photonic crystal slab ring resonator consisting of a directional coupler and bent waveguides,” J. Opt. Soc. Am. B 24, 1951–1959 (2007).
[CrossRef]

Jiang, J.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Kaneko, T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

Kim, G.-H.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Kim, J.-S.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Kim, S.

Kim, S.-H.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Kimerling, L. C.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Kokubun, Y.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

Komori, K.

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, and M. Itoh, “Short photonic-crystal directional coupling optical switch of extended optical bandwidth using flat dispersion,” Jpn. J. Appl. Phys. 50, 032201 (2011).
[CrossRef]

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, T. Yatagai, and M. Itoh, “Development of curved two-dimensional photonic crystal waveguides,” Opt. Commun. 281, 5788–5792 (2008).
[CrossRef]

S.-H. Jeong, J. Sugisaka, N. Yamamoto, M. Okano, and K. Komori, “Resonant characteristics in a two-dimensional photonic crystal ring resonator with a triangular lattice of air holes,” Jpn. J. Appl. Phys. 46, L534–L536 (2007).
[CrossRef]

S.-H. Jeong, N. Yamamoto, J. Sugisaka, M. Okano, and K. Komori, “GaAs-based two-dimensional photonic crystal slab ring resonator consisting of a directional coupler and bent waveguides,” J. Opt. Soc. Am. B 24, 1951–1959 (2007).
[CrossRef]

N. Yamamoto, T. Ogawa, and K. Komori, “Photonic crystal directional coupler switch with small switching length and wide bandwidth,” Opt. Express 14, 1223–1229 (2006).
[CrossRef]

N. Yamamoto, Y. Watanabe, and K. Komori, “Design of photonic crystal directional coupler with high extinction ratio and small coupling length,” Jpn. J. Appl. Phys. 44, 2575–2578 (2005).
[CrossRef]

K. Furuya, N. Yamamoto, Y. Watanabe, and K. Komori, “Novel ring waveguide device in a 2D photonic crystal slab: transmittance simulated by finite-difference time-domain analysis,” Jpn. J. Appl. Phys. 43, 1995–2001 (2004).
[CrossRef]

Kuller, L.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Langenhorst, R.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Lee, Y.-H.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Levy, U.

Little, B. E.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Ludwig, R.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Mendlovic, D.

Monifi, F.

M. David, F. Monifi, A. Ghaffari, and M. S. Abrishamian, “Heterostructure wavelength division demultiplexers using photonic crystal ring resonators,” Opt. Commun. 281, 4028–4032 (2008).
[CrossRef]

Nakamura, Y.

Noda, S.

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]

Nordin, G. P.

Ogawa, T.

Okano, M.

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, and M. Itoh, “Short photonic-crystal directional coupling optical switch of extended optical bandwidth using flat dispersion,” Jpn. J. Appl. Phys. 50, 032201 (2011).
[CrossRef]

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, T. Yatagai, and M. Itoh, “Development of curved two-dimensional photonic crystal waveguides,” Opt. Commun. 281, 5788–5792 (2008).
[CrossRef]

S.-H. Jeong, N. Yamamoto, J. Sugisaka, M. Okano, and K. Komori, “GaAs-based two-dimensional photonic crystal slab ring resonator consisting of a directional coupler and bent waveguides,” J. Opt. Soc. Am. B 24, 1951–1959 (2007).
[CrossRef]

S.-H. Jeong, J. Sugisaka, N. Yamamoto, M. Okano, and K. Komori, “Resonant characteristics in a two-dimensional photonic crystal ring resonator with a triangular lattice of air holes,” Jpn. J. Appl. Phys. 46, L534–L536 (2007).
[CrossRef]

Pan, W.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

Park, H.-G.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Pieper, W.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Rafizadeh, D.

Ryu, H.-Y.

S.-H. Kim, H.-Y. Ryu, H.-G. Park, G.-H. Kim, Y.-S. Choi, Y.-H. Lee, and J.-S. Kim, “Two-dimensional photonic crystal hexagonal waveguide ring laser,” Appl. Phys. Lett. 81, 2499–2501 (2002).
[CrossRef]

Sato, S.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid,” IEEE Photon. Technol. Lett. 11, 691–693 (1999).
[CrossRef]

Shaw, H. J.

Song, B.-S.

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]

Stair, K. A.

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Stokes, L. F.

Sugimoto, Y.

Sugisaka, J.

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, and M. Itoh, “Short photonic-crystal directional coupling optical switch of extended optical bandwidth using flat dispersion,” Jpn. J. Appl. Phys. 50, 032201 (2011).
[CrossRef]

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, T. Yatagai, and M. Itoh, “Development of curved two-dimensional photonic crystal waveguides,” Opt. Commun. 281, 5788–5792 (2008).
[CrossRef]

S.-H. Jeong, J. Sugisaka, N. Yamamoto, M. Okano, and K. Komori, “Resonant characteristics in a two-dimensional photonic crystal ring resonator with a triangular lattice of air holes,” Jpn. J. Appl. Phys. 46, L534–L536 (2007).
[CrossRef]

S.-H. Jeong, N. Yamamoto, J. Sugisaka, M. Okano, and K. Komori, “GaAs-based two-dimensional photonic crystal slab ring resonator consisting of a directional coupler and bent waveguides,” J. Opt. Soc. Am. B 24, 1951–1959 (2007).
[CrossRef]

Taflove, A.

Tanaka, Y.

Thoen, E. R.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Tiberio, R. C.

Watanabe, Y.

N. Yamamoto, Y. Watanabe, and K. Komori, “Design of photonic crystal directional coupler with high extinction ratio and small coupling length,” Jpn. J. Appl. Phys. 44, 2575–2578 (2005).
[CrossRef]

K. Furuya, N. Yamamoto, Y. Watanabe, and K. Komori, “Novel ring waveguide device in a 2D photonic crystal slab: transmittance simulated by finite-difference time-domain analysis,” Jpn. J. Appl. Phys. 43, 1995–2001 (2004).
[CrossRef]

Weber, H. G.

R. Langenhorst, M. Eiselt, W. Pieper, G. Grosskopf, R. Ludwig, L. Kuller, E. Dietrich, and H. G. Weber, “Fiber loop optical buffer,” J. Lightwave Technol. 14, 324–335 (1996).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yamamoto, N.

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, and M. Itoh, “Short photonic-crystal directional coupling optical switch of extended optical bandwidth using flat dispersion,” Jpn. J. Appl. Phys. 50, 032201 (2011).
[CrossRef]

J. Sugisaka, N. Yamamoto, M. Okano, K. Komori, T. Yatagai, and M. Itoh, “Development of curved two-dimensional photonic crystal waveguides,” Opt. Commun. 281, 5788–5792 (2008).
[CrossRef]

S.-H. Jeong, J. Sugisaka, N. Yamamoto, M. Okano, and K. Komori, “Resonant characteristics in a two-dimensional photonic crystal ring resonator with a triangular lattice of air holes,” Jpn. J. Appl. Phys. 46, L534–L536 (2007).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the ring cavity. It consists of an I/O waveguide and a ring waveguide. These waveguides are optically coupled via a directional coupler. (b) The directional coupler is in the bar state. Light in the ring waveguide is strongly confined (high Q). (c) The directional coupler is in the cross state. Light in the ring waveguide is immediately extracted (low Q).

Fig. 2.
Fig. 2.

Surface SEM images of the (a) entire microring cavity and (b) flat-band directional coupler. The length of the ring waveguide is 520a with a curvature of 1.0°/a. The length of the flat-band directional coupler is 12a. Both ends are connected to a 5a long adiabatic connector.

Fig. 3.
Fig. 3.

Transmission spectra of the ring cavity (left side) and directional coupler (right side) at (a) 25.2°C, (b) 50.0°C, and (c) 68.8°C. The width of the resonance peak depends on the state of the directional coupler; broad peaks corresponds to the cross state, and sharp peaks correspond to the bar state. As the temperature is increased, the spectra are redshifted and the peak at 1370.9 nm (indicated by vertical dashed lines) becomes sharp.

Fig. 4.
Fig. 4.

Numerically simulated spectra of ring cavities modulated the refractive index of (a) the entire device and (b) only the directional coupler. The spectra are varied from (i) to (iv) by the modulation. The resonance peak of the identical ring resonance mode is indicated by arrows. The widths of the resonance peaks for (a) are hardly varied, while those for (b) are varied, with their peak position fixed.

Fig. 5.
Fig. 5.

Spectra of a single directional coupler with a flat band (upper) and a waveguide having two circularly curved 60° bends (lower). At the wavelength of the flat band (1368.5 nm), the variation of the transmittance of the bent waveguide is very small. The change of the Qring in a spectral shift by around a few nanometers is negligible. We can obtain a nearly equal control range between 1.9×103 and 1.7×104, even if the refractive index of only the directional coupler is modulated.

Equations (10)

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U(t)=exp(ωtQsys),
U(t)=exp(ωtQDC)exp(ωtQring),
1Qsys=1Qring+1QDC.
κ=IcrossIbar+Icross,
1κ=exp(2πωnT0QDC),
T0=Lnvg,
QDC=2πωnLnvnln(11κ).
Qsys1=FWHM of resonance-peakpeak wavelength.
I(ω)=14|(eike(ω)LDC+eiko(ω)LDC)+(eike(ω)LDCeiko(ω)LDC)2e(γ+ikwg(ω)Lring)2(eike(ω)LDC+eiko(ω)LDC)e(γ+ikwg(ω)Lring)|2,
Ts=Qω.

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