Abstract

Slow light has a variety of applications, in particular for enhanced nonlinear effects like four-wave mixing and high-harmonic generation. Here, we propose a photonic crystal coupled-cavity waveguide with an ultracompact arrangement of the constituent cavities in the propagation direction, and use an optimization algorithm to tune several structural parameters to engineer slow light with a constant group index ng over a wide bandwidth. We propose several specific silicon designs, including one with ng37 over a 20 nm wavelength range and another one with ng116 over an 8.8 nm band, which yields a group index–bandwidth product of 0.66—a record value among all slow-light devices. The design is experimentally beneficial because of its small footprint and straightforward fabrication and could find applications in optical storage or switching, and in generating quantum states of light.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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[Crossref]

U. P. Dharanipathy, M. Minkov, M. Tonin, V. Savona, and R. Houdré, Appl. Phys. Lett. 105, 101101 (2014).
[Crossref]

H. Takesue, N. Matsuda, E. Kuramochi, and M. Notomi, Sci. Rep. 4, 3913 (2014).
[Crossref]

S. Haddadi, P. Hamel, G. Beaudoin, I. Sagnes, C. Sauvan, P. Lalanne, J. A. Levenson, and A. M. Yacomotti, Opt. Express 22, 12359 (2014).
[Crossref]

M. Minkov and V. Savona, Sci. Rep. 4, 5124 (2014).
[Crossref]

2013 (3)

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, Opt. Express 21, 28233 (2013).
[Crossref]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, and M. Notomi, Nat. Commun. 4, 2725 (2013).
[Crossref]

M. Minkov and V. Savona, Phys. Rev. B 87, 125306 (2013).

2012 (2)

2011 (1)

2010 (3)

2009 (5)

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
[Crossref]

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, Opt. Lett. 34, 359 (2009).
[Crossref]

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photonics 3, 206 (2009).
[Crossref]

2008 (4)

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, Opt. Express 16, 6227 (2008).
[Crossref]

T. F. Krauss, Nat. Photonics 2, 448 (2008).
[Crossref]

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
[Crossref]

2007 (3)

D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, Opt. Express 15, 1228 (2007).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[Crossref]

S. Hughes, Phys. Rev. Lett. 98, 083603 (2007).
[Crossref]

2006 (1)

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).

2005 (4)

D. Mori and T. Baba, Opt. Express 13, 9398 (2005).
[Crossref]

B. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[Crossref]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 2 (2005).

2003 (1)

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[Crossref]

Akahane, Y.

B. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[Crossref]

Andreani, L. C.

Asano, T.

B. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[Crossref]

Azzini, S.

Baba, T.

Badolato, A.

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).
[Crossref]

Baets, R.

Bajoni, D.

Beaudoin, G.

Beggs, D. M.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, J. Opt. 12, 104004 (2010).
[Crossref]

Bogaerts, W.

Combrié, S.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

Corcoran, B.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, Opt. Express 18, 22915 (2010).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photonics 3, 206 (2009).
[Crossref]

De Gabet, R.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

Dharanipathy, U. P.

U. P. Dharanipathy, M. Minkov, M. Tonin, V. Savona, and R. Houdré, Appl. Phys. Lett. 105, 101101 (2014).
[Crossref]

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, Opt. Express 21, 28233 (2013).
[Crossref]

Dumon, P.

Ebnali-Heidari, M.

Eggleton, B. J.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, Opt. Express 18, 22915 (2010).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photonics 3, 206 (2009).
[Crossref]

Galli, M.

Gerace, D.

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).
[Crossref]

M. Galli, D. Gerace, K. Welna, T. F. Krauss, L. O’Faolain, G. Guizzetti, and L. C. Andreani, Opt. Express 18, 26613 (2010).
[Crossref]

L. C. Andreani and D. Gerace, Phys. Rev. B 73, 235114 (2006).

Gomez-Iglesias, A.

Grassani, D.

Grillet, C.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, Opt. Express 18, 22915 (2010).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photonics 3, 206 (2009).
[Crossref]

Guizzetti, G.

Haddadi, S.

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[Crossref]

Hamel, P.

Harada, K.

Helt, L. G.

Houdré, R.

U. P. Dharanipathy, M. Minkov, M. Tonin, V. Savona, and R. Houdré, Appl. Phys. Lett. 105, 101101 (2014).
[Crossref]

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, Opt. Express 21, 28233 (2013).
[Crossref]

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, Opt. Lett. 34, 359 (2009).
[Crossref]

Hughes, S.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

S. Hughes, Phys. Rev. Lett. 98, 083603 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 2 (2005).

Hugonin, J. P.

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
[Crossref]

Jágerská, J.

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, Opt. Lett. 34, 359 (2009).
[Crossref]

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

Jaouën, Y.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

Jensen, J. S.

Karle, T.

Kato, T.

Krauss, T. F.

Kuramochi, E.

H. Takesue, N. Matsuda, E. Kuramochi, and M. Notomi, Sci. Rep. 4, 3913 (2014).
[Crossref]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, and M. Notomi, Nat. Commun. 4, 2725 (2013).
[Crossref]

N. Matsuda, T. Kato, K. Harada, H. Takesue, E. Kuramochi, H. Taniyama, and M. Notomi, Opt. Express 19, 19861 (2011).
[Crossref]

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 2 (2005).

Lai, Y.

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).
[Crossref]

Lalanne, P.

Le Thomas, N.

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, Opt. Lett. 34, 359 (2009).
[Crossref]

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

Levenson, J. A.

Li, J.

Liscidini, M.

Matsuda, N.

H. Takesue, N. Matsuda, E. Kuramochi, and M. Notomi, Sci. Rep. 4, 3913 (2014).
[Crossref]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, and M. Notomi, Nat. Commun. 4, 2725 (2013).
[Crossref]

N. Matsuda, T. Kato, K. Harada, H. Takesue, E. Kuramochi, H. Taniyama, and M. Notomi, Opt. Express 19, 19861 (2011).
[Crossref]

Mazoyer, S.

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Phys. Rev. Lett. 103, 063903 (2009).
[Crossref]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[Crossref]

Melloni, A.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, J. Opt. 12, 104004 (2010).
[Crossref]

Michaeli, A.

Minkov, M.

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).
[Crossref]

U. P. Dharanipathy, M. Minkov, M. Tonin, V. Savona, and R. Houdré, Appl. Phys. Lett. 105, 101101 (2014).
[Crossref]

M. Minkov and V. Savona, Sci. Rep. 4, 5124 (2014).
[Crossref]

M. Minkov and V. Savona, Phys. Rev. B 87, 125306 (2013).

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, Opt. Express 21, 28233 (2013).
[Crossref]

Monat, C.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, Opt. Express 18, 22915 (2010).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photonics 3, 206 (2009).
[Crossref]

Mori, D.

Mørk, J.

Moss, D. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photonics 3, 206 (2009).
[Crossref]

Munro, W. J.

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, and M. Notomi, Nat. Commun. 4, 2725 (2013).
[Crossref]

Noda, S.

B. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[Crossref]

Notomi, M.

H. Takesue, N. Matsuda, E. Kuramochi, and M. Notomi, Sci. Rep. 4, 3913 (2014).
[Crossref]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, and M. Notomi, Nat. Commun. 4, 2725 (2013).
[Crossref]

N. Matsuda, T. Kato, K. Harada, H. Takesue, E. Kuramochi, H. Taniyama, and M. Notomi, Opt. Express 19, 19861 (2011).
[Crossref]

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 2 (2005).

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[Crossref]

O’Brien, D.

O’Faolain, L.

Patterson, M.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

Pirotta, S.

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).
[Crossref]

Ramunno, L.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 2 (2005).

Rossi, A.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. Rossi, R. De Gabet, and Y. Jaouën, Phys. Rev. Lett. 102, 1 (2009).
[Crossref]

Sagnes, I.

Salib, M.

Sauvan, C.

Savona, V.

M. Minkov and V. Savona, Sci. Rep. 4, 5124 (2014).
[Crossref]

Y. Lai, S. Pirotta, G. Urbinati, D. Gerace, M. Minkov, V. Savona, A. Badolato, and M. Galli, Appl. Phys. Lett. 104, 241101 (2014).
[Crossref]

U. P. Dharanipathy, M. Minkov, M. Tonin, V. Savona, and R. Houdré, Appl. Phys. Lett. 105, 101101 (2014).
[Crossref]

M. Minkov, U. P. Dharanipathy, R. Houdré, and V. Savona, Opt. Express 21, 28233 (2013).
[Crossref]

M. Minkov and V. Savona, Phys. Rev. B 87, 125306 (2013).

Schulz, S. A.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, J. Opt. 12, 104004 (2010).
[Crossref]

Settle, M. D.

Shinya, A.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, Nat. Photonics 1, 49 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, Phys. Rev. B 72, 2 (2005).

Sigmund, O.

Sipe, J. E.

Song, B.

B. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003).
[Crossref]

Sorel, M.

Strain, M. J.

Takesue, H.

H. Takesue, N. Matsuda, E. Kuramochi, and M. Notomi, Sci. Rep. 4, 3913 (2014).
[Crossref]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, and M. Notomi, Nat. Commun. 4, 2725 (2013).
[Crossref]

N. Matsuda, T. Kato, K. Harada, H. Takesue, E. Kuramochi, H. Taniyama, and M. Notomi, Opt. Express 19, 19861 (2011).
[Crossref]

Tanabe, T.

M. Notomi, E. Kuramochi, and T. Tanabe, Nat. Photonics 2, 741 (2008).
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Lumerical Solutions, Inc., https://www.lumerical.com/tcad-products/fdtd/ .

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) CCW composed of coupled L3 PhC cavities; the propagation direction is the vertical, y axis. The unit cell of the infinite structure is marked by dashed lines. For dispersion optimization, the radius of all holes marked in red is varied by an amount Δr1, and that of all holes marked in green by Δr2. (b) Tight-binding dispersion of a chain of cavities with first- and second-neighbor coupling, t1 and t2. The dashed lines show the folded bands in the case of two cavities included in the unit cell, which is an equivalent representation.
Fig. 2.
Fig. 2. (a) Cavity–cavity coupling in a system of two cavities arranged as shown in the top inset, depending on the radius change Δr of the holes marked in red. Values obtained with the GME (blue line) and the FDTD (red crosses) methods are shown. Bottom right inset, frequency of the symmetric (yellow) and antisymmetric (purple) modes versus Δr. (b) Same as (a) but for a different arrangement, shown in the top left inset.
Fig. 3.
Fig. 3. (a) Electric field |Ey| profile of the mode marked by a black cross in (b). The green and red holes are modified as in Fig. 1(a), while the white holes are shifted outward by an amount Δx and have a radius changed by Δr3. (b) Wavelength dispersion of the optimized design; the black dashed line marks the Brillouin zone for periodicity 2Ly. Modes from the dashed-line band propagate in the direction opposite to the one of the solid-line band. The operational bandwidth Δω is marked by a light red region [extending into panels (c) and (d)]. (c) Group index dispersion; in light yellow, the region ng(1±ΔR) is marked. (d) Dispersion of the radiative losses.
Fig. 4.
Fig. 4. Designs with (a)–(c) ng=116, G=0.66; (d)–(f) ng=88, G=0.56; (h)–(j) ng=51, G=0.43. The same plotting and color scheme is employed as in Figs. 3(b)3(d).

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