Abstract

Surface Bloch modes induced on three-dimensional dielectric photonic crystals with a complete photonic bandgap are evanescently decaying states at surfaces and have large field overlap with low-index media, resulting in narrow spectrum linewidth and simultaneously a large resonance shift due to a perturbation of the refractive index in the background media. Surface Bloch resonance states are analyzed for (001), (100), and (110) woodpile surface planes. Low-loss, high-sensitivity surface Bloch modes are also analyzed on a flat-top (001) woodpile planar surface. These analyzed surface Bloch modes are confined in a subwavelength scale and are expected to form a basis set used for optical resonance sensing.

© 2011 Optical Society of America

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References

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2011 (1)

T. Yoshie, L. Tang, and S.-Y. Su, Sensors 11, 1972 (2011).
[CrossRef]

2010 (1)

L. Tang and T. Yoshie, J. Vac. Sci, Technol. B 28, 301 (2010).
[CrossRef]

2009 (3)

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

K. Ishizaki and S. Noda, Nature 460, 367 (2009).
[CrossRef] [PubMed]

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

2008 (1)

F. Vollmer, S. Arnold, and D. Keng, Proc. Natl. Acad. Sci. USA 105, 20701 (2008).
[CrossRef] [PubMed]

2007 (2)

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

L. Tang and T. Yoshie, Opt. Express 15, 17254 (2007).
[CrossRef] [PubMed]

2006 (3)

2004 (1)

2001 (2)

B.E.Sernelius, ed., Surface Modes in Physics (Wiley, 2001).
[CrossRef]

M. Qiu and S. He, Phys. Lett. A 282, 85 (2001).
[CrossRef]

1991 (1)

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

1977 (1)

1939 (1)

W. Shockley, Phys. Rev. 56, 317 (1939).
[CrossRef]

1932 (1)

V. I. Tamm, Zeitschrift für Physik A 76, 849 (1932).
[CrossRef]

Armani, A.

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

Arnold, S.

F. Vollmer, S. Arnold, and D. Keng, Proc. Natl. Acad. Sci. USA 105, 20701 (2008).
[CrossRef] [PubMed]

Brommer, K.

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Chen, H.

Flagan, R. P.

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

Fraser, S.

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

He, S.

M. Qiu and S. He, Phys. Lett. A 282, 85 (2001).
[CrossRef]

Ho, W.

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

Hong, C.

Hsiao, Y.

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

Imada, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Ishizaki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

K. Ishizaki and S. Noda, Nature 460, 367 (2009).
[CrossRef] [PubMed]

Joannopoulos, J.

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Keng, D.

F. Vollmer, S. Arnold, and D. Keng, Proc. Natl. Acad. Sci. USA 105, 20701 (2008).
[CrossRef] [PubMed]

Kulkarni, R.

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

Lee, P.

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

Lu, T.

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

McNab, S.

Meade, R.

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Moll, N.

Nakamori, T.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Noda, S.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

K. Ishizaki and S. Noda, Nature 460, 367 (2009).
[CrossRef] [PubMed]

Okano, M.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Ota, Y.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Poon, A.

Qiu, M.

M. Qiu and S. He, Phys. Lett. A 282, 85 (2001).
[CrossRef]

Rahachou, A.

Rappe, A.

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Shockley, W.

W. Shockley, Phys. Rev. 56, 317 (1939).
[CrossRef]

Su, S.-Y.

T. Yoshie, L. Tang, and S.-Y. Su, Sensors 11, 1972 (2011).
[CrossRef]

Suzuki, K.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Takahashi, S.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Tamm, V. I.

V. I. Tamm, Zeitschrift für Physik A 76, 849 (1932).
[CrossRef]

Tang, L.

T. Yoshie, L. Tang, and S.-Y. Su, Sensors 11, 1972 (2011).
[CrossRef]

L. Tang and T. Yoshie, J. Vac. Sci, Technol. B 28, 301 (2010).
[CrossRef]

L. Tang and T. Yoshie, Opt. Express 15, 17254 (2007).
[CrossRef] [PubMed]

Tsia, K.

Vahala, K. J.

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

Vlasov, Y.

Vollmer, F.

F. Vollmer, S. Arnold, and D. Keng, Proc. Natl. Acad. Sci. USA 105, 20701 (2008).
[CrossRef] [PubMed]

Yariv, A.

Yeh, P.

Yoshie, T.

T. Yoshie, L. Tang, and S.-Y. Su, Sensors 11, 1972 (2011).
[CrossRef]

L. Tang and T. Yoshie, J. Vac. Sci, Technol. B 28, 301 (2010).
[CrossRef]

L. Tang and T. Yoshie, Opt. Express 15, 17254 (2007).
[CrossRef] [PubMed]

Zozoulenko, I.

Appl. Phys. Lett. (1)

T. Lu, Y. Hsiao, W. Ho, and P. Lee, Appl. Phys. Lett. 94, 141110 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Vac. Sci, Technol. B (1)

L. Tang and T. Yoshie, J. Vac. Sci, Technol. B 28, 301 (2010).
[CrossRef]

Nat. Mater. (1)

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, Nat. Mater. 8, 721 (2009).
[CrossRef] [PubMed]

Nature (1)

K. Ishizaki and S. Noda, Nature 460, 367 (2009).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Lett. A (1)

M. Qiu and S. He, Phys. Lett. A 282, 85 (2001).
[CrossRef]

Phys. Rev. (1)

W. Shockley, Phys. Rev. 56, 317 (1939).
[CrossRef]

Phys. Rev. B (1)

R. Meade, K. Brommer, A. Rappe, and J. Joannopoulos, Phys. Rev. B 44, 10961 (1991).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

F. Vollmer, S. Arnold, and D. Keng, Proc. Natl. Acad. Sci. USA 105, 20701 (2008).
[CrossRef] [PubMed]

Science (1)

A. Armani, R. Kulkarni, S. Fraser, R. P. Flagan, and K. J. Vahala, Science 317, 783 (2007).
[CrossRef] [PubMed]

Sensors (1)

T. Yoshie, L. Tang, and S.-Y. Su, Sensors 11, 1972 (2011).
[CrossRef]

Zeitschrift für Physik A (1)

V. I. Tamm, Zeitschrift für Physik A 76, 849 (1932).
[CrossRef]

Other (2)

B.E.Sernelius, ed., Surface Modes in Physics (Wiley, 2001).
[CrossRef]

J.Homola, ed., Surface Plasmon Resonance-Based Sensors (Springer, 2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Dispersion relations for (a)  ( 001 ) , (b)  ( 100 ) and (c)  ( 110 ) surface Bloch modes. Dark gray zones are above the light line, and light gray zones are photonic bands. The index n b is 1.0 for ( 001 ) modes, and the surface termination value t is varied. The analyzed indices ( n b ) are 1.0 and 1.33 for the other modes. Insets show mode profiles ( E z , E x , E z , respectively) at the blue circle points in the dispersion. Γ = ( 0 , 0 , 0 ) . The vector k is represented in a unit of ( 2 Π / a 1 , 2 Π / a 2 , 2 Π / a 3 ) . For ( 001 ) modes, X 1 = ( 1 / 2 , 0 , 0 ) , X 2 = ( 0 , 1 / 2 , 0 ) , M = ( 1 / 2 , 1 / 2 , 0 ) where a 1 = a 2 = a and a 3 = 4 h . For ( 100 ) modes, X 1 = ( 0 , 1 / 2 , 0 ) , X 2 = ( 0 , 0 , 1 / 2 ) , M = ( 0 , 1 / 2 , 1 / 2 ) where a 1 = a 2 = a and a 3 = 4 h . For ( 110 ) modes, X 1 = ( 1 / 2 , 0 , 0 ) , X 2 = ( 0 , 1 / 2 , 0 ) , M = ( 1 / 2 , 1 / 2 , 0 ) where a 1 = a 3 = 2 a and a 2 = 4 h . The plane wave expansion method was used for calculations.

Fig. 2
Fig. 2

Waveguide Q factor dependence on number of unit cells for n b = 1.0 and 1.33, and the normalized sensitivity S versus the background medium index n b for k i . Analysis of (a)  ( 001 ) , (b)  ( 100 ) , and (c)  ( 110 ) surfaces. The surface plane vectors k i are ( 1 / 2 , { i 1 } / 12 , 0 ) , ( 0 , 1 / 2 , { i 1 } / 12 ) for ( 001 ) and ( 100 ) woodpiles. For ( 110 ) woodpile, k i is defined as k 1 = ( 1 / 2 , 1 / 4 , 0 ) , k 2 = ( 1 / 2 , 3 / 8 , 0 ) , k 3 = ( 1 / 2 , 1 / 2 , 0 ) , k 4 = ( 3 / 8 , 1 / 2 , 0 ) , and k 5 = ( 1 / 4 , 1 / 2 , 0 ) .

Fig. 3
Fig. 3

( 001 ) surface Bloch modes of flat-top woodpile photonic crystal with silicon filling in air space of the last rod stacking layer: (a) Normalized sensitivity S compared with the refractive index of a volume above the surface n bt . The surface is a thin silicon slab. The surface plane vector k i is ( 1 / 2 , { i 1 } / 12 , 0 ) in the same unit as the ones in Fig. 1a. (b)  E z component profile at k = k 1 = X 1 in a supercell.

Equations (1)

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S ( n b ) = n b bg ε 0 | E ( r ) | 2 d V all ε ( r ) | E ( r ) | 2 d V ,

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