Abstract

We present a simple analytic formalism to explain the unique resonance phenomenon in subwavelength high- contrast gratings (HCG). We show that the resonances are due to strong coupling between two surface-normal waveguide array modes resulting from abrupt and large index contrast. Simple expression for HCG quality factor is derived that agrees with spectral-fitting approaches reported in literature.

© 2011 Optical Society of America

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2010 (1)

2009 (1)

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

2008 (2)

2007 (1)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 1, 119 (2007).
[CrossRef]

2006 (1)

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

2003 (1)

2000 (1)

1998 (1)

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

1997 (1)

1994 (1)

1993 (2)

1981 (1)

Asatryan, A. A.

Baets, R.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Boons, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Botten, L. C.

Caekebeke, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Chang-Hasnain, C. J.

V. Karagodsky, F. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 18, 16973 (2010).
[CrossRef] [PubMed]

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 17282 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 2, 180 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 1, 119 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

V. Karagodsky, M. C. Y. Huang, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008), paper JTuA128.

Chase, C.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Chavel, P.

de Sterke, C. M.

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

Dhoedt, B.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Fan, S.

Gaylord, T. K.

Goeman, S.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Grann, E. B.

Haggans, C. W.

Huang, M. C. Y.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 17282 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 2, 180 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 1, 119 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

V. Karagodsky, M. C. Y. Huang, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008), paper JTuA128.

Hugonin, J. P.

Joannopoulos, J. D.

Karagodsky, V.

V. Karagodsky, F. Sedgwick, and C. J. Chang-Hasnain, Opt. Express 18, 16973 (2010).
[CrossRef] [PubMed]

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

V. Karagodsky, M. C. Y. Huang, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008), paper JTuA128.

Kaushik, S.

Kern, J.

Kostuk, R. K.

Lalanne, P.

Li, L.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

McPhedran, R. C.

Moewe, M.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 17282 (2008).
[CrossRef] [PubMed]

Moharam, M. G.

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

Nicorovici, N. P.

Pesala, B.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Pommet, D. A.

Robinson, P. A.

Sedgwick, F.

Sedgwick, F. G.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Suh, W.

Van Daele, P.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Vandeputte, K.

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

Zhou, Y.

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 17282 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 2, 180 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 1, 119 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, IEEE J. Sel. Top. Quantum Electron. 15, 1485 (2009).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photonics Technol. Lett. 16, 518 (2004).
[CrossRef]

S. Goeman, S. Boons, B. Dhoedt, K. Vandeputte, K. Caekebeke, P. Van Daele, and R. Baets, IEEE Photonics Technol. Lett. 10, 1205 (1998).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

L. Li, J. Mod. Opt. 40, 553 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Nat. Photon. (2)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 1, 119 (2007).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, Nat. Photon. 2, 180 (2008).
[CrossRef]

Opt. Express (2)

Other (1)

V. Karagodsky, M. C. Y. Huang, and C. J. Chang-Hasnain, in Conference on Lasers and Electro-Optics (CLEO) (Optical Society of America, 2008), paper JTuA128.

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Figures (2)

Fig. 1
Fig. 1

(a) High-contrast grating (HCG) resonator schematic. Λ denotes grating period. (b) Surface-normal reflectivity spectrum of HCG resonator, where the resonance is manifested by a very sharp transition between 0% and 100% reflectivity values. (c) Contour plot of the first four HCG grating modes that sum up to the overall resonator supermode in (d).

Fig. 2
Fig. 2

Validation of the HCG resonance condition det [ I ( ρ φ ) 2 ] = 0 and of the Q-factor formulation in Eqs. (3, 4). (a) Surface-normal reflectivity spectra of an HCG-R consisting of five resonances calculated using RCWA [15], (b) determinant versus wavelength, (c) the HCG Q factor obtained from Eqs. (3, 4) compared with that from Fano fitting. The overall Q factor of the HCG is maximal among Q 1 and Q 2 . The Q-factor spikes are shown to precisely predict the wavelengths of the resonances in (a). (d) The dependence of HCG-R Q factor on HCG thickness (blue), as dictated by Eq. (4), compared with a uniform dielectric FP layer (Eq. (2)). The uniform layer Q oscillates (not plotted) between maximum and minimum values (both plotted) as a function of thickness. This variation is very small compared with Q HCG .

Equations (4)

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det [ I ( ρ φ ) 2 ] = 0.
Q = 2 π n gr t λ | ρ 1 ρ 2 | .
Q j = 2 π n gr t g λ | r j 1 r j 2 | , where     r j = eigenvalues ( ρ φ ) .
Q HCG = max j ( Q j )

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