Abstract

In this paper, we present a comparative study of the tuning efficiency and sensitivity of guided resonances (GRs) in photonic crystal (PC) holed slabs based on periodic and aperiodically-ordered unit cells, aimed at assessing the applicability of these important technology platforms to ultra-compact optical sensors and active devices. In particular, with specific reference to square-lattice periodic PCs and aperiodically-ordered Ammann-Beenker photonic quasi-crystals, we study the effects of the hole radius, slab thickness, and refractive index on the GR sensitivity and tunability with respect to variation in the hole refractive index. Finally, we carry out a theoretical and numerical analysis in order to correlate the GR shift with the field distribution of the unperturbed (air holes) structures. Our results indicate that the spatial arrangement of the holes may strongly influence the tuning and sensitivity efficiency, and may provide new degrees of freedom and tools for the design and optimization of novel photonic devices for both sensing and telecommunication applications.

© 2010 OSA

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2010

2009

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

L. Shi, P. Pottier, M. Skorobogatiy, and Y.-A. Peter, “Tunable structures comprising two photonic crystal slabs--optical study in view of multi-analyte enhanced detection,” Opt. Express 17(13), 10623–10632 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-13-10623 .
[CrossRef] [PubMed]

K. J. Lee, J. Jin, B.-S. Bae, and R. Magnusson, “Optical filters fabricated in hybrimer media with soft lithography,” Opt. Lett. 34(16), 2510–2512 (2009).
[CrossRef] [PubMed]

I. Gallina, M. Pisco, A. Ricciardi, S. Campopiano, G. Castaldi, A. Cusano, and V. Galdi, “Guided resonances in photonic crystals with point-defected aperiodically-ordered supercells,” Opt. Express 17(22), 19586–19598 (2009),
 http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19586 .
[CrossRef] [PubMed]

H. Y. Song, S. Kim, and R. Magnusson, “Tunable guided-mode resonances in coupled gratings,” Opt. Express 17(26), 23544–23555 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-26-23544 .
[CrossRef]

M. Huang, A. A. Yanik, T.-Y. Chang, and H. Altug, “Sub-wavelength nanofluidics in photonic crystal sensors,” Opt. Express 17(26), 24224–24233 (2009),
 http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-24224 .
[CrossRef]

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

2008

2007

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

2006

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73(11), 115126 (2006).
[CrossRef]

J. Song, R. Proietti Zaccaria, M. B. Yu, and X. W. Sun, “Tunable Fano resonance in photonic crystal slabs,” Opt. Express 14(19), 8812–8826 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-19-8812 .
[CrossRef] [PubMed]

2005

2004

2003

W. Suh and S. H. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003).
[CrossRef] [PubMed]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

2002

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

2001

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63(12), 125107 (2001).
[CrossRef]

1999

1997

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

1995

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B Condens. Matter 52(11), 7982–7986 (1995).
[CrossRef] [PubMed]

Altug, H.

Astratov, V. N.

Bae, B.-S.

Brueck, S. R. J.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

Busch, A.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Bussmann, K.

Campopiano, S.

Carter, M.

Casey, J.

Castaldi, G.

Chang, T.-Y.

Cingolani, R.

Colvin, V. L.

Consales, M.

A. Cusano, M. Giordano, A. Cutolo, M. Pisco, and M. Consales, “Integrated development of chemoptical fiber nanosensors,” Curr. Anal. Chem. 4(4), 296–315 (2008).
[CrossRef]

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73(11), 115126 (2006).
[CrossRef]

Culshaw, I. S.

Cusano, A.

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

I. Gallina, M. Pisco, A. Ricciardi, S. Campopiano, G. Castaldi, A. Cusano, and V. Galdi, “Guided resonances in photonic crystals with point-defected aperiodically-ordered supercells,” Opt. Express 17(22), 19586–19598 (2009),
 http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19586 .
[CrossRef] [PubMed]

A. Cusano, M. Giordano, A. Cutolo, M. Pisco, and M. Consales, “Integrated development of chemoptical fiber nanosensors,” Curr. Anal. Chem. 4(4), 296–315 (2008).
[CrossRef]

Cutolo, A.

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

A. Cusano, M. Giordano, A. Cutolo, M. Pisco, and M. Consales, “Integrated development of chemoptical fiber nanosensors,” Curr. Anal. Chem. 4(4), 296–315 (2008).
[CrossRef]

D’Orazio, A.

De Angelis, C.

De La Rue, R.

De Vittorio, M.

Eddy, C.

Fan, S.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98(3), 033102 (2005).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Fan, S. H.

Galdi, V.

Gallina, I.

Giordano, M.

A. Cusano, M. Giordano, A. Cutolo, M. Pisco, and M. Consales, “Integrated development of chemoptical fiber nanosensors,” Curr. Anal. Chem. 4(4), 296–315 (2008).
[CrossRef]

Grande, M.

Hane, K.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

Harris, J. S.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

Henry, R.

Holm, R.

Huang, M.

Jin, J.

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Johnson, S. R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Kanamori, Y.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

Kanskar, M.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Kilic, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73(11), 115126 (2006).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 .
[CrossRef] [PubMed]

Kim, M.

Kim, S.

Kitani, T.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007).
[CrossRef]

Krauss, T. F.

Lee, K. J.

Lee, M. M.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

Levi, O.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

Locatelli, A.

Lousse, V.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73(11), 115126 (2006).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 .
[CrossRef] [PubMed]

MacKenzie, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Magnusson, R.

Mittleman, D. M.

Modotto, D.

Morin, R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Ochiai, T.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63(12), 125107 (2001).
[CrossRef]

Pacradouni, V.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Paddon, P.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

Passaseo, A.

Peter, Y.-A.

Pisco, M.

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

I. Gallina, M. Pisco, A. Ricciardi, S. Campopiano, G. Castaldi, A. Cusano, and V. Galdi, “Guided resonances in photonic crystals with point-defected aperiodically-ordered supercells,” Opt. Express 17(22), 19586–19598 (2009),
 http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19586 .
[CrossRef] [PubMed]

A. Cusano, M. Giordano, A. Cutolo, M. Pisco, and M. Consales, “Integrated development of chemoptical fiber nanosensors,” Curr. Anal. Chem. 4(4), 296–315 (2008).
[CrossRef]

Pottier, P.

Prasad, T.

Prather, D.

Proietti Zaccaria, R.

Rainò, G.

Ricciardi, A.

Rosenberg, A.

Sakoda, K.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63(12), 125107 (2001).
[CrossRef]

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B Condens. Matter 52(11), 7982–7986 (1995).
[CrossRef] [PubMed]

Shamamian, V.

Shi, L.

Shi, S.

Skolnick, M. S.

Skorobogatiy, M.

Solgaard, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73(11), 115126 (2006).
[CrossRef]

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98(3), 033102 (2005).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 .
[CrossRef] [PubMed]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
[CrossRef]

Song, H. Y.

Song, J.

Stevenson, R. M.

Stomeo, T.

Suh, W.

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98(3), 033102 (2005).
[CrossRef]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12(8), 1575–1582 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 .
[CrossRef] [PubMed]

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[CrossRef]

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M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

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Zhang, J.

O. Levi, M. M. Lee, J. Zhang, V. Lousse, S. R. J. Brueck, S. Fan, and J. S. Harris, “Sensitivity analysis of a photonic crystal structure for index-of-refraction sensing,” Proc. SPIE 6447, 2–9 (2007).

Appl. Phys. Lett.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003).
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Figures (11)

Fig. 1
Fig. 1

Lattice geometry in the Cartesian reference system: (a) Octagonal Ammann-Beenker supercell; (b) square lattice cell.

Fig. 2
Fig. 2

GR wavelength shift as a function of the hole refractive index in a PQC supercell [cf. Figure 1(a)] with high-index (n slab = 3.418) slab for the lowest-order z-even (a,b) and z-odd (c,d) modes, and different values of the hole radius (a, c) and slab thickness (b, d).

Fig. 3
Fig. 3

As in Fig. 2, but for the periodic PC case [cf. Figure 1(b)].

Fig. 4
Fig. 4

As in Fig. 2, but for a low-index (n slab = 1.58) slab.

Fig. 5
Fig. 5

As in Fig. 3, but for a low-index (n slab = 1.58) slab.

Fig. 6
Fig. 6

Sensitivity–tuning efficiency as a function of the hole refractive index in a PQC supercell [cf. Figure 1(a)] with high index (n slab = 3.418) slab for the lowest-order z-even (a,b) and z-odd (c,d) modes, and different values of the hole radius (a, c) and slab thickness (b, d).

Fig. 7
Fig. 7

As in Fig. 6, but for the periodic PC case [cf. Figure 1(b)].

Fig. 8
Fig. 8

As in Fig. 6, but for a low-index (n slab = 1.58) slab.

Fig. 9
Fig. 9

As in Fig. 7, but for a low-index (n slab = 1.58) slab.

Fig. 10
Fig. 10

Electric field amplitudes (at the slab center x-y plane) for x- and y-components of the lowest order z-even degenerate modes, in the PQC (a) and PC (b) case, with high-index slab.

Fig. 11
Fig. 11

GR wavelength shift calculated via full-wave modal analysis and perturbative model [cf. Equation (5)], pertaining to the lowest order z-even mode, in the PC (r = 0.275a) and PQC (r = 0.25a) case, with a high-index (n slab = 3.418) slab of thickness t = 0.75a.

Tables (4)

Tables Icon

Table 1 Normalized GR frequencies in the unperturbed PQC with high index (n slab = 3.418) slab for the lowest-order z-even and z-odd modes, for various values of the hole radius and slab thickness

Tables Icon

Table 2 As in Table 1, but for the periodic PC case [cf. Figure 1(b)]

Tables Icon

Table 3 As in Tables 1 and 2, but for a low-index (n slab = 1.58) slab

Tables Icon

Table 4 Maximum sensitivity-tuning efficiencies observed (for n holes = 1.5) in the PQC and PC cases (cf. Figures 6-9)

Equations (5)

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( r a ) P C = 82 4 + 3 2 ( r a ) P Q C 1.1 ( r a ) P Q C ,
S ( n h o l e s ) = λ n h o l e s .
Δ λ = λ 0 ( n h o l e s 2 1 ) h o l e s E ( r ) E 0 * ( r ) d r c a v i t y [ n 2 ( r ) E ( r ) E 0 * ( r ) + η 0 2 H ( r ) H 0 * ( r ) ] d r ,
n ( r ) = { n slab , in the slab, 1 , in the holes and background .
Δ λ λ 0 ( n h o l e s 2 1 ) h o l e s | E 0 ( r ) | 2 d r 2 c a v i t y n 2 ( r ) | E 0 ( r ) | 2 d r ,

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