Abstract

We present a robust method for computing the reflection of arbitrarily shaped and sized beams from finite thickness photonic crystals. The method is based on dividing the incident beam into plane waves, each of which can be solved individually using Bloch periodic boundary conditions. This procedure allows us to take a full advantage of the crystal symmetry and also leads to a linear scaling of the computation time with respect to the number of plane waves needed to expand the incident beam. The algorithm for computing the reflection of an individual plane wave is also reviewed. Finally, we find an excellent agreement between the computational results and measurement data obtained from opals that are synthesized using polystyrene and poly(methyl methacrylate) microspheres.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2004 (5)

M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

K. Varis and A. R. Baghai-Wadji, “A Novel 3D Pseudo-Spectral Analysis of Photonic Crystal Slabs,” ACES J. 19, 101–111 (2004).

X. Zhang, “Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. B 70, 195,110 (2004).
[CrossRef]

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

S. Guo, F. Wu, and S. Albin, “Photonic band gap analysis using finite-difference frequency-domain method,” Opt. Express 12, 1741–1746 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1741.
[CrossRef] [PubMed]

2003 (6)

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
[CrossRef]

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

A. R. Baghai-Wadji, “A Symbolic Procedure for the Diagonalization of Linear PDEs in Accelerated Computational Engineering,” in Lecture Notes in Computer Science,  vol 2630, F. Winkler and U. Langer, eds., pp. 347–360 (Springer-Verlag, Heidelberg, Germany, 2003).
[CrossRef]

M. T. Manzuri-Shalmani and A. R. Baghai-Wadji, “Elemental field distributions in corrugated structures with large-amplitude gratings,” Electron. Lett. 39, 1690–1691 (2003).
[CrossRef]

F. Bresson, C.-C. Chen, G.-C. Chi, and Y.-W. Chen, “Simplified sedimentation process for 3D photonic thick layers/bulk crystals with a stop-band in the visible range,” Appl. Surf. Sci. 217, 281–288(2003).
[CrossRef]

2002 (3)

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

M. Bardosova and R. H. Tredgold, “Ordered layers of monodispersive colloids,” J. Mater. Chem. 12, 2835–2842 (2002).
[CrossRef]

Z.-Z. Gu, A. Fujishima, and O. Sato, “Fabrication of High-Quality Opal Films with Controllable Thickness,” Chem. Mater. 14, 760–765 (2002).
[CrossRef]

2001 (2)

2000 (4)

Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–605 (2000).
[CrossRef] [PubMed]

S. W. Leonard, H. M. van Driel, A. Birner, U. Gsele, and P. R. Villeneuve, “Single-mode transmission in two-dimensional macroporous silicon photonic crystal waveguides,” Opt. Lett. 25, 1550–1552 (2000).
[CrossRef]

M. Müller, R. Zentel, T. Maka, S. G. Romanov, and C. M. Sotomayor Torres, “Dye-Containing Polymer Beads as Photonic Crystals,” Chem. Mater. 12, 2508–2512 (2000).
[CrossRef]

1999 (2)

1998 (2)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

L.-M. Li and Z.-Q. Zhang, “Multiple-scattering approach to finite-sized photonic band-gap materials,” Phys. Rev. B 58, 9587–9590 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

P. R. Villeneuve and M. Pich, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
[CrossRef]

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

1992 (2)

J. B. Pendry and A. MacKinnon, “Calculation of Photon Dispersion Relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys.: Condens. Matter 4, 7389–7400 (1992).
[CrossRef]

1991 (1)

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic Band Structure: The Face-Centered-Cubic Case Employing Nonspherical Atoms,” Phys. Rev. Lett. 67(17), 2295–2299 (1991).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gaps in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

1959 (1)

W. G. Spitzer and J. M. Whelan, “Infrared absorption and electron effective mass in n-type gallium arsenide,” Phys. Rev. 114, 59–63 (1959).
[CrossRef]

Albin, S.

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Anand, S.

M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
[CrossRef]

Aoki, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

Aoyagi, Y.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

Arlinghaus, E. G.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

Astratov, V. N.

Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
[CrossRef]

Baba, T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

Baghai-Wadji, A. R.

K. Varis and A. R. Baghai-Wadji, “A Novel 3D Pseudo-Spectral Analysis of Photonic Crystal Slabs,” ACES J. 19, 101–111 (2004).

A. R. Baghai-Wadji, “A Symbolic Procedure for the Diagonalization of Linear PDEs in Accelerated Computational Engineering,” in Lecture Notes in Computer Science,  vol 2630, F. Winkler and U. Langer, eds., pp. 347–360 (Springer-Verlag, Heidelberg, Germany, 2003).
[CrossRef]

M. T. Manzuri-Shalmani and A. R. Baghai-Wadji, “Elemental field distributions in corrugated structures with large-amplitude gratings,” Electron. Lett. 39, 1690–1691 (2003).
[CrossRef]

Bardosova, M.

M. Bardosova and R. H. Tredgold, “Ordered layers of monodispersive colloids,” J. Mater. Chem. 12, 2835–2842 (2002).
[CrossRef]

Baryshev, A. V.

Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
[CrossRef]

Bertone, J. F.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-Crystal Colloidal Multilayers of Controlled Thickness,” Chem. Mater. 11, 2131–2140 (1999).
[CrossRef]

Birner, A.

Biswas, R.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K.-M. Ho, “Optical Photonic Crystals Synthesized from Colloidal Systems of Polystyrene Spheres and Nanocrystalline Titania,” J. Lightwave Technol. 17, 1970–1974 (1999).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Bjarklev, A.

A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Bogaerts, W.

A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Bresson, F.

F. Bresson, C.-C. Chen, G.-C. Chi, and Y.-W. Chen, “Simplified sedimentation process for 3D photonic thick layers/bulk crystals with a stop-band in the visible range,” Appl. Surf. Sci. 217, 281–288(2003).
[CrossRef]

Brock, R. S.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gaps in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Chen, C.-C.

F. Bresson, C.-C. Chen, G.-C. Chi, and Y.-W. Chen, “Simplified sedimentation process for 3D photonic thick layers/bulk crystals with a stop-band in the visible range,” Appl. Surf. Sci. 217, 281–288(2003).
[CrossRef]

Chen, Y.-W.

F. Bresson, C.-C. Chen, G.-C. Chi, and Y.-W. Chen, “Simplified sedimentation process for 3D photonic thick layers/bulk crystals with a stop-band in the visible range,” Appl. Surf. Sci. 217, 281–288(2003).
[CrossRef]

Chi, G.-C.

F. Bresson, C.-C. Chen, G.-C. Chi, and Y.-W. Chen, “Simplified sedimentation process for 3D photonic thick layers/bulk crystals with a stop-band in the visible range,” Appl. Surf. Sci. 217, 281–288(2003).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–605 (2000).
[CrossRef] [PubMed]

Colvin, V. L.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-Crystal Colloidal Multilayers of Controlled Thickness,” Chem. Mater. 11, 2131–2140 (1999).
[CrossRef]

Constant, K.

Egen, M.

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

Elson, J. M.

Felici, T.

A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Fujishima, A.

Z.-Z. Gu, A. Fujishima, and O. Sato, “Fabrication of High-Quality Opal Films with Controllable Thickness,” Chem. Mater. 14, 760–765 (2002).
[CrossRef]

Gallagher, D.

A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic Band Structure: The Face-Centered-Cubic Case Employing Nonspherical Atoms,” Phys. Rev. Lett. 67(17), 2295–2299 (1991).
[CrossRef]

Griesebock, B.

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

Gsele, U.

Gu, Z.-Z.

Z.-Z. Gu, A. Fujishima, and O. Sato, “Fabrication of High-Quality Opal Films with Controllable Thickness,” Chem. Mater. 14, 760–765 (2002).
[CrossRef]

Guo, S.

Hede, M.

M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

Heiny, R.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Hirayama, H.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

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S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
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Hu, X.-H.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Hwang, K. S.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-Crystal Colloidal Multilayers of Controlled Thickness,” Chem. Mater. 11, 2131–2140 (1999).
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Inoshita, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

Jacobs, K. M.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Jaskorzynska, B.

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
[CrossRef]

Jiang, P.

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-Crystal Colloidal Multilayers of Controlled Thickness,” Chem. Mater. 11, 2131–2140 (1999).
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[CrossRef]

Johnson, S. G.

Jonsson, F.

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Kaplyanskii, A. A.

Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
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N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys.: Condens. Matter 4, 7389–7400 (1992).
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Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
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Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
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A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Leonard, S. W.

Leung, K. M.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic Band Structure: The Face-Centered-Cubic Case Employing Nonspherical Atoms,” Phys. Rev. Lett. 67(17), 2295–2299 (1991).
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L.-M. Li and Z.-Q. Zhang, “Multiple-scattering approach to finite-sized photonic band-gap materials,” Phys. Rev. B 58, 9587–9590 (1998).
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Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
[CrossRef]

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S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Lu, J. Q.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
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M. Müller, R. Zentel, T. Maka, S. G. Romanov, and C. M. Sotomayor Torres, “Dye-Containing Polymer Beads as Photonic Crystals,” Chem. Mater. 12, 2508–2512 (2000).
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[CrossRef]

Meng, L.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

Midrio, M.

A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Miyazaki, H. T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

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N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys.: Condens. Matter 4, 7389–7400 (1992).
[CrossRef]

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A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Müller, M.

M. Müller, R. Zentel, T. Maka, S. G. Romanov, and C. M. Sotomayor Torres, “Dye-Containing Polymer Beads as Photonic Crystals,” Chem. Mater. 12, 2508–2512 (2000).
[CrossRef]

Mulot, M.

M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
[CrossRef]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–605 (2000).
[CrossRef] [PubMed]

Norris, D. J.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

D. J. Norris and Y. A. Vlasov, “Chemical Approaches to Three-Dimensional Semiconductor Photonic Crystals,” Adv. Mater. 13, 371–376 (2001).
[CrossRef]

Pendry, J. B.

J. B. Pendry and A. MacKinnon, “Calculation of Photon Dispersion Relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
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P. R. Villeneuve and M. Pich, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
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M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

Qui, M.

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
[CrossRef]

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Romanov, S.

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

Romanov, S. G.

M. Müller, R. Zentel, T. Maka, S. G. Romanov, and C. M. Sotomayor Torres, “Dye-Containing Polymer Beads as Photonic Crystals,” Chem. Mater. 12, 2508–2512 (2000).
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Sakoda, K.

K. Sakoda, Optical properties of photonic crystals (Springer-Verlag, Berlin, 2001).

Sato, O.

Z.-Z. Gu, A. Fujishima, and O. Sato, “Fabrication of High-Quality Opal Films with Controllable Thickness,” Chem. Mater. 14, 760–765 (2002).
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Schniedergers, M.

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Scriven, L. E.

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

Seekamp, J.

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Shinya, N.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
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Sigalas, M. M.

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K.-M. Ho, “Optical Photonic Crystals Synthesized from Colloidal Systems of Polystyrene Spheres and Nanocrystalline Titania,” J. Lightwave Technol. 17, 1970–1974 (1999).
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S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Søndergaard, T.

A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Sotomayor Torres, C. M.

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

M. Müller, R. Zentel, T. Maka, S. G. Romanov, and C. M. Sotomayor Torres, “Dye-Containing Polymer Beads as Photonic Crystals,” Chem. Mater. 12, 2508–2512 (2000).
[CrossRef]

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gaps in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
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W. G. Spitzer and J. M. Whelan, “Infrared absorption and electron effective mass in n-type gallium arsenide,” Phys. Rev. 114, 59–63 (1959).
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N. Stefanou, V. Karathanos, and A. Modinos, “Scattering of electromagnetic waves by periodic structures,” J. Phys.: Condens. Matter 4, 7389–7400 (1992).
[CrossRef]

Strassner, M.

M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

Subramania, G.

Swillo, M.

M. Mulot, M. Swillo, M. Qiu, M. Strassner, M. Hede, and S. Anand, “Investigation of Fabry-Perot cavities based on 2D Photonic crystals fabricated in InP membranes,” J. Appl. Phys 95, 5928–5930 (2004).
[CrossRef]

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
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A. Bjarklev, W. Bogaerts, T. Felici, D. Gallagher, M. Midrio, A. Lavrinenko, D. Mogitlevtsev, T. Søndergaard, D. Taillaert, and B. Tromborg, “Comparison of strengths/weaknesses of existing numerical tools and outlining of modelling strategy,” A public report on Picco project (2001), http://www.intec.rug.ac.be/picco/download/D8 report.pdf.

Talneau, A.

M. Mulot, S. Anand, M. Swillo, M. Qui, B. Jaskorzynska, and A. Talneau, “Low-loss InP-based photonic-crystal waveguides etched with Ar/Cl2 chemically assisted ion beam ething,” J. Vac. Sci. Technol. B 21, 900–903 (2003).
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Tayeb, G.

Tiedemann, A.

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–605 (2000).
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Varis, K.

K. Varis and A. R. Baghai-Wadji, “A Novel 3D Pseudo-Spectral Analysis of Photonic Crystal Slabs,” ACES J. 19, 101–111 (2004).

Villeneuve, P. R.

Vlasov, Y. A.

D. J. Norris and Y. A. Vlasov, “Chemical Approaches to Three-Dimensional Semiconductor Photonic Crystals,” Adv. Mater. 13, 371–376 (2001).
[CrossRef]

Y. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, “Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals,” Phys. Rev. E 61, 5784–5793 (2000).
[CrossRef]

Voss, R.

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

Whelan, J. M.

W. G. Spitzer and J. M. Whelan, “Infrared absorption and electron effective mass in n-type gallium arsenide,” Phys. Rev. 114, 59–63 (1959).
[CrossRef]

Wu, F.

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic Band Structure: The Face-Centered-Cubic Case Employing Nonspherical Atoms,” Phys. Rev. Lett. 67(17), 2295–2299 (1991).
[CrossRef]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604–605 (2000).
[CrossRef] [PubMed]

Yang, P.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Ye, J.

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Zentel, R.

M. Egen, R. Voss, B. Griesebock, R. Zentel, S. Romanov, and C. M. Sotomayor Torres, “Heterostructures of Polymer Photonic Crystal Films,” Chem. Mater. 15, 3786–3792 (2003).
[CrossRef]

M. Müller, R. Zentel, T. Maka, S. G. Romanov, and C. M. Sotomayor Torres, “Dye-Containing Polymer Beads as Photonic Crystals,” Chem. Mater. 12, 2508–2512 (2000).
[CrossRef]

F. Jonsson, C. M. Sotomayor Torres, J. Seekamp, M. Schniedergers, A. Tiedemann, J. Ye, and R. Zentel, “Artificially inscribed defects in opal photonic crystals,” Microelectr. Eng. (to appear 2005).

Zhang, X.

X. Zhang, “Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. B 70, 195,110 (2004).
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L.-M. Li and Z.-Q. Zhang, “Multiple-scattering approach to finite-sized photonic band-gap materials,” Phys. Rev. B 58, 9587–9590 (1998).
[CrossRef]

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

ACES J. (1)

K. Varis and A. R. Baghai-Wadji, “A Novel 3D Pseudo-Spectral Analysis of Photonic Crystal Slabs,” ACES J. 19, 101–111 (2004).

Adv. Mater. (2)

D. J. Norris and Y. A. Vlasov, “Chemical Approaches to Three-Dimensional Semiconductor Photonic Crystals,” Adv. Mater. 13, 371–376 (2001).
[CrossRef]

D. J. Norris, E. G. Arlinghaus, L. Meng, R. Heiny, and L. E. Scriven, “Opaline Photonic Crystals: How Does Self-Assembly Work?” Adv. Mater. 16, 1393–1399 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81(17), 3122–3124 (2002).
[CrossRef]

Appl. Surf. Sci. (1)

F. Bresson, C.-C. Chen, G.-C. Chi, and Y.-W. Chen, “Simplified sedimentation process for 3D photonic thick layers/bulk crystals with a stop-band in the visible range,” Appl. Surf. Sci. 217, 281–288(2003).
[CrossRef]

Chem. Mater. (4)

P. Jiang, J. F. Bertone, K. S. Hwang, and V. L. Colvin, “Single-Crystal Colloidal Multilayers of Controlled Thickness,” Chem. Mater. 11, 2131–2140 (1999).
[CrossRef]

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Figures (5)

Figure 1.
Figure 1.

A schematic representation of the discretization. The unit cell in the slab is limited by planes z=0 and z=h and is periodic with a 1 and a 2. Electric fields are expanded in plane waves on light blue planes and magnetic on dark brown. The plane wave expansions in adjacent planes are related to each other through finite differences. Outside the slab, for z<0 and z>h, the fields are expanded in outgoing eigenvectors. The eigenvector expansion is used to terminate the finite difference grid by relating the electric field at z=-(1/2)Δ to the magnetic field at z=0 and similarly for the other cladding.

Figure 2.
Figure 2.

The wave vectors of the incident and reflected fields. a) A single plane wave with a wave vector (K 0-w 0 u z ) is incident from the homogeneous medium (HM) to the surface of the photonic crystal (PC) and b) its reflection is expressed in terms of the different Bragg orders, both propagating and evanescent (not shown). c) An incident beam is decomposed to plane waves with wave vectors [K m -wm u z ] and d) the reflection is expressed in terms of the corresponding Bragg orders.

Figure 3.
Figure 3.

Measured and simulated reflection spectra from a typical PMMA on silicon opal. Numerical aperture of 0.55 corresponds to 50x magnifying optics with a spot size of about 3 µm and numerical aperture 0.3 corresponds to 10x magnification and a spot size of 15 µm.

Figure 4.
Figure 4.

A typical SEM image of the polystyrene on GaAs opal.

Figure 5.
Figure 5.

Reflection from a polystyrene on GaAs opal for different incident angles: a) ϕ=20°, b) ϕ=30° and c) ϕ=40°. d) The incidence angle and the measurement data is as in c) but the simulated reflection is computed using a random mixture of FCC and HCP lattices. Curves marked with stars are simulated and continuous lines are measured.

Equations (21)

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𝓛 ( x , y , ε , μ , ω ) Ψ = z Ψ ,
𝓛 = [ 0 𝓐 𝓑 0 ] ,
𝓐 = [ x ( j ω ε ) 1 y x ( j ω ε ) 1 x + j ω μ y ( j ω ε ) 1 y j ω μ y ( j ω ε ) 1 x ] .
Ψ K ( r , z ) = exp ( j K · r ) n Ψ n ( z ) exp ( j G n · r ) ,
Ψ K ( r , ( i + 0.5 ) Δ ) = Ψ K ( r , ( i 0.5 ) Δ ) + Δ [ 𝓛 Ψ K ( r , z ) ] z = i Δ ,
Ψ n ( z ) = Ψ n exp ( j λ z ) ,
Ψ K ( r , z ) = exp ( j K · r ) n exp ( j G n · r ) [ ( a K , n + Ψ K , n 1 + + b K , n + Ψ K , n 2 + ) exp ( j w K , n z )
+ ( a K , n Ψ K , n 1 + b K , n Ψ K , n 2 ) exp ( j w K , n z ) ] ,
λ K , n = ± w K , n = ± ( ω 2 ε μ K + G n 2 ) 1 2 ,
Ψ K , n 1 ± = α K , n [ ± w K , n ω μ 0 k x k y k y 2 + ω 2 ε μ ] , Ψ K , n 2 ± = β K , n [ k x k y k y 2 ω 2 ε μ ± w K , n ω ε 0 ] ,
u z · [ 𝓔 ( Ψ K , n 1 ± ) × 𝓗 ( Ψ K , n 2 ± ) * ] = u z · [ 𝓔 ( Ψ K , n 2 ± ) × 𝓗 ( Ψ K , n 1 ± ) * ] = 0 ,
u z · [ 𝓔 ( Ψ K , n l ± ) × 𝓗 ( Ψ K , n l ± ) * ] = { ± 1 , w K , n 2 > 0 0 , w K , n 2 0 ,
M ( ω , K ) f = b ,
Ψ inc ( r , z ) = m exp ( j K m · r j w m z ) ( c m 1 Ψ m 1 + c m 2 Ψ m 2 ) ,
Ψ refl ( r , z ) = m exp ( j K m · r ) ( c m 1 Θ m 1 + c m 2 Θ m 2 ) ,
Θ m l = n exp ( j G n · r + j w m , n z ) ( a m , m l Ψ m , n 1 + + b m , n l + Ψ m , n 2 + ) , l = 1 , 2 .
P = 1 2 { S d 2 r m , m 𝓔 ( c m 1 Θ m 1 + c m 2 Θ m 2 ) × 𝓗 ( c m 1 Θ m 1 + c m 2 Θ m 2 ) * exp [ j ( K m K m ) · r ] } ,
R = Σ m { c m 1 2 R m 1 + [ c m 1 ( c m 2 ) * R m 12 ] + c m 2 2 R m 2 } Σ m ( c m 1 2 + c m 2 2 ) ,
R m l = n δ ( w m , n ) ( a m , n l + 2 + b m , n l + 2 ) , l = 1 , 2 ,
R m 12 = 2 n δ ( w m , n ) [ a m , n 1 + ( a m , n 2 + ) * + b m , n 1 + ( b m , n 2 + ) * ] .
R = Σ m 2 π Δ K ( K m + 0.5 Δ K ) c m 2 R m Σ m 2 π Δ K ( K m + 0.5 Δ K ) c m 2 ,

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