Abstract

The guided mode resonances (GMRs) of diffraction gratings surrounded by low index materials can be designed to produce broadband regions of near perfect reflection and near perfect transmission. These have many applications, including in optical isolators, in hybrid lasers cavities and in photovoltaics. The excitation of rapid GMRs occurs in a background of slowly varying Fabry-Perot oscillation, which produces Fano resonances. We demonstrate the critical role of the polarity of adjacent Fano resonances in the formation of the broadband features. We design gratings for photovoltaic applications that operate at wavelengths where material absorption must be considered and where light is incident at non-normal angles.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. D. Maystre, “Diffraction gratings: An amazing phenomenon,” Comptes Rendus Phys. 14, 381–392 (2013).
    [Crossref]
  2. C. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
    [Crossref]
  3. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
    [Crossref] [PubMed]
  4. S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26, 584–586 (2001).
    [Crossref]
  5. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
    [Crossref]
  6. P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Light. Technol. 24, 2442–2449 (2006).
    [Crossref]
  7. Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
    [Crossref]
  8. T. Glaser, S. Schröter, H. Bartelt, H.-J. Fuchs, and E.-B. Kley, “Diffractive optical isolator made of high-efficiency dielectric gratings only,” Appl. Opt. 41, 3558–3566 (2002).
    [Crossref] [PubMed]
  9. A. Taghizadeh, J. Mørk, and I.-S. Chung, “Ultracompact resonator with high quality-factor based on a hybrid grating structure,” Opt. Express 23, 17282–17287 (2015).
    [Crossref]
  10. Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114, 73601 (2015).
    [Crossref]
  11. S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470 (1990).
    [Crossref]
  12. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  13. R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39, 4337–4340 (2014).
    [Crossref] [PubMed]
  14. S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Reports Prog. Phys. 77, 126402 (2014).
    [Crossref]
  15. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A. 20, 569–572 (2003).
    [Crossref]
  16. A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
    [Crossref] [PubMed]
  17. L. C. Hirst and N. J. Ekins-Daukes, “Fundamental losses in solar cells,” Prog. Photovoltaics Res. Appl. 19(3), 286–293 (2010).
  18. P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
    [Crossref]
  19. C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
    [Crossref]
  20. T. P. White, N. N. Lal, and K. R. Catchpole, “Tandem solar cells based on high-efficiency c-Si bottom cells: Top cell requirements for $¿ 30%$ efficiency,” IEEE J. Photovoltaics 4, 208–214 (2014).
    [Crossref]
  21. H. J. Snaith, “Perovskites: The emergence of a new era for low-cost, high-efficiency solar cells,” J. Phys. Chem. Lett 4, 3623–3630 (2013).
    [Crossref]
  22. M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501, 395–398 (2013).
    [Crossref] [PubMed]
  23. B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.
  24. “EMUstack: An open-source package for Bloch mode based calculations of scattering matrices,” physics.usyd.edu.au/emustack .
  25. K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
    [Crossref]
  26. K. R. Catchpole and M. A. Green, “A conceptual model of light coupling by pillar diffraction gratings,” J. Appl. Phys. 101, 063105 (2007).
    [Crossref]
  27. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2005).
  28. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, 1996).
    [Crossref]
  29. L. C. Botten, R. C. McPhedran, and J. M. Lamarre, “Inductive grids in the resonant region: Theory and experiment,” Int. J. Infrared Millimeter Waves 6, 949 (1985).
    [Crossref]
  30. B. S. Richards, “Single-material TiO2 double-layer antireflection coatings,” Sol. Energy Mater. Sol. Cells 79, 369–390 (2003).
    [Crossref]
  31. I.-S. Chung, “Study on differences between high contrast grating reflectors for TM and TE polarizations and their impact on VCSEL designs,” Opt. Express 23, 16730 (2015).
    [Crossref] [PubMed]

2015 (4)

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Ultracompact resonator with high quality-factor based on a hybrid grating structure,” Opt. Express 23, 17282–17287 (2015).
[Crossref]

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114, 73601 (2015).
[Crossref]

I.-S. Chung, “Study on differences between high contrast grating reflectors for TM and TE polarizations and their impact on VCSEL designs,” Opt. Express 23, 16730 (2015).
[Crossref] [PubMed]

2014 (4)

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39, 4337–4340 (2014).
[Crossref] [PubMed]

T. P. White, N. N. Lal, and K. R. Catchpole, “Tandem solar cells based on high-efficiency c-Si bottom cells: Top cell requirements for $¿ 30%$ efficiency,” IEEE J. Photovoltaics 4, 208–214 (2014).
[Crossref]

S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Reports Prog. Phys. 77, 126402 (2014).
[Crossref]

2013 (3)

D. Maystre, “Diffraction gratings: An amazing phenomenon,” Comptes Rendus Phys. 14, 381–392 (2013).
[Crossref]

H. J. Snaith, “Perovskites: The emergence of a new era for low-cost, high-efficiency solar cells,” J. Phys. Chem. Lett 4, 3623–3630 (2013).
[Crossref]

M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501, 395–398 (2013).
[Crossref] [PubMed]

2012 (3)

C. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref] [PubMed]

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

2010 (1)

L. C. Hirst and N. J. Ekins-Daukes, “Fundamental losses in solar cells,” Prog. Photovoltaics Res. Appl. 19(3), 286–293 (2010).

2007 (1)

K. R. Catchpole and M. A. Green, “A conceptual model of light coupling by pillar diffraction gratings,” J. Appl. Phys. 101, 063105 (2007).
[Crossref]

2006 (1)

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Light. Technol. 24, 2442–2449 (2006).
[Crossref]

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

2003 (2)

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A. 20, 569–572 (2003).
[Crossref]

B. S. Richards, “Single-material TiO2 double-layer antireflection coatings,” Sol. Energy Mater. Sol. Cells 79, 369–390 (2003).
[Crossref]

2002 (1)

2001 (2)

S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26, 584–586 (2001).
[Crossref]

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

1993 (1)

1990 (1)

1985 (1)

L. C. Botten, R. C. McPhedran, and J. M. Lamarre, “Inductive grids in the resonant region: Theory and experiment,” Int. J. Infrared Millimeter Waves 6, 949 (1985).
[Crossref]

Asatryan, A. A.

Atwater, H. A.

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref] [PubMed]

Bagby, J. S.

Bailie, C. D.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Ballif, C.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Bartelt, H.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2005).

Botten, L. C.

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

L. C. Botten, R. C. McPhedran, and J. M. Lamarre, “Inductive grids in the resonant region: Theory and experiment,” Int. J. Infrared Millimeter Waves 6, 949 (1985).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Bowring, A. R.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Buonassisi, T.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Burschka, J.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Byrne, M. A.

Catchpole, K. R.

T. P. White, N. N. Lal, and K. R. Catchpole, “Tandem solar cells based on high-efficiency c-Si bottom cells: Top cell requirements for $¿ 30%$ efficiency,” IEEE J. Photovoltaics 4, 208–214 (2014).
[Crossref]

K. R. Catchpole and M. A. Green, “A conceptual model of light coupling by pillar diffraction gratings,” J. Appl. Phys. 101, 063105 (2007).
[Crossref]

Chang-Hasnain, C.

C. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

Chang-Hasnain, C. J.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

Chavel, P.

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Light. Technol. 24, 2442–2449 (2006).
[Crossref]

Christoforo, M. G.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Chung, I.-S.

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Ultracompact resonator with high quality-factor based on a hybrid grating structure,” Opt. Express 23, 17282–17287 (2015).
[Crossref]

I.-S. Chung, “Study on differences between high contrast grating reflectors for TM and TE polarizations and their impact on VCSEL designs,” Opt. Express 23, 16730 (2015).
[Crossref] [PubMed]

Collin, S.

S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Reports Prog. Phys. 77, 126402 (2014).
[Crossref]

de Sterke, C. M.

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Deng, H.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114, 73601 (2015).
[Crossref]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

Dossou, K. B.

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Ekins-Daukes, N. J.

L. C. Hirst and N. J. Ekins-Daukes, “Fundamental losses in solar cells,” Prog. Photovoltaics Res. Appl. 19(3), 286–293 (2010).

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A. 20, 569–572 (2003).
[Crossref]

Fuchs, H.-J.

Glaser, T.

Grätzel, M.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Green, M. A.

K. R. Catchpole and M. A. Green, “A conceptual model of light coupling by pillar diffraction gratings,” J. Appl. Phys. 101, 063105 (2007).
[Crossref]

Hane, K.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Haug, F.-j.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Hirst, L. C.

L. C. Hirst and N. J. Ekins-Daukes, “Fundamental losses in solar cells,” Prog. Photovoltaics Res. Appl. 19(3), 286–293 (2010).

Holovsky, J.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Light. Technol. 24, 2442–2449 (2006).
[Crossref]

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A. 20, 569–572 (2003).
[Crossref]

Johnston, M. B.

M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501, 395–398 (2013).
[Crossref] [PubMed]

Kanamori, Y.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Kley, E.-B.

Lal, N. N.

T. P. White, N. N. Lal, and K. R. Catchpole, “Tandem solar cells based on high-efficiency c-Si bottom cells: Top cell requirements for $¿ 30%$ efficiency,” IEEE J. Photovoltaics 4, 208–214 (2014).
[Crossref]

Lalanne, P.

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Light. Technol. 24, 2442–2449 (2006).
[Crossref]

Lamarre, J. M.

L. C. Botten, R. C. McPhedran, and J. M. Lamarre, “Inductive grids in the resonant region: Theory and experiment,” Int. J. Infrared Millimeter Waves 6, 949 (1985).
[Crossref]

Lawrence, F. J.

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Ledinsky, M.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Lee, J. Z.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Liu, M.

M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501, 395–398 (2013).
[Crossref] [PubMed]

Löper, P.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Magnusson, R.

Mailoa, J. P.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

Maystre, D.

D. Maystre, “Diffraction gratings: An amazing phenomenon,” Comptes Rendus Phys. 14, 381–392 (2013).
[Crossref]

McGehee, M. D.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

McPhedran, R. C.

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

L. C. Botten, R. C. McPhedran, and J. M. Lamarre, “Inductive grids in the resonant region: Theory and experiment,” Int. J. Infrared Millimeter Waves 6, 949 (1985).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Moharam, M. G.

Moon, S.-J.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Mørk, J.

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Ultracompact resonator with high quality-factor based on a hybrid grating structure,” Opt. Express 23, 17282–17287 (2015).
[Crossref]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

Nguyen, W. H.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Nicolas, D.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Niesen, B.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Noufi, R.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Pellet, N.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Polman, A.

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref] [PubMed]

Poulton, C. G.

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Remes, Z.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Richards, B. S.

B. S. Richards, “Single-material TiO2 double-layer antireflection coatings,” Sol. Energy Mater. Sol. Cells 79, 369–390 (2003).
[Crossref]

Sai, H.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Salleo, A.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Schröter, S.

Snaith, H. J.

M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501, 395–398 (2013).
[Crossref] [PubMed]

H. J. Snaith, “Perovskites: The emergence of a new era for low-cost, high-efficiency solar cells,” J. Phys. Chem. Lett 4, 3623–3630 (2013).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Sturmberg, B. C. P.

K. B. Dossou, L. C. Botten, A. A. Asatryan, B. C. P. Sturmberg, M. A. Byrne, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Modal formulation for diffraction by absorbing photonic crystal slabs,” J. Opt. Soc. Am. A 29, 817–831 (2012).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

Suh, W.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A. 20, 569–572 (2003).
[Crossref]

Taghizadeh, A.

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Ultracompact resonator with high quality-factor based on a hybrid grating structure,” Opt. Express 23, 17282–17287 (2015).
[Crossref]

Tibuleac, S.

Unger, E. L.

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

Wang, S. S.

Wang, Z.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114, 73601 (2015).
[Crossref]

Watson, G. N.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, 1996).
[Crossref]

White, T. P.

T. P. White, N. N. Lal, and K. R. Catchpole, “Tandem solar cells based on high-efficiency c-Si bottom cells: Top cell requirements for $¿ 30%$ efficiency,” IEEE J. Photovoltaics 4, 208–214 (2014).
[Crossref]

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, 1996).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2005).

Wolf, S. D.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Yang, W.

C. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

Yugami, H.

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Yum, J.-H.

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

Zhang, B.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114, 73601 (2015).
[Crossref]

Adv. Opt. Photonics (1)

C. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4, 379–440 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. Lett. 78, 142–143 (2001).
[Crossref]

Comptes Rendus Phys. (1)

D. Maystre, “Diffraction gratings: An amazing phenomenon,” Comptes Rendus Phys. 14, 381–392 (2013).
[Crossref]

Energy Environ. Sci. (1)

C. D. Bailie, M. G. Christoforo, J. P. Mailoa, A. R. Bowring, E. L. Unger, W. H. Nguyen, J. Burschka, N. Pellet, J. Z. Lee, M. Grätzel, R. Noufi, T. Buonassisi, A. Salleo, and M. D. McGehee, “Semi-transparent perovskite solar cells for tandems with silicon and CIGS,” Energy Environ. Sci. 8, 956–963 (2015).
[Crossref]

IEEE J. Photovoltaics (2)

T. P. White, N. N. Lal, and K. R. Catchpole, “Tandem solar cells based on high-efficiency c-Si bottom cells: Top cell requirements for $¿ 30%$ efficiency,” IEEE J. Photovoltaics 4, 208–214 (2014).
[Crossref]

P. Löper, B. Niesen, S.-J. Moon, D. Nicolas, J. Holovsky, Z. Remes, M. Ledinsky, F.-j. Haug, J.-H. Yum, S. D. Wolf, and C. Ballif, “Organic-inorganic halide perovskites: Perspectives for silicon-based tandem solar cells,” IEEE J. Photovoltaics 4, 1545–1551 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (1)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16, 518–520 (2004).
[Crossref]

Int. J. Infrared Millimeter Waves (1)

L. C. Botten, R. C. McPhedran, and J. M. Lamarre, “Inductive grids in the resonant region: Theory and experiment,” Int. J. Infrared Millimeter Waves 6, 949 (1985).
[Crossref]

J. Appl. Phys. (1)

K. R. Catchpole and M. A. Green, “A conceptual model of light coupling by pillar diffraction gratings,” J. Appl. Phys. 101, 063105 (2007).
[Crossref]

J. Light. Technol. (1)

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Light. Technol. 24, 2442–2449 (2006).
[Crossref]

J. Opt. Soc. Am. A (2)

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

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A. 20, 569–572 (2003).
[Crossref]

J. Phys. Chem. Lett (1)

H. J. Snaith, “Perovskites: The emergence of a new era for low-cost, high-efficiency solar cells,” J. Phys. Chem. Lett 4, 3623–3630 (2013).
[Crossref]

Nat. Mater. (1)

A. Polman and H. A. Atwater, “Photonic design principles for ultrahigh-efficiency photovoltaics,” Nat. Mater. 11, 174–177 (2012).
[Crossref] [PubMed]

Nature (1)

M. Liu, M. B. Johnston, and H. J. Snaith, “Efficient planar heterojunction perovskite solar cells by vapour deposition,” Nature 501, 395–398 (2013).
[Crossref] [PubMed]

Opt. Express (2)

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Ultracompact resonator with high quality-factor based on a hybrid grating structure,” Opt. Express 23, 17282–17287 (2015).
[Crossref]

I.-S. Chung, “Study on differences between high contrast grating reflectors for TM and TE polarizations and their impact on VCSEL designs,” Opt. Express 23, 16730 (2015).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114, 73601 (2015).
[Crossref]

Prog. Photovoltaics Res. Appl. (1)

L. C. Hirst and N. J. Ekins-Daukes, “Fundamental losses in solar cells,” Prog. Photovoltaics Res. Appl. 19(3), 286–293 (2010).

Reports Prog. Phys. (1)

S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Reports Prog. Phys. 77, 126402 (2014).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

B. S. Richards, “Single-material TiO2 double-layer antireflection coatings,” Sol. Energy Mater. Sol. Cells 79, 369–390 (2003).
[Crossref]

Other (5)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2005).

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, 1996).
[Crossref]

B. C. P. Sturmberg, K. B. Dossou, F. J. Lawrence, C. G. Poulton, R. C. McPhedran, C. M. de Sterke, and L. C. Botten, “EMUstack: an open source route to insightful electromagnetic computation via the Bloch mode scattering matrix method,” Comp. Phys. Comm., submitted.

“EMUstack: An open-source package for Bloch mode based calculations of scattering matrices,” physics.usyd.edu.au/emustack .

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (186 KB)      Transmission and complex transmission coefficient, which is shown in red during guided mode resonances and in blue when dominated by the Fabry-Perot resonances.
» Visualization 2: MP4 (169 KB)      Transmission and complex transmission coefficient, which is shown in red during guided mode resonances and in blue when dominated by the Fabry-Perot resonances.

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Figures (10)

Fig. 1
Fig. 1 Schematic of a grating of period d and thickness h, consisting of high and low index rulings: nH, nL. Also shown are the incident wave vector k0 at an angle of θ, its x-component and the propagation constant β of a slab waveguide mode. The field of the slab waveguide mode is illustrated in red.
Fig. 2
Fig. 2 (a) Reflection, (b) transmission, and (c) absorption spectra as a function of grating thickness. In (d) we magnify a section of (c) and overlay the results of the model described in the text: the dashed and solid white curves are the F-P resonances of the 0 and ±1 orders respectively; the green curves are like the solid white curves but uses heff; the cyan dots approximate the waveguide modes; the blue curve marks the trough in resonance amplitude; and the yellow dot-dashed line is the cut-off of the ±1 orders in nH.
Fig. 3
Fig. 3 Ey(x) field distributions of (a) BM-A and (b) BM-B of the example grating for λd = 9/8. The edges of the inclusions are indicated in pink and the x-axis is normalised to the period. (c) and (d) show the Fourier decompositions of the fields of (a) and (b) respectively.
Fig. 4
Fig. 4 Transmission spectrum for the weak grating with h = 520 nm. The red curve includes loss (and is marked by the horizontal white dashed in line in Fig. 2(b)), while the black curve is calculated for the same grating but ignoring loss. Individual resonances are labelled.
Fig. 5
Fig. 5 (a) Transmission spectrum where the thickness of the grating is adjusted as a function of λ such that Eq. 7 is satisfied, indicated by the diagonal dotted line in Fig. 2(b). (b) Transmission along the same diagonal line, where the t corresponding to the F-P resonance has been subtracted, leaving the transmission due to the GMRs.
Fig. 6
Fig. 6 Schematic of the trajectories of t(ωr) through the complex-plane, where blue curves represent the change in t due to the F-P resonance and red curves due to GMRs. The insets illustrate the line-shapes of the transmission associated with each trajectory (in (d) following just the red curve). (a), (b) Illustrate how GMRs whose residues lie on opposite sides of the real axis produce lines-shapes of opposite symmetry, despite the loops having the same starting point. (c) Shows the trajectory of two consecutive F-P resonances, whose low Q-factors makes them merge without going through the origin. (d) Features the same GMR as in (b), but occurring on the other side of a F-P resonance, which is seen to produce the opposite symmetry Fano resonance.
Fig. 7
Fig. 7 Transmittance of the surface grating structure. In (a) the transmission is a function of real angular frequencies, while in (b) the transmission is calculated across a range of complex frequencies.
Fig. 8
Fig. 8 (a) Reflection spectrum corresponding to the dot-dashed line in Fig. 2(a) (fL = 0.05, h = 210 nm). (b) Reflection spectrum of a grating with fL = 0.35 and h = 150 nm (indicated by dot-dashed line in (d)). (c) Reflection spectra with fL = 0.2 as a function of grating thickness. (d) Reflection spectra with fL = 0.35 as a function of grating thickness. Additional resonances occur at short wavelengths in (c), where the waveguide modes are excited by the ±2 PW orders.
Fig. 9
Fig. 9 Absorption for our canonical grating (fL = 0.05) at angles of incidence of (a) θ = 5°, (b) θ = 20°. (c) The F-P resonances of the m = +1 (dotted) and the m = 1 (dashed) PW order at θ = 5°. The solid lines are for normal incidence and different colours are different WG orders. (d) The transmission spectrum corresponding to the marked slice through (b).
Fig. 10
Fig. 10 (a)–(c) Reflection spectra and (d)–(f) absorption spectra of gratings as a function of their thickness. In (a), (d) d = 450 nm, while in (b), (e) d = 540 nm. The spectra of the stacked structure; grating with d = 450 nm, 1 µm thick air spacer, grating with d = 540 nm, is shown in (c), (f), where the y-axis gives the thickness of each grating, which are equal. In all cases f TiO 2 = 0.25 and the angle of incidence is 45°.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

k z , 0 = k eff cos ( θ g ) = n eff 2 π λ cos ( θ g ) ,
β WG = k x , m = k eff sin ( θ g ) + m G = k eff sin ( θ g ) + 2 π m d ,
k z , ± 1 = k eff 2 k x , ± 1 2 .
h eff , m = h + 2 i γ m ,
γ m = k air 2 ( k air sin ( θ ) + m G ) 2 ,
Δ k z = 2 π l h ,
h = p 2 n eff λ .
r = [ ν ν 1 ] sin ( k h ) 2 i cos ( k h ) + [ ν + ν 1 ] sin ( k h ) ,
ω p = ω r , p + i ω i , p = c n TF [ p π h i ln ( ρ 1 ) h ] ,
Q p = ω r , p 2 ω i , p .
t ( ω r ) Re s ω p t ( ω ) ω r ω p ,
[ Re ( t ) , Im ( t ) ] = i 2 ω i , p | Re s ω p t ( ω ) | [ sin ( φ ) , cos ( φ ) ] ,
Re s ω p t ( ω ) = i ( 1 ) p 2 n out n TF ( n out n TF ) 2 .

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