Abstract

We calculate the maximal absorption enhancement obtainable by guided mode excitation in a weakly absorbing dielectric slab over wide wavelength ranges. The slab mimics thin film silicon solar cells in the low absorption regime. We consider simultaneously wavelength-scale periodicity of the texture, small thickness of the film, modal properties of the guided waves and their confinement to the film. Also we investigate the effect of the incident angle on the absorption enhancement. Our calculations provide tighter bounds for the absorption enhancement but still significant improvement is possible. Our explanation of the absorption enhancement can help better exploitation of the guided modes in thin film devices.

© 2012 Optical Society of America

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References

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  1. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
    [CrossRef]
  2. J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
    [CrossRef]
  3. A. Naqavi, K. Söderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19, 128–140 (2011).
    [CrossRef]
  4. F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
    [CrossRef]
  5. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18, A366–A380 (2010).
    [CrossRef]
  6. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
    [CrossRef]
  7. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron Devices 29, 300–305 (1982).
    [CrossRef]
  8. H. R. Stuart and D. G. Hall, “Thermodynamic limit to light trapping in thin planar structures,” J. Opt. Soc. Am. A 14, 3001–3008 (1997).
    [CrossRef]
  9. O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
    [CrossRef]
  10. C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
    [CrossRef]
  11. J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
    [CrossRef]
  12. C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Opt. Express 18, A335–A341 (2010).
    [CrossRef]
  13. M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
    [CrossRef]
  14. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15, 16986–17000 (2007).
    [CrossRef]
  15. C. Heine and R. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34, 2476–2482 (1995).
    [CrossRef]
  16. T. Tamir, “Integrated optics,” in Topics in Applied Physics, T. Tamir, ed., 2nd. rev. ed. (Springer, 1979).
  17. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

2012 (1)

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

2011 (3)

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
[CrossRef]

F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
[CrossRef]

A. Naqavi, K. Söderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19, 128–140 (2011).
[CrossRef]

2010 (5)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Opt. Express 18, A335–A341 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18, A366–A380 (2010).
[CrossRef]

O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[CrossRef]

2008 (1)

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

2007 (1)

2003 (1)

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

1997 (1)

1995 (1)

1982 (1)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron Devices 29, 300–305 (1982).
[CrossRef]

Alexander, D.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Atwater, H. A.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Bailat, J.

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Ballif, C.

A. Naqavi, K. Söderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19, 128–140 (2011).
[CrossRef]

F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
[CrossRef]

C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F. Haug, T. Söderström, C. Ballif, and F. Lederer, “Comparison and optimization of randomly textured surfaces in thin-film solar cells,” Opt. Express 18, A335–A341 (2010).
[CrossRef]

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Battaglia, C.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Beckers, T.

Bermel, P.

Bittkau, K.

Boccard, M.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Callahan, D. M.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
[CrossRef]

Cantoni, M.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Carius, R.

Charrière, M.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Cody, G. D.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron Devices 29, 300–305 (1982).
[CrossRef]

Despeisse, M.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Dominé, D.

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Escarré, J.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Fahr, S.

Fan, S.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18, A366–A380 (2010).
[CrossRef]

Fesquet, L.

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Grandidier, J.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
[CrossRef]

Hall, D. G.

Haug, F.

Haug, F. J.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Haug, F.-J.

A. Naqavi, K. Söderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19, 128–140 (2011).
[CrossRef]

F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Heine, C.

Herzig, H. P.

Hsu, C. M.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Isabella, O.

O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
[CrossRef]

Joannopoulos, J. D.

Kimerling, L. C.

Kluth, O.

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

Krc, J.

O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
[CrossRef]

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

Lederer, F.

Luo, C.

Moll, F.

O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
[CrossRef]

Morf, R.

Munday, J. N.

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
[CrossRef]

Naqavi, A.

F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
[CrossRef]

A. Naqavi, K. Söderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19, 128–140 (2011).
[CrossRef]

Paeder, V.

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Python, M.

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Raman, A.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18, A366–A380 (2010).
[CrossRef]

Rockstuhl, C.

Scharf, T.

Shah, A.

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Smole, F.

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

Söderström, K.

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
[CrossRef]

A. Naqavi, K. Söderström, F.-J. Haug, V. Paeder, T. Scharf, H. P. Herzig, and C. Ballif, “Understanding of photocurrent enhancement in real thin film solar cells: towards optimal one-dimensional gratings,” Opt. Express 19, 128–140 (2011).
[CrossRef]

Söderström, T.

Stuart, H. R.

Tamir, T.

T. Tamir, “Integrated optics,” in Topics in Applied Physics, T. Tamir, ed., 2nd. rev. ed. (Springer, 1979).

Topic, M.

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

Vallat-Sauvain, E.

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron Devices 29, 300–305 (1982).
[CrossRef]

Yu, Z.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18, A366–A380 (2010).
[CrossRef]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[CrossRef]

Zeman, M.

O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
[CrossRef]

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

Zeng, L.

ACS Nano (1)

C. Battaglia, C. M. Hsu, K. Söderström, J. Escarré, F. J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. Alexander, and M. Cantoni, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6, 2790–2797 (2012).
[CrossRef]

Adv. Mater. (1)

J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Thin-film solar cells: light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. 23, 1272–1276 (2011).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Electron Devices (1)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron Devices 29, 300–305 (1982).
[CrossRef]

J. Appl. Phys. (1)

F.-J. Haug, K. Söderström, A. Naqavi, and C. Ballif, “Resonances and absorption enhancement in thin film silicon solar cells with periodic interface texture,” J. Appl. Phys. 109, 084516 (2011).
[CrossRef]

J. Non-Cryst. Solids (1)

M. Python, E. Vallat-Sauvain, J. Bailat, D. Dominé, L. Fesquet, A. Shah, and C. Ballif, “Relation between substrate surface morphology and microcrystalline silicon solar cell performance,” J. Non-Cryst. Solids 354, 2258–2262 (2008).
[CrossRef]

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

Nat. Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Opt. Express (4)

Phys. Status Solidi A (1)

O. Isabella, F. Moll, J. Krč, and M. Zeman, “Modulated surface textures using zinc oxide films for solar cells applications,” Phys. Status Solidi A 207, 642–646 (2010).
[CrossRef]

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

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[CrossRef]

Thin Solid Films (1)

J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topič, “Effect of surface roughness of ZnO: Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426, 296–304 (2003).
[CrossRef]

Other (2)

T. Tamir, “Integrated optics,” in Topics in Applied Physics, T. Tamir, ed., 2nd. rev. ed. (Springer, 1979).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (6)

Fig. 1.
Fig. 1.

Schematics of a slab with a 1D periodic texture. The field phase variations are symbolically shown with sinusoidal patterns. The green and red curves correspond to the cases where TRC and Bragg condition are satisfied respectively.

Fig. 2.
Fig. 2.

Dispersion of a film with refractive index n=4 and thickness d=200nm in TE polarization. The guided modes (green curves) occur between the light line of air (dashed black) and dielectric (dotted-dashed blue). The periodic texture excites the guided modes where they satisfy Bragg condition (vertical lines). The dashed horizontal lines correspond to 600 and 1200 nm. Resonances are illustrated by the red circles.

Fig. 3.
Fig. 3.

(a) Enhancement factor introduced by 1D gratings in TE polarization versus the normalized period (Λ/λ) for the slab (d=200nm, n=4). Dashed: wavelength range from 600 to 800 nm. Solid with markers: wavelength range from 800 to 1200 nm. Bold solid: Yu’s model (thick absorber). (b) Same as (a) but for TM polarization. (c) Dispersion diagram of the slab for TE polarization. (d) Same as (c) for TM polarization. The horizontal dashed lines in (c) and (d) correspond to the wavelengths 600, 800, and 1200 nm.

Fig. 4.
Fig. 4.

(a) Schematic view of the grating under in-plane oblique incidence. (b) Shift of the resonant energy of the positive and negative orders due to the change of the incident angle from 0° to 20°. (c) Angular dependence of the F under TE-polarized illumination over the wavelength range (600–800) nm. (d) Same as (c) for TM-polarized illumination. (e) Same as (c) for the wavelength range (800–1200) nm. (f) Same as (e) for TM-polarized illumination.

Fig. 5.
Fig. 5.

(a) F under TE-polarized illumination over the wavelength range (600–800) nm for the incident angles of 20° and 60°. (b) Same as (a) but for TM polarization.

Fig. 6.
Fig. 6.

Energy overlap as a function of photon energy (eV) and phase index for (a) even modes under TE-polarized light, (b) odd modes under TE-polarized light, (c) even modes under TM-polarized light, and (d) odd modes under TM-polarized light. The energy range corresponds to the wavelengths between 600 and 1200 nm. The red dotted curves represent the guided modes corresponding to each case.

Equations (18)

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

k=2mπ/Λ.m:integer,Λ:grating period,
da/dt=[jω0(Nγe+γi)/2]a+jγeS,
F=2πMγi/(αdΔωN),
α=nγi/c,
da/dt=(jωγ/2)a+,da/dz=(jkα/2)a+,
dzdt=vp=ωk=γiαwg=cnwg,
αwg=nwgγi/c.
F=2πcnwgdΔωMNη.
k,m=k,m+k0sinθ,
E(dz)=E(0)eαwgdz=E(0)[ηeαdz+(1η)].
Ee={cos(kxx)/cos(kxd/2)|x|d/2,exp(α(|x|d/2))|x|>d/2.
Eo={sin(kxx)/sin(kxd/2)|x|d/2,exp(α(xd/2))x>d/2,exp(α(x+d/2))x<d/2,
η=(n2|Eslab|2dx)/(n2|Eslab|2dx+|Eair|2dx).
Ex=jωεzHy,
Ez=jωεxHy.
I=|E|2=|Ex|2+|Ez|2.
Ie={μ0ε0n2kx2sin2(kxx)+k2cos2(kxx)k02cos2(kxd/2)|x|d/2μ0ε0exp(2α(|x|d/2))|x|>d/2,
Io={μ0ε0n2kx2cos2(kxx)+k2sin2(kxx)k02sin2(kxd/2)|x|d/2μ0ε0exp(2α(|x|d/2))|x|>d/2,

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