Exact field solution to guided wave propagation in lossy thin films

doi:10.1364/OE.19.020159

Exact field solution to guided wave propagation in lossy thin films

James R. Nagel, Steve Blair, and Michael A. Scarpulla »View Author Affiliations

Optics Express, Vol. 19, Issue 21, pp. 20159-20171 (2011)
http://dx.doi.org/10.1364/OE.19.020159

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Abstract

Wave guidance is an important aspect of light trapping in thin film photovoltaics making it important to properly model the effects of loss on the field profiles. This paper derives the full-field solution for electromagnetic wave propagation in a symmetric dielectric slab with finite absorption. The functional form of the eigenvalue equation is identical to the lossless case except the propagation constants take on complex values. Additional loss-guidance and anti-guidance modes appear in the lossy model which do not normally exist in the analogous lossless case. An approximate solution for the longitudinal attenuation coefficient α_z is derived from geometric optics and shows excellent agreement with the exact value. Lossy mode propagation is then explored in the context of photovoltaics by modeling a thin film solar cell made of amorphous silicon.

OCIS Codes
(310.2790) Thin films : Guided waves
(310.6805) Thin films : Theory and design

ToC Category:
Thin Films

History
Original Manuscript: July 29, 2011
Revised Manuscript: August 30, 2011
Manuscript Accepted: September 3, 2011
Published: September 29, 2011

Citation
James R. Nagel, Steve Blair, and Michael A. Scarpulla, "Exact field solution to guided wave propagation in lossy thin films," Opt. Express 19, 20159-20171 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20159

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References

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, NY, 1989).
J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, Cambridge, MA, 2000).
G. H. Owyang, Foundations of Optical Waveguides (Elsevier, New York, NY, 1981).
C. R. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, Boston, MA, 2003).
A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, NY, 1983).
S. Miyanaga and H. Fujiwara, “Effects of absorption on the propagation constants of guided modes in an asymmetric slab optical waveguide,” Opt. Commun.64, 31–35 (1987). [CrossRef]
K. Fujii, “Dispersion relations of TE-mode in a 3-layer slab waveguide with imaginary-part of refractive index,” Opt. Commun.171, 245–251 (1999). [CrossRef]
T. D. Visser, H. Blok, and D. Lenstra, “Modal analysis of a planar waveguide with gain and losses,” IEEE J. Quantum Electron.31, 1803–1810 (1995). [CrossRef]
A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A20, 1617–1628 (2003). [CrossRef]
A. W. Snyder and J. D. Love, “Goos-Hanchen shift,” Appl. Opt.15, 236–238 (1973). [CrossRef]
Lumerical Solutions Inc., http://www.lumerical.com/ .
T. D. Visser, H. Blok, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron.33, 1763–1766 (1997). [CrossRef]
G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C Solid State10, 467–477 (1977). [CrossRef]
Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107, 17491–17496 (2010). [CrossRef] [PubMed]
J. A. Snyman, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms (Applied Optimization) (Springer, 2005). [PubMed]

Balanis, C. A.
Blok, H.
Fan, S.
Fujii, K.
Fujiwara, H.
Kong, J. A.
Lenstra, D.
Lipson, M.
Love, J. D.
Miyanaga, S.
Owyang, G. H.
Pollock, C. R.
Raman, A.
Siegman, A. E.
Snyder, A. W.
Snyman, J. A.
Thutupalli, G. K. M.
Tomlin, S. G.
Visser, T. D.
Yu, Z.

Appl. Opt.

A. W. Snyder and J. D. Love, “Goos-Hanchen shift,” Appl. Opt.15, 236–238 (1973). [CrossRef]

IEEE J. Quantum Electron.

T. D. Visser, H. Blok, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron.33, 1763–1766 (1997). [CrossRef]
T. D. Visser, H. Blok, and D. Lenstra, “Modal analysis of a planar waveguide with gain and losses,” IEEE J. Quantum Electron.31, 1803–1810 (1995). [CrossRef]

J. Opt. Soc. Am. A

A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A20, 1617–1628 (2003). [CrossRef]

J. Phys. C Solid State

G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C Solid State10, 467–477 (1977). [CrossRef]

Opt. Commun.

S. Miyanaga and H. Fujiwara, “Effects of absorption on the propagation constants of guided modes in an asymmetric slab optical waveguide,” Opt. Commun.64, 31–35 (1987). [CrossRef]
K. Fujii, “Dispersion relations of TE-mode in a 3-layer slab waveguide with imaginary-part of refractive index,” Opt. Commun.171, 245–251 (1999). [CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

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

Other

J. A. Snyman, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms (Applied Optimization) (Springer, 2005). [PubMed]
Lumerical Solutions Inc., http://www.lumerical.com/ .
C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, NY, 1989).
J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, Cambridge, MA, 2000).
G. H. Owyang, Foundations of Optical Waveguides (Elsevier, New York, NY, 1981).
C. R. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, Boston, MA, 2003).
A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, NY, 1983).

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