## First-principle calculation of solar cell efficiency under incoherent illumination |

Optics Express, Vol. 21, Issue S4, pp. A616-A630 (2013)

http://dx.doi.org/10.1364/OE.21.00A616

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### Abstract

Because of the temporal incoherence of sunlight, solar cells efficiency should depend on the degree of coherence of the incident light. However, numerical computation methods, which are used to optimize these devices, fundamentally consider fully coherent light. Hereafter, we show that the incoherent efficiency of solar cells can be easily analytically calculated. The incoherent efficiency is simply derived from the coherent one thanks to a convolution product with a function characterizing the incoherent light. Our approach is neither heuristic nor empiric but is deduced from first-principle, i.e. Maxwell’s equations. Usually, in order to reproduce the incoherent behavior, statistical methods requiring a high number of numerical simulations are used. With our method, such approaches are not required. Our results are compared with those from previous works and good agreement is found.

© 2013 OSA

## 1. Introduction

1. L. Tsakalakos, *Nanotechnology for Photovoltaics* (CRC, 2010) [CrossRef] .

2. J. Nelson, *The Physics of Solar Cells* (Imperial College, 2003) [CrossRef] .

3. M. Zeman, R.A.C.M.M. van Swaaij, J. Metselaar, and R.E.I. Schropp, “Optical modeling of a-Si:H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. **88**, 6436–6443 (2000) [CrossRef] .

6. O. Deparis, J.P. Vigneron, O. Agustsson, and D. Decroupet, “Optimization of photonics for corrugated thin-film solar cells,” J. Appl. Phys. **106**, 094505 (2009) [CrossRef] .

7. J. Gjessing, A.S. Sudbø, and E.S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. **110**, 033104 (2011) [CrossRef] .

8. A. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. **112**, 113107 (2012) [CrossRef] .

11. M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. **71**, 811–818 (1981) [CrossRef] .

14. J. P. Vigneron, F. Forati, D. André, A. Castiaux, I. Derycke, and A. Dereux, “Theory of electromagnetic energy transfer in three-dimensional structures,” Ultramicroscopy **61**, 21–27 (1995) [CrossRef] .

8. A. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. **112**, 113107 (2012) [CrossRef] .

15. A. Jin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells **92**, 1689–1696 (2008) [CrossRef] .

16. L. Zhao, Y. Zuo, C. Zhou, H. Li, W. Diao, and W. Wang, “A highly efficient light-trapping structure for thin-film silicon solar cells,” Sol. Energy **84**, 110–115 (2010) [CrossRef] .

*J*supplied by the solar cell is given by: where

*A*(

*λ*) is the absorption spectrum and

*S*(

_{G}*λ*) the global power spectral density of the sun. In most studies, the absorption spectrum

*A*(

*λ*) is computed from numerical codes which propagate the electromagnetic field. Nevertheless, such computed

*A*(

*λ*) is calculated from coherent fields and then we write

*A*(

*λ*) =

*A*(

_{coh}*λ*). This quantity does not correspond to the required effective incoherent absorption

*A*(

_{incoh}*λ*) experienced by the solar cell. In order to theoretically predict the performance of a solar cell, it is therefore very important to improve numerical methods and to take incoherent incident light into account, i.e. to use

*A*(

*λ*) =

*A*(

_{incoh}*λ*) in Eq. (1).

*I*∝

*E*·

*E*

^{*}= |

*E*|

^{2}. The way the square modulus of the fields enters into the calculation of the absorption (reflectance, transmittance) of the system is far from being trivial (see, for example, the case of RCWA method, in Appendix B). In any case, there exists no transfer function relating

*linearly*the solar cell absorption to the incident Poynting vector flux. The fact that the relevant quantities (absorbed flux, photocurrent,...) do not obey the superposition principle (since

*I*∝ |

*E*|

^{2}) prevents us from applying common principles of the linear response theory [17]. In particular, the incoherent response cannot be treated in the same way as the coherent one, a fact that is known for long time in optics [18], at least for simple cases, such as thin films.

19. J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D **33**, 3139–3145 (2000) [CrossRef] .

27. R. Santbergen, A. H.M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express **21**, A262–A267 (2013) [CrossRef] [PubMed] .

## 2. Incoherent absorption

*A*(

_{incoh}*ω*) is physically different from the coherent one

*A*(

_{coh}*ω*). Indeed,

*A*(

_{coh}*ω*) can be considered as an intrinsic property of the solar cell which only depends on its geometry and on its constitutive materials. By contrast,

*A*(

_{incoh}*ω*) reflects the effective measured response of the solar cell while it interacts with its environment, i.e. for instance when the photocurrent is produced and flows in a closed electrical circuit.

*A*can be obtained from at least two ways. In FDTD for instance, Eq. (2) can be used as such, since maps of the electromagnetic field are directly computed. In RCWA, reflection

*R*and transmission

*T*are calculated and

*A*is deduced from

*A*= 1 −

*R*−

*T*. In the following, we consider a RCWA formalism of the light propagation (see appendix B), and we use it to determine the effective incoherent absorption

*A*(

_{incoh}*ω*) (see Appendix A). The main results of Appendix A are summarized hereafter.

*A*(

_{incoh}*ω*) results from the convolution product, noted ★, between the coherent absorption

*A*(

_{coh}*ω*) and the incoherence function

*I*(

*ω*): This extremely simple formula is easy to use in practice. But its demonstration is not obvious and is therefore detailed in Appendix A. Eq. (7) can also be used to compute incoherent reflection and transmission spectra from their coherent counterparts (see appendix A).

## 3. Numerical application

*x*,

*z*) plane is the plane of incidence (polar and azimuthal angles equal to 0) (see Fig. 1(a)). The permittivities of materials are taken from the literature [28]. The second step is the convolution of the coherent absorption spectrum with the incoherence function

*I*(

*ω*). This step leads to the incoherent absorption spectra.

*x*direction and 15 plane waves along the

*y*direction), it takes a few hours. The second step is very fast. It takes only a few minutes on a personal computer. It is an important improvement in terms of computational time, in comparison with other computational methods [19

19. J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D **33**, 3139–3145 (2000) [CrossRef] .

27. R. Santbergen, A. H.M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express **21**, A262–A267 (2013) [CrossRef] [PubMed] .

26. W. Lee, S.Y. Lee, J. Kim, S. C. Kim, and B. Lee, “A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length,” Opt. Express **20**, A941–A953 (2012) [CrossRef] [PubMed] .

*τ*= 5 fs). The weak discrepancies are due to the absence of incoherent permittivity response in the Fresnel approach.

_{c}26. W. Lee, S.Y. Lee, J. Kim, S. C. Kim, and B. Lee, “A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length,” Opt. Express **20**, A941–A953 (2012) [CrossRef] [PubMed] .

26. W. Lee, S.Y. Lee, J. Kim, S. C. Kim, and B. Lee, “A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length,” Opt. Express **20**, A941–A953 (2012) [CrossRef] [PubMed] .

**20**, A941–A953 (2012) [CrossRef] [PubMed] .

*et al*. It is therefore possible to account for the light incoherence with a simple method, which does not require long computational times contrary to other previously reported methods.

8. A. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. **112**, 113107 (2012) [CrossRef] .

*m*= 3). The period of the corrugation is 500 nm and its height is 300 nm. The absorption spectra according to various coherence times are shown in Fig. 2(b). We notice that the value of the coherence time affects the absorption spectrum. The highest coherence time (here 95 fs) leads to the strongest oscillations in the spectrum. Physically, these oscillations are due to Fabry-Perot resonances (in the thin-slab) and to guided mode resonances (enabled by the corrugation). With the decrease of

*τ*, these oscillations are expected to be smoothened which is actually observed when

_{c}*τ*< 20 fs. This smoothing effect is indeed observed when measuring absorption spectra with an incoherent source.

_{c}## 4. Conclusion

## A. Appendix: Demonstration of the convolution formula

## A.1. Scattering matrix as response function

11. M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. **71**, 811–818 (1981) [CrossRef] .

14. J. P. Vigneron, F. Forati, D. André, A. Castiaux, I. Derycke, and A. Dereux, “Theory of electromagnetic energy transfer in three-dimensional structures,” Ultramicroscopy **61**, 21–27 (1995) [CrossRef] .

*ε*) through Fourier series. The electromagnetic field is then described by Bloch waves also expanded in Fourier series. In this formalism, the Maxwell’s equations take the form of a matricial first-order differential equation in the

*z*variable. The

*z*axis is perpendicular to the plane (

*x*,

*y*) where the permittivity is periodic (Fig. 1(a)). The essence of the method is to solve this equation but is not the topic of the present article.

*S*) which is calculated by solving Maxwell equations using Fourier series (see Appendix B). Let us define

*F*as the scattered field and

_{scat}*F*as the incident field, such that the associated supervectors are:

_{in}## A.2. R, T, A coefficients for a coherent monochromatic incident wave

*ω*. The response |

_{c}*F*(

_{X}*t*)〉 of the device is given by [17] where ★ denotes the convolution product. The response can then be written explicitely as: where is the Fourier transform of

*S*scattering matrix defined in (A.9). We note that

_{X}*S*(

_{X}*t*) must be real.

*X*stands either for the reflected (

*R*) or the transmitted (

*T*) wave. Reflection

*R*and transmission

_{coh}*T*coefficients associated with a coherent process can be obtained thanks to: and The absorption

_{coh}*A*is then simply given by the energy conservation law: i.e.

_{coh}*A*= 1 −

_{coh}*R*−

_{coh}*T*. The incident Ponyting flux

_{coh}*J*(

_{in}*t*), i.e. turns out to be time independent (see Eq. (B.13) in Appendix B). Therefore, the time-averaged incident flux

*J*is identical to

_{in}*J*(

_{in}*t*) This result is only valid as far as the incident wave is coherent.

## A.3. R, T, A coefficients for an incoherent monochromatic incident wave

*m*(

*t*) is a modulation which ensures the incoherent behaviour. On average,

*m*(

*t*) has a coherence time equal to

*τ*(see Fig. 1(b)). Thanks to the Wiener-Khinchine theorem, the autocorrelation function of a random process has a spectral decomposition given by the power spectrum of that process [17]. The function

_{c}*m*(

*t*) is then equally characterized by its spectral density: where is the Fourier transform of

*m*(

*t*).

*X*again stands for the reflected (

*R*) or transmitted (

*T*) wave but now with

### A.3.1. Effective response approach

*ω*and an average duration equal to the coherence time

_{c}*τ*. The coherence time plays a key role while light propagates since it prevents constructive interferences from taking place. But it also changes the way matter responds to light. Indeed, a specific medium mainly interacts with light thanks to electronic and ionic motions of its components. As a consequence, the response of a medium to an incident electromagnetic wave is not instantaneous and occurs according to the dielectric relaxation time. If the incoherence time

_{c}*τ*is short enough in comparison with the relaxation time, the medium response is not coherent. In this case, the medium response is not simply given by the value of the permittivity at

_{c}*ω*=

*ω*.

_{c}*T*such that

_{c}*T*≫

_{c}*τ*. The time

_{c}*T*is the sampling time interval [26

_{c}**20**, A941–A953 (2012) [CrossRef] [PubMed] .

29. B.O. Seraphin, *Solar Energy Conversion, Solid-State Physics Aspects* (Springer-Verlag, 1979) [CrossRef]

*T*≫

_{c}*τ*is well verified in solar cells.

_{c}*J*is given by [26

_{X,incoh}**20**, A941–A953 (2012) [CrossRef] [PubMed] .

*J*(

_{X}*t*), noted

*J*(

_{X}*ω*): We note that where

*δ*is the Dirac distribution. Since

*T*≫

_{c}*τ*,

_{c}*J*(

_{X}*ω*) should have a frequency distribution spreading over Δ

*ω*∼ 1/

*τ*around zero frequency, quite comparable to

_{c}*D*(

*ω*), the spectral density of the random process. We can therefore assume that the angular frequencies

*ω*for which

*J*(

_{X}*ω*) is significantly different from zero are such that

*T*≫ 1/

_{c}*ω*, i.e.

*T*→ +

_{c}**∞**roughly speaking. We can then fairly consider the following substitution: (1/2

*π*)sin(

*ωT*/2)/(

_{c}*ωT*/2) → (1/

_{c}*T*)

_{c}*δ*(

*ω*). As a result, we get:

### A.3.2. Incoherent response

*U*(

_{X}*ω*) =

*m*(

*ω*)

*S*(

_{X}*ω*+

*ω*) and

_{c}*t*sign denotes the transpose of the matrix. Then, (A.32) becomes: from which, by writing explicitly the convolution product, one deduces Since

*m*(−

*ω*′) =

*m*

^{*}(

*ω*′) and

### A.3.3. Incident flux

*J*. For a non dispersive incident medium, we get: Following the same argument as in section A.3.1, at a given angular frequency

_{in,incoh}*ω*, we assume that the effective flux impinging on the device

_{c}*J*is given by the time average: where

_{in,incoh}*J*is the incident flux for the coherent wave, see Eq. (A.19). Using the same calculation as in section A.3.1 for estimating the time average, one deduces: As a consequence, one gets:

_{in}### A.3.4. R, T, A coefficients

## B. Appendix: Coupled waves analysis (RCWA) formalism

12. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B **67**, 085415 (2003) [CrossRef] .

14. J. P. Vigneron, F. Forati, D. André, A. Castiaux, I. Derycke, and A. Dereux, “Theory of electromagnetic energy transfer in three-dimensional structures,” Ultramicroscopy **61**, 21–27 (1995) [CrossRef] .

*z*, which is used to define the layer thickness, i.e. the layer extends from

*z*=

*Z*to

_{I}*z*=

*Z*(Fig. 1(a)). One sets

_{III}*ρ*=

*x*

_{1}

**a**

_{1}+

*x*

_{2}

**a**

_{2}, according to the unit cell basis (

**a**

_{1},

**a**

_{2}). In such a system, Bloch’s theorem leads to the following electromagnetic field expression in the layer [12

12. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B **67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

12. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B **67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

*Ē*

_{//}and

*H̄*

_{//}are the electric and magnetic field components parallel to the layer surface. In the layer, one can then write [12

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

*I*and

*III*stand for the incident medium and emergence medium respectively, and the superscripts + and − denote the positive and negative direction along the

*z*axis for backward (+) and forward (−) field propagation. For each vector

**g**of the reciprocal lattice,

*s*and

*p*polarization amplitudes of the reflected field, respectively, and

*s*and

*p*polarization amplitudes of the incident field, respectively.

*T*[12

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

*S*[12

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

**67**, 085415 (2003) [CrossRef] .

**61**, 21–27 (1995) [CrossRef] .

*I*, for the transmitted flux in medium

*III*, and for the reflected flux in medium

*I*. In (B.13–B.15), Θ(

*x*) is the Heaviside function: i.e. Θ(

*x*) = 1 if

*x*> 0 and Θ(

*x*) = 0 otherwise.

## Acknowledgments

## References and links

1. | L. Tsakalakos, |

2. | J. Nelson, |

3. | M. Zeman, R.A.C.M.M. van Swaaij, J. Metselaar, and R.E.I. Schropp, “Optical modeling of a-Si:H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. |

4. | P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. |

5. | E. Yablonovitch and G. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE |

6. | O. Deparis, J.P. Vigneron, O. Agustsson, and D. Decroupet, “Optimization of photonics for corrugated thin-film solar cells,” J. Appl. Phys. |

7. | J. Gjessing, A.S. Sudbø, and E.S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. |

8. | A. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys. |

9. | K.S. Kunz and R.J. Luebbers, |

10. | A. Taflove, |

11. | M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. |

12. | M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B |

13. | J.P. Vigneron and V. Lousse, “Variation of a photonic crystal color with the Miller indices of the exposed surface,” Proc. SPIE |

14. | J. P. Vigneron, F. Forati, D. André, A. Castiaux, I. Derycke, and A. Dereux, “Theory of electromagnetic energy transfer in three-dimensional structures,” Ultramicroscopy |

15. | A. Jin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells |

16. | L. Zhao, Y. Zuo, C. Zhou, H. Li, W. Diao, and W. Wang, “A highly efficient light-trapping structure for thin-film silicon solar cells,” Sol. Energy |

17. | R. G. Brown and P. Y. C Hwang, |

18. | M. Born and E. Wolf, |

19. | J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D |

20. | C.L. Mitsas and D.I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt. |

21. | M.C. Troparevsky, A.S. Sabau, A.R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. Express |

22. | A. Niv, M. Gharghi, C. Gladden, O. D. Miller, and X. Zhang, “Near-Field Electromagnetic Theory for Thin Solar Cells,” Phys. Rev. Lett. |

23. | C.C. Katsidis and D.I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt. |

24. | J.S.C. Prentice, “Optical genration rate of electron-hole pairs in multilayer thin-film photovoltaic cells,” J. Phys. D |

25. | E. Centurioni, “Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers,” Appl. Opt. |

26. | W. Lee, S.Y. Lee, J. Kim, S. C. Kim, and B. Lee, “A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length,” Opt. Express |

27. | R. Santbergen, A. H.M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express |

28. | E.D. Palik, |

29. | B.O. Seraphin, |

30. | E. Hecht, |

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(040.5350) Detectors : Photovoltaic

(300.6170) Spectroscopy : Spectra

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Photovoltaics

**History**

Original Manuscript: March 14, 2013

Revised Manuscript: May 8, 2013

Manuscript Accepted: May 9, 2013

Published: May 23, 2013

**Citation**

Michaël Sarrazin, Aline Herman, and Olivier Deparis, "First-principle calculation of solar cell efficiency under incoherent illumination," Opt. Express **21**, A616-A630 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S4-A616

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### References

- L. Tsakalakos, Nanotechnology for Photovoltaics (CRC, 2010). [CrossRef]
- J. Nelson, The Physics of Solar Cells (Imperial College, 2003). [CrossRef]
- M. Zeman, R.A.C.M.M. van Swaaij, J. Metselaar, and R.E.I. Schropp, “Optical modeling of a-Si:H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys.88, 6436–6443 (2000). [CrossRef]
- P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys.62, 243–249 (1987). [CrossRef]
- E. Yablonovitch and G. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE29, 300–305 (1982).
- O. Deparis, J.P. Vigneron, O. Agustsson, and D. Decroupet, “Optimization of photonics for corrugated thin-film solar cells,” J. Appl. Phys.106, 094505 (2009). [CrossRef]
- J. Gjessing, A.S. Sudbø, and E.S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys.110, 033104 (2011). [CrossRef]
- A. Herman, C. Trompoukis, V. Depauw, O. El Daif, and O. Deparis, “Influence of the pattern shape on the efficiency of front-side periodically patterned ultrathin crystalline silicon solar cells,” J. Appl. Phys.112, 113107 (2012). [CrossRef]
- K.S. Kunz and R.J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, 1993).
- A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).
- M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am.71, 811–818 (1981). [CrossRef]
- M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B67, 085415 (2003). [CrossRef]
- J.P. Vigneron and V. Lousse, “Variation of a photonic crystal color with the Miller indices of the exposed surface,” Proc. SPIE6128, 61281G (2006). [CrossRef]
- J. P. Vigneron, F. Forati, D. André, A. Castiaux, I. Derycke, and A. Dereux, “Theory of electromagnetic energy transfer in three-dimensional structures,” Ultramicroscopy61, 21–27 (1995). [CrossRef]
- A. Jin and J. Phillips, “Optimization of random diffraction gratings in thin-film solar cells using genetic algorithms,” Sol. Energy Mater. Sol. Cells92, 1689–1696 (2008). [CrossRef]
- L. Zhao, Y. Zuo, C. Zhou, H. Li, W. Diao, and W. Wang, “A highly efficient light-trapping structure for thin-film silicon solar cells,” Sol. Energy84, 110–115 (2010). [CrossRef]
- R. G. Brown and P. Y. C Hwang, Introduction to random signals and applied kalman filtering (John Willey and Sons, 1992).
- M. Born and E. Wolf, Principles of optics (Cambridge University Press, 1999).
- J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D33, 3139–3145 (2000). [CrossRef]
- C.L. Mitsas and D.I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt.34, 1678–1683 (1995). [CrossRef] [PubMed]
- M.C. Troparevsky, A.S. Sabau, A.R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. Express18, 24715–24721 (2010). [CrossRef] [PubMed]
- A. Niv, M. Gharghi, C. Gladden, O. D. Miller, and X. Zhang, “Near-Field Electromagnetic Theory for Thin Solar Cells,” Phys. Rev. Lett.109, 138701 (2012). [CrossRef] [PubMed]
- C.C. Katsidis and D.I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt.41, 3978–3987 (2002). [CrossRef] [PubMed]
- J.S.C. Prentice, “Optical genration rate of electron-hole pairs in multilayer thin-film photovoltaic cells,” J. Phys. D32, 2146–2150 (1999). [CrossRef]
- E. Centurioni, “Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers,” Appl. Opt.44, 7532–7539 (2005). [CrossRef] [PubMed]
- W. Lee, S.Y. Lee, J. Kim, S. C. Kim, and B. Lee, “A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length,” Opt. Express20, A941–A953 (2012). [CrossRef] [PubMed]
- R. Santbergen, A. H.M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express21, A262–A267 (2013). [CrossRef] [PubMed]
- E.D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
- B.O. Seraphin, Solar Energy Conversion, Solid-State Physics Aspects (Springer-Verlag, 1979) [CrossRef]
- E. Hecht, Optics (Pearson Education, 2002)

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