Abstract

The one-dimensional nonlocal diffusion model for holographic recording in photopolymers proposed by Sheridan et al. [J. Opt. Soc. Am. A 17, 1108 (2002)] is rewritten in dimensionless form by introduction of four dimensionless variables. The dimensionless nonlocal diffusion equation is rigorously solved by use of the finite-difference time-domain method and compared with the four-harmonic-component approximation. In general, the error in the four-harmonic-component approximation increases as RD and σD decrease. The dynamic behavior of holographic grating formations based on DuPont OmniDex613 photopolymers (recorded with UV light of free-space wavelength 363.8 nm) are experimentally studied by use of the real-time diffraction-monitoring technique. By application of rigorous coupled-wave analysis (RCWA), the growth curves of experimentally monitored diffraction efficiencies are converted to the corresponding refractive-index modulations. After the holographic recording reaches steady state, the refractive-index modulation is ∼0.01. Furthermore, the conversion from diffraction efficiencies to refractive-index modulations is also accomplished by use of Kogelnik’s theory (corrected for reflection losses) and compared to the RCWA. As a result, the error in refractive-index modulations estimated by Kogelnik’s theory at steady state is ∼30%. The effects of postbaking conditions on the refractive-index modulation are investigated for the first time to the authors’ knowledge. To accomplish this we baked the holographic grating samples at various temperatures (Tb=90, 120, 150 °C) for three time periods (tb=1, 1.5,2 h). In general, it was found that refractive-index modulation can increase from ∼0.01 to ∼0.02 after baking. Finally, we estimated the characteristic parameters including diffusion coefficient and the nonlocal response length by fitting the theoretical model to the experimental data for the recording UV wavelength of 363.8 nm.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2002 (3)

2001 (4)

G. Zhang, G. Montemezzani, and P. Günter, “Narrow-bandwidth holographic reflection filters with photopolymer films,” Appl. Opt. 40, 2423–2427 (2001).
[CrossRef]

J. T. Sheridan, M. Downey, and F. T. O’Neill, “Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses,” J. Opt. A 3, 477–488 (2001).
[CrossRef]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model,” J. Appl. Phys. 90, 3142–3148 (2001).
[CrossRef]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449–463 (2001).
[CrossRef]

2000 (3)

1999 (3)

1998 (2)

J. Yeh, A. Harton, and K. Wyatt, “Reliability study of holographic optical elements made with DuPont photopolymer,” Appl. Opt. 26, 6270–7264 (1998).
[CrossRef]

S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design of high-efficiency volume grating couplers for line focusing,” Appl. Opt. 37, 2278–2287 (1998).
[CrossRef]

1997 (3)

1996 (2)

1995 (4)

1994 (1)

G. Zhao and P. Mouroulis, “Diffusion model of holographic formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

1993 (1)

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

1987 (1)

1985 (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for think holographic gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Ashley, P. R.

Calixto, S.

Caulfield, H. J.

U. S. Rhee, H. J. Caulfield, C. S. Vikram, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
[CrossRef] [PubMed]

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Colvin, V. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[CrossRef]

Downey, M.

J. T. Sheridan, M. Downey, and F. T. O’Neill, “Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses,” J. Opt. A 3, 477–488 (2001).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Günter, P.

Harris, A. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[CrossRef]

Harton, A.

J. Yeh, A. Harton, and K. Wyatt, “Reliability study of holographic optical elements made with DuPont photopolymer,” Appl. Opt. 26, 6270–7264 (1998).
[CrossRef]

Huang, Q.

Hwang, H. C.

Jenkins, B. K.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for think holographic gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kostuk, R. K.

Krylov, V. N.

Kwon, J. H.

Larson, R. G.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[CrossRef]

Lawrence, J. R.

Lion, Y.

Mikhailov, V. N.

Mirsalehi, M. M.

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Montemezzani, G.

Moreau, V.

Morozov, V.

Mouroulis, P.

G. Zhao and P. Mouroulis, “Extension of diffusion model of holographic photopolymer,” J. Mod. Opt. 42, 2571–2573 (1995).
[CrossRef]

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 15, 528–532 (1995).
[CrossRef]

G. Zhao and P. Mouroulis, “Diffusion model of holographic formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

Neff, J.

O’Neill, F. T.

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Adjusted intensity nonlocal diffusion model of photopolymer grating formation,” J. Opt. Soc. Am. B 19, 621–629 (2002).
[CrossRef]

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials by use of analytical nonlocal diffusion model,” Appl. Opt. 41, 845–852 (2002).
[CrossRef]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model,” J. Appl. Phys. 90, 3142–3148 (2001).
[CrossRef]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449–463 (2001).
[CrossRef]

J. T. Sheridan, M. Downey, and F. T. O’Neill, “Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses,” J. Opt. A 3, 477–488 (2001).
[CrossRef]

Piazzolla, S.

Psaltis, D.

Pu, A.

Renotte, Y.

Rhee, U. S.

U. S. Rhee, H. J. Caulfield, C. S. Vikram, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
[CrossRef] [PubMed]

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Schilling, M. L.

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[CrossRef]

Schultz, S. M.

Shamir, J.

U. S. Rhee, H. J. Caulfield, C. S. Vikram, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
[CrossRef] [PubMed]

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Sheridan, J. T.

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Adjusted intensity nonlocal diffusion model of photopolymer grating formation,” J. Opt. Soc. Am. B 19, 621–629 (2002).
[CrossRef]

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials by use of analytical nonlocal diffusion model,” Appl. Opt. 41, 845–852 (2002).
[CrossRef]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model,” J. Appl. Phys. 90, 3142–3148 (2001).
[CrossRef]

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449–463 (2001).
[CrossRef]

J. T. Sheridan, M. Downey, and F. T. O’Neill, “Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses,” J. Opt. A 3, 477–488 (2001).
[CrossRef]

J. T. Sheridan and J. R. Lawrence, “Nonlocal-response diffusion model of holographic recording in photopolymer,” J. Opt. Soc. Am. A 17, 1108–1114 (2000).
[CrossRef]

Vikram, C. S.

U. S. Rhee, H. J. Caulfield, C. S. Vikram, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
[CrossRef] [PubMed]

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Weitzel, K. T.

Wild, U. P.

Woo, K. C.

Wyatt, K.

J. Yeh, A. Harton, and K. Wyatt, “Reliability study of holographic optical elements made with DuPont photopolymer,” Appl. Opt. 26, 6270–7264 (1998).
[CrossRef]

Yeh, J.

J. Yeh, A. Harton, and K. Wyatt, “Reliability study of holographic optical elements made with DuPont photopolymer,” Appl. Opt. 26, 6270–7264 (1998).
[CrossRef]

Zhang, G.

Zhao, G.

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 15, 528–532 (1995).
[CrossRef]

G. Zhao and P. Mouroulis, “Extension of diffusion model of holographic photopolymer,” J. Mod. Opt. 42, 2571–2573 (1995).
[CrossRef]

G. Zhao and P. Mouroulis, “Diffusion model of holographic formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

Zhou, H. J.

Appl. Opt. (12)

J. Yeh, A. Harton, and K. Wyatt, “Reliability study of holographic optical elements made with DuPont photopolymer,” Appl. Opt. 26, 6270–7264 (1998).
[CrossRef]

S. Calixto, “Dry polymer for holographic recording,” Appl. Opt. 26, 3904–3910 (1987).
[CrossRef] [PubMed]

Q. Huang and P. R. Ashley, “Holographic Bragg grating input–output couplers for a polymer waveguide at an 850-nm wavelength,” Appl. Opt. 36, 1198–1203 (1997).
[CrossRef] [PubMed]

S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design of high-efficiency volume grating couplers for line focusing,” Appl. Opt. 37, 2278–2287 (1998).
[CrossRef]

R. K. Kostuk, “Dynamic hologram recording characteristics in DuPont photopolymers,” Appl. Opt. 38, 1357–1363 (1999).
[CrossRef]

S. M. Schultz, E. N. Glytsis, and T. K. Gaylord, “Design, fabrication, and performance of preferential-order volume grating waveguide couplers,” Appl. Opt. 39, 1223–1232 (2000).
[CrossRef]

U. S. Rhee, H. J. Caulfield, C. S. Vikram, and J. Shamir, “Dynamics of hologram recording in DuPont photopolymer,” Appl. Opt. 34, 846–853 (1995).
[CrossRef] [PubMed]

H. J. Zhou, V. Morozov, and J. Neff, “Characterization of DuPont photopolymers in infrared light for free-space optical interconnects,” Appl. Opt. 34, 7457–7459 (1995).
[CrossRef] [PubMed]

A. Pu and D. Psaltis, “High-density recording in photopolymer-based holographic three-dimensional disks,” Appl. Opt. 35, 2389–2398 (1996).
[CrossRef] [PubMed]

G. Zhang, G. Montemezzani, and P. Günter, “Narrow-bandwidth holographic reflection filters with photopolymer films,” Appl. Opt. 40, 2423–2427 (2001).
[CrossRef]

F. T. O’Neill, J. R. Lawrence, and J. T. Sheridan, “Comparison of holographic photopolymer materials by use of analytical nonlocal diffusion model,” Appl. Opt. 41, 845–852 (2002).
[CrossRef]

V. Moreau, Y. Renotte, and Y. Lion, “Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model,” Appl. Opt. 41, 3427–3435 (2002).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for think holographic gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Appl. Phys. (2)

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material parameter estimation using a nonlocal diffusion based model,” J. Appl. Phys. 90, 3142–3148 (2001).
[CrossRef]

V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. 81, 5913–5923 (1997).
[CrossRef]

J. Mod. Opt. (2)

G. Zhao and P. Mouroulis, “Diffusion model of holographic formation in dry photopolymer materials,” J. Mod. Opt. 41, 1929–1939 (1994).
[CrossRef]

G. Zhao and P. Mouroulis, “Extension of diffusion model of holographic photopolymer,” J. Mod. Opt. 42, 2571–2573 (1995).
[CrossRef]

J. Opt. A (1)

J. T. Sheridan, M. Downey, and F. T. O’Neill, “Diffusion-based model of holographic grating formation in photopolymers: generalized non-local material responses,” J. Opt. A 3, 477–488 (2001).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

G. Zhao and P. Mouroulis, “Second order grating formation in dry holographic photopolymers,” Opt. Commun. 15, 528–532 (1995).
[CrossRef]

Opt. Eng. (1)

U. S. Rhee, H. J. Caulfield, J. Shamir, C. S. Vikram, and M. M. Mirsalehi, “Characteristics of the DuPont photopolymer for angularly multiplexed page-oriented holographic memories,” Opt. Eng. 32, 1839–1847 (1993).
[CrossRef]

Opt. Lett. (3)

Optik (Stuttgart) (1)

J. R. Lawrence, F. T. O’Neill, and J. T. Sheridan, “Photopolymer holographic recording material,” Optik (Stuttgart) 112, 449–463 (2001).
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Other (2)

C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1992), Chap. 8.

International Mathematics and Statistics Library, IMSL Inc., User’s Manual: Math/Library, Ver. 1.0 (IMSL, Houston, Texas, 1987), pp. 847–858.

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Figures (13)

Fig. 1
Fig. 1

(a) Profiles of monomer concentration Φm within one grating period at various dimensionless times tD for several dimensionless nonlocal variance parameters σD (σD=0.0, 0.62, 1.23), where RD=1.0, α=0.0, and ν=0.5. (b) Profiles of polymer concentration Φp for the same parameters as in (a).

Fig. 2
Fig. 2

Harmonic components of polymer concentrations that correspond to Fig. 1(b) at various dimensionless times tD for several dimensionless nonlocal variance parameters σD (σD=0.0, 0.62, 1.23), where RD=1.0, α=0.0, and ν=0.5. Φp,q represents the qth harmonic of the polymer-concentration profile.

Fig. 3
Fig. 3

Polymer-concentration profiles Φp at steady state for various values of RD (RD=0.05, 0.1, 1.0, 10.0, 50.0), where α=0.0, ν=0.5, and σD=0.0. The larger value of RD corresponds to a smaller grating period, a higher diffusion coefficient, or a lower exposure irradiance (lower polymerization rate).

Fig. 4
Fig. 4

Saturation values of the first three harmonics of polymer concentrations as functions of RD (on a log scale) for various values of σD (σD=0.0, 0.62, 1.23, 1.85).

Fig. 5
Fig. 5

Nonlinearity of polymer concentration at steady state as a function of RD (on a log scale) for various values of σD (σD=0.0, 0.62, 1.23, 1.85). χp,qs represents the nonlinearity of the qth harmonic of the polymer concentration at steady state.

Fig. 6
Fig. 6

Errors of the first harmonic of polymer concentration owing to the four-harmonic-component approximation with respect to the FDTD method as a function of RD (on a log scale) for various values of σD (σD=0.0, 0.62, 1.23, 1.85).

Fig. 7
Fig. 7

Schematic diagram of the real-time diffraction-monitoring experiment with DuPont OmniDex613 photopolymers. An argon-ion laser with free-space wavelength λ0,w=363.8 nm is used as a writing beam to create the fringe interference, and a He–Ne laser with free-space wavelength λ0,r=632.8 nm is used to monitor the temporal behavior of hologram recording. The incident angle of the writing beams is θ=30°, resulting in a grating period of Λ=363.8 nm. The incident angle of the reading beam is θb,o=60.42°, which satisfies the first-order Bragg condition.

Fig. 8
Fig. 8

Experimentally monitored diffraction efficiency as a function of exposure time for unslanted transmission gratings recorded on DuPont OmniDex 613 photopolymers by use of various values of exposure irradiance I0.

Fig. 9
Fig. 9

Experimental refractive-index modulations converted from monitored diffraction efficiencies (as shown in Fig. 8) by use of RCWA with seven-harmonic retention, as a function of exposure time for unslanted transmission gratings recorded on DuPont OmniDex 613 photopolymers by use of various exposure irradiances I0.

Fig. 10
Fig. 10

Errors in refractive-index modulation estimated by use of Kogelnik’s theory with respect to RCWA for various exposure irradiances I0. Seven orders have been retained in RCWA.

Fig. 11
Fig. 11

Effects of postbaking conditions on refractive-index modulation for various exposure irradiances I0. The holographic-grating samples were baked at three different temperatures Tb for three time periods tb(=1, 1.5, 2 h).

Fig. 12
Fig. 12

Comparison of theoretical models and experimentally obtained refractive-index modulations for various exposure irradiances I0. Solid curves are the theoretical results based on the RCWA with seven diffracted orders retained in the analysis and with characteristic parameters listed in Table 1.

Fig. 13
Fig. 13

Configuration for determining correction factors of the Fresnel reflection loss. The sample consists of a glass substrate with thickness hs, a grating with thickness hg, and a Mylar layer with thickness hm. The refractive indices of the glass, the grating, and the Mylar layer are ns, ng, and nm, respectively. The incident beam has wavelength λ0,r and incident angle θb,o. Rf Fresnel reflection coefficient at the interface between air and glass; Rf, Fresnel reflection coefficient at the interface between glass and the grating–Mylar combination.

Tables (2)

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Table 1 Characteristic Parameters of Holographic Grating Formations Based on DuPont OmniDex613 Photopolymers for Exposure to λ0,w=363.8 nm UV Light

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Table 2 Saturation Refractive-Index Modulations Calculated from Experimental Data with RCWA or Kogelnik’s Theory with Corrections for Fresnel Losses

Equations (39)

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Φm(x, t)t=xD(x, t) Φm(x, t)x--G(x, x)F(x)Φm(x, t)dx,
F(x)=κI0ν[1+V cos(Kx)]ν,
D(x, t)=D0exp[-αF(x)t],
G(x, x)=12πσexp-(x-x)22σ,
Φp(x, t)=0t- G(x, x)F(x)Φm(x, t)dxdt.
RD=D0K2/κI0ν,
σD=σK2,
tD=κI0νt,
xD=Kx.
Φm(xD, tD)tD=RDxDDD(xD, tD) Φm(xD, tD)xD-- GD(xD, xD)FD(xD)×Φm(xD, tD)dxD,
Φp(xD, tD)=0tD- GD(xD, xD)FD(xD)×Φm(xD, tD)dxDdtD,
FD(xD)=[1+V cos(xD)]ν,
DD(xD, tD)=exp[-αFD(xD)tD],
GD(xD, xD)=12πσDexp-(xD-xD)22σD.
n(xD, tD)=CpΦp(xD, tD)+CmΦm(xD, tD)cos ϕ,
Φm(i, j)1-2C2(i, j-1) ΔtDΔxD2Φm(i, j-1)+C2(i ,j-1) ΔtDΔxD2+C1(i, j-1) ΔtD2ΔxD×Φm(i+1, j-1)+C2(i ,j-1) ΔtDΔxD2-C1(i, j-1) ΔtD2ΔxD×Φm(i-1, j-1)-ΔtDC3(i, j-1),
C1(i, j-1)=RDDD(xD,i, tD,j-1)xD,
C2(i, j-1)=RDDD(xD,i, tD,j-1),
C3(i, j-1)ΔxD2fD(1, j-1)+2 k=2N-1fD(k, j-1)+fD(N, j-1),
fD(k, j-1)=GD(xD,i, xD,k)F(xD,k)×Φm(xD,k, tD,j-1).
Φp(i, j)ΔtD2C3(i, 0)+2 k=1j-1 C3(i, k)+C3(i, j).
ΔtD12ΔxD2RD.
Φu,q(tD) 1N-1i=1N-1Φu(xD,i, tD)cos(qxD,i)
(u=m, p).
χp,qs=|Φp,qs||Φp,1s|(q>1),
Error=|Φp,1s,FDTD-Φp,1s,LHC|Φp,1s,FDTD 100,
DE1=IDIinc,
Error=Δn1,RCWA-Δn1,KogΔn1,RCWA 100,
ferror(RD, σD, κ, ϕ, Cp, Cm)
=ti[Δn1,model(RD, σD, κ, ϕ, Cp, Cm, ti)
-Δn1,exp(ti)]2,
κ=10[(1-Rf)I0]1/2tsat,
Cp=Δn1sΦp,1s,
D0=κΛ2RD[(1-Rf)I0]1/24π2,
σ=ΛσD2π.
Δn1,Kog=λ0,rsin θBπhgsin-1
×DE1(1-Rf)(1-Rf)(1-Rf)(1-Rf)1/2,
Δn1,Kog=λ0,rsin θBπhgsin-1DE1(1-Rf)(1-Rfmi)1/2
DE1c=DE11-Rf=fRCWA(Δn1),

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