Abstract

A novel technique using a cubic interpolated propagation or constrained interpolation profile (CIP) scheme for numerical analysis of light propagation in dielectric media is proposed. One- and two-dimensional calculations of the propagation of short Gaussian pulses are performed. The validity of the proposed technique is confirmed by applying it to the examination of the reflection from dielectric media. Using the CIP scheme, the optical force acted upon a dielectric disc is also calculated and it is shown that the direction of the calculated force is consistent with the direction predicted from theory.

© 2006 Optical Society of America

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References

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  1. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat.,  14, 302–307 (1966)
    [Crossref]
  2. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd edition, (Artech House, Norwood, MA, 2005)
  3. P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66, 136–138 (1995)
    [Crossref]
  4. D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
    [Crossref]
  5. C. J. Barrett, P. L. Rochon, and A. L. Natansohn, “Model of laser-driven mass transport in thin films of dye-functionalized polymers,” J. Chem. Phys. 109, 1505–1516 (1998)
    [Crossref]
  6. P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotoropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9, 323–328 (1998)
    [Crossref]
  7. T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, “Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers,” Phys. Rev. Lett. 80, 89–92 (1998)
    [Crossref]
  8. J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
    [Crossref]
  9. D. Barada, M. Itoh, and T. Yatagai, “Computer simulation of photoinduced mass transport on azobenzene polymer films by particle method,” J. Appl. Phys. 96, 4204–4210 (2004)
    [Crossref]
  10. D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Numerical analysis of photoinduced surface relief grating formation by particle method,” Opt. Rev. 12, 271–273 (2005)
    [Crossref]
  11. D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Proposal of novel model for photoinduced mass transport and numerical analysis by electromagnetic-induced particle transport method,” Jpn. J. Appl. Phys. 45, 465–469 (2006)
    [Crossref]
  12. H. Takewaki, A. Nishiguchi, and T. Yabe, “The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations,” J. Comput. Phys. 61, 261–268 (1985)
    [Crossref]
  13. H. Takewaki and T. Yabe, “The cubic-interpolated pseudo particle (CIP) method: application to nonlinear and multi-dimensional hyperbolic equations,” J. Comput. Phys. 70, 355–372 (1987)
    [Crossref]
  14. T. Yabe and E. Takei, “A new higher-order Godunov method for general hyperbolic equations,” J. Phys. Soc. Jpn. 57, 2598–2601 (1988)
    [Crossref]
  15. T. Yabe and T. Aoki, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver,” Comput. Phys. Commun. 66, 219–232 (1991)
    [Crossref]
  16. T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
    [Crossref]
  17. T. Yabe and P. Y. Wang, “Unified numerical procedure for compressible and incompressible fluid,” J. Phys. Soc. Jpn. 60, 2105–2108 (1991)
    [Crossref]
  18. T. Yabe, F. Xiao, and T. Utsumi, “Constrained interpolation profile method for multiphase analysis,” J. Comput. Phys. 169, 556593 (2001)
    [Crossref]
  19. T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
    [Crossref]
  20. Y. Ogata, T. Yabe, and K. Odagaki, “An accurate numerical scheme for Maxwell equation with CIP-method of characteristics,” Commun. Copmut. Phys. 1, 311–335 (2006)
  21. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377–382 (1981)
    [Crossref]
  22. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994)
    [Crossref]

2006 (2)

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Proposal of novel model for photoinduced mass transport and numerical analysis by electromagnetic-induced particle transport method,” Jpn. J. Appl. Phys. 45, 465–469 (2006)
[Crossref]

Y. Ogata, T. Yabe, and K. Odagaki, “An accurate numerical scheme for Maxwell equation with CIP-method of characteristics,” Commun. Copmut. Phys. 1, 311–335 (2006)

2005 (1)

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Numerical analysis of photoinduced surface relief grating formation by particle method,” Opt. Rev. 12, 271–273 (2005)
[Crossref]

2004 (2)

D. Barada, M. Itoh, and T. Yatagai, “Computer simulation of photoinduced mass transport on azobenzene polymer films by particle method,” J. Appl. Phys. 96, 4204–4210 (2004)
[Crossref]

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

2001 (1)

T. Yabe, F. Xiao, and T. Utsumi, “Constrained interpolation profile method for multiphase analysis,” J. Comput. Phys. 169, 556593 (2001)
[Crossref]

1998 (4)

C. J. Barrett, P. L. Rochon, and A. L. Natansohn, “Model of laser-driven mass transport in thin films of dye-functionalized polymers,” J. Chem. Phys. 109, 1505–1516 (1998)
[Crossref]

P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotoropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9, 323–328 (1998)
[Crossref]

T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, “Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers,” Phys. Rev. Lett. 80, 89–92 (1998)
[Crossref]

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

1995 (2)

P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66, 136–138 (1995)
[Crossref]

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
[Crossref]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994)
[Crossref]

1991 (3)

T. Yabe and T. Aoki, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver,” Comput. Phys. Commun. 66, 219–232 (1991)
[Crossref]

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

T. Yabe and P. Y. Wang, “Unified numerical procedure for compressible and incompressible fluid,” J. Phys. Soc. Jpn. 60, 2105–2108 (1991)
[Crossref]

1988 (1)

T. Yabe and E. Takei, “A new higher-order Godunov method for general hyperbolic equations,” J. Phys. Soc. Jpn. 57, 2598–2601 (1988)
[Crossref]

1987 (1)

H. Takewaki and T. Yabe, “The cubic-interpolated pseudo particle (CIP) method: application to nonlinear and multi-dimensional hyperbolic equations,” J. Comput. Phys. 70, 355–372 (1987)
[Crossref]

1985 (1)

H. Takewaki, A. Nishiguchi, and T. Yabe, “The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations,” J. Comput. Phys. 61, 261–268 (1985)
[Crossref]

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377–382 (1981)
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat.,  14, 302–307 (1966)
[Crossref]

Aoki, T.

T. Yabe and T. Aoki, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver,” Comput. Phys. Commun. 66, 219–232 (1991)
[Crossref]

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

Barada, D.

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Proposal of novel model for photoinduced mass transport and numerical analysis by electromagnetic-induced particle transport method,” Jpn. J. Appl. Phys. 45, 465–469 (2006)
[Crossref]

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Numerical analysis of photoinduced surface relief grating formation by particle method,” Opt. Rev. 12, 271–273 (2005)
[Crossref]

D. Barada, M. Itoh, and T. Yatagai, “Computer simulation of photoinduced mass transport on azobenzene polymer films by particle method,” J. Appl. Phys. 96, 4204–4210 (2004)
[Crossref]

Barrett, C. J.

C. J. Barrett, P. L. Rochon, and A. L. Natansohn, “Model of laser-driven mass transport in thin films of dye-functionalized polymers,” J. Chem. Phys. 109, 1505–1516 (1998)
[Crossref]

Batalla, E.

P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66, 136–138 (1995)
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994)
[Crossref]

Fiorini, C.

P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotoropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9, 323–328 (1998)
[Crossref]

Fukuda, T.

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Proposal of novel model for photoinduced mass transport and numerical analysis by electromagnetic-induced particle transport method,” Jpn. J. Appl. Phys. 45, 465–469 (2006)
[Crossref]

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Numerical analysis of photoinduced surface relief grating formation by particle method,” Opt. Rev. 12, 271–273 (2005)
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd edition, (Artech House, Norwood, MA, 2005)

Holme, N. C. R.

T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, “Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers,” Phys. Rev. Lett. 80, 89–92 (1998)
[Crossref]

Ikeda, F.

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

Ima, H. N.

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

Ishikawa, T.

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

Itoh, M.

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Proposal of novel model for photoinduced mass transport and numerical analysis by electromagnetic-induced particle transport method,” Jpn. J. Appl. Phys. 45, 465–469 (2006)
[Crossref]

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Numerical analysis of photoinduced surface relief grating formation by particle method,” Opt. Rev. 12, 271–273 (2005)
[Crossref]

D. Barada, M. Itoh, and T. Yatagai, “Computer simulation of photoinduced mass transport on azobenzene polymer films by particle method,” J. Appl. Phys. 96, 4204–4210 (2004)
[Crossref]

Jiang, X. L.

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

Johansen, P. M.

T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, “Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers,” Phys. Rev. Lett. 80, 89–92 (1998)
[Crossref]

Kadota, Y.

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

Kim, D. Y.

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
[Crossref]

Kumar, J.

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
[Crossref]

Lee, T. S.

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

Lefin, P.

P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotoropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9, 323–328 (1998)
[Crossref]

Li, L.

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
[Crossref]

Mizoe, H.

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

Morikia, H.

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. 23, 377–382 (1981)
[Crossref]

Natansohn, A.

P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66, 136–138 (1995)
[Crossref]

Natansohn, A. L.

C. J. Barrett, P. L. Rochon, and A. L. Natansohn, “Model of laser-driven mass transport in thin films of dye-functionalized polymers,” J. Chem. Phys. 109, 1505–1516 (1998)
[Crossref]

Nishiguchi, A.

H. Takewaki, A. Nishiguchi, and T. Yabe, “The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations,” J. Comput. Phys. 61, 261–268 (1985)
[Crossref]

Nunzi, J. M.

P. Lefin, C. Fiorini, and J. M. Nunzi, “Anisotoropy of the photoinduced translation diffusion of azo-dyes,” Opt. Mater. 9, 323–328 (1998)
[Crossref]

Odagaki, K.

Y. Ogata, T. Yabe, and K. Odagaki, “An accurate numerical scheme for Maxwell equation with CIP-method of characteristics,” Commun. Copmut. Phys. 1, 311–335 (2006)

Ogata, Y.

Y. Ogata, T. Yabe, and K. Odagaki, “An accurate numerical scheme for Maxwell equation with CIP-method of characteristics,” Commun. Copmut. Phys. 1, 311–335 (2006)

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

Pedersen, T. G.

T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, “Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers,” Phys. Rev. Lett. 80, 89–92 (1998)
[Crossref]

Ramanujam, P. S.

T. G. Pedersen, P. M. Johansen, N. C. R. Holme, and P. S. Ramanujam, “Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers,” Phys. Rev. Lett. 80, 89–92 (1998)
[Crossref]

Rochon, P.

P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66, 136–138 (1995)
[Crossref]

Rochon, P. L.

C. J. Barrett, P. L. Rochon, and A. L. Natansohn, “Model of laser-driven mass transport in thin films of dye-functionalized polymers,” J. Chem. Phys. 109, 1505–1516 (1998)
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd edition, (Artech House, Norwood, MA, 2005)

Takei, E.

T. Yabe and E. Takei, “A new higher-order Godunov method for general hyperbolic equations,” J. Phys. Soc. Jpn. 57, 2598–2601 (1988)
[Crossref]

Takewaki, H.

H. Takewaki and T. Yabe, “The cubic-interpolated pseudo particle (CIP) method: application to nonlinear and multi-dimensional hyperbolic equations,” J. Comput. Phys. 70, 355–372 (1987)
[Crossref]

H. Takewaki, A. Nishiguchi, and T. Yabe, “The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations,” J. Comput. Phys. 61, 261–268 (1985)
[Crossref]

Takizawa, K.

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

Tripathy, S.

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

Tripathy, S. K.

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
[Crossref]

Utsumi, T.

T. Yabe, F. Xiao, and T. Utsumi, “Constrained interpolation profile method for multiphase analysis,” J. Comput. Phys. 169, 556593 (2001)
[Crossref]

Wang, P. Y.

T. Yabe and P. Y. Wang, “Unified numerical procedure for compressible and incompressible fluid,” J. Phys. Soc. Jpn. 60, 2105–2108 (1991)
[Crossref]

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

Xiao, F.

T. Yabe, F. Xiao, and T. Utsumi, “Constrained interpolation profile method for multiphase analysis,” J. Comput. Phys. 169, 556593 (2001)
[Crossref]

Yabe, T.

Y. Ogata, T. Yabe, and K. Odagaki, “An accurate numerical scheme for Maxwell equation with CIP-method of characteristics,” Commun. Copmut. Phys. 1, 311–335 (2006)

T. Yabe, H. Mizoe, K. Takizawa, H. Morikia, H. N. Ima, and Y. Ogata, “Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme,” J. Comput. Phys. 194, 55–77 (2004)
[Crossref]

T. Yabe, F. Xiao, and T. Utsumi, “Constrained interpolation profile method for multiphase analysis,” J. Comput. Phys. 169, 556593 (2001)
[Crossref]

T. Yabe and P. Y. Wang, “Unified numerical procedure for compressible and incompressible fluid,” J. Phys. Soc. Jpn. 60, 2105–2108 (1991)
[Crossref]

T. Yabe and T. Aoki, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver,” Comput. Phys. Commun. 66, 219–232 (1991)
[Crossref]

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, and F. Ikeda, “A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers,” Comput. Phys. Commun. 66, 233–242 (1991)
[Crossref]

T. Yabe and E. Takei, “A new higher-order Godunov method for general hyperbolic equations,” J. Phys. Soc. Jpn. 57, 2598–2601 (1988)
[Crossref]

H. Takewaki and T. Yabe, “The cubic-interpolated pseudo particle (CIP) method: application to nonlinear and multi-dimensional hyperbolic equations,” J. Comput. Phys. 70, 355–372 (1987)
[Crossref]

H. Takewaki, A. Nishiguchi, and T. Yabe, “The cubic-interpolated pseudo-particle (CIP) method for solving hyperbolic-type equations,” J. Comput. Phys. 61, 261–268 (1985)
[Crossref]

Yatagai, T.

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Proposal of novel model for photoinduced mass transport and numerical analysis by electromagnetic-induced particle transport method,” Jpn. J. Appl. Phys. 45, 465–469 (2006)
[Crossref]

D. Barada, T. Fukuda, M. Itoh, and T. Yatagai, “Numerical analysis of photoinduced surface relief grating formation by particle method,” Opt. Rev. 12, 271–273 (2005)
[Crossref]

D. Barada, M. Itoh, and T. Yatagai, “Computer simulation of photoinduced mass transport on azobenzene polymer films by particle method,” J. Appl. Phys. 96, 4204–4210 (2004)
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat.,  14, 302–307 (1966)
[Crossref]

Appl. Phys. Lett. (3)

P. Rochon, E. Batalla, and A. Natansohn, “Optically induced surface gratings on azoaromatic polymer films,” Appl. Phys. Lett. 66, 136–138 (1995)
[Crossref]

D. Y. Kim, S. K. Tripathy, L. Li, and J. Kumar, “Laser-induced holographic surface relief gratings on nonlinear optical polymer films,” Appl. Phys. Lett. 66, 1166–1168 (1995)
[Crossref]

J. Kumar, L. Li, X. L. Jiang, D. Y. Kim, T. S. Lee, and S. Tripathy, “Gradient force: the mechanism for surface relief grating formation in azobenzene functionalized polymers,” Appl. Phys. Lett. 72, 2096–2098 (1998)
[Crossref]

Commun. Copmut. Phys. (1)

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Supplementary Material (4)

» Media 1: GIF (128 KB)     
» Media 2: GIF (631 KB)     
» Media 3: GIF (241 KB)     
» Media 4: GIF (690 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of the numerical model for reflection. Here, the position in optical length ξi is equal to xi . The boundary between two media with different refractive indices is placed at x = xi + Δl. The solid, dashed and dotted lines are ψ +x (t - Δt), ψ +x (t) and R i+1 ψ +x , respectively. The value R +x ψ +x is obtained by multiplying the reflection of ψ +x (t) in which the axis of reflection is xi + Δl with reflectance R i+1.

Fig. 2.
Fig. 2.

Comparison of Gaussian pulse propagation. The solid red and dashed green lines are the pulse shapes obtained by the CIP and FDTD methods, respectively. (a), (b), (c) and (d) show the y-components of the electric field after 0 s, 10 s, 30 s and 50 s, respectively. (e) shows the result after 50 s in the range from 8 μm to 10 μm. [Media 1]

Fig. 3.
Fig. 3.

Time difference of Gaussian pulse propagation by various boundary position. The red, green, blue, magenta and cyan lines are the profile of the Gaussan pulse when the shift amounts of the boundary position are 0 nm, 10 nm, 20 nm, 50 nm and 100 nm, respectively.

Fig. 4.
Fig. 4.

Schematic diagram of the two-dimensional light propagation case. A dielectric disc with two-micron radius is placed at the center of the calculation area. A Gaussian pulse originates from the bottom of the figure and the angle between the propagation direction and the y-axis is 30°. The amplitude of the electromagnetic field is constant along the direction perpendicular to the propagation direction. The values of the radiation layer placed at the edge of the calculation area are determined by the electromagnetic field from the Gaussian pulse propagating through the medium with n = 1.

Fig. 5.
Fig. 5.

Electric field distribution obtained by the numerical result of the propagation of the Gaussian pulse with TM polarization after 20 fs. (a) and (b) are the results obtained by the CIP and FDTD methods, respectively. [Media 2]

Fig. 6.
Fig. 6.

Magnetic field distribution obtained by the numerical result of the propagation of the Gaussian pulse with TE polarization after 20 fs. (a) and (b) are the results obtained by the CIP and FDTD methods, respectively. [Media 3]

Fig. 7.
Fig. 7.

Result of optical field and force calculation. (a) and (b) are results after 8 and 12 fs, respectively. Dotted circle shows dielectric disc and arrows are the directions of optical force. The length of the arrows is the strength of the optical force. [Media 4]

Fig. 8.
Fig. 8.

Result of optical field and force calculation. (a) and (b) are results after 20 and 30 fs, respectively.

Fig. 9.
Fig. 9.

Result of optical field and force calculation after 40 fs. (a) and (b) are the results obtained by the CIP and FDTD methods, respectively. The optical force calculation is performed by only CIP method.

Equations (61)

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× E = μ 0 H t ,
× H = ε E t ,
ε = n ε 0 ,
μ 0 H t = c × ( ε E ),
ε E t = c × ( μ 0 H ),
μ 0 H z t = c ε E y x ,
ε E y t = c μ 0 H z x .
ψ + x t + c ψ + x x = 0 ,
ψ x t c ψ x x = 0 ,
ψ + x = μ 0 H z + ε E y ,
ψ x = μ 0 H z ε E y , .
d x d ξ = 1 n .
ψ + x t + c 0 ψ + x ξ = 0 ,
ψ x t c 0 ψ x ξ = 0 ,
ψ + x′ / n t + c 0 ψ + x′ / n ξ = 0 ,
ψ x′ / n t c 0 ψ x′ / n ξ = 0 ,
ψ + x′ = ψ + x x ,
ψ x′ = ψ x x .
ψ ± x t ξ i ψ ± x ( t Δt , ξ i c 0 Δt ) Δt = 0 ,
ψ ± x ( t , ξ i ) = ψ ± x ( t Δt , ξ i c 0 Δt ) ,
Ψ i ± x ( ξ ) = a i , 3 ± x ( ξ ξ i ) 3 + a i , 2 ± x ( ξ ξ i ) 2 + a i , 1 ± x ( ξ ξ i ) + a i , 0 ± x .
a i , 0 ± x = ψ i ± x .
a i , 1 ± x = ψ i ± x′ ,
a i , 2 ± x = 3 ( ψ i 1 ± x ψ i ± x ) ( Δ ξ i ± x ) 2 2 ψ i ± x′ + ψ i 1 ± x′ Δ ξ i ± x ,
a i , 3 ± x = ψ i ± x′ ψ i 1 ± x′ ( Δ ξ i ± x ) 2 2 ( ψ i 1 ± x ψ i ± x ) ( Δ ξ i ± x ) 3 ,
Δ ξ i + x = ξ i 1 ξ i ,
Δ ξ i x = ξ i + 1 ξ i .
H z + x = ψ + x 2 μ 0 ,
H y + x = ψ + x 2 ε .
E y + x ( t , ξ i ) E y + x ( t Δt , ξ i c 0 Δ t ) = ε ( ξ i ) ε ( ξ i c 0 Δ t ) = n ( ξ i ) n ( ξ i c 0 Δ t ) .
ψ + x t Δ t ξ i c 0 Δ t = μ 0 H z + x t Δ t ξ i c 0 Δ t + ε ( ξ i ) E y + x t Δ t ξ i c 0 Δ t .
ψ + x t ξ i = T i + x ψ + x t Δ t ξ i c 0 Δ t ,
T i + x = 2 n ( ξ i ) n ( ξ i ) + n ( ξ i c 0 Δ t ) .
ψ x t Δ t ξ i c 0 Δ t = μ 0 H z + x t Δ t ξ i c 0 Δ t + ε ( ξ i ) E y + x t Δ t ξ i c 0 Δ t ,
ψ x t ξ = R i + x ψ + x t Δ t ξ i c 0 Δ t , ,
R i + x = n ( ξ i ) n ( ξ i c 0 Δ t ) n ( ξ i ) + n ( ξ i c 0 Δ t ) .
ξ ( x i Δ x ) = { x i + n ( x i ) Δ l n ( x i + Δ x ) ( Δ x + Δ l ) Δ l < 0 x i n ( x i ) Δ x Δ l 0 ,
ξ ( x i + Δ x ) = { x i + n ( x i ) Δ l + n ( x i + Δ x ) ( Δ x Δ l ) Δ l 0 x i + n ( x i ) Δ x Δ l < 0 .
ψ i + x ( t ) = T i + x ψ + x t Δ t ξ i c 0 Δ t + R i x ψ x t Δ t ξ i + c 0 Δ t 2 Δ l ,
ψ i x ( t ) = T i x ψ x t Δ t ξ i + c 0 Δ t + R i + x ψ + x t Δ t ξ i c 0 Δ t + 2 Δ l ,
ψ i + x′ ( t ) = T i + x ψ + x t Δ t ξ i c 0 Δ t R i x ψ x t Δ t ξ i + c 0 Δ t 2 Δ l ,
ψ i x′ ( t ) = T i x ψ x t Δ t ξ i + c 0 Δ t R i + x ψ + x t Δ t ξ i c 0 Δ t + 2 Δ l ,
T i x = 2 n ( ξ i ) n ( ξ i ) + n ( ξ + c 0 Δ t ) ,
R i x = n ( ξ i ) n ( ξ i + c 0 Δ t ) n ( ξ i ) + n ( ξ i + c 0 Δ t ) .
F = P E + μ 0 P t × H ,
P E x = ε 0 χ [ E x E x x + E y E x y + E z E x z ] .
E x x y x = E x x + Δ x y E x x Δ x y 2 Δ x .
P t = χ × H .
ε 0 E y x t = μ 0 H z x t
= ε 0 exp [ ( t t 0 x / c 0 ) 2 2 w t 2 ] ,
ε 0 E y x t x = μ 0 H z x t x
= ε 0 c 0 ( t t 0 ) x c 0 2 w t 2 exp [ ( t t 0 x / c 0 ) 2 2 w t 2 ] .
ψ + x t + c ψ + x x = 0 ,
ψ x t c ψ x x = 0 ,
ψ + x = [ μ 0 H z + ε E y μ 0 H y ε E z ] ,
ψ x = [ μ 0 H z ε E y μ 0 H y + ε E z ] .
ψ + y t + c ψ + y x = 0 ,
ψ y t c ψ y x = 0 ,
ψ + y = [ μ 0 H z ε E x μ 0 H x + ε E z ] ,
ψ y = [ μ 0 H z + ε E x μ 0 H x ε E z ] .
G x y t = { exp [ ( t t 0 ( s ̂ · r ) / c 0 ) 2 2 w t 2 ] t s ̂ r / c 0 0 t < s ̂ r / c 0 ,

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