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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  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 and 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 dyefunctionalized 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. Onedimensional 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 dyefunctionalized 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 and 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. Onedimensional 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. Onedimensional 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 dyefunctionalized polymers," J. Chem. Phys. 109,1505-1516 (1998)
[CrossRef]

Batalla, E.

P. Rochon and 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]

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 and 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 dyefunctionalized 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 and 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 dyefunctionalized polymers," J. Chem. Phys. 109,1505-1516 (1998)
[CrossRef]

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, 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]

T. Yabe and T. Aoki, "A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. Onedimensional solver," Comput. Phys. Commun. 66,219-232 (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 and 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)

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)

Comput. Phys. Commun. (2)

T. Yabe and T. Aoki, "A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. Onedimensional 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]

IEEE Trans. Antennas Propagat. (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]

IEEE Trans. Electromagn. Compat. (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]

J. Appl. Phys. (1)

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]

J. Chem. Phys. (1)

C. J. Barrett, P. L. Rochon and A. L. Natansohn, "Model of laser-driven mass transport in thin films of dyefunctionalized polymers," J. Chem. Phys. 109,1505-1516 (1998)
[CrossRef]

J. Comput. Phys. (5)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114,185-200 (1994)
[CrossRef]

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

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]

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]

J. Phys. Soc. Jpn. (2)

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

T. Yabe and P. Y. Wang, "Unified numerical procedure for compressible and incompressible fluid, " J. Phys. Soc. Jpn. 60,2105-2108 (1991)
[CrossRef]

Jpn. J. Appl. Phys. (1)

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]

Opt. Mater. (1)

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

Opt. Rev. (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]

Phys. Rev. Lett. (1)

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]

Other (1)

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

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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