Abstract

The discrete-dipole approximation is applied to vector diffraction analysis in a system with large-numerical-aperture (NA) optics and subwavelength targets. Distributions of light diffracted by subwavelength dielectric targets are calculated in a solid angle that corresponds to a NA of 0.9, and their dependence on incident polarization, target shape, and target size is studied. Electric field distributions inside the target are also shown. Basic features of the vector diffraction are clearly demonstrated. This technique facilitates understanding of the vectorial effects in systems that are expected to be applied in the future to optical data storage.

© 2001 Optical Society of America

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References

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  1. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  2. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  3. T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
    [CrossRef]
  4. K. Shimura, T. D. Milster, “Analysis of three-dimensional distributions of scattered light by the discrete dipole approximation,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 162–164.
  5. B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
    [CrossRef]
  6. B. T. Draine, P. J. Flatau, “The discrete dipole approximation for scattering and absorption of light by irregular particles,” http://www.astro.princeton.edu/~draine/DDSCAT.html .
  7. N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
    [CrossRef]
  8. M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
    [CrossRef]
  9. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).
    [CrossRef]
  10. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
    [CrossRef]
  11. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives: erratum”; “Certain computational aspects of vector diffraction problems: erratum,” J. Opt. Soc. Am. A 10, 382–383 (1993).
    [CrossRef]
  12. D. G. Flagello, T. D. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
    [CrossRef]

1999

N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
[CrossRef]

1998

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

1996

1994

1993

1989

1986

1973

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Comberg, U.

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

Draine, B. T.

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

Flagello, D. G.

Flatau, P. J.

Goodman, J.

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

Mansuripur, M.

Milster, T. D.

D. G. Flagello, T. D. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
[CrossRef]

K. Shimura, T. D. Milster, “Analysis of three-dimensional distributions of scattered light by the discrete dipole approximation,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 162–164.

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Piller, N. B.

N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Rosenbluth, A. E.

Shimura, K.

K. Shimura, T. D. Milster, “Analysis of three-dimensional distributions of scattered light by the discrete dipole approximation,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 162–164.

Taubenblatt, M. A.

Tran, T. K.

Wriedt, T.

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

Astrophys. J.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by non-spherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

B. T. Draine, J. Goodman, “Beyond Clausius–Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685–697 (1993).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

T. Wriedt, U. Comberg, “Comparison of computational scattering methods,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998).
[CrossRef]

Opt. Commun.

N. B. Piller, “Coupled-dipole approximation for high permittivity materials,” Opt. Commun. 160, 10–14 (1999).
[CrossRef]

Other

B. T. Draine, P. J. Flatau, “The discrete dipole approximation for scattering and absorption of light by irregular particles,” http://www.astro.princeton.edu/~draine/DDSCAT.html .

K. Shimura, T. D. Milster, “Analysis of three-dimensional distributions of scattered light by the discrete dipole approximation,” in Diffractive Optics and Micro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), pp. 162–164.

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Figures (13)

Fig. 1
Fig. 1

Layout of the target and the collection optics assumed in the calculations.

Fig. 2
Fig. 2

Distribution of light diffracted by a small dielectric disk: (a) irradiance distribution, (b) cross section of (a). The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 3
Fig. 3

Distribution of light diffracted by a large dielectric disk: (a) irradiance distribution, (b) cross section of (a). The diameter and the thickness of the disk are λ and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 4
Fig. 4

Distribution of light diffracted by a small dielectric square plate: (a) irradiance distribution, (b) cross section of (a). The length of a side and the thickness of the square are λ/2×λ/2 and λ/50, respectively. The refractive index of the plate is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 5
Fig. 5

Distribution of light diffracted by a small dielectric disk: (a) irradiance distribution, (b) cross section of (a). The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 64° (p polarization).

Fig. 6
Fig. 6

Distribution of light diffracted by a large dielectric disk: (a) irradiance distribution, (b) cross section of (a). The diameter and the thickness of the disk are λ and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 64° (p polarization).

Fig. 7
Fig. 7

Distribution of light diffracted by a small dielectric disk: (a) irradiance distribution, (b) cross section of (a). The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 64° (s polarization).

Fig. 8
Fig. 8

Distribution of light diffracted by a large dielectric disk: (a) irradiance distribution, (b) cross section of (a). The diameter and the thickness of the disk are λ and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 64° (s polarization).

Fig. 9
Fig. 9

Electric field distribution at a top surface of a small dielectric disk: (a) amplitude for x, y, and z components; (b) phase corresponding to (a). The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 10
Fig. 10

Electric field distribution at a top surface of a small dielectric square plate: (a) amplitude for x, y, and z components, (b) phase corresponding to (a). The size of a side and the thickness of the square are λ/2×λ/2 and λ/50, respectively. The refractive index of the plate is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 11
Fig. 11

Dependence of the error elocal|A×P-Einc|/|Einc| on the number of iterations for a small dielectric disk. The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 12
Fig. 12

Dependence of the error efar|Efar-Eref|2dαdβ/|Eref|2dαdβ on the number of iterations for a small dielectric disk. The distribution of the diffracted light calculated with P obtained by 13 iterations is used as Eref. The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Fig. 13
Fig. 13

Dependence of the error efar|Efar-Eref|2dαdβ/|Eref|2dαdβ on the spacing between dipoles d for a small dielectric disk. The distribution of the diffracted light calculated with P obtained with d=1.6 nm (λ/406) is used as Eref. The diameter and the thickness of the disk are λ/2 and λ/50, respectively. The refractive index of the disk is 2.15. The incident light is linearly polarized, and the incident angle is 0°.

Equations (10)

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Pj=αjEinc,j-kjAjkPk,
Einc, j=E0 exp(ik·rj-iωt),
Ajk=14π0 exp(ikrjk)rjkk2(rˆjkrˆjk-13)+ikrjk-1rjk2(3rˆjkrˆjk-13)(jk),
αjCM=3d30j-0j+20,
αjLDR=αjCM1+(αjCM/d3)[(b1+nj2b2+nj2b3S)(kd)2-(2/3)i(kd)3],S=j=13(aˆjeˆj2),
k=1NAjkPk=Einc,j,
elocal|A×P-Einc||Einc|5×10-5,
Efar(r)=14π0 k2 exp(ikr)r j=1Nexp(-ikrˆ·rj)×(rˆrˆ-13)Pj,
Ej=Pj/αj.
efar|Efar-Eref|2dαdβ|Eref|2dαdβ,

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