Abstract

Using vector diffraction theory and an exact method for computing reflection coefficients for multilayer structures, we analyze the effects of high-numerical-aperture focusing on the state of polarization in optical data storage systems. The focused incident beam is decomposed into a spectrum of plane waves, and the reflected beam is obtained by the superposition of these plane waves after they are independently reflected from the multilayer. Plots of polarization rotation angle and ellipticity for several disk structures are presented.

© 1991 Optical Society of America

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References

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  1. M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
    [CrossRef]
  2. E. Wolf, “Electromagnetic diffraction in optical systems: an integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
    [CrossRef]
  3. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
  4. A. Boivin, J. Dow, E. Wolf, “Energy flow in the neighborhood of focus,” J. Opt. Soc. Am. 57, 1171–1175 (1967).
    [CrossRef]
  5. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
    [CrossRef]
  6. J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formation and example,” J. Opt. Soc. Am. A 9, 1614–1626 (1990).
    [CrossRef]
  7. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  8. R. A. Chipman, “Polarization aberrations,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1987).
  9. A. Hardy, D. Treves, “Structure of the electromagnetic field near the focus of a stigmatic lens,” J. Opt. Soc. Am. 63, 85–90 (1973).
    [CrossRef]
  10. H. Kubota, S. Inoue, “Diffraction images in the polarizing microscope,” J. Opt. Soc. Am. 49, 191–198 (1959).
    [CrossRef] [PubMed]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
    [CrossRef]
  13. P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
    [CrossRef]

1990 (2)

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formation and example,” J. Opt. Soc. Am. A 9, 1614–1626 (1990).
[CrossRef]

1989 (2)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
[CrossRef]

1986 (1)

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

1982 (1)

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

1973 (1)

1967 (1)

1959 (3)

E. Wolf, “Electromagnetic diffraction in optical systems: an integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

H. Kubota, S. Inoue, “Diffraction images in the polarizing microscope,” J. Opt. Soc. Am. 49, 191–198 (1959).
[CrossRef] [PubMed]

Boivin, A.

Chase, S.

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

Chipman, R. A.

J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formation and example,” J. Opt. Soc. Am. A 9, 1614–1626 (1990).
[CrossRef]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

R. A. Chipman, “Polarization aberrations,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1987).

Connell, G. A. N.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

Dow, J.

Goodman, J. W.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hardy, A.

Inoue, S.

Kubota, H.

Mansuripur, M.

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
[CrossRef]

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

McGuire, J. P.

J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formation and example,” J. Opt. Soc. Am. A 9, 1614–1626 (1990).
[CrossRef]

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Rosenvold, R.

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

Ruane, M.

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

Treves, D.

Wolf, E.

A. Boivin, J. Dow, E. Wolf, “Energy flow in the neighborhood of focus,” J. Opt. Soc. Am. 57, 1171–1175 (1967).
[CrossRef]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems: an integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

Wolniansky, P.

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

J. Appl. Phys. (3)

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6475 (1990).
[CrossRef]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

P. Wolniansky, S. Chase, R. Rosenvold, M. Ruane, M. Mansuripur, “Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1−x, alloys,” J. Appl. Phys. 60, 346–351 (1986).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
[CrossRef]

J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formation and example,” J. Opt. Soc. Am. A 9, 1614–1626 (1990).
[CrossRef]

Opt. Eng. (1)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Proc. R. Soc. London Ser. A (2)

E. Wolf, “Electromagnetic diffraction in optical systems: an integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[CrossRef]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. A. Chipman, “Polarization aberrations,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1987).

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Figures (12)

Fig. 1
Fig. 1

Collimated, linearly polarized beam of light is brought to focus by a lens. E is the electric field vector, which shows the direction of linear polarization for the various rays.

Fig. 2
Fig. 2

Schematic diagram showing the objective lens and the optical data storage medium in an optical disk system. The incident beam at the objective is collimated and linearly polarized along the X direction. The substrate in configuration (a) is the medium of incidence, while in (b) the beam is incident from the air side. The lens is corrected for all aberrations, including those due to the thick substrate in configuration (a).

Fig. 3
Fig. 3

Plots of intensity in the focal plane of the lens for the components of polarization along the X, Y, and Z axes. Also shown are the contour plots of intensity in each case. The maximum value of Ix is 0.736, while the maximum values of Iy and Iz are 0.166E-3 and 0.025, respectively.

Fig. 4
Fig. 4

Plots of reflected intensity in the exit pupil of the objective for the three components of polarization. The disk is assumed to be a perfect reflector. Maximum values of Ix, Iy, and Iz are 0.36E-7, 0.58E-14, and 0.29E-13, respectively.

Fig. 5
Fig. 5

Reflected intensity and polarization distributions in the exit pupil of the objective. The disk is an aluminum reflector with (n, k) = (2.75, 8.31). (a) Plot of intensity for the X component of polarization; Ixmax = 0.31E-7. (b) Plot of intensity for the Y component of polarization; Iymax = 0.25E-10. (c) Contour plot of Iy. (d) Polarization rotation relative to X; θmin = −0.54°, θmax = +0.54°. (e) Polarization ellipticity; min = −1.71°, max = +1.71°.

Fig. 6
Fig. 6

Distribution of reflected intensity in the exit pupil of the objective. The disk consists of a glass substrate (n0 = 1.53) coated with a dielectric layer (n1 = 2, d1 = 207.5 nm), and the beam is incident from the substrate side. (a) Plot of intensity for the X component of polarization; IXmax = 0.22E-8. (b) Plot of intensity for the Y component of polarization; Iymax = 0.47E-10.

Fig. 7
Fig. 7

Reflected intensity distribution in the plane of the disk (i.e., at the focal plane of the lens) for the Y component of polarization. The disk consists of a glass substrate (n0 = 1.5), coated with 83 nm of magnetic material and capped with 103.75 nm of a dielectric layer (n = 2). The incidence configuration is that of Fig. 2(b). The maximum value of Iy is 0.95E-4, and the total power contained in the Y component of polarization is 0.43E-3.

Fig. 8
Fig. 8

Distributions of the reflected intensity and polarization in the exit pupil of the objective lens for the disk structure described in the caption to Fig.7. (a) Plot of intensity for the X component of polarization; Ixmax = 0.88E-8. (b) Plot of intensity for the Y component of polarization; Iymax = 0.58E-10. (c) Contour plot of Iy. (d) Polarization rotation relative to X; θmin = −0.10°, θmax = +1.64°. (e) Polarization ellipticity; min = −4.91°, max = +5.16°.

Fig. 9
Fig. 9

Reflected intensity distribution in the plane of the disk (i.e., at the focal plane of the lens) for the Y component of polarization. The disk is an air-incidence quadrilayer structure consisting of a glass substrate, 332 nm of aluminum, 143 nm of a dielectric material (n = 1.449), 20 nm of magnetic material, and another 143 nm of dielectric (n = 1.449). The maximum value of Iy is 0.76E-4, and the total power contained in the Y component of polarization is 0.12E-3.

Fig. 10
Fig. 10

Distributions of the reflected intensity and polarization in the exit pupil of the objective lens for the disk structure described in the caption to Fig. 9. (a) Plot of intensity for the X component of polarization; Ixmax = 0.20E-8. (b) Plot of intensity for the Y component of polarization; Iymax = 0.64E-11. (c) Contour plot of Iy. (d) Polarization rotation relative to X; θmax = +3.51°. (e) Polarization ellipticity; max = +2.49°.

Fig. 11
Fig. 11

Distributions of the reflected intensity and polarization in the exit pupil of the objective lens for an air-incidence quadrilayer consisting of an aluminum coated glass substrate, 207.5 nm of SiO2, 20.75 nm of magnetic material, and another 207.5nm of SiO2. The results presented here were obtained when the off-diagonal element xy of the dielectric tensor of the magneto-optic layer was set to zero. (a) Plot of intensity for the X component of polarization; Ixmax = 0.95E-8. (b) Plot of intensity for the Y component of polarization; Iymax = 0.11E-9. (c) Contour plot of Iy. (d) Polarization rotation relative to X; θmin = −2.75°, θmax = +2.75°. (e) Polarization ellipticity; min = −7.62°, max = +7.62°.

Fig. 12
Fig. 12

Contour plots of Iy for the quadrilayer structure described in the caption to Fig. 11, with the off-diagonal elements of the dielectric tensor now restored: (a) Magnetization up, (b) magnetization down.

Tables (1)

Tables Icon

Table I Calculated Values of Reflectivity (R) for a Dielectric Layer of Refractive Index n1 = 2.00 and Thickness d1, Coated upon a Glass Substrate of Refractive Index n0 = 1.53

Equations (2)

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R = | 1 - n - i k 1 + n + i k | 2 = 0.868.
S 1 - S 2 S 1 + S 2 = 2 | r y r x | cos ( ϕ y - ϕ x ) = 0.024.

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