Abstract

Off-axis polarized monopole illumination is applied to a hyper-numerical-aperture (NA) (NA>1) microscopic system. Illumination artifacts due to vector effects are observed, which are asymmetric and depend on illumination conditions. A model based on rigorous coupled wave theory is used to simulate image profiles for dielectric, semiconductor, and metal gratings with different monopole locations and polarization states. A solid immersion lens microscope is used to image different types of samples including MoSi photomask, patterned silicon wafer, and chrome photomask. The experimental images are in good agreement with simulation results.

© 2010 Optical Society of America

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  1. J. Zhang, M. Lang, T. D. Milster, and T. Chen, “Fabrication and testing of a GaP SIL with NA=2.64,” Proc. SPIE 6620, 66201Z (2007).
    [CrossRef]
  2. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
    [CrossRef]
  3. B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
    [CrossRef]
  4. M. Lang, E. Aspnes, and T. D. Milster, “Geometrical analysis of third-order aberrations for a solid immersion lens,” Opt. Express 16, 20008–20028 (2008).
    [CrossRef] [PubMed]
  5. Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
    [CrossRef]
  6. T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32, 124–126 (2007).
    [CrossRef]
  7. S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High-resolution subsurface microscopy technique,” Appl. Phys. Lett. 78, 4071–4073 (2001).
    [CrossRef]
  8. S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).
  9. E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London, Ser. A 253, 349–357 (1957).
  10. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2094 (1986).
    [CrossRef]
  11. D. G. Flagello, T. D. Milster, and A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A Opt. 13, 53–64 (1996).
    [CrossRef]
  12. J. S. Jo, T. D. Milster, and J. K. Erwin, “Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope,” Opt. Eng. (Bellingham) 41, 1866–1875 (2002).
    [CrossRef]
  13. M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
    [CrossRef]
  14. K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
    [CrossRef]
  15. P. R. T. Munro and P. Török, “Calculation of the image of an arbitrary vectorial electromagnetic field,” Opt. Express 15, 9293–9307 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. S. H. Yang, T. D. Milster, J. R. Park, and J. Zhang, “High-numerical-aperture image simulation using Babinet’s principle,” J. Opt. Soc. Am. A 27, 1012–1023 (2010).
    [CrossRef]
  18. H. H. Hopkins, “On the diffraction theory of optical imagines,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
    [CrossRef]
  19. S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
    [CrossRef]

2010 (2)

S. H. Yang, T. D. Milster, J. R. Park, and J. Zhang, “High-numerical-aperture image simulation using Babinet’s principle,” J. Opt. Soc. Am. A 27, 1012–1023 (2010).
[CrossRef]

S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
[CrossRef]

2008 (2)

2007 (3)

2002 (2)

J. S. Jo, T. D. Milster, and J. K. Erwin, “Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope,” Opt. Eng. (Bellingham) 41, 1866–1875 (2002).
[CrossRef]

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

2001 (2)

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High-resolution subsurface microscopy technique,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

1999 (1)

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
[CrossRef]

1996 (1)

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

1994 (1)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

1986 (1)

1957 (1)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London, Ser. A 253, 349–357 (1957).

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical imagines,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
[CrossRef]

Aspnes, E.

Chen, T.

S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
[CrossRef]

T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32, 124–126 (2007).
[CrossRef]

J. Zhang, M. Lang, T. D. Milster, and T. Chen, “Fabrication and testing of a GaP SIL with NA=2.64,” Proc. SPIE 6620, 66201Z (2007).
[CrossRef]

Erwin, J. K.

J. S. Jo, T. D. Milster, and J. K. Erwin, “Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope,” Opt. Eng. (Bellingham) 41, 1866–1875 (2002).
[CrossRef]

Feke, G. D.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
[CrossRef]

Flagello, D. G.

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

Furuki, M.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Ghislain, L. P.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
[CrossRef]

Goldberg, B. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High-resolution subsurface microscopy technique,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Grober, R. D.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
[CrossRef]

Hansen, D.

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical imagines,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
[CrossRef]

Ippolito, S. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High-resolution subsurface microscopy technique,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Ishimoto, T.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Jo, J. S.

J. S. Jo, T. D. Milster, and J. K. Erwin, “Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope,” Opt. Eng. (Bellingham) 41, 1866–1875 (2002).
[CrossRef]

Kim, Y. S.

S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).

Kino, G. S.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Kondo, T.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Kriezis, Em. E.

Lang, M.

M. Lang, E. Aspnes, and T. D. Milster, “Geometrical analysis of third-order aberrations for a solid immersion lens,” Opt. Express 16, 20008–20028 (2008).
[CrossRef] [PubMed]

J. Zhang, M. Lang, T. D. Milster, and T. Chen, “Fabrication and testing of a GaP SIL with NA=2.64,” Proc. SPIE 6620, 66201Z (2007).
[CrossRef]

Mamin, H. J.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Mansuripur, M.

Masuhara, S.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Milster, T. D.

S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
[CrossRef]

S. H. Yang, T. D. Milster, J. R. Park, and J. Zhang, “High-numerical-aperture image simulation using Babinet’s principle,” J. Opt. Soc. Am. A 27, 1012–1023 (2010).
[CrossRef]

M. Lang, E. Aspnes, and T. D. Milster, “Geometrical analysis of third-order aberrations for a solid immersion lens,” Opt. Express 16, 20008–20028 (2008).
[CrossRef] [PubMed]

T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32, 124–126 (2007).
[CrossRef]

J. Zhang, M. Lang, T. D. Milster, and T. Chen, “Fabrication and testing of a GaP SIL with NA=2.64,” Proc. SPIE 6620, 66201Z (2007).
[CrossRef]

J. S. Jo, T. D. Milster, and J. K. Erwin, “Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope,” Opt. Eng. (Bellingham) 41, 1866–1875 (2002).
[CrossRef]

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

S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).

Munro, P. R. T.

Nakaoki, A.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Park, J. R.

S. H. Yang, T. D. Milster, J. R. Park, and J. Zhang, “High-numerical-aperture image simulation using Babinet’s principle,” J. Opt. Soc. Am. A 27, 1012–1023 (2010).
[CrossRef]

S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).

Rosenbluth, A. E.

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

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Saito, K.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Studenmund, W. R.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Terris, B. D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Török, P.

Totzeck, M.

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
[CrossRef]

Unlu, M. S.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High-resolution subsurface microscopy technique,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London, Ser. A 253, 349–357 (1957).

Wu, Q.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
[CrossRef]

Yamamoto, M.

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Yang, S. H.

S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
[CrossRef]

S. H. Yang, T. D. Milster, J. R. Park, and J. Zhang, “High-numerical-aperture image simulation using Babinet’s principle,” J. Opt. Soc. Am. A 27, 1012–1023 (2010).
[CrossRef]

T. Chen, T. D. Milster, S. H. Yang, and D. Hansen, “Evanescent imaging with induced polarization by using a solid immersion lens,” Opt. Lett. 32, 124–126 (2007).
[CrossRef]

S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).

Zhang, J.

S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
[CrossRef]

S. H. Yang, T. D. Milster, J. R. Park, and J. Zhang, “High-numerical-aperture image simulation using Babinet’s principle,” J. Opt. Soc. Am. A 27, 1012–1023 (2010).
[CrossRef]

J. Zhang, M. Lang, T. D. Milster, and T. Chen, “Fabrication and testing of a GaP SIL with NA=2.64,” Proc. SPIE 6620, 66201Z (2007).
[CrossRef]

S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).

Appl. Phys. Lett. (4)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388–390 (1994).
[CrossRef]

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75, 4064–4066 (1999).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High-resolution subsurface microscopy technique,” Appl. Phys. Lett. 78, 4071–4073 (2001).
[CrossRef]

J. Mod. Opt. (1)

S. H. Yang, T. D. Milster, J. Zhang, and T. Chen, “Characteristics of evanescent polarization imaging,” J. Mod. Opt. 57, 783–797 (2010).
[CrossRef]

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

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

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

Jpn. J. Appl. Phys., Part 1 (1)

K. Saito, T. Ishimoto, T. Kondo, A. Nakaoki, S. Masuhara, M. Furuki, and M. Yamamoto, “Readout method for read only memory signal and air gap control signal in a near field optical disc system,” Jpn. J. Appl. Phys., Part 1 41, 1898–1902 (2002).
[CrossRef]

Opt. Eng. (Bellingham) (1)

J. S. Jo, T. D. Milster, and J. K. Erwin, “Phase and amplitude apodization induced by focusing through an evanescent gap in a solid immersion lens microscope,” Opt. Eng. (Bellingham) 41, 1866–1875 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttgart) (1)

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
[CrossRef]

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

H. H. Hopkins, “On the diffraction theory of optical imagines,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London, Ser. A 253, 349–357 (1957).

Proc. SPIE (1)

J. Zhang, M. Lang, T. D. Milster, and T. Chen, “Fabrication and testing of a GaP SIL with NA=2.64,” Proc. SPIE 6620, 66201Z (2007).
[CrossRef]

Other (1)

S. H. Yang, J. Zhang, Y. S. Kim, T. D. Milster, and J. R. Park, “Microscope system for blu-ray disk samples” (submitted to Appl. Opt.).

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Figures (19)

Fig. 1
Fig. 1

Sketch of a SIL microscope. An incoherent tungsten source is used as the source. The color filter and linear polarizer are used to select the wavelength and polarization state of the illumination. An iris is placed in the aperture stop to set the partial coherence and location of the monopole. The illumination light focuses through the objective lens and SIL on the sample surface. Light is reflected back to the microscope to form an image on the CCD camera. A second linear polarizer is used to choose the native (uncrossed polarization) or induced (crossed polarization) image.

Fig. 2
Fig. 2

Example of off-axis monopole illumination in the pupil plane. Considering only the diameter of the monopole, the partial coherence is σ = 0.167 . The center of the monopole is located at α c = 0.67 , β c = 0 . n SIL is the refractive index of the SIL material. The white circle shows the illumination boundary in the pupil plane with σ = 1 .

Fig. 3
Fig. 3

Optical path for imaging of the SIL microscope. A vector version of Abbe’s theory of imaging is used to consider the partial coherence. For periodic structures, RCWT is used to simulate the vector diffraction from the sample. An illumination mask is applied in the stop so that an off-axis polarized monopole illuminates the object.

Fig. 4
Fig. 4

Angle definition in RCWT. Grating vector is in the x direction. θ is the angle between the incident light and the z axis. ϕ is the rotation angle about the z axis. ψ inc is the polarization angle for the incident light. ψ inc = 0 ° for p-polarized light and ψ inc = 90 ° for s-polarized light.

Fig. 5
Fig. 5

Four types of polarized off-axis monopole illumination sources are used in the simulation with different center locations and polarizations. (a) Case 1: center ( α c , β c ) = ( 0.67 , 0 ) with s-polarization, (b) Case 2: center ( α c , β c ) = ( 0.67 , 0 ) with p-polarization, (c) Case 3: center ( α c , β c ) = ( 0 , 0.67 ) with s-polarization, (d) Case 4: center ( α c , β c ) = ( 0 , 0.67 ) with p-polarization.

Fig. 6
Fig. 6

RCWT simulation of native and induced image profiles of MoSi gratings on a FS substrate with monopole center at ( α c , β c ) = ( 0.67 , 0 ) and different polarizations. (Cases 1 and 2) (a) ( α c , β c ) = ( 0.67 , 0 ) with s-polarization, (b) ( α c , β c ) = ( 0.67 , 0 ) with p-polarization. [ n FS = 1.546 , N MoSi = 2.229 + 0.080 i , grating period = 5 μ m , duty cycle = 10 % , MoSi width = 500   nm , grating height = 68   nm , σ = 0.167 , and NA = 1.48 at λ = 550   nm . For all k ̂ , | A ill ( k ̂ ) | = 1 .]

Fig. 7
Fig. 7

RCWT simulation of native and induced image profiles of MoSi gratings on a FS substrate with monopole center at ( α c , β c ) = ( 0 , 0.67 ) and different polarizations. (Cases 3 and 4) (a) ( α c , β c ) = ( 0 , 0.67 ) with s-polarization, (b) ( α c , β c ) = ( 0 , 0.67 ) with p-polarization. [ n FS = 1.546 , N MoSi = 2.229 + 0.080 i , grating period = 5 μ m , duty cycle = 10 % , MoSi width = 500   nm , grating height = 68   nm , σ = 0.167 , and NA = 1.48 at λ = 550   nm . For all k ̂ , | A ill ( k ̂ ) | = 1 .]

Fig. 8
Fig. 8

RCWT simulation of native and induced image profiles of Si gratings on a Si substrate with monopole center at ( α c , β c ) = ( 0.67 , 0 ) and different polarizations. (Cases 1 and 2) (a) ( α c , β c ) = ( 0.67 , 0 ) with s-polarization, (b) ( α c , β c ) = ( 0.67 , 0 ) with p-polarization. [ N Si = 4.127 + 0.0137 i , grating period = 5 μ m , duty cycle = 20 % , Si width = 1 μ m , grating height = 170   nm , σ = 0.167 , and NA = 1.48 at λ = 550   nm . For all k ̂ , | A ill ( k ̂ ) | = 1 .]

Fig. 9
Fig. 9

RCWT simulation of native and induced image profiles of Si gratings on a Si substrate with monopole center at ( α c , β c ) = ( 0 , 0.67 ) and different polarizations. (Cases 3 and 4) (a) ( α c , β c ) = ( 0 , 0.67 ) with s-polarization, (b) ( α c , β c ) = ( 0 , 0.67 ) with p-polarization. [ N Si = 4.127 + 0.0137 i , grating period = 5 μ m , duty cycle = 20 % , Si width = 1 μ m , grating height = 170   nm , σ = 0.167 , and NA = 1.48 at λ = 550   nm . For all k ̂ , | A ill ( k ̂ ) | = 1 .]

Fig. 10
Fig. 10

RCWT simulation of native and induced image profiles of chrome gratings on a FS substrate with monopole center at ( α c , β c ) = ( 0.67 , 0 ) and different polarizations. (Cases 1 and 2) (a) ( α c , β c ) = ( 0.67 , 0 ) with s-polarization, (b) ( α c , β c ) = ( 0.67 , 0 ) with p-polarization. [ n FS = 1.546 , N CR = 2.314 + 3.136 i , grating period = 5 μ m , duty cycle = 40 % , Cr width = 2 μ m , grating height = 100   nm , σ = 0.167 , and NA = 1.48 at λ = 550   nm . For all k ̂ , | A ill ( k ̂ ) | = 1 .]

Fig. 11
Fig. 11

RCWT simulation of native and induced image profiles of chrome gratings on a FS substrate with monopole center at ( α c , β c ) = ( 0 , 0.67 ) and different polarizations. (Cases 3 and 4) (a) ( α c , β c ) = ( 0 , 0.67 ) with s-polarization, (b) ( α c , β c ) = ( 0 , 0.67 ) with p-polarization. [ N CR = 2.314 + 3.136 i , grating period = 5 μ m , duty cycle = 40 % , Cr width = 2 μ m , grating height = 100   nm , σ = 0.167 , and NA = 1.48 at λ = 550   nm . For all k ̂ , | A ill ( k ̂ ) | = 1 .]

Fig. 12
Fig. 12

Electric field irradiance distribution from a FDTD model of a rectangular ( 500   nm × 900   nm × 100   nm ) Cr object in air illuminated with a plane wave at 42° in the x - z plane with s-polarization (y direction). The irradiance distribution shown here is for the y field component, which corresponds to native images in RCWT simulation results. An asymmetric intensity distribution is observed for the x profile under Case 1 illumination. A symmetric intensity distribution is observed for the y profile under Case 3 illumination. The phenomena observed in FDTD results match well with RCWT simulation results. White color indicates higher irradiance. The dashed box is the boundary of the Cr object.

Fig. 13
Fig. 13

Experimental native images and line profiles for s- and p-polarized sources at ( α c , β c ) = ( 0.67 , 0 ) (Cases 1 and 2). (a) Native image with s-polarization, (b) line profile of native image with s-polarization, (c) native image with p-polarization, (d) line profile of native image with p-polarization. The sample is an isolated MoSi line, with a height of 68 nm and a width of 500 nm. The experimental results are in good agreement with the simulation results in Figs. 6a, 6b.

Fig. 14
Fig. 14

Experimental native images and line profiles for s- and p-polarized sources at ( α c , β c ) = ( 0 , 0.67 ) (Cases 3 and 4). (a) Native image with s-polarization, (b) line profile of native image with s-polarization, (c) native image with p-polarization, (d) line profile of native image with p-polarization. The sample is the isolated MoSi line, with a height 68 nm and a width of 500 nm. The experimental results are in good agreement with the simulation results in Figs. 7a, 7b.

Fig. 15
Fig. 15

Experimental native and induced polarization images for a patterned silicon wafer with source center at ( α c , β c ) = ( 0.67 , 0 ) , σ = 0.167 and different polarizations (Cases 1 and 2). (a) Native image with s-polarization, (b) induced image with s-polarization, (c) native image with p-polarization, (d) induced image with p-polarization.

Fig. 16
Fig. 16

Experimental native and induced polarization images for a patterned silicon wafer with source center at ( α c , β c ) = ( 0 , 0.67 ) , σ = 0.167 and different polarizations (Cases 3 and 4). (a) Native image with s-polarization, (b) induced image with s-polarization, (c) native image with p-polarization, (d) induced image with p-polarization.

Fig. 17
Fig. 17

Experimental native and induced polarization images for chrome patterns on a FS substrate with source center at ( α c , β c ) = ( 0.67 , 0 ) , σ = 0.167 and different polarizations (Cases 1 and 2). (a) Native image with s-polarization, (b) induced image with s-polarization, (c) native image with p-polarization, (d) induced image with p-polarization.

Fig. 18
Fig. 18

Experimental native and induced polarization images for chrome patterns on a FS substrate with source center at ( α c , β c ) = ( 0 , 0.67 ) , σ = 0.167 and different polarizations (Cases 3 and 4). (a) Native image with s-polarization, (b) induced image with s-polarization, (c) native image with p-polarization, (d) induced image with p-polarization.

Fig. 19
Fig. 19

Experimental native polarization images for MoSi isolated lines on a FS substrate in a DIC SIL microscope with different illumination conditions (Cases 1–4). (a) Native image with Case 1 illumination, (b) native image with Case 2 illumination, (c) native image with Case 3 illumination, (d) native image with Case 4 illumination. The MoSi isolated line has a height of 68 nm and a width of 500 nm.

Equations (3)

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A SRC ( k ̂ , ψ SRC ) = A SRC ( k ̂ ) [ cos   ψ SRC sin   ψ SRC ] ,
U ill ( r ) = A ill ( k ̂ ) exp ( i k r ) ,
A ill ( k ̂ ) = [ A s A p ] = 1 α 2 + β 2 [ β α α β ] A SRC ( k ̂ , ψ inc ) ,

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