Abstract

A single scanning nano-slit is used to study aerial image characteristics. Finite-difference time-domain simulations reveal that, in the far field of such a slit, the detected image contrast is very high over a large spatial frequency range regardless of the polarization direction. In the near field, the TM polarization shows a decrease in contrast at larger spatial frequencies. Experiments verify this characteristic using a 125nm wide slit on an aluminum mask at a wavelength of 658nm. Unlike the light transmission characteristics of a nano-slit, which are greatly influenced by slit width and metal mask thickness, it is shown that image contrast measurement is almost insensitive to small changes in these parameters. It is found that defects on the metal mask play an important role in accurate analysis of the system.

© 2010 Optical Society of America

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References

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  1. http://www.photon-inc.com/support/library/pdf/nanoscans.pdf
  2. http://cvimellesgriot.com/Products/Slits-and-Pinholes-fieldinterchangeable.aspx
  3. T. A. Brunner and R. R. Allen, “In situ measurement of an image during lithographic exposure,” IEEE Electron Device Lett. 6, 329–331 (1985).
    [CrossRef]
  4. T. E. Adams, “Application of latent image metrology in microlithography,” Proc. SPIE 1464, 294–312 (1991).
    [CrossRef]
  5. C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).
  6. T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
    [CrossRef]
  7. J. Xue, K. Moen, and C. J. Spanos, “Integrated aerial image sensor: design, modeling, and assembly,” J. Vac. Sci. Technol. B24, 3088–3093 (2006).
  8. R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
    [CrossRef]
  9. X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–1635 (2002).
    [CrossRef]
  10. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12, 6106–6121 (2004).
    [CrossRef] [PubMed]
  11. T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  12. S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
    [CrossRef]
  13. http://le-csss.asu.edu/nova.
  14. http://www.optics.arizona.edu/Milster/optiscan/OptiScan_MENU_PAGE.htm
  15. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Section 7.4, pp. 279–280.
  16. F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
    [CrossRef] [PubMed]

2006 (1)

J. Xue, K. Moen, and C. J. Spanos, “Integrated aerial image sensor: design, modeling, and assembly,” J. Vac. Sci. Technol. B24, 3088–3093 (2006).

2004 (1)

2003 (2)

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
[CrossRef]

2002 (2)

X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–1635 (2002).
[CrossRef]

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

2000 (1)

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1996 (1)

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

1991 (1)

T. E. Adams, “Application of latent image metrology in microlithography,” Proc. SPIE 1464, 294–312 (1991).
[CrossRef]

1985 (1)

T. A. Brunner and R. R. Allen, “In situ measurement of an image during lithographic exposure,” IEEE Electron Device Lett. 6, 329–331 (1985).
[CrossRef]

Adams, T. E.

T. E. Adams, “Application of latent image metrology in microlithography,” Proc. SPIE 1464, 294–312 (1991).
[CrossRef]

Allen, R. R.

T. A. Brunner and R. R. Allen, “In situ measurement of an image during lithographic exposure,” IEEE Electron Device Lett. 6, 329–331 (1985).
[CrossRef]

Astilean, S.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Section 7.4, pp. 279–280.

Brunner, T. A.

T. A. Brunner and R. R. Allen, “In situ measurement of an image during lithographic exposure,” IEEE Electron Device Lett. 6, 329–331 (1985).
[CrossRef]

Ebbesen, T. W.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Fields, C. H.

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Hagiwara, T.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Hamatani, M.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Hesselink, L.

X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–1635 (2002).
[CrossRef]

Higashibata, S.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Inoue, J.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Kaneko, K.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Kondo, N.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Krenz, K. D.

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

Kunz, R. R.

R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
[CrossRef]

Lalanne, Ph.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Lazec, H. J.

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Lezec, H. J.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Mansuripur, M.

Martin-Moreno, L.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Moen, K.

J. Xue, K. Moen, and C. J. Spanos, “Integrated aerial image sensor: design, modeling, and assembly,” J. Vac. Sci. Technol. B24, 3088–3093 (2006).

Moloney, J. V.

Nishinaga, H.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Oldham, W. G.

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

Palamaru, M.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Rathman, D. D.

R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
[CrossRef]

Ray-Chaudhuri, A. K.

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

Shi, X.

X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–1635 (2002).
[CrossRef]

Spanos, C. J.

J. Xue, K. Moen, and C. J. Spanos, “Integrated aerial image sensor: design, modeling, and assembly,” J. Vac. Sci. Technol. B24, 3088–3093 (2006).

Spector, S. J.

R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
[CrossRef]

Stulen, R. H.

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

Suzuki, K.

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Section 7.4, pp. 279–280.

Wolff, P. A.

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Xie, Y.

Xue, J.

J. Xue, K. Moen, and C. J. Spanos, “Integrated aerial image sensor: design, modeling, and assembly,” J. Vac. Sci. Technol. B24, 3088–3093 (2006).

Yeung, M.

R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
[CrossRef]

Zakharian, A. R.

IEEE Electron Device Lett. (1)

T. A. Brunner and R. R. Allen, “In situ measurement of an image during lithographic exposure,” IEEE Electron Device Lett. 6, 329–331 (1985).
[CrossRef]

J. Vac. Sci. Technol. (2)

C. H. Fields, W. G. Oldham, A. K. Ray-Chaudhuri, K. D. Krenz, and R. H. Stulen, “Direct aerial image measurements to evaluate the performance of an extreme ultraviolet projection lithography system,” J. Vac. Sci. Technol. B14, 4000–4003 (1996).

J. Xue, K. Moen, and C. J. Spanos, “Integrated aerial image sensor: design, modeling, and assembly,” J. Vac. Sci. Technol. B24, 3088–3093 (2006).

Jpn. J. Appl. Phys. (1)

X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–1635 (2002).
[CrossRef]

Nature (1)

T. W. Ebbesen, H. J. Lazec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Opt. Commun. (1)

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (1)

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Proc. SPIE (3)

R. R. Kunz, D. D. Rathman, S. J. Spector, and M. Yeung, “Monolithic detector array comprised of >1000 aerial image sensing elements,” Proc. SPIE 5040, 1441–1455 (2003).
[CrossRef]

T. Hagiwara, M. Hamatani, N. Kondo, K. Suzuki, H. Nishinaga, J. Inoue, K. Kaneko, and S. Higashibata, “Self calibration of wafer scanners using aerial image sensor,” Proc. SPIE 4691, 871–881 (2002).
[CrossRef]

T. E. Adams, “Application of latent image metrology in microlithography,” Proc. SPIE 1464, 294–312 (1991).
[CrossRef]

Other (5)

http://www.photon-inc.com/support/library/pdf/nanoscans.pdf

http://cvimellesgriot.com/Products/Slits-and-Pinholes-fieldinterchangeable.aspx

http://le-csss.asu.edu/nova.

http://www.optics.arizona.edu/Milster/optiscan/OptiScan_MENU_PAGE.htm

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), Section 7.4, pp. 279–280.

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Figures (12)

Fig. 1
Fig. 1

Design of the w = 100 nm wide slit fabricated on a t = 110 nm thick aluminum mask. The aluminum is deposited on a glass substrate. The length L of the slit into the plane of the drawing is L = 50 μm .

Fig. 2
Fig. 2

(a) Top view and (b) cross-sectional profile of the slit. The slit is fabricated using a FIB. The slit is 50 μm long and 125 nm wide at the aluminum mask–glass substrate interface. The aluminum mask is 120 nm thick. The slit has a smooth cross-sectional profile and an 85 nm deep etching into the glass substrate. The cross-sectional SEM view is obtained from a test slit fabricated with identical FIB parameters to that of the final slit.

Fig. 3
Fig. 3

FDTD simulation domain geometry is shown in the boxed area. For accuracy, the slit profile is based on the fabrication results that are shown in Fig. 2. At λ = 658 nm , the material of the mask (aluminum) has a complex refractive index of 1.53 + 7.88 i and the material of the substrate (glass) has a refractive index of 1.53. The incident plane waves are varied in the x z plane and have a component along the positive z direction. The electric fields at the bottom of the FDTD calculation area are propagated, using the angular spectrum technique, to a distance of 1.1 mm through two interfaces, to the detector. Fresnel losses are accounted for at the glass–air interfaces. The detector is a CMOS linear detector (TSL140CS-LF from TAOS) with an array of 128 × 1 pixels.

Fig. 4
Fig. 4

Simulated contrast plots for (a) TE and (b) TM polarizations. The dotted line curve is obtained from field information at a plane 10 nm after the slit. It shows a decrease in contrast as the spatial frequency increases with TM illumination, while the contrast is constantly above 0.99 for TE illumination. The bold curve is obtained by using propagated electric fields at a plane corresponding to where the detector is located in the experiment ( 1.1 mm after the slit). The bold-curve plots show a relatively constant contrast of higher than 0.99 over the entire spatial frequency range for both TE and TM illumination. There is a large evanescent component in the TM case that dominates the minimum transmitted power at the 10 nm plane and is not propagated toward the detector plane, thus increasing contrast for the propagated fields measured at the detector. The fringe half-pitch corresponding to Δ θ = 90 ° between k 1 and k 2 is 233 nm .

Fig. 5
Fig. 5

FDTD simulation of two TM-polarized plane waves incident on the slit in orthogonal directions. k 1 and k 2 represent the two waves, and their orthogonal electric field polarizations are represented by a ^ 1 and a ^ 2 , respectively. (a) U X and (b) U Z components of the TM-polarized illumination when the slit is aligned with a bright fringe of the U X component. (c) U X and (d) U Z components of the TM-polarized illumination when the slit is aligned with a bright fringe of the U Z component. The U Z component fringe has a maximum transmittance when the U Z dark fringe is aligned with the slit (b) and a minimum transmission when a bright fringe is aligned with the slit (d). The U X component fringe has a maximum transmittance when the U X bright fringe is aligned with the slit (a) and a minimum transmission when a dark fringe is aligned with the slit (c). These phenomena cause transmission modulation at the slit output despite zero polarization contrast at the slit input. Each incoming plane wave has an amplitude of 1 V / m .

Fig. 6
Fig. 6

Simulated contrast plots with varying slit widths for the (a) TE and (b) TM polarizations. The width of the slit is measured along the glass–metal interface. The original shape of the slit, as shown in Fig. 2, is maintained throughout. TM polarization is more affected by slit width changes than TE polarization. These curves are obtained with the field information from a plane 10 nm after the slit. (Width of the fabricated slit is 125 nm .)

Fig. 7
Fig. 7

Simulated contrast plots with varying aluminum mask thicknesses for (a) TE and (b) TM illumination. The fabricated thickness of the mask is 120 nm . Both the TE and TM polarizations do not show significant dependence with mask thickness over a 70 nm range. These curves are obtained with the field information from a plane 10 nm after the slit.

Fig. 8
Fig. 8

Schematic of the experimental setup. The wavelength used is 658 nm . TE and TM polarizations are chosen by rotating the half-wave plate and the Glan–Thompson prism. Straight fringes are produced along the illuminated surface of the aluminum mask. The fringes are oriented normal to the mask and parallel to the slit. The distance between the back of the mask and the top of the CMOS detector is approximately 1.1 mm .

Fig. 9
Fig. 9

Outputs of the CMOS linear detector array at one scan position. (a) Slit positioned over a bright fringe (maximum slit transmission). Variation of output power versus pixel position is due to diffraction from the slit. The horizontal axis is the pixel number (a total of 128 pixels). The vertical axis shows relative units of power. All 128 pixels show a nearly uniform dark count of 0.11 units. The transmitted power is represented by the nearly Gaussian curve superimposed on the dark count. Approximately 50 pixels of the detector pick up the transmitted light through the slit. The dark count is subtracted and the remaining power is integrated to obtain the total integrated power that is detected after transmission through the slit. (b) Slit positioned over a dark fringe (minimum slit transmission) predominantly consists of dark count due to negligible slit transmission.

Fig. 10
Fig. 10

Contrast as a function of slit tilt (in the plane of the mask), for 250 and 1000 nm half-pitch fringes. (a) TE and (b) TM polarization. As expected, 250 nm half-pitch fringes are more sensitive to the slit tilt than 1000 nm half-pitch fringes.

Fig. 11
Fig. 11

Experimental and simulated contrast plots for the (a) TE and (b) TM polarizations. The error bars on each data point for the experimental plot show the standard deviation over four readings. The simulation data points represent an average contrast over the PZT vibration displacement of ±15 nm, and the error bars denote the maximum and minimum contrast over the same displacement. The experiment and simulation compare well for the TE polarization. For TM polarization, the experimental contrasts are slightly lower than in the simulation, especially at higher spatial frequencies.

Fig. 12
Fig. 12

Simulated contrast plots with a 50 nm × 50 nm and a 10 nm × 20 nm ( width × depth ) metal defect on the glass–metal interface at a distance of Δ × = 2 μm from the slit for (a) TE and (b) TM polarizations. The TM-polarization contrast shows a reduction in contrast in the presence of a defect, especially at the higher spatial frequencies, while the TE-polarization contrast is not affected by the defect. This result indicates that the presence of nanometer scale defects could be a reason for the decrease in the TM-polarized fringe contrast, as seen in Fig. 11.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

SBR = P slit / P mask ,
C Sim = ( P max P min ) / ( P max + P min ) ,
U 1 = A 1 a ^ 1 exp [ j ( k 1 r ω t ) ] ,
U 2 = A 2 a ^ 2 exp [ j ( k 2 r ω t ) ] ,
V p = Re { a ^ 1 a ^ 2 } .
Λ 1 / 2 = λ / 4 sin ( Δ θ 1 / 2 ) ,
C Exp = ( P max * P min * ) / ( P max * + P min * ) ,

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