Abstract

A new grating phase mask is designed that allows the cancellation of the zeroth transmitted order in a diffraction configuration where the grating period is smaller than twice the exposure wavelength. An analytical treatment based on the true-mode method delivers the structure parameters, achieving 100% interference contrast. This modal approach is used to describe the modal operation of the giant reflection to zero-order device.

© 2007 Optical Society of America

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References

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  1. S.-W. Ahn, K.-D. Lee, J.-S. Kim, S.-H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, "Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography," Nanotechnology 16, 1874-1877 (2005).
    [CrossRef]
  2. A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
    [CrossRef]
  3. J. Y. Suratteau, M. Cadilhac, and R. Petit, "On the numerical study of deep dielectric lamellar gratings," J. Opt. 14, 273-288 (1983).
    [CrossRef]
  4. A. V. Tishchenko and N. Lyndin, "The true modal method solves intractable problems: TM incidence on fine metal slits (but the C method also!)," Workshop on Grating Theory, Clermont-Ferrand, France, June 2004.
  5. D. Delbeke, R. Baets, and P. Muys, "Polarization-selective beam splitter based on a highly efficient simple binary diffraction grating," Appl. Opt. 43, 6157-6165 (2004).
    [CrossRef] [PubMed]
  6. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, "An intelligible explanation of highly efficient diffraction in deep dielectric rectangular transmission gratings," Opt. Express 13, 10448-10456 (2005).
    [CrossRef] [PubMed]

2005

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S.-H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, "Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography," Nanotechnology 16, 1874-1877 (2005).
[CrossRef]

A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, "An intelligible explanation of highly efficient diffraction in deep dielectric rectangular transmission gratings," Opt. Express 13, 10448-10456 (2005).
[CrossRef] [PubMed]

2004

1983

J. Y. Suratteau, M. Cadilhac, and R. Petit, "On the numerical study of deep dielectric lamellar gratings," J. Opt. 14, 273-288 (1983).
[CrossRef]

Appl. Opt.

J. Opt.

J. Y. Suratteau, M. Cadilhac, and R. Petit, "On the numerical study of deep dielectric lamellar gratings," J. Opt. 14, 273-288 (1983).
[CrossRef]

Nanotechnology

S.-W. Ahn, K.-D. Lee, J.-S. Kim, S.-H. Kim, J.-D. Park, S.-H. Lee, and P.-W. Yoon, "Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography," Nanotechnology 16, 1874-1877 (2005).
[CrossRef]

Opt. Express

Opt. Quantum Electron.

A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

Other

A. V. Tishchenko and N. Lyndin, "The true modal method solves intractable problems: TM incidence on fine metal slits (but the C method also!)," Workshop on Grating Theory, Clermont-Ferrand, France, June 2004.

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Figures (12)

Fig. 1
Fig. 1

Phase mask structure comprising a silica substrate and a binary corrugation in a high index film.

Fig. 2
Fig. 2

(Color online) Transverse electric field of the propagating TE guided modes of order 0, 1, 2 over two periods.

Fig. 3
Fig. 3

Interferometer analogy of the two-mode transmission through the grating region.

Fig. 4
Fig. 4

Phase masks with a period wavelength ratio close to 1: (a) standard fused-silica phase mask, (b) high index contrast LPCVD S i 3 N 4 phase mask.

Fig. 5
Fig. 5

(Color online) Normalized TE 0 and TE 2 modal field profiles in the corrugation of the (a) fused-silica phase mask and (b) that of the Si 3 N 4 structure.

Fig. 6
Fig. 6

(Color online) Representation of the TE 0 and TE 2 modal fields, incidence plane wave front and ± first order transmitted plane wave fronts over two periods at both interfaces of the grating.

Fig. 7
Fig. 7

Cutoff lines of even (solid curves) and odd (dotted curves) TE modes in the (f, p) space, a = 0.47. The two vertical lines are the cutoff lines of the first and second diffraction orders in the cover medium of index n 2 . P is the operation point of the designed phase mask.

Fig. 8
Fig. 8

Coefficients of the S matrix: i and j = 0 or 2 (mode index).

Fig. 9
Fig. 9

(Color online) Phasor representation of the three contributions to zeroth-order transmission in the silicon nitride phase mask.

Fig. 10
Fig. 10

(Color online) Zeroth-order transmission in the silicon nitride phase mask versus the grating layer thickness in nanometer.

Fig. 11
Fig. 11

(Color online) Zeroth-order transmission in the GIRO grating versus the layer thickness in nanometers.

Fig. 12
Fig. 12

(Color online) Phasor representation of the three contributions to zeroth-order transmission in the GIRO device.

Tables (2)

Tables Icon

Table 1 Reflection and Transmission Coefficients in the Optimized Si3N4 Phase Mask

Tables Icon

Table 2 Coefficient of the S Matrix of the Grating of the GIRO Device

Equations (19)

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cos k 1 r cos k 2 ( Λ r ) 1 2 ( k 1 k 2 + k 2 k 1 ) sin k 1 r ×   sin k 2 ( Λ r ) = cos k y Λ ,
k 1 tan k 1 r 2 + k 2 tan k 2 ( Λ r ) 2 = 0 ,
k 2 tan k 1 r 2 + k 1 tan k 2 ( Λ r ) 2 = 0.
E j ( y ) = { a 1 cos k 1 j ( y r 2 ) , 0 y r a 2 cos k 2 j ( y Λ + r 2 ) , r y Λ ,
a 1 = a 2 cos ( k 2 ( Λ r ) 2 ) cos ( k 1 r 2 ) .
E j ( y ) = E j ( y ) 1 Λ 0 Λ E j ( y ) E j * ( y ) d y .
E 0 = E i t 0 e j φ 0 ,
E 2 = E i t 2 e j φ 2 ,
t j = t s j t j c ,
t s j = 0 Λ E p E j * ( y ) d y = E p 0 Λ E j * ( y ) d y ,
t j c = 0 Λ E j ( y ) E p * d y = E p * 0 Λ E j ( y ) d y .
t j ( 0 Λ E j ( y ) d y ) 2 .
E 0 + E 2 = E i ( t 0 e j φ 0 + t 2 e j φ 2 ) = 0.
| t 0 | = | t 2 | ,
φ 0 = φ 2 + π .
k 0 d ( n e 0 n e 2 ) = π .
| 0 Λ E 2 ( y ) d y | | 0 Λ E 0 ( y ) d y | 1 = 0.
n 1 tan [ k 0 n 1 r 2 ] + n 2 tan [ k 0 n 2 ( Λ r ) 2 ] = 0.
tan [ p f a ] + a tan [ p ( 1 f ) ] = 0.

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