Abstract

The structure of transmission blazed binary gratings for optical limiting is designed with the form– birefringence theory. This kind of grating has subwavelength features, can imitate the transmission blazed grating effectively, and has higher efficiencies than a transmission blazed grating with a subwave length structure. The diffraction efficiencies are calculated and analyzed. For the normal incident light with 10.6μm wavelength, the transmissivities for the designed grating at 0° deviation angle for TE and TM polarizations are 0.05% and 5.09%, respectively, which are basically identical to the results of the finite-difference time-domain method. The diffraction efficiencies of the first transmitted order for TE and TM polarizations are 93.95% and 83.88%, respectively.

© 2008 Optical Society of America

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2005

D. W. Wilson, R. E. Muller, P. M. Echternach, and J. P. Backlund, “Electron-beam lithography for micro- and nano-optical applications,” Proc. SPIE 5720, 68-77 (2005).
[CrossRef]

2002

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

2001

1999

1996

1995

1994

B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518-3526 (1994).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

1993

Astilean, S.

Backlund, J. P.

D. W. Wilson, R. E. Muller, P. M. Echternach, and J. P. Backlund, “Electron-beam lithography for micro- and nano-optical applications,” Proc. SPIE 5720, 68-77 (2005).
[CrossRef]

Borghi, R.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Cai, L. Z.

Cambril, E.

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

Chavel, P.

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

P. Lalanne, S. Astilean, and P. Chavel, “Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff,” J. Opt. Soc. Am. A 16, 1143-1156 (1999).
[CrossRef]

Chen, Y.

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

Echternach, P. M.

D. W. Wilson, R. E. Muller, P. M. Echternach, and J. P. Backlund, “Electron-beam lithography for micro- and nano-optical applications,” Proc. SPIE 5720, 68-77 (2005).
[CrossRef]

Frezza, F.

Fukai, I.

S. Kagami and I. Fukai, “Application of boundary-element method to electromagnetic field problems,” in Proceedings of IEEE Conference on Microwave Theory and Techniques (IEEE, 1984), pp. 455-461.
[CrossRef]

Gale, M. T.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Gallagher, N. C.

B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518-3526 (1994).
[CrossRef]

Gaylord, T. K.

Goodman, J. W.

J. W. Goodman, Introduction of Fourier Optics (McGraw-Hill, 1968).

Grann, E. B.

Haidner, H.

Jin, G. F.

G. F. Jin, Binary Optics (National Defence Industry Press, 1998).

Kagami, S.

S. Kagami and I. Fukai, “Application of boundary-element method to electromagnetic field problems,” in Proceedings of IEEE Conference on Microwave Theory and Techniques (IEEE, 1984), pp. 455-461.
[CrossRef]

Lalanne, P.

Lee, M. S. L.

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

Li, C. F.

Lichtenberg, B.

B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518-3526 (1994).
[CrossRef]

Liu, H. K.

Moharam, M. G.

Muller, R. E.

D. W. Wilson, R. E. Muller, P. M. Echternach, and J. P. Backlund, “Electron-beam lithography for micro- and nano-optical applications,” Proc. SPIE 5720, 68-77 (2005).
[CrossRef]

Ohkawa, S.

K. Yashiro and S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” in Proceedings of IEEE Conference on Antennas and Propagation (IEEE, 1985), pp. 383-389.

Pajewski, L.

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Pommet, D. A.

Rodier, J. C.

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

Rossi, M.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Santarsiero, M.

Schettini, G.

Schutz, H.

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Sheridan, J. T.

Streibl, N.

Turunen, J.

Wilson, D. W.

D. W. Wilson, R. E. Muller, P. M. Echternach, and J. P. Backlund, “Electron-beam lithography for micro- and nano-optical applications,” Proc. SPIE 5720, 68-77 (2005).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Yashiro, K.

K. Yashiro and S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” in Proceedings of IEEE Conference on Antennas and Propagation (IEEE, 1985), pp. 383-389.

Zhao, J. H.

Appl. Opt.

J. Opt. A Pure Appl. Opt.

M. S. L. Lee, P. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, “Imaging with blazed-binary diffractive elements,” J. Opt. A Pure Appl. Opt. 4, S119-S124 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518-3526 (1994).
[CrossRef]

M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556-3566 (1994).
[CrossRef]

Proc. SPIE

D. W. Wilson, R. E. Muller, P. M. Echternach, and J. P. Backlund, “Electron-beam lithography for micro- and nano-optical applications,” Proc. SPIE 5720, 68-77 (2005).
[CrossRef]

Other

S. Kagami and I. Fukai, “Application of boundary-element method to electromagnetic field problems,” in Proceedings of IEEE Conference on Microwave Theory and Techniques (IEEE, 1984), pp. 455-461.
[CrossRef]

K. Yashiro and S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” in Proceedings of IEEE Conference on Antennas and Propagation (IEEE, 1985), pp. 383-389.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

G. F. Jin, Binary Optics (National Defence Industry Press, 1998).

J. W. Goodman, Introduction of Fourier Optics (McGraw-Hill, 1968).

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Figures (11)

Fig. 1
Fig. 1

Optical limiter: (a) the incident light is weak and (b) the incident light is strong.

Fig. 2
Fig. 2

Transmission blazed grating.

Fig. 3
Fig. 3

Blazed-index grating.

Fig. 4
Fig. 4

BBG with subwavelength features.

Fig. 5
Fig. 5

Blazed binary grating.

Fig. 6
Fig. 6

One period of BBG.

Fig. 7
Fig. 7

Diffraction efficiencies of the different transmitted orders when parallel TE polarization light goes through the designed BBG in normal incidence.

Fig. 8
Fig. 8

Diffraction efficiencies of the different transmitted orders when parallel TM polarization light goes through the designed BBG in normal incidence.

Fig. 9
Fig. 9

Effective refractive indices.

Fig. 10
Fig. 10

First-order diffraction efficiencies of the BBG and the TBG.

Fig. 11
Fig. 11

First-order diffraction efficiencies of the TBG under normal incidence with TE and TM polarizations.

Tables (2)

Tables Icon

Table 1 Fill Factors and the Width of Spaces and Ridges in One Period

Tables Icon

Table 2 Diffraction Efficiencies of All Orders

Equations (22)

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

d = l λ sin θ .
n sin α = sin ( α + θ ) .
h = d tan α .
h = l λ n cos θ = l λ n 1 ( l λ d ) 2 .
n TE eff = n 1 2 ( 1 f ) + n 2 2 f ,
n TM eff = 1 1 f n 1 2 + f n 2 2 ,
n ( m ) = ( 1 f ( m ) ) + f ( m ) × n 2 ,
n ( m ) = 1 + m n 1 M 1 ,
f ( m ) = 2 m ( n + 1 ) ( M 1 ) + m 2 ( n 1 ) ( n + 1 ) ( M 1 ) 2 ,
t s ( x ) = m = 0 M 1 { exp ( i k n ( m ) h ) rect [ x ( m + 1 2 ) p p ] } .
t ( x ) = t s ( x ) * n = 0 N 1 δ ( x n d ) ,
FT { t ( x ) } = FT { t s ( x ) } × FT { n = 0 N 1 δ ( x n d ) } ,
FT { t s ( x ) } = 1 d m = 0 M 1 { exp [ i k n ( m ) h i 2 π ξ ( m + 1 2 ) p ] × p sin c ( p ξ ) } ,
FT { t s ( x ) } = sin c ( p ξ ) M exp ( i k h ) exp ( i π p ξ ) × 1 exp [ M ( i k n 1 M 1 h i 2 π p ξ ) ] 1 exp ( i k n 1 M 1 h i 2 π p ξ ) .
FT { t ( x ) } = sin c ( p ξ ) M exp ( i k h ) exp ( i π p ξ ) × 1 exp [ M ( i k n 1 M 1 h i 2 π p ξ ) ] 1 exp ( i k n 1 M 1 h i 2 π p ξ ) 1 exp ( i 2 π d ξ N ) N [ 1 exp ( i 2 π d ξ ) ] .
I = | FT { t ( x ) } | 2 = sin c 2 ( p ξ ) ( M N ) 2 × sin 2 [ M 2 ( k n 1 M 1 h 2 π p ξ ) ] sin 2 [ 1 2 ( k n 1 M 1 h 2 π p ξ ) ] × sin 2 ( N π d ξ ) sin 2 ( π d ξ ) .
η = 4 n ( n + 1 ) 2 × sin c 2 ( p ξ ) × sin 2 [ M 2 ( k n 1 M 1 h 2 π p ξ ) ] M 2 sin 2 [ 1 2 ( k n 1 M 1 h 2 π p ξ ) ] × sin 2 ( N π d ξ ) N 2 sin 2 ( π d ξ ) .
η = 4 n ( n + 1 ) 2 × sin c 2 ( l M ) × sin 2 [ M 2 ( k n 1 M 1 h 2 π l M ) ] M 2 sin 2 [ 1 2 ( k n 1 M 1 h 2 π l M ) ] × sin 2 ( N π l ) N 2 sin 2 ( π l ) ,
n TM eff = 1 1 m n 2 n 1 M 1 ( 2 + m n 1 M 1 ) .
η TM = 4 n ( n + 1 ) 2 × sin c 2 ( l M ) M 2 × sin 2 ( N π l ) N 2 sin 2 ( π l ) × | m = 0 M 1 exp [ i 2 π h λ n TM eff i 2 π l M ( m + 1 2 ) ] | 2 .
T TM = 4 n ( n + 1 ) 2 × ( 1 tan 2 θ tan 2 ( 2 α + θ ) ) ,
T TE = 4 n ( n + 1 ) 2 × ( 1 sin 2 θ sin 2 ( 2 α + θ ) ) .

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