Abstract

A comparison of antireflection surfaces based on the two-dimensional binary gratings and thin-film coatings is presented. First, a two-dimensional hybrid binary grating is proposed and analyzed by use of a vector-based implementation of the rigorous coupled-wave analysis method. The optimum parameters of the structure are determined and the effects that changing them have on spectral characteristics of the structure are studied. Then this structure is compared with multilayer thin-film antireflection filters. These filters are designed by genetic algorithm and needle methods, which are powerful methods for multilayer filter design. The comparison results show that the sensitivity of the grating to changes in the incident wavelength is high. However, a reflectance of the order of 10−3% at the design wavelength can be achieved. The sensitivity of designed antireflection thin-film filters to wavelength changes is lower, however, and the minimum achievable reflectance is higher.

© 2005 Optical Society of America

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References

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2004 (1)

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, S. H. Keshmiri, “Design of multilayer polarizing beam splitters using genetic algorithm,” Opt. Commun. 233, 57–65 (2004).
[CrossRef]

2001 (1)

1997 (3)

1996 (2)

1995 (2)

1994 (1)

1993 (1)

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

1992 (3)

1979 (1)

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Neviere, “Crossed gratings: a theory and its application,” Appl. Phys. 18, 39–52 (1979).
[CrossRef]

1978 (2)

D. Maystre, M. Neviere, “Electromagnetic theory of crossed gratings,” J. Opt. 9, 301–306 (1978).
[CrossRef]

P. Vincent, “A finite difference method for dielectric and conducting crossed gratings,” Opt. Commun. 26, 293–296 (1978).
[CrossRef]

Baylard, C.

Becker, M. F.

Bräuer, R.

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Bryngdahl, O.

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Cox, J. A.

D. C. Dobson, J. A. Cox, “An integral equation method for biperiodic diffraction structures,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 106–113 (1991).
[CrossRef]

DeBell, G. W.

Derrick, G. H.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Neviere, “Crossed gratings: a theory and its application,” Appl. Phys. 18, 39–52 (1979).
[CrossRef]

Dobrowolski, J. A.

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), pp. 42.1–42.130.

Dobson, D. C.

D. C. Dobson, J. A. Cox, “An integral equation method for biperiodic diffraction structures,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 106–113 (1991).
[CrossRef]

Furman, S. A.

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, 1992).

Gaylord, T. K.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Grann, E. B.

Greffet, J.-J.

Han, S. T.

Kao, C.-Y.

Keshmiri, S. H.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, S. H. Keshmiri, “Design of multilayer polarizing beam splitters using genetic algorithm,” Opt. Commun. 233, 57–65 (2004).
[CrossRef]

Lalanne, P.

Li, L.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (IOP, 2001).
[CrossRef]

Maystre, D.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Neviere, “Crossed gratings: a theory and its application,” Appl. Phys. 18, 39–52 (1979).
[CrossRef]

D. Maystre, M. Neviere, “Electromagnetic theory of crossed gratings,” J. Opt. 9, 301–306 (1978).
[CrossRef]

McPhedran, R. C.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Neviere, “Crossed gratings: a theory and its application,” Appl. Phys. 18, 39–52 (1979).
[CrossRef]

Michielssen, E.

D. S. Weile, E. Michielssen, “Genetic algorithms optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

E. Michielssen, S. Ranjithan, R. Mittra, “Optimal multilayer filter design using real-coded genetic algorithms,” IEE Proc. J 139, 413–420 (1992).

Mirsalehi, M. M.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, S. H. Keshmiri, “Design of multilayer polarizing beam splitters using genetic algorithm,” Opt. Commun. 233, 57–65 (2004).
[CrossRef]

Mittra, R.

E. Michielssen, S. Ranjithan, R. Mittra, “Optimal multilayer filter design using real-coded genetic algorithms,” IEE Proc. J 139, 413–420 (1992).

Moharam, M. G.

Morris, G. M.

Neviere, M.

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Neviere, “Crossed gratings: a theory and its application,” Appl. Phys. 18, 39–52 (1979).
[CrossRef]

D. Maystre, M. Neviere, “Electromagnetic theory of crossed gratings,” J. Opt. 9, 301–306 (1978).
[CrossRef]

M. Neviere, E. Popov, Light Propagation in Periodic Media (Marcel Dekker, 2003).

Noponen, E.

Nourian, M.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, S. H. Keshmiri, “Design of multilayer polarizing beam splitters using genetic algorithm,” Opt. Commun. 233, 57–65 (2004).
[CrossRef]

Peng, G. S.

Pommet, D. A.

Popov, E.

M. Neviere, E. Popov, Light Propagation in Periodic Media (Marcel Dekker, 2003).

Ranjithan, S.

E. Michielssen, S. Ranjithan, R. Mittra, “Optimal multilayer filter design using real-coded genetic algorithms,” IEE Proc. J 139, 413–420 (1992).

Shokooh-Saremi, M.

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, S. H. Keshmiri, “Design of multilayer polarizing beam splitters using genetic algorithm,” Opt. Commun. 233, 57–65 (2004).
[CrossRef]

Tikhonravov, A. V.

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, 1992).

Tikhonravov, V.

Trubetskov, M. K.

Tsao, Y. L.

Turunen, J.

Versaevel, P.

Vincent, P.

P. Vincent, “A finite difference method for dielectric and conducting crossed gratings,” Opt. Commun. 26, 293–296 (1978).
[CrossRef]

Walser, R. M.

Weile, D. S.

D. S. Weile, E. Michielssen, “Genetic algorithms optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

Yang, J.-M.

Appl. Opt. (3)

Appl. Phys. (1)

G. H. Derrick, R. C. McPhedran, D. Maystre, M. Neviere, “Crossed gratings: a theory and its application,” Appl. Phys. 18, 39–52 (1979).
[CrossRef]

IEE Proc. J (1)

E. Michielssen, S. Ranjithan, R. Mittra, “Optimal multilayer filter design using real-coded genetic algorithms,” IEE Proc. J 139, 413–420 (1992).

IEEE Trans. Antennas Propag. (1)

D. S. Weile, E. Michielssen, “Genetic algorithms optimization applied to electromagnetics: a review,” IEEE Trans. Antennas Propag. 45, 343–353 (1997).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. (1)

D. Maystre, M. Neviere, “Electromagnetic theory of crossed gratings,” J. Opt. 9, 301–306 (1978).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (3)

P. Vincent, “A finite difference method for dielectric and conducting crossed gratings,” Opt. Commun. 26, 293–296 (1978).
[CrossRef]

M. Shokooh-Saremi, M. Nourian, M. M. Mirsalehi, S. H. Keshmiri, “Design of multilayer polarizing beam splitters using genetic algorithm,” Opt. Commun. 233, 57–65 (2004).
[CrossRef]

R. Bräuer, O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[CrossRef]

Opt. Lett. (1)

Other (7)

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, 1992).

D. C. Dobson, J. A. Cox, “An integral equation method for biperiodic diffraction structures,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 106–113 (1991).
[CrossRef]

M. Neviere, E. Popov, Light Propagation in Periodic Media (Marcel Dekker, 2003).

M. G. Moharam, “Coupled wave analysis of two dimensional dielectric gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE883, 8–11 (1988).
[CrossRef]

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (IOP, 2001).
[CrossRef]

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), pp. 42.1–42.130.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

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Figures (10)

Fig. 1
Fig. 1

(a) Structure of the 2-D hybrid binary grating. (b) 2-D grating analysis coordinate system.

Fig. 2
Fig. 2

Reflection versus angle of incidence (α) at 550 nm for a 2-D hybrid binary grating.

Fig. 3
Fig. 3

Reflection versus incident wavelength (the design wavelength is equal to 550 nm) for a 2-D hybrid binary grating.

Fig. 4
Fig. 4

Reflectance versus relative grating depth for a 2-D hybrid binary grating.

Fig. 5
Fig. 5

Chromosome structure for designing thin-film filters with the GA.

Fig. 6
Fig. 6

Refractive-index profile of the GA-designed AR filter.

Fig. 7
Fig. 7

Refractive-index profile of the needle-designed AR filter.

Fig. 8
Fig. 8

Reflectance versus angle of incidence for GA- and needle-designed AR filters at 550 nm.

Fig. 9
Fig. 9

Reflection versus incident wavelength for GA- and needle-designed AR filters.

Fig. 10
Fig. 10

Reflection versus (a) wavelength and (b) angle of incidence (at 550 nm) for a QW layer AR coating.

Tables (1)

Tables Icon

Table 1 Comparison of Spectral Characteristics of an AR 2-D Hybrid Binary Grating and AR Thin-Film Filters

Equations (27)

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ɛ ( x , y ) = p , q ɛ p q exp [ j 2 π ( p Λ x x + q Λ y y ) ] ,
ɛ p q = ɛ I δ p 0 δ q 0 + ( ɛ III ɛ I ) [ sin ( π g p ) π p sin ( π g q ) π q sin ( π f p ) π p sin ( π f q ) π q ] ,
E 1 = u exp ( j k 1 r ) + m , n R m n exp ( j k 1 m n r ) ,
E 3 = m , n T m n exp [ j k 3 m n ( r d ) ] ,
k 1 = 2 π λ 0 ɛ I ( sin α cos δ x ̂ + sin α sin δ ŷ + cos α ) ,
k 1 m n = k x m x ̂ + k y n ŷ + k z 1 m n ,
k 3 m n = k x m x ̂ + k y n ŷ + k z 3 m n ,
u = ( cos ψ cos α cos δ sin ψ sin δ ) x ̂ + ( cos ψ cos α sin δ + sin ψ cos δ ) ŷ sin α cos ψ .
k z 1 m n = [ ( 2 π ɛ I / λ 0 ) 2 k x m 2 k y n 2 ] 1 / 2 ,
k z 3 m n = [ ( 2 π ɛ III / λ 0 ) 2 k x m 2 k y n 2 ] 1 / 2 .
E 2 = m , n S m n ( z ) exp ( j σ m n r ) ,
H 2 = ( ɛ 0 / μ 0 ) 1 / 2 m , n U m n ( z ) exp ( j σ m n r ) ,
× E 2 = j ω μ 0 H 2 , × H 2 = j ω ɛ 0 ɛ ( x , y ) E 2 ,
[ x y U ˙ x U ˙ y ] = [ 0 C D 0 ] [ S x S y U x U y ] V ˙ = XV .
r = ( n + N ) + ( 2 N + 1 ) ( m + N ) + 1 ,
C = [ ( j / k 0 ) K x [ A ] K y ( j / k 0 ) K x [ A ] K x j K 0 j K 0 ( j / k 0 ) K y [ A ] K y ( j / k 0 ) K y [ A ] K x ] ,
D = [ ( j / k 0 ) K x K y ( j / k 0 ) K x 2 + j K 0 [ ɛ ] j K 0 [ ɛ ] + ( j / k 0 ) K y 2 ( j / k 0 ) K y K x ] ,
υ i = k = 1 4 ( 2 N + 1 ) 2 q k w i , k exp ( λ k z ) , i = 1 , , 4 ( 2 N + 1 ) 2 ,
V = Ŵ ( z ) Q = [ Ŵ 1 ( z ) Ŵ 2 ( z ) Ŵ 3 ( z ) Ŵ 4 ( z ) ] Q ,
z = 0 u x δ r , ( N + 1 ) + N ( 2 N + 1 ) + R x = S x ( 0 ) , u y δ r , ( N + 1 ) + N ( 2 N + 1 ) + R y = S y ( 0 ) , δ r , ( N + 1 ) + N ( 2 N + 1 ) ( k 1 y u z k 1 z u y ) K z 1 R y + K y R z = k 0 U x ( 0 ) , δ r , ( N + 1 ) + N ( 2 N + 1 ) ( k 1 z u x k 1 x u z ) + K z 1 R x K x R z = k 0 U y ( 0 ) , z = d T x = S x ( d ) , T y = S y ( d ) , K z 3 T y + K y T z = k 0 U x ( d ) , K z 3 T x K x T z = k 0 U y ( d ) .
z = 0 K x R x + K y R y + K z 1 R z = 0 , z = d K x T x + K y T y + K z 3 T z = 0 .
D E 1 = Re ( K z 1 / k 1 z ) R R * ,
D E 3 = Re ( K z 3 / k 1 z ) T T * .
F = 1 i | R desired ( λ i ) R design ( λ i ) | ,
G S = S ( G k ) .
G C = C ( G S ) .
G M = M ( G C ) .

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