Abstract

We theoretically investigate optical birefringence originating from subwavelength structures in intrinsic birefringent media. Assuming alternating layers of isotropic and anisotropic materials, the propagation of optical waves is simulated on the basis of the finite difference time domain method. Optical polarization changes throughout the structure reveal the birefringence of the layered structure as a whole. In addition, the birefringence is also analyzed on the basis of effective medium theory. The results indicate that the optical birefringence of the structure as a whole can be modified by the magnitude and direction of the intrinsic birefringence of the anisotropic layers. This theoretical prediction will be useful for micro- and nanofabrication in optical devices.

© 2010 Optical Society of America

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    [CrossRef]

2008 (2)

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

G. M. Lerman and U. Levy, “Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064,” Opt. Lett. 33, 2782–2784 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Schrauwen, F. V. Laere, D. V. Thourhout, and R. Baets, “Focused-ion-beam fabrication of slanted grating couplers in silicon-on-insulator waveguides,” IEEE Photon. Tech. Lett. 19, 816–818 (2007).
[CrossRef]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

2006 (3)

2005 (3)

2003 (2)

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S.-L., and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

2002 (2)

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[CrossRef]

W. Yu, T. Konishi, T. Hamamoto, H. Toyota, T. Yotsuya, and Y. Ichioka, “Polarization-multiplexed diffractive optical elements fabricated by subwavelength structures,” Appl. Opt. 41, 96–100 (2002).
[CrossRef] [PubMed]

2001 (3)

A. G. Lopez and H. G. Craighead, “Subwavelength surface-relief gratings fabricated by microcontact printing of self-assembled monolayers,” Appl. Opt. 40, 2068–2075 (2001).
[CrossRef]

S. Tanaka, M. Nakano, M. Umeda, K. Ito, S. Nakamura, and Y. Hatamura, “Simulation of near-field photolithography using the finite-difference time-domain method,” J. Appl. Phys. 89, 3547–3553 (2001).
[CrossRef]

C. Ochiai, O. Yavas, M. Takai, A. Hosono, and S. Okuda, “Fabrication process of field emitter arrays using focused ion and electron beam induced reaction,” J. Vac. Sci. Technol. B 19, 933–935 (2001).
[CrossRef]

2000 (1)

E. E. Kriezis and S. J. Elston, “Light wave propagation in liquid crystal displays by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[CrossRef]

1999 (2)

M. Fujimoto, Y. Okuno, and T. Matsuda, “Numerical evaluation of polarization-selective characteristics of a binary relief grating with subwavelength structures,” Opt. Rev. 6, 501–506 (1999).
[CrossRef]

G. P. Nordin and P. C. Deguzman, “Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region,” Opt. Express 5, 163–168 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

H. Kikuta, Y. Ohira, and K. Iwata, “Achromatic quarter-wave plates using the dispersion of form birefringence,” Appl. Opt. 36, 1566–1572 (1997).
[CrossRef] [PubMed]

C. Yang and P. Yeh, “Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings,” J. Appl. Phys. 81, 23–29 (1997).
[CrossRef]

1996 (3)

1995 (4)

H. Kikuta, H. Yoshida, and K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

I. Richter, P.-C. Sun, F. Xu, and Y. Fainman, “Design considerations of form birefringent microstructures,” Appl. Opt. 34, 2421–2429 (1995).
[CrossRef] [PubMed]

G. Campbell and R. K. Kostuk, “Effective-medium theory of sinusoidally modulated volume holograms,” J. Opt. Soc. Am. A 12, 1113–1117 (1995).
[CrossRef]

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67, 3114–3116 (1995).
[CrossRef]

1994 (2)

1993 (1)

1987 (1)

1984 (1)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), pp. 205–208.

1977 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. Mag. 14, 302–307 (1966).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Baets, R.

J. Schrauwen, F. V. Laere, D. V. Thourhout, and R. Baets, “Focused-ion-beam fabrication of slanted grating couplers in silicon-on-insulator waveguides,” IEEE Photon. Tech. Lett. 19, 816–818 (2007).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems,” IEEE Trans. Antennas Propag. Mag. 44, 110–117 (1996).
[CrossRef]

Biener, G.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[CrossRef]

Bomzon, Z.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2006), pp. 837–840.

Brauer, R.

Bryngdahl, O.

Campbell, G.

Cheng, C.-C.

Chou, S. Y.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67, 3114–3116 (1995).
[CrossRef]

Craighead, H. G.

Deguzman, P. C.

Elston, S. J.

E. E. Kriezis and S. J. Elston, “Light wave propagation in liquid crystal displays by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[CrossRef]

Emoto, A.

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Escuti, M. J.

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14, 11870–11884 (2006).
[CrossRef] [PubMed]

Fainman, Y.

Fujimoto, M.

M. Fujimoto, Y. Okuno, and T. Matsuda, “Numerical evaluation of polarization-selective characteristics of a binary relief grating with subwavelength structures,” Opt. Rev. 6, 501–506 (1999).
[CrossRef]

Fujita, J.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Gauthier, R. C.

Gedne, S. C.

A. Taflove and S. C. Gedne, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Grann, E. B.

Hamamoto, T.

Han, C.-W.

Hasman, E.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[CrossRef]

Hatamura, Y.

S. Tanaka, M. Nakano, M. Umeda, K. Ito, S. Nakamura, and Y. Hatamura, “Simulation of near-field photolithography using the finite-difference time-domain method,” J. Appl. Phys. 89, 3547–3553 (2001).
[CrossRef]

Hosono, A.

C. Ochiai, O. Yavas, M. Takai, A. Hosono, and S. Okuda, “Fabrication process of field emitter arrays using focused ion and electron beam induced reaction,” J. Vac. Sci. Technol. B 19, 933–935 (2001).
[CrossRef]

Hugonin, J.-P.

Ichioka, Y.

Igaku, Y.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Ishida, M.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Ishigaki, H.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Ito, K.

S. Tanaka, M. Nakano, M. Umeda, K. Ito, S. Nakamura, and Y. Hatamura, “Simulation of near-field photolithography using the finite-difference time-domain method,” J. Appl. Phys. 89, 3547–3553 (2001).
[CrossRef]

Iwata, K.

H. Kikuta, Y. Ohira, and K. Iwata, “Achromatic quarter-wave plates using the dispersion of form birefringence,” Appl. Opt. 36, 1566–1572 (1997).
[CrossRef] [PubMed]

H. Kikuta, H. Yoshida, and K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

Jiang, J.

Jin, G.-F.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S.-L., and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Kawatsuki, N.

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Kikuta, H.

H. Kikuta, Y. Ohira, and K. Iwata, “Achromatic quarter-wave plates using the dispersion of form birefringence,” Appl. Opt. 36, 1566–1572 (1997).
[CrossRef] [PubMed]

H. Kikuta, H. Yoshida, and K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

Kim, H.-C.

Kimura, Y.

Kleiner, V.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[CrossRef]

Komuro, M.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Konishi, T.

Kostuk, R. K.

Krauss, P. R.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67, 3114–3116 (1995).
[CrossRef]

Kriezis, E. E.

E. E. Kriezis and S. J. Elston, “Light wave propagation in liquid crystal displays by the 2-D finite-difference time-domain method,” Opt. Commun. 177, 69–77 (2000).
[CrossRef]

Laere, F. V.

J. Schrauwen, F. V. Laere, D. V. Thourhout, and R. Baets, “Focused-ion-beam fabrication of slanted grating couplers in silicon-on-insulator waveguides,” IEEE Photon. Tech. Lett. 19, 816–818 (2007).
[CrossRef]

Lalanne, P.

Lerman, G. M.

Levy, U.

Liu, H.-T.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S.-L., and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Lopez, A. G.

Matsuda, T.

M. Fujimoto, Y. Okuno, and T. Matsuda, “Numerical evaluation of polarization-selective characteristics of a binary relief grating with subwavelength structures,” Opt. Rev. 6, 501–506 (1999).
[CrossRef]

Matsui, S.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Mnaymneh, K.

Moharam, M. G.

Morris, G. M.

Nakamura, S.

S. Tanaka, M. Nakano, M. Umeda, K. Ito, S. Nakamura, and Y. Hatamura, “Simulation of near-field photolithography using the finite-difference time-domain method,” J. Appl. Phys. 89, 3547–3553 (2001).
[CrossRef]

Nakano, M.

S. Tanaka, M. Nakano, M. Umeda, K. Ito, S. Nakamura, and Y. Hatamura, “Simulation of near-field photolithography using the finite-difference time-domain method,” J. Appl. Phys. 89, 3547–3553 (2001).
[CrossRef]

Namatsu, H.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Nezhad, M.

Nishida, N.

Niv, A.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[CrossRef]

Nordin, G. P.

Ochiai, C.

C. Ochiai, O. Yavas, M. Takai, A. Hosono, and S. Okuda, “Fabrication process of field emitter arrays using focused ion and electron beam induced reaction,” J. Vac. Sci. Technol. B 19, 933–935 (2001).
[CrossRef]

Ochiai, Y.

S. Matsui, Y. Igaku, H. Ishigaki, J. Fujita, M. Ishida, Y. Ochiai, H. Namatsu, and M. Komuro, “Room-temperature nanoimprint and nanotransfer printing using hydrogen silsequioxane,” J. Vac. Sci. Technol. B 21, 688–692 (2003).
[CrossRef]

Oh, C.

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14, 11870–11884 (2006).
[CrossRef] [PubMed]

Ohira, Y.

Ohota, Y.

Okuda, S.

C. Ochiai, O. Yavas, M. Takai, A. Hosono, and S. Okuda, “Fabrication process of field emitter arrays using focused ion and electron beam induced reaction,” J. Vac. Sci. Technol. B 19, 933–935 (2001).
[CrossRef]

Okuno, Y.

M. Fujimoto, Y. Okuno, and T. Matsuda, “Numerical evaluation of polarization-selective characteristics of a binary relief grating with subwavelength structures,” Opt. Rev. 6, 501–506 (1999).
[CrossRef]

Ono, H.

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Ono, Y.

Ping, L.

Pommet, D. A.

Raguin, D. H.

Renstrom, P. J.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25 nm vias and trenches in polymers,” Appl. Phys. Lett. 67, 3114–3116 (1995).
[CrossRef]

Richter, I.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Scherer, A.

Schrauwen, J.

J. Schrauwen, F. V. Laere, D. V. Thourhout, and R. Baets, “Focused-ion-beam fabrication of slanted grating couplers in silicon-on-insulator waveguides,” IEEE Photon. Tech. Lett. 19, 816–818 (2007).
[CrossRef]

Sekiguchi, T.

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation and Bragg diffraction in thick polarization gratings,” Jpn. J. Appl. Phys. 47, 7963–7967 (2008).
[CrossRef]

Sun, P.-C.

Taflove, A.

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C. Yang and P. Yeh, “Artificial uniaxial and biaxial dielectrics with the use of photoinduced gratings,” J. Appl. Phys. 81, 23–29 (1997).
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A. Taflove and S. C. Gedne, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2006), pp. 837–840.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), pp. 205–208.

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Figures (7)

Fig. 1
Fig. 1

(a) Perspective and (b) top view of the fundamental subwavelength alternating structure consisting of two media, A and B. The period T on the x axis is equal to the summation of the widths of media A (a) and B (b); d denotes the thickness of the structure along the z axis.

Fig. 2
Fig. 2

Top view of the two-dimensional FDTD analysis region for the subwavelength structure.

Fig. 3
Fig. 3

Typical dependence of the form birefringence on the period T normalized by the incident wavelength. The refractive indices of media A and B are 1.5 and 1.0, respectively, at F = 0.5 , d = 600 nm , and λ = 1.0 μm .

Fig. 4
Fig. 4

(a) Form birefringence as a function of the filling factor F. The refractive indices of media A and B are 1.5 and 1.0, respectively ( T = 280 nm , d = 1.0 μm , λ = 633 nm ). (b) Form birefringence calculated from FDTD analysis with different structure thicknesses d. The inset ellipsoids show the output polarization states ( T = 280 nm , F = 0.5 , and λ = 633 nm ).

Fig. 5
Fig. 5

Form birefringence as a function of the refractive index difference between isotropic media A and B ( T = 280 nm , F = 0.5 , d = 600 nm , and λ = 633 nm ).

Fig. 6
Fig. 6

Form birefringence as a function of the refractive index difference of medium A ( Δ n A = n A y - n A x ). For Δ n A = 0 , both n A x and n A y were isotropically set to 1.5 ( T = 280 nm , F = 0.5 , d = 600 nm , and λ = 633 nm ). Schematic representations above the graph indicate the refractive index ellipsoids of media A and B that correspond to the lateral axis of the graph.

Fig. 7
Fig. 7

(a) Form birefringence as a function of the direction of n A e with respect to the intrinsic birefringence ( Δ n A = n A e - n A o ) of medium A ( T = 280 nm , F = 0.5 , d = 600 nm , and λ = 633 nm ). (b) Direction of the slow axis with respect to the Δ n F depending on the direction of n A e . Schematic representations above the graphs indicate the refractive index ellipsoids of media A and B that correspond to the lateral axis of the graphs.

Equations (8)

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

n x 2 = n 0 x 2 + π 2 3 T 2 λ 2 F 2 ( 1 - F ) 2 n 0 x 6 n 0 y 2 ( 1 n A x 2 - 1 ) 2 ,
n y 2 = n 0 y 2 + π 2 3 T 2 λ 2 F 2 ( 1 - F ) 2 ( n A y 2 - 1 ) 2 ,
1 n 0 x 2 = F n A x 2 + ( 1 - F ) ,
n 0 y 2 = F n A y 2 + ( 1 - F ) .
Δ n F = n y - n x .
ε = ε 0 [ ε x x ε x y ε x z ε y x ε y y ε y z ε z x ε z y ε z z ] ,
ε x x = n o 2 + ( n e 2 - n o 2 ) cos 2 θ cos 2 ϕ , ε x y = ε y x = ( n e 2 - n o 2 ) cos 2 θ sin ϕ cos ϕ , ε x z = ε z x = ( n e 2 - n o 2 ) sin θ cos θ cos ϕ , ε y y = n o 2 + ( n e 2 - n o 2 ) cos 2 θ sin 2 ϕ , ε y z = ε z y = ( n e 2 - n o 2 ) sin θ cos ϕ sin ϕ , ε z z = n o 2 + ( n e 2 - n o 2 ) sin 2 θ ,
E out = R ( α ) [ exp ( i k d n 1 ) 0 0 exp ( - i k d n 2 ) ] E in ,

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