Abstract

We propose an optical wave plate using a metal nano-grid. The wave plate operates in reflection mode. A single-mode truncated mode-matching theory is presented as a general method to design such nano-grid wave plates with the desired phase difference between the reflected TM and TE polarizations. This analytical theory allows angled incidence calculations as well, and numerical results agree-well with comprehensive finite-difference time-domain electromagnetic simulations. Due to the subwavelength path-length, the reflective wave plate is expected to have improved broad-band functionality over existing zero-order transmissive wave plates, for which an example is provided. The proposed wave plate is simple and compact, and it is amenable to existing nanofabrication techniques. The reflective geometry is especially promising for applications including liquid-crystal displays and laser feedback experiments.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2008 (1)

2007 (1)

2006 (2)

Y. Ekinci, H. H. Solak, C. David, and H. Sigg, "Bilayer Al wire-grids as broadband and high-performance polarizers," Opt. Express 14, 2323 - 2334 (2006).
[CrossRef] [PubMed]

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

2005 (4)

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

J. Wang, F. Liu, and X. Deng, "Monolithically integrated circular polarizers with two-layer nano-gratings fabricated by imprint lithography," J. Vac. Sci. Technol. B 23, 3164-3167 (2005).
[CrossRef]

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
[CrossRef] [PubMed]

D. Kim, "Polarization characteristics of a wire-grid polarizer in a rotating platform," Appl. Opt. 44, 1366-1371 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Birefringence in two-dimensional bulk photonic crystals applied to the construction of quarter waveplates," Opt. Express 11, 125 - 133 (2003).
[CrossRef] [PubMed]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Experimental demonstration of photonic crystal waveplates," Appl. Phys. Lett. 82, 1036 - 1038 (2003).
[CrossRef]

2001 (1)

2000 (2)

Z. M. Zhu and T. G. Brown, "Nonperturbative analysis of cross coupling in corrugated metal films," J. Opt. Soc. Am. A 17, 1798-1806 (2000).
[CrossRef]

A. M. Radojevic, R. M. Osgood, M. Levy, A. Kumar, and H. Bakhru, "Zeroth-order half-wave plates of LiNbO3 for integrated optics applications at 1.55 mu m," IEEE Photon. Technol. Lett. 12, 1653-1655 (2000).
[CrossRef]

1997 (1)

1994 (2)

E. M. Korenic, S. D. Jacobs, J. K. Houghton, A. Schmid, and F. Kreuzer, "Nematic polymer liquid-crystal wave plate for high power lasers at 1054-nm," Appl. Opt. 33, 1889-1899 (1994).
[CrossRef] [PubMed]

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

1993 (1)

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

1977 (1)

H. S. Cole and R. A. Kashnow, "New reflective dichroic liquid-crystal display device," Appl. Phys. Lett. 30, 619-621 (1977).
[CrossRef]

1971 (1)

P. K. Cheo and C. D. Bass, "Efficient wire-grid duplexer polarizer for CO2 lasers," Appl. Phys. Lett. 18, 565-567 (1971).
[CrossRef]

1969 (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1965 (1)

Ando, S.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

Bacon, J.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Bakhru, H.

A. M. Radojevic, R. M. Osgood, M. Levy, A. Kumar, and H. Bakhru, "Zeroth-order half-wave plates of LiNbO3 for integrated optics applications at 1.55 mu m," IEEE Photon. Technol. Lett. 12, 1653-1655 (2000).
[CrossRef]

Bass, C. D.

P. K. Cheo and C. D. Bass, "Efficient wire-grid duplexer polarizer for CO2 lasers," Appl. Phys. Lett. 18, 565-567 (1971).
[CrossRef]

Blair, S.

Brown, T. G.

Buonanno, M.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Chen, A. N. L.

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

Chen, L.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
[CrossRef] [PubMed]

Cheo, P. K.

P. K. Cheo and C. D. Bass, "Efficient wire-grid duplexer polarizer for CO2 lasers," Appl. Phys. Lett. 18, 565-567 (1971).
[CrossRef]

Chiao, R. Y.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Experimental demonstration of photonic crystal waveplates," Appl. Phys. Lett. 82, 1036 - 1038 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Birefringence in two-dimensional bulk photonic crystals applied to the construction of quarter waveplates," Opt. Express 11, 125 - 133 (2003).
[CrossRef] [PubMed]

Cole, H. S.

H. S. Cole and R. A. Kashnow, "New reflective dichroic liquid-crystal display device," Appl. Phys. Lett. 30, 619-621 (1977).
[CrossRef]

Dagenais, M.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

David, C.

Deguzman, P.

Deng, J.

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
[CrossRef] [PubMed]

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

Deng, X.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
[CrossRef] [PubMed]

J. Wang, F. Liu, and X. Deng, "Monolithically integrated circular polarizers with two-layer nano-gratings fabricated by imprint lithography," J. Vac. Sci. Technol. B 23, 3164-3167 (2005).
[CrossRef]

Doumuki, T.

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Ekinci, Y.

Graham, A.

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

Graham, H. A.

Hickmann, J. M.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Experimental demonstration of photonic crystal waveplates," Appl. Phys. Lett. 82, 1036 - 1038 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Birefringence in two-dimensional bulk photonic crystals applied to the construction of quarter waveplates," Opt. Express 11, 125 - 133 (2003).
[CrossRef] [PubMed]

Houghton, J. K.

Inoue, Y.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

Jacobs, S. D.

Jiang, S. J.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Kashnow, R. A.

H. S. Cole and R. A. Kashnow, "New reflective dichroic liquid-crystal display device," Appl. Phys. Lett. 30, 619-621 (1977).
[CrossRef]

Kawachi, M.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

Kim, D.

Kojima, K.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Korenic, E. M.

Kreuzer, F.

Kumar, A.

A. M. Radojevic, R. M. Osgood, M. Levy, A. Kumar, and H. Bakhru, "Zeroth-order half-wave plates of LiNbO3 for integrated optics applications at 1.55 mu m," IEEE Photon. Technol. Lett. 12, 1653-1655 (2000).
[CrossRef]

Levy, M.

A. M. Radojevic, R. M. Osgood, M. Levy, A. Kumar, and H. Bakhru, "Zeroth-order half-wave plates of LiNbO3 for integrated optics applications at 1.55 mu m," IEEE Photon. Technol. Lett. 12, 1653-1655 (2000).
[CrossRef]

Liu, F.

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
[CrossRef] [PubMed]

J. Wang, F. Liu, and X. Deng, "Monolithically integrated circular polarizers with two-layer nano-gratings fabricated by imprint lithography," J. Vac. Sci. Technol. B 23, 3164-3167 (2005).
[CrossRef]

Liu, X.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Liu, Y.

Lu, Y.

Matsumoto, S.

McCormick, C. F.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Experimental demonstration of photonic crystal waveplates," Appl. Phys. Lett. 82, 1036 - 1038 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Birefringence in two-dimensional bulk photonic crystals applied to the construction of quarter waveplates," Opt. Express 11, 125 - 133 (2003).
[CrossRef] [PubMed]

Morgan, R. A.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Nordin, G.

O’Brien, N.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Ohmori, Y.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

Osgood, R. M.

A. M. Radojevic, R. M. Osgood, M. Levy, A. Kumar, and H. Bakhru, "Zeroth-order half-wave plates of LiNbO3 for integrated optics applications at 1.55 mu m," IEEE Photon. Technol. Lett. 12, 1653-1655 (2000).
[CrossRef]

Pan, Z. Q.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Peterson, E. W.

Radojevic, A. M.

A. M. Radojevic, R. M. Osgood, M. Levy, A. Kumar, and H. Bakhru, "Zeroth-order half-wave plates of LiNbO3 for integrated optics applications at 1.55 mu m," IEEE Photon. Technol. Lett. 12, 1653-1655 (2000).
[CrossRef]

Sawada, T.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

Schmid, A.

Sciortino, J. P.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Sciortino, P.

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
[CrossRef] [PubMed]

J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

Sigg, H.

Sim, E.

Solak, H. H.

Solli, D. R.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Experimental demonstration of photonic crystal waveplates," Appl. Phys. Lett. 82, 1036 - 1038 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, "Birefringence in two-dimensional bulk photonic crystals applied to the construction of quarter waveplates," Opt. Express 11, 125 - 133 (2003).
[CrossRef] [PubMed]

Takahashi, H.

Y. Inoue, Y. Ohmori, M. Kawachi, S. Ando, T. Sawada, and H. Takahashi, "Polarization mode converter with polyimide half waveplate in silica-based planar lightwave circuits," IEEE Photon. Technol. Lett. 6, 626-628 (1994).
[CrossRef]

Tamada, H.

Varghese, R.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Walters, F.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
[CrossRef] [PubMed]

Wang, J.

J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, "High-performance nanowire-grid polarizers," Opt. Lett. 30, 195-197 (2005).
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J. Wang, J. Deng, X. Deng, F. Liu, P. Sciortino, A. N. L. Chen, and A. Graham, "Innovative high-performance nanowire-grid polarizers and integrated isolators," IEEE J. Sel. Top. Quantum Electron. 11, 241-253 (2005).
[CrossRef]

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[CrossRef]

Wang, J. J.

X. Liu, X. Deng, J. P. Sciortino, M. Buonanno, F. Walters, R. Varghese, J. Bacon, L. Chen, N. O’Brien, and J. J. Wang, "Large area, 38 nm half-pitch grating fabrication by using atomic spacer lithography from aluminum wire grids," Nano Lett. 6, 2723 - 2727 (2006).
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Yang, Z.

Young, J. B.

Zhang, W.

Zhu, Z. M.

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Supplementary Material (2)

» Media 1: MPG (660 KB)     
» Media 2: MPG (400 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Schematic showing the metal nano-grid on a metal substrate. (a) The conventions of the TM and the TE polarizations are shown: the electric field of the TM polarization and the magnetic field of the TE polarization are parallel to the x-direction. (b) Enlargement of the cross-section of the grid structure (circled in (a)). The dielectric region above the grid, the grid region and the metal substrate are referred to as regions A, B and C.

Fig. 2.
Fig. 2.

Comprehensive numerical simulation results showing the waveforms of the reflected TE and TM polarizations for (a) a quarter-wave plate (h = 107.4nm) and (b) a half-wave plate (h = 174.7nm). Animations showing the electric field around the grid region are given for the TM polarization (Media 1) and the TE polarization (Media 2).

Fig. 3.
Fig. 3.

Theoretical calculation and comprehensive numerical simulation results showing the phase differences between the reflected TE and TM modes, under different incident angles.

Equations (14)

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tanh ( β TM 2 k 0 2 ε m d m 2 ) tanh ( β TM 2 k 0 2 ε d d d 2 ) = ε m ε d β TM 2 k 0 2 ε d β TM 2 k 0 2 ε m
tanh ( β TE 2 k 0 2 ε m d m 2 ) tan ( k 0 2 ε d β TE 2 d d 2 ) = β TE 2 k 0 2 ε d k 0 2 ε m β TE 2
tan ( k 0 2 ε m d m 2 ) tan ( k 0 2 ε d d d 2 ) = ε d ε m ,
H A ( x , y = 0 , z = 0 + ) = cos θ i ( 1 r TM t ) y ̂ + sin θ i ( 1 + r TM t ) z ̂ ,
E A ( x , y = 0 , z = 0 + ) = k 0 ( 1 + r TM t ) μ 0 x ̂ ,
H B ( x , y = 0 , z = 0 ) = t TM t H d cosh [ β TM 2 k 0 2 ε d ( x + d d 2 ) ] ( cos θ t y ̂ + sin θ t z ̂ )
H B ( x , y = 0 , z = 0 ) = t TM t H m cosh [ β TM 2 k 0 2 ε m ( x + d m 2 ) ] ( cos θ t y ̂ + sin θ t z ̂ )
H d = cosh [ β TM 2 k 0 2 ε m d m 2 ] cosh [ β TM 2 k 0 2 d d 2 ] .
θ t = arcsin ( k 0 sin θ i β TM ) .
E A , ( z = 0 + ) = E B , ( z = 0 ) ;
H A , ( z = 0 + ) = H B , ( z = 0 ) .
d d / 2 d m / 2 E A , × H A , * dx = d d / 2 d m / 2 E B , × H A , * dx .
d d / 2 d m / 2 E B , × H A , * dx = d d / 2 d m / 2 E B , × H B , * dx .
Δϕ = Arg ( r TM b ) Arg ( r TE t ) + 2 h β TM cos [ arcsin ( k 0 sin θ i β TM ) ] 2 h k 0 tan [ arcsin ( k 0 sin θ i β TM ) ] sin θ i ,

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