Abstract

Recently, a novel holographic diffraction grating made of polymer slices alternated to homogeneous films of nematic liquid crystal (POLICRYPS) was realized. We study the optical performance of the POLICRYPS gratings by both numerical simulations and experiments. Characterization of the grating at normal and conical reading mount are performed. The diffraction efficiency depends strongly on the angles of incidence. Besides, the characterization of the diffraction efficiency at Bragg angle incidence is studied. A uniform high diffraction efficiency is achieved when the incident wave satisfies the Bragg condition.

© 2008 Optical Society of America

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  1. J. Margerum, A. Lackner, E. Ramos, G. Smith, N. Vaz, J. Kohler, and C. Allison, "Polymer dispersed liquid crystal film devices," U.S. Patent (1992).
  2. R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).
  3. D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
    [CrossRef]
  4. R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, "Development of a new kind of switchable holographic grating made of liquid-crystal films separated by slices of polymeric material," Opt. Lett. 29, 1261- 1263 (2004). URL http://www.opticsinfobase.org/abstract.cfm?URI=jdt-2-1-38.
    [CrossRef]
  5. L. De Sio, R. Caputo, A. De Luca, A. Veltri, C. Umeton, and A. V. Sukhov, "In situ optical control and stabilization of the curing process of holographic gratings with a nematic film-polymer-slice sequence structure," Appl. Opt. 45, 3721 - 3727 (2006). URL http://www.opticsinfobase.org/abstract.cfm? URI=ao-45-16-3721.
    [CrossRef]
  6. R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
    [CrossRef]
  7. R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
    [CrossRef]
  8. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969). URL http://adsabs.harvard.edu/abs/1969BSTJ.48.2909K.
  9. K. Rokushima and J. Yamakita, "Analysis of anisotroic dielectric gratings," J. Opt. Soc. Am. A 73, 901 (1983).
    [CrossRef]
  10. E. N. Glytsis and T. K. Gaylord, "Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings," J. Opt. Soc. Am. A 4, 2061 (1987).
    [CrossRef]
  11. S. Mori, K. Mukai, J. Yamakita, and K. Rokushima, "Analysis of dielectric lamellar gratings coated with anisotropic layers," J. Opt. Soc. Am. A 7, 1661 (1990).
    [CrossRef]
  12. G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035 - 1047 (1997). URL http://link.aps.org/abstract/PRE/v55/p1035.
    [CrossRef]
  13. J. B. Harris, T. W. Preist, E. L. Wood, and J. R. Sambles, "Conical diffraction from multicoated gratings containing uniaxial materials," J. Opt. Soc. Am. A 13, 803 (1996).
    [CrossRef]
  14. L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
    [CrossRef]
  15. X. Wei, "Three Dimensional Rigorous Model for Optical Scattering Problems," Ph.D. thesis, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft (2006). URL http://www.optica.tn.tudelft.nl/publications/summary/wei.asp.
  16. X. Wei, A. J. Wachters, and H. P. Urbach, "Finite-element model for three-dimensional optical scattering problems," J. Opt. Soc. Am. A 24, 866-881 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=josaa-24-3-866.
    [CrossRef]
  17. Norland, "Norland Optical Adhesive 61," URL http://www.norlandprod.com/adhesives/ noa61pg2.html.
  18. A. Veltri, R. Caputo, C. Umeton, and A. V. Sukhov, "Model for the photoinduced formation of diffraction gratings in liquid-crystalline composite materials," Appl. Phys. Lett. 84, 3492-3494 (2004). URL http://link.aip.org/link/?APPLAB/84/3492/1.
    [CrossRef]
  19. M. Xu, H. P. Urbach, and D. K. G. de Boer, "Simulations of birefringent gratings as polarizing color separator in backlight for flat-panel displays," Opt. Express 15, 5789-5800 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5789.
    [CrossRef]
  20. URL http://www.math.tu-berlin.de/ilupack/.
  21. O. Schenk and K. Gartner, "Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO," J. Future Generation Computer Systems 20, 475-487 (2004).
    [CrossRef]
  22. O. Schenk and K. Gartner, "On fast factorization pivoting methods for symmetric indefinite systems," Elec. Trans. Numer. Anal. 23, 158-179 (2006).
  23. R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, and H. J. Cornelissen, "Short period holographic structures for backlight display applications," Opt. Express 15, 10,540 - 10,552 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-17-10540.

2006

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

O. Schenk and K. Gartner, "On fast factorization pivoting methods for symmetric indefinite systems," Elec. Trans. Numer. Anal. 23, 158-179 (2006).

2004

O. Schenk and K. Gartner, "Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO," J. Future Generation Computer Systems 20, 475-487 (2004).
[CrossRef]

2002

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
[CrossRef]

2000

R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
[CrossRef]

1998

L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
[CrossRef]

1996

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

J. B. Harris, T. W. Preist, E. L. Wood, and J. R. Sambles, "Conical diffraction from multicoated gratings containing uniaxial materials," J. Opt. Soc. Am. A 13, 803 (1996).
[CrossRef]

1990

1987

1983

K. Rokushima and J. Yamakita, "Analysis of anisotroic dielectric gratings," J. Opt. Soc. Am. A 73, 901 (1983).
[CrossRef]

Adams, W. W.

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

Bunning, T. J.

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

Caputo, R.

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
[CrossRef]

De Sio, L.

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

Gartner, K.

O. Schenk and K. Gartner, "On fast factorization pivoting methods for symmetric indefinite systems," Elec. Trans. Numer. Anal. 23, 158-179 (2006).

O. Schenk and K. Gartner, "Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO," J. Future Generation Computer Systems 20, 475-487 (2004).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Harris, J. B.

Karapinar, R.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
[CrossRef]

Li, L.

L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
[CrossRef]

Lucchetta, D. E.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
[CrossRef]

Manni, A.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
[CrossRef]

Mori, S.

Mukai, K.

Natatajan, L. V.

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

Preist, T. W.

Rokushima, K.

Sambles, J. R.

Schenk, O.

O. Schenk and K. Gartner, "On fast factorization pivoting methods for symmetric indefinite systems," Elec. Trans. Numer. Anal. 23, 158-179 (2006).

O. Schenk and K. Gartner, "Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO," J. Future Generation Computer Systems 20, 475-487 (2004).
[CrossRef]

Simoni, F.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
[CrossRef]

Sukhov, A. V.

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
[CrossRef]

Sutherland, R. L.

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

Tondiglia, V. P.

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

Umeton, C. P.

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
[CrossRef]

Ushakov, R. F.

R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
[CrossRef]

Veltri, A.

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

Wood, E. L.

Yamakita, J.

Elec. Trans. Numer. Anal.

O. Schenk and K. Gartner, "On fast factorization pivoting methods for symmetric indefinite systems," Elec. Trans. Numer. Anal. 23, 158-179 (2006).

J. Appl. Phys.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, "Phase-only modulation by nanosized polymerdispersed liquid crystals," J. Appl. Phys. 91, 6060 - 6065 (2002).
[CrossRef]

J. Display Technology

R. Caputo, L. De Sio, A. Veltri, C. P. Umeton, and A. V. Sukhov, "POLICRYPS switchable holographic grating: a promising grating electro-optical pixel for high resolution display application," J. Display Technology,  2, 38-51 (2006).
[CrossRef]

J. Exp. Theor. Phys.

R. Caputo, A. V. Sukhov, C. P. Umeton, and R. F. Ushakov, "Formation of a grating of submicron nematic layers by photopolymerization of nematic-containing mixtures," J. Exp. Theor. Phys. 91, 1190-1197 (2000).
[CrossRef]

J. Future Generation Computer Systems

O. Schenk and K. Gartner, "Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO," J. Future Generation Computer Systems 20, 475-487 (2004).
[CrossRef]

J. Mod. Opt.

L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313 (1998).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

R. L. Sutherland, V. P. Tondiglia, L. V. Natatajan, T. J. Bunning, and W. W. Adams, "Electro-Optical Switching Characteristics of Volume Holograms in Polymer Dispersed Liquid Crystals," J. Nonlinear Opt. Phys. Mater. 5, 89 (1996).

J. Opt. Soc. Am. A

Other

R. Caputo, L. De Sio, M. J. J. Jak, E. J. Hornix, D. K. G. de Boer, and H. J. Cornelissen, "Short period holographic structures for backlight display applications," Opt. Express 15, 10,540 - 10,552 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-17-10540.

G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035 - 1047 (1997). URL http://link.aps.org/abstract/PRE/v55/p1035.
[CrossRef]

X. Wei, "Three Dimensional Rigorous Model for Optical Scattering Problems," Ph.D. thesis, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft (2006). URL http://www.optica.tn.tudelft.nl/publications/summary/wei.asp.

X. Wei, A. J. Wachters, and H. P. Urbach, "Finite-element model for three-dimensional optical scattering problems," J. Opt. Soc. Am. A 24, 866-881 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=josaa-24-3-866.
[CrossRef]

Norland, "Norland Optical Adhesive 61," URL http://www.norlandprod.com/adhesives/ noa61pg2.html.

A. Veltri, R. Caputo, C. Umeton, and A. V. Sukhov, "Model for the photoinduced formation of diffraction gratings in liquid-crystalline composite materials," Appl. Phys. Lett. 84, 3492-3494 (2004). URL http://link.aip.org/link/?APPLAB/84/3492/1.
[CrossRef]

M. Xu, H. P. Urbach, and D. K. G. de Boer, "Simulations of birefringent gratings as polarizing color separator in backlight for flat-panel displays," Opt. Express 15, 5789-5800 (2007). URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-9-5789.
[CrossRef]

URL http://www.math.tu-berlin.de/ilupack/.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969). URL http://adsabs.harvard.edu/abs/1969BSTJ.48.2909K.

J. Margerum, A. Lackner, E. Ramos, G. Smith, N. Vaz, J. Kohler, and C. Allison, "Polymer dispersed liquid crystal film devices," U.S. Patent (1992).

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, "Development of a new kind of switchable holographic grating made of liquid-crystal films separated by slices of polymeric material," Opt. Lett. 29, 1261- 1263 (2004). URL http://www.opticsinfobase.org/abstract.cfm?URI=jdt-2-1-38.
[CrossRef]

L. De Sio, R. Caputo, A. De Luca, A. Veltri, C. Umeton, and A. V. Sukhov, "In situ optical control and stabilization of the curing process of holographic gratings with a nematic film-polymer-slice sequence structure," Appl. Opt. 45, 3721 - 3727 (2006). URL http://www.opticsinfobase.org/abstract.cfm? URI=ao-45-16-3721.
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

(a) Coordinate system and angles θ and ϕ ; (b) Calculated x-component of the dielectric modulation; (c) Cross-section of the grating geometry and wave propagationg direction of TM polarization. Respectively, k TM or k TE indicates the wave vector of the TM or TE polarization and Ŝ is the unit vector along the Poynting vector of the TM polarized wave.

Fig. 2.
Fig. 2.

(a)Bragg condition in (x, z)-plane; (b)Bragg condition in 3D space.

Fig. 3.
Fig. 3.

Experimental set-up for both normal and conical incidence.

Fig. 4.
Fig. 4.

The diffraction efficiency of TM polarization at normal incidence, i.e. ϕ i =0° and 0°≤θ i ≤30° for (a) red light (633 nm) and (b) green light (532 nm). The star-dashed lines are experimental measurements and the dot-solid lines are calculations. In the legend, -1T denotes the -1 st diffracted order of the transmitted field, etc.

Fig. 5.
Fig. 5.

Conical incidence configuration: the rays of incidence form a cone with respect to the normal of the POLICRYPS grating.

Fig. 6.
Fig. 6.

The diffraction efficiency of TM polarization at conical incidence, for 0°≤ϕ i ≤70° and θ i θ B , for (a) red light (633 nm) θ i =15° and for (b) green light (532 nm) θ i =13°. The star-dashed lines are experimental measurements and the dot-solid lines are simulations. In the legend, -1T denotes the -1 st diffracted order of the transmitted field, etc.

Fig. 7.
Fig. 7.

Polarization analysis (based on simulation results) of the diffracted orders at the conical mount for 633 nm red light with (a) TM polarization analyzer and (b) TE polarization analyzer. The dash-dot lines are the same plots of the simulations results as in Fig. 6(a) and are included here as a reference for the two decomposed linear polarization in each order. In the legend, -1T denotes the -1 st diffracted order of the transmitted field, etc.

Fig. 8.
Fig. 8.

(a) Measured angular distribution (θ d ,ϕ d ) of the diffraction efficiency of the -1 st diffracted order for the reading beam of 633 nm when the incident angles (θ i ,ϕ i ) follow the Bragg condition as discussed in Sec. 3.2. (b) Diffraction efficiency along the center (accordingly the incidence with Bragg angles marked with stars) and edges (accordingly incidence deviating from the Bragg condition marked with triangles (-2°) and with circles (+2°)) of the ribbon in (a). The solid lines indicate simulated results, and the dashed lines experimental measurements.

Tables (1)

Tables Icon

Table 1. The dielectric permittivity of the vertical slices which parallel to the z-axis, into which the NLC has been divided to approximate the calculated profile shown in Fig. 1(b).

Equations (23)

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

ε x ( ξ ) = [ ε + ( ε eff ε ) ν ¯ ( ξ ) ] σ ( ξ ) + ε pol ν ( ξ ) ,
ε x ( ξ ) = ε σ ( ξ ) .
ε x ( ξ ) = ε pol ν ( ξ ) .
ε x ( ξ ) = ε eff σ ( ξ ) + ε pol ( ξ ) ν ( ξ ) .
E = ( E x E y E z ) = A ( cos θ i 0 sin θ i ) , TM Polarization
E = ( E x E y E z ) = A ( 0 1 0 ) , TE Polarization
ε = = ( ε xx 0 0 0 ε yy 0 0 0 ε zz ) ,
i ω μ 0 H y = i · [ 1 D Q T x ( k y E y ω 0 μ 0 H y ) ] + i · [ 1 D M z ( k y E y ω μ 0 H y ) ] ,
i ω ε 0 ε yy E y = i k y ω μ 0 · [ 1 D N x ( k y E y ω μ 0 H y ) ] i k y ω μ 0 · [ 1 D Q z ( k y E y ω μ 0 H y ) ] i ω μ 0 Δ E y ,
= ( x z ) ,
D = ( ω 2 ε 0 μ 0 ε xx k y 2 ) ( ω 2 ε 0 μ 0 ε zz k y 2 ) ,
N = ( ω 2 ε 0 μ 0 ε zz k y 2 0 0 ω 2 ε 0 μ 0 ε xx k y 2 ) ,
Q = N ( 0 1 1 0 ) = ( 0 ( ω 2 ε 0 μ 0 ε zz k y 2 ) ω 2 ε 0 μ 0 ε xx k y 2 0 ) .
M = D N 1 = ( ω 2 ε 0 μ 0 ε xx k y 2 0 0 ω 2 ε 0 μ 0 ε zz k y 2 ) ,
k = ( k x k y k z ) = k o n i ( sin θ i cos ϕ i sin θ i sin ϕ i cos θ i ) ,
2 k x · Λ = 2 π · m
sin θ i cos ϕ i = m · λ 2 n i Λ .
sin θ B = λ 2 n i Λ , for ϕ i = 0 ° ,
sin θ B = λ 2 n i Λ cos ϕ i , for ϕ i 0 ° .
tan α = tan θ sin ϕ ,
sin β = sin θ cos ϕ .
n d cos ϕ d sin θ d = n i cos ϕ i sin θ i + m λ Λ ,
n d sin ϕ d sin θ d = n i sin ϕ i sin θ i .

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