Abstract

A simple and efficient solution for coupling a collimated light beam into a thin light guide is presented. The approach is based on two gratings, with their grating lines perpendicular to each other, fabricated into the opposite surfaces of the light guide. The presented numerical simulation shows that an optimized double-sided solution for unpolarized light enables around 2–7 times higher incoupling efficiencies than what is possible with conventional solution based on only one grating. Experimental verification is made by using UV-replicated binary gratings on both sides of a PMMA foil.

© 2007 Optical Society of America

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References

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2006

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2003

2002

2001

1997

1996

1994

1993

L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40, 553-573 (1993).
[CrossRef]

Aoyama, S.

Cambril, E.

Chavel, P.

Chien, K.

Cornelissen, H.

de Beaucoudrey, N.

Fujieda, I.

Funamoto, A.

Gaylord, T. K.

Glytsis, E. N.

Honkanen, M.

Imanaka, K.

Jefimovs, K.

Jiang, J.

Kaikuranta, T.

Kuittinen, M.

Laakkonen, P.

Lautanen, J.

Levola, T.

T. Levola, "Diffractive optics for virtual reality displays," J. Soc. Inf. Disp. 15, 467-475 (2006).
[CrossRef]

Li, L.

Maikisch, J. S.

Miller, M.

Noponen, E.

Nordin, G. P.

Parikka, M.

Shieh, H. D.

Siitonen, S.

Tervo, J.

Tossavainen, N.

Turunen, J.

Vahimaa, P.

Wang, B.

Wu, S.

Appl. Opt.

K. Chien and H. D. Shieh, "Time-multiplexed three-dimensional displays based on directional backlights with fast-switching liquid-crystal displays," Appl. Opt. 45, 3106-3110 (2006).
[CrossRef] [PubMed]

K. Chien, H. D. Shieh, and H. Cornelissen, "Polarized backlight based on selective total internal reflection at microgrooves," Appl. Opt. 43, 4672-4676 (2004).
[CrossRef] [PubMed]

K. Chien and H. D. Shieh, "Design and fabrication of an integrated polarized light guide for liquid-crystal-display illumination," Appl. Opt. 43, 1803-1834 (2004).
[CrossRef]

S. Aoyama, A. Funamoto, and K. Imanaka, "Hybrid normal-reverse prism coupler for light-emitting diode backlight systems," Appl. Opt. 45, 7273-7278 (2006).
[CrossRef] [PubMed]

M. Miller, N. de Beaucoudrey, P. Chavel, J. Turunen, and E. Cambril, "Design and fabrication of slanted binary surface relief gratings for a planar optical interconnection," Appl. Opt. 36, 5717-5727 (1997).
[CrossRef] [PubMed]

S. Wu, T. K. Gaylord, J. S. Maikisch, and E. N. Glytsis, "Optimization of anisotropically etched silicon surface relief gratings for substrate-mode optical interconnects," Appl. Opt. 45, 15-21 (2006).
[CrossRef] [PubMed]

I. Fujieda, "Theoretical considerations for arrayed waveguide display," Appl. Opt. 41, 1391-1399 (2002).
[CrossRef] [PubMed]

M. Parikka, T. Kaikuranta, P. Laakkonen, J. Lautanen, J. Tervo, M. Honkanen, M. Kuittinen, and J. Turunen, "Deterministic diffractive diffusers for displays," Appl. Opt. 40, 2239-2246 (2001).
[CrossRef]

S. Siitonen, P. Laakkonen, P. Vahimaa, K. Jefimovs, M. Kuittinen, M. Parikka, K. M¨onkk¨onen, and A. Orpana, "Coupling of light from an LED into a thin light guide by diffractive gratings," Appl. Opt. 43, 5631-5636 (2004).
[CrossRef] [PubMed]

S. Siitonen, P. Laakkonen, P. Vahimaa, M. Kuittinen, and N. Tossavainen, "White LED light coupling into light guides with diffraction gratings," Appl. Opt. 45, 2623-2630 (2006).
[CrossRef] [PubMed]

J. Mod. Opt.

L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40, 553-573 (1993).
[CrossRef]

J. Opt. Soc. Am. A

J. Soc. Inf. Disp.

T. Levola, "Diffractive optics for virtual reality displays," J. Soc. Inf. Disp. 15, 467-475 (2006).
[CrossRef]

Opt. Express

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Figures (7)

Fig. 1.
Fig. 1.

The geometry of the two sided incoupler in which the grating lines are perpendicularly oriented.

Fig. 2.
Fig. 2.

Ray propagation inside the grating are for rays with efficiency > 1 % (a) and with efficiency < 0.2 % (b). The total number of rays in (b) is 45.

Fig. 3.
Fig. 3.

Incoupled diffraction efficiency chart for the double-sided grating as a function of the position with the light guide thickness of L = 0.75 mm and the grating size 6 mm × 6 mm with (a) TE-polarization input and (b) TM-polarization input.

Fig. 4.
Fig. 4.

Incoupled diffraction efficiency chart for a double-sided gratings as a function of the position with the light guide thickness of L = 0.375 mm and the grating size 6 mm × 6 mm with (a) TE-polarization input and (b) TM-polarization input.

Fig. 5.
Fig. 5.

A layout of double-sided incoupler structure (above) and the cross section SEM pictures of replicated gratings: The incoupler grating is on the top surface (left) and the perpendicular grating is on the bottom surface (right).

Fig. 6.
Fig. 6.

Integrating sphere measurement geometry: (a) reflected rays and (b) transmitted rays.

Fig. 7.
Fig. 7.

A plastic foil of thickness L=0.63 mm with a double-sided 6 mm × 6 mm replicated grating, illuminated with a HeNe laser beam.

Tables (3)

Tables Icon

Table 1. Complex amplitudes Ei , i=(x, y, z), diffraction efficiencies η g, and ray efficiencies ηr (upper table), and wave-vector components ki and propagation angles (lower table) for the rays 1–6 illustrated in Fig. 1. The rays marked with (*) are coupled into the light guide.

Tables Icon

Table 2. Computed and measured diffraction efficiencies of double-sided incoupler grating with the light guide thicknesses of 0.38 mm and 0.63 mm for TE-, TM- and unpolarized input light. Experimental incoupling efficiencies are calculated with η ic,m = 1−R mT m.

Tables Icon

Table 3. Same as Table 2 but for one-sided incoupler grating with the light guide thicknesses of 0.315 mm and 0.565 mm.

Equations (3)

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

θ = arccos ( k z k ) ,
φ = arctan ( k y k x ) .
η ic = 1 R T J ,

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