Abstract

We have designed a high-efficiency array generator composed of subwavelength grooves etched in a GaAs substrate for operation at 4.5μm. The method used combines rigorous coupled wave analysis with an optimization algorithm. The optimized beam splitter has both a high efficiency (96%) and a good intensity uniformity (0.2%). The fabrication error tolerances are numerically calculated, and it is shown that this subwavelength array generator could be fabricated with current electron beam writers and inductively coupled plasma etching. Finally, we studied the effect of a simple and realistic antireflection coating on the performance of the beam splitter.

© 2011 Optical Society of America

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    [CrossRef]

2010

2009

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

2008

2007

2006

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

2004

1999

1997

1996

1995

1993

E. Sidick, “Design and rigorous analysis of high-efficiency array generators,” Appl. Opt. 32, 2599–2605 (1993).
[CrossRef] [PubMed]

H. Haidner, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475(1993).
[CrossRef]

1992

1991

1986

J. Leger, “Coherent beam addition of GaAlAs lasers by binary phase gratings,” Appl. Phys. Lett. 48, 888–890(1986).
[CrossRef]

1985

R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36(1985).
[CrossRef]

K. Schittkowski, “NLQPL: a FORTRAN-subroutine solving constrained nonlinear programming problems,” Ann. Oper. Res. 5, 485–500 (1985).

1977

H. Dammann, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Bansropun, S.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

Cassette, S.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

Chang, C. H.

Dammann, H.

H. Dammann, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Ehbets, P.

Farn, M.

Freese, W.

Gao, L.

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

Granet, G.

Haidner, H.

H. Haidner, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475(1993).
[CrossRef]

Huet, O.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

Hugonin, J. P.

J. P. Hugonin and P. Lalanne, Reticolo software for grating analysis (Institut d’Optique, 2005).

Hutley, M.

P. Lalanne and M. Hutley, Artificial Media Optical Properties: Subwavelength Scale (Marcel Dekker, 2003).

Kikuta, H.

Lalanne, P.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

P. Lalanne, “Depth dependence of the effective properties of subwavelength gratings,” J. Opt. Soc. Am. A 14, 450–458(1997).
[CrossRef]

P. Lalanne, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

P. Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

P. Lalanne and M. Hutley, Artificial Media Optical Properties: Subwavelength Scale (Marcel Dekker, 2003).

J. P. Hugonin and P. Lalanne, Reticolo software for grating analysis (Institut d’Optique, 2005).

Lee, M.-S. L.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

M.-S. L. Lee, “Blazed binary diffractive gratings with antireflection coating for improved operation at 10.6 μm,” Opt. Eng. 43, 2583–2588 (2004).
[CrossRef]

Leger, J.

J. Leger, “Coherent beam addition of GaAlAs lasers by binary phase gratings,” Appl. Phys. Lett. 48, 888–890(1986).
[CrossRef]

Li, E.

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

Li, L.

Loiseaux, B.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

Lu, F.

Miller, J.

Moharam, M. G.

Nordin, G. P.

Pabœuf, D.

Päivänranta, B.

Petit, R.

R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36(1985).
[CrossRef]

Prongué, D.

Ribot, C.

Sauvan, C.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

C. Sauvan, “Broadband blazing with artificial dielectrics,” Opt. Lett. 29, 1593–1595 (2004).
[CrossRef] [PubMed]

Schittkowski, K.

K. Schittkowski, “NLQPL: a FORTRAN-subroutine solving constrained nonlinear programming problems,” Ann. Oper. Res. 5, 485–500 (1985).

Shen, S.-W.

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

Sidick, E.

Stork, W.

Tong, H.-P.

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

Tyan, R.-C.

Wood, A. P.

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

Yan, S.

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

Yi, D.

Zhou, C.

Zhou, C.-L.

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

Ann. Oper. Res.

K. Schittkowski, “NLQPL: a FORTRAN-subroutine solving constrained nonlinear programming problems,” Ann. Oper. Res. 5, 485–500 (1985).

Appl. Opt.

Appl. Phys. Lett.

J. Leger, “Coherent beam addition of GaAlAs lasers by binary phase gratings,” Appl. Phys. Lett. 48, 888–890(1986).
[CrossRef]

Electromagnetics

R. Petit, “Homogenization techniques as applied in the electromagnetic theory of gratings,” Electromagnetics 5, 17–36(1985).
[CrossRef]

Infrared Phys.

H. Haidner, “Diffraction grating with rectangular grooves exceeding 80% diffraction efficiency,” Infrared Phys. 34, 467–475(1993).
[CrossRef]

J. Mod. Opt.

P. Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Acta

H. Dammann, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Eng.

M.-S. L. Lee, “Blazed binary diffractive gratings with antireflection coating for improved operation at 10.6 μm,” Opt. Eng. 43, 2583–2588 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

S. Yan, E. Li, C.-L. Zhou, S.-W. Shen, L. Gao, and H.-P. Tong, “Designing high efficiency uniform-intensity splitter with binary-phase subwavelength structure,” Proc. SPIE 7133, 713334 (2009).
[CrossRef]

M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. P. Wood, C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffractive optics,” Proc. SPIE 6029, 602919 (2006).
[CrossRef]

Other

J. P. Hugonin and P. Lalanne, Reticolo software for grating analysis (Institut d’Optique, 2005).

P. Lalanne and M. Hutley, Artificial Media Optical Properties: Subwavelength Scale (Marcel Dekker, 2003).

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Figures (11)

Fig. 1
Fig. 1

Geometry of the binary-phase grating problem.

Fig. 2
Fig. 2

Solid curve, one period of the ideal continuous phase profile to separate seven beams; dots, discretized phase levels.

Fig. 3
Fig. 3

Width dependence of the effective index of a subwavelength ridge for TE polarization.

Fig. 4
Fig. 4

Profile of a period of the subwavelength binary grating.

Fig. 5
Fig. 5

Diffracted orders from the continuous profile and the subwavelength grating. Squares, continuous profile; dots, subwavelength grating before optimization; crosses, subwavelength grating after optimization.

Fig. 6
Fig. 6

Ridge widths of the initial (circles) and optimized (crosses) subwavelength profiles.

Fig. 7
Fig. 7

Dependence of the subwavelength grating on ridge depth error. Below, central diffraction orders for Δ h = 400 nm (A), Δ h = 0 nm (B), and Δ h = 400 nm (C).

Fig. 8
Fig. 8

Dependence of the subwavelength grating on the ridge positioning error.

Fig. 9
Fig. 9

Geometry of the AR structure for the subwavelength grating.

Fig. 10
Fig. 10

Dependence of the subwavelength grating efficiency, uniformity, and reflectivity on AR layer thickness errors.

Fig. 11
Fig. 11

Left, dependence of the subwavelength grating efficiency and uniformity on illuminating wavelength detuning; right, dependence of the subwavelength efficiency and uniformity grating on misalignment.

Tables (2)

Tables Icon

Table 1 Performances of the Ideal Continuous Phase Profile Compared to the Subwavelength Binary Profile and the Optimized Subwavelength Binary Profile

Tables Icon

Table 2 AR Coating Optimization

Equations (6)

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

η = i = M M I i / i I i ,
U = ( max ( I i ) min ( I i ) ) / ( max ( I i ) + min ( I i ) ) ,
Λ S < λ max ( n 1 , n 2 ) + n 1 sin ( θ max ) ,
h = α λ 2 ( n max n min ) = 2.04 μm ,
f ( L ) = [ i = M M | I i η N | ] P η Q ,
R = 1 i I i = 19.9 % .

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