Abstract

The development of the dual-band IR imaging polarimetry creates the need for achromatic phase retarder used in dual-band. Dielectric grating with the period smaller than the illuminating wavelength presents a strong form-birefringence. With this feature, the combination of several subwavelength gratings can be used as achromatic phase retarders. We proposed a combination of 4 subwavelength structured gratings (SWGs) used as an achromatic quarter-wave plate (QWP) applied to MWIR & LWIR bandwidths. Design method using effective medium theory and optimization algorithms is described in detail. The simulation results led to the possibility of an dual-band achromatic QWP whose retardance deviates from 90° by <±0.75° with the fast axis unfixed and by <±1.35° with the fast axis fixed over MWIR(3-5μm) & LWIR(8-12μm) bandwiths.

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References

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    [CrossRef]
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    [CrossRef]
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2009 (2)

G. G. Kang, Q. F. Tan, and G. F. Jin, “Optimal Design of an Achromatic Angle-Insensitive Phase Retarder Used in MWIR Imaging Polarimetry,” Chin. Phys. Lett. 26(074218), 1–4 (2009).

I. Yamada, K. Takano, M. Hangyo, M. Saito, and W. Watanabe, “Terahertz wire-grid polarizers with micrometer-pitch Al gratings,” Opt. Lett. 34(3), 274–276 (2009).
[CrossRef] [PubMed]

2006 (2)

J. B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31(2), 265–267 (2006).
[CrossRef] [PubMed]

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

2004 (2)

2003 (1)

2001 (1)

1998 (1)

1997 (1)

1995 (1)

1975 (1)

1949 (1)

G. Destriau and J. Prouteau, “Realisation d’um quart d’onde quasi acromatique par juxtaposition de deux lames cristallines de meme nature,” J. Phys. Radium 10(2), 53–55 (1949).
[CrossRef]

1941 (2)

R. C. Jones, “A New Calculus for the Treatment of Optical Systems I. Description and Discussion of the Calculus,” J. Opt. Soc. Am. A 31(7), 488–493 (1941).
[CrossRef]

R. C. Jones, “A New Calculus for the Treatment of Optical Systems II. Proof of Three General Equivalence Theorems,” J. Opt. Soc. Am. A 31, 493–499 (1941).

Azzam, R. M. A.

Bokor, N.

Davidson, N.

Dereniak, E. L.

Descour, M. R.

Destriau, G.

G. Destriau and J. Prouteau, “Realisation d’um quart d’onde quasi acromatique par juxtaposition de deux lames cristallines de meme nature,” J. Phys. Radium 10(2), 53–55 (1949).
[CrossRef]

Fainman, Y.

Frey, B. J.

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Friesem, A. A.

Gallot, G.

Hangyo, M.

Hasman, E.

Hirai, Y.

Hugonin, J. P.

Iwata, K.

Jin, G. F.

G. G. Kang, Q. F. Tan, and G. F. Jin, “Optimal Design of an Achromatic Angle-Insensitive Phase Retarder Used in MWIR Imaging Polarimetry,” Chin. Phys. Lett. 26(074218), 1–4 (2009).

Jones, R. C.

R. C. Jones, “A New Calculus for the Treatment of Optical Systems I. Description and Discussion of the Calculus,” J. Opt. Soc. Am. A 31(7), 488–493 (1941).
[CrossRef]

R. C. Jones, “A New Calculus for the Treatment of Optical Systems II. Proof of Three General Equivalence Theorems,” J. Opt. Soc. Am. A 31, 493–499 (1941).

Kang, G. G.

G. G. Kang, Q. F. Tan, and G. F. Jin, “Optimal Design of an Achromatic Angle-Insensitive Phase Retarder Used in MWIR Imaging Polarimetry,” Chin. Phys. Lett. 26(074218), 1–4 (2009).

Kikuta, H.

Lalanne, P.

Leviton, D. B.

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Madison, T. J.

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Masson, J. B.

Ohira, Y.

Okano, M.

Prouteau, J.

G. Destriau and J. Prouteau, “Realisation d’um quart d’onde quasi acromatique par juxtaposition de deux lames cristallines de meme nature,” J. Phys. Radium 10(2), 53–55 (1949).
[CrossRef]

Richter, I.

Saito, M.

Scholl, J. F.

Shechter, R.

Spinu, C. L.

Sun, P. C.

Takano, K.

Tan, Q. F.

G. G. Kang, Q. F. Tan, and G. F. Jin, “Optimal Design of an Achromatic Angle-Insensitive Phase Retarder Used in MWIR Imaging Polarimetry,” Chin. Phys. Lett. 26(074218), 1–4 (2009).

Tebow, C. P.

Title, A. M.

Volin, C. E.

Watanabe, W.

Xu, F.

Yamada, I.

Yamamoto, K.

Yotsuya, T.

Appl. Opt. (6)

Chin. Phys. Lett. (1)

G. G. Kang, Q. F. Tan, and G. F. Jin, “Optimal Design of an Achromatic Angle-Insensitive Phase Retarder Used in MWIR Imaging Polarimetry,” Chin. Phys. Lett. 26(074218), 1–4 (2009).

J. Opt. Soc. Am. A (4)

P. Lalanne and J. P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15(7), 1843–1851 (1998).
[CrossRef]

R. C. Jones, “A New Calculus for the Treatment of Optical Systems I. Description and Discussion of the Calculus,” J. Opt. Soc. Am. A 31(7), 488–493 (1941).
[CrossRef]

R. C. Jones, “A New Calculus for the Treatment of Optical Systems II. Proof of Three General Equivalence Theorems,” J. Opt. Soc. Am. A 31, 493–499 (1941).

R. M. A. Azzam and C. L. Spinu, “Achromatic angle-insensitive infraredquarter-wave retarder based on total internal reflection at the Si–SiO2 interface,” J. Opt. Soc. Am. A 21, 2019–2022 (2004).
[CrossRef]

J. Phys. Radium (1)

G. Destriau and J. Prouteau, “Realisation d’um quart d’onde quasi acromatique par juxtaposition de deux lames cristallines de meme nature,” J. Phys. Radium 10(2), 53–55 (1949).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006).
[CrossRef]

Other (2)

D. Kalyanmoy, Muiti-Objective Optimization Using Evolutionary Algorithms (John Wiley & Sons, 2009).

Instrument networks discussion, “Infrared Spectrum transmittance”(Instrument networks, 2009) http://bbs.instrument.com.cn/shtml/20090906/2098092/

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of a dielectric grating. It has a period of d, groove depth of h and a filling factor of f. The width of the ridge is fd in case n1<n2

Fig. 2
Fig. 2

Birefringence of CdS, CdSe and SWG

Fig. 3
Fig. 3

Birefringence spectra curves with respect to different grating periods

Fig. 4
Fig. 4

Schematic diagram for the proposed combination of 4 SWGs. K is the grating vector and θ is the orientation angle.

Fig. 5
Fig. 5

Retardance spectra curves with respect to different number of gratings

Fig. 6
Fig. 6

Calculated results of achromatic QWP with the fast axis unfixed (a) Phase retardance dispersion curve. (b) Orientation angle dispersion curve.

Fig. 7
Fig. 7

Calculated results of achromatic QWP with the fast axis fixed (a) Phase retardance dispersion curve. (b) Orientation angle dispersion curve.

Tables (2)

Tables Icon

Tab.1 Parameters of QWP with its fast axis unfixed

Tables Icon

Tab. 2 Parameters of QWP with its fast axis fixed

Equations (17)

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

n T E ( 0 ) = [ f n 2 2 + ( 1 f ) n 1 2 ] 1 / 2
n T M ( 0 ) = [ f n 2 2 + ( 1 f ) n 1 2 ] 1 / 2
n T E ( 2 ) = [ ( n T E ( 0 ) ) 2 + 1 3 ( d λ ) 2 π 2 f 2 ( 1 f ) 2 ( n 2 2 n 1 2 ) 2 ] 1 / 2
n T M ( 2 ) = [ ( n T M ( 0 ) ) 2 + 1 3 ( d λ ) 2 π 2 f 2 ( 1 f ) 2 ( n 2 2 n 1 2 ) 2 ( n T M ( 0 ) ) 6 ( n T E ( 0 ) ) 2 ] 1 / 2
ϕ ( λ ) = 2 π λ Δ n ( λ ) h
Δ n ( λ ) = ϕ 2 π h λ
J ( ϕ , θ ) = [ cos ϕ / 2 + i cos 2 θ sin ϕ / 2 i sin 2 θ sin ϕ / 2 i sin 2 θ sin ϕ / 2 cos ϕ / 2 i cos 2 θ sin ϕ / 2 ]
J = [ a b b a ]
i = 1 n J ( ϕ i , θ i ) = R ( ω ¯ ) J ( ϕ ¯ , θ ¯ ) = [ A B B A ]
R ( ω ¯ ) = [ cos ω ¯ sin ω ¯ sin ω ¯ cos ω ¯ ]
A = cos ω ¯ cos ϕ ¯ 2 + i sin ϕ ¯ 2 [ cos ω ¯ cos 2 θ ¯ sin ω ¯ sin 2 θ ¯ ]
B = sin ω ¯ cos ϕ ¯ 2 + i sin ϕ ¯ 2 [ cos ω ¯ sin 2 θ ¯ + sin ω ¯ cos 2 θ ¯ ]
tan 2 ϕ ¯ 2 = | Im A | 2 + | Im B | 2 | Re A | 2 + | Re B | 2
tan 2 θ ¯ = Im B + Re B Re A Im A Im A Re B Re A Im B
M i n { f u n c t i o n 1 = λ | ϕ λ ¯ ( h i , θ i ) π / 2 | f u n c t i o n 2 = max | ϕ λ ¯ ( h i , θ i ) | λ ( 3 μ m 5 μ m ) ( 8 μ m 12 μ m ) s . t .0 < h i < fabrication limits
M i n { f u n c t i o n 1 = λ | ϕ λ ¯ ( h i , θ i ) π / 2 | f u n c t i o n 2 = max | ϕ λ ¯ ( h i , θ i ) | f u n c t i o n 3 = S T D [ θ λ ¯ ( h i , θ i ) ] λ ( 3 μ m 5 μ m ) ( 8 μ m 12 μ m ) s . t .0 < h i < fabrication limits
d t h = λ n 1 + n 2

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