Abstract

Achromatic wave plates are ideal components for use with tunable and multiline laser systems, broadband sources, and in astronomical instrumentation. The present study deals with the design and characteristics of two different quarter-wave achromatic retarders in the 500–700 nm range, using a cascaded system of two birefringent plates. The first of these shows a variation of less than ±0.5°, whereas the second system shows a variation of ±4° where the azimuth remains constant. Finally, a comparison between the two systems is made. The succinct and simple Jones matrix formalism has been used to derive the general expression for the equivalent retardation and azimuth of the combinations. It appears that the proposed arrangement has the promise of producing good achromatic combinations.

© 2012 Optical Society of America

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References

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  1. S. Pancharatnam, “Achromatic combinations of birefringent plates, Part II. An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. 41A, 137–144 (1955).
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    [CrossRef]
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    [CrossRef]
  9. H. Kikuta, Y. Ohira, and K. Iwata, “Achromatic quarter-wave plates using the dispersion of form birefringence,” Appl. Opt. 36, 1566–1572 (1997).
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    [CrossRef]
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    [CrossRef]
  13. H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
    [CrossRef]
  14. A. V. Samoylov and V. S. Samoylov, “Achromatic and super-achromatic zero-order waveplates,” in Proceedings of Laser and Fiber-Optical Networks Modeling 2003 (IEEE, 2003), pp. 119–121.
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    [CrossRef]
  16. J. B. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. 31, 265–267 (2006).
    [CrossRef]
  17. A. Saha, K. Bhattacharya, and A. K. Chakraborty, “Reconfigurable achromatic half-wave and quarter-wave retarder in near infrared using crystalline quartz plates,” Opt. Eng. 50, 034004 (2011).
    [CrossRef]
  18. G. Destriau and J. Prouteau, “Realization of a quarter wave quasi achromatic juxtaposition of two crystal plates similar,” J. Phys. Radium 10, 53–55 (1949).
    [CrossRef]
  19. S. Chandrasekhar, “The dispersion and thermo-optic behaviour of vitreous silica,” Proc. Indian Acad. Sci. 34A, 275–282 (1951).

2011 (1)

A. Saha, K. Bhattacharya, and A. K. Chakraborty, “Reconfigurable achromatic half-wave and quarter-wave retarder in near infrared using crystalline quartz plates,” Opt. Eng. 50, 034004 (2011).
[CrossRef]

2008 (1)

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

2007 (1)

H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
[CrossRef]

2006 (1)

2003 (1)

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

2002 (1)

P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
[CrossRef]

2001 (1)

1998 (1)

P. Hariharan, “Broadband super-achromatic retarders,” Meas. Sci. Technol. 9, 1678–1681 (1998).
[CrossRef]

1997 (1)

1995 (1)

P. Hariharan, “Achromatic retarders using quartz and mica,” Meas. Sci. Technol. 6, 1078–1079 (1995).
[CrossRef]

1994 (1)

P. Hariharan and D. Malacara, “A simple achromatic half-wave retarder,” J. Mod. Opt. 41, 15–18 (1994).
[CrossRef]

1988 (1)

1971 (1)

1968 (1)

1967 (1)

D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
[CrossRef]

1955 (1)

S. Pancharatnam, “Achromatic combinations of birefringent plates, Part II. An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. 41A, 137–144 (1955).

1951 (1)

S. Chandrasekhar, “The dispersion and thermo-optic behaviour of vitreous silica,” Proc. Indian Acad. Sci. 34A, 275–282 (1951).

1949 (1)

G. Destriau and J. Prouteau, “Realization of a quarter wave quasi achromatic juxtaposition of two crystal plates similar,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Bachels, T.

H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
[CrossRef]

Beckers, J. M.

Benecke, C.

H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
[CrossRef]

Bhattacharya, K.

A. Saha, K. Bhattacharya, and A. K. Chakraborty, “Reconfigurable achromatic half-wave and quarter-wave retarder in near infrared using crystalline quartz plates,” Opt. Eng. 50, 034004 (2011).
[CrossRef]

Chakraborty, A. K.

A. Saha, K. Bhattacharya, and A. K. Chakraborty, “Reconfigurable achromatic half-wave and quarter-wave retarder in near infrared using crystalline quartz plates,” Opt. Eng. 50, 034004 (2011).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, “The dispersion and thermo-optic behaviour of vitreous silica,” Proc. Indian Acad. Sci. 34A, 275–282 (1951).

Clark, D.

D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
[CrossRef]

Destriau, G.

G. Destriau and J. Prouteau, “Realization of a quarter wave quasi achromatic juxtaposition of two crystal plates similar,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Gallot, G.

Hariharan, P.

P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
[CrossRef]

P. Hariharan, “Broadband super-achromatic retarders,” Meas. Sci. Technol. 9, 1678–1681 (1998).
[CrossRef]

P. Hariharan, “Achromatic retarders using quartz and mica,” Meas. Sci. Technol. 6, 1078–1079 (1995).
[CrossRef]

P. Hariharan and D. Malacara, “A simple achromatic half-wave retarder,” J. Mod. Opt. 41, 15–18 (1994).
[CrossRef]

Harris, S. E.

Hodgkinson, I.

Ibn-Elhaj, Md.

H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
[CrossRef]

Iwata, K.

Jin, G.-F.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Jordanov, B.

Karvinen, P.

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

Kikuta, H.

Kolev, D.

Korte, E. H.

Liu, H.-T.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Lu, S.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Malacara, D.

P. Hariharan and D. Malacara, “A simple achromatic half-wave retarder,” J. Mod. Opt. 41, 15–18 (1994).
[CrossRef]

Masson, J. B.

McIntyre, C. M.

Ohira, Y.

Pancharatnam, S.

S. Pancharatnam, “Achromatic combinations of birefringent plates, Part II. An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. 41A, 137–144 (1955).

Passilly, N.

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

Prouteau, J.

G. Destriau and J. Prouteau, “Realization of a quarter wave quasi achromatic juxtaposition of two crystal plates similar,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Saha, A.

A. Saha, K. Bhattacharya, and A. K. Chakraborty, “Reconfigurable achromatic half-wave and quarter-wave retarder in near infrared using crystalline quartz plates,” Opt. Eng. 50, 034004 (2011).
[CrossRef]

Samoylov, A. V.

A. V. Samoylov and V. S. Samoylov, “Achromatic and super-achromatic zero-order waveplates,” in Proceedings of Laser and Fiber-Optical Networks Modeling 2003 (IEEE, 2003), pp. 119–121.

Samoylov, V. S.

A. V. Samoylov and V. S. Samoylov, “Achromatic and super-achromatic zero-order waveplates,” in Proceedings of Laser and Fiber-Optical Networks Modeling 2003 (IEEE, 2003), pp. 119–121.

Seiberle, H.

H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
[CrossRef]

Tervo, J.

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

Tsankov, D.

Turunen, J.

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

Ventola, K.

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

Wu, Q. H.

Yan, Y.-B.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Yi, D.-E.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Appl. Opt. (2)

Appl. Spectrosc. (1)

IEICE Trans. Electron. (1)

H. Seiberle, T. Bachels, C. Benecke, and Md. Ibn-Elhaj, “Volume photo-aligned retarders,” IEICE Trans. Electron. E90-C, 2088–2093 (2007).
[CrossRef]

J. Mod. Opt. (2)

P. Hariharan and D. Malacara, “A simple achromatic half-wave retarder,” J. Mod. Opt. 41, 15–18 (1994).
[CrossRef]

D. Clark, “Achromatic halfwave plates and linear polarization rotators,” J. Mod. Opt. 14, 343–350 (1967).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

N. Passilly, K. Ventola, P. Karvinen, J. Turunen, and J. Tervo, “Achromatic phase retardation by subwavelength gratings in total internal reflection,” J. Opt. A: Pure Appl. Opt. 10, 015001 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Radium (1)

G. Destriau and J. Prouteau, “Realization of a quarter wave quasi achromatic juxtaposition of two crystal plates similar,” J. Phys. Radium 10, 53–55 (1949).
[CrossRef]

Meas. Sci. Technol. (2)

P. Hariharan, “Broadband super-achromatic retarders,” Meas. Sci. Technol. 9, 1678–1681 (1998).
[CrossRef]

P. Hariharan, “Achromatic retarders using quartz and mica,” Meas. Sci. Technol. 6, 1078–1079 (1995).
[CrossRef]

Opt. Commun. (1)

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49–55 (2003).
[CrossRef]

Opt. Eng. (1)

A. Saha, K. Bhattacharya, and A. K. Chakraborty, “Reconfigurable achromatic half-wave and quarter-wave retarder in near infrared using crystalline quartz plates,” Opt. Eng. 50, 034004 (2011).
[CrossRef]

Opt. Laser Technol. (1)

P. Hariharan, “Broad-band apochromatic retarder: choice of materials,” Opt. Laser Technol. 34, 509–511 (2002).
[CrossRef]

Opt. Lett. (1)

Proc. Indian Acad. Sci. (2)

S. Pancharatnam, “Achromatic combinations of birefringent plates, Part II. An achromatic quarter-wave plate,” Proc. Indian Acad. Sci. 41A, 137–144 (1955).

S. Chandrasekhar, “The dispersion and thermo-optic behaviour of vitreous silica,” Proc. Indian Acad. Sci. 34A, 275–282 (1951).

Other (1)

A. V. Samoylov and V. S. Samoylov, “Achromatic and super-achromatic zero-order waveplates,” in Proceedings of Laser and Fiber-Optical Networks Modeling 2003 (IEEE, 2003), pp. 119–121.

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Figures (8)

Fig. 1.
Fig. 1.

Configuration of the two birefringent plates. The double arrow line indicates the direction of the fast axis.

Fig. 2.
Fig. 2.

Variation of birefringence of crystalline quartz with wavelength.

Fig. 3.
Fig. 3.

Wavelength dependent retardation Δ for the combination of λ/2 and λ/4 plates.

Fig. 4.
Fig. 4.

Wavelength dependent azimuth Ψ for the combination of λ/2 and λ/4 plates.

Fig. 5.
Fig. 5.

Percentage variation of retardation Δ with wavelength for the combination of λ/2 and λ/4 plates.

Fig. 6.
Fig. 6.

Wavelength dependent retardation Δ for the combination of two λ/4 plates.

Fig. 7.
Fig. 7.

Wavelength dependent azimuth Ψ for the combination of two λ/4 plates.

Fig. 8.
Fig. 8.

Percentage variation of retardation Δ with wavelength for the combination of two λ/4 plates.

Equations (12)

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

C(δ,0)=|eiδ/200eiδ/2|,
C(δ,ϕ)=|cosδ2+isinδ2cos2ϕisinδ2sin2ϕisinδ2sin2ϕcosδ2isinδ2cos2ϕ|.
C(Δ,ψ)=C(δ2,ϕ)C(δ1,0),
C(Δ,ψ)=|cosδ22+isinδ22cos2ϕisinδ22sin2ϕisinδ22sin2ϕcosδ22isinδ22cos2ϕ||eiδ1/200eiδ1/2|
=|ABB*A*|,
A=eiδ1/2(cosδ22+isinδ22cos2ϕ),
B=ieiδ1/2sinδ22sin2ϕ.
tan2Δ2=|ImA|2+|ImB|2|ReA|2+|ReB|2,
tan2Ψ=BB*AA*.
δ=2πλ0(neno)d,
ne21=0.665721λ2λ2(0.0600)2+0.503511λ2λ2(0.1060)2+0.214792λ2λ2(0.1190)2+0.539173λ2λ2(8.792)2+1.8076613λ2λ2(19.70)2,
no21=0.663044λ2λ2(0.0600)2+0.517852λ2λ2(0.1060)2+0.175912λ2λ2(0.1190)2+0.565380λ2λ2(8.844)2+1.675299λ2λ2(20.742)2.

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