Abstract

We analyze the method of phase subtraction in two identical optical structures to build an achromatic phase retarder. The two structures are made of right-angle prisms and are aligned orthogonal to each other. They are also made of materials of different refractive indices so that dispersion compensation can be taken advantage of. Essentially the phase retardation between the s and p waves in the first structure is subtracted from the phase retardation in the second structure. This can be done by reversing the roles of the s and p waves. By choosing the materials of the prisms properly, the phase retardation can be made to be constant over a broad spectral range. Indeed, calculations made with commercial optical glasses show that phase errors in the visible and near-infrared regions can be rather small. For example, for a 90° phase retarder (quarter-wave plate), a phase error of 0.35° can be obtained from 0.35 to 0.81 μm and from 0.59 to 1.26 μm.

© 1996 Optical Society of America

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References

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  1. N. N. Nagib, M. S. El-Bahrawy, “Phase retarders with variable angles of total internal reflection,” Appl. Opt. 33, 1218–1222 (1994).
    [CrossRef] [PubMed]
  2. N. N. Nagib, S. A. Khodier, “Optimization of a rhomb-type quarter-wave phase retarder,” Appl. Opt. 34, 2927–2930 (1995).
    [CrossRef] [PubMed]
  3. J. M. Bennett, “A critical evaluation of Rhomb-type quarter-wave retarders,” Appl. Opt. 9, 2123–2129 (1970).
    [CrossRef] [PubMed]
  4. P. Hariharan, P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
    [CrossRef]
  5. C. F. Buhrer, “High-order achromatic quarterwave combination plates and tuners,” Appl. Opt. 27, 3166–3169 (1988).
    [CrossRef] [PubMed]
  6. I. Filinski, T. Skettrup, “Achromatic phase retarders constructed from right-angle prisms: design,” Appl. Opt. 23, 2747–2751 (1984).
    [CrossRef] [PubMed]
  7. E. Spiller, “Totally reflecting thin-film phase retarders,” Appl. Opt. 23, 3544–3549 (1984).
    [CrossRef] [PubMed]
  8. E. Cojocaru, R. Dabu, V. Draganescu, T. Julea, F. Nichitiu, “Achromatic thin-film totally reflecting quarterwave retarders,” Appl. Opt. 28, 211–212 (1989).
    [CrossRef] [PubMed]
  9. E. Cojocaru, T. Julea, F. Nichitiu, “Infrared thin-film totally reflecting quarterwave retarders,” Appl. Opt. 30, 4124–4125 (1991).
    [CrossRef] [PubMed]
  10. H. Fabricius, “Achromatic prism retarder for use in polarimetric sensors,” Appl. Opt. 30, 426–429 (1991).
    [CrossRef] [PubMed]
  11. I. Filinski, T. Skettrup, “Achromatic optical compensator–modulator,” Appl. Opt. 28, 1720–1726 (1989).
    [CrossRef] [PubMed]
  12. J. H. Apfel, “Graphical method to design internal reflection phase retarders,” Appl. Opt. 23, 1178–1183 (1984).
    [CrossRef] [PubMed]
  13. J. H. Apfel, “Graphical method to design multilayer phase retarders,” Appl. Opt. 20, 1024–1029 (1981).
    [CrossRef] [PubMed]
  14. H. Bach, N. Neuroth, eds., The Properties of Optical Glass (Springer-Verlag, Berlin, 1995).
    [CrossRef]
  15. T. Preston, The Theory of Light (Macmillan, New York, 1901).
  16. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).
  17. M. Born, E. Wolf, Principles of Optics (Dover, New York, 1993).
  18. Schott Catalogue of Optical Glass, No. 10.000e (Schott Glass Technologies, Inc., Duryea, Pa. 18642, 1992).

1995 (1)

1994 (2)

N. N. Nagib, M. S. El-Bahrawy, “Phase retarders with variable angles of total internal reflection,” Appl. Opt. 33, 1218–1222 (1994).
[CrossRef] [PubMed]

P. Hariharan, P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

1991 (2)

1989 (2)

1988 (1)

1984 (3)

1981 (1)

1970 (1)

Apfel, J. H.

Bennett, J. M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Dover, New York, 1993).

Buhrer, C. F.

Ciddor, P. E.

P. Hariharan, P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Cojocaru, E.

Dabu, R.

Draganescu, V.

El-Bahrawy, M. S.

Fabricius, H.

Filinski, I.

Hariharan, P.

P. Hariharan, P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

Julea, T.

Khodier, S. A.

Nagib, N. N.

Nichitiu, F.

Preston, T.

T. Preston, The Theory of Light (Macmillan, New York, 1901).

Skettrup, T.

Spiller, E.

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Dover, New York, 1993).

Appl. Opt. (12)

J. H. Apfel, “Graphical method to design multilayer phase retarders,” Appl. Opt. 20, 1024–1029 (1981).
[CrossRef] [PubMed]

J. H. Apfel, “Graphical method to design internal reflection phase retarders,” Appl. Opt. 23, 1178–1183 (1984).
[CrossRef] [PubMed]

I. Filinski, T. Skettrup, “Achromatic phase retarders constructed from right-angle prisms: design,” Appl. Opt. 23, 2747–2751 (1984).
[CrossRef] [PubMed]

E. Spiller, “Totally reflecting thin-film phase retarders,” Appl. Opt. 23, 3544–3549 (1984).
[CrossRef] [PubMed]

C. F. Buhrer, “High-order achromatic quarterwave combination plates and tuners,” Appl. Opt. 27, 3166–3169 (1988).
[CrossRef] [PubMed]

I. Filinski, T. Skettrup, “Achromatic optical compensator–modulator,” Appl. Opt. 28, 1720–1726 (1989).
[CrossRef] [PubMed]

H. Fabricius, “Achromatic prism retarder for use in polarimetric sensors,” Appl. Opt. 30, 426–429 (1991).
[CrossRef] [PubMed]

E. Cojocaru, T. Julea, F. Nichitiu, “Infrared thin-film totally reflecting quarterwave retarders,” Appl. Opt. 30, 4124–4125 (1991).
[CrossRef] [PubMed]

N. N. Nagib, M. S. El-Bahrawy, “Phase retarders with variable angles of total internal reflection,” Appl. Opt. 33, 1218–1222 (1994).
[CrossRef] [PubMed]

N. N. Nagib, S. A. Khodier, “Optimization of a rhomb-type quarter-wave phase retarder,” Appl. Opt. 34, 2927–2930 (1995).
[CrossRef] [PubMed]

J. M. Bennett, “A critical evaluation of Rhomb-type quarter-wave retarders,” Appl. Opt. 9, 2123–2129 (1970).
[CrossRef] [PubMed]

E. Cojocaru, R. Dabu, V. Draganescu, T. Julea, F. Nichitiu, “Achromatic thin-film totally reflecting quarterwave retarders,” Appl. Opt. 28, 211–212 (1989).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Hariharan, P. E. Ciddor, “An achromatic phase-shifter operating on the geometric phase,” Opt. Commun. 110, 13–17 (1994).
[CrossRef]

Other (5)

H. Bach, N. Neuroth, eds., The Properties of Optical Glass (Springer-Verlag, Berlin, 1995).
[CrossRef]

T. Preston, The Theory of Light (Macmillan, New York, 1901).

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976).

M. Born, E. Wolf, Principles of Optics (Dover, New York, 1993).

Schott Catalogue of Optical Glass, No. 10.000e (Schott Glass Technologies, Inc., Duryea, Pa. 18642, 1992).

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Figures (6)

Fig. 1
Fig. 1

Proposed phase retarder made of eight right-angle prisms.

Fig. 2
Fig. 2

Phase retardation versus incident angle at refractive indices from 1.4 to 2 in 0.1 increments.

Fig. 3
Fig. 3

Sensitivity of phase retardation to incident angle variation at incident angles from 43° to 47° in 1° increments.

Fig. 4
Fig. 4

Phase retardation versus refractive index at incident angles from 43° to 47° in 1° increments.

Fig. 5
Fig. 5

Sensitivity of phase retardation to refractive-index variation at refractive indices from 1.45 to 1.95 in 0.1 increments.

Fig. 6
Fig. 6

Phase error δΓ of an achromatic quarter-wave retarder using Schott optical glass LaSF18A/PSK50 (solid curve, SF18/K11 (dotted curve), and SF58/PSK50 (dashed curve).

Tables (1)

Tables Icon

Table 1 Phase Error δΓ of Different Glass Combinations for an Achromatic Quarter-Wave Retarder in the Visible and Near-Infrared Regions a

Equations (8)

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Δ = 2 tan 1 [ cos θ ( n 2 sin 2 θ 1 ) 1 / 2 n sin 2 θ ] ,
Γ = Δ H Δ V = h = 1 4 m H Δ h υ = 1 4 m V Δ υ ,
Γ x = h = 1 4 m H 2 ( n h 2 1 ) n h 2 2 n h x υ = 1 4 m V 2 ( n υ 2 1 ) n υ 2 2 n υ x ,
S θ = Δ θ = 2 n sin θ n 2 sin 2 θ cos 2 θ cos 2 θ n 2 sin 2 θ + 1 ( n 2 sin 2 θ 1 ) 1 / 2 .
S θ = 2 n ( 3 n 2 ) ( n 2 1 ) n 2 2 .
S n = Δ n = 2 sin 2 θ cos θ n 0 2 sin 2 θ cos 2 θ 1 ( n 0 2 sin 2 θ 1 ) 1 / 2 .
S n = Δ n = 2 sin 2 θ cos θ 3 sin 2 θ cos 2 θ 1 ( 3 sin 2 θ 1 ) 1 / 2 .
δ Γ = 4 ( Δ h Δ υ ) π / 2 .

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