Abstract

Thin-film structures which contain totally reflecting boundaries can be designed to produce nearly arbitrary phase retardations. Examples are given for quarterwave retarders that are either achromatic or cover an extended range of incidence angles.

© 1984 Optical Society of America

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References

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  1. J. Apfel, “Phase Retardance of Periodic Multilayer Mirrors,” Appl. Opt. 21, 733 (1982).
    [CrossRef] [PubMed]
  2. O. S. Heavens, H. M. Liddell, “Staggered Broadband Reflecting Multilayers,” Appl. Opt. 5, 373 (1966); see also H. A. Macleod, Thin-Flim Optical Filters (American-Elsevier, New York, 1969) for additional references.
    [CrossRef] [PubMed]
  3. E. Spiller, “Broadening of Short Light Pulses by Many Reflections from Multilayer Dielectric Coatings,” Appl. Opt. 10, 557 (1971).
    [CrossRef] [PubMed]
  4. W. H. Southwell, “Multilayer Coatings Producing 90° Phase Change,” Appl. Opt. 18, 1875 (1979).
    [CrossRef] [PubMed]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  6. R. J. King, “Quarter-wave Systems Based on the Fresnel Rhomb Principle,” J. Sci. Instrum. 43, 617 (1966).
    [CrossRef]
  7. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), Chap. 6.
  8. R. Fletcher, M. J. D. Powell, “A Rapidly Convergent Descent Method for Minimization,” Comput. J. 6, 161 (1963).
    [CrossRef]
  9. P. W. Baumeister, “Optical Tunneling and its Applications to Optical Filters,” Appl. Opt. 6, 897 (1967).
    [CrossRef] [PubMed]
  10. N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972).
  11. J. H. Apfel, “Graphical Method to Design Internal Reflection Phase Retarders,” Appl. Opt. 23, 1178 (1984).
    [CrossRef] [PubMed]

1984 (1)

1982 (1)

1979 (1)

1971 (1)

1967 (1)

1966 (2)

1963 (1)

R. Fletcher, M. J. D. Powell, “A Rapidly Convergent Descent Method for Minimization,” Comput. J. 6, 161 (1963).
[CrossRef]

Apfel, J.

Apfel, J. H.

Baumeister, P. W.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Burke, J. J.

N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972).

Fletcher, R.

R. Fletcher, M. J. D. Powell, “A Rapidly Convergent Descent Method for Minimization,” Comput. J. 6, 161 (1963).
[CrossRef]

Heavens, O. S.

Kapany, N. S.

N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972).

King, R. J.

R. J. King, “Quarter-wave Systems Based on the Fresnel Rhomb Principle,” J. Sci. Instrum. 43, 617 (1966).
[CrossRef]

Liddell, H. M.

Powell, M. J. D.

R. Fletcher, M. J. D. Powell, “A Rapidly Convergent Descent Method for Minimization,” Comput. J. 6, 161 (1963).
[CrossRef]

Southwell, W. H.

Spiller, E.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

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Figures (10)

Fig. 1
Fig. 1

Thin-film structure on a prism used to produce a phase retardation between s- and p-polarized reflected light.

Fig. 2
Fig. 2

Difference in phase shift Δα = ϕpϕs for p- and s-polarized light totally reflected from within a prism of index np vs the angle of incidence of the prism.

Fig. 3
Fig. 3

Condition for the optical constants of two materials with index n1 and n2 to give total reflection and 90° phase retardation at the boundary between media 1 and 2.

Fig. 4
Fig. 4

Reflectivities Rs and Rp and phase retardation Δϕ = ϕpϕs as a function of incidence angle for a film of silver (index n2 = 0.05 + 2.87i) and an incident medium with n1 = 1.5. The plot contains the principal angle at 66.6° and the pseudo-Brewster angle at 56°.

Fig. 5
Fig. 5

Phase retardation for a single film of index nf coated on a prism of index np = 1.509 as a function of the normalized thickness d/λ for an angle of incidence of 45°.

Fig. 6
Fig. 6

Contours of constant phase retardation as a function of incidence angle and wave number for a single film of index nf = 2.05 and thickness 0.1λ0 on a prism of index np = 1.509.

Fig. 7
Fig. 7

Phase retardation as a function of wave number λ0/λ for a single film (full curve) and a three-layer system optimized to give 90° phase retardation in the region λ0/λ = 0.9–1.2 (dashed). Films are counted from the air side toward the prism.

Fig. 8
Fig. 8

Contours of constant phase retardation as a function of incidence angle and wave number for the three-layer system of Fig. 7

Fig. 9
Fig. 9

Contours of constant phase retardation for a three-layer coating optimized to give constant 90° phase retardation for angles of incidence between 44 and 50°.

Fig. 10
Fig. 10

Phase retardation vs wave number for a three-layer system, where the first film (from the air side) represents a waveguide and the second film is an air gap (tunnel film). The film closest to the prism has the same parameters as the single film in Fig. 7.

Tables (1)

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Table I Performance of Some Metals as Quarterwave Retarders a

Equations (14)

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r s = n 1 cos α 1 - n 2 cos α 2 n 1 cos α 1 + n 2 cos α 2 ,
r p = n 1 cos α 2 - n 2 cos α 1 n 1 cos α 2 + n 2 cos α 1 ,
n sin α = n 0 sin α 0 ,
cos α = 1 - ( n 0 / n ) 2 sin 2 α 0 .
n ˜ = n + i k .
r f = r t + r b exp ( 2 i β ) 1 + r t r b exp ( 2 i β ) ,
β = 2 π λ 0 n d cos α ,
β = 2 π λ 0 d n 2 - n 0 2 sin 2 α 0 .
M = ( cos β - i p sin β - i p sin β cos β )
Δ ϕ = ϕ p - ϕ s = arg r p / r s ,
tan Δ ϕ 2 = - cos α 1 sin 2 α 1 - ( n 2 / n 1 ) 2 sin 2 α 1 .
( n ˜ 2 / n ˜ 1 ) = ( 1 - tan 2 α 1 ) sin 2 α 1 .
Z ( n , d ) = α i , λ i ( Δ ϕ - 90 ° ) 2 ,
Y = a 0 + a 1 sin x ,

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