Abstract

Well known relationships exist between thicknesses and indices of a stack of optical layers which permit the definition of very good polarizers of light. One of the most famous types of polarizer is the MacNeille cube. In this case the hypotenuse face of an isosceles right angled prism is coated with a polarizing deposit and then cemented to the hypotenuse face of an identical prism. This polarizer can be used over a large spectral range located in the s vibration stop band. Unfortunately, the insertion losses for the p vibration are large when the angular field is larger than ±2°. Using very simple optical considerations, we design suitable coating structures that allow the use of cube polarizers over a wide angular range, typically ±10° in air, when Tp > 0.97 and Ts ≤ 10−3. However, the spectral range is reduced. Diagrams are given to calculate the thickness of the layers according to the substrate and the indices of the evaporated materials. The prism angle is also determined to have a symmetric angular field in air. Such polarizers are suitable for semiconductor lasers because they can be used without a collimating lens in spite of their large divergence. Good optical characteristics up to Tp ≈ 0.95 and Ts ≈ 10−4 over the range of ±5° have been measured for these polarizers manufactured in the Laboratoires de Marcoussis.

© 1989 Optical Society of America

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References

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  1. S. M. MacNeille, “Beam Splitter,” U.S. Patent2,403,731 (9July1946).
  2. M. Banning, “Practical Methods of Making and Using Multilayer Filters,” J. Opt. Soc. Am. 37, 792–797 (1947).
    [CrossRef] [PubMed]
  3. H. A. MacLeod, Thin Film Optical Filters (Macmillan, New York, 1986).
    [CrossRef]
  4. R. P. Netterfield, “Practical Thin Film Polarizing Beam Splitters,” Opt. Acta 24, 69–79 (1977).
    [CrossRef]
  5. J. Mouchart, “Revêtements optiques à structure périodique. I: Fonctions caractéristiques,” Appl. Opt. 20, 4201–4206 (1981).
    [CrossRef] [PubMed]

1981 (1)

1977 (1)

R. P. Netterfield, “Practical Thin Film Polarizing Beam Splitters,” Opt. Acta 24, 69–79 (1977).
[CrossRef]

1947 (1)

Banning, M.

MacLeod, H. A.

H. A. MacLeod, Thin Film Optical Filters (Macmillan, New York, 1986).
[CrossRef]

MacNeille, S. M.

S. M. MacNeille, “Beam Splitter,” U.S. Patent2,403,731 (9July1946).

Mouchart, J.

Netterfield, R. P.

R. P. Netterfield, “Practical Thin Film Polarizing Beam Splitters,” Opt. Acta 24, 69–79 (1977).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

R. P. Netterfield, “Practical Thin Film Polarizing Beam Splitters,” Opt. Acta 24, 69–79 (1977).
[CrossRef]

Other (2)

S. M. MacNeille, “Beam Splitter,” U.S. Patent2,403,731 (9July1946).

H. A. MacLeod, Thin Film Optical Filters (Macmillan, New York, 1986).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

MacNeille cube polarizer.

Fig. 2
Fig. 2

MacNeille cube polarizer centered at λ = 1. Transmittances T p and T s vs wavelength for the incidence θ0 = 0 in air (θsub = 45° in the substrate). The design of the coating is (LH)11 with nsub = 1.70, nL = 1.45, (nt)L = 0.447 μm, nH = 2.20, (nt)H = 0.298 μm.

Fig. 3
Fig. 3

MacNeille cube polarizer. Values of the p admittances y p for the substrate and the L and H layers vs incidence θ0 in air (in degrees).

Fig. 4
Fig. 4

MacNeille cube polarizer. Same as for Fig. 2 but with incidence θ0 = −2° in air.

Fig. 5
Fig. 5

Use of a symmetrical base. Values of the p admittance of the substrate (y p )sub and of the p Herpin equivalent admittance E p as a function of incidence θ0 for two different values of the parameter P.

Fig. 6
Fig. 6

Research for large field polarizer. Diagram of the angular existence of solutions vs the P parameter for λ = 1. The indices of materials are nsub = 1.70, n L = 1.45, and n H = 2.20.

Fig. 7
Fig. 7

Same as for Fig. 6 but for λ = 1.05 μm.

Fig. 8
Fig. 8

Same as for Fig. 6 but for λ = 1.10 μm.

Fig. 9
Fig. 9

Large field polarizer. Transmittance T s in decibels vs incidence θ0 for three different values of the parameter P. The design of the coating is (L/2 H L/2)11 with P = 1 (curve 1), P = 1.15 (curve 2), P = 1.30 (curve 3), and λ = 1.

Fig. 10
Fig. 10

Large field polarizer. Transmittance T p in decibels vs incidence θ0. Same coatings as for Fig. 9.

Fig. 11
Fig. 11

Large field polarizer. Theoretical transmittance T p as a function of incidence for three wavelengths: 1.50–1.55 and 1.60 μm. The design is (L/2 H L/2)11 with nsub = 1.70, nL = 1.45, and nH = 1.95. Optical thicknesses: (nt)L/2 = 0.303 μm, (nt)H = 0.43 μm.

Fig. 12
Fig. 12

Large field polarizer. Theoretical transmittance T s in decibels as a function of incidence θ0. Same coating as for Fig. 11.

Fig. 13
Fig. 13

Automatic test system: S, light source emitting at λ = 1.531 μm; L, Selfoc; C, chopper; B, Babinet compensator; G, Glazebrook polarizer; P, polarizer to test; R, receptor.

Fig. 14
Fig. 14

Measured values of transmittance T p in decibels (see Fig. 11) in the meridian plane (+) and perpendicular (×). These values are compared with the theory for the meridian plane (full line curve).

Fig. 15
Fig. 15

Measured values of transmittance T s in decibels. Same coating as for Fig. 14.

Equations (19)

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θ D = arcsin ( sin θ 0 n sub ) + θ sub .
( n cos θ ) L = ( n cos θ ) H ,
( n sin θ ) L = ( n sin θ ) H = ( n sin θ ) sub ,
n sub 2 = 2 n L 2 n H 2 n L 2 + n H 2 .
R p = ( 1 z 2 N 1 + z 2 N ) 2
= 2 ( n t ) L / 2 + ( n t ) H .
P = 2 ( n t ) L / 2 2 ( n t ) L / 2 + ( n t ) H .
( n t ) L / 2 = P / 2 ( n t ) H = ( 1 P ) .
E p = ( y p ) L ( u υ u + υ ) 1 / 2
R p = ( 1 q 2 1 + q 2 ) 2 1 / q = ( y p ) sub / E p .
n sub = 1 . 70 n L = 1 . 45 n H = 2 . 20
( n t cos θ ) L / 2 = λ 0 / 8 ( n t cos θ ) H = λ 0 / 4 .
( n t ) L / 2 = 0 . 2483 μ m ( n t ) H = 0 . 2483 μ m .
= σ 0 P = ρ P 0 ,
( n t ) L / 2 * = 0 . 125 μ [ 1 ( n sin θ ) sub 2 n L 2 ] 1 / 2 , ( n t ) H * = 0 . 25 μ [ 1 ( n sin θ ) sub 2 n H 2 ] 1 / 2 .
1 / σ 1 . 92 0 . 77 ρ .
ρ = 1 which involves ( n t ) L / 2 = 0 . 1944 μ m ( n t ) H = 0 . 2596 μ m 1 . 15 0 . 2485 μ m 0 . 2237 μ m 1 . 30 0 . 3162 μ m 0 . 1789 μ m .
substrate : n sub = 1 . 70 ( D 2050 Sovirel glass ) , layer : low index n L = 1 . 45 ( SiO 2 ) , high index n H = 1 . 95 ( substance 1 Merck ) ,
( n t ) L / 2 = 0 . 303 μ m ( n t ) H = 0 . 43 μ m .

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