Abstract

A centrosymmetric multilayer stack of two transparent thin-film materials, which is embedded in a high-index prism, is designed to function as an efficient polarizer or polarizing beam splitter (PBS) under conditions of frustrated total internal reflection over an extended range of incidence angles. The S(LH)kLHL(HL)kS multilayer structure consists of a high-index center layer H sandwiched between two identical low-index films L and high-index–low-index bilayers repeated (k times) on both sides of the central trilayer maintaining the symmetry of the entire stack. For a given set of refractive indices, all possible solutions for the thicknesses of the layers that suppress the reflection of p-polarized light at a specified angle, and the associated reflectance of the system for the orthogonal s polarization, are determined. The angular and spectral sensitivities of polarizing multilayer stacks employing 3, 7, 11, 15, and 19 layers of BaF2 and PbTe thin films embedded in a ZnS prism, operating at λ=10.6μm, are presented. The 15- and 19-layer stack designs achieve extinction ratios (ER) >30  dB in both reflection and transmission over a 46°–56° field of view inside the prism. Spectral analysis reveals additional discrete polarizing wavelengths other than the design wavelength (λ=10.6μm). The 11-, 15-, and 19-layer designs function as effective s-reflection polarizers (|Rs|2>99%) over a 23μm bandwidth. The effect of decreasing the refractive index contrast between the H and L layers on the resulting ER is also considered.

© 2007 Optical Society of America

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References

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2007 (1)

2006 (2)

2003 (1)

L. Li, "The design of optical thin film coatings," Opt. Photon. News 14, 24-30 (2003).
[CrossRef]

2000 (1)

1996 (1)

1989 (1)

1986 (1)

1979 (1)

1969 (1)

Appl. Opt. (8)

Opt. Lett. (1)

Opt. Photon. News (1)

L. Li, "The design of optical thin film coatings," Opt. Photon. News 14, 24-30 (2003).
[CrossRef]

Other (4)

CVD, Inc., 35 Industrial Parkway, Woburn, Mass. 01801.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995), Vol. II, Chap. 33.

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Embedded centrosymmetric multilayer thin-film device as a polarizing beam splitter (PBS) operating under conditions of frustrated total internal reflection. p and s are the linear polarizations parallel and perpendicular to the plane of incidence, respectively, and ϕ 0 is the angle of incidence.

Fig. 2
Fig. 2

Z 2 versus Z 1 such that R p = 0 at angles of incidence ϕ 0 from 45° to 55° in steps of 1° for centro-symmetric multilayer stacks with B a F 2 and PbTe thin films embedded in a ZnS substrate with refractive indices n 0 = 2.1919 ( ZnS ) , n 1 = 1.3926 ( BaF 2 ) , and n 2 = 5.6314 ( P b T e ) in the IR at λ = 10.6 μ m . Panel A1 corresponds to a trilayer design; panels B1, B2 and B3 correspond to the seven-layer design; while panels C1, C2, C3, C4 and C5 correspond to the 11-layer design.

Fig. 3
Fig. 3

Z 2 versus Z 1 such that R p = 0 at angles of incidence ϕ 0 from 45° to 55° in steps of 1° for the same material system as described in the caption of Fig. 2 for a 15-layer centrosymmetric design.

Fig. 4
Fig. 4

Z 2 versus Z 1 such that R p = 0 at angles of incidence ϕ 0 from 45° to 55° in steps of 1° for the same material system as described in the caption of Fig. 2 for a 19-layer centrosymmetric design.

Fig. 5
Fig. 5

Extinction ratios in reflection and transmission ( ER r and ER t ) in decibels for various centrosymmetric multilayer stacks with 3–19 layers embedded in a ZnS substrate are plotted versus the angle of incidence ϕ 0 from 46° to 56°. The material system is the same as given in the caption of Fig. 2, and the metric film thicknesses associated with different multilayer stacks are listed in Table 1.

Fig. 6
Fig. 6

Reflectances | R p | 2 and | R s | 2 for various centro-symmetric multilayer stacks with 3–19 layers embedded in a ZnS substrate are plotted versus the angle of incidence ϕ 0 from 46° to 56°. The material system is the same as given in the caption of Fig. 2, and the metric film thicknesses associated with different multilayer designs are listed in Table 1.

Fig. 7
Fig. 7

Extinction ratios in reflection and transmission ( ER r and ER t ) in decibels for various centrosymmetric multilayer stacks with 3–19 layers embedded in a ZnS substrate are plotted versus wavelength 8 λ 12 μ m . The material system is the same as given in the caption of Fig. 2, and the metric film thicknesses associated with different multilayer stack designs are listed in Table 1.

Fig. 8
Fig. 8

Reflectances | R p | 2 and | R s | 2 for various centrosymmetric multilayer stacks with 3–19 layers embedded in a ZnS substrate are plotted versus wavelength 8 λ 12 μ m . The material system is the same as given in the caption of Fig. 2, and the metric film thicknesses associated with different multilayer stack designs are listed in Table 1.

Fig. 9
Fig. 9

Extinction ratios in reflection ER r (panel A1) and transmission ER t (panel A2) in decibels for a 15-layer centrosymmetric structure that uses B a F 2 ( n 1 = 1.3926 ) as the low-index films and PbTe, Ge, or Si ( n 2 = 5.6314 , 4.0038, and 3.4177, respectively) as the high-index layers. The multilayer is embedded in a ZnS substrate with refractive index n 0 = 2.1919 . All refractive indices correspond to the operating wavelength λ = 10.6 μ m . The normalized and metric film thicknesses for these 15-layer designs are listed in Table 4.

Tables (4)

Tables Icon

Table 1 Normalized ( Z 1, Z 2) and Metric ( d 1, d 2) Thicknesses Corresponding to the Point of Intersection of the 50° and 55° Z 2-versus- Z 1 Curves in Panel A1 of Fig. 2, Panel B3 of Fig. 2, Panel C5 of Fig. 2, Panel A7 of Fig. 3, and Panel A9 of Fig. 4 for the 3-, 7-, 11-, 15-, and 19-Layer Designs, Respectively

Tables Icon

Table 2 Discrete Angles at Which the ER r Reaches a Peak in Panel A1 of Fig. 5

Tables Icon

Table 3 Discrete Wavelengths at Which the ER r of Fig. 7 Reaches a Positive or Negative Peak

Tables Icon

Table 4 Normalized ( Z 1, Z 2) and Metric ( d 1, d 2) Thicknesses for Dual-Angle (50° and 55°) PBS Using a 15-Layer Centrosymmetric Structure with BaF2 ( n 1 = 1.3926) as the Low-Index Films and PbTe, Ge, or Si ( n 2 = 5.6314, 4.0038, and 3.4177, Respectively) as the High-Index Layers a

Equations (6)

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R v = a n X 2 n + a n 1 X 2 n 1 + + a 0 b n X 2 n + b n 1 X 2 n 1 + + b 0 ,
v = p , s .
X i = exp ( j π Z i   cos   ϕ i ) ,
Z i = 4 d i n i λ .
r i j p = n j   cos   ϕ i n i   cos   ϕ j n j   cos   ϕ i + n i   cos   ϕ j , r i j s = n i   cos   ϕ i n j   cos   ϕ j n i   cos   ϕ i + n j   cos   ϕ j .
a n X 2 n + a n 1 X 2 n 1 + + a 0 = 0 .

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