Immersed Wide-Angle Polarizer

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In a recent paper,
    Philip Baumeister, "Rudiments of the design of an immersed polarizing beam divider with a narrow spectral bandwidth and enhanced angular acceptance," Applied Optics, Vol. 36, No. 16, 1 June 1997, pp. 3610-3613.

the author examines the problem of creating narrow-band wide-angle polarizers. He develops a theory for designing this type of coating based on MacNeille pairs of refractive indices. The paper also presents a three-material 17-layer design created using TFCalc. The example given below improves that design by using 17 layers of only two materials.

The goal here is to design a coating to be immersed in a glass (BK7) prism. It should transmit P polarization and reflect S polarization for wavelengths 613-653 nm and angles (in glass) 51-71 degrees. This is diagramed below; the shaded areas represent the cones of incoming and outgoing light.

Diagram

We use continuous optimization targets:
  • P Transmittance > 96% for wavelengths 613-653 nm
  • S Transmittance < 0.1% for wavelengths 613-653 nm
at angles 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, and 71 degrees. Note that by using continuous targets, we simplify the problem in two ways: (1) entering the targets is faster and less prone to errors and (2) we do not have to decide on how many discrete targets should be used in the 613-653 nm range; TFCalc decides during optimization.

The coating materials are SiO2 (index 1.45) and TiO2 (index 2.35). Starting with a single thin layer of TiO2, the designer used TFCalc's optimization capabilities to find a 17-layer design whose performance is shown below.

Plot of polarizer design

Note that this graph displays the transmittance for a range of angles and wavelengths; at each angle, the graph shows how much the transmittance varies in the wavelength range 613-653 nm.

Here is the design, with the first layer closest to the second glass and thickness given in nm: 

    TIO2      83.62
    SIO2      74.91
    TIO2      94.86
    SIO2     119.09
    TIO2      90.21
    SIO2     129.48
    TIO2      81.87
    SIO2     123.04
    TIO2      84.03
    SIO2     138.23
    TIO2      81.34
    SIO2     131.15
    TIO2      83.85
    SIO2     152.21
    TIO2      80.48
    SIO2     126.78
    TIO2      59.95

Thanks to Philip Baumeister for supplying this problem.

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