Dielectric Omnidirectional Reflector

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In a recent paper,

    Yoel Fink, Joshua N. Winn, Shanhui Fan, Chiping Chen, Jurgen Michel, John D. Joannopoulos, and Edwin L. Thomas, "A Dielectric Omnidirectional Reflector", Science, Vol 282, 27 Nov 1998, pp 1679-82.

the authors discuss manufacturing a dielectric reflector that reflects P and S polarized light well for all incident angles for a fairly wide range of wavelengths. Such a reflector has the advantages of a metallic reflector, without the absorption that comes with metals. Their 9-layer reflector is composed of two dielectric materials, low-index (L=1.6) polystyrene and high-index (H=4.6) tellurium. The usual design is (HL)^4 H, with each thickness 1 QWOT at 12.4 microns. However, the layer thicknesses can be varied somewhat to slightly increase the width of the reflectance band. Although the authors deposited their reflector on a NaCl substrate, it should work well on a variety of substrates.

Using optimization, the layer thicknesses can be adjusted to shift and widen the reflectance band. Ten continuous optimization targets were used:

    R = 100% for 10-15 microns and for angles 0, 10, 20, 30, 40, 50, 60, 70, 80, 89

The (HL)^4 H design was used as the initial design. Optimization adjusted the first 8 layers slightly; the thickness of the 9th layer -- the outermost layer -- was reduced by almost half. The plot below shows the performance of the optimized reflector with all angles 0-90 degrees superimposed. It can be seen that the P and S reflectance is very high (>95%) for all angles and all wavelengths 9.8 to 15.5 microns.

Plot of reflector design

Here is the design, with the first layer closest to the substrate and thickness given in nm:
    H    691.88
    L   2112.33
    H    700.83
    L   2089.58
    H    701.51
    L   2097.40
    H    696.76
    L   2165.33
    H    399.00

Commentary: the results of the Fink, et al paper follow from the standard theory of thin films. For commonly used dielectric materials, the index ratio H/L is low, which leads to a narrow wavelength range over which the mirror is an omnidirectional reflector. By using materials with a very high H/L ratio, this wavelength range becomes much wider, as illustrated in Figure 3 of their paper. Some news articles about this paper have called the omnidirectional mirror a "perfect" mirror, i.e., 100% reflector at all angles. This statement is true for only theoretical constructions having an infinite number of layers. Real mirrors of this type approach 100% reflectance, but never attain it.

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