Dielectric Sunglasses

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To demonstrate a new feature in TFCalc 3.2, we design sunglasses using two dielectric materials. For these sunglasses, we have the following requirements at normal incidence:

A. Transmittance < 1% for wavelengths 400-500 nm
B. Transmittance between 15 and 25% for wavelengths 510-790 nm
C. Transmittance < 1% for wavelengths 800-900 nm

The two coating materials are SiO2 and TiO2 on a glass substrate. Requirements A-C are entered as four continuous optimization targets; there is no need for the designer to decide where to place the individual targets -- TFCalc decides on the number and placement of the optimization targets.
Starting with a single thin layer of TiO2, the needle/tunneling method created (automatically) a sequence of optimal designs of increasing complexity. The ninth optimal design is a 29-layer coating whose performance is shown here.

Plot of sunglasses performance

Do continuous targets lead to better designs? In general, the answer is Yes. The graph below shows the performance of a coating designed using discrete targets every 10 nm (shown as circles). There are clearly two "leaks" (where the performance is not controlled between discrete targets) near 450 nm and another small leak at 515 nm.

Plot of sunglasses performance

Here is the design, with the first layer closest to the substrate and thickness given in nm.
    TiO2      69.95
    SiO2      32.82
    TiO2      32.68
    SiO2     111.15
    TiO2     106.07
    SiO2      93.12
    TiO2      28.13
    SiO2      69.00
    TiO2      57.75
    SiO2     172.27
    TiO2      60.40
    SiO2      94.82
    TiO2      50.14
    SiO2      73.58
    TiO2      44.78
    SiO2      90.29
    TiO2      27.17
    SiO2      59.58
    TiO2      62.56
    SiO2     113.66
    TiO2      68.53
    SiO2     189.07
    TiO2      63.17
    SiO2     129.47
    TiO2     110.55
    SiO2     123.90
    TiO2      73.89
    SiO2      32.41
    TiO2      21.12
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