Multilayer Films

  Agreement with theory for the following exercises is very dependent on the number of grid points. A minimum of 512 grid points is recommended.

• A Two-Layer Antireflection Coating
  Model a two-layer antireflection film for light of wavelength incident on dense barium crown glass for which . Use zirconium dioxide () and cerium flouride () to construct the two-layer film. The thickness of both layers should be , and the light should encounter the lower-index layer (cerium flouride) first. Compare the reflectance given by the transfer matrix of the system to the simulated reflectance for . Repeat the previous comparison for , , and . How must the antireflection film be changed in order to achieve a reflectance for which approaches zero?

  Remember that in order to achieve , the following condition must be satisfied[8]:

  

  where and are the refractive indices of the first and second materials encountered by incident light.

• A Three-Layer, Two-Wavelength Antireflection Coating
  Construct and test a three layer antireflection coating that is a perfect reflector at two wavelengths.
• An Eight-Layer Reflector  
  Create a high-reflectance film consisting of eight alternating layers of thickness of materials with high and low refractive indices. Let the material of high refractive index be zinc sulfide () and the material of low refractive index be magnesium fluoride (). Compare simulated reflectance with theoretical reflectance, R, given by

  

  where N is the number of two-layer stacks in the coating.

• Using Thin Films to Model a Fabry-Perot Interference Filter
    Construct a Fabry-Perot interference filter by coating both sides of a resonating cavity with a three-layer partially reflecting film of alternating low- and high- refractive index materials (see fig. ) What are the simulated and theoretical reflectances of this seven-layer Fabry-Perot interference filter? How does the filter respond to a noisy source?

    
  Figure: A multilayer Fabry-Perot interference filter (=low refractive index, =high refractive index).
  

• Modeling a Transmission Filter  
    Create a multilayer filter which allows for complete transmission of but reflects other wavelengths (see figure ).

    
  Figure: A multilayer transmittance filter.
  

  If you have access to a mathematical computation package, plot the reflectance as a function of wave number, , for filters of 1, 2, 3, and 4 layers. How does the vary with the number of layers used in the filter?

• A Beam-Splitter
    Modify the filter configuration of the previous exercise such that the spaces between layers are occupied by segments. Adjust the refractive index of these segments such that the transmittance and reflectance of are both approximately .
• Finite Pulse Width
  Load the Fabry-Perot interference filter stored in the file FABRY.WAV and make the following changes. Double click on the source and set the source function to user defined. Enter the following user defined function by clicking the Advanced Options button and entering the following formula in the parser text field:

  

  Select Detector graphs for both analysis graphs and use the blue attribute buttons to set one detector graph to show the right going wave and the other to show the left going wave. Run the simulation. What is the width of the pulse transmitted by the filter? The effect you see is very important when designing optics for femtosecond laser systems. Almost any optical component will have an effect on pulse shape.