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OptiLayer:  Your Partner in Design and Post-Production Characterization of Optical Coatings

 

Constrained Optimization

OptiLayer has a variety of options for constrained optimization. These options are aimed to meet various feasibility demands and to provide better manufacturing properties of coating designs.

For example, it is possible to specify boundary of layer thicknesses.

It is possible to set constraints for individual layer thicknesses. Each layer can have:·

  • Active (A),
  • Fixed (F) or 
  • Optical Fixed (O)

state, which indicates whether the thickness of this layer can vary during optimization. If the state is Optical Fixed, the physical thickness and refractive index vary but only so that their product, i.e., optical thickness, remains constant.

multilayer design no thin layers

Example 1. Optimization a solar cell structure

Optimization of a solar cell structure using Constrained optimization option of OptiLayer. Initial design: 5-layers solar cell. Note that upper SnO2 layer is adjacent to the BK7 glass and light incidence from the BK7 glass is considered.

constrained optimization

thin film design
Only thicknesses of two layers (internal amorphous silicon layer and top SnO2 conducting layer) are allowed to vary in the specified limits: from 150 to 600 nm and from 10 to 100 nm, respectively. constrained optimization

Example 2. Design of mirrors using quasi-rugate filters

Quasi-rugate filter a multilayer: 

• that may have layers with variable refractive indices limited by refractive indices of low and high index materials;

• that does not contain thin layers;

• with refractive index profiles  resembling a rugate refractive index profiles

• with spectral properties typical for rugate filters

For the design procedure a special material, so called changeable material, with variable refractive index is used. The design procedure is based on the constrained optimization of a special type. Constrained optimization is used in order to limit layer thicknesses and obtain designs without thin layers.

Design of the mirror with the suppressed second high reflection zone

Two-component (classical) solution

quasi-rugate coating

Transmittance of 68-layer two component mirror.

Quasi-rugate solution

quasi-rugate coating

 Transmittance of a quasi-rugate design.
 quasi-rugate coating Structure of 68-layer two-component design  quasi-rugate filter Refractive index profile of quasi-rugate solution

 Learn more in:   A.V. Tikhonravov, M.K. Trubetskov, and T.V. Amotchkina, "Application of constrained optimization to the design of quasi-rugate optical coatings," Appl. Opt. 47, 5103-5109 (2008).

 

 

Example 3. Design of quasi-rugate minus-filter

Constrained optimization option allows you to design multilayers with quarter-wave optical thicknesses of coating layers. For the design procedure a special material, so called changeable material, with variable refractive index is used. The design procedure is based on the constrained optimization of a special type. Constrained optimization is used in order to obtain designs consisting of quarter-wave layers. 
 
minus filter  minus filter
   
 Transmittance of 47-layer quasi-rugate minus filter  Refractive index profile of 47-layer quasi-rugate minus filter. All layers have quarter-wave optical thicknesses
Learn more in:   A.V. Tikhonravov, M.K. Trubetskov, and T.V. Amotchkina, "Application of constrained optimization to the design of quasi-rugate optical coatings," Appl. Opt. 47, 5103-5109 (2008).

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