Graphical: |
(1) Graphical/Argand diagram method (Vasicek, Turner, Muchmore) | Vector diagram analysis of reflection coefficients | For known integral thickness ratios, refractive indices are evaluated or for known refractive indices, thicknesses subjected to integral ratio conditions are evaluated. | | Constraints on both refractive indices and thicknesses. Method of evaluation is cumbersome and less efficient. Approximate reflection coefficient relations are used. |
Analytical: |
(2) Classical quarterwave method (Hass, Thun, Thelen) | Establishing ref. ind. relations using zero refl. condition, thicknesses set to m λ/4 (m = 1,2,3) | Determination of the refractive index of the layers for given ns and n0 | Simple design method | Often mismatch of the theoretical refractive index values with those of practical values arises. Limited scope for developing efficient designs (restricted to zero reflection-based designs and to λ/4 system) |
(3) Electrical filter design method (Young, Kucirkova) | Application of microwave network theory for optical admittance calculations | Evaluation of refractive indices for quarterwave thickness configurations | | Design analysis is complex. Mismatch of theoretical refractive-index values with material-index values arises. Limited to only quarterwave systems |
(4) Method of effective interfaces (Thetford, Baer) | Application of Fabry-Perot etalon theory to ARCs | Evaluation of thicknesses for given refractive-index configuration | Baer’s method offers analytical equations for evaluation of thicknesses | Thetford’s scheme is approximate and a trial and error approach. In Baer’s method, designs with zero base reflection can only be possible. Existence of dual set of solutions. Refractive-index limitations. Only two out of three thicknesses can be evaluated. |
(5) Exact synthesis method I (Kard, Mouchart) | Establishing closed form equations from zero reflection condition to determine the thicknesses | Evaluation of thicknesses for given refractive-index configuration | Simple method of evaluation | Ambiguity of dual set of solutions. Only two out of the three thicknesses can be evaluated. Possible to obtain only zero reflection based designs. Existence of ref index limitations (Kard’s scheme applicable to only symmetrical systems) |
(6) Exact synthesis method II—NTa (Nagendra, Thutupalli) | Formulation of suitable nonlinear equation for three-layer ARC from zero reflectance condition | Solving the nonlinear equation through Newton’s method to determine the thicknesses for a given combination of refractive indices | Method of evaluation is straightforward. No ambiguity of dual solutions | Similar to Mouchart’s method |
(7) Exact synthesis method III—NTb (Nagendra, Viswanathan, Thutupalli) | Establishing a theoretical formulation applicable for both zero and nonzero base reflectance and evolution of suitable nonlinear equation for three-layer ARCs | Direct synthesis of the nonlinear equation to determine the thicknesses for a given combination of refractive indices | Scope for both zero and nonzero reflectance-based designs and optimization through IRL R*. Flexibility over selection of materials. Provision for in situ correction. | Only two out of the three thicknesses can be evaluated exactly. Applicable to ARCs on transparent substrates |
Numerical: |
(8) Linear programming method (Baumiester et al). | Linear programming optimization to ARCs | Refractive-index optimization for quarterwave configurations | Refractive-index values can be bounded and realizable values can be achieved | Method involves complex programming. Applicable to quarterwave systems only |
(9) Refractive-index optimization method (Furman, Stolina) | Lagrange’s method of optimization applied to ARCs | For known thickness values, refractive indices are optimized. | | Involves complex optimization routine. Often optimized values should be rounded off to the nearest material values. Thicknesses are fixed a priori. |
(10) Method of least squares (Heavens, Liddel, Appa Rao) | Optimization of design variables using least-squares merit function | Optimization of thicknesses for given refractive indices | Scope for generating efficient designs | Mathematical analysis is complex. Needs extensive computation and a good starting design. |
(11) Evolutionary design method (Dobrowolski) | Merit function optimization | Both refractive-index and thickness optimization | Does not need a starting design. Flexibility over choice of Merit function. Realizable index values can be achieved. Efficient designs can be generated. | Involves complex mathematical analysis and computation |