Mixed Integer Programming with Kriging Surrogate Model Technique for Dispersion Control of Photonic Crystal Fibers

In this paper, mixed integer nonlinear programming (MINLP) optimization algorithm integrated with kriging surrogate-model is newly formulated to optimize the dispersion characteristics of photonic crystal fibers (PCFs). The MINLP is linked with full vectorial finite difference method (FVFDM) to optimize the modal properties of the PCFs. Through the optimization process, the design parameters can take real and/or integer values. The integer values can be used to selectively fill the PCF air holes to control its dispersion characteristics. However, the other optimization techniques deal with real design parameters where the PCF can be optimized using none or predefined infiltrated air holes. The MINLP algorithm is used to obtain an ultra-flat zero dispersion over a broadband of wavelength range from 1.25 to 1.6 μm using silica PCF selectively infiltrated with Ethanol material. To show the superiority of the proposed algorithm, nematic liquid crystal selectively infiltrated PCFs are also designed with high negative flat dispersion over wide range of wavelengths from 1.25 to 1.6 μm for the quasi transverse magnetic (TM) and the quasi transverse electric (TE) modes. Such designs have negative flat dispersions of − 163 ± 0.9 and − 170 ± 1.2 ps/Km nm, respectively over the studied wavelength range. Therefore, the MINLP algorithms could be used efficiently for the design and optimization of selectively filled photonic devices.