In this paper, we introduce a simulation-driven optimization approach for achieving the optimal design of electromagnetic wave (EMW) filters consisting of one-dimensional (1D) multilayer photonic crystal (PC) structures. The PC layers' thicknesses and/or material types are considered as designable parameters. The optimal design problem is formulated as a minimax optimization problem that is entirely solved by making use of readily available software tools. The proposed approach allows for the consideration of problems of higher dimension than usually treated before. In addition, it can proceed starting from bad initial design points. The validity, flexibility, and efficiency of the proposed approach is demonstrated by applying it to obtain the optimal design of two practical examples. The first is (SiC/Ag/SiO(2))(N) wide bandpass optical filter operating in the visible range. Contrarily, the second example is (Ag/SiO(2))(N) EMW low pass spectral filter, working in the infrared range, which is used for enhancing the efficiency of thermophotovoltaic systems. The approach shows a good ability to converge to the optimal solution, for different design specifications, regardless of the starting design point. This ensures that the approach is robust and general enough to be applied for obtaining the optimal design of all 1D photonic crystals promising applications.

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This work proposes a novel and powerful adaptive digital back propagation (A-DBP) method with a fast adaption process. Given that the total transmission distance is known, the proposed A-DBP algorithm blindly compensates for the linear and nonlinear distortions of optical fiber transmission systems and networks, without knowing the launch power and channel parameters. An adjoint-based optimization (ABO) technique is proposed to significantly accelerate the parameters estimation of the A-DBP. The ABO algorithm utilizes a sequential quadratic programming (SQP) method coupled with an adjoint sensitivity analysis (ASA) approach to rapidly solve the A-DBP training problem. The design parameters are optimized using the minimum overhead of only one extra system simulation. Regardless of the number of A-DBP design parameters, the derivatives of the training objective function with respect to all parameters are estimated using only one extra adjoint system simulation per optimization iterate. This is contrasted with the traditional finite-difference (FD)-based optimization methods whose sensitivity analysis calculations cost per iterate scales linearly with the number of parameters. The robustness, performance, and efficiency of the proposed A-DBP algorithm are demonstrated through applying it to mitigate the distortions of 4-span and 20-span optical fiber communication systems. Coarse-mesh A-DBPs with less number of virtual spans are also used to significantly reduce the computational complexity of the equalizer, achieving compensation performance higher than that obtained using the coarse-mesh DBP with the exact channel parameters and full number of virtual spans.

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