A new design method for a high-order series-coupled microring filter using Chebyshev filter condition was proposed and its application to the design of a wavelength-selective switch (WSS) was discussed. In the proposed method, the propagation loss in a microring resonator, coupling loss at a coupler, and a free spectral ranges (FSR) in a microring resonator are considered for the first time. It was found that for high-order series coupled microring resonators, the WSS designed using Chebyshev condition has more boxlike filter responses and high extinction ratio, compared with that designed using Butterworth condition, in the case where the round-trip loss in a microring is relatively large. In addition, the fourth-order series-coupled microring WSS with boxlike responses was successfully designed, considering Vernier effect for a larger FSR and shift in resonant wavelength.

In this paper we are concerned with designing an extremum seeking control law for nonlinear systems. This is a modification of a standard extremum seeking controller. It is equipped with an accelerator to the original one aimed at achieving the maximum operating point more rapidly. This accelerator is designed by making use of a polynomial identification of an uncertain output map, the Butterworth filter to smoothen the control, and analog-digital converters. Numerical experiments show how this modified approach can be well in control of the Monod model of bioreactors.