The pole-zero diagram is a tool that has been widely employed in digital and electronic filter design. It greatly facilitates filter design by producing a simple and direct visualization of parametrical behaviors and general spectral characteristics. In this paper, we propose new methods of applying pole-zero diagrams to photonic filter design, aimed at tailoring spectral characteristics. In particular, we demonstrate the effectiveness of this method in designing ring resonator-based filters for application to optical wavelength interleavers and deinterleavers. We show that there exist close relations between the pole-zero diagram of an optical filter and its wavelength response, and derive pole-zero diagrams for filters with various ring resonator configurations. Further, we propose a novel graphical technique using pole-zero diagrams for optimizing filter performance. As a practical example to demonstrate the effectiveness of the pole-zero approach, we present a new wavelength interleaver design with low crosstalk. This design was realized by superimposing the pole-zero diagrams of parallel and series-coupled ring resonator arrays.

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Cleavage of Si and Ge wafers in a vacuum produces spontaneous positive ion and electron emission with durations ranging from tens of microseconds up to 1.8 ms. The onset of emission is synchronous with the start of cleavage. The electron emission is explained by an Auger process energized by electron capture by a positive ion. The ion emission is about 10 7 cm 22 and is due to a peak in the surface atom vibrational energy distribution, showing that considerable energy is available for forming various surface structures. [S0031-9007 (98)05848-7] PACS numbers: 79.90. + b, 62.20.Mk

Optical ring-resonators could be used to synthesize filters with low crosstalk and flat passbands. Their application to DWDM interleaving has been proposed and investigated previously. However, a number of important issues related to this topic have not yet been considered and appropriately addressed. In this paper, we propose a novel scheme of a symmetrically parallel-coupled ring resonator array with coupling apodization. We show that it can be used to construct a wavelength interleaver with good performance and compact size. Various design factors have been considered. An optimization procedure was developed based on minimizing the channel crosstalk in the through and drop ports simultaneously by adjusting the ring-bus coupling coefficients. We show that apodization in coupling could suppress channel crosstalk effectively by choosing the optimal coupling coefficients. We also introduced the equalization of both the input and output coupling coefficients to eliminate notches in the passband. For a 50 -100 GHz DWDM applications, four rings is found to be the best choice for array size. A four-ring filter achieves crosstalk -24 dB, insertion loss at resonance <1 dB, and good passband flatness (shape factor >0.6).