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[1] A rigorous approach for modal analysis of two-dimensional photonic crystal waveguides consisting of layered arrays of circular cylinders is presented. The mode propagation constants and the mode field profiles can be accurately obtained by a simpler matrix calculus, using the one-dimensional lattice sums, the T matrix of an isolated circular cylinder, and the generalized reflection matrices for a multilayered system. Numerical examples of the dispersion characteristics and field distributions are presented for lowest even and odd transverse electric modes of a coupled two-parallel photonic crystal waveguide with a square lattice of dielectric circular cylinders in a background free space.Citation: Yasumoto, K., H. Jia, and K. Sun (2005), Rigorous modal analysis of two-dimensional photonic crystal waveguides,

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This manuscript presents the design of a low phase noise, high figure of merit (FoM) single-ended octagonal ring oscillator (RO). The proposed RO employs the pulse injection (PI) technique for performance enhancement. The PI technique is used for suppression of phase noise and spurious harmonics. Besides, a novel voltage dependent phase shifter is employed. The proposed RO has an output signal with voltage controlled phase. Different output signal phases can be obtained employing different selected voltages to control the output signal phase. The proposed injection locked ring oscillator (ILRO) represents a suitable implementation for phase shift keying. The proposed ILRO has a measured oscillation frequency of 4.9 GHz with a fine tuning range of 500 MHz. It has a measured phase noise of 2126.17 dBc/Hz @ 1MHz offset while consuming only 4.8 mW of DC power. The proposed ILRO has a FoM of 2193.17 dBc/Hz. This RO has been designed and implemented in 0.18 mm CMOS technology.