A polarization-insensitive recirculating delayed self-heterodyne method (PI-RDSHM) is proposed and demonstrated for the precise measurement of sub-kilohertz laser linewidths. By a unique combination of Faraday rotator mirrors (FRMs) in an interferometer, the polarization-induced fading is effectively reduced without any active polarization control. This passive polarization-insensitive operation is theoretically analyzed and experimentally verified. Benefited from the recirculating mechanism, a series of stable beat spectra with different delay times can be measured simultaneously without changing the length of delay fiber. Based on Voigt profile fitting of high-order beat spectra, the average Lorentzian linewidth of the laser is obtained. The PI-RDSHM has advantages of polarization insensitivity, high resolution, and less statistical error, providing an effective tool for accurate measurement of sub-kilohertz laser linewidth.

We demonstrate a coherent phase transfer via a 224 km cascaded fiber link comprising two 112 km links stabilized by two phase-locking loops, respectively. The optical signal is regenerated employing heterodyne optical phase locking (HOPL) after the first 112 km transfer. With a gain of more than 50 dB, the HOPL is capable of tracking the frequency of the incoming carrier with a fluctuation of 0.48 mHz and preserving the instability of the incoming laser to $6\times {10}^{-20}$ at 1000 s. The phase noise cancellation of each span is investigated, and the out-loop transfer instability of the 224 km link reaches $7.7\times {10}^{-19}$ at 10,000 s. The relation between the transfer instability of each span and that of the whole link is also deduced in the paper, in agreement with experimental results of the 224 km link.

A recirculating delayed self-heterodyne method with a short fiber is proposed for the precise measurement of sub-kHz laser linewidth. Using the recirculating delayed self-heterodyne interferometer with an only 2 km delayed fiber, a series of beat signals with different delay times are simultaneously measured. By simulating and fitting the power spectra of multiple high-order beat signals, the average linewidth of 944 Hz for a laser is obtained, which is basically in agreement with that obtained by the traditional beat frequency method. The proposed method can not only avoid a single measurement error, but also effectively reduce the frequency broadening induced by the 1/f

This paper presents the fundamental concept and formulation of short-open calibration (SOC) technique in 2.5D method of moments (MoM), and its application in commercial software. By de-embedding the port discontinuities and feeding network, the guided-wave characteristics of periodic planar transmission line structures, such as microstrip line, coplanar-waveguide electromagnetic band-gap, and metamaterial structures, can be extensively studied and analyzed. Especially, extraction of even- and odd-mode propagation constant and characteristic impedance of coupled microstrip line are discussed for synthesis and design of a few advanced bandpass filters.