On the basis of the overlap integral method, an approximate analytical model is derived to estimate the coupled optical power between axisymmetric Gaussian beams when transverse, axial, and angular misalignments simultaneously exist in three dimensions. Seven optical properties are derived from a detailed analysis of the model. Because the model is an approximate analytical solution to the overlap integral method, the existence of each property is also investigated by a numerical solution. Results show that all seven properties are intrinsic to the optical coupling phenomenon between Gaussian beams. Because numerous single-mode device-to-fiber coupling systems can be well described by use of Gaussian beams, the seven properties provide a solid basis to develop model-based algorithms for single-mode device-to-fiber alignment automation.
A non-intrusive OSNR measurement technique relying on the detailed spectral comparison of an optical signal with its "noise-free" spectrum is described, including mathematical basis, validity conditions and algorithmic steps. The technique's performance is experimentally demonstrated with 100G PM-QPSK and 200G PM-16QAM signals subject to fiber non-linearity induced by 100G PM-QPSK and 10G NRZ-OOK neighbors. The OSNR measurement performance is also demonstrated when root-raised cosine spectral shaping is applied to the signals, with channel spacings of 50GHz and 37.5GHz. Experimental results for OSNR levels up to 30dB and launch powers up to 3dB above the optimum BER launch conditions are shown for different system and signal configurations.
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