Optical network monitoring and soft failure identification such as optical filter shifting and filter tightening is increasingly significant in the future complex and dynamic optical networks. Center frequency shift of optical filtering device in optical network has a serious impact on the perfor-mance of multi-span transmission, especially in high spectrum efficiency faster-than-Nyquist (FTN) transmission systems with various optical switching and add/drop nodes. Existing moni-toring schemes generally have problem of high cost, high complexity and the inability to realize multi-channel online monitoring, which makes it difficult to be applied in wavelength division multiplexing (WDM) system with numerous nodes. In this paper, a monitoring scheme of fre-quency shift of optical filtering devices based on optical label (OL) is proposed and demonstrated. The signal spectrum of each channel is intentionally divided into many sub-bands with corre-sponding optical labels loading. The characters of spectrum power changing caused by frequency shift can be reflected on labels power changing of each sub-band, which are used to monitor and estimate the value of frequency shift by DSP algorithm. Simulation results shows that the that the monitoring errors of frequency shift can be kept below 0.5GHz reasonably after 10-span WDM transmission in FTN polarization multiplexing m-ary quadrature amplitude modulation (PM-mQAM) systems. In addition, 250km fiber transmission experiments are also carried out and the similar results are obtained, which further verify the feasibility of our proposed scheme. The characters of low cost, high reliability and efficiency make it a better candidate for practical ap-plication in the future FTN WDM networks.

We derive the thermal noise spectrum of the Fourier transform of the electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers. It is important to stress that no additional assumptions at all were used in this straightforward proof.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

This paper shows that by applying the Nyquist-Shannon sampling theorem, the spatial and temporal resolution of a simulation can be no more than half the resolution of the simulating reality. This has significant implications for not only the values of the observables in the simulation but also its physical laws. This progressive halving of nested simulations coupled with the minimum resolution compatible with the production of a simulation also sets a limit to the nestedness of a lineage of simulations (it is by no means infinite). The limit of nestedness is then used to calculate the probability that we are living in a simulation assuming a single base reality. This will be shown to be significantly lower than popular expectation. A Kardashev-like scale, with three variants, is also developed to gauge the technological advancement of a civilization in relation to the extent to which it can extract information from space and time.