Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements

Nonlinear spectrum distortions are caused by the peculiarities of the operation of charge-coupled device elements (CCD), in which the signal exposition time (Time of INTegration–TINT) is one of the significant parameters. A change of TINT on a CCD leads to a nonlinear distortion of the resulting spectrum. A nonlinear distortion of the spectrum, in turn, leads to errors in determining the central wavelength of fiber Bragg gratings (FBGs) and spectrally sensitive sensors, which, in general, negatively affects the accuracy of the measuring systems. This paper proposes an algorithm for correcting the nonlinear distortions of the spectrum obtained on a spectrum analyzer using CCD as a receiver. It is shown that preliminary calibration of the optical spectrum analyzer with subsequent mathematical processing of the signal makes it possible to make corrections in the resulting spectrum, thereby leveling the errors caused by measurements at different TINT.

Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements

Nonlinear spectrum distortions are caused by the peculiarities of the operation of charge-coupled device elements (CCD), in which the signal exposition time (TINT) is one of the significant parameters. A change of TINT on a CCD leads to a nonlinear distortion of the resulting spectrum. Nonlinear distortion of the spectrum, in its turn, leads to errors in determining the central wavelength of Fiber Bragg Gratings (FBG) and spectrally sensitive sensors, which, in general, negatively affects the accuracy of measuring systems. The paper proposes an algorithm for correcting nonlinear distortions of the spectrum obtained on a spectrum analyzer using CCD as a receiver. It is shown that preliminary calibration of the optical spectrum analyzer with subsequent mathematical processing of the signal makes it possible to make corrections in the resulting spectrum, thereby leveling the errors caused by measurements at different TINT.

Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators

We study a class of nonlinear operators that can be written as the composition of a linear operator and a nonlinear map. We obtain results on fixed point index based on parameters that are related to the definitions of nonlinear spectra. As a particular case, existence of positive solutions for a second-order differential equation with separated boundary conditions is proved. The result also provides a spectral interval for the corresponding Hammerstein integral operator.

Bounds on the Transmit Power of b-Modulated NFDM Systems in Anomalous Dispersion Fiber

The performance of various nonlinear frequency division multiplexed (NFDM) fiber-optic transmission systems has been observed to decrease with increasing signal duration. For a class of NFDM systems known as b-modulators, we show that the nonlinear bandwidth, signal duration, and power are coupled when singularities in the nonlinear spectrum are avoided. When the nonlinear bandwidth is fixed, the coupling results in an upper bound on the transmit power that decreases with increasing signal duration. Signal-to-noise ratios are consequently expected to decrease, which can help explain drops in performance observed in practice. Furthermore, we show that there is often a finite bound on the transmit power of b-modulators even if spectral singularities are allowed.