Chirped Fiber Bragg Gratings

Polarimetric measurements of PMD and differential group delay ripple in chirped fiber Bragg gratings

“…The average value ͗⌬͘ of the grating PMD depends on the grating chirp and the fiber birefringence as [1]:…”

“…Chirped Bragg gratings, with high negative chromatic dispersion coefficient, are promising components for dispersion compensation in a compact size [1], but measurements show that they could present a high polarization mode dispersion (PMD) and polarizationdependent loss (PDL). PMD has been demonstrated to be important in chromatic dispersion compensating fiber gratings [1][2][3][4][5]. The birefringence in these gratings is due to two factors: the fiber intrinsic birefringence and the birefringence induced by the writing process [1].…”

“…PMD has been demonstrated to be important in chromatic dispersion compensating fiber gratings [1][2][3][4][5]. The birefringence in these gratings is due to two factors: the fiber intrinsic birefringence and the birefringence induced by the writing process [1]. In an ideal chirped grating, for which the group delay is a linear function of wavelength, the differential group delay (DGD) between the two polarization modes, induced by the birefringence, is constant and proportional to the slope of group delay curve [1].…”

“…The birefringence in these gratings is due to two factors: the fiber intrinsic birefringence and the birefringence induced by the writing process [1]. In an ideal chirped grating, for which the group delay is a linear function of wavelength, the differential group delay (DGD) between the two polarization modes, induced by the birefringence, is constant and proportional to the slope of group delay curve [1]. On the other hand, ripples in the delay curve of real gratings may lead to spikes in the wavelength dependence of DGD.…”

“…The conjugate-gradient (CG) method, which is often used for the iterative solution of method-of-moments (MoM) matrix equations, requires two matrix-vector products [1] per iteration. Although several computationally efficient techniques have recently been introduced for performing these matrix-vector products, such as the fast-multipole method (FMM) [2] and the multilevel fast-multipole algorithm (MLFMA) [3], it is still desirable [4 -6] to reduce the total number of iterations when a iterative solver is repeatedly used to solve a set of matrix equations in order to accommodate parameter change, such as the frequency or the angle of incidence.…”