An inverse eigenvalue problem. Application: Graded-index optical fibers

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

“…The accuracy and eectiveness of the method are highly dependent on the thickness parameter values. The work presented in [54] seems very close to ours. However, the approach adopted in [54] diers from our solution methodology by several aspects, chief among them: (a) the ISPP is formulated in [54] as an optimization problem under constraints and is solved via the use of Lagrange multipliers, and (b) the Fréchét derivatives with respect to the refractive index prole are computed using a nite dierence (FD) approximation of order 1.…”

“…N P is typically between 2 and 4, for most refractive index proles of practical interest [60], [56] [58]. Note that the numerical results reported in [54] were obtained with N P = 2 and 3 only.…”

“…This ISPP occurs in network communications when developing optical waveguides that achieve a desired lightwave transmission. Extensive eort has been deployed in the last two decades to solve numerically this class of inverse spectral problems, as attested by the numerous publications (see, e.g., [44] [54]). Prior to that, an interesting attempt was made in the mid 70 s [55].…”

“…However, the approach adopted in [54] diers from our solution methodology by several aspects, chief among them: (a) the ISPP is formulated in [54] as an optimization problem under constraints and is solved via the use of Lagrange multipliers, and (b) the Fréchét derivatives with respect to the refractive index prole are computed using a nite dierence (FD) approximation of order 1. Due to the constraints considered in [54], the method is limited to continuous proles at the interface core-cladding and its eciency (accuracy and convergence) is sensitive to the FD step size value when approximating the derivatives. In the present work, we investigate the question of the uniqueness of the solution for the considered ISPP and characterize its Fréchet derivative with respect to the refractive index prole.…”

On some direct and inverse problems concerning guided modes in optical fibers

“…In the last ten years, the team whose members are the three estimated authors: Professor Abdelaziz Choutri, Dr. Abdelwahab Boureghda and Dr. Hayat Rezgui have been able to enrich the existing literature with many very important scientific works (articles, conference papers, presentations, videos, ...) in the fields of optical fibers, waveguides, inverse problems, direct problems, ... etc. We cite, as examples, the manuscripts [1][2][3][4][5][6][7][8][9][10] in which many current issues have been addressed and resolved with graphic and numerical illustrations, the conference papers [11][12][13] and the video presentations. 14,15 It should be noted that the reference 7 has been read 5300 times on the site: https://www.researchgate.net/, which surpasses the readability of 99% of the articles published on the same site since the year 2022.…”