On the higher order modes of elliptical optical fibers

Oblique scattering/hybrid wave propagation in elliptical homogeneous configurations & spectrum/preconditioning of the singular domain integral equation

“…(2.4), do not appear. This fact was also observed by Saad in [56] when he was missing some modes due to unfavorable numerical conditions. So to conclude, by keeping x 2 1 and setting h !…”

“…The elliptical dielectric waveguide maintains only hybrid modes, due to the lack of the symmetry of the configuration. As can be also seen from [38,51,56], these modes are split in two groups, the even modes and the odd modes. According to the definition given by Yeh in [77], the even group of modes corresponds to the equations that describe the even part of the axial component of the magnetic field, while, the odd group of modes corresponds to the equations that describe the odd part of the axial magnetic field component.…”

“…The finite element method is then again used in [14] to obtain the cutoff frequencies for the higher-order LP modes in fibers of arbitrary cross section and numerical results are given for circular as well as for elliptical cores, for various eccentricities. An alternative method to that of Mathieu series expansion, namely the point-matching numerical method, is used in [56] for the calculation of some higher-order hybrid modes. Then, in [50], a comparison between the Mathieu series expansion and the point-matching method employed in [56] is made, and discrepancies are resolved.…”

“…An alternative method to that of Mathieu series expansion, namely the point-matching numerical method, is used in [56] for the calculation of some higher-order hybrid modes. Then, in [50], a comparison between the Mathieu series expansion and the point-matching method employed in [56] is made, and discrepancies are resolved. An experimental approach is presented in [20] for the cutoff calculation of some first higher-order modes in elliptical dielectric waveguides.…”

“…Η µέθοδος των πεπερασµένων στοιχείων έχει χρησιµοποιηθεί στην [14], προκειµένου να υπολογιστούν οι συχνότητες αποκοπής για τους ανώτερους τάξης ρυθµούς, και υπό το πρίσµα της ασθενούς κυµατοδήγησης, σε ίνες αυθαίρετης διατοµής, και δίνονται αριθµητικά αποτελέσµατα για ίνες µε ελλειπτικό πυρήνα για διάφορες εκκεντρότητες. Στην [50], γίνεται x PREFACE σύγκριση µεταξύ της µεθόδου των συναρτήσεων Μάθιου, της µεθόδου που χρησιµοποιήθηκε στην [56], και ερµηνεύονται διάφορες αποκλίσεις. Μια πειραµατική προσέγγιση παρουσιάζεται στην [20], για τον υπολογισµό της αποκοπής κάποιων ρυθµών υψηλότερης τάξης σε διηλεκτρικούς ελλειπτικούς κυµατοδηγούς.…”