Eigenfunction expansions of source-excited electromagnetic fields in cylindrically stratified unbounded gyrotropic media

Abstract

We consider electromagnetic fields excited by spatially bounded, arbitrary given sources in the presence of a cylindrical guiding structure immersed in an infinitely extended homogeneous gyrotropic background medium whose permittivity and permeability are both describable by tensors with nonzero off-diagonal elements. The axis of symmetry of the considered cylindrical structure is assumed to coincide with the gyrotropic axis. The total field is sought in terms of the vector modal solutions of source-free Maxwell's equations. By demanding completeness of the modal spectrum and using a continuity argument, we determine the content of the modal spectrum and obtain an eigenfunction expansion of the source-excited field in terms of discrete-and continuous-spectrum modes.

Ηλεκτρομαγνητική Προσομοίωση Μη Επίπεδων Διατάξεων Με Τη Μέθοδο Των Πεπερασμένων Διαφορών

“…Ç äéáôïìÞ áõôÞ åßíáé ç äéóäéÜóôáôç ãåùìåôñßá ðïõ ðñïóïìïéþíåôáé óôï ðåäßï ôçò óõ÷íüôçôáò ìå óêïðü ôçí åîáãùãÞ ôùí éäéïôéìþí êáé ôùí éäéïäéáíõóìÜôùí. ÐÝñáí ôïõ ó÷åäéáóìïý ìéêñïêõìáôéêþí óôïé÷åßùí, ç ãíþóç ôùí éäéïóõíáñôÞóåùí ìéáò äéÜôáîçò åßíáé âáóéêü óôïé÷åßï óå áñéèìçôéêÝò ìåèüäïõò, üðùò óôç ìÝèïäï ÐñïóáñìïãÞò Ñõèìþí (Mode Matching, MM, [3{5]), åíþ ìå ôï áíÜðôõãìá ôïõ ðåäßïõ óå éäéïóõíáñôÞóåéò åßíáé äõíáôÞ êáé ç ìåëÝôç ðñïâëçìÜôùí óôá ïðïßá ìïíôåëïðïéåßôáé êáé ç ðçãÞ äéÝãåñóçò, [6].…”

“…ÐáñÜëëçëá, ôï áíÜðôõãìá ôïõ çëåêôñïìáãíçôéêïý ðåäßïõ óå éäéïóõíáñôÞóåéò åßíáé âáóéêÞò óçìáóßáò ôüóï ãéá áñéèìçôéêÝò (ð.÷. ÌÝèïäïò ÐñïóáñìïãÞò Ñõèìþí, (Mode Matching), [3,4] Þ ÌÝèïäïò Ñïðþí (Method of Moments), [91{93]) üóï êáé ãéá çìé-áíáëõôéêÝò ôå÷íéêÝò åðßëõóçò çëåêôñïìáãíçôéêþí ðñïâëçìÜôùí, [6]. Óêïðüò ôïõ êåöáëáßïõ áõôïý åßíáé ç óýíôïìç ðåñéãñáöÞ êÜðïéùí åê ôùí ðáñáðÜíù ðåñéðôþóåùí, åóôéÜaeïíôáò óôá óçìåßá åêåßíá üðïõ ç ãíþóç ôùí éäéïôéìþí êáé éäéïäéáíõóìÜôùí äéáäñáìáôßaeåé êáèïñéóôéêü ñüëï.…”

“…[58,59], ôçí êýñéá þèçóç ôçí Ýäùóå ï Yee, [60] ôï 1966, ï ïðïßïò åéóÞãáãå Ýíá ÷þñï äéáêñéôïðïßçóçò óôïí ïðïßï ÷ñçóéìïðïéïýíôáé äýï áëëçëïóõíäåüìåíá ðëÝãìáôá ìåôáôïðéóìÝíá ìåôáîý ôïõò êáôÜ ìéóü êåëß (interleaved grids), üðùò óôï ó÷Þìá 4. 6. ¼ðùò êáé óôçí ðåñßðôùóç ôçò FDFD (ç ïðïßá Üëëùóôå åßíáé ìåôåîÝëéîç ôçò FDTD), óôéò áêìÝò ôïõ åíüò ðëÝãìáôïò ïñßaeåôáé ôï çëåêôñéêü ðåäßï, åíþ óôéò áêìÝò ôïõ Üëëïõ ðëÝãìáôïò ïñßaeåôáé ôï ìáãíçôéêü ðåäßï.…”

“…Ôï ëïãéêü äéÜãñáììá ôçò ðñïãñáììáôéóôéêÞò äéáäéêáóßá ðïõ õëïðïéåß ôç ìÝèïäï ðáñáëåßðåôáé áðü ôï ðáñüí êåöÜëáéï êáé äßíåôáé óôï ðáñÜñôçìá É. 6.1 Äéáêñéôïðïßçóç óå ïñèïãþíéï êáìðõëüãñáììï ðëÝãìá Ç ðñïôåéíüìåíç ìÝèïäïò ðåðåñáóìÝíùí äéáöïñþí óôï ðåäßï ôçò óõ÷íüôçôáò ãéá ïñèïãþíéá êáìðõëüãñáììá óõóôÞìáôá óõíôåôáãìÝíùí âáóßaeåôáé óôç äéáêñéôïðïßçóç üëùí ôùí ôåëåóôþí êëßóçò, áðüêëéóçò êáé åîùôåñéêïý ãéíïìÝíïõ ôùí åîéóþóåùí ((5.31)-(5.33)) óå Ýíá ïñèïãþíéï êáìðõëüãñáììï ðëÝãìá. Ïé ôåëåóôÝò áõôïß ìåôáôñÝðïíôáé óå ðßíáêåò, ìå ìéá äéáäéêáóßá ðáñüìïéá ìå áõôÞ ðïõ ÷ñçóéìïðïéåßôáé óôçí êëáóóéêÞ ÊáñôåóéáíÞ FDFD ìÝèïäï, [109].…”

“…ÐáñÜëëçëá, óôçí êáôáêüñõöç êáìðýëùóç ï ñõèìüò TE 01 ðáñá-ìÝíåé ó÷åäüí áíåðçñÝáóôïò óå üëï ôï åîåôáaeüìåíï öÜóìá. Áíôßèåôá, óôçí ðåñßðôùóç ôçò ðëÜãéáò êáìðýëùóçò ïé êáìðýëåò äéáóðïñÜò ôïõ ñõèìïý TE 01 ìåôáôïðßaeïíôáé óçìáíôéêÜ ðñïò ôá åðÜíù, åíþ ç ðñïò ôá åðÜíù ìåôáôüðéóç ôïõ TE 10 êáé ç ðñïò ôá êÜôù ìåôáôüðéóç ôïõ TE 20 ñõèìïý åßíáé ó÷åôéêÜ ìéêñüôåñç.Ïé ëüãïé êáìðýëùóçò (R=b) ôïõ ó÷Þìáôïò 7.3á êáé (R=a) ôïõ ó÷Þìáôïò 7.3â Þôáí ßóïé ìå 2 ãéá ôá áðïôåëÝóìáôá ôùí ó÷çìÜôùí 7.5 êáé 7 6…”