Wave Propagation 2010 Part 8

Tham khảo tài liệu 'wave propagation 2010 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 202 Wave Propagation At the boundaries of the considering regions at 0 n- Y and 0 n2 the mentioned above boundary conditions for tangential and normal components of electric field must be satisfied. Substituting into the boundary conditions the expressions for the field components and taking into account that - cos n - y cosY we have the following four equations Pa cosY a - Pa cos n - YÌ C - Pa cosz D 0 SmPa cos Y a SdPa cos n - y C - SdPa cosy D 0 B - C - D 0 -SpB Sdc -SdD 0 where pa cos n - yỴ đpa ụ dụ ụ oS -Y A nontrivial solution of the system exists when the determinant is equal to zero Pa cosy Sm Sd pa cosY 0 0 0 -pa cos n-Y -pa cosY 0 pa cos n-y -pa cosY 1 -1 -1 - p d 1 -1 By expansion the determinant we have Sm Sd pa cosY Pa cos n-ý Pa cosY Sp Sd Pa cos n - ý - Pa cos ý pa cos y pa cos n - y - pa cosY Sp Sd pa cos n - y pa cos y 0. Numerical calculations of the functions in 2 were carried out with the aid of the hypergeometric function. Taking into account the identity Olver 1974 d d-F a b c z abF a 1 b 1 c 1 z we find a . . I . I _ sin0 I _ _ 1 cos0 d0pa cos0 -sin0dpa ụ dụụ cos0 a a F - 1 a 2 2 --2 -0pa -cos0 sin0dpa ụ ldụụ -cos0 a a 1 n F -a 1 a 2 2 1 os0 and therefore X a a 11 I 1 -cosớl dp ụ dụ -F -a 1 a 2 2 ----- I a ụH ụụ cos0 2 I 2 J Nanofocusing of Surface Plasmons at the Apex of Metallic Tips and at the Sharp Metallic Wedges. Importance of Electric Field Singularity 203 i a a 1 1 cosd dp u di. -F -a 1 a 2 2 ---- I. avH u cose 2 J 2 J By substituting these expressions into 2 we have 1 -a 1 a 2 2 c ì X I 2 J I i - - 1 - cos n-y f I f _ _ 1 - cosy ll 1 F -a a 1 1 ------------ I 1 -- FI -a a 1 1 -_ I I d JI 2 JI d JI 2 JJ r __ . . 1 -cosyl F -a a 1 1 ---_ X J 2 J r IJ _ _ 1 - cos n-y I i I f _ _ 1 - cosy Il 1 - F -a 1 a 2 2 -- y - 1 -- FI -a 1 a 2 2 -----co_y l 0. I d JI 2 J J d JI 2 JJ If the particular case when 1 d 1 is considered this equation is transformed into dpa cosr p a -cosr mpa -cosr pa cosr 0. Since py cosy - sin yF Pa cosy and pa .