复旦大学：《电动力学》学生课堂报告_关于“光学黑洞那点事儿”的课堂报告

Something About Optical blackhole LiL(李力) Dept Phys., Fudan Univ AikiNogard@gmail.com 091229 ED 10min presentation

Something About Optical Blackhole Li Li (李力) Dept. Phys., Fudan Univ. Aiki.Nogard@gmail.com 091229 ED 10min presentation

Introduction Appl. Phys. Lett. 95, 041106(2009)

Appl. Phys. Lett. 95, 041106(2009)

Something About Optical Blackhole Outline Introduction Begin with Maxwell Equation Mathematica o Comso

Outline • Introduction • Begin with Maxwell Equation • Mathematica • Comsol

Begin with Maxwell Equation>>Eikonal Function E(,t)(E( iot Hr D ( Ho(r)) S(r=ns.r =2。2z no 27 real scalar function 元444 of position 0 Ho(r) Are/ir

0 0 E(r,t) E (r) H(r,t) H (r) i t e −          =     0 0 0 E (r) H (r) e e ik r ik ns r e e h h               = =       0 0 0 2 2 2 k s s ns         = = = S r ns r ( ) =  real scalar function of position

Begin with Maxwell Equation>>Play with Good Friends V·D=0 (VS)2=n2 le VS=0 aB V×E VS×e-ph=0 t h VS=O V·B=0 VS×h+Ee=0 V×H aD n=√EL c at Short Wave Limit 。→>∞ E(r1)(E(r) 0 食 e H(r,+)(Ho() VS (e.VInE+ve) V·EEn=0 Eo(r)elikoslvsxe-uh V V×E0-i0H=0 Ho(r) h V·H=0 hVS=-,(hVln+V·h) V ×h0 认EE=0 VS×h+Ee V 0 i

0 1 0 1 D B E c t B D H c t   =      = −       =     =   0 0 0 0 0 0 0 0 0 0 0 0 E E ik H H H ik E       =    − =     =     + = 0 0 E(r,t) E (r) H(r,t) H (r) i t e −          =     0 0 0 E (r) H (r) e ik S e h         =     0 0 0 0 1 ( ln ) 1 1 ( ln ) 1 e S e e ik S e h e ik h S h h ik S h e h ik       = −  +        − = −        = −  +       + = −     0 0 0 0 e S S e h h S S h e     =    − =    =     + = Short Wave Limit 0 k →  2 2 ( )  = S n n = 

Begin with Maxwell Equation>>Aim at the trajectory (VS)2=n2 n=√EL Foundmental Equation of Geometrical Optics e·VS=0 VS×e-Mh=0/ⅤSVS vsd h VS=0 VS VS OC VS×h+Ee=0 as

2 2 ( )  = S n n =  0 0 0 0 e S S e h h S S h e     =    − =    =     + = S S n   S S s n S   = =  d r n S ds = 

Begin with Maxwell Equation>>Aim at the trajectory dd Vn Uniform Medium: neconst 0 Straight Line

d d r n n ds ds     =    Uniform Medium： n=const. 2 2 0 d r ds = Straight Line

Begin with Maxwell Equation>>Spherical Symmetry -60 R 2 Appl.Phys.Lett.95,041106(2009) nd=const. Bigger n n=n( s

0 2 2 2 rR d c n c      − = − −  n n r = ( ) Appl. Phys. Lett. 95, 041106(2009) nd const = . Bigger n!

Something About Optical Blackhole Outline Introduction Begin with Maxwell Equation Mathematica o Comso

Outline • Introduction • Begin with Maxwell Equation • Mathematica • Comsol

Mathematica>> Constant Refractive Index Result of this calculation 0-b0=-C Scattering State C n∝ c const. Refractive Index Function WaterBall

n const  . 0 2 2 2 r R d c n c      − = − − 