k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19)
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1 TOTAL INTRNAL RFLTION Kmacs pops Sc h vcos a coplaa, l s cosd h cd pla cocds wh h X pla; hc 0. y y y osd h cas whch h lgh s cd fom h mdum of hgh dx of faco >. Fo cd agls ga ha h ccal agl s 1 ( /, h hooal compo of (.. h compo x of h cd wav wll b ga ha h magud of h asmd lgh s vco = (/ '. Ths s show h fgu blow; oc s oo small o sasfy h qud macs bouday codo, x x (19 Thus, h s o al vco o sasfy h codo (19 wh >. as = as > c Slow mdum c ' fas mdum ' X ' < Sll s law o bg fulflld Fg. 0 Toal al flco. Fo > h lgh of h al-vaabl wavvco (asmd wav us ou o b oo small o sasfy h bouday codo x x. Tha s, dos o xs a al-vaabl wav-vco abl o sasfy h mac codos (Sll s law a h bouday. Th mplcao s ha h cd wav s fully flcd (h s o popagag asmd wav pag h dco.
2 Th s a way o g aoud hs lmao. W allow h Idd, v hough h magud of s fxd ad qual o, Noc, x ( x ( ' could b ga ha pu complx umb, ' f o b a complx vco. ( wh gav; ha s, f w a Accodgly, l s cosd a asmd wav of complx vco, (, 0, complx vco (0 whos modulus squa x x x ( 0 x ( j x s qud o sasfy, (0 ' Th complx wav-vco (, 0, j s h abl o sasfy h Sll s law fo cd agls >, Noc also x o, (1 x x x ' (1
3 as = as > c Slow mdum fas mdum < c ( x, 0, omplx vco Fg. 1 Noc o h gh-sd dagam ha h vasc wav popagas alog h fac wh wav-vco compo x, ( x > (/. x X Nx, fo a gv cd agl >, l s fgu ou h cospodg valu of. Th macs codo x x x mpls, x x S S. x x S ( Usg hs valu (1, gvs, x x S S S (3 Usg s 1 ( /
4 S Sc fo > (3 I summay, Icdwav Rflcd wav Tasm d wav - o (4 - (4 o - o, wh ( x, 0, j (4 o x x x j γ - ω ω x o j ( x x - ω o - Fo h pacula cas a hads, w a h posv sg (ohws w would hav a wav cayg f gy. γ x x - ω o (fo < 0 - o - o < c ' x ( x, 0, j ' X o γ x x - ω Fg. Th facd wav popagas oly paalll o h sufac (wh wav-vco x ad s auad xpoally (dcay faco alog h vcal dco h mdum of low dx of faco.
5 So, dos xs lcomagc fld h mdum of low dx of faco, bu s auad xpoally byod h fac. No gy flow (o popagag gy cosss vcally h fac. Dyamcs pops How o copoa h complx vco Fs, Sll s law sas s / Noc, Hc, o has, s s s s o h Fsl quaos? s. I ms of h ccal agl (5 s 1 fo > (5 s a complx agl wh >. [ Noc, fo a complx agl / j o obas 1 s ( / j 1 1 ( j 1 >1 ] L s valua also h cos of h complx agl. O o had, w hav ' os os, o h oh had, whch gvs os Usg h xpsso fo gv (3, os S whch gvs, os S S Sc 1 1 fo > (6
6 Noc fom (4 ad (6 ha h complx agl sasfs, s cos 1 (7 Th xpsso fo cos, obad abov fo h cas wh > a sd ow h Fsl s quaos: Fo T o s- polaao o o os os os os Amplud flco coffc o o os os os Amplud asmsso coffc Noc ha fo a complx os, as gv (6, h magud of s qual o1, as xpcd a oal al flco cas. 1 (8 Fo TM o p- polaao o os os o os os Amplud flco coffc o o os os os Amplud asmsso coffc Noc also ha (6 mpls, 1 (6 Noc ha boh cass, T ad TM polaao, h complx os gv (4 suls complx amplud flco coffcs. I mpls ha, ud oal al flco codos, h s (7 a chag h phas of h flcd wav. Fsl s hombus. Ths phas chags ca b uld o cov o yp of polaao o aoh. Fo xampl a Fsl s hombus, laly polad lgh wh qual T ad TM polaao ampluds s covd by wo succssv al flcos (ach volvg a lav phas chag of 45 o o cculaly polad lgh.
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