Chapter 3 Plane EM Waves and Lasers in Distinct Media

Transcription

1 hap Pla Wavs a ass sc a - Nomal Icc a a Pla oucg oua a a Ic pla wav: flcv wav: Toal fl: oucg boua a s Sag wav: Zo ull of a - amum of a -λ Zo ull of a - amum of a -λ g. -pola pla wav f amplu6mvm popagas co a mpgs omall o a coucg pla a. a W a. b m h locao as o h coucg pla wh. Sol. 8 ω f ω c Ω µ a a a 6 a 6 s b

2 g. gh-ha cculal pla wav ps b mpgs omall o a pfcl coucg wall a. a m h polaao of h flc wav. b F h uc cu o h coucg wall. Sol. a - s lf-ha cculal-pola a -popaga. b J a a a a a a J - Oblqu Iccs a a Pla oucg oua as Ppcula Polaao T: a s a s s Icc pla wav: s [ a ] s - s s [ ] a s as Paalll Polaao T: a s a s s Ic pla wav: a s [ ] s - s s s

3 g. ufom susoal pla wav 8 6 a s c o a pfcl coucg pla a. a F h fquc a wavlgh of h wav. b m h c agl. c F a of h flc wav. Sol. T cas: a λ ω ω f v p b a a 7 c a - Nomal Icc a a Pla lcc oua Ic pla wav: o o flc wav: o o Tasm wav: o o ou of agal fl compo a flco coffc: Γ Tasmsso coffc: τ a Γτ τ τ τ τ as Γ> > : amum a ma - o ma -λ - mum a m - o m -λ - as Γ< < : a a ma -λ. a m -λ Sag wav ao SW: m ma Γ Γ Γ S S S

4 g. Wha coo occus omal c cas? Sag wav ao? Sol. Γ Γ asoabl o Γ Γ S

5 - Oblqu Iccs a a Pla lcc oua as Ppcula Polaao T: a s a s a s. Ic pla wav: s s s o o flc wav: s s s o o Tasm facv wav: s s s o o ou of agal fl compos a s s s s s s s s s Γ p p v v s s a Γ τ. No: Sll s aw hols ol cas of losslss ma. ws agl: No flco occus wh s µ µ µ µ µ µ f μ μ

6 Poof Γ µ µ µ s s s. µ µ µ g. ufom pla wav 6 mum μ s c o a pla of mum 6 9μ a. a Is ppcula polaao o paalll polaao? b F h fquc a wavlgh of h wav mum. c W ow h flc agl a h facv agl of h asm wav. W ow h u popagao vcos of h c wav â h flc wav â a h asm wav â spcvl. ompu h flco a h asmsso coffcs. f F a of h flc wav. g F a of h asm wav. Sol. a pla Ppcula polaao T b ω ω µ λ λ c 8 f c s s s s a a a µ µ Γ f Γ a g I mum µ 9 s a

7 as Paalll Polaao T: a s a s a s Ic pla wav: s s s flc wav: s s s o Tasm wav: s s s o. ou of agal fl compos a s s p p v v Γ a Γ ws agl: No flco occus wh s µ µ If μ μ a a.

8 g. ufom pla wav 8 6 a s c o a pla of mum 6 9μ a. a Is ppcula polaao o paalll polaao? b F h fquc a wavlgh of h wav mum. c W ow h facv agl of h asm wav. Is qual o h ws agl? W ow h u popagao vcos of h c wav â h flc wav â a h asm wav â spcvl. ompu h flco a h asmsso coffcs. f F a of h flc wav. g F a of h asm wav. Sol. a a 8 6 b 8 6 ω m λ m λ 9 8 ω f c s s Paalll polaao T s s s s a a a µ µ 9 Γ 6 9 f g I mum 6 ω µ 9 9 s a 9 8

9 Sll s aw: s s p p v v a Th flco coffc: Γ a h asmsso coffc: τ Γ s s s s fo ppcula polaao T Γ s s a a fo paalll polaao T Th ma a call gh-ha maals cas μ a a posv. ll h aual ma a gh-ha. owv som afcal maals such as a fw phooc csals ma b lf-ha. I mpls ha h ffcv valus of μ a a gav. Th facv agl as wll as s posv cas of oblqul-c lgh passg h fac bw h sc gh-ha ma. Tha s h c lgh a h asm lgh a h oppos ss of h omal l of h fac. ampl of a oblqul-c las bam passg a slab ma of lf-ha mum:

10 g. lgh a s c fom a oblqul o a aspa sh of hcss wh a of faco as show h fgu. Th agl of cc s. F a b h sac l a h po of a c h amou of h laal splacm l of h mgg a. s s Sol. a s s b a s s c s s s s [s s ] s s

11 - Toal flco a cal gl c I cas of > o > : f ccal agl as c s s Whl > c s s > s ± s a s a s α s as wh s α a s g. lcomagc wav fom a uwa souc wh ppcula polaao s c o a wa-a fac a. Usg μ a 8 fo fsh wa f a ccal agl c b flco coffc Γ c asmsso coffc τ a auao fo ach wavlgh o h a. Sol. s 9s a s c 6.8 b. 66. Γ c τ Γ.89 8 α s. λ λ uao p wavlgh s -log α 9 wh λ λ 8 9 g. of wa a opcal fquc.7 f a a sac u wa ls a lluma ccula aa of a aus m. Sol. s c 9. a 9.. m.7

12 g. Fo pvg fc of wavs ghbog fbs a fo mchacal poco vual opcal fbs a usuall cla b a maal of a low facv as show h fgu wh >. a pss h mamum agl of c a ms of a fo moal as c o h co s fac o b app s h co b oal al flco. oal as a hos ha pass hough h fb as. Th agl a s call h accpac agl s a s h umcal apu N of h fb. Sol. sφ s a ϕ φ > c s s c s a < sϕ φ s a < s a < wh g. m such ha lgh s cof wh h o. Sol. s s c s s s s g. ssumg fo glass calcula h pcag of h c lgh pow flc bac b h psm. Sol. s c < a psm 6 6 τ a psm τ psm a 6 6 oal % No: Th ph of focus OF of a opcal magg ssm s usuall f as OF.λ N.

13 -6 Nomal Icc a Th-la lcc Ifacs I mum Γ I mum I mum ou of agal fl compos a & f Z s s a a ffcv flco coffc Γ Z Z g. If o flco occus f h lao amog a. Sol. Γ s s s s s o Z Z as : as :... o λ... o λ Qua-wav mpac asfom alf-wav mpac asfom g. aspa lcc coag s appl o glass μ o lma h flco of lgh λ.7μm. m h qu lcc cosa a hcss of h coag. Sol. a 6.7 λ

14 -7 Opcal Tho of ul-a Flms Nomal cc: : ' ' : ' ' s s O τ Γ wh λ Γ τ Opcal asf ma: s s Γ a τ Oblqu cc: ] [ ] s[ ] s[ ] [ p p wh p T o p T -flcg flm: Γ a λ ffcv opcal asf ma of -la flm:. gh-flcac flm: sac of N ala qua-wav las of hgh h a low l maals h h l l h h l l N h l N l h Γ N l h N l h.

15 g. m h ffcv flcacs of a gh-la sac N a h-la sac N of ZS h. a g F l Sol. a Γ [ ]. 99 b Γ [ ] g. Th lao bw h flcv a h cc agl.

16 -8 Fab-Po soaos Fab-Po soao: ghwav s soa bw wo paalll plas. Pah ffc bw wo succssv as: Toal oupu -fl: ' δ δ ' ' ' ' ' δ wh δ λ ffc a s h hcss. Toal oupu s Fab-Po soao: ' s h opcal phas I I T δ I T s δ wh T a Tabsopo. Tasmac of Fab-Po soao: I T wh I F s δ F s call h coffc of fss. I s a masum of h shapss of h fc fgs. No ha F bcoms lag as wll as cass. I T δ c N ma occus f δ N O f. I λ λ I T δ c N m occus f δ N O f. I λ λ Fab-Po soao ca b us as a opcal spcal aal. c F spcal ag fquc: f N f N Naual clavag plas: Smcouco lass usuall ul h aual clavag plas as h boh paalll mos of h Fab-Po soao. ll cs: If a pla sg h a l h hl s call ll cs of h pla. No: hl os -hl h l os -hl c.

17 No: Gas s aual clavag pla s -pla. S s a G s aual clavag pla a -pla. -9 Iouco o ass Smula msso: phoo ucs a lco o fall ow fom a hgh-g lvl o a low-g lvl. h gas aoh phoo wh h sam wavlgh a h sam phas. asc chaacscs of lass:. lgm.. Small boag agl.. Sgl wavlgh.. gh ohc. asg coos:. Populao vso: ca hgh-g lvl has mo lcos ha a low-g lvl.

18 g. Th g-lvl ssm of a ub las: Th populao vso occus bw h masabl sa a h gou sa.. Pumpg ssms: Ulg cu vg o oh mhos o pump lcos fom a low-g lvl o a hgh-g lvl.. Opcal soaos: Th las lgh avss bac a foh wh a opcal soao o ga h smula msso. pplcao of lass: as Po as Pcup a as Sghollmao

19 as f sug as acupucu as acupucu mach as sca a s applcaos - Gal Opcal soaos a as os Gal las soao: Two mos wh a a spaao. Sabl coo: If a las mum s sua wh a usabl soao o sabl las ca m. as mos: T m mo f m spos h hooal co a spos h vcal co.

20 Gaussa bam T mo: Fuamal las mo a opcal soao o a lsl mum.. ψ - b a scala fl ' [ ψ ψ ψ ψ wh ψ ψ. ssum ψ >>ψ << ψ ψ-ψ. ψ p{-[p q]} wh. Subsu ψ p{-[p q]} o ψ-ψ -q -q- q -P q q a P -q. qs s sab qq a P -q P-lq. S q w λ a λ ψp{-[-lq q ]} ] [ ] [ p w w w wh ] [ w λ w ] [ w w λ a w λ a w q λ. was: ww a p[- w ] am vg agl of Gaussa bam: bam ] [ a w λ.

21 am Shap: shap las bam a s sbuo. Tasfomao of h Gaussa bam popagag hough a opcal lm law: q q q ma: I ca b ul o scb a a popagag hough a opcal lm ou ou ' ' Fo casca of opcal lms

22 as a passs a plaa lcc fac: Poof ou ou a ou a s ou s as a passs a lcc of hcss : Poof ou a ou. If. as a passs a h ls of focal lgh f: f Poof ou ou a ou a - f - f f as a passs a sphcal lcc fac: wh > f h sufac s cocav; < f h sufac s cov. Poof ou ou a ou s ou s - a - - as a s flc b a sphcal mo:

23 g. Oba h ffcv focal lgh of h h ls ssm. Sol f f6.76mm g. Show ha ls-ma s fomula f wh o > f h sufac s cov o gh; ohws o <. Poof f f g. os a ssm of wo closl-coac h lss of focal lghs f a f spcvl. Th ma s f f f f. c h ffcv focal lgh f s pss b f f f.

24 g. Gaussa bam popaga a sac f spac a pass a h ls of focal lgh f. h avs a sac f spac. m h ma. Sol. f f f f f Thom Th sabl coo of a opcal soao compos of wo sphcal mos of cuvau a a spaao s. Poof O ou p: haacsc polomal s λ -λ-λ -λ. Sabl soao f λ a λ s maga: -. g. Show ha h Fab-Po soao s a sabl soao. Sol. fulflls h sabl coo.

25 g. os wo soaos: a cm cm cm. b cm cm cm. Whch s a sabl soao? Sol. a --> I s o a sabl soao! b <..7.8< I s a sabl soao! g. Gaussa bam s focus b a ls. Th was of Gaussa bam s w whch s loca o h sufac of a ls of focal lgh f. m h mso of h was w of h oupu bam a s locao l. λ λ Sol. pla q w w q pla q q a a b q wh af f a b bλw q. pla q q a l a b l λ q q l a b a b q w a b [ l] a b a b a f l a b fλ w <f a w fλ w fλ w λ w l<f h alsc focal lgh of a Gaussa bam s lss ha h al focal lgh of h ls. I cas of v sho λ w fλ w fλ w λ w mus vlop h sho-λ las o a aa so h hgh-s opcal s. Ohws h log-λ las ca o b focus wh a small ag o c a small p. Thus covoal VV uls 6m bu blu-a V uls blu lgh m. h sam aso w mus ul sho-wavlgh lgh o fabca h mass of h I pas compsg vcs.

26 - Gags a Phooc sals Gag: Pocal sucu fo opcal ffaco. Phooc sals: as of opcal scas.

27 g. ompaso bw ps of 9 b phooc csal wavgus. b K. Y... Tsa 蔡佳辰 T.. Wg 翁宗誠 Y.. Kuo 郭奕 麟. W. Kao 高智偉 K. Y. h 陳奎元 a Y. J. 林宇仁

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