Chng 2NHNG KHI NIM C BN V QUANG PHI TUYN-HIN TNG PHT SNG HI BC HAI

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Ni dung

H phng trnh Maxwell

Phng trnh sng in t

H phng trnh Maxwell

Mi trng bnh thngMi trng phi tuyn

l t thm l hng s in mij l mt dng l mt in tch khiMi trng phi tuyn thng l in mi j=0, =0

H phng trnh Maxwell trong mi trng

Hai phng trnh sng

Ly rota hai v phng trnh (1), ta c:

Phng trnh sng in t

Phng trnh sng in t

Nu xt mi trng phi t tnh = 0

Phng trnh sng in t trong mi trng phi tuyn

Phn ny nhm tr li cu hi: ti sao nh sng cng cao c th i mu khi qua mi trng vt liu?

Xt in trng tc ng vo mi trng vt cht

in trng s tc dng lc in ln cc electron

Ht nhn (mu ) cng tc dng lc ln cc electronCc lc tc dng ln electron gm: lc in trng, lc ht nhnCc lc ny gy ra gia tc cho electron

Fht nhn ty thuc vo in trng mnh hoc yu

Khi in trng yu

(1)

Gi sElectron lch khi v tr cn bng t lch x t l tuyn tnh vi lc ht nhn

y l mt phng trnh vi phn tuyn tnh theo xKhi in trng mnhElectron lch khi v tr cn bng nhiu lch x khng t l tuyn tnh vi lc ht nhn

y l mt phng trnh vi phn phi tuyn i vi x

Khi in trng yu

(1)

Gi s

Khi in trng mnh

Nghim x ca phng trnh ny c dng:

Tc l electron dao ng iu ha vi tn s .Nghim x ca phng trnh ny c dng: Chiu vo in trng tn s nhng electron li dao ng vi tn s 2 .

Nghim x ca phng trnh ny c dng: (1)Nu vit biu thc cng in trng di dng s phc:

Nghim x ca phng trnh ny c dng:

Nu vit biu thc cng in trng di dng s phc:

Nghim x ca phng trnh ny c dng:

Bi ton: Xt s tng tc gia nh sng n sc v mi trng tinh th. Gi s tinh th c chiu di L. Sng u vo ny c dng: Dng phng trnh sng trong mi trng phi tuyn tm sng Eout thot ra khi tinh th. Bit sng ny c tn s 2, s sng k2

Bi ton: Xt s tng tc gia nh sng n sc v mi trng tinh th. Gi s tinh th c chiu di L. Sng u vo ny c dng: Dng phng trnh sng trong phng trnh phi tuyn tm sng Eout thot ra khi tinh th. Bit sng ny c tn s 2.

Hng gii: Dng phng trnh sng

1.Vit li phng trnh sng trn cho Eout .2.Gi nh Eout c dng no :3.i lng cn tm l bin ca sng E2 4. tnh hai s hng bn v tri, chng ta ch cn ly o hm.5. tnh phn cc, dng cng thc P2 =N.e.x(2) (2)Trong N l s phn t trn n v th tch.

Cui cng chng ta tm c:Trong

Vn quan trng nht: Hiu sut pht sng hi bc hai=kh nng chuyn nh sng tn s sang nh sng tn s 2

Hiu sut=cng nh sng u ra/cng nh sng u voCng nh sng t l vi bnh phng cng in trngCui cng ta tnh c hiu sut:

Trong ton hc, ta c:Hiu sut ph thuc vo s hng Khi eSHG cng t gi tr cc i bng:iu kin hp phaiu kin ng b v khng gian

t c iu kin hp pha c nhiu cch, mt trong nhng cch l dng tinh th. Do , chng ta s n li mt s kin thc v tinh th.

Khi ni n cu trc chng ta phi xt n 2 yu t:Cc thnh phn c bn trong cu trcQuy lut sp xp cc thnh phn c bn

Cc thnh phn c bn trong cu trcQuy lut sp xp cc thnh phn c bn n vQuy lut sp xp: lp i lp li cc n v

Tm li, v mt cu trc, tinh th l mt mi trng tun hon, trong c mt nhm nguyn t lp i lp li.Nhm nguyn t ny l thnh phn c bn, c trng cho tng tinh th. Ta thng gi chng l n v.

Tnh bt ng hng:

Tinh th l mt mi trng bt ng hng, tc l cc tnh cht vt l theo nhng hng khc nhau th khc nhau.

Hin tng lng chitHin tng lng chit l hin tng tia sng b tch lm hai khi i vo mi trng tinh th. (nh ng)

Trong tinh th c mt phng m khi truyn theo , nh sng khng b tch lm hai, phng gi l trc quang hc ca tinh th.

Nhng tinh th c mt phng nh vy gi l tinh th n trc.

Nhng tinh th c hai phng nh vy gi l tinh th lng trc.

Trong hai tia b tch, tia tun theo nh lut khc x gi l tia thng, chit sut tia thng c gi tr khng i, k hiu l no.

Tia khng tun theo nh lut khc x gi l tia bt thng, chit sut tia bt thng thay i, gi tr chit sut ca n ph thuc vo s nh hng ca n so vi trc quang hc, k hiu l nH.

V d: Gi s tinh th trong hnh l tinh th n trc. Trc quang hc ca n to vi tia bt thng mt gc .

Trc quang hc

Phng phn cc l phng ca vector cng in trng.

Tia thng v tia bt thng c phng phn cc vung gc nhau.

i vi tinh th n trc, tinh th c chit sut tia bt thng nh hn chit sut tia thng gi l tinh th n trc m. Vd: KDP.

i vi tinh th n trc, tinh th c chit sut tia bt thng ln hn chit sut tia thng gi l tinh th n trc dng. Vd: Bng lan (CaCO3).

Mi quan h gia cc i lng sng: k: ln ca vector sng (rad/m): tn s (Hz) (mt s sch k hiu l f).

: tn s gc (rad/s)0: bc sng trong chn khng (m)n:chit sutCh : khi truyn trong mi trng c chit sut n, bc sng ca nh sng thay i nhng tn s nh sng khng thay i, mu sc nh sng do tn s quyt nh.

Xt li biu thc tnh hiu sut tng qut:Trong biu thc ny, hm c dng:

Cc v tr cc i ca hmCc i th hai ch bng 5% cc i th nht. Ta gi di tinh th c hiu sut tng tc quang phi tuyn cao l di kt hp.

trn ta c:i vi mi trng bnh thng, chit sut n thay i theo nn k khng th bng khng hiu sut cc i. i vi tinh th n trc m, gi s sng ti (hai sng c cng tn s ) l tia thng v sng hi l tia bt thng.

Hai i lng ny c th bng nhau ng vi mt gc nht nh.

l gc hp pha.

Tng tc gia cc sng c bn (sng o) hnh thnh sng hi (sng bt thng, sng H).o

e

T s gia cng sut v cng sut cc i (khi hp pha) ca sng hi l:

V x ph thuc vo gc nn trong thc nghim chng ta c th kim tra h thc ny bng cch o t s cng sut theo hoc hiu - .

Trong cc th nghim quang phi tuyn, thng thng ngi ta s dng chm laser c bin dng Gauss (chm Gauss) v chm ny c cht lng tt nht.

Phn b cng theo phng ngang ca chm Gauss.

Phn b cng chm Gauss trong khng gian ba chiu.

Chm Gauss nhn theo phng dc.

V cu trc sng ca chm Gauss, gn c chm sng l sng phng xa c chm sng l sng cu.

c chm, cng ln nht nn qu trnh tng tc phi tuyn xy ra hiu qu nht, v th chng ta thng t tinh th trong c chm.LTinh th

Tng tc quang phi tuyn c th xem l tng tc gia cc sng phng trong mi trng phi tuyn c chng ta kho st trn.

Tuy nhin, cht ch hn, chng ta cn iu chnh cc kt qu trn.

trn, v xt sng phng, chng ta s dng biu thc cng in trng l:Tc l bin E l hng s.Tuy nhin, i vi chm Gauss, bin ca n thay i theo phng ngang, nn lc ny:

V cng thc tnh cng sut cng khc:

Bng phng php tng t nh trn, chng ta tnh c hiu sut l:

Loi tng tcBc sng voBc sng raGc hp pha ()