B GIO DC V O TO

TRNG I HC KHOA HC T NHIN

KHOA KHOA HC VT LIU

B MN VT LIU NANO V MNG MNG

--------

TIU LUN TT NGHIP

TI

ONE-DIMENSIONAL PHOTONIC CRYSTALS

GING VIN HNG DN

Th.s NG HI NG

SINH VIN THC HIN

NGUYN C VNG

tp H CH MINH, thng 12 nm 2013

B GIO DC V O TO

TRNG I HC KHOA HC T NHIN

KHOA KHOA HC VT LIU

B MN VT LIU NANO V MNG MNG

--------

TIU LUN TT NGHIP

TI

ONE-DIMENSIONAL PHOTONIC CRYSTALS

GING VIN HNG DN

Th.s NG HI NG

SINH VIN THC HIN

NGUYN C VNG

tp H CH MINH, thng 12 nm 2013

Li cm n

Li u tin,em xin by t li cm n chn thnh v su sc nht n thy Th.s

NG HI NG tn tnh hng dn em hon thnh bi lun ny.

Em xin chn thnh cm n cc thy c trng i hc khoa hc t nhin ging

dy em trong nhng nm hc i hc v em xin by t lng bit n su sc n cc

thy c khoa KHOA HC VT LIU chuyn nghnh Vt Liu Nano & Mng

Mng tn tnh ch dy v gip em tch ly nhng kin thc v cng qu bu.

Xin gi li cm n su sc v chn thnh nht ti cc bn lp mng mng K10

gip mnh trong nhng nm hc qua.

SINH VIN

Nguyn c Vng

MC LC

Mc lc.

M u ..................................................................................................

I .Tng quan v tinh th photonic.

1. Tinh th quang t mt chiu

1.1. Mng a lp.

1.2. Bn cht vt l ca cc vng cm quang..

1.3. Kch thc ca vng cm quang

1.4.Trng thi m trong vng cm photonic

1.5. nh v nh sng bng sai hng.

1.6. nh v nh sng trng thi b mt.

1.7. Gng ph n x mi hng

2. Cc phng php tnh n chiu xc nh ca tinh th..

2.1. Phng php tnh mt phn n chiu xc nh ca tinh th

2.1.1 Cc ma trn chuyn i.

2.1.2 Phng php mng cch t nhiu x..

3. Phng php ch to cc PC 1D trn c s n mn in ho phin silic...

Kt lun..

Nguyn c Vng

1

M U

Tinh th quang t (PC) l mt loi vt liu mi, c ch to da trn tng v

s tng t nhiu mt gia photon v in t. PC l mt vt liu c cu trc tun hon

v hng s in mi m n biu hin tng tc mnh vi nh sng do c chu k tun

hon c bc sng ca nh sng. Cc photon khi chuyn ng trong tinh th s i qua

cc vng c chit sut cao xen k vi cc vng c chit sut thp. i vi mt photon

s tng phn v chit sut ny ging nh mt th nng tun hon m mt electron b

tc dng khi i qua mt tinh th in t. Do tnh tun hon dn n trong tinh th

quang t cng xut hin mt vng cm quang (PBG): tc l c mt di tn s trong

cc photon khng th truyn qua c cu trc ny. PC s chn nh sng vi cc bc

sng nm trong vng cm quang, trong khi cho php cc bc sng khc truyn qua t

do.Vng cm ny ph thuc vo gc, to ra c mu sc phn x thay i r rt theo

gc.

Cc PC c th c s dng iu khin, giam gi cc bc x t pht v thit k

cc ngun bc x mi. PC v PC c cha cc khuyt tt (l dng tinh th quang t c

cha cc b cng hng cht lng cao v to ra s nh x mnh bn trong cc

khuyt tt) u c th s dng iu khin cc pht x t pht v ci thin cc c

tnh ca laser . Tu thuc vo dng PC c s dng (c hoc khng c khuyt tt) m

cc ngun to ra c th l n sc hoc a sc tc l cc laser hoc cc it pht quang

. PC cng c s dng nh cc cht cch quang hon ho v khng c mt mt, cc

ng dng ny ca PC da trn tnh cht giam gi nh sng trong cc bung vi cng

hng nu tn s nh sng nm trong vng cm quang ca tinh th quang t. Cc thit

b chnh c pht trin da trn tnh cht c bn ny ca PC l cc bung vi cng

hng , cc ng dn sng v cc v tr dn sng un cong t ngt , cc b tch sng ,

cc b ni v cc b kt hp . Ngoi ra, mt trong nhng ng dng quan trng ca PC

l ch to cc phn t phi tuyn trong cc mch tch hp quang nh phn t lu tr

thng tin quang , cc phn t lgc v cc b hn ch nng lng quang . y s l cc

linh kin then cht ch to nn cc h thng my tnh lng t trong tng lai.

Nguyn c Vng

2

Hin ti cc nghin cu v PC 1D ch to bng phng php n mn in ho phin

silic trn th gii u hng ti:

- Ci tin cht lng v iu khin chnh xc vng hot ng ca PC 1D

hng ti ng dng lm cc b lc quang hc, cc bung vi cng hng, cc ng dn

sng, cc sensor ho sinh,

- a cc tm pht x vo cc bung cng hng ca PC 1D, nghin cu cc

pht x ny to ra cc thit b iu khin v giam gi nh sng, cc laser pht mt

v ch to cc ngun sng mi .

- M phng nghin cu cc tnh cht quang ca PC 1D, xem xt s ph hp gia

m phng v thc nghim t iu khin chnh xc qu trnh ch to PC 1D.

V vy nghin cu ch to c cc PC 1D c cht lng tt (cc lp c chit sut cao

v thp nm xen k nhau u n, ph phn x c cng phn x cao, mu ng

u khng b rn nt) bng phng php n mn in ho phin silic nhm mc ch

ch to c cc b lc quang hc, cc bung vi cng hng trn c s PC 1D, kho

st tnh cht quang ca chng.

Nguyn c Vng

3

I . Tng quan v tinh th photonic

Mt lnh vc mi ca vt liu nano l tinh th photonic, l tinh th th hin cu trc

in mi tun hon vi chu k lp li c kch thc so snh c vi bc sng nh

sng, n biu l tng tc mnh vi nh sng. Hin nay c rt nhiu nghin cu c bn

v cc qu trnh quang hc trong tinh th photonic ha hn rt nhiu nhng ng dng

cng ngh, bao gm c trong my tnh v thng tin quang. Cc tinh th photonic c th

l cc cu trc in t tun hon theo mt (1D), hai (2D) v ba chiu (3D). Chng

thng c mt vng cm quang: tc l c mt di tn s trong cc photon khng

th truyn qua c cu trc ny. Chu k tun hon ca tinh th t l vi bc sng

ca anh sng trong vng cm.

Hnh 1. Cu trc tinh th photonic 1D, 2D v 3D l cc cu trc tun hon hng sin

mi ca cc vt liu.

Cc cu trc ng vi nhng khng gian 1D, 2D hay 3D. Cu trc 3D c s ph hp

tt, tng t nh l cu trc ca cht rn. C th coi tinh th photonic nh mt mng

nhiu x quang hc theo 1, 2 hoc 3 chiu. Khi nhng l thuyt c bit n v

mng th hon ton c th p dng trong trng hp mng tinh th photonic. S khc

nhau c bn l mt mng thng th c s dng b mt ranh gii vi mi trng

ngoi, trong khi tinh th photonic th cng c dng nh vy nhng bn trong.

Nguyn c Vng

4

Cc cu trc tinh th photonic c nhn ra u tin vo nm 1987 bi Eli

Yablonovich, sau ti Bell Communications Research New Jersey. Vo nm 1991,

Yablonovich v cc cng s ch to c tinh th photonic u tin bng cc l

khoan c hc c ng knh c milimet trong mt khi vt liu c chit sut 3,6; n

ngn cn s lan truyn cc sng micro theo bt k hng no-ni cch khc, n th

hin mt vng cm quang 3D.

Hin nay, trn th gii v Vit Nam ang c nhiu nghin cu ch to v tnh cht

ca tinh th photonic, mt trong nhng hng nghin cu nghin cu ch to tinh th

photonic l ch to tinh th photonic 1D v tinh th opal nhn to 3D, vic a cc

chm lng t vo trong cc opal ang l hng nghin cu ca mt s phng th

nghim trn th gii.

Tnh cp thit

- Khoa hc v cng ngh nano ang tr thnh mt trong nhng lnh vc nghin

cu pht trin mnh nht trong nhng nm gn y.

- Vic ch to tinh th photonic c rt nhiu ha hn ng dng trong k thut in

t, vin thng v my tnh

1. Tinh th quang t mt chiu

Phn tch tinh th quang t mt chiu vi mc ch l ch to thnh cng cc b lc

quang hc v bung vi cng hng trn c s PC 1D da trn phng php n mn

in ho phin silic. Trong cu trc n gin nht ny chng ta vn c th thy r

Nguyn c Vng

5

c mt s tnh cht quan trng ca tinh th quang t ni chung nh vng cm quang

v cc mode nh x xung quanh cc khuyt tt. Cc tnh cht quang ca PC 1D c th

c bit r nhng bng cch th hin cc kt qu theo cu trc vng v vng cm

quang, chng ta c th xem xt cc hin tng mi nh phn x a hng cng nh

chun b cho cc h thng hai chiu v ba chiu phc tp hn.

1.1. Mng a lp

Cc tinh th quang t n gin nht, tinh th quang t mt chiu c th hin

trong hnh 1 l mt h thng bao gm cc lp vt liu vi hng s in mi khc nhau

cn c gi l mt mng a lp. Cch truyn thng phn tch h thng ny l

tng tng mt sng phng truyn qua vt liu v xem xt tng cc sng phn x sau

khi phn x mi mt phn cch gia hai mi trng. Ngoi ra chng ta cng c th

tip cn theo mt cch khc l phn tch cc cu trc vng, y l mt cch tip cn

n gin hn tng qut v cc tinh th quang t phc tp, tinh th quang t hai v

ba chiu. Bng cch p dng lp lun i xng, chng ta c th m t cc mode in

t truyn trong tinh th. Cc vt liu tun hon theo trc oz v ng nht trong mt

phng xy.

Hnh 2 :mng in mi a lp ( tinh th photonic 1D )

Thut ng mt chiu c s dng bi v gi tr ca hm in mi z ch tun

hon theo trc z. Cu trc ny gm cc lp vt liu vi chit sut khc nhau c gi tr

khng i nm xen k nhau (Mu xanh l v xanh da tri) vi chu k khng gian l a.

Nguyn c Vng

6

Chng ta tng tng mi lp l ng nht v m rng v hn theo trc x v y, v s

tun hon theo trc z cng c m rng ra v hn.

Nh chng ta bit, c th phn loi cc mode s dng k//, kz v n (tng ng l

vect sng trong mt phng, vect sng theo trc z v s vng). Cc vect sng xc

nh cch m cc mode bin i thng qua cc ton t v s lng vng tng theo tn

s. Ta c th biu din cc mode di dng hm Bloch theo phng trnh (1.1).

S dng cc kt qu bit l nu vecto c s l az th vecto c s ca mng o l

(2/a)z v vng Brillouin l /a

Nguyn c Vng

7

c hng s in mi khng i, khi mi trng l ng nht theo c ba hng

(GaAs dng khi). Hnh gia l cho h thng mng a lp GaAs/GaAlAs c hng s

in mi cc lp ln lt l 13 v 12. Hnh bn phi l cho h thng mng a lp c

tng phn hng s in mi cao hn nhiu l mng GaAs/khng kh vi chit sut

tng ng l 13 v 1. Hnh bn tri c tnh ton cho mt mi trng ng cht m

c gn cho mt chu k l a. Tuy nhin chng ta cng bit rng trong mi trng

ng cht, tc nh sng b suy gim ph thuc vo chit sut. Cc mode nm dc

theo ng sng, c cho bi:

(1.2)

Bi v chng ta khng nh rng k lp li ngoi vng Brillouin, nh sang b phn

x quay tr li vng khi n i n bin phn cch. Ta c th gii quyt vn ny mt

cch n gin khi thay k+2/a bng k3. Hnh gia, khi m mi trng gn nh ng

nht th cng ging nh trng hp ng nht nhng c s khc bit quan trng l

c mt di tn s gia nhnh thp v nhnh cao ca cc ng m cc mode c tn s

ny khng c php trong tinh th vi bt k gi tr no ca k. Chng ta gi di ny

l vng cm quang (PBG). Hnh bn phi cho thy vng cm quang ny c m rng

khi tng phn chit sut gia cc lp cnh nhau tng ln.

Chng ta s quan tm k hn ti PBG bi v rt nhiu ng dng y tim nng ca

tinh th quang t hai v ba chiu cho n nay vn ph thuc hon ton vo v tr v

rng ca vng cm quang. V d nh mt tinh th vi mt vng cm quang c th

c dng lm b lc quang hc di hp khi loi b tt c cc tn s nm trong vng

cm quang hoc mt bung vi cng hng ch to da trn tinh th quang t s ch

cho mt s tn s nht nh truyn qua trong khi loi b tt c cc tn s khc trong

vng cm quang. Vng cm gia cc cc di n=1 v n=2 xy ra bin ca vng

Brillouin ti k=/a. By gi chng ta tp trung vo cu trc vng ca hnh gia trong

hnh 3 tng ng vi cu hnh ca h ng nht c nhiu lon nh. Vi k= /a, mode

ny c bc sng l 2a, ngha l gp hai ln hng s mng. C hai cch sp xp cho

loi mode ny, chng ta c th b tr nhng im nt trong mi mt lp c chit sut

thp hay trong mi lp c cao. Bt k mt cch sp xp no khc u vi phm

tnh cht i xng ca c s v cch sp xp ca n.

Nguyn c Vng

8

Nhng nghin cu v l thuyt bin i in t dn n nhn nh rng nhng

mode tn s thp tp trung nng lng (in trng) ca n trong vng in mi cao

v nhng mode tn s cao li tp trung nng lng ca n vng in mi thp . Vi

nhng nhn nh ny chng ta c th hiu c ti sao c mt s khc nhau v tn s

gia 2 trng hp ny. Mode ngay di vng cm (c tn s thp hn) tp trung

nng lng nhiu hn trong vng c =13 nh c th hin trong hnh 4c.

Mode ngay trn vng cm (c tn s cao hn) s tp trung nng lng vng c

hng s in mi thp hn vi =12 nh th hin trn hnh 4d.

Cc vng trn v di vng cm c th phn bit c da vo ni nng lng tp

trung: trong cc vng c cao hay cc vng c thp. c bit iu ny rt quan trng

khi xt cc tinh th quang t hai v ba chiu c nghin cu cc phn tip theo

th vng c chit sut thp thng l khng kh. V l do ny, ta c th xem vng bn

trn PBG nh vng khng kh (air band), cn vng pha di PBG l vng in mi

(dielectric band). iu ny hon ton tng t vi cu trc vng nng lng ca in

t trong cht bn dn, trong vng dn v vng ho tr c ngn cch vi nhau bi

vng cm in t. Phng php da trn nh l bin i in t ny c th c m

rng nghin cu cc tinh th quang t c s tng phn chit sut ln. Trong

trng hp ny, nng lng trng cho c hai vng u tp trung cc lp c hng s

in mi cao nhng theo cc cch khc nhau l vng 1 th nhiu hn vng 2.

Nh vy, vng cm quang hc ny sinh do s khc nhau v s nh x nng lng ca

trng in t trong cc vng c hng s in mi khc nhau. Do chng ta vn c

th dng thut ng vng khng kh cho vng pha trn v vng in mi cho vng

pha di.

Chng ta a ra cc kt lun cho phn ny l: trong cu trc mt chiu, mt vng

cm lun xut hin bin hoc tm ca vng Brillouin. Cui cng, chng ta nhn

mnh rng cc vng cm quang lun xut hin trong tinh th quang t mt chiu vi

bt k tng phn hng s in mi no. Khi tng phn hng s in mi cng

thp, vng cm quang cng nh v vng cm quang bt u xut hin khi 1/21.

M t mode dao ng v mt nng l ng ca in tr ng trn nh v y vng

cm photonic thng qua m h nh sau:

a)in trng ca mode nh vng 1

Nguyn c Vng

9

b) in trng ca mode nh vng 2

c)Mt nng lng nh x trong in trng ,nh vng 1

d)Mt nng lng nh x trong in trng,y vng 2

Hnh 4: Cc mode kt hp vi khong cch vng cm thp nht ca cu trc vng

c biu din hnh gia hnh 3, ti k=/a. (a) in trng ca vng 1; (b) in

trng ca vng 2; (c) Mt nng lng in trng |E|2/8 ca vng 1; (d) Mt

nng lng in trng ca vng 2. Trong m t cc mng a lp, mu xanh da tri

biu th lp c hng s in mi cao hn (=13)

Hnh 4 m t s phn b nng lng in trng trong cu trc vng cho vng 1 v

vng 2 . Ta thy rng ,s phn b in trng gia 2 vng trn khng c s khc bit

ln gia 2 vng , dn n c mt v ng nh cha cc tn s khng c php, do

s t p trung nng lng in trng gia 2 v ng c chnh lch ln , th vng cm

s cng rng ( nh vng cm trong tr ng hp hnh bn phi ca hnh 3 : chnh

lch ca s tp trung nng lng in trng t l vi sai khc hng s in mi

ca 2 mng.

S tp trung nng lng in trng ca trng hp ny c m t nh sau:

Nguyn c Vng

10

a)in trng ca mode nh vng 1

b) in trng ca mode nh vng 2

c)Mt nng lng nh x trong in trng ,nh vng 1

d)Mt nng lng nh x trong in trng,y vng 2

Hnh 5: m t s tp trung nng lng in trng ca 2 vng 1 v 2 c chnh

lch cao

Kt lun : tinh th photonic 1D lun lun c v ng cm xut hin, vng cm c m

ra ngay khi c s khc bit hng s in mi gia hai mng khc cht nhau. rng

ca vng cm ty thuc vo chnh lch ca s tp trung nng lng in trng

trong 2 vng , hay chnh lch gia 2 hng s in mi c 2 mng tng ng

1.3. Kch thc ca vng cm quang.

Vng cm quang ca tinh th quang t c th c m t thng qua rng tn s

ca n, nhng y vn cha phi l cch tnh ton thc s ng n. T phng

trnh Maxwell ta c th rt ra kt lun nu tinh th c m rng bi tha s s th

Nguyn c Vng

11

vng cm quang tng ng s c rng /s. Mt c tnh na cng rt quan trng

ca tinh th quang t l mc c lp ca tinh th c xc nh bi t s /m

(tnh ra phn trm) trong m l tn s gia vng cm quang. Khi h thng c

v phng to hoc thu nh th thang tn s phi thay i cho ph hp nhng t s

/m khng i. V vy khi chng ta nhc n kch thc ca vng cm quang tc

l chng ta ni n t s /m. Cng v l do ny m trong biu hnh 3 v trong

cc biu cu trc vng th tn s v vect sng c tnh theo n v khng th

nguyn a/2c v ka/2. Tn s khng th nguyn l tng ng vi a/, trong

l bc sng trong chn khng (=2c/).

Trong mt mng a lp vi tnh tun hon yu, chng ta c th suy ra cng thc n

gin cho kch thc ca vng cm quang. Theo , nu gi s hai vt liu cu to nn

mng a lp c hng s in mi ln lt l v +, v b dy tng ng l (a-d)

v d. Nu tng phn hng s in mi l yu (/

Nguyn c Vng

12

/=1/12 v d=0,5a (Tng ng vi hnh gia hnh 3), tnh ton theo cng thc (1.3)

d on kch thc ca vng cm quang l 2,65% l kt qu tng i ph hp vi

cc tnh ton chnh xc bng s (2,55%).

Cng thc (1.3) cng cho thy d on l t s /m s cc i khi d=0,5a nhng

kt qu ny ch ph hp khi / nh. Tng qut hn, chng ta c th a ra cng thc

cho / tu bng cch s dng cc nghin cu ca Yeh (1988). Theo , khi hai vt

liu vi chit sut ln lt l n1 v n2 v chiu dy ln lt l d1 v d2=a-d1 th kch

thc vng cm l cc i khi d1n1=d2n2 tng ng vi d1=an2/(n1+n2). Trong

trng hp ring ny tn s m s c tnh l:

(1.4)

Theo bc sng trong chn khng m =2c/m tho mn biu thc m/n1=4d1 v

m/n2=4d2. iu ny cng c ngha l mi lp s c dy quang hc chnh xc l

mt phn t bc sng. V l do ny m kiu mng a lp nh trn cn c gi l

mt khi phn t sng. L do ti sao vng cm quang l cc i i vi khi phn t

sng lin quan ti tnh cht l cc sng phn x t mi lp u cng pha tn s m.

V vy, i vi vng cm quang gia hai vng u tin ca khi phn t sng, t s

/m l:

(1.5)

Tr li hnh 3, trng hp hnh bn phi l mt mng a lp vi tng phn song

hng s in mi l 13:1 v d1=d2=0,5a, y khng phi l mt khi phn t bc

sng. V nh lng, ta thy cu trc ny to ra vng cm quang 51,9%. Nu ta chn

d10,217a, cu trc ny s tr thnh khi phn t sng vi vng cm quang l 76,6%

nh tnh ton theo cng thc (1.5). Kt qu tnh ton chnh xc l 76,3%.

1.4.Trng thi m trong vng cm photonic

Nguyn c Vng

13

Trong v ng cm photonic khng c bt c trng thi in t no tn ti c, hay

ni cch khc khng c mt mode in t no c php truyn qua tinh th ,m

c tn s nm trong vng cm photonic c.

Ta bit rng : cc trng thi quang hc ca tinh th v mi trng khng kh c th

hin thng qua hnh sau:

Hnh 7: gin m t cc trng thi trong khng kh v tinh th

Trn hnh 7 ta thy rng , ng xin gc mu en chnh l ng nh sng ca

khng kh, trn ng ny l nn nh sng, cc tr ng thi trong nn n y m rng

ra ngoi khng kh, v l nhng trng thi lin tc .(chng c gi l cc trng

thi m rng ). Nhng trng thi di ng nh sng ny, chnh l nhng trng

thi trong tinh th, (vng mu xm) Vng mu tr ng cn li di ng nh sng

chnh l vng nhng trng thi m .Nu nh nhng vng mu xm ny khng xen ph

ln nhau , li mt khong mu trng, chnh l vng cm.

Trong vng cm , ch cha nhng trng thi m, m trng thi m l mt trng thi

suy gim khi i vo trong tinh th , cch xa bin tin th cng nhiu , th s suy gim

cng mnh , dn n b trit ti u v khng th l ra bin kia ca tinh th.

Nhn xt i vi tinh th photonic 1D hay l mng a lp , s khng c s thm nhp

nh sng vo bn trong tinh th nu nh nh sng chiu n c tn s nm trong vng

Nguyn c Vng

14

cm , hay ni cch khc nh sng chiu vo c trng thi quang hc l trng thi

m.

Mt khi nim na ta cng cn quan tm l truyn nh sng theo tr c m v trc

tt, m y c ngh a l truyn nh sng theo hng tun hon , c vng cm c

m ra khi c s khc bit gia hai hng s in mi ca hai mng. Cn truyn sng

theo trc tt (trc x), l truyn nh sng phng vung gc vi trc m , c ngha l

truyn nh s ng vo trong mi tr ng in mi. Truyn sng theo ph ng ny hon

ton khng c s chn lc tn s nh truyn sng theo trc m ( trc z)

Hnh 8 a. Truyn sng theo trc tt b. Truyn sng theo trc m

1.5. nh v nh sng bng sai hng

M hnh sai hng :

Hnh 9: sai hng l mt mng c hng s in mi khc so vi tinh th photonic 1D

Hnh 10: sai hng l dng kp ca m ng c hng s in mi thp

Nguyn c Vng

15

Trong mng n l p , nhng mode in t c php truyn i mt cch b nh

thng, khng c s chn lc tn s, c ngha l khng c s cn tr nhng sng in

t d bt c tn s no. Nu nh tinh th photonic 1D cng nh vy, th chng c g

l th v vi tinh th photonic c. Mt khc ci tnh cht quan trng ca tinh th

photonic 1D l tnh lc nh sng v c kh nng nh v nh sng bng sai hng vi

tn s bc buc l nm trong v ng cm.

Hnh 11: m t phn b mt trng thi theo cu trc vng c sai hng.

Qua th trn ta thy mt tnh cht rt tuyt vi l sai hng c to ra, th n s

xut hin mt peak trng thi bn trong vng c m . Chnh peak trng thi ny, cho

php nh v nh sng. V khi ny trng thi m ca nh sng s kt hp vi trng thi

sai hng cho php truyn sng nh sng dc theo 2 bin ca sai hng.

1.6. nh v nh sng trng thi b mt

Nu nh vic nh v nh sng b ng trng thi sai hng trong v ng cm, th ta

cng c cch khc nh nh sng bng trng thi b mt, trn nguyn tc, trng thi

ny c nh v trong v ng cm. Do ta la chn nh sng chiu n c tn s

thch hp cho kh nng nh v nh sng trong b mt.

Nguyn c Vng

16

Hnh 12: m t nh v nh sng bng b mt

1.7. Gng ph n x mi hng

Ta bit rng, nhng trong cu trc v ng quang h c, ng nh sng l ranh gii

giatrng thi m rng b n trong khng kh (trn ng nh sng) , di ng nh

sng l trng thi m v trng thi bn trong in mi. Ngi ta vn c th thit k

c mt mng a lp cho mc ch phn x mt tn s xc nh trc. Nguyn tc

thit k m ng a lp cho phn x , tun th theo 2 nguyn tc sau:

a. k// phi tn ti trong mt giao tip gia cc m ng in mi.

b. nh sng chiu vo b mt ca mng phi c tn s

Ch : s lp in mi cng nhiu , h s phn x ca m ng a lp cng cao

Hnh 13. th m t vng tn s cho ph n x mi hng

Nguyn c Vng

17

V vng cm photonic cho loi gng cho phn x mi hng v mi phn cc ny

c m t theo quan h gia cc hng s in mi ca khng kh, ca 2 loi mng ),

c m t thng qua hnh sau:

Hnh 14: kch thc ca vng cm cho phn x mi hng l hm ca

cc hng s in mi

2. Cc phng php tnh n chiu xc nh ca tinh th.

y l phng php rt tng qut nghin cu s lan truyn cc sng in t

trong bt k loi cu trc no, c tun hon hay khng. Vi phng php ny, cc

phng trnh Maxwell l gin on trong khng gian v thi gian theo s c

Yee v Taflove ngh. Cu trc nh vy cng l gin on. S tin trin theo thi

gian ca trng in t nhn c bng cch tch phn dn dn theo thi gian. nu

skch thch l xung. Php bin i Fourier ca sp ng ca vt liu cho ta ph tn

sca cu trc. Phng php ny c s dng nghin cu s nhiu x ti b mt

tip xc ca mt tinh th photonic.

2.1. Phng php tnh mt phn n chiu xc nh ca tinh th

2.1.1 Cc ma trn chuyn i

Nguyn c Vng

18

Phng php cc ma trn chuyn i c s dng rt rng ri tnh ton cc cu

trc tun hon theo mt chiu theo quang hc, v nht l cho cc gng Bragg. N cho

php thu c cc h s truyn qua v phn x ca mt cu trc vi chiu dy xc

nh, nhng chiu nm ngang khng xc nh.

Php tnh ton c thc hin trn vic phn tch cu trc thnh cc lp mng c

bn. H s truyn qua v phn xc tnh ton i vi mi mt lp mng ct

xy dng nn ma trn chuyn i. Ma trn c tnh ton i vi mi mt bc sng

v mt tinh th lm t mt cht tn sc nh vy, c thc nghin cu. Cc ph phn

x v truyn qua i vi ton b mt tinh thc tnh ton bng cch kt hp cc s

thch hp ca ma trn chuyn i. Phng php ny rt ch li bit c ph truyn

qua hoc phn x c thc hy vng i vi mt tinh th c kch thc xc nh.

2.1.2 .Phng php mng cch t nhiu x

Phng php ny coi mt vt liu vi cc vng cm nh mt tp hp cc cch t

nhiu x lin tip nhau . Trong mi mt min phn cch cc cch t ny, trng c

trin khai theo dng Rayleigh, c ngha l trn tt c cc sng phng c th c, v cc

h s khc nhau ca php trin khai ny th c lin h vi nhau trong hai lp lin k

bi cc tnh cht nhiu x ca cch t m n phn cch n, chng c tnh ton

bng l thuyt tch phn cch t. Li gii ca h cc ma trn lin quan gia cc h s

Rayleigh cho s bit s nhiu x ca ton b vt liu

3.Phng php ch to cc PC 1D trn c s n mn in ho phin silic

Nguyn c Vng

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Bng cch iu chnh nng dung dch n mn, mt dng in v thi gian n

mn, ta c th to ra mt lp silic xp c dy v chit sut xc nh. V vy bng

cch n mn lin tip to ra cc lp xp c chit sut v b dy thay i tun hon

theo mt chiu v tho mn iu kin phn x Bragg, chng ta c th ch to cc PC

1D hot ng trong vng bc sng mong mun. Qu trnh thit lp mt dng n

mn v thi gian n mn c lp trnh trn my tnh v vy m bo c chnh

xc cao.

Phng php ch to cc PC 1D trn c s n mn in ho phin silic hin nay ang

c cc phng nghin cu trn th gii rt quan tm v nhng u im vt tri ca

n nh:

- Phng php v thit b ch to n gin v r tin.

- C th iu khin c chnh xc cu trc ca cc lp xp, v vy to ra c nhng

PC c cht lng tt, phn x cao.

- C th thay i d dng cu trc ca cc lp xp t to ra c hng lot mu

hot ng tri di t vng nhn thy n vng hng ngoi gn.

- D dng thit k cc khuyt tt trong PC 1D to ra cc bung vi cng hng, cc

ng dn snglm vt liu ch to cc linh kin iu khin, giam gi v kim sot

nh sng.

- Vt liu silic xp c xp cao, d dng thm thu cc cht lng v vy rt thun

tin ch to cc sensor sinh hc v ho hc.

Phng php n mn in ho phin silic ch to nn PC 1D mi ch c pht

hin t cui nhng nm 90 ca th k trc, tuy nhin ch trong mt thi gian ngn s

lng cc cng trnh khoa hc cng b v phng php ny tng chng mt. Hin

nay, cc nghin cu ch to PC 1D bng phng php ny ang tp trung vo vic a

cc tm pht x vo bung vi cng hng v nghin cu tnh cht pht x ca chng;

ngoi ra, cc hng khc cng ang rt c quan tm nh s dng PC 1D lm cc

ng dn sng quang, cc sensor sinh hc v ho hc...Cc PC 1D c mong i c

nh hng ln n s pht trin cng ngh trong vic ch to cc linh kin ca cc

thit b quang iu khin, giam gi, kim sot s pht x v truyn nh sng trong

khng gian 1D.

Nguyn c Vng

20

KT LUN

Cc tinh th quang t do c s tun hon v chit sut dn n hnh thnh cu trc

vng cm quang l vng trong khng c mt trng thi truyn dn quang no c

php tn ti. Ging nh cht bn dn, PC c vng cm quang cng khng to c

nhiu ng dng nu khng cha cc khuyt tt kim sot c. Khuyt tt s to ra

cc trng thi c php i vi mt s tn s photon ring bit trong PBG t dn

n cc ng dng kim sot nh sng hoc dn sng tng ng vi cc dng khuyt tt

im hoc khuyt tt ng.

Cc PC c th c s dng iu khin, giam gi cc bc x t pht v thit k

cc ngun bc x mi. PC cng c s dng nh cc cht cch quang hon ho v

khng c mt mt. Cc thit b chnh c pht trin da trn tnh cht c bn ny ca

PC l cc bung vi cng hng, cc ng dn sng v cc v tr dn sng un cong t

ngt, cc b tch sng, cc b ni v cc b kt hp

Cc PC 1D da trn silic xp c cu trc vng cm quang theo mt chiu, phn

x cao v d dng to ra cc khuyt tt bng cch thay i chit sut hoc b dy ca

mt lp trong cu trc mng a lp. Cc PC 1D l vt liu c bn pht trin cc linh

kin 1D nh cc b lc quang hc, cc bung vi cng hng, cc gng iu hng

v thit b d cc cht.