4 . S pe ctro s c opic In s trum ent ation Spectrometer , Interferometer, (Detector :

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4 . S p e c t ro s c o pic In s t ru m e n t at io n

Spectr ometer , Int erfer om et er , (Detector : 양자광학2)

4 .1 S pe c tro g raph an d M on oc h rom at ors S pe c trom e t e r : (optical) frequency an aly sis

Prism (disper sion ) / Gr ating (diffr action )

=> im aging position function of 1) S pe c tro g raph : phot ogr aphic

=> simult an eou s m easurement of a lar ge r egion of 2) M on oc hrom at or : phot oelectric

=> succes siv e measurem ent , high res olution/ sen sitivity

* OM A (optical multich annel an aly zer )

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< B as ic c h arac t e ri s tic s of s pe c trom e t e r>

- Speed, S/ N r atio

- Av ailable w av elen gth r egion - Spectr al resolving pow er : /

- F ree spectr al r ange

1) Speed

frequency s canning speed, detector respon se, int egr ation tim e, ...

2) S/ N r atio

detector s en sitivity , etendue (light g athering pow er ) r adiant flux w ithin the spectr al interv al d ,

d = I^* ( A / A _s) T ( ) d (A : slit area, : accept ance angle) (4.2)

* eten due, U A

3) Av ailable w av elen gth r egion

spectr al tr an smis sion (prism ), diffr action efficiency (gr ating ) 4) Spectr al resolving pow er , R

R = | / | = | / |

R ayleigh ' s criterion for the r esolution ;

T he centr al diffr action m ax imum of I₁( - ₁) coincide w ith the fir st minimum of I₂( - ₂)

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< re s olv in g pow er of a s p e c trom et e r >

angular seper ation , ;

= ( d / d ) (4.4)

w here, d / d : an gular disper sion dist an ce, x bet w een t w o im ages

x = f₂ = f₂ d

d = dx

d (4.5)

w here, ^dx

d : linear disper sion diffr action effect ;

I ( ) = I₀

(

s in ( a s in / )

a s in /

)

² ^I⁰

(

^{s in ( a}a / ^{/ )}

)

² ^(4.7)

=> w idth of slit im age : x^{d if f r}_s = f₂( / a ) (4.8) In or der t o resolv e t w o m axim a,

x f₂

a (4.9a )

R = | / | a ( d / d ) (4.10)

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diffr action by the entr ance slit ,

2 = 2

b a

f₁ , b_{m in} 2 f₁/ a

= ( f / a + b) d dx

if bm in = 2 f / a = b => = ( 3 f / a ) d dx

P rac tic al lim it of re s olu tion ;

R = / = ( a

3 ) d / d = a 3f

dx d

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< P rac tic al lim it of re s olu tion >

P ri s m s pe c trom et e r

minimum deviation : r ay path in the prism is par allel t o the b ase g

d

d = d

d n d n

d 이므로,

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그러므로 / a ( d / d )로부터, 최대 resolving pow er는

n s in ( / 2) = s in ( + ) / 2 = s in ₁ 이므로,

P rac tic al lim it of re s olu tion

Gratin g s pe c trom e t e r

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ex ) F or Littrow m ount ( = ) => 2 d s in = m

; blazed gr ating

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F rom (4.22), d ( s in s in ) = m ,

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5) F ree spectr al r ange ;

x ( ) 가 서로 1:1로 대응되는 파장 영역

- prism : w hole r an ge of norm al disper sion of prism m at erial - gr ating : diffr action order m에 대해,

m _m = d s in 로부터

= d s in

(

m¹ - 1

m + 1

)

⁼ m ( m + 1)^{d s in}

: higer order 일수록 감소

4 .2 In t e rf erom e t er

: high r esolving pow er

- n arrow ing the linew idth of las er

- m onitoring the emis sion spectrum of laser - controlling and st abilization of las er frequency

1) Michelson int erfer om et er 2) M ach - Zehnder interfer ometer

3) Multiple beam int erferom et er (F abry - Per ot cavity , et alon ) 4) Int erferen ce filt er

5) Ly ot filter

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1 ) M ic h e l s on in t e rf erom et e r

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2 ) M ach - Zeh n de r in t erf e rom e t e r

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3 ) M ultiple b e am in t e rf erom e t er (F abry - P e rot c av ity , e t alon )

w here, F = 4R / ( 1 - R )² : Airy function

= 2 s / + : ph ase differn ce bet w een adjacent r ay s

s = 2 d n² - s in ² : path differnce bet w een adj acent r ay s

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F ree spectr al r ang e,

F W HM ,

Resolvin g pow er , R

R = = F^*

w here, F^* = R 1 - R =

2 F ; F innes e

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mutiple beam interfer ometer - et alon : fix ed dist an ce

- F abry - Per ot cavity : fr equency scann able

< e t alon >

w alk - off los s

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< int e rf e rom e t e r, c av ity >

- v acuum / air - spaced type

- pres sure t ank type

- confocal type

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4 ) In t e rf ere n c e filt er

r eflectivity of a dielectric int erface for norm al incidence

R | _{= 0} =

(

ⁿⁿ¹¹ ^{- n}^{+ n}²²

)

²

multilayer dielectric coating s

; 경계면에서의 피할수 없는 반사를 없애거나, 단층 코팅으로는 얻을 수 없는 고반사도를 얻을 수 있음.

: 다층 경계면에서 반사된 field 들간의 간섭효과를 이용

* 응용 : high reflection mirr or (보강간섭 : _m = 2 m )

anti- reflection (AR ) w indow (상쇄간섭 : m = ( 2 m + 1)

int erfer ence filter (n = n ( ))

< h ig h re fle c tion c o atin g >

(1) tw o- lay er coating

n₁d₁ = / 4 , n₂d₂ = / 2 for n₁ > n₂ > n₃ n₁d₁ = n₂d₂ = / 4 for n₁ > n₂ ; n₃ > n₂

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t ot al r eflected amplitude

A = A 1 + A 2 + A 3

= R₁A ₀ + R₂ ( 1 - R₁ )A ₀ + R₃( 1 - R₂) ( 1 - R₁ )A ₀

(2) multilayer coating

* computer simulation

< an ti - re fle c tion c o atin g >

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* _m = ( 2 m + 1) => n₂d₂ = / 2

* R₁ = ( 1 - R₁) R₂ => R₁ =

(

ⁿⁿ¹¹ ^{- n}^{+ n}²²

)

² ^{= R}² ⁼

(

ⁿⁿ²² ^{- n}^{+ n}³³

)

²

=> n₂ = n₁n₃

ex ) 공기- 유리, n₂ = 1 . 5 = 1 . 23

< int e rf e ren c e f ilt e r >

; multi- beam int erferom et er와 multi- lay er coating의 조합

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5 ) Ly ot f ilt e r

; birefring ent cry st al을 통과하는 광의 편광상태 변화를 이용

ph ase differnce betw een tw o orthog on al fields ,

= k0( n0 - ne) L = 2 nL

ex ) = 2 m : 편광상태 불변

= ( 2 m + 1) : / 2- plat e

= ( 2 m + 1

2 ) : / 4- plate tr an smis sion

T ( ) = T0 cos ²

(

^{n L}

)

free spectr al r ang e

= c

( n₀ - n_e) L

< m ulti - c om pon en t s Ly ot filt e r>

; lar ge free spectr al r ange & n arrow F W HM

tr an smis sion through N - Ly ot filter w ith differ ent len gth L^m,

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< tu n able Ly ot filt e r>

m = 2 n d m

- refr activ e index , n - dist an ce, d

- rot ation of the solid et alon

- optical path ch ange in a birefring ent cry st al

(1) electro- optic control

(2) an gle tunin g