™ »ª <® £ · T „ ç ¡‚ Ð · … è ¡A jP · ™ »Z Ì * ° · - ! H. > 0 ² ? · + 2 ø ¶ B0 å  ∗

8 û” ¼ ß Ã Å DC  ¹ ÅM X ê sÊ Ý T Ž Ò Þ ß f Ä 0 n É; c 8 ý” X ¢ þ { ÚY Û Ã Å :  Ž ì Å Y 8 È

5

2 Ê k Ä u œ X N Ë U c lT c l8 ý ° Ë Ñò i >± n Ç „ ÇÊ Ý ” Ö «˜  ×



™ »ª <® £ · T „ ç ¡‚ Ð · … è ¡A jP  ·  ™ »Z Ì * ° · - ! H. > 0 ² ? ·  + 2 ø ¶ B0 å  ^∗

% ò

z Œ ™@ /† < Ɠ § Ó ü t o † < Æõ ,  â í ß – 712-749 (2005¸   10 Z 4 15{ 9  ~ à Î6 £ §)

e 

¦ x  2 ; :  ƒ  (porphyrin : Zn) ' ‘  W 1 h Ë : Ó  o& ñ ~ à Ì} Œ •Ü ¼– РÒ'  ü @Â Ò “   dc„  l  © œõ  s 1 l x    Z O 

` 

¦ s 6   x # Œ ‰ & ³$  >  7 £ x    H F  gÏ ã J] X  ´ òõ \  ¦ › ' a8 £ ¤ % i  . ü @Â Ò “   „  l  © œs  E

0

= 1.2 V/µm s 

“

¦,     s 1 l x 5 Å q • ¸ v

q

= 33.4 µm/s{ 9  M :, s 1 l x     ~ ½ ÓZ O `  ¦  6   x t  · ú §€ Œ ¤`  ¦ M :˜ Ð  3C  s  © œ 7 £ x

ô  Ç s 1 p q > Ã º Γ = 624 cm

⁻¹

\  ¦ % 3 % 3  . ¢ ¸ô  Ç z  ´+ « >& h Ü ¼– Ð % 3 # Q”   E

0

ü < v

^q

\  @ /ô  Ç s 1 p q > à ºü <  r] X ´ ò Ö 

¦`  ¦ s  : r / B G‚  õ  r Ð 3 x ? /l † < ÊÜ ¼– Ð+ ‹ s  F  g   ™ D ¥ ½ + Ë_  K $ 3 K \  ¦ ½ ¨ % i  .

PACS numbers: 42.65.H, 61.30, 64.70.M

Keywords: F  gÏ ã J] X  ´ òõ ,     s 1 l xZ O , W 1 h Ë : Ó  o& ñ , e  ¦ x  2 ;: ƒ  , s  F  g   ™ D ¥ ½ + Ë

I. " e  ] Ø

f

. Ë – ÐÕ ªÏ þ › l Õ ü t ì  r  ü < f . Ë – ÐÕ ªÏ þ › l 2 Ÿ ¤ B | 9 \  › ' a ô  Ç ƒ  

½

¨  H F  g & ñ ˜ Ð % ƒo \  e ” # Q" f B Ä º ×  æ כ ¹ô  Ç Â Òì  r`  ¦ t  

“

¦ e ”   H X <, # Œ Q f . Ë – ÐÕ ªÏ þ › l 2 Ÿ ¤ B | 9  ×  æ : £ ¤ y  F  gÏ ã J] X  B 

| 9

“ É r l 2 Ÿ ¤c ” _    © œõ  y Œ •• ¸, 0 A © œ 1 p x Ü ¼– Ð  ×  æ  o 0 p x

# Œ “ ¦x 9 • ¸_  X <s ' \  ¦ $  © œ, 4 Ÿ ¤" é ¶ ½ + É Ã º e ” “ ¦ & ñ ˜ Ð % ƒ o

 5 Å q • ¸ B Ä º  Ø Ôl  M :ë  H \  X <s '  $  © œ  © œu , F  g & ñ

˜

Ð % ƒo , F  g J ‡   “  d ”  Õ ªo “ ¦ z  ´r ç ß –  Œ ™ " é ¶ { 9 ^ ‰ % ò  © œ

\

 › ' a >   ) a 1 l x& h  f . Ë – ÐÕ ªÏ þ › 1 p x Ü ¼– Ð 6 £ x6   x ÷ &“ ¦ e ”   [1–3].

F 

gÏ ã J] X  B | 9 \ " f_  & ñ ˜ Ð$  © œ“ É r y n C\  _ K  Ï ã J] X Ò  ¦ s 

² ú

˜ t   H F  gÏ ã J] X  ´ òõ (photorefractive effect)\  _ ô  Ç  כ Ü

¼– Ð Õ ª õ & ñ “ É r  6 £ § õ  ° ú   . B | 9 \  ç ß –[ O & h “   ¿ º Y U s

$ c ” `  ¦ { 9   r v €   B | 9  ? / Ò\  µ 1 ߓ ¦ # Q¿ ºî  r Á º] (_  Å

Òl & h “       ë ß –[ þ t # Qt “ ¦, F  g„   (optical charges)

Ò q

t$ í  ) a  . € ª œs “ : r õ  6 £ § s “ : r“ É r \ P & h  S X ‰ í ß –î  r1 l x õ  „  l  © œ

\

 _ ô  Ç ³ ðÀ Óî  r1 l x`  ¦ “ ¦, Õ ª   õ  „   _  ì  r o (charge separation) ü < / B N ç ß – „    © œ(space charge field)s  + þ A$ í ÷ &

#

Q B | 9 _  Ï ã J] X Ò  ¦ s    › ¸  ) a  .

þ

jœ í_  F  gÏ ã J] X  ‰ & ³ © œ“ É r 1966¸   y © œÄ »„  $ í é ß –  & ñ “   LiNbO 3 \ " f › ' a8 £ ¤ ÷ &% 3 “ ¦, s Ê ê þ j   H  t  LiNbO ³ ü < † < Ê a

 BaTiO 3 , SBN, BSO 1 p x _  Á ºl  F  gÏ ã J] X    & ñ [ þ t s   © œ

@

/& h Ü ¼– Ð €  •ô  Ç Y Us $  c ” _  y © œ• ¸– Ð F  gÏ ã J] X  ´ òõ \  ¦ % 3 `  ¦ Ã

º e ”   H B Ä º ´ òõ & h “   B | 9 – Ð · ú ˜ 94 R e ”   [4–6]. Õ ª Q

∗

E-mail: [email protected]

Tel: 053-810-2342, Fax: 053-810-4616

 1990¸  \  Ä »l  Ó ü t| 9 \ " f• ¸ þ jœ í– Ð F  gÏ ã J] X s  › ' a8 £ ¤ ÷ &

#

Q q ‚  + þ A Ä »l    & ñ $ í  © œ\  s 6   x ÷ &% 3 Ü ¼ 9 [7], 1991¸  

\

  H Durcharme 1 p x“ É r e  ¦ o  Q B | 9 \ " f þ jœ í_  F  gÏ ã J] X 

´

òõ \  ¦ › ' a8 £ ¤ % i   [8]. ¢ ¸ô  Ç, Á ºl  F  gÏ ã J] X    & ñ s 
 F  g Ï

ã J] X  “ ¦ì  r   ° ú  “ É r l ” > r _  F  gÏ ã J] X  B | 9 ÷  r ë ß –  m   Ó  o& ñ

\

 l œ íô  Ç F  g † < ÆB | 9 s  F  gÏ ã J] X  B | 9 – Ð" f 0 p x$ í s  e ” 6 £ § s

 Rudenkoü < Sukhov Õ ªo “ ¦ Khoo\  _ K  ] jl ÷ &% 3   [9,10]. : £ ¤ y , Khoo  H C 60 õ  Methyl-Redü < ° ú  “ É r Ò  o™ è

'

‘   ) a W 1 h Ë : Ó  o& ñ Ü ¼– РÒ'  dc „  l  © œ \ " f F  g Ä »• ¸

„

 l  © œ\  _ ô  Ç W 1 h Ë : Ó  o& ñ _  ~ ½ ӆ ¾ Ó  F C \ P  ´ òõ \  ¦ › ' a 8

£

¤ % i “ ¦, Ó  o& ñ ? / Ò_  / B N ç ß – „    © œ + þ A$ í õ & ñ õ  Õ ª   õ 

–

Ð Ò q tl   H ž Ðß ¼, Ó  o& ñ ~ ½ ӆ ¾ Ó _  F C \ P õ  F  g   ™ D ¥ ½ + Ë ´ ò õ

 1 p x`  ¦ l Õ ü t % i   [10, 11]. Õ ªo “ ¦ þ j   H ‘ : r ƒ  ½ ¨z  ´\ 

"

f  H e  ¦ x  2 ; :  ƒ  (Porphyrin : Zn) Ò  o™ è ' ‘   ) a W 1



h Ë : Ó  o& ñ ~ à Ì} Œ •\  ü @Â Ò „  l  © œ`  ¦ “   €  " f s  F  g   ™ D ¥

½

+ Ë z  ´+ « >`  ¦ à º' Ÿ  # Œ Ó  o& ñ ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç F  gÏ ã J] X 

´

òõ (orientational photorefractive effect)\  ¦ › ' a8 £ ¤ % i “ ¦, ü

@Â Ò dc„  l  © œs  E 0 = 0.57 V/µm ü < E 0 = 1 V/µm“    â Ä

º\  Γ = 170 cm ⁻¹ _  s 1 p q > à ºü < n 2 ≈ 10 ⁻² cm ² /W _ 

 H Ï ã J] X Ò  ¦   › ¸° ú כ`  ¦ % 3 % 3   [12].

F 

gÏ ã J] X  B | 9 \ " f s  F  g   ™ D ¥ ½ + Ë s 1 p q`  ¦ 7 £ x r v l  0 A ô

 Ç ~ ½ ÓZ O [ þ t“ É r ü @Â Ò dc „  l  © œ`  ¦ “   €  " f ¿ º l 2 Ÿ ¤c ” 

×

 æ ô  Ç c ” _  Å Ò à º\  ¦   › ¸r &  s  F  g   ™ D ¥ ½ + Ë`  ¦ à º' Ÿ  



 H moving grating technique [13] õ  B | 9 \  ac „  l  © œ`  ¦

“

    H ~ ½ ÓZ O  [14] Õ ªo “ ¦ linear motor\  ¦ s 6   x # Œ B 

| 9

`  ¦     7 ˜'  ~ ½ ӆ ¾ ÓÜ ¼– Ð f ” ] X  s 1 l x r v   H s 1 l x     Z O

(grating translation technique) [15, 16] 1 p x s  e ”  . ‘ : r

-362-



7 Hë  H \ " f  H e  ¦ x  2 ;: ƒ  s  ' ‘   ) a W 1 h Ë : Ó  o& ñ ~ à Ì} Œ •\  dc „  l  © œ`  ¦ “   €  " f s 1 l x    Z O `  ¦ à º' Ÿ  # Œ ‰ & ³$ 

>  7 £ x    H F  gÏ ã J] X  ´ òõ \  ¦ › ' a8 £ ¤ “ ¦, ü @Â Ò “   „  l 



© œ_  ß ¼l ü < ~ ½ ӆ ¾ Ó,     s 1 l x 5 Å q • ¸_  ß ¼l ü < ~ ½ ӆ ¾ Ó\  @ / ô

 Ç s 1 p q > à ºü <  r] X ´ òÖ  ¦`  ¦ z  ´+ « >& h Ü ¼– Ð 8 £ ¤& ñ % i  . ¢ ¸ ô

 Ç Ó ü t| 9  ~ ½ Ó& ñ d ” õ  Ó  o& ñ ~ ½ ӆ ¾ Ó _  ž Ðß ¼ ç  H+ þ A ~ ½ Ó& ñ d ” Ü ¼– Ð Â

Ò'  % 3 “ É r s  : r / B G‚  `  ¦ z  ´+ « >° ú כõ  r Ð 3 x ? /l † < ÊÜ ¼– Ð+ ‹ q 

“

§, ì  r$ 3  % i  .

II. T  Â ] Ø

Ó 

o& ñ _  Ó ü t| 9 ~ ½ Ó& ñ d ” “ É r d ” (1)– Ð Å Ò# Q”    [9].

∂n ^±

∂t + γ R n ⁺ n ⁻ ± 1

e ∇ · ~ J ^± = αI (1.1)

J ~ ^± = eµ ^± n ^± E ∓ k ~ _B T µ ^± ∇n ^± (1.2)

∇ · ~ E = 4πe

ε (n ⁺ − n ⁻ ) (1.3)

#

Œl " f n ^±   H e  ¦ x  2 ; :  ƒ  s  ' ‘   ) a Ó  o& ñ \ " f µ 1 ÏÒ q tô  Ç

€

ª œs “ : r õ  6 £ § s “ : r _  x 9 • ¸s “ ¦, γ R “ É r F   ½ + Ë  © œÃ º, J ^±   H

€

ª œs “ : r õ  6 £ § s “ : r _  „  À Ó x 9 • ¸, µ ^±   H s 1 l x • ¸, ፠ H f  ¨ à º

>

à º, e  H „   _  „   | ¾ Ó, ε“ É r Ä »„   © œÃ º, k B   H Boltzman



© œÃ º, T   H ] X @ /“ : r • ¸, I  H Y Us $  c ” _  [ jl s  . ~ E  H „   l

 © œÜ ¼– Ð ü @ ҄  l  © œõ  B | 9  ? / Ò\  Ä »• ¸  ) a / B N ç ß – „   



© œ_  ½ + ËÜ ¼– Ð Å Ò# Q”   . d ” (1.1)“ É r s “ : r[ þ t _  q Ö  ¦ ~ ½ Ó& ñ d ”  s

“ ¦, d ” (1.2)“ É r 8 ú x „  À Óx 9 • ¸\  ¦
 ? /  H X <, „  l  © œs  Ÿ í

†

< ʝ ) a ' Í   P : † ½ ӓ É r s “ : r[ þ t _  ³ ðÀ Óü < › ' a > ÷ &“ ¦, ¿ º  P : † ½ Ó

“ É

r € ª œ(6 £ §) s “ : r _  x 9 • ¸ \  _ ô  Ç  כ Ü ¼– Ð \ P & h  S X ‰ í ß –õ  › ' a

>

  ) a † ½ Ós  . d ” (1.3)  H Poisson ~ ½ Ó& ñ d ” s  .

s

1 l x    Z O `  ¦ s 6   x ô  Ç s  F  g   ™ D ¥ ½ + Ë\ " f / B N ç ß –& h Ü ¼– Ð Å Ò l

& h “   c ” _  [ jl   H d ” (2)ü < ° ú  s  ³ ð‰ & ³ ) a  .

I(~ r, t) = I 0 (t)[1 + m cos(~ q · ~ r − Ωt)]

= I 0 (t) + I 1

2 e ^{i(~ q·~ r−Ωt)} + c.c. (2)

#

Œl " f c.c.  H 4 Ÿ ¤ ™ è / B NÓ  os “ ¦, I 0 (t)  H B | 9 \  { 9  ÷ &  H 8 ú x l

2 Ÿ ¤c ” _  [ jl , m“ É r   › ¸ U  ·s , ~q  H     7 ˜' , Ω = qv q , q = |~ q|, v _q   H ~ q ~ ½ ӆ ¾ ÓÜ ¼– Ð_  B | 9  s 1 l x 5 Å q • ¸s  . / B N ç ß –& h  Ü

¼– Ð Å Òl & h “   ç ß –[ O  Á º] ( I(~r, t)\  _  # Œ   › ¸  ) a € ª œ·6 £ § s

“ : r _  x 9 • ¸ü <, „  À Ó x 9 • ¸, 8 ú x „  l  © œ“ É r ç ß –[ O Á º] (ü < ° ú  

“ É

r + þ AI – Ð ³ ð‰ & ³ ) a  .

Y (~ r, t) = Y ₀ (t) + 1

2 Y ₁ e ^{i(~ q·~ r−Ωt)} + c.c. (3) d ”

(3)\ " f Y 0   H / B N ç ß –& h Ü ¼– Ð { 9 & ñ ô  Ç † ½ ÓÜ ¼– Ð n ^± 0 , J ₀ ^± , ~ E 0 s 

“

¦, ^Y 2

¹

e ^{i(~ q·~ r−Ωt)} “ É r   › ¸  ) a † ½ ÓÜ ¼– Ð Y ¹   H n ^± ₁ , J ₁ ^± , ~ E 1 `  ¦
 

? / 9, ~ E 0   H ü @Â Ò “   „  l  © œs “ ¦, ~ E 1 “ É r / B N ç ß – „    © œ s

 .

…

 ;…  ;y       H ”  ; Ÿ ¤   H  (slowly-varying amplitude approximation) ü < F  g„    à º" î r ç ß – τ ü < Maxwell ¢ - a  o r  ç

ß – τ ^d  s \  τ  τ ^d _  › ' a > \  ¦ & ñ €  , Ó  o& ñ _  Ó ü t| 9  ~ ½ Ó

&

ñ d ” Ü ¼– РÒ'   6 £ § õ  ° ú  s  / B N ç ß – „    © œ\  @ /ô  Ç 1>  p ì  r

~

½ Ó& ñ d ” `  ¦ % 3   H  .

∂E 1

∂t + gE _q = mh g = B

A , h = C A A = 1

τ d

(1 + 2τ _d τ + E _D

E q

+ i E ₀ sin β E q

ν − i2b)

B = 2

τ τ _d (1 + E D

E _M + E D

2E _q + E ₀ ² sin ² β 2E _q E _M + E _D ²

E q E M

+ i E 0 sin β 2E q

ν − ib) C = 1

τ τ _d (iE D ν − E 0 sin β) (4)

#

Œl " f ν = ^µ µ

⁺⁺

^−µ +µ

⁻⁻

, b = Ωτ d = qv q τ d ) s “ ¦, E ^q   H Ÿ í o

„

 l  © œ(saturating field), E M   H ³ ðÀ Ó „  l  © œ(drift field), E _D   H S X ‰ í ß – „  l  © œ(diffusion field), ⍠ H B | 9 _  l Ö  ¦e ”  y Œ • s

 .

d ”

(4)Ü ¼– РÒ'  s 1 l x    Z O `  ¦ s 6   x ô  Ç s  F  g   ™ D ¥ ½ + Ë_ 

 â

Ä º, & ñ  © œ  © œI _  / B N ç ß – „    © œ_  ß ¼l  |E ¹ | c ” _  ç ß –[ O J 

‡

 õ  / B N ç ß – „    © œ  s _  0 A © œ   s (phase shift) φ  H   6

£

§ õ  ° ú  s  ³ ð‰ & ³ ) a  .

|E 1 | = m

2 [ E _D ² ν ² + E ₀ ² sin ² β

X ² + Y ² ] ^1/2 (5)

φ = tan ⁻¹ [ E D νX + E 0 sin βY

E _D νY − E ₀ sin βX ] (6)

#

Œl " f X = 1+E ^D /E M +E D /2E q +E ² ₀ sin ² β/2E q E M + E _D ² /2E q E M , Y = E 0 ν sin β/2E q − b s  . d ” (5)ü < d ” (6)

“ É

r s 1 l x    Z O `  ¦  6   x t  · ú §“ É r  â Ä ºü < Ä » ô  Ç + þ AI – Ð Å

Ò# Qt  9 [12], s & h “ É r  © œÃ º Y \ " f     s 1 l x 5 Å q • ¸ü <

› '

a >   ) a † ½ Ó b Ÿ í† < ʝ ) a    H & h s  . Fig. 1(a)  H ü @Â Ò “  

„

 l  © œs  E ⁰ = 0.5 V/µm“    â Ä º,     s 1 l x 5 Å q • ¸_  ß ¼ l

ü < ~ ½ ӆ ¾ Ó\  @ /ô  Ç / B N ç ß – „    © œ_  z  ´Ã ºÂ Òü < ) ‡Ã ºÂ Ò\  ¦ s 



: r& h Ü ¼– Ð r Ó ý t Y Us ‚   ô  Ç   õ \  ¦
 ? /“ ¦, Fig. 1(b)  H

 

  s 1 l x 5 Å q • ¸\  @ /ô  Ç 0 A © œ   s \  ¦ ˜ Ð# Œï  r  . ü @Â Ò “  

 „  l  © œ_  [ jl ü <    _  s 1 l x 5 Å q • ¸ B | 9  ? /_  / B N ç ß –

„

   © œõ  0 A © œ   s \  l # Œ† < Ê`  ¦ · ú ˜ à º e ”  .

s

1 l x    Z O \  _ K  Ò q t$ í  ) a / B N ç ß – „    © œõ  ü @Â Ò “  

„

 l  © œ“ É r Ó  o& ñ ~ ½ ӆ ¾ Ó \  ¦ F C \ P r v “ ¦   õ & h Ü ¼– Ð Ï ã J] X  Ò

 ¦   › ¸\  ¦  l r †   . Ó  o& ñ _  F C \ P  y Œ •• ¸ θ 1  1 s 



“ ¦ & ñ €  , ž Ðß ¼ ç  H+ þ A ~ ½ Ó& ñ d ” Ü ¼– РÒ'  Ó  o& ñ ~ ½ ӆ ¾ Ó  F

C \ P \  _ ô  Ç Ï ã J] X Ò  ¦   › ¸ ∆n“ É r

∆n = (n _|| − n _⊥ ) n _||

n ⊥

sin(2β)θ ₁ cos(~ q · ~ r − Ωt + φ)

= δn 1 cos(~ q · ~ r − Ωt + φ) (7) õ

 ° ú  s  Å Ò# Q”   . # Œl " f n ⊥   H Ó  o& ñ ~ ½ ӆ ¾ Ó  » ¡ ¤ õ  à ºf ”  ô

 Ç Ï ã J] X Ò  ¦ s “ ¦, n ||   H Ó  o& ñ ~ ½ ӆ ¾ Ó  » ¡ ¤ õ  ¨ î ' Ÿ ô  Ç Ï ã J] X Ò  ¦, δn ₁ = (n _|| − n _⊥ )(n _|| /n _⊥ ) sin(2β)θ ₁   H Ï ã J] X Ò  ¦   › ¸_  ”  

;

Ÿ ¤, θ 1 = (E ₀ |E 1 | cos β)/(E _c ² + E ₀ ² )  H Ó  o& ñ _  F C \ P  y Œ •s  9, E ^c   H Freedericksz „  l  © œs  .

III. ÷ m Ç] M ö õ m Í À X Ø8 ý

‘

: r z  ´+ « >\ " f  H ¿ ºa  20 µm “   e  ¦ x  2 ;: ƒ  s  ' ‘   ) a W

1 h Ë : Ó  o& ñ ~ à Ì} Œ •`  ¦  6   x % i  . W 1 h Ë : Ó  o& ñ “ É r   © œs  589 nm \ " f ∆n = 0.2246 (n || = 1.7462, n _⊥ = 1.5216) s 

“

¦, ∆ε = 13.8“   E7`  ¦  6   x % i “ ¦, Ó  o& ñ \  ' ‘ ô  Ç Ò  o™ è



 H 530 nm   H % ƒ_  É Ò É r > \ P    © œ@ /\ " f f  ¨ à º ´ ú §“ É r e  ¦ x

 2 ; :  ƒ  `  ¦  6   x % i  . e  ¦ x  2 ; :  ƒ  _  0 l x • ¸  H W 1 

Fig. 1. Space charge field (a) and phase shift (b) for moving velocity (E 0 = 0.5 V/µm).

h Ë

: Ó  o& ñ 0 l x • ¸_  0.5 wt %– Ð % i  . s  F  g   ™ D ¥ ½ + Ë s 1 p q`  ¦ 8

£ ¤& ñ l  0 Aô  Ç z  ´+ « >_  > h| Ä Ì• ¸  H Fig. 2 ü < ° ú   . ¿ º l 2 Ÿ ¤ c ”

“ É r   © œs  λ = 514 nm“   p ¼ # F  g ) a Ar-ion Y Us $ \  ¦   6

 

x % i “ ¦, ¿ º l 2 Ÿ ¤c ” _  [ jl   H y Œ •y Œ • 254 mW/cm ² s  .

Ò 

re  ¦ \    # Qï  r ü @Â Ò “   dc„  l  © œ_  ~ ½ ӆ ¾ ӓ É r +z s “ ¦, l  Ö

 ¦e ”  y Œ •“ É r β = +35 ^◦ , { 9     H ¿ º l 2 Ÿ ¤c ” _   s y Œ •“ É r 2θ inc = 26 ^◦ s  . s 1 l x    Z O `  ¦ s 6   x l  0 A # Œ ‚  + þ A

—

¸' \  ¦  6   x # Œ B | 9 `  ¦ +x ~ ½ ӆ ¾ ÓÜ ¼– Ð s 1 l x r (   . B | 9  _

 s 1 l x 5 Å q • ¸ v x ü <     7 ˜'  ~q ~ ½ ӆ ¾ Ó_  s 1 l x 5 Å q • ¸ v q  s 

\

  H v q = v x cos β _  › ' a >  $ í w n ô  Ç .  r] X ´ òÖ  ¦“ É r 633 nm _  p ¼ # F  g ) a He-Ne Y Us $ \  ¦ Bragg y Œ •Ü ¼– Ð B | 9 \  { 9 



r &  8 £ ¤& ñ % i  . l 2 Ÿ ¤c ” _  { 9  y Œ •s  θ ^inc = 13 ^◦ _   â Ä

º z  ´+ « >& h “   Braggy Œ •“ É r θ Bragg = 16 ^◦ s  .

Fig. 2. Schematic of experimental setup (I a and I b are intensities of writing beams, θ inc is the half-angle of wave mixing, β is the tilt angle, ~ q is the grating vector, ~ E 0 is the applied electric field, v x is the real velocity of the sample and v q is the moving velocity along ~ q).

Fig. 3. Typical experimental results for two beam cou- pling gain with an applied dc field accompanied by the moving grating (Region I and III: v q = 0, Region II: v q

= 24.6 µm/s).

Fig. 3“ É r ü @Â Ò “   „  l  © œ_  ß ¼l  0.9 V/µms “ ¦   



 s 1 l x 5 Å q • ¸ 24.6 µm/s { 9  M :, z  ´r ç ß –Ü ¼– Ð 8 £ ¤& ñ ô  Ç s  F  g 

 ™ D ¥ ½ + Ë_  z  ´+ « >   õ s  . ü @Â Ò dc „  l  © œ \ " f ¿ º c ” s  1

l

x r \  { 9  ÷ &€   I b   H s 1 p q s  ÷ &“ ¦, I ^a “ É r ’ < Hz  ´s  ÷ &  H \ 



-t  „  ² ú ˜(energy transfer)‰ & ³ © œs  › ' a ¹ 1 Ï÷ &“ ¦(% ò % i (I)), & ñ



© œ  © œI \ " f    \  ¦ s 1 l x r v €  , I ₂  / å L  y  7 £ x    H

 כ

`  ¦ · ú ˜ à º e ”  (% ò % i  (II)). s  כ “ É r s 1 l x    Z O s  / B N ç ß –

„

   © œõ  0 A © œ  s  ° ú כ`  ¦    or &  s 1 p q 7 £ x; Ÿ ¤‰ & ³ © œ`  ¦ œ í A

 l  M :ë  H s  .

s

 F  g   ™ D ¥ ½ + Ë\ " f s  : r& h , z  ´+ « >& h  s 1 p q > à º  H y Œ •y Œ •   6

£

§ õ  ° ú  s  ³ ð‰ & ³ ) a   [10].

Γ = 4πδn 1

λ w cos θ inc

sin φ (8a)

Γ = [ln(Gm 0 ) − ln(m 0 + 1 − G)] cos θ _inc

d (8b)

#

Œl " f λ w   H l 2 Ÿ ¤c ” _    © œs “ ¦, m 0   H { 9  ÷ &  H l 2 Ÿ ¤c ”  [

jl _  q , d  H B | 9 _  ¿ ºa , G = I ² (with I 1 )/I 2 (with − out I 1 )   H s 1 p q s  . d ”  (8a)ü < ° ú  s  s 1 p q > à º  H Ï ã J] X Ò  ¦

Fig. 4. Gain coefficients against applied dc field for vary- ing moving velocities. The solid lines are theoretical curves.

Fig. 5. Gain coefficients for direction of applied dc field.

The solid lines are theoretical curves.



 › ¸ ”  ; Ÿ ¤ δn 1 õ  0 A © œ  › ¸ † ½ Ó sin φ_  Y  L Ü ¼– Ð ³ ð‰ & ³÷ &Ù ¼

–

Ð ü @Â Ò “   „  l  © œõ      s 1 l xZ O s  s 1 p q > à º\  › ' a >  H

†

d`  ¦ · ú ˜ à º e ”  .  € ª œô  Ç    _  s 1 l x 5 Å q • ¸\ " f ü @Â Ò “  

 „  l  © œ\    É r s 1 p q > à º_  z  ´+ « >° ú כõ  s  : r/ B G‚  `  ¦ Fig.

4 \ 
 ? /% 3  . s 1 l x    _  5 Å q • ¸ 33.4 µm/ss “ ¦, ü @ Â

Ò “   dc„  l  © œs  1.2 V/µm{ 9  M :, s 1 l x    Z O `  ¦ s 6   x

t  · ú §“ É r  â Ä º˜ Ð  3C  s  © œ 7 £ x ô  Ç s 1 p q > à º Γ = 624 cm ⁻¹ `  ¦ % 3 % 3  . Fig. 5  H ü @Â Ò “   dc „  l  © œ_  ~ ½ ӆ ¾ Ó

\

   É r s 1 p q > à ºs  . s 1 l x    Z O `  ¦  6   x t  · ú §“ É r  â Ä

º(7 £ ¤, v q = 0) \   H ü @Â Ò “   „  l  © œ_  ~ ½ ӆ ¾ Ós   7 €   s

1 p q > à º Γ → −Γ– Ð ì ø ̈́  ÷ &  H  ⠆ ¾ Ó`  ¦ ˜ Ð% i “ ¦,    \  ¦ 23 µm/s _  5 Å q • ¸– Ð s 1 l x r v   H  â Ä º\   H „  l  © œ_  ~ ½ ӆ ¾ Ó õ

 Á º › ' a >  „  l  © œ_  [ jl  7 £ x † < Ê\     s 1 p q > à º

° ú

כs  / å L  y  7 £ x  # Œ € ª œ_  þ j@ /° ú כ\  • ¸² ú ˜ô  Ç Ê ê  r  y Œ ™

™

è   H  ⠆ ¾ Ó`  ¦ ˜ Ð% i  . ¢ ¸ô  Ç, „  l  © œ_  ~ ½ ӆ ¾ Ós  +z ~ ½ ӆ ¾ Ó

“

   â Ä º −z ~ ½ ӆ ¾ Ó{ 9  M :˜ Ð   8  H þ j@ / s 1 p q > à º\  ¦ & ’ 



.

 

 _  s 1 l x 5 Å q • ¸_  ~ ½ ӆ ¾ Ó\  @ /K  z  ´+ « >& h Ü ¼– Ð 8 £ ¤& ñ ô  Ç s

1 p q > à ºü < s  : r / B G‚  “ É r Fig. 6 õ  ° ú   .     s 1 l x 5 Å q • ¸

 +z~ ½ ӆ ¾ ӓ    â Ä º     s 1 l x 5 Å q • ¸ & | 9 à º2 Ÿ ¤ s 1 p q > à º



 H € ª œ_  þ j@ /° ú כ\  • ¸² ú ˜ ô  Ç Ê ê y Œ ™™ è % i “ ¦, −z ~ ½ ӆ ¾ ÓÜ ¼– Ð

 

 _  s 1 l x 5 Å q • ¸ & t >  ÷ &€   s 1 p q > à º  H v q = 0{ 9  M

:_  ° ú כÜ ¼– РÒ'  & h & h  y Œ ™™ è # Œ 6 £ § _  þ j™ è° ú כ\  • ¸² ú ˜ô  Ç Ê

ê  r  7 £ x  % i  .

Fig. 7“ É r v q = 0 õ  v ^q = 20.4 µm/s _   â Ä º, ü @Â Ò “  

 „  l  © œ_  ~ ½ ӆ ¾ Ó\  @ /ô  Ç  r] X ´ òÖ  ¦`  ¦ ˜ Ð# Œï  r  .  r] X  ´ ò Ö

 ¦“ É r

η = sin ² ( πδn 1 d λ r cos θ Bragg

) (9)

ü

< ° ú  s  Å Ò# Qt “ ¦, z  ´+ « >& h   r] X ´ òÖ  ¦“ É r η(%) = × 100 – Ð

&

ñ _  % i  . # Œl " f λ r “ É r „ à Ð c ” _    © œs  . v q = 0{ 9  M

:,  r] X ´ òÖ  ¦“ É r „  l  © œ_  ~ ½ ӆ ¾ Ó\  › ' a > \ O s  „  l  © œ_  ß ¼

Fig. 6. Gain coefficients against direction of moving ve-

locity. The solid lines are theoretical curves.

Fig. 7. Diffraction efficiencies for direction of applied dc field. The solid lines are theoretical curves.

Fig. 8. Diffraction efficiencies against direction of moving velocity. The solid line is theoretical curve.

l

\  @ /K " f @ /g A& h Ü ¼– Ð
 z Œ ™`  ¦ · ú ˜ à º e ”  . Õ ª Q
   



\  ¦ s 1 l x r v >  ÷ &€  , ° ú  “ É r ß ¼l _  „  l  © œ ° ú כs  • ¸ „   l

 © œ_  ~ ½ ӆ ¾ Ó\     Ï ã J] X Ò  ¦   › ¸° ú כs  ² ú ˜ t Ù ¼– Ð  r] X 

´

òÖ  ¦“ É r q @ /g A& h “     õ \  ¦ t >   ) a  . Fig. 8“ É r ü @ Ò

“

  „  l  © œs  1.2 V/µm{ 9  M :,     s 1 l x 5 Å q • ¸_  ~ ½ ӆ ¾ Ó

\

   É r z  ´+ « >& h Ü ¼– Ð 8 £ ¤& ñ ô  Ç  r] X ´ òÖ  ¦ õ  s  : r / B G‚  s  .



r] X ´ òÖ  ¦“ É r v q = 0 » ¡ ¤ \  @ /K  q @ /g A& h “    ⠆ ¾ Ó`  ¦ ˜ Ð% i 

“

¦,     s 1 l x 5 Å q • ¸ þ j@ /  r] X ´ òÖ  ¦`  ¦ t   H : £ ¤& ñ 5 Å q

•

¸ (v q ≈ −10 µm/s) – РÒ'  Y O # Q| 9 à º2 Ÿ ¤  r] X ´ òÖ  ¦ s  y Œ ™

™

è   H  ⠆ ¾ Ó`  ¦ ˜ Ð% i  .

Fig. 4 \ " f Fig. 8 t _  — ¸Ž  H z  ´+ « >   õ \  ¦ r Ð 3 x ? /l  ô

 Ç   õ , z  ´+ « >`  ¦  © œ ¸ ú ˜ [ O " î   H s  : r/ B G‚  Ü ¼– РÒ'  % 3 

“ É

r Ó ü t o   © œÃ º ° ú כ[ þ t“ É r  6 £ § õ  ° ú   : τ ^d = 23 ± 1 ms s “ ¦, ν = 0.4, E _C = 1.45 ± 0.05 V/µm, E _q = 0.285 ± 0.015 V/µm, E M = 0.255 ± 0.015 V/µm, Õ ªo “ ¦ E ^D = 0.11 V/µm s  .

IV. + s Ç Â ] Ø

‘

: r  7 Hë  H \ " f  H ü @Â Ò “   dc „  l  © œõ  s 1 l x    Z O \  _

ô  Ç s  F  g   ™ D ¥ ½ + Ë z  ´+ « >Ü ¼– РÒ'  ‰ & ³$ y  7 £ x    H F  gÏ ã J] X 

´

òõ \  ¦ › ' a8 £ ¤ % i “ ¦,     s 1 l x 5 Å q • ¸_  ß ¼l ü < ~ ½ ӆ ¾ Ó, ü @ Â

Ò “   „  l  © œ_  [ jl ü < ~ ½ ӆ ¾ Ó\  @ /ô  Ç s 1 p q > à ºü <  r] X 

´

òÖ  ¦ _   ⠆ ¾ Ó`  ¦ › ¸  % i  . Ó ü t| 9  ~ ½ Ó& ñ d ” õ  Ó  o& ñ ~ ½ ӆ ¾ Ó  _

 ž Ðß ¼ ç  H+ þ A ~ ½ Ó& ñ d ” Ü ¼– РÒ'  / B N ç ß – „    © œõ  0 A © œ   › ¸, Ï

ã J] X Ò  ¦   › ¸\  @ /ô  Ç ³ ð‰ & ³`  ¦ l Õ ü t % i “ ¦, s  : r& h “   s 1 p q

>

à ºü <  r] X ´ òÖ  ¦`  ¦ ½ ¨ % i  . ¢ ¸ô  Ç z  ´+ « >& h Ü ¼– Ð 8 £ ¤& ñ ô  Ç s

1 p q > à ºü <  r] X ´ òÖ  ¦`  ¦ r Ð 3 x ? /l  † < ÊÜ ¼– Ð+ ‹ z  ´+ « >   õ \  ¦

 © œ ¸ ú ˜ [ O " î   H Ó ü t| 9   © œÃ º ° ú כ[ þ t`  ¦ ½ ¨ % i  .

P

c p 8 ý ò k >

s

  7 Hë  H“ É r 2004 † < Ƹ  • ¸ % ò z Œ ™@ /† < Ɠ § ƒ  ½ ¨¸  ] j(000-A- 106-070) à º' Ÿ \  _ ô  Ç  כ { 9 m  .

Y

c p w Š à U Ø ”  ô

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Two-Beam-Coupling Gain Enhancement in Porphyrin : Zn-doped Nematic Liquid Crystals by Using a Grating Translation Technique

with an Applied DC Field

Eun Ju Kim, Sang Jo Lee, Hye Ri Yang, Gun Yeup Kim, Jin Hyuk Kwon and Chong Hoon Kwak ^∗ Department of Physics, Yeungnam University, Gyeongsan 712-749

(Received 15 October 2005)

We observed a large two-beam-coupling gain enhancement in porphyrin : Zn-doped nematic liquid crystals by using a grating translation technique with an applied dc field. The high gain coefficient of Γ = 624 cm

⁻¹

was obtained for an the applied dc field of E

0

= 1.2 V/µm and a moving velocity of v

q

= 33.4 µm/s. This value of Γ which is three times larger than that obtained without using a grating translation technique. We also experimentally measured the gain coefficients and the diffraction efficiencies against the directions of E

0

. Our v

q

, and theoretic predictions, showied good agreement with the experimental data.

PACS numbers: 42.65.H, 61.30, 64.70.M

Keywords: Photorefractive effect, Grating translation technique, Nematic liquid crystal, Porphyrin : Zn, Two beam coupling

∗

E-mail: [email protected]