ç ß –  \  @ / # Œ ü @Â Ò “ dc „ l  © œ\   É r s 1 p q > à ºü < r] X ´ òÖ ¦` ¦ 8 £ ¤& ñ % i . ¢ ¸ô Ç, z ´+ « > õ



 ç ß –  \  @ / # Œ ü @Â Ò “   dc „  l  © œ\    É r s 1 p q > à ºü <  r] X ´ òÖ  ¦`  ¦ 8 £ ¤& ñ % i  . ¢ ¸ô  Ç, z  ´+ « >   õ 

\ 

¦ B | 9  ~ ½ Ó& ñ d ” õ  ž Ðß ¼ ç  H+ þ A ~ ½ Ó& ñ d ” Ü ¼– РÒ'  % 3 “ É r s  : r / B G‚  õ  q “ §, ì  r$ 3 † < ÊÜ ¼– Ð+ ‹ F  gÏ ã J] X  ´ òõ _    



 ç ß –   _ ” > r$ í `  ¦ › ¸  % i  .

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

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

I. " e  ] Ø

W

1 h Ë : Ó  o& ñ \  l œ íô  Ç F  gÏ ã J] X  B | 9 “ É r  H F  g † < Æ& h  q 1 p x

~

½ Ó$ í (optical anisotropy)õ  „  l  F  g † < Æ ´ òõ  (electro-optic effect) \  _ K  Z  }“ É r  r] X ´ òÖ  ¦`  ¦ t “ ¦, „  l / F  g † < Æ& h Ü ¼

–

Ð ] j# Q 0 p x  9, à º ms ∼ µs _    É r 6 £ x ² ú š : £ ¤$ í , Õ ª o

“ ¦ ± ú “ É r ½ ¨1 l x „  · ú š`  ¦ € 9 כ ¹– Ð   H 1 p x _   © œ& h  M :ë  H \  1 l x

&

h

 f . Ë – ÐÕ ªÏ þ ›, F  g & ñ ˜ Ð% ƒo , F  g Û ¼0 Ag A, F  g J ‡   “  d ” , 0 A



© œ / B NÓ  o 1 p x _   € ª œô  Ç ì  r  – Ð 6 £ x6   x ÷ &“ ¦ e ”   [1,2].

1994¸   Rudenkoü < Sukhov\  _ K  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  ˜ Г ¦  ) a s Ê ê [3],

š

¸Z þ t ± ú ˜ t  Ó  o& ñ \  › ' a ô  Ç ƒ  ½ ¨  Ö ¸ µ 1 Ïy  ”  ' Ÿ ÷ &“ ¦ e ”   [4-11]. Khoo  H dc „  l  © œ \ " f F  g Ä »• ¸ „  l  © œ\  _ K  W

1 h Ë : Ó  o& ñ _  ~ ½ ӆ ¾ Ó [ þ t s  F C \ P † < ÊÜ ¼– Ð+ ‹  H Ï ã J] X Ò  ¦   

›

¸\  ¦ % 3 >  ÷ &  H Ó  o& ñ ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç F  gÏ ã J] X  ´ òõ  (reorientational photorefractive effect)\  ¦ þ jœ í– Ð › ' a8 £ ¤ 

%

i “ ¦ [4], F  g Ä »• ¸ „  l  © œ\  _ K  Ó  o& ñ ? / Ò_  / B N ç ß – „   



© œs  + þ A$ í ÷ &  H õ & ñ õ  Õ ª   õ – Ð Ò q tl   H ž Ðß ¼, Ó  o& ñ ~ ½ Ó

†

¾ Ó _  F C \ P  ‰ & ³ © œ, Õ ªo “ ¦ F  g   ™ D ¥ ½ + Ë ´ òõ  1 p x`  ¦  [ jy  l

Õ ü t % i   [4,5]. ¢ ¸ô  Ç JanossyÕ ªÒ  ¨ [6] õ  Marrucci Õ ªÒ  ¨ [7]“ É r Ó  o& ñ \  Ò  o™ è\  ¦ ' ‘  €   Ï ã J] X Ò  ¦   › ¸ ‰ & ³$ y  7 £ x

   H Ò  o™ è ´ òõ  (dye effect)\  ¦ ˜ Г ¦ % i “ ¦, methyl-red [8], C 60 [2], carbon nanotubes [9] 1 p x _  Ò  o™ è ' ‘   ) a Ó  o

&

ñ \ " f s  ‰ & ³ © œs  › ' a8 £ ¤ ÷ &% 3  . 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 B 

| 9

\ " f Ó  o& ñ ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç F  gÏ ã J] X  ´ òõ \  ¦ › ' a8 £ ¤

% i “ ¦, Ó  o& ñ _  B | 9  ~ ½ Ó& ñ d ” õ  ž Ðß ¼ ç  H+ þ A ~ ½ Ó& ñ d ” Ü ¼– РÒ

∗

E-mail: [email protected]

'

 s  F  g   ™ D ¥ ½ + Ë_  K $ 3 K \  ¦ ½ ¨ % i   [10]. ¢ ¸ô  Ç, Ò  o™ è

'

‘   ) a W 1 h Ë : Ó  o& ñ ~ à Ì} Œ •\  ü @Â Ò dc „  l  © œ`  ¦ “   # Œ s

1 l x    Z O  (grating translation)`  ¦ à º' Ÿ † < ÊÜ ¼– Ð+ ‹ F  gÏ ã J ] X

 ´ òõ _  7 £ x; Ÿ ¤ ‰ & ³ © œ`  ¦ ˜ Г ¦ % i   [11].

‘

: r  7 Hë  H \ " f  H e  ¦ x  2 ;: ƒ  s  ' ‘   ) a W 1 h Ë : Ó  o& ñ ~ Ã Ì }

Œ

•\  s  F  g   ™ D ¥ ½ + Ë z  ´+ « >`  ¦ à º' Ÿ  # Œ “ ¦   r] X s  µ 1 ÏÒ q t  t

 · ú §  H Bragg % ò % i \ " f_   € ª œô  Ç     ç ß –  \  @ / # Œ ü

@Â Ò “   dc „  l  © œ\    É r s 1 p q > à ºü <  r] X ´ òÖ  ¦`  ¦ 8 £ ¤

&

ñ % i  . ¢ ¸ô  Ç, z  ´+ « >   õ \  ¦ B | 9  ~ ½ Ó& ñ d ” õ  ž Ðß ¼ ç  H+ þ A ~ ½ Ó

&

ñ d ” Ü ¼– РÒ'  % 3 “ É r s  : r/ B G‚  Ü ¼– Ð r Ð 3 x ? /l † < ÊÜ ¼– Ð+ ‹ Ó ü t

| 9

 © œÃ º\  ¦ ½ ¨ % i “ ¦, f . Ë – ÐÕ ªÏ þ › l 2 Ÿ ¤ õ  ™ è \  › ' aº   ) a r 



© œÃ º_  ü @ ғ   „  l  © œ\  @ /ô  Ç _ ” > r$ í `  ¦ › ¸  % i  .

II. T  Â ] Ø

Fig. 1 õ  ° ú  s  ç ß –[ O & h “   ¿ º l 2 Ÿ ¤c ” s  B | 9 \  { 9   



 H  â Ä º, B | 9  ? / Ò_  Å Òl & h “   ç ß –[ O Á º] (  H I(~ r, t) = I 0 (t)(1 + m cos ~ q · ~ r) = I 0 (t) + I 1

2 e ^{i~ q·~ r} + c.c. (1) ü

< ° ú  s  ³ ð‰ & ³ ) a  . # Œl " f c.c.  H 4 Ÿ ¤ ™ è/ B NÓ  o`  ¦
 ? / 9, m = ²

√ I

I

I

+I

“ É r   › ¸ U  ·s  (modulation depth), I a ü < I b   H y

Œ

•y Œ • { 9     H l 2 Ÿ ¤c ” _  [ jl s  .   H      à º 7 ˜' s 

“

¦, q = |~q| = ^2π Λ

, Λ _g   H     ç ß –  s  .

/ B

N ç ß –& h Ü ¼– Ð Å Òl & h “   ç ß –[ O Á º] ( I(~r, t) \  _ K  B | 9 

?

/_  € 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 Ó î  r1 l x`  ¦ “ ¦, Õ ª   õ  „    ì  r o  (charge separa-

tion) ü < / B N ç ß – „    © œ (space charge field)s  + þ A$ í  ) a  . Ó  o

-559-

Fig. 1. Schematic of two beam coupling geometry ( 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 ˆ n ⁰ , ~ E ₀ is the applied electric field, ˆ n is the director axis and is the reoriented director axis.).

&

ñ _  B | 9 ~ ½ Ó& ñ d ”  [10,11]Ü ¼– РÒ'  B | 9  ? /\  + þ A$ í  ) a & ñ  © œ



© œI \ " f_  / B N ç ß – „    © œ_  ß ¼l  |E 1 |   H

|E 1 | = m

2 [ E _D ² ν ² + E ₀ ² sin ² β

X ² + Y ² ]

(2.1) s

“ ¦, c ” _  ç ß –[ O Á º] (ü < & ñ  © œ  © œI \ " f_  / B N ç ß – „    © œ   s

_  0 A © œ  s  (phase shift)  H

φ = tan ⁻¹ [ E D νX + E 0 sin βY

E _D νY − E ₀ sin βX ] (2.2)

–

Ð Å Ò# Q”   . # Œl " f X = (1 + E ^E

+ _2E ^E

q

+ ^E _2E

^sin

^β

q

E

+

E

2E

E

), y = ( ^E

_2E ^{ν sin β}

q

) s “ ¦, ⍠ H B | 9 _  l Ö  ¦e ”  y Œ •• ¸, E 0   H ü @Â Ò “   „  l  © œ, E ^D   H S X ‰ í ß – „  l  © œ (diffusion field), E q   H Ÿ í o „  l  © œ (saturating field), E M “ É r ³ ðÀ Ó

„

 l  © œ (drift field), ν = ^µ µ

^−µ +µ

, ¹ _µ = _µ ¹

+ _µ ¹

, µ ^±   H s 

“

: r[ þ t _  s 1 l x • ¸s  .

Fig. 2(a)  H     ç ß –  s  Λ ^g = 1 µm ü < Λ ^g = 1.5 µm _

  â Ä º, ü @Â Ò “   „  l  © œ_  ~ ½ ӆ ¾ Ó\    É r / B N ç ß – „    © œ E ₁ _  z  ´Ã ºÂ Òü < ) ‡Ã ºÂ Ò\  ¦ s  : r& h Ü ¼– Ð r Ó ý t Y Us ‚   ô  Ç    õ

s “ ¦, Fig. 2(b)  H ü @Â Ò “   „  l  © œ\  @ /ô  Ç 0 A © œ  s  _

 s  : r / B G‚  s  .

B

| 9 ? /\  { 9  ô  Ç ¿ º l 2 Ÿ ¤c ” \  _ K  + þ A$ í  ) a / B N ç ß – „   



© œ“ É r Ó  o& ñ ~ ½ ӆ ¾ Ó _  F C \ P \  l “     H X <, Ó  o& ñ _  F C 

\ P

 y Œ •• ¸ θ   Œ •“ ¦ 
_  ò ø Í$ í > à º K ë ß –`  ¦ “ ¦ 9½ + É M :,

ž

Ðß ¼ ç  H+ þ A~ ½ Ó& ñ d ”  [4]“ É r

γ νis

∂θ

∂t = K( ∂ ² θ

∂z ² + ∂ ² θ

∂x ² ) + |~ Γ E | (3.1)

|~ Γ E | = ∆εε 0 | ˆ n ⁰ · ~ E( ˆ n ⁰ × ~ E)| (3.2)

Fig. 2. (a) Complex representation of space charge field for applied electric field and (b) phase shift variation against electric field.

n ˆ ⁰ = [sin θ, 0, cos θ] (3.3)

E = ~ ~ E 0 + | ~ E 1 | cos(~ q · ~ r + φ) (3.4)

= [|E ₁ | cos β cos(~ q · ~ r + φ), 0, |E ₁ | sin β cos(~ q · ~ r + φ) + E ₀ ]

–

Ð Å Ò# Q”   (Fig. 1 ‚ à Л ¸). # Œl " f γ νis   H Leslie & h $ í >  Ã

ºs “ ¦, ∆ε = ε k - ε _⊥   H Ä »„    © œÃ º , ε ⁰   H ”  / B N _  Ä »„   Ö

 ¦, ˆ n ⁰ “ É r F C \ P  ) a Ó  o& ñ ~ ½ ӆ ¾ Ó _  ~ ½ ӆ ¾ Ó`  ¦
  · p . / B N ç ß –

„

   © œs  B Ä º  Ø Ô>  & ñ  © œ © œI  ° ú כ\  • ¸² ú ˜ô  Ç “ ¦ & ñ

€  , ž Ðß ¼ |~Γ E |  H ü @Â Ò “   „  l  © œ E 0 ü < & ñ  © œ © œI \ " f _

 / B N ç ß – „    © œ_  ß ¼l  |E 1 | \ ë ß – _ ” > r ô  Ç .   " f Ó  o& ñ _

 F C \ P  y Œ •• ¸ θ  1 “    â Ä º |~Γ ^E |  H   H  & h Ü ¼– Ð

|~ Γ E | ≈ ^∆εε ₂

[|E 1 | ² (2θ cos 2β + sin 2β) cos ² (~ q · ~ r + φ)

−E ₀ ² θ + 2E ₀ |E ₁ |(cos β − 2θ sin β) cos(~ q · ~ r + φ)] (4)

  ) a  .

ž

Ðß ¼ ç  H+ þ A ~ ½ Ó& ñ d ” _  r • ¸K \  ¦

θ(~ r, t) = θ 1 (t) cos(~ q · ~ r + φ) (5)

M1 ∼ M4 : mirrors, P1 ∼ P3 : polarizers, D1 ∼ D4 : detectors).



 & ñ €  , d ” (3)õ  d ” (4)– РÒ'  θ 1 (t) \  › ' a ô  Ç 1>  p ì  r

~

½ Ó& ñ d ” `  ¦ % 3 `  ¦ à º e ”  .

∂θ 1 (t)

∂t + X ⁰ θ 1 (t) = Y ⁰ (6.1)

X ⁰ = K γ νis

K _g ² + ε ef f {E ₀ ² − 3

4 |E 1 | ² cos 2β}, Y ⁰ = ε ef f E 0 |E 1 | cos β (6.2)

#

Œl " f ε ef f = ^∆εε _γ

vIs

  H Ä »´ ò Ä »„    © œÃ º s “ ¦, E C = q Kq

∆εε

  H Freedericksz „  l  © œs  .

d ”

(6.1)\ " f Ó  o& ñ ~ ½ ӆ ¾ Ó _  F C \ P y Œ •• ¸ θ 1 (t)  H ¿ º l  2

Ÿ ¤c ” \  _ ô  Ç f . Ë – ÐÕ ªÏ þ › l 2 Ÿ ¤ õ & ñ _   â Ä º\   H

θ ₁ (t) = Y ⁰

X ⁰ (1 − e ^−X

^t ) (7.1) s

“ ¦, ¿ º l 2 Ÿ ¤c ”  ×  æ ô  Ç c ” `  ¦ ] j ô  Ç f . Ë – ÐÕ ªÏ þ › ™ è  õ & ñ _

  â Ä º\   H

θ 1 (t) = Y ⁰

X ⁰ e ^−X

^t (7.2)

–

Ð Å Ò# Q”   . # Œl " f X ⁰ = ¹ _τ = _γ ^K

νis

|~ q| ² + ε ef f E ₀ ² , Y ⁰ = ε _{ef f} E ₀ |E ₁ | cos β s “ ¦, X ⁰ = ¹ _τ   H f . Ë – ÐÕ ªÏ þ ›_  l 2 Ÿ ¤ õ  ™ è

\  › ' a >   ) a r  © œÃ º_  % i à ºs  .

 

² D G ü @Â Ò “   „  l  © œ E 0 ü < & ñ  © œ © œI \ " f_  / B N ç ß – „  

 © œ_  ß ¼l  |E ¹ | \  _ ô  Ç Ó  o& ñ ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç Ï ã J ] X

Ò  ¦   › ¸  H

δn ₁ (t) = n _k n ⊥

(n _k − n _⊥ ) sin(2β)θ ₁ (t) (8)

s

  [10,11]. # Œl " f n k   H Ó  o& ñ ~ ½ ӆ ¾ Ó  » ¡ ¤ õ  ¨ î ' Ÿ ô  Ç Ï ã J ] X

Ò  ¦ s “ ¦, n ⊥   H ~ ½ ӆ ¾ Ó  » ¡ ¤ õ  à ºf ” “   Ï ã J] X Ò  ¦ s  .

Fig. 4. Typical experimental data for two beam coupling experiment (β = +35 ^◦ , E 0 = 0.9 V/µm).

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 µm \ " f ∆n = 0.2246 (n k = 1.7462, n ⊥ = 1.5216) s 

“

¦, ∆ε = 13.8“   E7`  ¦  6   x % i “ ¦, e  ¦ x  2 ;: ƒ  _  0 l x • ¸



 H W 1 h Ë : Ó  o& ñ 0 l x • ¸_  0.5 wt%– Ð % i  . s 1 p q > à ºü <  r ] X

´ òÖ  ¦`  ¦ 8 £ ¤& ñ l  0 Aô  Ç z  ´+ « >_  > h| Ä Ì• ¸  H Fig. 3 õ  ° ú   .

¿

º l 2 Ÿ ¤c ” “ É r   © œs  λ ^w = 514 nm “   Ar-ionY Us $ \  ¦   6

x % i “ ¦, F Ò q tc ” “ É r   © œs  λ ^r = 633 nm“   He-Ne Y Us 

$

\  ¦  6   x % i  . B | 9 – РÒ'  þ j@ /_   r] X ´ òÖ  ¦ ° ú כ`  ¦ % 3  l

 0 A # Œ ¿ º l 2 Ÿ ¤c ” õ  F Ò q tc ” “ É r — ¸¿ º p ¼ # F  g Ü ¼– Ð % i 

“

¦, ¿ º l 2 Ÿ ¤c ” _  [ jl   H y Œ •y Œ • I a = I _b = 112 mW/cm ² s 

“

¦, F Ò q tc ” _  [ jl   H I r = 4 mW/cm ² s  . B | 9 _  l Ö  ¦ e ”

 y Œ •“ É r β = +35 ^◦ s  .

B

| 9 _  l Ö  ¦e ”  y Œ • β = +35 ^◦ s “ ¦, ü @Â Ò “   „  l  © œ _

 [ jl  E 0 = 0.9 V/µm“    â Ä º s  F  g   ™ D ¥ ½ + Ë z  ´+ « >_  z 

´r ç ß – 8 £ ¤& ñ   õ s  . e  ¦ x  2 ;: ƒ  s  ' ‘   ) a Ó  o& ñ ~ à Ì} Œ •

\

 ü @Â Ò dc „  l  © œ`  ¦ “  ô  Ç  © œI \ " f ¿ º l 2 Ÿ ¤c ” s  B | 9 

\

 { 9   ÷ &€   I _b   H s 1 p q s  ÷ &“ ¦, I ^a “ É r ’ < Hz  ´s  ÷ &  H \  - t

 „  ² ú ˜ ‰ & ³ © œs  › ' a ¹ 1 Ï÷ &  H X <, s  כ “ É r e  ¦ x  2 ;: ƒ  s  ' ‘ 

 )

a Ó  o& ñ s  „  + þ A& h “   F  gÏ ã J] X  B | 9 e ” `  ¦
  · p .

Fig. 5  H “ ¦   r] X s  µ 1 ÏÒ q t t  · ú §  H Bragg% ò % i  ? /\ 

"

f  € ª œô  Ç     ç ß –  \  @ /ô  Ç, ü @Â Ò “   dc „  l  © œ\   

 É

r & ñ  © œ © œI _  s 1 p q > à ºü <  r] X ´ òÖ  ¦ _  8 £ ¤& ñ   õ \  ¦
 

? / 9, z  ´‚  “ É r r Ð 3 x ? /l ô  Ç s  : r/ B G‚  s  . s  F  g   ™ D ¥ ½ + Ë _

  â Ä º, Ò  o™ è ' ‘  W 1 h Ë : Ó  o& ñ \ " f F  gÏ ã J] X  ´ òõ \  ¦ 8 £ ¤

&

ñ l  0 Aô  Ç s  : r& h , z  ´+ « >& h  s 1 p q > à º Γ   H y Œ •y Œ • Γ = 4πδn 1 (t)

λ _w cos θ _inc sin φ (9.1)

Fig. 5. Gain coefficients and diffraction efficiencies against applied dc field for various grating periods. The solid lines are theoretical curves.

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

d (9.2) s

“ ¦ [5], F Ò q tc ” \  _ ô  Ç s  : r& h   r] X ´ òÖ  ¦ η(t)“ É r

η(t) = sin ² ( πδn 1 (t)d λ r cos θ B

) (10)

–

Ð Å Ò# Q”    [5]. z  ´+ « >& h   r] X ´ òÖ  ¦“ É r η(%) = ^{ r]} _{È Òõ} ^{X ÷} _ ^& _ ^{ H c ” }

 H c ” 

× 100 – Ð & ñ _  % i  . # Œl " f λ w   H l 2 Ÿ ¤c ” _    © œ, λ r “ É r F

Ò q tc ” _    © œ, 2θ ^inc   H l 2 Ÿ ¤c ” _  { 9  y Œ •, θ ^B   H F Ò q tc ”  _

 Bragg { 9  y Œ •, m ^o   H { 9  ÷ &  H l 2 Ÿ ¤c ”  [ jl _  q , G

= I _b (with I _a )/I _b (without I _a )  H s 1 p q, d  H B | 9 _  ¿ ºa  s

 . Fig. 5– РÒ'      ç ß –  s  a % v   | 9 à º2 Ÿ ¤ s 1 p q > à º ü

<  r] X ´ òÖ  ¦ _  ° ú כs  ‰ & ³$  >  y Œ ™™ è† < Ê`  ¦ · ú ˜ à º e ”  .   



 ç ß –  s  Λ g = 1.5 µm“    â Ä º, ü @Â Ò “   „  l  © œs  E 0

= 0.8 V/µm \ " f þ j@ /_  s 1 p q > à º Γ = 187 cm ⁻¹ \  ¦ % 3 

%

3 “ ¦, ü @Â Ò “   „  l  © œs  E ⁰ = 1.25 V/µm \ " f η = 21

% _  þ j@ /  r] X ´ òÖ  ¦`  ¦ % 3 % 3  .

Fig. 6. Real-time diffraction efficiencies for a grating period of Λ _g = 1.0 µm. The solid lines are theoretical curves. The arrows (↓) represent at the moment one of writing beams turned off.

 

  ç ß –  s  Λ ^g = 1 µm s “ ¦, ü @Â Ò “   dc „  l  © œs  y

Œ

•y Œ • E ⁰ = 0.3 V/µm ü < E ⁰ = 1.5 V/mum“    â Ä º, z  ´r  ç

ß –  r] X ´ òÖ  ¦“ É r Fig. 6 õ  ° ú  s 
 ? / 9, z  ´‚  “ É r r Ð 3 x ? / l

ô  Ç s  : r / B G‚  s  . Fig. 6\ " f  o¶ ú ˜³ ð(↓)  H ¿ º l 2 Ÿ ¤c ” 

×

 æ ô  Ç c ” `  ¦ ] j  # Œ f . Ë – ÐÕ ªÏ þ ›`  ¦ ™ è    H í  H ç ß –`  ¦
 



· p .

Fig. 7“ É r     ç ß –  s  Λ ^g = 1.5 µm { 9  M :, ü @Â Ò “   dc

„

 l  © œs  y Œ •y Œ • E ⁰ = 0.3 V/µm ü < E ⁰ = 1.5 V/µm“    â Ä

º, z  ´r ç ß –  r] X ´ òÖ  ¦ _  8 £ ¤& ñ   õ s  9, z  ´‚  “ É r r Ð 3 x ? /l  ô

 Ç s  : r / B G‚  s  .  o¶ ú ˜³ ð(↓)  H ¿ º l 2 Ÿ ¤c ”  ×  æ ô  Ç c ” `  ¦ ] j

 # Œ f . Ë – ÐÕ ªÏ þ ›`  ¦ ™ è    H í  H ç ß –`  ¦
  · p . Fig. 6õ  Fig. 7 – РÒ'  ° ú  “ É r ß ¼l _  ü @Â Ò „  l  © œ \ " f     ç ß –

 

s   H  â Ä º r  © œÃ º τ   H  H ° ú כ`  ¦ t  9, f . Ë – ÐÕ ªÏ þ ›`  ¦ l  2

Ÿ

¤ “ ¦ ™ è    H X <  8 š ¸ ½ ™ r ç ß –s    a Ë >`  ¦ · ú ˜ à º e ”  .

Fig. 8“ É r     ç ß –  s  Λ ^g = 1 µm ü < Λ ^g = 1.5 µm _

  â Ä º, r  © œÃ º_  % i à º 1/τ _  ü @Â Ò “   dc „  l  © œ\  @ / ô

 Ç _ ” > r$ í `  ¦
 ? / 9, z  ´‚  “ É r s  : r/ B G‚  s  . Fig. 5\ 

"

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

Fig. 7. Real-time diffraction efficiencies for a grating period of Λ g = 1.5 µm. The solid line is theoretical curve. The solid lines are theoretical curves. The arrows (↓) represent at the moment one of writing beams turned off.

+

«

>   õ \  ¦  © œ ¸ ú ˜ [ O " î   H Ó ü t| 9   © œÃ º  H  6 £ § õ  ° ú   .

Leslie & h $ í > à º  H γ νis = 1.24 ± 0.02 P a · s s “ ¦, Ä »´ ò Ä

»„    © œÃ º   H ε ef f = 98 ± 2 µm ² /V ² · s s  . “ : r • ¸

18 ^◦ C { 9  M :, E7_  Leslie & h $ í > à º γ vis = 0.3 P a · s“  

 כ

\  q  # Œ [12], e  ¦ x  2 ;: ƒ   Ò  o™ è ' ‘   ) a W 1 h Ë : Ó  o

&

ñ (E7)_  & h $ í > à º €  • 4C  7 £ x    H   õ \  ¦ % 3 % 3  .

IV. + s Ç Â ] Ø

e

 ¦ x  2 ;: ƒ  (Porphyrin:Zn)s  ' ‘   ) a W 1 h Ë : Ó  o& ñ ~ Ã Ì }

Œ

•\  s  F  g   ™ D ¥ ½ + Ë z  ´+ « >`  ¦ à º' Ÿ  # Œ  € ª œô  Ç     ç ß –  \ 

@

/ # Œ ü @Â Ò “   dc „  l  © œ\    É r s 1 p q > à ºü <  r] X ´ ò Ö

 ¦`  ¦ 8 £ ¤& ñ % i  . B | 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'  f . Ë – ÐÕ ªÏ þ › l 2 Ÿ ¤ õ & ñ õ  ™ è õ & ñ _   â Ä

º Ó  o& ñ ~ ½ ӆ ¾ Ó _  F C \ P  y Œ •• ¸\  _ ô  Ç Ï ã J] X Ò  ¦   › ¸ü < s 

Fig. 8. Dependence of 1/τ on applied dc electric field at various grating periods. The solid lines are theoretical predictions.

1 p

q > à º,  r] X ´ òÖ  ¦`  ¦ s  : r& h Ü ¼– Ð Ä »• ¸ % i Ü ¼ 9 z  ´+ « >  õ  ü

< r Ð 3 x ? /l † < ÊÜ ¼– Ð+ ‹  € ª œô  Ç     ç ß –  _   â Ä º ü @Â Ò “  

 „  l  © œ\    É r r  © œÃ º_  _ ” > r$ í `  ¦ › ¸  % i  . ¢ ¸ô  Ç Ò 

o™ è ' ‘   ) a W 1 h Ë : Ó  o& ñ _  Leslie & h $ í > à º γ νis = 1.24

± 0.02 P a · s ü < Ä »´ ò Ä »„    © œÃ º  ε ^{ef f} = 98 ± 2 µm ² /V ²

· s\  ¦ % 3 % 3  .

Y

c p w Š à U Ø ”  ô

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Eun Ju Kim, Hye Ri Yang, Gun Yeup Kim, Sun Yong Park and Chong Hoon Kwak ^∗ Department of Physics, Yeungnam University, Gyeongsan 712-749

(Received 10 November 2006)

We measured the gain coefficients and the diffraction efficiencies for various grating periods in porphyrin:Zn-doped nematic liquid crystals by using a two-beam coupling experiment under the influence of an applied dc field. Based on the material equations and the torque balance equation, we theoretically derived the expressions for the gain coefficient and diffraction efficiency, showing good agreement with the experimental results and investigated the dependence of the photorefractive effect on the grating period.

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

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

∗

E-mail: [email protected]