{ ÚY Û Ã Å : Ž ì ÅT Y 8 Èc Ü R u œ X N Ë U c lT c l8 ý ° Ë Ñò i >± n Ç „ ÇÊ Ý • ¤X N Ë õ m Í A 0V Ä

þ

{ ÚY Û Ã Å :  Ž ì ÅT  Y 8 Èc Ü R u œ X N Ë U c lT c l8 ý ° Ë Ñò i >± n Ç „ ÇÊ Ý • ¤X N Ë õ m Í A 0V Ä



™ »ª <® £ · T „ ç ¡‚ Ð · … è ¡A jP  ·  ™ »Z Ì * ° · T  ø ¶ B0 å  ·  + 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)s  ' ‘   ) a W 1 h Ë : Ó  o& ñ ~ à Ì} Œ •\  ü @Â Ò dc „  l  © œ`  ¦ “   €  " f s  F  g 

 ™ D ¥ ½ + Ë z  ´+ « >`  ¦ à º' Ÿ  # Œ F  gÏ ã J] X  ´ òõ \  ¦ › ' a8 £ ¤ “ ¦, ü @Â Ò “   „  l  © œ_  ß ¼l ü < ~ ½ ӆ ¾ Ó, B | 9 _  l Ö  ¦e ”  y

Œ

•_  ~ ½ ӆ ¾ Ó 1 p x  € ª œô  Ç z  ´+ « > › ¸| \  @ /K  s 1 p q > à ºü <  r] X ´ òÖ  ¦`  ¦ 8 £ ¤& ñ % i  . ü @Â Ò “   „  l  © œ\  @ / K

 s 1 p q > à ºü <  r] X ´ òÖ  ¦“ É r „  l  © œ_  ° ú כs  & | 9 à º2 Ÿ ¤  Ø Ô>  7 £ x  # Œ þ j@ /° ú כ\  • ¸² ú ˜ô  Ç Ê ê " f" fy  y Œ ™

™

è   H  ⠆ ¾ Ó`  ¦ ˜ Ð% i Ü ¼ 9, þ j@ /° ú כ[ þ t“ É r y Œ •y Œ •   É r „  l  © œ_  ° ú כ\ " f
 z Œ ¤ . Ó ü t| 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‚  `  ¦ z  ´+ « >   õ ü < r Ð 3 x ? /l  † < ÊÜ ¼– Ð+ ‹ s 1 p q > à ºü <  r] X ´ òÖ  ¦ _   ⠆ ¾ Ó

` 

¦ ì  r$ 3  % i “ ¦, ü @Â Ò “   © œ_  ß ¼l  E

0

= 1.24 V/µm“    â Ä º\  Ï ã J] X Ò  ¦   › ¸ ”  ; Ÿ ¤ _  ß ¼l  δn

1

= 4.4 × 10

⁻³

\  ¦ % 3 % 3  .

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) M :ë  H \  z  ´r ç ß – f . Ë – ÐÕ ªÏ þ ›õ  F  g& ñ ˜ Ð % ƒo , 0 A



© œ / B NÓ  o Õ ªo “ ¦ F  g Û ¼0 Ag A 1 p x _  ì  r  \  6 £ x6   x ÷ &“ ¦ e ”  .

Khoo \  _ K  W 1 h Ë : Ó  o& ñ _  ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç F  g Ï

ã J] X  ´ òõ  (reorientational photorefractive effect) þ jœ í

–

Ð ˜ Г ¦  ) a s  Ê ê [1], Ó  o& ñ õ  › ' a > ô  Ç F  gÏ ã J] X  B | 9 \  › ' a ô  Ç

ƒ

 ½ ¨  Ö ¸ µ 1 Ïy  ”  ' Ÿ ÷ &# Q M ® o   [2–5]. ¢ ¸ô  Ç, Janossy Õ ªÒ  ¨ [6] õ  Marrucci Õ ªÒ  ¨ [7] \  _ K  Ó  o& ñ \  Ò  o™ è\  ¦ ' ‘  €   Ï

ã J] X Ò  ¦   › ¸_  ß ¼l  ‰ & ³$ y  7 £ x    H Ò  o™ è ´ òõ  (dye effect)  ˜ Г ¦÷ &% 3 “ ¦, methyl-red [2], C ⁶⁰ [3, 4], carbon nanotubes [5] 1 p x _  Ò  o™ è ' ‘   ) a Ó  o& ñ Ü ¼– РÒ'  s  ‰ & ³



© œs  › ' a8 £ ¤ ÷ &% 3  .

Ó 

o& ñ ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç F  gÏ ã J] X  ´ òõ   H  6 £ § _  õ 

&

ñ Ü ¼– Ð [ O " î  ) a  . B | 9 \  ç ß –[ O & h “   ¿ º Y Us $ 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 ð À

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  ) a  .   ² D G, F  g Ä »

∗

E-mail: [email protected]

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

•

¸ / B N ç ß – „    © œõ  ü @Â Ò “   „  l  © œ\  _ ô  Ç ž Ðß ¼ Ó  o& ñ _

 ~ ½ ӆ ¾ Ó » ¡ ¤`  ¦ F C \ P r v >  ÷ &“ ¦, s  Qô  Ç F C \ P  ´ òõ 



 H B | 9  ? /\   H Ï ã J] X Ò  ¦   › ¸\  ¦ µ 1 ÏÒ q tr †    [1]. s ü < ° ú  

“ É

r Ò  o™ è ' ‘  W 1 h Ë : Ó  o& ñ \ " f_      + þ A$ í \  _ ô  Ç F  g„  

 µ 1 ÏÒ q tõ  / B N ç ß – „    © œ_  + þ A$ í " é ¶ o   H F  gÏ ã J] X    & ñ _  B j

&

m 7 £ § õ  Ä »   . t ë ß –, Á ºl  F  gÏ ã J] X    & ñ _  Ï ã J] X Ò  ¦



 › ¸  H „  l  © œ\  @ /K  ‚  + þ A& h Ü ¼– Ð q Y V   H Pockels ´ ò õ

“    כ \  ì ø ÍK , W 1 h Ë : Ó  o& ñ \ " f_  Ï ã J] X Ò  ¦   › ¸  H / B N ç ß –

„

   © œõ  ü @Â Ò “   „  l  © œ\  _ ô  Ç Ó  o& ñ ~ ½ ӆ ¾ Ó _  F C 

\ P

\  _ ô  Ç  כ s “ ¦ Ï ã J] X Ò  ¦   › ¸ „  l  © œ_  ] jY  L \  q Y V

  H Kerr ´ òõ ü < ° ú  s 
 è ß –  [8].

‘

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

B

N ç ß – „    © œõ  Ï ã J] X Ò  ¦   › ¸, s 1 p q > à º,  r] X ´ òÖ  ¦`  ¦ s  : r

&

h Ü ¼– Ð > í ß – # Œ F  gÏ ã J] X  B j& m 7 £ §`  ¦ [ O " î “ ¦, e  ¦ x  2 ; :



ƒ  s  ' ‘   ) a W 1 h Ë : Ó  o& ñ ~ à Ì} Œ •\  s  F  g   ™ D ¥ ½ + Ëz  ´+ « >`  ¦ Ã

º' Ÿ  # Œ ü @Â Ò “   „  l  © œ_  ~ ½ ӆ ¾ Óõ  ß ¼l , B | 9 _  l Ö  ¦ e ”

 y Œ •• ¸ 1 p x _   € ª œô  Ç › ¸| \ " f s 1 p q > à ºü <  r] X ´ òÖ  ¦`  ¦ 8

£ ¤& ñ % i  . ¢ ¸ô  Ç, z  ´+ « >  õ \  ¦ s  : r/ B G‚  õ  q “ §, ì  r$ 3  

% i  .

II. T  Â ] Ø

1.  ¹ Å  Ä Z ØP ; c 8 ý” X ¢ Œ Ÿ «‡ ˜ m  ¹ Å X ê s ] k ùV R Ë Ó 

o& ñ \  @ /ô  Ç Ó ü t| 9 ~ ½ Ó& ñ d ”  [9]“ É r

∂n ^±

∂t + γ _R n ⁺ n ⁻ ± 1

e ∇ · ~ J ^± = αI (1.1)

-345-

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, ~ E 0 is the applied electric field, ˆ n is the director axis and ˆ n

⁰

is the reoriented director axis.).

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

∇ · ~ E = e εε 0

(n ⁺ − n ⁻ ) (1.3)

–

Ð Å Ò# Q”   . # Œl " f n ^±   H e  ¦ x  2 ; :  ƒ  s  ' ‘   ) a Ó  o& ñ

\

" f µ 1 ÏÒ q tô  Ç € ª œ·6 £ § s “ : r _  x 9 • ¸s “ ¦, γ R “ É r F   ½ + Ë  © œÃ º, J ^±   H 8 ú x „  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 c ” _  [ jl , ~ E  H ü @Â Ò “   „  l  © œ ~ E ₀ ü <

/ B

N ç ß – „    © œ ~ E 1 _  ½ + Ës  . d ” (1.1)“ É r s “ : r[ þ t _  q Ö  ¦ ~ ½ Ó

&

ñ d ” s “ ¦, d ” (1.2)  H 8 ú x „  À Ó x 9 • ¸– Ð+ ‹ ' Í   P : † ½ ӓ É r „   l

 © œ\  _ ô  Ç s “ : r[ þ t _  ³ ðÀ Óü < › ' a >   ) a † ½ Ós “ ¦, ¿ º  P : † ½ Ó

“ É

r € ª œ(6 £ §) s “ : r _  x 9 • ¸ \  _ ô  Ç \ P & h  S X ‰ í ß –õ  › ' a >   ) a † ½ Ó s

 . d ” (1.3)“ É r Poisson ~ ½ Ó& ñ d ” s  .

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

º] (\  ¦ + þ A$ í r v  9, s ü < ° ú  “ É r / B N ç ß –& h Ü ¼– Ð Å Òl & h “   ç ß – [ O

Á º] (  H

I = I ₀ (t)(1 + m cos ~ q · ~ r) = I ₀ (t) + I ₁

2 e ^{i~ q·~ r} + c.c. (2) ü

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

√ I

_a

I

_b

I

a

+I

b

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

Œ

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

“ ¦, q = |~q| = ^2π Λ

_g

, Λ _g   H     ç ß –  s  .

/ B

N ç ß –& h Ü ¼– Ð Å Òl & h “   ç ß –[ O Á º] ( \  @ /K    › ¸  ) a € ª œ·6 £ § s

“ : r _  x 9 • ¸ü < 8 ú x „  l  © œ“ É r n ^± = n ^± ₀ (t) + 1

2 n ^± (t)e ^{i~ q·~ r} + c.c. (3.1)

E = ~ ~ E ₀ (t) + 1 2

E ~ ₁ (t)e ^{i~ q·~ r} + c.c. = E _x x + E ˆ _z z ˆ (3.2) õ

 ° ú  s  Ñ ü t à º e ”  . # Œl " f E x = ¹ ₂ E 1x (t)e ^{i~ q·~ r} + c.c. s 

“

¦, E z = E 0 (t) + ¹ ₂ E 1z (t)e ^{i~ q·~ r} + c.c. s  . d ” (2)ü < d ” (3)\ 

"

f Y 0 (t) † ½ ӓ É r / B N ç ß –& h Ü ¼– Ð { 9 & ñ ô  Ç † ½ Ós “ ¦, ¹ ₂ Y 1 (t)e ^{i~ q·~ r} † ½ ӓ É r /

B

N ç ß –& h Ü ¼– Ð   › ¸  ) a † ½ Ó`  ¦
  · p . # Œl " f Y <sup>0</sup> (t)  H I 0 (t), n <sup>±</sup> <sub>0</sub> (t), ~ E 0 (t)\  ¦, Y 1 (t)  H I 1 (t), n <sup>±</sup> <sub>1</sub> (t), ~ E 1 (t)`  ¦
  · p .

d ”

(2)ü < d ” (3)`  ¦ Ó ü t| 9 ~ ½ Ó& ñ d ”  d ” (1)\  @ /{ 9  # Œ > í ß – €  



© œÃ º† ½ ӓ É r

∂n 0

∂t + γ R n ² ₀ = αI 0

n ⁺ ₀ = n ⁻ ₀ = n 0 (4.1) s

“ ¦, 1  t à º† ½ ӓ É r

∂n ⁺ ₁

∂t + (γ R n 0 + iq z µ ⁺ E 0 + D ⁺ q ² )n ⁺ ₁ + γ R n 0 n ⁻ ₁ +iµ ⁺ n 0 (E 1x q x + E 1z q z ) = αI 1

∂n ⁻ ₁

∂t + (γ _R n ₀ − iq _z µ ⁻ E ₀ + D ⁻ q ² )n ⁻ ₁ − γ _R n ₀ n ⁺ ₁

−iµ ⁻ n ₀ (E _1x q _x + E _1z q _z ) = αI ₁ E · ~ ~ K g = −i e

εε 0

∆n (4.2)

ü

< ° ú   . # Œl " f ∆n = n ⁺ 1 − n ⁻ ₁ s “ ¦, q ^x = q cos β, q x z = q sin β, ⍠ H l Ö  ¦e ”  y Œ •• ¸, D ^± = ^k

^B

^{T µ} _e

^±

  H S X ‰ í ß – > à ºs 



. d ” (4.1)– РÒ'  & ñ  © œ © œI _   â Ä º € ª œ·6 £ § s “ : r _  ¨ î ç  H x 9 

•

¸  H n 0 = q

αI

0

γ

_R

e ” `  ¦ · ú ˜ à º e ”  .

d ”

(4)\  ¦     7 ˜'  \  @ / # Œ & ñ o  €  

~ q · [ ∂ ² E ~ 1

∂t ² + (a + b) ∂ ~ E 1

∂t + (ab − c ² ) ~ E 1 ]

= ~ q · [i emγ R n ² ₀

εε ₀ {(µ ⁺ + µ ⁻ ) ~ E ₀ i + k B T

e (µ ⁺ − µ ⁻ )~ q}]

−~ q · [ e

εε ₀ {2n ² ₀ γ R (µ ⁺ + µ ⁻ ) +K _g ² n 0

2k B T

e µ ⁺ µ ⁻ } ~ E 1 ]

−~ q · [ en 0

εε 0

(µ ⁺ + µ ⁻ ) ∂ ~ E 1

∂t ] (5)

\

 ¦ % 3 `  ¦ à º e ”  . # Œl " f a = γ ^R n 0 + iq z µ ⁺ E 0 + q ² D ⁺ , b = γ R n 0 − iq z µ ⁻ E 0 + q ² D ⁻ , c = γ R n 0 s  . d ” (5)\ " f

~

q = q ˆ q _k s “ ¦ / B N ç ß – „    © œ ~ E 1 _  ~ ½ ӆ ¾ ӓ É r      à º 7 ˜' 

~

q _  ~ ½ ӆ ¾ Óõ  ° ú  Ü ¼ 9, ü @Â Ò “   „  l  © œ ~ E 1   H ~ q ü < d ” (6)_ 

› '

a > \  ¦ ”   .

~

q · ~ E 0 = (q ˆ q _k ) · {(E 0 sin β) ˆ q _k + (E 0 cos β) ˆ q _⊥ }

= qE 0 sin β (6)

. # Œl " f ˆ q _k   H      à º 7 ˜' _  é ß –0 A 7 ˜' s “ ¦, ˆ q ⊥   H   



  à º 7 ˜' ü < à ºf ” ô  Ç 7 ˜' s  .

d ”

(5)ü < d ” (6)Ü ¼– РÒ'   6 £ § õ  ° ú  s  / B N ç ß – „    © œ\  › ' a ô

 Ç 2>  Û ¼º ú ˜  p ì  r ~ ½ Ó& ñ d ” `  ¦ % 3 `  ¦ à º e ”  .

∂ ² E 1

∂t ² + A ∂E 1

∂t + BE 1 = mC A = 1

τ d

[1 + 2τ _d τ + E _D

E q

+ i E ₀ sin β E q

ν]

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 ² _D

2E _q E _M + i E 0 sin β 2E _q ν]

C = 1

τ d τ [iE _D ν − E ₀ sin β] (7)

#

Œl " f τ d = _en ^εε

⁰

0

(µ

⁺

+µ

⁻

)   H Maxwell ¢ - a  o r ç ß –s “ ¦, τ =

1

γ

_R

n

₀

  H F  g„    à º" î r ç ß –, ν = ^µ µ

⁺⁺

^−µ +µ

⁻⁻

= ^D _D

⁺+

^−D +D

⁻⁻

, E D =

k

B

T K

g

e   H S X ‰ í ß – „  l  © œ(diffusion field), E q = _K ^en

⁰

g

εε

0

  H

Ÿ

í o „  l  © œ(saturating field), E M = ^γ

^R

ⁿ _K

⁰

^(µ

⁺

^+µ

⁻

⁾

g

µ

⁺

µ

⁻

=

γ

R

n

0

K

_g

µ   H ³ ðÀ Ó „  l  © œ (drift field), µ ¹ = _µ ¹

₊

+ _µ ¹

−

s  .

/ B

N ç ß – „    © œs  r ç ß –\  @ / # Œ …  ;…  ;y       H ”  ; Ÿ ¤   H



 (slowly-varying amplitude approximation)\  ¦ & ñ 

€

 , d ” (7)“ É r

∂E ₁

∂t + gE ₁ = mh g = B

A = 2 τ

[1 + _E ^E

^D

M

+ _2E ^E

^D

q

+ ^E _2E

²⁰

^sin

²

^β

q

E

M

+ _E ^E

^2D

q

E

M

+ i ^E

⁰

_2E ^{sin β}

q

ν]

[1 + ^2τ _τ

^d

+ ^E _E

^D

q

+ i ^E

⁰

_E ^{sin β}

q

ν]

h = 1 A C = 1

τ

[iE D ν − E 0 sin β]

[1 + ^2τ _τ

^d

+ ^E _E

^D

q

+ i ^E

⁰

_E ^{sin β}

q

ν] (8)

õ

 ° ú  s  ³ ð‰ & ³ ) a  . d ” (8)– РÒ'  r ç ß –\  @ /ô  Ç / B N ç ß – „   



© œ_  K   H

E 1 (t) = mh

g (1 − e ^−gt ) = E 1 (∞)(1 − e ^−gt ) (9) s

“ ¦, & ñ  © œ  © œI \ " f_  / B N ç ß – „    © œ E 1 (∞)  H E ₁ (∞) = m

2 1

X ² + Y ² [(E _D νY − E ₀ sin βX)

+i(E D νX − E 0 sin βY )] (10)

–

Ð Å Ò# Q”   . # Œl " f X = (1 + E ^E

_M^D

+ _2E ^E

^D

q

+ ^E _2E

⁰²

^sin

²

^β

q

E

_M

+

E

_D²

E

q

E

M

), Y = ( ^E

⁰

_2E ^{ν sin β}

q

) s  .

d ”

(10)Ü ¼– РÒ'  & 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 ] ^1/2 (11) 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 ] (12)

–

Ð Å Ò# Q”   .

ë

ß –€  •, d ” (12)\ " f ü @Â Ò “   „  l  © œ E 0  0s €  , φ = 90 ^◦   ) a  . s  כ “ É r BaTiO 3 ü < ° ú  “ É r S X ‰ í ß – „  l  © œs  t 

C

& h “  , „  + þ A& h “   Á ºl  F  gÏ ã J] X  B | 9 \ " f ü @Â Ò „  l  © œs 

\ O

  H  â Ä º φ = 90 ^◦ “    כ õ  ° ú  “ É r   õ s  . Fig. 2(a)  H

Fig. 2. (a) Space charge field for applied electric field

and (b) phase shift variation against electric field.

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  . ± 2 V/µm s  © œ_  Z  }“ É r „  l  © œs  “  ÷ &€   F  g Ï

ã J] X     (photorefractive grating)_  0 A © œs  [ jl      (intensity grating) ü < ° ú   
 π ÷ &# Q F  gÏ ã J] X  ´ òõ   



f ” `  ¦ · ú ˜ à º e ” Ü ¼ 9 z  ´+ « >& h Ü ¼– Е ¸ S X ‰ “  ½ + É Ã º e ”   (Fig.

8 ‚ à Л ¸).

2. u œ X N Ë < 09 0° ‚ Ç; c 8 ý” X ¢ ò i >± n Ç õ t Ú
ì Å º Ó 

o& ñ _  F C \ P  y Œ •• ¸ θ  Œ •“ ¦ 
_  ò ø Í$ í  © œÃ º Kë ß –`  ¦

“

¦ 9½ + É M :, ž Ðß ¼ ç  H+ þ A~ ½ Ó& ñ d ”  [1]“ É r γ _vis ∂θ

∂t = K( ∂ ² θ

∂z ² + ∂ ² θ

∂x ² ) + | ~ Γ _E | (13) , õ  ° ú   (Fig. 1 ‚ à Л ¸). # Œl " f γ ^vis   H Leslie & h $ í > à ºs 

“

¦, | ~ Γ E | = ∆εε 0 | ˆ n

⁰

· ~ E( ˆ n

⁰

× ~ E)|  H „  l  © œ\  _ ô  Ç Ó  o& ñ ~ ½ Ó

†

¾ Ó  ž Ðß ¼_  ß ¼l \  ¦
 ? / 9, ˆ n

⁰

“ É r F C \ P  ) a Ó  o& ñ ~ ½ ӆ ¾ Ó



_  ~ ½ ӆ ¾ Ó`  ¦
  · p . ˆ n

⁰

õ  ~ E  H n ˆ

⁰

= [sin θ, 0, cos θ]

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

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

|E 1 | sin β cos(~ q · ~ r + φ) + E 0 ] (14) ü

< ° ú  s 
 è ­ q à º e ” Ü ¼ 9, Ó  o& ñ _  F C \ P  y Œ •• ¸ θ  1“    â Ä º | ~ Γ _E |  H   H  & h Ü ¼– Ð

| ~ Γ E | ≈ ∆εε ₀

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

−2E ₀ ² θ + 2E 0 |E 1 |(cos β − 2θ sin β) cos(~ q · ~ r + φ)](15)

  ) a  . # Œl " f ∆ε = ε k − ε _⊥   H Ä »„    © œÃ º \  ¦
  · p



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

θ(~ r, t) = θ 1 (t) cos(~ q · ~ r + φ) (16)



 & ñ €  , d ” (13)õ  d ” (15)– РÒ'  θ 1 \  › ' a ô  Ç 1>  p ì  r

~

½ Ó& ñ d ” `  ¦ % 3 `  ¦ à º e ”  .

∂θ ₁

∂t + X

⁰

θ ₁ = Y

⁰

X

⁰

= K

γ vis

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 (17)

#

Œl " f ε ef f = ^∆εε _γ

⁰

vis

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

²

∆εε

₀

  H Freedericksz „  l  © œs  .

d ”

(17)– РÒ'  & ñ  © œ © œI _   â Ä º θ 1 (∞)  H

θ 1 (∞) = E ₀ |E 1 | cos β

E _C ² + (E ₀ ² − ³ ₄ |E 1 | ² cos 2β) (18)

–

Ð Å Ò# Q”   . W 1 h Ë : Ó  o& ñ õ  ° ú  “ É r é ß –» ¡ ¤ @ /g A“    â Ä º s  © œ F 

g‚  _  “ ¦Ä » Ï ã J] X Ò  ¦“ É r

n e (β) = n _k n _⊥ q

n ² _k cos ² (β) + n ² _⊥ sin ² (β)

(19)

s

“ ¦, Ó  o& ñ ~ ½ ӆ ¾ Ó  F C \ P \  _ ô  Ç Ï ã J] X Ò  ¦   › ¸  H   H  & h  Ü

¼– Ð

∆n = n _e (β + θ) − n _e (β) ≈ n _k n ⊥

(n _k − n ⊥ )θ sin 2β (20) s

 . # 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  .

Ó 

o& ñ _   â Ä º s  F  g   ™ D ¥ ½ + Ë\ " f_  s 1 p q > à ºü <  r] X ´ òÖ  ¦ [10]“ É r

Γ = 4πδn ₁ λ w cos θ inc

sin φ (21.1)

η = sin ² ( πδn 1 d λ r cos θ B

) (21.2)

δn 1 = n _k

n _⊥ (n _k − n _⊥ )

× E 0 |E 1 | cos β

E _C ² + (E ₀ ² − ³ ₄ |E 1 | ² cos 2β) · sin2β (21.3) õ

 ° ú  s  Å Ò# Q”   . # Œl " f δn 1 “ É r Ï ã J] X Ò  ¦   › ¸_  ”  ; Ÿ ¤ s 

“

¦, 2θ ^inc   H l 2 Ÿ ¤c ” _  { 9  y Œ •, θ ^B   H Bragg › ¸| `  ¦  Ø Ô



 H F Ò q tc ” _  { 9  y Œ •, λ ^w   H l 2 Ÿ ¤c ” _    © œ, λ ^r “ É r F Ò q tc ”  _

   © œ, d  H B | 9 _  ¿ ºa s  .

d ”

(21.1)\ " f ü @Â Ò “   „  l  © œ_  ~ ½ ӆ ¾ Ós  E ⁰ → −E 0 – Ð ì

ø Í@ / ÷ &  H  â Ä º ¢ ¸  H B | 9 _  l Ö  ¦e ”  y Œ •s  β → −β – Ð ì

ø Í@ / ÷ &€  , \  -t  „  ² ú ˜ (energy transfer) ‰ & ³ © œs  ì ø ̈́  

÷ &“ ¦   ² D G s 1 p q > à º Γ → −Γ – Ð ì ø Í@ / H † d`  ¦ \ V8 £ ¤ ½ + É Ã

º e ”  . Õ ª Q
, d ” (21.2)– РÒ'   r] X ´ òÖ  ¦“ É r ü @Â Ò “  

„

 l  © œ_  ~ ½ ӆ ¾ Óõ  l Ö  ¦e ”  y Œ •_  ~ ½ ӆ ¾ Ó\  Á º › ' a † < Ê`  ¦ · ú ˜ à º e ” 



.

III. ÷ m Ç] M öU ê s0 n É õ m Í + s ÇÊ Ý

‘

: r z  ´+ « >\ " f  6   x ô  Ç e  ¦ x  2 ; :  ƒ  s  ' ‘   ) a W 1 h Ë : Ó  o

&

ñ Ò  re  ¦“ É r  6 £ § _  õ & ñ Ü ¼– Ð ] j Œ •÷ &% 3  . Ä º‚  , e  ¦ x  2 ; :



ƒ  `  ¦ W 1 h Ë : Ó  o& ñ \  ' ‘  # Œ s  כ `  ¦ “ §ì ø Íl \  ¦ s 6   x

# Œ 24r ç ß – [ O # Q Å Ò% 3  . — ¸Ž  H ] j Œ •õ & ñ “ É r  © œ“ : r \ " f s  À

Ò# Q& ’ Ü ¼ 9 e  ¦ x  2 ; :  ƒ  _  0 l x • ¸  H W 1 h Ë : Ó  o& ñ \  @ / 

Fig. 3. Sample (porphyrin:Zn-doped nematic liquid crys- tals) structure.

Fig. 4. The transmittance spectra of porphyrin : Zn- doped nematic liquid crystals for various applied dc fields.

Fig. 5. Experimental setup for measuring gain coefficient and diffraction efficiency (BS : beam splitter, M1 ∼ M4 : mirrors, D1 ∼ D4 : detectors).

#

Œ 0.5 wt %– Ð ] j Œ •÷ &% 3  . ï  r q   ) a e  ¦ x  2 ; :  ƒ  s  ' ‘ 

  ) a W 1 h Ë : Ó  o& ñ “ É r ô  ÇA á ¤ €  s  ITO– Ð  ïh A ) a Ä »o  ! s q\ 

—

¸[ j › ' a ‰ & ³ © œ`  ¦ s 6   x # Œ ç  H{ 9  >  ì  r Ÿ ír (   . s M : ] j



Œ

•  ) a B | 9 _  ¿ ºa   H Ä »o  ! s q_  ç ß –  \  _  # Œ   & ñ ÷ &  H X

<, ‘ : r z  ´+ « >\ " f  H Ä »o  ! s q  s \  20 /mum_  / B N ç ß –  (spacer)\  ¦ ¿ º# Q ç ß –  `  ¦ Ä »t  % i  (Fig. 3 ‚ à Л ¸).

e

 ¦ x  2 ; :  ƒ  “ É r  Òí ß –@ /† < Ɠ § “ ¦ì  r  / B N † < Æõ \ " f f ” ] X 

½

+ Ë$ í ô  Ç  כ `  ¦  6   x % i “ ¦, Ó  o& ñ “ É r Merck  _  E7 W 1 h Ë : Ó 

o& ñ `  ¦  6   x % i  . W 1 h Ë : Ó  o& ñ “ É r “ : r • ¸ 20 ^◦ C,   © œs  589 nm \ " f ∆n = 0.2246(n e = 1.7462, n ₀ = 1.5216) s 

“

¦, ∆ε = +13.8s  .

Fig. 4  H ] j Œ •  ) a B | 9 – РÒ'  8 £ ¤& ñ ô  Ç ü @Â Ò “   „  l  © œ

\

   É r È Òõ  Û ¼& 7 ˜à Ô! 3  8 £ ¤& ñ   õ s  . ü @Â Ò “   „  l 



© œ_  [ jl  9 þ t à º2 Ÿ ¤ È Òõ • ¸  H 7 £ x  % i “ ¦, 510 nm   H % ƒ _

   © œ % ò % i @ /\ " f f  ¨ à º ´ ú §€ Œ ¤ .

Fig. 6. Typical experimental data for two beam coupling experiment (β = +35 ^◦ , E 0 = 1.2 V/µm).

Fig. 7. Diffraction efficiencies against polarization angle of reading beam.

s

 F  g   ™ D ¥ ½ + Ë z  ´+ « >_   © œu • ¸  H Fig. 5 ü < ° ú   . l 2 Ÿ ¤c ” 

“

É r 514 nm   © œ_  Ar-ion Y Us $ \  ¦  6   x % i “ ¦, „ à Ð c ” 

“

É r 633 nm   © œ_  He-Ne Y Us $ \  ¦  6   x % i  . l 2 Ÿ ¤c ”  _

 { 9  y Œ •“ É r 2θ inc = 20 ^◦ s “ ¦,  r] X ´ òÖ  ¦`  ¦ 8 £ ¤& ñ l  0 A ô

 Ç „ à Ð c ” _  { 9  y Œ •“ É r Bragg y Œ •“   θ B ≈ 13 ^◦ – Ð % i  .

l

2 Ÿ ¤c ” “ É r B | 9 – РÒ'   H Ï ã J] X Ò  ¦   › ¸\  ¦ % 3 l  0 A # Œ s 



© œ F  g‚  Ü ¼– Ð % i “ ¦, ¿ º l 2 Ÿ ¤c ” _  [ jl   H I a = I b = 280 mW/cm ² s  . ^λ 4 0 A © œ t ƒ  l ü < ¼ # F  g  \  ¦ s 6   x # Œ „ à Ð



c ” _  ¼ # F  g`  ¦   r (  “ ¦ — ¸Ž  H ¼ # F  g \  @ /K  „ à Ð c ” _  [

jl   H I p = 4.2 mW/cm ² s  . ¢ ¸ô  Ç ~ à Ì} Œ •_  l Ö  ¦e ”  y Œ •

“

É r β = +35 ^◦ – Ð, ü @Â Ò “   „  l  © œ“ É r ±E 0 – Ð    or v  9 z 

´+ « > % i  . Fig. 6“ É r β = +35 ^◦ s “ ¦, ü @Â Ò “   „  l  © œ _

 [ jl  E 0 = 1.2 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. 7“ É r s  F  g   ™ D ¥ ½ + Ëz  ´+ « >\ " f ¿ º l 2 Ÿ ¤c ” s  s  © œ F  g‚  

“

   â Ä º 7 £ ¤ p ¼ # F  g ) a l 2 Ÿ ¤c ” s  B | 9 \  { 9     H  â Ä º, „ à Ð



c ” _  ¼ # F  g \    É r  r] X ´ òÖ  ¦`  ¦ 8 £ ¤& ñ ô  Ç  כ s  . „ à Ð c ” 

Fig. 8. Gain coefficients against direction of applied dc field (a) and tilt angle (b).

_

 ¼ # F  g \  @ /ô  Ç  r] X ´ òÖ  ¦“ É r s  : r \ " f \ V8 £ ¤ ô  Ç ú <ü < ° ú  s  ü

@Â Ò “   „  l  © œ_  ~ ½ ӆ ¾ Óõ   H Á º › ' a  9, „ à Ð c ” s  s  © œ F 

g‚  “    â Ä º þ j@ / 22 %_  Z  }“ É r  r] X ´ òÖ  ¦`  ¦ % 3 % 3  . Fig.

7 \ " f ϕ  H e ” _ _  ‚  ¼ # F  g ) a c ” \  @ / # Œ s ¼ # F  g $ í ì  r s  s

À ҍ  H y Œ •`  ¦
  · p . Å Òl & h “       D h ”   B | 9 \  e ”

_ _  ‚  ¼ # F  g ) a „ à Ð c ” `  ¦ { 9  r v €   „ à Ð c ” _  p ¼ # F  g

$ í

ì  r ë ß –s  Ï ã J] X Ò  ¦    o\  ¦ Ö ¼   r] X ÷ &“ ¦,   ² D G „ à Ð c ” _ 

¼

# F  g \    É r  r] X ´ òÖ  ¦“ É r sin ² ϕ \  q Y U   H + þ AI   ) a  .

\

 -t  „  ² ú ˜ ‰ & ³ © œ`  ¦ s K  l  0 AK  ü @Â Ò “   „  l  © œ_ 

~

½ ӆ ¾ Óõ  l Ö  ¦e ”  y Œ •_  ~ ½ ӆ ¾ Ó\  @ /ô  Ç s 1 p q > à º\  ¦ 8 £ ¤& ñ % i 



. Fig. 8(a)  H „  l  © œ_  ~ ½ ӆ ¾ Ós  +z ~ ½ ӆ ¾ Ó(E 0 ) õ  Õ ª ì ø Í@ /

~

½ ӆ ¾ Ó(−E ⁰ ){ 9  M : ü @Â Ò “   „  l  © œ_  [ jl \    É r s 1 p q

>

à º_   Ҡ ñ ì ø ̈́  H † d`  ¦ ˜ Ð# Œï  r  . 7 £ ¤, ü @Â Ò “   „  l 

 ©

œ_  ~ ½ ӆ ¾ Ó`  ¦  Ë ¨>  ÷ &€   ¿ º l 2 Ÿ ¤c ” [ þ t _  \  -t  „  ² ú ˜s  ì

ø ̈́  H † d`  ¦ > p w ô  Ç . Fig. 8(b)  H l Ö  ¦e ”  y Œ • β = 35 ^◦ ü < β =

−35 ^◦ { 9  M : s 1 p q > à º_   ⠆ ¾ Ós  ì ø ̈́  ÷ &  H ‰ & ³ © œ`  ¦
  · p



.   ² D G, e  ¦ x  2 ; :  ƒ  s  ' ‘   ) a Ó  o& ñ \ " f_  \  -t  „  

² ú

˜_  ~ ½ ӆ ¾ Ós  ü @Â Ò “   „  l  © œõ  l Ö  ¦e ”  y Œ •\  _ K    & ñ H

†

d`  ¦ · ú ˜ à º e ”  .

Fig. 9  H ü @Â Ò “   dc „  l  © œ\  @ /ô  Ç s 1 p q > à ºü <  r ] X

´ òÖ  ¦`  ¦ 8 £ ¤& ñ ô  Ç   õ s  9, z  ´‚  “ É r r Ð 3 x ? /l ô  Ç s  : r / B G

‚

 s  . z  ´+ « >   õ ü < s  : r / B G‚  õ _  r Ð 3 x ? /l – РÒ'    6

£

§ _  Ó ü t| 9   © œÃ º ° ú כ[ þ t`  ¦ ½ ¨ % i  :ν = 0.4, E D = 0.11

Fig. 9. Gain coefficients and diffraction efficiencies for applied dc field. The solid lines are theoretical curves.

V/µm, E q = 0.29 V/µm, E M = 0.27 V/µm, E C = 1.42 V/µm s  . ü @Â Ò “   „  l  © œ_  [ jl \  @ /K  s 1 p q > à º ü

<  r] X ´ òÖ  ¦ _  þ j@ /° ú כ[ þ t“ É r y Œ •y Œ •   É r „  l  © œ ° ú כ\ " f
 

z Œ ¤“ ¦, ü @Â Ò “   „  l  © œ_  ° ú כs  & | 9 à º2 Ÿ ¤ 7 £ x   



r  y Œ ™™ è   H  ⠆ ¾ Ó`  ¦ ˜ Ð% i  . s  Qô  Ç y Œ ™™ è  ⠆ ¾ ӓ É r ü @ Ò

“

  „  l  © œ_  [ jl  & | 9 à º2 Ÿ ¤ Ó  o& ñ [ þ t s  y © œô  Ç ü @Â Ò „   l

 © œ ~ ½ ӆ ¾ ÓÜ ¼– Ð C \ P  # Œ F C \ P  ´ òõ   Œ • t l  M :ë  H s

 . 0 A_  Ó ü t| 9   © œÃ º ° ú כ[ þ t – РÒ'  ü @Â Ò “   „  l  © œ_  [ j l

 E 0 = 1.24 V/µm { 9  M :, Ï ã J] X Ò  ¦   › ¸ ”  ; Ÿ ¤ _  ß ¼l  δn 1 = 4.4 × 10 ⁻³ \  ¦ % 3 % 3  .

IV. + s Ç Â ] Ø

‘

: 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 Ó  o& ñ ~ ½ ӆ ¾ Ó  F C \ P 

\

 _ ô  Ç F  gÏ ã J] X  ´ òõ \  ¦ › ' a ¹ 1 Ï % i Ü ¼ 9, ü @Â Ò “   „  l  © œ _

 ~ ½ ӆ ¾ Ó, B | 9 _  l Ö  ¦e ”  y Œ • 1 p x _  › ¸| \ " f s 1 p q > à ºü <  r ] X

 : £ ¤$ í `  ¦ › ¸  % i  . Ó  o& ñ _  Ó ü t| 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‚  `  ¦ z  ´+ « >& h Ü ¼– Ð % 3 “ É r s  1

p

q > à º,  r] X ´ òÖ  ¦ õ  r Ð 3 x ? /l  † < ÊÜ ¼– Ð+ ‹ Ó  o& ñ ~ ½ ӆ ¾ Ó  F  C

\ P \  _ ô  Ç F  gÏ ã J] X  B j& m 7 £ §`  ¦ [ O " î “ ¦, 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 õ  ƒ  ½ ¨› ¸“ §  Ö ¸6   x õ ] j(202-A-251-020)\  _

ô  Ç  כ { 9 m  .

Y

c p w Š à U Ø ”  ô

[1] I. C. Khoo, H. Li, and Y. Liang, Opt. Lett. 19, 1723

(1994).

[2] I. C. Khoo, S. Slussarenko, B. D. Guenther, Min-Yi Shih, P. Chen and W. V. Wood, Opt. Lett. 23, 253, (1988).

[3] I. C. Khoo, Opt. Lett. 20, 2137 (1995).

[4] J. Mun, C. S. Yoon, H. W. Kim, S. A. Choi and J.

D. Kim, Appl. Phys. Lett. 79, 1933 (2001).

[5] W. Lee and Ch.-S. Chiu, Opt. Lett. 26, 521 (2001).

[6] I. Janossy, A. D. Lloyd and B. S. Wherrer, Mol.

Cryst. Liq. Cryst., 179, 1 (1990).

[7] L. Marrucci, D. Paparo, P. Maddalena, E. Massera,

E. Prudnikova and E. Santamato, J. Chem.

Phys. 107, 9783 (1997).

[8] I. C. Khoo, Liquid Crystals: Physical Properties and Nonliner Optical Phenomena (John Wiley and Sons, New York, 1995).

[9] E. V. Rudenko and A. V. Sukhov, JEPT. 78, 875 (1994).

[10] P. Yeh, Introduction to Photorefractive Nonlinear Optics, (John Wiley and Sons, New York, 1993).

Measurement and Analysis of Photorefractive Effects in Porphyrin : Zn-doped Nematic Liquid Crystals

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

(Received 15 October 2005)

We observed the photorefractive effect in porphyrin : Zn-doped nematic liquid crystals by using a two-beam-coupling experiment under the influence of an applied dc field (E

0

) and we measured the gain coefficients and the diffraction efficiencies for various experimental conditions by varying the magnitude of E

0

and the direction of E

0

, the tilt angle (β). As E

0

was increased the gain coef- ficient and the diffraction efficiency rapidly increased to their maximum values and then gradually decreased but the positions of their maximum values appeared to be different for different values of applied dc fields. We used on the material equations for a nematic liquid crystal and the torque balance equation to obtain theoretical date for comparison the experimental data. The comparison showed good agreement and a change in the amplitude of the refractive index of δn

1

= 4.4 × 10

⁻³

was obtained for an applied dc field of E

0

= 1.24 V/µm .

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]