Measurement of the Nonlinear Absorption Coefficient by Using a Knife-edge X-scan Method

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+þA f¨Ãº >Ãº\¦ 8£¤&ñ½+É Ãº eH ºú±ú x»¡¤ ÅÒZO`¦ ]jîß %i¦, sFg f¨Ãº (two photon absorption)\¦ ¦9 # K$3&h s:rd`¦ Ä»¸ %i. q&ñ|9 ºúï>s×¼ As2S3~ÃÌ}õ LiNbO3:Fe, BaTiO3, SBN:Ce1pxõ °ú Ér FgÏãJ]X &ñ B|9`¦ s6 x # 8£¤&ñôÇ z´+«> õ\¦ Ä»¸)a s:rdõ_ r Ð

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x?/l\¦ :xK q+þA f¨Ãº >Ãº\¦ &ñ %i. &ñ)a q+þA f¨Ãº >ÃºH βAs₂S₃ = 0.509 cm/W, βBaTiO₃ = 268 cm/MW, βLiNbO₃:Fe= 0.681 cm/kW, βSBN:Ce= −0.699 cm/kW s 9, l>r_ 7HëH

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"f 8£¤&ñôÇ q+þA f¨Ãº >Ãºü< Ä»ôÇ °úכõ ÂÒ ñ\¦ Ð%i.

PACS numbers: 42.65.K

Keywords: ºú±úÅÒZO, As2S3, BaTiO3, LiNbO3:Fe, SBN:Ce, q+þA f¨Ãº >Ãº

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(knife edge x-scan method)Ér {9ìøÍ&hÜ¼Ð q+þA Fg

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Æ >Ãº\¦ 8£¤&ñ H 3 ¦¸ Òqt$íZO (third harmonic generation), »¡¤@ Fg D¥½+ËZO (degenerate four wave

∗E-mail: [email protected]

mixing) [2,3], l©\ _K Ä»¸)a 2 ¦¸ Òqt$íZO (electric field induced second harmonic generation), ³ð

e¦Ý¼7H ¸'a ½+ËZO (surface plasmon waveguide coupling), Fg<Æ&h Kerr >sàÔZO (optical Kerr gate) [4, 5], q+þA çß[O> (nonlinear interferometry) [6], "é¶ r

ZO (ellipse rotation) [7], c =/BG 8£¤&ñZO (beam distor- tion measurement) [8] °ú Ér ~½ÓZOõ ²úo, l>r_ ºú±ú ÅÒ

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r 7HëH\"fH ºú±ú x»¡¤ ÅÒZO`¦ s6 x # q&ñ|9 º

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0Au\¦ x⁰¦ ¿º B|9`¦ ÈÒõôÇ Êê_ 0> oH d

(1)õ °ú .

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Fig. 1. Experimental setup for knife edge x-scan.

P = Z _∞

−∞

Z _x⁰

−∞

Iout(x, y) dxdy (1)

#

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° ú

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dI

dz⁰ = − (α0+ βI) I (2)

#

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h

1 + (z/z0)² i

, Ä»´òU´s (effective length)H Lef f = (1 − exp [−α0L])/a0, LÉr B|9_ ¿ºa, z0 = kw₀²±

2Ð ÅÒ#QtH Rayleigh r]X os. Ér q°úכ (q < 1)`¦ &ñ ¦ d (3)`¦ q\ @/ # Taylor /åLÃº

>hôÇ 6£§ d (1)\ @/{9 # >íß q+þA Fg<Æ B

|9`¦ ÈÒõôÇ Êê_ c 0> oH d (4)ü< °ú .

P (x⁰) = P0

X∞ n=0

(−q)ⁿ n + 1

h

Erf³p

2 (n + 1)x⁰ .

w

´ + 1

i

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#

l"f P0H πw₀²I0

±2Ð í&h\"f_ c 0>, Erf (•)H error <ÊÃºs. n = 0 âÄº d (4)H q+þA Fg<Æ B|9 s

\O`¦ M:_ ºú±ú ÅÒZO õü< °ú [1].

Fig. 2. Theoretical power and intensity curve for vari- ous q.

Fig. 3. Measured gaussian beam profile without sample.

Fig. 2H í&h\"f_ c [jlü< q+þA f¨Ãº\ K{©

H q\¦ −0.5, 0, 0.5ü< °ú s [j t âÄº\ @/ # ½©

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a LiNbO3:Fe &ñ`¦ 6 x %i¦, SBN:CeÉr a × b × c

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ã

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h½¨ ~½ÓZOÜ¼Ð, {9c_ 0>\¦ 1.0 mW ÂÒ' 5.5 mW

t 0.5 mW çßÜ¼Ð 7£x "f q+þA Fg<Æ B|9

yy 10rm q+þA Fg<Æ B|9`¦ ÈÒõôÇ Êê_ c 0

> o\¦ 8£¤&ñ %i.

q

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(q ¿ 1) K$3&hÜ¼Ð Ä»¸)a s:rd d (4)H d (5) ü< °ú s çßéß > 1 H½+É Ãº e.

P (x⁰) ∼= P0

©£Erf¡√

2x⁰± w¢

+ 1¤

− (q/2) [Erf (2x⁰/w) + 1]} . (5) Fig. 4H q&ñ|9 ºúï>s×¼ As2S3~ÃÌ} x9 BaTiO3, LiNbO3:Fe, SBN:Ce 1pxõ °ú Ér FgÏãJ]X &ñ B|9\"f ½©

o)a c 0> o x9 Õª c 0> o\¦ pìrôÇ c [j l

\¦ d (5)Ð rÐ3x?/lôÇ õs. c0> 5.5 mW\

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f 8£¤&ñ)a q+þA Fg<Æ B|9 As2S3, BaTiO3, LiNbO3:Fe, SBN:Ce_ c 0> o d (5)ü< ¸ú {9u<Ê`¦ ·ú Ãº e

. d (5)Ð &ñôÇ q+þA f¨Ãº >ÃºH βAs2S3 = 0.509 cm/W, βBaTiO3= 268 cm/MW, βLiNbO3:Fe= 0.681 cm/kW , βSBN:Ce = −0.699 cm/kWü< °ú ¤.

Table 1Ér q+þA Fg<Æ B|9 As2S3, BaTiO3, LiNbO3, SBN:Ce\ rÐ3x?/l # &ñôÇ q+þA f¨Ãº >Ãº ü

< ÃÐ¦ëH³\"f /åL)a q+þA f¨Ãº >Ãº\¦ q§ôÇ ³ð s

. ÃÐ¦ëH³\ /åL)a q+þA f¨Ãº >Ãºü< ºú±ú x»¡¤ Å

ÒZOÜ¼Ð 8£¤&ñ # c0>o\¦ K$3&h s:rdÜ¼Ð r

Ð3x?/l # &ñôÇ q+þA f¨Ãº >ÃºH q5pwôÇ °úכ_ ß

¼l\¦ f`¦ ·ú Ãº e.

Fig. 4. Knife edge x-scan data with theoretical curves for various nonlinear optical materials.

Fig. 5H c0> 5.5 mW\"f q+þA Fg<Æ B|9\ @/ ô

| 9

s \OH âÄº (q = 0)_ cìøÍâÐ SBN:Ce B|9_ c ì

ø

Íâs 8 ß¼ 9 sH Fig. (2)_ õ Fig. 5 x9 Table 1_ õü< 1lx{9 > FgÏãJ]X Fg<Æ B|9 SBN:Ce_ q +

þ

A f¨Ãº >Ãº_ ÂÒ ñ 6£§ (−)e`¦ ·p.

Measurement of the Nonlinear Absorption Coefficient by Using a Knife-edge X-scan Method

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