ISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 4, October 2013

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1 SSN: SO 9:8 Certfed nternatonal Journal of Engneerng nnovatve Technology (JET) Volue 3 ssue 4 October 3 nfluence of Kerr Effect on Tweeer Center Locaton n Nonear Medu Van Na Hoang Thanh Le Cao Quang Quy Ho NETECHPRO Vetna Acadey of Scence Technology Abstract - The nfluence of the Kerr effect on the tweeer center locaton of lnear delectrc Nan partcle n nonear edu rradated by the ntense Gaussan bea s nvestgated. The expressons of the focal length of nonear lens ntensty dstrbuton of fed Gaussan bea n nonear edu longtudnal transverse gradent forces actng on delectrc partcle are derved. The dstrbuton of the optcal forces n the cylnder of nonear edu s sulated the oton of the tweeer center s dscussed for sae cases of nonear refractve ndex coeffcent. where ( ) s the axu ntensty at the pont () relatng to the total power ( ) ( / ) P / are the radus of the bea at (of bea wast) respectvely / s the Raylegh range s the wavelength of laser x y s the radal coordnate. ndex Ters-Kerr effect nonear edu optcal tweeer optcal force self-focusng.. NTRODUCTON The prevous works [ ] the optcal tweeer to trap the delectrc nanopartcle ebedded n a Kerr edu s concerned. The dstrbuton of the optcal forces actng on the nanopartcle n the Kerr edu has been dscussed []. n work [] the self-focusng relatng to Kerr effect affectng on the optcal forces have been concerned the nfluence of the nonear coeffcent on optcal forces s nvestgated wth the approxaton of the plane-wave laser bea. Unfortunately ths approxaton has not allowed evaluate the nfluence of thckness of the nonear edu on the optcal forces tweeer center locaton whch are two portant qualtes of the tweeer. Therefore n ths paper the nfluence of the self-focusng of the ntense Gaussan laser bea on the dstrbuton of optcal force actng on delectrc nanopartcle s nvestgated. Ths artcle s organed as follows: n Sec. we derve the expressons of the optcal forces concernng self-focusng whch s arsen fro the Kerr effect n the nonear edu rradated by the ntense Gaussan laser bea (sphercal wave); n Sec.3 we present the sulated dstrbuton of the ntensty optcal forces n a cylnder of nonear edu dscusson about the oton of tweeer center locaton.. OPTCAL FORCES As a exaple we consder an optcal tweeer to trap a delectrc nanopartcles n the cylnder of Kerr edu (Fg.). A sphercal wave of the laser bea descrbed by Gaussan functon rradatng the delectrc nanopartcle ebedded n Kerr edu ts ntensty s gven by [3]: exp () () Fg. Sketch of optcal tweeer wth Kerr edu usng Gaussan bea. The Gaussan transverse ntensty dstrbuton () s ncdent upon the Kerr edu whose refractve ndex s altered to n ( ) n n ( ) () where n s the lnear refractve ndex the nonear refractve ndex coeffcent n of the edu s assued to be postve. As a result of ths nonear response (f laser bea s ntense enough) the refractve ndex of the edu s larger at the center of laser bea than at ts perphery wth the result that the edu s n effect turned nto a postve lens whch potentally leads to self-focusng occurred f the power s greater than the crtcal power [4 5] Pcr.896 (3) 4 nn Assung the radus of the bea at entrance face of the Kerr edu s n ( d) where d eans the wast locaton (dstance fro bea wast to entrance face ). Fro () () we have d n ( ) n n exp (4) () As well known the Kerr appears powerfuly n the cylnder lted by () d / where s a nterger so we can use the followng approxaton exp (5) 34

2 SSN: SO 9:8 Certfed nternatonal Journal of Engneerng nnovatve Technology (JET) Volue 3 ssue 4 October 3 Substtutng (5) nto (4) we have n ( ) n n N N (6) () exp () where N n n N n (7) where () () M( ) M ( f ) f As shown n work [6] fro (6) the Kerr edu cylnder wth thckness of becoes the nonear lens M ( ). () wth the focal length s gven by Usng () () the ntensty dstrbuton of fed 4 ( / ) Gaussan bea at plane d consequence n f (8) the optcal force dstrbuton can be sulated. N n n For splcty we assue that the radus (a) of the lnear partcle s uch saller than the wavelength of the laser Consequently the Gaussan bea () wll be fed to gven as [3] new one (Fg.) whose ntensty ( ) M ( ) exp wth M where (9) M f f are the new wast radus wast locaton fro entrance face Raylegh range of fed bea M M / r r / ( f ) r r M f / f / s the Raylegh range of the nput Gaussan bea. hen the Kerr effect can be gnored.e. f then M consequently Eq.(9) consdes wth Eq. (). n Eq. (9) the ter gves us the change of wast locaton. Eq. (9) s ntensty of fed Gaussan bea propagatng through the frst Kerr edu cylnder wth radus () thckness. Next ths bea wth be focused by the second thrd th th nonear lens (second thrd th th Kerr edu cylnder) wth focal length f gven as: where f ( / ( ) ) n M ( ) () M M r / r r ( ) / ( f( ) ) Mr f / f. And then the ntensty of fed Gaussan bea at ext face of th Kerr edu cylnder wll be gven as: (.e. a ) n ths case we can treat the delectrc partcle as a pont dpole. e also assue that the refractve ndex of the delectrc partcle s n n n.e. the necessary condton for trappng operaton of the tweeer usng Gaussan bea satsfed [7]. Usng () the relatve refractve ndex s gven by n n n ( ) n ( ) n n ( ) (3) Usng (3) as shown n work [8 9] we have the scatterng cross sectons ( ) polarabltes ( ) of partcle n nonear edu as follows: n a n ( ) n ( ) 4 3 n ( ) (4) 3 n ( ) n ( ) 4 n ( ) a n ( ) n (4) As shown n prevous works [ ] the transverse gradent force s reduced to: n ( ) F ˆ grad (5) cn ( ) the total longtudnal force s gven by: F ( ) F ( ) F ( ) total grad scat n ( ) n ( ) ck ( ) ( ) n ( ) n ( ) c (6) The general Exps. (5) (6) descrbe the redstrbuton of transverse gradent force longtudnal force n phase dependng on paraeter collecton plane 35

3 (. SSN: SO 9:8 Certfed nternatonal Journal of Engneerng nnovatve Technology (JET) n d ) wth chosen nterger. Volue 3 ssue 4 October n c /. wth wth wth n edu. REDSTRBUTON OF NTENSTY AND OPTCAL FORCE AND MOTON OF AST LOCATON AND TEEZER CENTER Consder a Kerr edu wth nonear refractve ndex coeffcent of n c / whch s see as the lowest one lnear refractve ndex of n. 33 s rradated by the laser bea of wavelength of.6. Consequently fro (3) the crtcal power s cr nn P t decreases when the nonear refractve ndex coeffcent ncreases. And consderng the Gaussan bea wth wast radus of the self-focusng effect occurs when the axu ntensty s greater than P cr.7 8 / c n followng nuercal sulaton we choose paraeters of delectrc partcle as: a n s n. 59. The nput Gaussan bea wth / c whose wast locaton ) of edu of thckness of d at ext face ( (Fg.a) s fed dependng on the refractve ndex coeffcent.e. n edu wth n c / fed one of.8 n c / the wast radus decreases to.4 ts wast locaton oves a dstance of d 3.8 Fg.c respectvely). d 6.8 (Fg.b ). Fg.. ntensty dstrbuton n plane - ( a) nput Guassan bea wth / 8 c d wth new radus of fed wast of ; b) Modfed Gaussan bea dstance fro entrance face to new wast edu wth n c / new n ; c) Modfed Gaussan bea The oton of wast locaton consequently leads to ove of the tweeer center nfluence the force dstrbuton. These questons wll be nvestgated n detal as follows. The transverse gradent force F longtudnal grad force Ftotal are calculated by expresson (3) (4) n the ranges: ( 4 4). The dstrbutons of the transverse gradent force (Fg.3) longtudnal gradent force (Fg.4) total longtudnal force (Fg.5) n the sphase plane are sulated shown as follows. a) b) c) Fg 3. Upper: Dstrbuton of transverse gradent force (N) on the phase plane (); Mddle: () downer: ( -d). a): n b): n c / c): n c /. Fro Fg.3 the dstrbuton of the transverse gradent force n plane () s slar to that of ntensty. Here s dfferent that the absolute agntude of axu force n plane () decreases fro. N 3. N (Fg.3a) downto (Fg.3c) wth ncreasng of the nonear refractve ndex coeffcent. nstead of that the daeter of trap regon n specen plane (=) ncreases fro 3 (Fg.3a) upto 4.5 (Fg.3c). Meanwhle that propertes are alost not changed n the wast plane ( -d). As prncple the trap center where the all forces wll be ero locates n the wast plane as shown n Fg.3.e. t 36

4 oves a dstance of d 3.8 SSN: SO 9:8 Certfed nternatonal Journal of Engneerng nnovatve Technology (JET) (Fg.4b) d Volue 3 ssue 4 October 3 n the tweeer center oves ore ore far fro (Fg.4a) d 6.8 (Fg.4c) respectvely. Moreover wth ncreasng of refractve ndex coeffcent the tweeer center backs ore ore far fro the ext face of edu. Fg. 4. Dstrbuton of the longtudnal gradent forces F (N) n phase plane (). a): n b): grad n c / c): n c /. But the consdered tweeer uses one bea so the partcle s acted by the scatt force F scat (see Eq.6). Snce that the tweeer center whch s shown n Fg.3 Fg.4 oves forward as shown n Fg.5. Fnally the trap center s pulled to the ext face of edu the total longtudnal force n specen plane decreases. Fg. 5. Dstrbuton of the longtudnal forces F total (N) n phase plane () (upper) n the bea axs (downer). a): n b): n c / c): n c /. V. CONCLUSON The expresson of ntensty of the fed Gaussan bea the optcal forces actng on the lnear nanopartcle ebedded n Kerr edu are derved wth approxaton that the nonear lens appears on the cylnder of thckness radus ( ). n the Raylegh rege n expressons of optcal forces are resulted. The cascade sulated results for sngle Gaussan bea tweeer show: ) the tweeer center s pulled behnd the specen plane f refractve ndex coeffcent n s sall; ) wth ncreasng of nfront of specen plane the agntude of total longtudnal force decreases; ) wth ncreasng of n the optcal forces decrease that eans the stablty of the partcle decreases; v) the tweeer center s always kept n the bea axs. n other words the Kerr effect wll affectng on the dstrbuton of optcal forces especally on longtudnal one the oton of tweeer center n the bea axs. The attentons should be pad on probles when the edu surroundng the nanopartcle s senstve to Kerr effect ay when the partcle hangs n edu. Moreover those above entoned propertes depend on other paraeters as of nput Gaussan bea d of nonear edu also. Those questons wll be nvestgated n detal n the furture. REFERENCES [] Quang Quy Ho Van Na Hoang J. Phys. Scen. Appl. Vol. No. () [] Hoang Van Na Cao Thanh Le Ho Quang Quy Coun. n Phys. Vol.3 No. (3) 55. [3] B.E.A. Saleh M.C. Tech Fundaentals of photoncs A lley-nterscence Publcaton John lley & Sons nc. New York (99) 84. [4] Gaeta A. L. Phys. Rev. Lett. 84 () 358. [5] Fbch G. Gaeta A. L. "Crtcal power for self-focusng n bulk eda n hollow wavegudes" Opt. Lett. 5 () 335. [6] L.V. Taracow Laser physcs MR Pub. Moscov (983) pp [7] Ker C. Neuan Steven M. Block Optcal trappng Revew of Scence nstruents Vol. 75 No.9 (4) pp [8] C. L. Zhao L. G. ang X. H. Lu Phys. Let. A (6) pp [9] L.G. ang et al Opt. Lett. 3 (7) pp [] H. Kress Ernest H. K. Steler G. Grffths A. Rohrbach Phys. Rev. E (5). [] H. Q. Quy M. V. Luu H. D. Ha D. Zhuang Chnes Optcs Letters 8 () [] Quang Quy Ho J. Phys. Scen. Appl. Vol. No.9 () AUTHOR S PROFLE Van Na Hoang s born 977 n Hatnh provnce of Vetna. He receved bachelor () aster degree of physcal scence (6) at Vnh Unversty Vetna He has 5 publshed scentfc works. Hs nterestng felds are nonear optcs laser applcatons. Now he s a Ph.D students. 37

5 SSN: SO 9:8 Certfed nternatonal Journal of Engneerng nnovatve Technology (JET) Thanh Le Cao s born 964 n Hatnh provnce of Vetna. He receved bachelor degree of physcs (988) Ph. D degree of atheatc-physcs at Vnh Unversty. He has ore than publshed scentfc works. Hs nterestng felds are dye laser laser applcatons. Up to now he has advsed ore than Master Ph.D students copleted thess s. Volue 3 ssue 4 October 3 Quang Quy Ho s born 954 n Nghean provnce of Vetna. He receved aster degree of atheatc-physcs at Coperrnc Unversty Pol 978 Ph. D degree of atheatc-physcs at Vetna Acadey of Scence Technology 99. He has ore than 9 publshed scentfc works. Hs nterestng felds are laser nonear optcs laser applcatons. Up to now he has advsed ore than 6 Master Ph.D students copleted thess s. 38