Analysis of the Probing Process in Electro-Optic Sampling System Based on EO Effect

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1 Anlysis of the Probing Process in lectro-optic Smpling System Bsed on O ffect # Qin Song, Xinmeng Liu, Jun He, Jingyun Mio, Hui Hung Division of lectronics nd Informtion Technology, Ntionl Institute of Metrology College of Informtion science nd technology, Beijing Norml University 8 th, st Rod 3 rd North Ring, Choyng Dist., Beijing, Chin, 0003, #songq@nim.c.cn Abstrct The probing process nd bsic theory of detection in O smpling system re discussed. Two different types of O crystl re nlyzed nd experiment setups re designed for them, respectively. This nlysis provides preconditions to the mesurement of ultrfst electromgnetic signl such s microwve, high-speed electric pulse, nd THz pulse. Keywords: lectro-optic effect, LiTO 3, GAs, phse retrdnce, lectro-optic smpling. Introduction The development of techniques on probing high-speed electricl pulse hs been driven by the rpid dvnces in high-speed electronic components from fst trnsistors in both silicon [] nd GAs/AlGAs [] to fst photodiode nd photoconductive switches with picosencond rise time. Opticl techniques re pproprite for ultrfst mesurement of these devices, becuse they overcome mny of the limittions imposed by conventionl electronic test systems. The primry conventionl test instruments for high-speed pulse re the smpling oscilloscope nd network nd spectrum nlyzers. Since the electricl signls to be mesured hve to be conveyed to the test instrument, n electricl probe cpble of high-speed opertion must be used. Such electricl probes suffer from severl problems [3]. A vriety of opticl techniques hve been developed to ddress the limittions ssocited with conventionl electricl testing. These methods tke dvntge of recent nd continuing dvnces in high repetition rte femtosecond lser sources nd their ppliction in opticl smpling experiments. The bility to use opticl pulses to mesure the properties of electricl devices nd circuits relies on some physicl property tht llows the electricl signl to modulte test bem. The most widely exploited physicl phenomenon for this purpose is the electro-optic effect nd photoconductive smpling. The ltter hs nrrower bndwidth nd the mesurement resolution of it is limited by the life time of minority crriers. Therefore O effect is more nd more populr in recent decde, which is bsed on the polrizbility of mteril to n pplied electric field. It hs n extremely brod response bnd width into the THz frequency regime limited only by the resonnt coupling to infrred lttice vbrtions [3]. THz bndwidth is more thn enough for the mesurement of electronic signl. This pper emphsis on nlysis of the probing process in O smpling system relied on O effect. The bsic theory is introduced nd two most commonly exmples re presented nd compred. Furthermore, the pproximtion condition is discussed.. Anlysis of probing process bsed on lectro-optic (O) effect. Introduction of O effect nd the derivtion in LiTO3 nd GAs The O effect refers to the process by which n electric field cn lter the refrctive index of mteril. The O effect offers mens of trnsferring informtion from the electricl to the opticl domins by modulting the polriztion nd/or phse of opticl rdition trnsmitted through n electro-opticlly ctive medium. In most O smpling system including probes of highspeed electric pulse, the O effect emphsis on the nisotropic mterils requirements for O effects nd the quntittive description of these effects by the O tensor. The ction of n externl pplied -field is to deform the zero field index ellipsoid, in formul ().

2 x x x ( ) ( ) ( ) () n n n 3 3 The expression for new index ellipsoid referred to the principl xes xxx3 is given by x x x x x x x x x () Where the vlues of the coefficients tensor of the mteril by re clculted from the pplied field nd the electro-optic n 3 3 n x x n 3 x (3) Now, prticulr mteril illustrted which is the simplest cse is one of the most commonly used mterils for the ultrfst electric pulse probing pplictions is lithium tntlite, LiTO 3. LiTO 3 is birefringent mteril with point group symmetry 3m. The form of the contrcted mtrix for mteril of this symmetry is [0] ijk (4) If the cse in which the pplied -filed in the crystl is long the c-xis is considered, tht is, by convention, tken to be the direction, the eqution (3) gives

3 n n n 3 x (5) Which, fter multiplied out, leds to reltions: 3 x3 no 3 x3 no 33 3 x3 ne (6) Then, the new index ellipsoid with electric field pplied is 3x3 x 3x3 x 33x3 x3 n0 n0 ne (7) And t lst, we could clculte the new 3 () n n0 3n0 x3 3 () n n0 3n0 x3 (8) 3 (3) n3 ne 33ne x3 Where. Usully, only two indexes nd polriztions re tken into considertion since the electric field pplied on LiTO 3 is long x 3 direction. Thus, the propgtion of the probe lser pulse bem is expressed: e Aexp j[ tcn x] (9) e Aexp j[ t c n x ] 3 When thickness of the crystl is L, the phse retrdnce tht is the difference in phse experienced by rys polrized long the two opticl xes would be

4 3 3 / cn n3 no ne L n0 3 ne 33 L (0) Where is the wve length of the probe lser. From (0) we cn see tht the phse retrdnce hs two relted prts, one is sttic phse shift tht is independent on the externl electric field, the other is electric induced phse shift. Another exmple is little more complicted, concerns the O effect in GAs which is cubic mteril nd hs point group symmetry 43m. So it is not birefringent in the zero field cse. The contrcted O tensor for GAs is given by ijk () In n pplied -field with components long ll the principl xes, the index ellipsoid cn be derived from equtions () nd (3) nd is described by x x x r4 xx3x r4 xx 3x r4 xx x3 () n n n 3 3 If we consider specific exmple in which field is pplied only long the x 3 direction, 3, then this reltion reduces to x x x r4 xx x3 (3) n n n 3 3 In eqution (3), the finl cross term on the left side mens tht the reltion cnnot be directly cst in the form of n index ellipsoid. Such cse is different from LiTO3 in which trnsformtion is required to find new coordinte xes for which the reltionship cn be put in the form of n ellipsoid. The cross term in this instnce only involves the xx xis, thus, the x3 xis is unchnged by the trnsformtion. If the coordinte xes re rotted 45 degree, the trnsformed coordinte xes re x x ' ' x x ' ' x x (4) Then qution (3) cn be written, ' ' ' x3 x 4 x3 x 4 x3 no no no (5)

5 which is gin in the form of n index ellipsoid in the trnsformed coordinte frme. In such coordinte frme, opticl wves propgting in the x3 direction nd polrized long ' ' the xx directions will see refrctive indexes tht vry with pplied field x3 s n n n n n n n n 3 x' o 4 o x3 3 x' o 4 o x3 x3' o (6) The sme principle nd method for clculte the phse retrdnce in GAs s in LiTO3: 3 / cnx ' nx' 4no L x3 (7). lectro-optic smpling system for mesurement of ultrfst electromgnetic wves The bsic theory of O smpling technology is liner O effect of O crystls which hs been employed to mesure ultrfst electric pulse by Kolner erly in 983 [4]. Tody, O effect hs been widely pplied to mesure free spce THz rdition [5,6] nd the electric field of the plnr microwve devices [7-9]. The O smpling mesurement is typicl pump-probe detection system in which the lser bem is split into two pths. One is to generte ultrfst signl, the other is to detect the signl by O effect. When the probe pulse nd the ultrfst electromgnetic wves pss through the O crystl simultneously, the ultrfst M wves will cuse the chnge of the index of O crystl which results in the chnge of polriztion of probe lser pulse. The time domin wveform of the mesured signl cn be obtined by detecting the chnge of the polriztion nd djusting the dely between the probe pulse nd the signl. The schemtic digrm of generl O smpling system is shown in Fig.. The detils of liner O effect bsed on which the probing of the electric field is relized will be discussed in the following. Fig. schemtic digrm of generl O smpling system.3 Design nd nlysis of blnced-detection of electric fields by photoreceiver

6 Fig. scheme for birefringent crystl such s LiTO3 Fig. 3 scheme for non-birefringent crystl such s GAs Fig. nd 3 show the two experiment designs for the O detection of LiTO3 nd GAs, respectively, which re detils of opticl polriztion stte nlyzer in Fig.. Before the continunce of mthemticl deduction, the role of these opticl components will be explined. A polrizer mkes sure the probe bem is liner polriztion which is rotted by hlf wve plte (HWP) to certin ngle so tht the probe bem hs two equl polriztion components long the two principl xis of O crystl. These xis re nmed o- nd e- xis in the following description: o e While the probe bem is propgting through the O crystl, the polriztion components of the o- nd e- xis experience different phse shift. From eqution (0), we could see tht there re two phse shift components which re sttic phse shift nd e-field induced phse shift. In order to mke the mesured proportionl to the externl e-field, Bbinet compenstor should be utilized when birefringent O crystl is used such s LiTO3 without n externl e-field. When non-birefringent O crystl is employed, eqution (7) is pplicble, so the compenstor is not necessry. Then, only e-field induced phse shift remins tht cn be converted into n mplitude vrition nd seprted by the ppliction of QWP nd Wollston prism. At lst, orthogonl probe bem components re subtrcts by the photoreceiver. In Fig., the liner polriztion of the probe bem is rotted by the HWP by n ngle of 4 to the xes of the crystl, then: cos sin 4 (8) Where 0 is the originl electric field of the probe lser bem. Now, the probe bem hs two equl components long the e-xis nd o-xis. After propgting through the LiTO3, the two field components experience different phse retrdtion nd induced sttic phse shift. The compenstor is mde of qurtz which is positive crystl, note tht the LiTO3 is

7 negtive crystl, so if the xes of compenstor is plced s the sme direction s LiTO3, this phse shift could be compensted to mke the probe bem bck to liner polriztion stte s is expressed in qu.(8). After o-component nd e-component seprted by Wollston prism, intensity of the two components re output signl of the photoreceiver is zero. The deduction process is I o o nd I e e, thus the 0 crystl 0 i 0 i 0 e e 0 compenstor 0 i i 0 0 e e (9) Then, when the -field pplied to the crystl, there is: e i (0) The Jones mtrix of QWP, with its fst xis hving n ngle of the coordinte system is W i i () The -field fter the QWP then is i i ie 3 i 0 i i e i e with the o- nd e-xis of () The WP seprtes the o- nd e- component from ech other. Finlly, the photoreceiver subtrcts the intensities I o nd I e. Thus, the output signl is i i i i I I I i e i e ie ie 4 0 o e 0 sin( ) (3) When the cse is s Fig. 3, electricl field of input liner polrized lser bem in rbitrry ngle is: cos 0 sin Jones Mtrix of QWP cn be expressed s: cos isin ( i) cos sin ( i) cos sin sin icos Where is the ngle of opticl xis of QWP with the X coordinte. GAs is not birefringence crystl. When there is no electricl field, polriztion stte of incident lser bem doesn t chnge fter propgting through GAs. Polriztion stte of lser fter pssing through QWP:

8 = cos cos isin ( i) cos sin 0 ( i) cos sin sin icos sin cos cos cos sin sin i(sin cos cos sin sin ) 0 sin sin cos sin cos i(cos sin cos sin cos ) To get blnce, o- nd e- component should hve sme intensity which is expressed s following: (cos cos cos sin sin ) (sin cos cos sin sin ) (sin sin cos sin cos ) (cos sin cos sin cos ) 4 4 cos cos sin cos cos sin cos 4cos sin cos sin cos 0 cos cos( ) 0 So the blnce condition is. Put the opticl xis of GAs prllel to tht of QWP, 4 when electricl field is pplied on GAs, phse difference is generted. The Jones Mtrix of GAs is expressed s: i i cos e sin ( e ) cos sin i i ( e ) cos sin sin e cos After pssing through GAs, polriztion stte of light is expressed s: i i i cos e sin ( e ) cos sin cos cos e sin 0 i i 0 i ( e ) cos sin sin e cos sin sin e cos After pssing through QWP: i i cos isin ( i) cos sin cos e sin cos ie sin 0 i 0 i ( i) cos sin sin i cos sin e cos sin ie cos i i i i I 0 (cos ie sin )(cos ie sin ) (sin ie cos )(sin ie cos ) I 0 i sin sin 0 sin sin (4) The reltion expressed in eqution (3) nd (4) obviously rests upon the ssumption tht the vlue of is very smll. The hlf wve voltge of LiTO3 nd GAs is.8kv/cm nd 3.3kV/cm [], respectively, which is the voltge needed to get phse shift in verticl modultion. Our detection mechnism is horizontl modultion, so the HWV cn be clculted by the following equltion: d Vhorizontl Vverticl L In which the dicttion of prmeters re the sme s uq. (0) nd (7). In the most typicl experiment of ultrfst pulse mesurement [],[3], the vlue of L is bout /4 nd 3/0. So, d the HWV is round 700V/cm, nd 3.9kV/cm for the two crystls. In prctice, the voltge

9 pplied is usully less thn 0V, thus phse retrdnce is pretty smll tht mens sin. Therefore, the sine reltion cn be regrded s liner reltion, nd the output current is directly proportionl to the phse retrdnce which is proportionl to the externl pplied -field in both cses. 3. Conclusion We nlyzed the probing process in O smpling system bsed on O effect. The O effect mechnism by LiTO3 nd GAs crystls re illustrted. The reltion between the externl -field nd the phse retrdnce is subtrcted respectively. Then, the detection principle of the mesured signl using photoreceiver is clculted nd discussed for two experimentl cses. This work offers the fundmentl theory of detection mechnism through O effect which is importnt for the future design nd nlysis in such O smpling system of ultrfst mesurement setups. References [] Ptton et l. 75GHz ft SiGe-Bse Heterojunction Bipolr Trnsistors, I lectron. Device Lett., 990, p.7 [] Cirillo Jr., N.C., nd J.K. Abrokwh, 8.5ps Ring Oscilltor Gte Dely With Self-Aligned Gte Modultion-doped n-(al,g)as/gas FTs, 43 rd Annul Device Reserch Conference. Boulder, Colordo, Pper IIA-7 June 985 [3] Mourou, G.A., D. M. Bloom, nd C.H. Lee. Picosecond lectronics nd Opto-electronics. Berlin: Springer-Verlg, 985 pp. -8 [4] Kolner B H, Bloom D M, Cross P S. lectro-optic smpling with picoseconds resolution. letronics letters, 983, 9: [5] Wu Q, Zhng X C. Ultrfst electro-optic field sensors. Applied Physics Letters, 996, 68: [6] Wu Q, Zhng X C. Free spce electro-optics smpling of mid-infrred pulses. Applied Physics Letters, 997, 7:85-86 [7] Vldmnis J A. THz-bndwidth prober for high-speed devices nd integrted circuits. lectronics Letters, 987,3: [8] Nuss M C, Kisker D W, et l. fficient genertion of 480fs electricl pulses on trnsmission lines by photoconductive switching in metlorgnic chemicl vpour deposited CdTe. Applied Physics Letters, 989,54:57-59 [9] Sno, Shibt T, Mechnism of subpicosecond electricl pulse genertion by symmetric excittion. Applied Physics Letters, 989, 55: [0] Yriv A., nd P. Yeh, Opticl Wves in Crystls, New York: John Wiley & Sons, 984 [] Fujio Sito, Ultr high speed opticl device,998, p06 [] D. Willims, P. Hle, T. Clement, nd C. M. Wng, Uncertinty of the NIST electrooptic smpling system, NIST Technicl Note 535 (004). [3] M. Bieler, M. Spitzer, G. Hein, U. Siegner, F. Schnieder, T. Tischler, nd W. Heinrich, "Brodbnd chrcteriztion of microwve probe for picosecond electricl pulse mesure-ments", Mes. Sci. Technol. 5, 694 (004)

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