AFRL-AFOSR-UK-TR-07-004 Optial otrol of graphee plasmo usig liquid rystal layer 9K New Oe Viktor Yuriyovyh Reshetyak SCIENCE AND TECHNOLOGY CENTER IN UKRAINE 03/0/07 Fial Report DISTRIBUTION A: Distributio approved for publi release. Air Fore Researh Laboratory AF Offie Of Sietifi Researh (AFOSR)/ IOE Arligto, Virgiia 03 Air Fore Materiel Commad
FORM SF 98 https://livelik.ebs.afrl.af.mil/livelik/llisapi.dll Page of 3//07 REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-088 The publi reportig burde for this olletio of iformatio is estimated to average hour per respose, iludig the time for reviewig istrutios, searhig existig data soures, gatherig ad maitaiig the data eeded, ad ompletig ad reviewig the olletio of iformatio. Sed ommets regardig this burde estimate or ay other aspet of this olletio of iformatio, iludig suggestios for reduig the burde, to Departmet of Defese, Exeutive Servies, Diretorate (0704-088). Respodets should be aware that otwithstadig ay other provisio of law, o perso shall be subjet to ay pealty for failig to omply with a olletio of iformatio if it does ot display a urretly valid OMB otrol umber. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.. REPORT DATE (DD-MM-YYYY). REPORT TYPE 3. DATES COVERED (From - To) 0-03-07 Fial 0 Jul 05 to 30 Ju 06 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Optial otrol of graphee plasmo usig liquid rystal layer 9K New Oe 5b. GRANT NUMBER STCU-P65 5. PROGRAM ELEMENT NUMBER 60F 6. AUTHOR(S) Viktor Yuriyovyh Reshetyak 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) SCIENCE AND TECHNOLOGY CENTER IN UKRAINE METALISTIV 7A KYIV, 03057 UA 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) EOARD Uit 455 APO AE 094-455. DISTRIBUTION/AVAILABILITY STATEMENT A DISTRIBUTION UNLIMITED: PB Publi Release 8. PERFORMING ORGANIZATION REPORT NUMBER 0. SPONSOR/MONITOR'S ACRONYM(S) AFRL/AFOSR IOE. SPONSOR/MONITOR'S REPORT NUMBER(S) AFRL-AFOSR-UK-TR-07-004 3. SUPPLEMENTARY NOTES 4. ABSTRACT The projet is devoted to the basi researh ad establishes possible optial ways to otrol the surfae plasmo polarito i graphee layer. A system omprises the graphee ribbos gratig plaed betwee a emati liquid rystal (LC) ad a isotropi dieletri. Iidet light wave exites a plasmo i the graphee ribbos, whih ifluees the light propagatio i the system. The gratig struture of the graphee moolayer is eessary to provide the plasmo exitatio beause there is a huge wave vetor mismath betwee the graphee plasmoi wave ad the iidet eletromageti wave. I graphee strutures the resoat plasmo frequey depeds o the dieletri properties of layers plaed above ad below the graphee sheet or ribbo. I our ase, it meas that plasmo frequey must deped o the LC dieletri permittivity. The LC dieletri permittivity depeds o the LC diretor orietatioal state, whih a be otrolled by exteral field. Therefore, a propagatio of the surfae plasmo polarito i graphee layer a be tued by reorietig the LC diretor usig exteral eletri or mageti fields. 5. SUBJECT TERMS ovel orgai-iorgai strutures, graphee ad liquid rystal layers,, plasmoi waves i graphee, EOARD, STCU 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF a. REPORT Ulassified b. ABSTRACT Ulassified. THIS PAGE Ulassified ABSTRACT SAR 8. NUMBER OF PAGES 3 9a. NAME OF RESPONSIBLE PERSON CUMMINGS, RUSSELL 9b. TELEPHONE NUMBER (Ilude area ode) 0-44-895-660 Stadard Form 98 (Rev. 8/98) Presribed by ANSI Std. Z39.8
STCU PROJECT P65 - FINAL REPORT FF PAGE Short form File/page Exeutive summary SF.do PAGE Cooperatio with foreig ollaborators SF.do PAGE Publiatios SF.do PAGE Prospets of future developmet (for fial report oly) SF.do PAGE Full form Projet mai idea FF.do PAGE Tehial approah FF.do PAGE Tehial progress overview FF.do PAGE 7 Curret status of the projet FF.do PAGE 0 Summary of persoel ommitmet FF.do PAGE 0 Desriptio of travels FF.do PAGE 0 Iformatio about major equipmet ad materials aquired, other diret osts, related to the projet FF.do PAGE 0. Expressio for plasmo frequey i the hybrid system with the LC layer. 4. Results ad Disussio T..do PAGE 3. Plasmo frequey depedee o the orietatioal state of the LC layer. 4. Results ad Disussio T..do PAGE 3 3. Expressios for oeffiiets of light refletio ad trasmissio i the hybrid system. 4. Results ad Disussio T..do PAGE 4 4. Optimal parameters for ative otrol of light propagatio ad refletio. 4. Results ad Disussio T..do PAGE 3 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE Projet mai idea The projet is devoted to the basi researh ad establishes possible optial ways to otrol the surfae plasmo polarito i graphee layer. A system omprises the graphee ribbos gratig plaed betwee a emati liquid rystal (LC) ad a isotropi dieletri. Iidet light wave exites a plasmo i the graphee ribbos, whih ifluees the light propagatio i the system. The gratig struture of the graphee moolayer is eessary to provide the plasmo exitatio beause there is a huge wave vetor mismath betwee the graphee plasmoi wave ad the iidet eletromageti wave. I graphee strutures the resoat plasmo frequey depeds o the dieletri properties of layers plaed above ad below the graphee sheet or ribbo. I our ase, it meas that plasmo frequey must deped o the LC dieletri permittivity. The LC dieletri permittivity depeds o the LC diretor orietatioal state, whih a be otrolled by exteral field. Therefore, a propagatio of the surfae plasmo polarito i graphee layer a be tued by reorietig the LC diretor usig exteral eletri or mageti fields. After establishig the plasmo freguey depedee o the LC diretor orietatioal state we shall study a light wave propagatio aross the system uder osideratio. We shall alulate the absorptio, refletio, ad trasmissio oeffiiets ad show that otrol of the orietatioal state of the LC layer eables us to maipulate by magitude of the absorptio/refletio maxima. These results will allow suggestig a ew type of the graphee miro-ribbo gratig strutures to otrol light beams propagatio. Tehial approah Depedee of plasmo frequey o the LC diretor orietatioal state. Shemati of the hybrid system, LC graphee moolayer isotropi dieletri, is preseted i Fig.. z d, diretor y ˆ graphee LC σ 3 ε x Fig.. Shemati of the hybrid system: LC graphee moolayer isotropi dieletri. We use the followig desigatios: ˆ is the LC dieletri tesor, graphee surfae odutivity,, is the isotropi dieletri permittivity, is the are the LC diretor agles. We write the Maxwell equatios for system show i Fig. ad seek their solutio i the followig form: ) for the wave i the LC ( z 0) ( ) E E e x x z z iqx t Qz E e e, H e H e, () ) for the wave i the isotropi dieletri ( z 0 ) ( ) E E e x x z z iqx t Qz y y iqx ( Qz E e e, H e H e. () y y iqx ( Q z 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 3 Substitutig (), (3) ito Maxwell's equatios we take ito aout that the LC dieletri tesor has a geeral form where o optial frequeies xx xy xz ˆ xy yy yz xz yz zz, (3) ij o ij e o dd i j. (4) Here d is the diretor Cartesia ompoet,, are the refrative idies for ordiary ad extraordiary waves i o e i the LC, respetively. To the expressios obtaied after substitutio (), () ito Maxwell's equatios we must add the boudary oditios, x z0 x z0 y y x z0 z0 E E, H H E (5) Demadig the boudary oditios (5) to be satisfied we obtai after some algebrai trasformatios a dispersio equatio for plasmo wave propagatig i the graphee xxzz xz i, (6) zz 0 q q were xx os si, zz xz o e o o e o os, e o os si os (7) ad the LC diretor agles are show i Fig.. The graphee surfae odutivity i (6), i geeral ase, a be expressed as a sum of two terms, it ra it er, where the first term orrespods to the itrabad eletro trasitios ad the seod term gives otributio from the iterbad trasitios. For kt B ad for the Fermi eergy EF kbt it a be approximately writte as [], ie EF ie EF i / it ra, it er l (8) i/ 4 EF i/ I the oretarded limit q / the dispersio equatio (6) simplifies ad we arrive at expressio q i 0 xxzz xz, (9) It is see that ifluee of the LC orietatioal state o the dispersio equatio is desribed by term 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 4, si os os / si si (0) xx zz xz e o o e Refletio ad trasmissio oeffiiets. Cosider a graphee miro-ribbo gratig i the xy-plae plaed betwee a emati LC layer (aisotropi top substrate) ad a isotropi dieletri substrate. Eah miro-ribbo i the gratig is a sigle layer graphee with the ribbo alog the y-axis, where d is the miro-ribbo width ad is the gratig spaig (Fig. ). A plae moohromati wave propagates alog the z-axis from the side of the LC ad exites the plasmos i the graphee miro-ribbos. We assume semi-ifiite substrates that allows us to eglet the effets of multiple refletios; i the y - diretio the system is ifiite. To simplify alulatios we suppose the LC diretor to be oly reorieted i the xz-plae, where the agle desribes the diretor deviatio from the z-axis. We also set the mageti vetor of the iidet wave to be perpediular to the xz-plae (TM-wave). z k i ћω LC y ˆ d e Graphe x Fig.. Shemati of the graphee miro-ribbo gratig struture. d is the ribbo width, is the gratig spaig, is the diretor agle with the z-axis, ˆ is the LC dieletri tesor, is the isotropi substrate dieletri permittivity, is the graphee odutivity, e is a ormal to the graphee plae, ad ki is the wave vetor of a iidet plae moohromati wave. Beause of the strog ofiemet of the surfae plasmo-polaritos (SPPs) i the ribbos, oly the thi layer of the LC substrate ear the graphee ifluees the SPPs. Therefore, we a set the LC diretor orietatio i the whole substrate to be homogeeous ad equal to the diretor orietatio of this layer ear the graphee. The LC optial dieletri tesor a be writte i the form ij oij ( e o ) i j, i x, y, z, where i deotes the ompoets of the diretor =(si,0,os ); o ad e are the refrative idies of the ordiary ad extraordiary waves, respetively []. We suppose that the TM-wave is ormally iidet i the LC o the graphee gratig. As it follows from the Maxwell equatios, eletri ad mageti vetors of this wave i the LC take the form: k E E e E e e, H E e e, E ( / ) E, () i( ki z i i ( ki z i ix x iz z i ix y iz xz zz ix 0 with the dispersio equatio k i. () xz xx zz 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 5 For refleted ad trasmitted waves, we use the Fourier-Floquet expasio with respet to the oordiate x. Satisfyig the Maxwell equatios, the eletri ad mageti vetors of these waves a be writte as follows: i) for the refleted wave / E k k e k k e a e H zz r zz r xz x xz r xx z / xx xz zz i ( kxkrz r 0 xx xz / zz a e ey, i ( kxkrz, (3) with the dispersio equatio k k xz xz r xx k zz zz zz ; (4) ii) for the trasmitted wave E e e H i ( k xkt z k k b e t t x z i ( k xkt z t 0 b e ey,, (5) with the dispersio equatio k t k. (6) Here k /, is the umber of a Floquet spatial harmoi. We defie the urret desity i the plae of the graphee gratig as j s ( x) Etx (z = 0) ex, where ( x) withi eah miro-ribbo ad ( x) 0 i the gaps betwee miro-ribbos. Substitutig Etx (z = 0) from eq. (5), we obtai i ( k x j s ( x) ktb e ex. (7) To obtai equatios for oeffiiets a, b of the Fourier-Floquet expasios (3), (5) we use the boudary oditios: e Hi Hr Ht js z0 ex 0, e Ei Er Et z0 ey 0. Now we substitute eqs. (), (3), (5) for eletri ad mageti vetors ad eq.(7) for the urret desity j s ito eqs. (8). The, usig the dispersio equatios (), (4), (6) we arrive at (8) 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 6 i x xz 4 ( x) xz xx a b e xx Eix 0 zz 0 zz, (9) a b e Eix 0. (0) i x 4 4 zz Multiplyig eqs. (9), (0) by e i m x the rage [0, ] we obtai the set of equatios for oeffiiets a, b :, where m is a iteger ad itegratig these equatios over x i 4 b E a ix 0 4 zz, () 4 d xz xx zz 0 zz i e mm ( ) 0 4 4 m i ( m) d zz ( m) d xx / xz zz 0 4 a m Eix a i e i d E ( ). 0 ix 0 0 I the ifrared ad terahertz spetral regios the itrabad otributio to the graphee odutivity domiates. The, i the radom phase approximatio the D odutivity of graphee a be writte as [3] where ee F () i, (3) i EF is the Fermi eergy of graphee, is the eletro relaxatio time, e is the eletro harge. The refletio ad trasmissio oeffiiets are defied as R E H E H, * * Re( r r) / Re( i i) T E H E H. (4) * * Re( t / Re( i i) 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 7 The graphee absorptio oeffiiet is A ( R T). Numerially solvig equatios ()-(3) the oeffiiets a, b are obtaied. Usig formulas (3), (5) to fid the eletri ad mageti vetors of the refleted ad trasmitted waves ad after their substitutio ito formula (4), we alulate the refletio, trasmissio, ad absorptio oeffiiets. Tehial progress overview I Fig. 3 we show depedee of quatity, o the LC diretor agles, for two pairs of the refrative idies of the ordiary ad extraordiary waves i the LC, o, e. Fig. 3., (a) versus, (b) : (a) o.53, e.94 ; (b) o.94, e.53. Below i Fig. 4 we also show for illustratio the ross-setios of futio, by vertial plaes. (a) Fig. 4. Cross-setios of futio, (b) by vertial plaes: (a) o.53, e.94 ;(b) o.94, e.53 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 8 Aalyzig formula (0) (or Figs. 3, 4) we a olude that ratio max / mi resposible for iterval of tuig the plasmo wave vetor (or frequey) by the LC diretor reorietatio equals e / oif e oor o / eif o e. It is eessary to ote that i the retarded regio ( q zz / ) where istead of formula (9) we have to use formula (6), the small orretio to this estimatio a arise from zz i deomiator of formula (6). As material of the emati layer, we use the high birefrigee ( 0.4 ) LC mixture W79 with 0.53, e.94 at.064 μm [4]. The birefrigee of W79, whih is kow i visible ad ear-ir regios of spetrum, was extrapolated to mid-ir ad THz frequeies usig the exteded Cauhy dispersio formulas obtaied for the LC mixture E7 [5]. I our study, we hose either a low dieletri ostat material (e.g. hexagoal boro itride, h-bn, hbn - 3 ) [6, 7] or a high dieletri ostat material (silio, Si, Si.7 ) [8] as the isotropi substrate material. The physial parameters of the graphee gratig i our simulatios are as follows: the gratig spaig was fixed at μm, the miro-ribbo width was varied as d 0.3, ad 0.. For evaluatio of the 6 eletro relaxatio time we used the formula EF /( evf ), where is the arrier mobility, vf 30 m s - was the Fermi veloity i graphee [0]. Settig EF 0.64 ev [9] ad the arrier mobility 0.5 m /(V s) we get the arrier satterig time 0.3 ps. The simulatios were performed i the wavelegth rage 4.5-55 μm (0-5.45 THz) with a temperature T 300 K. The overgee of the omputatioal proedure used with respet to higher Fouquet harmois is eessary. I order to esure the required auray of alulatios, it was suffiiet to selet the umber of harmois N 400 i eqs. (), (). Results of our umerial alulatios of absorptio, refletio, ad trasmissio spetra of the graphee gratig are show i Figs. 5 ad 6. Fig. 5 illustrates the hage of the absorptio, refletio, ad trasmissio spetra of the graphee gratig for two limitig values of the LC diretor agle 0 ad 90 o, ad a ribbo width to gratig spaig ratio d / 0.5. Curves ad orrespod to the ases of a isotropi substrate with either a low or a high dieletri ostat, respetively. Maxima i the absorptio ad refletio spetra are related to the exitatio of the plasmos i the graphee miro-ribbos. Withi our frequey rage two plasmo peaks i urves are observed. The ratio of the resoat frequeies orrespodig to these peaks is equal to, whih agrees with the results obtaied i paper [9] for the graphee gratig plaed betwee two isotropi dieletri substrates. As we a see from Fig. 5, values of these maxima deped o the LC diretor orietatio. I partiular, the rotatio of the LC diretor by 90 leads to a hage of the absorptio maximum value by approximately 4% whe (h-bn substrate) ad by 6% whe.7 (Si substrate). 3 Absorptio 0.6 0.5 0.4 0.3 0. 0. (a) 0.0 5 0 5 30 35 40 45 50 Wavelegth (m) Refletio, Trasmissio.0 0.8 0.6 0.4 0. (b) T R 0.0 5 0 5 30 35 40 45 50 Wavelegth (m) (a) (b) Fig. 5. Absorptio (a), refletio ad trasmissio (b) spetra of the graphee miro-ribbo gratig at differet agles of the emati diretor: 0- solid lie, 90 - dash-dot lie. Substrate dieletri ostat: 3 - urves,.7 - urves. Ratio d / 0.5. T R 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 9 I Fig. 6, the hage of the absorptio, refletio, ad trasmissio spetra of the graphee gratig at the two limitig values of the LC diretor agle is show for two values of the ribbo width to gratig spaig ratio, d / 0.3 ad d / 0.7. I this ase, the rotatio of the LC diretor by 90 leads to the hage i the absorptio by approximately 4% whe d / 0.3 ad by 8% whe d / 0.7. A ompariso of the results preseted i Figs. 5, 6 shows that the effet of the LC diretor rotatio ireases with a irease of the isotropi substrate dieletri ostat ad the ribbo width to gratig spaig ratio d /. 0.4.0 Absorptio 0.3 0. 0. 0.0 5 0 5 30 35 40 45 50 55 Wavelegth (m) Refletio, Trasmissio 0.8 0.6 0.4 0. T R 0.0 5 0 5 30 35 40 45 50 55 Wavelegth (m) a) (b) Fig. 6. Absorptio (a), refletio ad trasmissio (b) spetra of the graphee miro-ribbo gratig at differet agles of the emati diretor: 0 - solid lie, 90 - dash-dot lie. Ratio d / 0.3 - urves, d / 0.7 - urves. Substrate dieletri ostat.7. O sietifi results of the projet oe paper is published, oe paper is prepared for publiatio, ad four reports o iteratioal oferees were delivered. Referees.. H. Lu et al. Si. Rep. 5, 8843; DOI:0.038/srep08443(05).. P. G. de Gees ad J. Prost. The Physis of Liquid Crystals, ser. Iteratioal Series of Moographs o Physis. (Oxford, U. K.: Oxford Uiv. Press, 995). 3. M. Jabla, H. Bulja, ad M. Soljačić, Plasmois i graphee at ifrared frequeies, Phys. Rev. B 80(4), 45435 (009). 4. E. Nowiowski-Kruszeliki, J. Kędzierski, Z. Raszewski, L. Jaroszewiz, R. Dąbrowski, M. Kojdeki, W. Pieek, P. Perkowski, K. Garbat, M. Olifierzuk, M. Sutkowski, K. Ogrodik, P. Morawiak, ad E. Miszzyk, High birefrigee liquid rystal mixtures for eletro-optial devies, Optia Appliata 4(), 67-80 (0). 5. J. Li, S. T. Wu, S. Brugioi, R. Meui, ad S. Faetti, Ifrared refrative idies of liquid rystals, J. Appl. Phys. 97, 07350 (005). 6. N. Ohba, K. Miwa, N. Nagasako, ad A. Fukumoto, First-priiples study o strutural, dieletri, ad dyamial properties for three BN polytypes, Phys. Rev. B63(), 507 (00). 7. C. R. Dea, A. F. Youg, I. Meri, C. Lee, L. Wag, S. Sorgefrei, K. Wataabe, T. Taiguhi, P. Kim, K. L. Shepard, ad J. Hoe, Boro itride substrates for high-quality graphee eletrois, Nat. Naotehol. 5(0), 7-76 (00). 8. N. K. Emai, Di Wag, T.-F. Chug, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Che, ad A. Boltasseva, Plasmo resoae i multilayer graphee aoribbos, Laser Photois Rev. 9(6), 650-655 (05). 9. A. Yu. Nikiti, F. Guiea, F. J. Garia-Vidal, ad L. Marti-Moreo, Surfae plasmo ehaed absorptio ad suppressed trasmissio i periodi arrays of graphee ribbos, Phys. Rev. B85(8), 08405 (0). R T 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE 0 0. W. Gao, J. Shu, C. Qiu, ad Q. Xu, Exitatio of plasmoi waves i graphee by guided-mode resoaes, ACS Nao 6(9), 7806-783 (0). Curret status of the projet. Сurret tehial status of the projet: o shedule. Summary of persoel ommitmet. Professors of Taras Shevheko Natioal Uiversity of Kyiv V. Yu. Reshetyak, I. P. Pikevyh ad Dr. V. I. Zadorozhii fulfilled the tasks durig the reported period. Prof. V. Yu. Reshetyak - developed the mathematial model of the hybrid system with the LC layer, - obtaied expressios for plasmo frequey i the hybrid system with the LC layer, - alulated the graphee plasmo frequey i depedee o the orietatioal state of the LC layer, - obtaied equatios desribig light propagatio i the hybrid system with plasmo exitatio i the graphee, - developed umerial methods for alulatio oeffiiets of light refletio ad trasmissio i the hybrid system, - optimized the hybrid system parameters for ative otrol of light propagatio ad refletio. Prof. I.P. Pikevyh - obtaied ad solved equatios for the diretor ad eletri field i the LC ell, - studied the ifluee of ahorig o the LC ell boudaries o the diretor i the ell bulk, - studied the otrol of plasmo frequey by DC field ad iidet light field, - obtaied expressios for oeffiiets of light refletio ad trasmissio i the hybrid system, - studied ifluee of the LC layer orietatioal state o light refletio ad trasmissio i the hybrid system. Dr. V.I. Zadorozhii fulfilled umerial alulatios of light refletio ad trasmissio oeffiiets i depedee o the ahorig oditios o the LC ell boudaries. Variatios i the sheduled amouts of efforts. Prof. V. Yu. Reshetyak ad Prof. I.P. Pikevyh fulfilled the followig tasks plaed iitially for Dr. V.I. Zadorozhii: alulatio of the graphee plasmo frequey i depedee o the orietatioal state of the LC layer (Reshetyak), develop umerial methods for alulatio oeffiiets of light refletio ad trasmissio i the hybrid system (Reshetyak) study the ifluee of ahorig o the LC ell boudaries o the diretor i the ell bulk (Pikevyh). Desriptio of travels. Travel of prof. V. Yu. Reshetyak for partiipatio i Coferee o Photorefrative Materials, Villars, Switzerlad, 6-9 Jue 05. Report was delivered o sietifi results of the projet. Travel of prof. V. Yu. Reshetyak for partiipatio i 9th Iteratioal Cogress o Advaed Eletromageti Materials i Mirowaves ad Optis, Oxford, UK, 7- September 05; Travels of prof. V. Yu. Reshetyak ad prof. I. P. Pikevyh for partiipatio i 6th Topial Meetig o the Optis of Liquid Crystals, Sopot, Polad, 3-8 September, 05. Report was delivered o sietifi results of the projet. Travels of prof. V. Yu. Reshetyak ad prof. I. P. Pikevyh for partiipatio i Iteratioal oferee "Flowig Matter 06", Porto, Portugal, -5 Jauary 06. Report was delivered o sietifi results of the projet. Iformatio about major equipmet ad materials aquired, other diret osts, related to the projet. There was ot purhase of equipmet or materials, ad other diret osts have ot bee spet. Table Rediretio Referee doumets &date () L New requested ategory, or old ategory with ew ost () Grat - FWS Requested ost (ew) (3) Quarter 4 Origial (old) ategory (4) Estimated ost (old) (5) Redireted ost (6) old ew 7778.75 Grats-NFWS, Equipmet, Materials, 3500 478.75 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
STCU PROJECT P65 - FINAL REPORT FF PAGE Other diret osts Total 478.75 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.