THz intervalence band antipolaritons

Transcription

1 THz itrvalc bad atipolaritos FARAGAI, Iuwa A ad PEREIRA, Mauro < Availabl from Shffild Hallam Uivrsity Rsarch Archiv (SHURA) at: This documt is th author dpositd vrsio. You ar advisd to cosult th publishr's vrsio if you wish to cit from it. Publishd vrsio FARAGAI, Iuwa A ad PEREIRA, Mauro (2014). THz itrvalc bad atipolaritos. Joural of Physics: Cofrc Sris, 526 (1), Copyright ad r-us policy S Shffild Hallam Uivrsity Rsarch Archiv

2 2014 J. Phys.: Cof. Sr THz itrvalc bad atipolaritos This cott has b dowloadd from IOPscic. Plas scroll dow to s th full txt. Viw th tabl of cotts for this issu, or go to th joural hompag for mor Dowload dtails: IP Addrss: This cott was dowloadd o 25/09/2014 at 11:08 Plas ot that trms ad coditios apply.

3 4th Workshop o Thory, Modllig ad Computatioal Mthods for Smicoductors Joural of Physics: Cofrc Sris 526 (2014) THz itrvalc bad atipolaritos Iuwa A Faragai ad Mauro F Prira Matrials ad Egirig Rsarch Istitut, Shffild Hallam Uivrsity, S1 1WB, Shffild, UK m.prira@shu.ac.uk Abstract. THz polaritos ad atipolaritos hav strog pottial for dvic applicatios ad ar a challgig fild of fudamtal studis. I this papr, w start from a umrically xact oquilibrium may body solutios ad adjust it to a simplifid oliar dilctric costat approach to th optical suscptibility. Th rsultig xprssio is isrtd i th wav quatio to dscrib th couplig of TE-polarizd THz radiatio with a itrvalc bad trasitio i GaAs/Al 0.3 Ga 0.7 As multipl quatum wlls mbddd i microcavitis. Th rgy disprsios rlatios ladig to THz polaritos ar ivstigatd. Hr w focus o th impact of dphasig ad scattrig procsss for diffrt structurs ad xcitatio coditios i a ivrtd mdium ladig to atipolaritos. 1. Itroductio Itrsubbad basd THz polarito mittrs ar attractig major rsarch itrst [1,2]. Th couplig of THz radiatio with itrsubbad trasitios i microcavitis ca lad to furthr tuability ad improvd quatum fficicy ad may play a major rol i futur THz matrials ad dvics [3]. I this papr w xtd ad complmt th rsults of Rfs. [4,5] by ivstigatig th ifluc of dphasig ad scattrig mchaisms o TE mod, THz atipolaritos i diffrt structurs basd o GaAs/Al 0.3 Ga 0.7 As multipl quatum wlls. As i th cas of coductio bad trasitios, polaritos [6-8] ad atipolaritos [9] ca b ralizd with ithr absorptiv (passiv) or gai (ivrtd) mdia. Howvr, i cotrast to itrcoductio bad trasitios, both trasvrs lctric (TE) ad trasvrs magtic (TM) polarizd cavity mods [10] ar possibl. 2. Mathmatical Approach ad Modl Equatios Th iput to th dilctric costat usd hr is obtaid by slf-cosistt valuatio of maybody Noquilibrium Gr's Fuctios (NGF). Th umrical mthod is summarizd as follows. Th THz suscptibility χ(ω) is xtractd from Kldysh Gr's Fuctios, [ ] (1) Hr ad ar th trasitio dipol momt ad th oquilibrium populatio diffrc btw hol subbads ad. Mor dtails of th rormalizd rgis, lctrolctro scattrig ad Coulomb matrix lmts ar giv i Rfs. [11-17]. Th systm is globally out of quilibrium. Th hols ar thrmalizd i th uppr hol subbad (this is th lctro- Cott from this work may b usd udr th trms of th Crativ Commos Attributio 3.0 licc. Ay furthr distributio of this work must maitai attributio to th author(s) ad th titl of th work, joural citatio ad DOI. Publishd udr licc by Ltd 1

4 4th Workshop o Thory, Modllig ad Computatioal Mthods for Smicoductors Joural of Physics: Cofrc Sris 526 (2014) hol ad ot th coductio-valc bad pictur) ad th lowst hol bad is cosidrd to b mpty. Th dilctric fuctio is obtaid by adjustig th full umrical solutio to a Lortzia, amly (2) is th total optical suscptibility,, ar backgroud dilctric costat, photos ad trasitio frqucis btw subbads rspctivly. Th costat is giv by [14], whr N w is th umbr of QWs, L w ad dot rspctivly th QW ad cavity cor lgths. Hr is th dphasig trm, whil is du to dipol couplig ad masurs th oscillator strgth of th trasitio. Th disprsio rlatios show i Fig.2 ar obtaiig by substitutig Eq. (2) ito Maxwlls' quatios [9,10]. Itroducig, for th cavity rsoac ad, th rfrc rsoac frqucy (for o trasitio btw subbads 1 ad 2, ad, w obtai th disprsio rlatio, ( ) ( ), ad. (3) Th gomtry cosidrd i this work is show i Fig. 1. I ordr to sur that icidt light rachs th sampl i th cavity with a suitabl icidc agl, a prism mad of a high rfractiv matrial is placd o top of th sampl. Figur 1. Sampl structur. Light is cofid through total itral rflctio by low rfractiv idx AlAs layrs blow ad abov th cavity cor, which cotais 170 GaAs quatum wlls, ach sparatd by 150m Al 0.3 Ga 0.7 As barrir xcpt th last top barrir layr which was st to 250m ad ths lad to cavity lgths qual to 26.6µm ad 28.5µm for th 5m ad 10m MQW structurs rspctivly. Th top ad bottom layrs of AlAs ar both st to 1300 m ad th compltd th sampl with a top 5m GaAs to avoid AlAs oxidatio du to air itrfac. Th corrspodig cavity paramtrs ar: cavity rsoacs = mV / mV; backgroud dilctric costat b = / ad th ffctiv mdium costat = / for 5m / 10m MQW sampls. 2. Numrical Rsults ad Discussio THz atipolaritos du to itractig TE- polarizd cavity mods ad itrvalc bad trasitios i th gai rgim ar show xt for two diffrt sampls, i which th cavitis hav ithr 10m or 5m GaAs/Al 0.3 Ga 0.7 As MQWs. Figur 2 shows th ifluc of dphasig ' ' ad th ffct of chagig th carrir dsity ' N', o th THz itrvalc bad atipolarito disprsios for a sampl followig th gomtric structur show i Fig. 1 for 5m ( (a) ad (b)) ad 10m ( (c) ad (d) ) MQWs rspctivly. Sic th lowst bad is assumd to b mpty, this also corrspods to th populatio diffrc. 2 dot rspctivly th first ad scod subbads. ad ω ar obtaid by adjustig th full umrical maybody xprssio to th Lortzia approximatio i Eq. 2. Th icrasig dphadig for fixd carrir dsitis simulats tim rsolvd xprimts i which th ost of dphasig ca b moitord. Th dphasig icrass from th outr curvs towards th ctr. Aalogously to th itrbad xcito [18] ad th TM mod itr-coductio bad cass [19], 2

5 4th Workshop o Thory, Modllig ad Computatioal Mthods for Smicoductors Joural of Physics: Cofrc Sris 526 (2014) a d i t r v a l c b a d Figur 2. THz itrvalc bad atipolaritos du to couplig of a TE polarizd cavity mod ad itrvalc bad xcitatios: (a) Lw = 5m, N = cm 2 = mv, ω = (b) Lw = 5m, N = cm 2, = mv, = m. (c) Lw = 10m, N = cm 2, = , = (d) Lw = 10m, N = cm 2, = , = Not that th 5 m MQWs hav trasitios with largr trasitio rgis tha th 10 m MQWs so for th sam dphasig, th atipolarito faturs ar strogr. Compar th dashd lis i both cass. For largr dsitis, th absolut valu of th logitudial-trasvrs (LT) splittig icrass. This icrasd oscillator strgth lads to a strogr sparatio of th two brachs. Not howvr th itrplay of largr quatum wll width (ad thus largr factor) ad largr oscillator strgths that mak th brach sparatio comparabl for th sam dsity. I othr words, v though is largr for th 5 m MQWs, du to bttr lctroic ovrlap, is largr i th structur cotaiig 10 m MQWs, roughly quilibratig th ffct. This study furthr suggsts that sampls with diffrt wll widths i th activ rgio might lad to largr tuability (s th diffrt rgy rags) i applicatios whr th atipolarito couplig might b usd. I w hav ivstigatd th itractio of TE Mod THz radiatio ad itrvalc bad trasitios i quatum wll gai mdia. This ca lad to itrstig THz basd dvics basd o TE mods i cotrast with itr-coductio bad trasitios that oly coupl to TM polarizd radiatio. A Noquilibrium May Body Approach for th optical rspos byod th Hartr-Fock approximatio is usd as iput to th ffctiv dilctric fuctio formalism for th polarito problm. Th rgy disprsios rlatios i th THz rag ar obtaid by adjustig th full umrical solutios to simpl aalytical xprssios to improv clarity, allowig a broad audic to ivstigat similar phoma. Th mthod allows to combi prdictiv microscopic optical rsposs with a simpl dilctric modl for th cavity ladig to a powrful dsig tool for THz polaritoics. 3

6 4th Workshop o Thory, Modllig ad Computatioal Mthods for Smicoductors Joural of Physics: Cofrc Sris 526 (2014) Ackowldgmts Th authors ackowldg support from COST ACTIONs MP1204 ad BM1205. I.A. Faragai's rsarch is supportd by th KUST-Wudil udr TETFUND, Nigria Rfrcs [1] S. D Librato, C. Ciuti ad C. C. Phillips, Trahrtz lasig from itrsubbad polarito-polarito scattrig i asymmtric quatum wlls, Phy. Rv. B. 87, (R) (2013). [2] M. Gisr, G. Scalari, F. Castllao, M. Bck ad J. Faist, Room tmpratur trahrtz polarito mittr Applid Physics Lttrs 101, (2012). [3] M.F. Prira, TERA-MIR radiatio: matrials, gratio, dtctio ad applicatios, Opt Quat Elctro 46, pp (2014). [4] I. A. Faragai ad M. F. Prira, Itractio of valc bad xcitatios ad trahrtz TE-polarizd cavity mods, Optical ad Quatum Elctroics, Opt Quat Elctro 46, pp , (2014). [5] M.F. Prira ad I.A. Faragai, Couplig of THz with itrvalc bad trasitios i microcavitis, Optics Exprss, Vol. 22, Issu 3, pp (2014). [6] D. Dii, R. Köhlr, A. Trdicucci, G. Biasiol, L. Sorba, ad F. Bltram, Microcavity Polarito Splittig of Itrsubbad Trasitios, Phys. Rv. Ltt. 90, (2003). [7] A. A. Aappara, A. Trdicucci ad F. Bltram, Cavity polaritos from xcitd-subbad trasitios, App. Phys. Ltt., 91, (2007). [8] S. d Librato,ad C. Ciutti, Stimulatd scattrig ad lasig of itrsubbad cavity polaritos, Phys. Rv. Ltt. 102, (2009) [9] M. F. Prira Jr. Itrsubbad atipolaritos: Microscopic approach, Phys. Rv. B 75, (2007). [10] M.F. Prira Jr. ad H. Wzl, Itrplay of Coulomb ad oparabolicity ffcts i th itrsubbad absorptio of lctros ad hols i quatum wlls, Phys. Rv. B70, (2004 [11] M. F. Prira Jr., Itrvalc trasvrs-lctric mod trahrtz lasig without populatio ivrsio, Phys. Rv. B 78, (2008). [12] T. Schmilau ad M.F. Prira Jr., Noquilibrium may body thory for quatum trasport i trahrtz quatum cascad lasrs, Appl. Phys. Ltt. 95, (2009). [13] T. Schmilau ad M.F. Prira, Impact of momtum dpdt matrix lmts o scattrig ffcts i quatum cascad lasrs, physica status solidi b 246, 329 (2009). [14] M.F. Prira Jr, R. Nladr, A. Wackr, D.G. Rvi, M.R.Soulby, L.R. Wilso, J.W. Cockbur, A.B. Krysa, J.S. Robrts, ad R.J. Airy, Charactrizatio of Itrsubbad Dvics Combiig a Noquilibrium May Body Thory with Trasmissio Spctroscopy Exprimts, Joural of Matrials Scic: Matrials i Elctroics 18, 689 (2007). [15] M.F. Prira Jr, R. Nladr, A. Wackr, D.G. Rvi, M.R.Soulby, L.R. Wilso, J.W. Cockbur, A.B. Krysa, J.S. Robrts, ad R.J. Airy, "Charactrizatio of Itrsubbad Dvics Combiig a Noquilibrium May Body Thory with Trasmissio Spctroscopy Exprimts", Joural of Matrials Scic: Matrials i Elctroics 18, 689 (2007). [16] M. F. Prira ad S. Tomić, Itrsubbad gai without global ivrsio through dilut itrid bad girig, Appl. Phys. Ltt. 98, (2011) [17] M.F. Prira Jr., Microscopic approach for itrsubbad-basd thrmophotovoltaic structurs i th THz ad Mid Ifrard, JOSA B Vol. 28, Iss. 8, pp (2011). [18] A. Quattropai, W. Czaja, Physica Scripta T29, 162 (1989) [19] M.F. Prira, Th ifluc of dphasig i th couplig of light with itrsubbad trasitios, Microlctroics Joural 40, 841 (2009). 4