（光学专业论文）半导体介质中光学双稳态和四波混频的理论研究.pdf

? ? ? ? ? ? ? ? ?1? ? ? ? ? ? ? ? ?2? ? ? ? ? ? ? ?3? ?-? ? ? ? 25%? ? i ? abstract in this thesis we have discussed mainly the nonlinear optical phenomena of optical bistability (ob) and four-wave mixing (fwm) in the semiconductor quantum well (sqw) structures. following the introduction of the growth mechanism of sqw and basic theory of the phenomena of ob and fwm, we present relevant semi-classical theory and study ob and fwm in sqw theoretically using this semi-classical approximation. the main work of our paper consists of the following sections: (1) we investigate ob based on intersubband transitions in an asymmetric sqw struc- ture that has equidistant transitions between three subbands. the system is simultaneously coupled by a fundamental fi eld and its second harmonic. the second harmonic fi eld acts as a control fi eld and signifi cantly infl uences the ob. in addition, the two-color coherent control of ob by the relative phase of the fundamental and the second harmonic fi elds is shown. the infl uence of the electronic cooperation parameter on the ob behavior is also discussed. (2) the behavior of ob in a triple sqw structure with tunnelling-induced interference is studied, where the system is driven coherently by the probe laser inside the unidirectional ring cavity. the results show that the properties of ob can be controlled effi ciently by tun- ing the parameters of the system such as laser frequency and tunnelling-induced frequency splitting. (3) we propose an effi cient fwm scheme in an asymmetric semiconductor dou- ble quantum-well (sdqw) structure based on intersubband transitions, and obtain the corresponding explicit analytical expressions for the input probe and generated fwm pulsed fi elds by use of the coupled schr oinger-maxwell approach. under the resonant and phase-matched conditions, the fwm effi ciency versus several variables is also discussed in details and the maximum fwm effi ciency of the system under study is greater than 25%. key words:optical bistability; four-wave mixing; semiconductor quantum well; intersub- band transitions ii ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1? 1.1? ?1,2? ? ?electromagnetically induced transparency?eit? ? ?coherent population trapping?cpt? ? ? ? ?3? ? ? ?46?7,8? ?9?2003? xiao?7? ? ? ?eit? ? ? ?8?eit? ? ?2004? ?5,6? ? ? ? ? ? ? ? ? ? ?1019? ? ?1014,2031? ?20,22,23? ? ?21?12,2528?2931? ? ?10ps1? ? ? ? ? ? ? ? ? ? ? ?stark? dynes?paspalakis? ?24? 1 ? ? 1-1?m1-m3? ?ld1?ld2?pb1-pb4 ?fr? ? apd? sas?7 ? ? ? ?gao? ?31? ? ? ? ? ? ? ? ? ? ? ? ? ?-? ? 2 ? (1) ? ? ? ?1969?32?1976? ?33? ? ? ? ? ?34,35?7,8? ?36? ?37?3840? ? ?40?20022003? ?xiao? ?7?5cm?67.5?37cm? ? ? ? ? m2?pbs? ?1-1? ? ? ?1976?gibbs?na?f-p? ? ?gaas?insb?linbo3? ?gaalas/gaas?joshi?xiao? ? ? ? ?16?li? ?18? ? ?fano-? ?li?19? ? ? ? ? ? ? ? ? ? ? ? ?gaas?insb? ?,? ? ?10?2?1?2? ? ? ?1012? ? ? (2) ? ?four-wave mixing? fwm? 3 ? ? 1-2 ?pr?bs?nd? ? & 60?43 ? ? ? ? ? ? ? ?41? ? ? ? ? ? ?franken?42? ? ? ? ? ? ? ? ? ? ? ?feinberg?jain?1979?43,44? ? ?1-2? ? ? 100% ? ?2001?1?deng45? ? ? ? ?kerr? ? ? ? 2003?8? wu? ?46?eit? ?eit? ? ? ? ? ?2004?9? ? ? ? 4 ? x y z 1 d 3 d 2 d 1 d x e g e ( )a( )b ? 1-3 (a)? (b)?48 ? ?47? ? ? (3) ? ? ? ? ? ? ? ? ? ? ? ? 6 50nm? ?1-3?a? ? ? ? ? ?mbe?lpe?vpe? ? ?gaas/(al,ga)as? ? ? ?gaas? ?(al,ga)as? ?gaas?(al,ga)as? ? ?1-3 ?b? ? ? ?-? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 5 ? ? 1-4 ?49 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?48? 1.2? 1.2.1? ? ?1-4?49? ?ii? ? ?it? ?ii?oa? ?ii?ib? ?i 0 c? ?it ? ?ii?ce? ? 6 ? l 1 ? e 2 e , tt ie, ii ie 1 m 2 m ? 1-5 ?-? 1 m l 2 m 4 m r=1 3 m r=1 i p e t p e 0 ? 1-6 ? ?ce?ob? ?ec? ?ib? ?i 0 b? ?ecd? ? ?ia?i 0 a?ii? ?ao?abcd? ? ? ? ? ? ? ? ? ? ? ? ? ?-? ? ?1-5? 1-6? ? ?50 en+1(0) = te i+ f(en(0) (?1.1) ?z = 0?(n + 1) ?m1? ?n?f(e)? 7 ? ? ? f(en(n) = releikl 0 en(0)(?1.2) ?l 0 ?l? ? ?r = 1 t ? ? ? ? ?en+1(0) = en(0) = e0? ?1.1? e0= te i+ f(e0) (?1.3) ?1.2? e0= te i 1 rel+ikl 0 (?1.4) ? et= te(l) =te 0e(+ik)l (?1.5) ? et ei = teik(ll 0) elikl 0 r (?1.6) ?-? ? et ei = telikl 0 e2l2ikl 0 r (?1.7) ? ? ? ? ?1?k ? eikl 0 ? ? ? ?l 1?el 1 + l? ?1.6? et ei = t t + l (?1.8) ? ? = 0/(1 + i)?i = it/t ? ?1.8? ei t= et t(1 + 0l/t 1 + it/t )(?1.9) 8 ? ?1.9? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2? ?re() = 0? ? ? = ilkl 0 (i= im()? it= |et|2? it= |et|2? ? ? ?n(i) = n0+ n2i ? ? = 0+ 2it? ?| 1? ?1.6? ii= it1 + r(0+ 2it)2/t 2 (?1.10) ? ?n?i ? ?i ?l? ? i ? ? ? 1.2.2? ? ?p (2) nl?e ? ?(2)= 0? ?p (3) nl = 0(3)e3? ?48? ? ? ? ?1? 2?3? e(t)= 1 2e1(1)e i1t + c.c. + 1 2e2(2)e i2t + c.c. + 1 2e3(3)e i3t + c.c. = x q=1,2,3 1 2e2(q)e iqt (?1.11) ? q= q?e(q) = e(q)? ? p (3) nl(t) = 1 80 (3) x q,r,l=1,2,3 e(q)e(r)e(l)expi(q+ r+ l)t(?1.12) 9 ? ?216(= 63)?1, ,31 ,21 2, ,1 2 3? ? ?p (3) nl(4 = 2+ 3 1)? ? p (3) nl(4 = 2+ 3 1) = 6 80 (3)e(2)e(3)e(1) (?1.13) ? e(4)e(2)e(3)e(1)? ? ? ? ? ?48? ? ? ? ? ? 2e 0 2e t2 = 0 2pnl t2 (?1.14) ? ? e(t) = x q=1,4 1 2eq(q)exp(iqt) (?1.15) ? q= q? e(q) = e(q)? ? p (3) nl(t) = 0 (3)e3(t) = 1 23 0(3) x p,q,r=1,2,3,4 e(p)e(q)e(r)expi(p+q+r)t (?1.16) ? 512(= 83) ? ? ?1.15? ? ?1.16? ? ?1.14? ? ? ? 2+ k2 qe(q) = 0 2 qp (3) (nl)(q),(q = 1,2,3,4) (?1.17) ?p (3) (nl)(q)?q? ?1+ 4= 2+ 3? ?1?2?3?4= 2+ 3 1?4? ?p (3) (nl)(4)? p (3) (nl)(4 = 2+ 3 1) = 1 40 (3)6e2e3e 1 + 6(|e1|2+ |e2|2+ |e3|2+ |e4|2/2)e4 (?1.18) ?1.17? ? 2+k2 4e4 = 1 400 2 4 (3)6e2e3e 1+6(|e1| 2 +|e2|2+|e3|2+|e4|2/2)e4 (?1.19) ?1?2?3? ?1.18?1.19? ? ? 10 ? ?1+4= 2+3? ? ? ? ? ?e2e3e 1?1? 2?3?4? ? ? ? ? ? ? ?3|ej|2? ? ?6 p 3|ej| 2 ? 1.3? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?-? ? ? ?25%? ? ? ? 11 ? 2? 2.1? ? ?51?schr odinger picture? ? ?heisenberg picture?interaction picture? ? ? ? ? ? ? ? ? ? ? ?1? ? i t|si = h|si |s(t)i = eih(t)t/|s(0)i tas = 0 i ts = hi,s hasi = hs|as|si = tr(sas)(?2.1) ? ?2? ? |h(t)i = |h(0)i = |s(0)i i tah(t) = ah(t),h(t) ah= eih(t)t/aseih(t)t/ hahi = hh(t)|ah|h(t)i = hs|as|si = tr(s(0)ah)(?2.2) ?3? h = ha+ hb hi= eihat/hbeihat/ i t|ii = hi|ii |ii = eihat/|si ai= eihat/aseihat/ i tai(t) = ai(t),hi(t) 12 ? e g a ? ? ? 2-1 ? i= eihat/seihat/ i ti = hi,i haii = hi|ai|ii = hs|as|si = tr(sas)(?2.3) ? ? ? ? ? 2.2? ? ? ? ? ? ?2-1? ? ? ? ? ? ? ? ? ? ?52? 2.2.1? ?2-1? |ei?|gi? ? ? ?a? ?e?g? ?a= e g? h = ha+ hl+ hi ? ha? hl? hi? ? ? ? 13 ? ? ? h = ha+ hi(?2.4) ? ?|ei?|gi? ?|ei? |gi? ? ha= p2 2m + e|eihe| + g|gihg|(?2.5) ?m? p ? ? ? ? ? ? hi= e r e( r0,t) = d e( r0,t)(?2.6) d ? ? e( r0,t)? e( r0,t) = e0cos(t) ?e0?2.6? ?hi?|ei? |gi? hi=(|eihe| + |gihg|)d e0(|eihe| + |gihg|)cos(t) =(deg|eihg| + dge|gihe|)e0cos(t) =(0|eihg| + 0|gihe|)cos(t) (?2.7) ?0= dege0 ?rabi?deg= he|d |gi = d ge = |deg|ei? ? = 0?cos(t) = 1 2(e it + eit)? ? hi= 0 2 (eit|eihg| + eit|gihe|) + (eit|eihg| + eit|gihe|)(?2.8) ? ?2.8? ?eit|eihg|?eit|gihe|? ? ? hi= (eit|eihg| + eit|gihe|)(?2.9) ? = 0 2 ?rabi? ? ?2.5?2.9? ? h=ha+ hi 14 ? = p2 2m + e|eihe| + g|gihg| (eit|eihg| + eit|gihe|)(?2.10) ? ? rabi? ? ? ? h = e|eihe| + g|gihg| (eit|eihg| + eit|gihe|)(?2.11) ? ? ? ? ? ? ?|gihg| = 1 |eihe|?2.11? ? hs= h0+ hi= a|eihe| (eit|eihg| + eit|gihe|)(?2.12) ?a= e g? ?g= eg= 0? ?1?h0= a|eihe|? ?2.3? ? ? ? hi i =eih0t/hieih0t/ =eih0t/(eit|eihg| + eit|gihe|)eih0t/ =(ei(a)t|eihg| + ei(a)t|gihe|) =(eit|eihg| + eit|gihe|)(?2.13) ? = a ? ? ?2?h0= |eihe|? ? ? hi i =eih0t/hieih0t/ =eih0t/|eihe| (eit|eihg| + eit|gihe|)eih0t/ =|eihe| (ei()t|eihg| + ei()t|gihe|) =|eihe| (|eihg| + |gihe|)(?2.14) ? ? ? ? ? ? ? ? ? 2.2.2? ? ? ? 15 ? ? ? ?1? ? ? |(t)i = ce(t)|ei + cg(t)|gi(?2.15) ? ce(t)?cg(t)?|ei?|gi? ? |ei = 1 0 ! |gi = 0 1 ! ? ?t? ? ? |(t)i = ce(t) cg(t) ! (?2.16) ? = |(t)ih(t)|? (t) = ce(t)ce(t)ce(t)cg(t) c e(t)cg(t) cg(t)cg(t) ! = eeeg gegg ! (?2.17) ? ?ee?gg? ? ? ? ? ?t? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?eg?ge? ? ?2.14?2.15?i|(t)i t = hi|(t)i? ? ce(t) t =ice(t) + icg(t) cg(t) t =ice(t)(?2.18) ?2? ? ?ii t = hi,i? ?ij? ij= i k(hikkj ikhkj) (i,j = e,g)(?2.19) ? ee=i(eg ge) gg=i(eg ge) eg=ieg i(ee gg) ge=ige+ i(ee gg)(?2.20) 16 ? ?2.20? ee+ gg= 0? ?|ei? ?|gi? ? ?eg= ge? ?