Ghosh, S

Rishi, M P

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Ind ian  J. Phys. 77B (2). 223-227 (2003)2:< UPAmplitude modulation and demodulation of electromagnetic wave in magnetised diffusive semiconductorsS Ghosh* and M P RishiSchool of Studies in Physics, Vikrain University, Uiiain-456 010, Madhya Pradesh, IndiaE-mail . drsanjayghoshi^ r^ediffmail.comReceived 12 June 2002, accepted 4 December 2002Vhsirad Analytical investigations arc made for the amplitude modulation as well as demodulation of an electromagnetic wave propagating inllusivc semiconductor medium Using hydrodynamical model of semiconductor plasmas, we have found the value of modulation indices for both side I modes Analyses arc made in different wave number regions over a wide range of cyclotron frequency. It has been seen that diffusion of charge k'is inoclities amplitude modulation and demodulation process effectively Numerical estimations are made for n-lnSb crystal irradiated by pump L- id iicquciicy 1 6 Tera sec Complete absorfition of the waves takes place in all the possible wave lengths regimes when the cyclotron frequency (II iKkoiucs exactly equal to carrier frequency provided one neglects the collision term in modulation/dcmodulation indiceskiYMords Nonlinear phenomena, acouslo-optical effects, high frequency effects, plasma effects.rvr.S No. 32 3S.Mw1. Introductionn) the important problems in communication systems is hill ()l developing an effective method of modulation as well as icniodulaiion of waves. It is a well-known fact that when an iiniiuHlulaicd electromagnetic wave propagates through Ihe pliisma with periodically varying parameters it gets modulated in amplitude. Max etal[i] already predicted that finite amplitude clcciromagnctic wave in a nonlinear dispersive medium can hecome modulafionally unstable. The study of modulation can made with respect to amplitude as well as frequency and phase Amplitude modulation (AM) is one of the oldest forms ihodulation. The efficiency of AM can either equal or exceed h^ai of all other modulation processes such as frequency and/ pha.se modulations. AM is commonly encountered as a Pri^ liminary step in many complex modulation schemes.amplitude modulation type system transmits the carrier iiiid both side bands simultaneously. This often makes for '^■^‘xirnuni simplicity andeconomy particularly at low power out- Puis. In communication processes, amplitude modulation is veryCo,^ responding Authorhelpful to save power by using single band transmission technique.Photo-induced light scattering in photo refractive and Acousto-optic (AO) materials is another area of extensive research due to its potential application in optoelectronics [2-4]. Acousto-optic interaction in dielectrics and semiconductors is playing an increasing role in optical modulation and beam steering [2, 3]. However, in integrated optoelectronic device applications, the AO modulation process becomes a serious limitation due to high power requirements. The most direct approach to this problem is to tailor new material with more desirable AO properties.The stimulus for the investigation of this type in gaseous plasma stems from the work of Volkov [5] who during the study of the stability of the plane electromagnetic wave propagating through an unmagnetised plasma anticipated self modulation of the electromagnetic waves in plasma. On the other side, the problem of amplitude modulation in semiconductor plasma has been studied by a number of workers [6-9]. The modulation of microwave while propagating through a piezoelectrically active semiconducting media duly irradiated by an acoustic wave was©2003IACS224 S Ghosh and M P Rishifirst predicted by Mathur and Sagoo [81. The modulation of a laser beam produced due to certain plasma effects in semiconductor was reported by Sen and Kaw |91. Lashmorc- Davics [I()| has described a mechanism for the spontaneous break up of shear-Alfven wave above a certain threshold and has shown that the same mechanism could be effectively applied to study the modulational instability of other finite amplitude waves in plasmas. The earlier workers |6-9| have found a change in the modulation of an amplitude modulated electromagnetic wave. 1’wo different mechanisms were also propo.scd by Sodha and Kaw 11 l| and Gin/bcrg and Gurevich 1 12| which were experimentally verified by Cutolo (13]. 77iis particular change m mcKlulalion raises the possibility of demodulation of an amplitude modulated wave hence become interesting.In most cases of investigation ol nonlinear optical interactions, the non-local effects such as diffusion of the excitation density responsible for the nonlinear refractive index change has been ignored The study of reflection and transmtssion of a Gaussian beam incident upon an interface that separates a linear and a nonlinear diffusive media has stimulated the idea to include dillusion in computation of nonlinearclectromagnctic wave interaction in hulk and nonlinear- nonlineai interlaces ( M, 15]. It is iound that increased diffusion makes light transmission more dilliciill and lend to wash out the local equilibria of the equivalent potential representing unstable or stable IH nonlinear surlace waves 116| 7 'he high mobility of optically excited charge carriers makes iliffusion effects particularly relevant in semiconductor technology as they (chaigc carriers) travel signilicant distances belore recombining. Recently, the picsent authors 117), probably first time, reported the diffusion induced acousto-optic frequency modulation interaction in magnetised semiconductors. They have shown that the picscncc ol enhanced dillusion due to excess charge carriers elleclively amplily the frequency modulated beam in the dispersion-less acoustic wave regime.Motivated by above discussions in this article wc have presented the acousto-optic amplitude modulation of an intense electromagnetic beam in a strain dependent diffusive semiconductor crystal. The effect of dillusion of the charge carriers on the nonlinear interaction of the laser beam adds new dimensions to the analysis presented in /Mype semiconductor |4] The intense pump beam clectroslrictively generates an acoustic wave within the semiconductor medium that induces an mteraciion between the free carriers (through electron plasma wave) and the acoustic phonons (through material vibration). This interaction induces a strong space^charge field that modulates the pump beam. Thus, the applied optical and generated acoustic waves in an acousto-optic modulator can produce amplitude modulation and demodulation effect at acoustic wave frequency. It is found that the presence of magnetic field is favourable for the phenomenon under study.2. Theoretical formulationThis section deals with the theoretical formulation of modulation index of amplitude modulated laser beam in diffusive semiconductor. We have considered hydrodynamical model of a homogeneous semiconductor pla.sma of infinite extent ( i e k .J < \ ,  where is the wave number of acoustic mode and I the mean free path of electron ). The medium considered is an n type InSb plasma immersed in a sutic magnetic field (B ) pointing along 7.-axis which is irradiated by an intense pump'( k ) and parametrically generated acoustic wave along x-axis) The low frequency perturbations are assumed to be due to theacoustic wave produced by acoustic polari.sation mthe crystal. f3ue to the acousto-optical potential fields accompanying the acoustic wave, the electron concentration oscillates at the acoustic frequency. The pump wave then gives rise to a transverse current density at the frequency (o  ^ and ( ± <w„), where to,, is the frequency of the pump wipe Thc.se side band current densities produce side band electric licld vectors and this way the pump wave gets modulated \ln the subsequent analysis, the side bands will be represented hy the sullixes ±, where + stands for the mode propagating wnh frequency (to,, + to,,) and - stands for (to^ -  to„) mode.Wc consider the equations of lattice dynamics in ordei to find the perturbed current density in crystal in presence o! acousto-optic coupling which arc as follows:-u c a-u ^ du d t  ,,~  " 1 7(I)( 2 )Bq. ( 1 ) describes the lattice vibrations in an acouslo-opiiL crystal of material density p; c\ Tf and y are respcciivcly clastic constant , refractive index and phenomenological damping constant of the medium. The space charge field Rj is determined from Poisson's equation (2) in which last lemi on RHS represents the contribution of acousto-optic polarisationUsing eqs. ( 1 ) and (2), one can obtain the perturbed earner concentration as". = [ 2 p « v; (l + M2) -  (ol l i y  w ,  }j  • [e(»7'  -  l)£o] ' • <3) in which is the shear acoustic speed in the crystal lattice1. i f i  2 k ( » 7 ' - i ) £ o r  (£o/^rgivenbyv,, = -  a n d A ^ = i-----------------L  = 1 -!Lj L is\ P )  2c Cqthe dimensionless acousto-optic coupling coefficient due toAmplitude modulation and demodulation of electromagnetic wave etc 225The oscillatory electron fluid velocity in presence of the imp electric field as well as that due to the fields of theIcband modes can be obtained by using the electronomentum transfer equation including diffusion effects asi)\ Vn^  + +vv .^ +Vj x 1I,]= Dv- ^ ,  (4)r l tk ,There {Diffusion coefficient), in which the carrierobiliiy Hr is g iven  byThe subscript j  stands for 0, + and -  modes, m  and v arc spcciivcly the effective mass of the electrons and the iciiomcnological electron collision frequency. Using eq. (4), ic velocity components can be obtained ascE^OcOf + v)1 +Dvk-(o:(5)-eE,(0,m [ o f  + ( / ( 0 , + v ) ' j1 + D v/0CO^(6)mis the electron cyclotron frequency and1 winch ft;, =■1n„r'niFn e\p|^/[w^r - dependence of the field quantities. The oiiil iiansvcrsc current density in the medium is given byIS the plasma frequency. Here, wc have assumedhnlal (7)^  d t (8)£.+(,cOu+v)^j 'By equating the real parts of above equation, through rationalisation, we findEq mP{k„ ±2k)cA^coq((oI - coI - v ^)+ + 0 5  + V'-)(a»^-(Uo+v'^)‘ +4v^a>oj1 +vDk^(o: (10)rtliL'ic exp represents the current generatedliiL In imcraction of the pump with acoustic wave. Using eqs. M)\n ihc wave equation given byand neglecting Qxp{Tik^^x) in comparison to 1 , we obtain the ’^^ picssions for modulation indices asU may be seen from above expression that the carrier diffusion effectively modify the value of modulation indices in semiconductor plasma.3. Results and discussionIn this .section, wc analyse eq. ( 10) to discuss the amplitude modulation and demodulation due to acousto-optic interaction m the presence and absence of carrier diffusion. One can see that diffusion process modifies the results effectively. Eq. (10) for the modulation index in semiconductor materials can be analysed and discussed in two different wave number regimes viz. (\)k^^>2k, and (ii)^\, < 2 .^(i) When k ^  >2k :In this wave number regime, the amplitude of the side band modes ) always remain oui of phase with pump wave in the permissible cyclotron frequency range. However, when the carrier frequency becomes equal to the cyclotron frequency, complete absorption of waves takes place provided one neglects the collision term in cq. (10). These out of phase side-bands then interact with the pump wave under this condition to produce demodulated acoustic wave. Hence m k^  ^>2k regime, one can always get demodulation. The demodulation index is found to be maximum at a particular value of magnetic field when 0), = (0^,.As a typical case, numerical estimations have been made for /i-InSb at 77K using the physical constants: 771 = 0.014 m^ j , €[ = 17.8, V = 4x  lO'Uec ', = 1 *6 x 10'-\sec ', p  = 5.8x lO^kgm '^, y = 2 X 10’*^ sec ' ; being the free electron mass. The crystal is assumed to be irradiated with an acoustic intensity = lO'^  W m'^ at frequency £0  ^ = 10'" sec '. The variations of£ . 1  . ( i .- 0  yar ‘ j  with the applied magnetostatic field ( co^)are depicted in Figures 1 and 2 in absence and in presence of carrier diffusion respectively. In the considered case, diffusion coefficient D (= KT/mv) has been taken equal to 0.23829 Kec' on the basis of physical constants chosen above. It may226 S Ghosh and M P Rishibe inferred from Figures I and 2 that the demodulation indices of both ihe side bands increase with cyclotron frequency (ai, < QJp). These indices become maximum at = cUq .A  slight tuning ((O^ > cOf^ ) at this resonance point, decrease both the indices abruptly to zero. It may be inferred from these figures that dif f usion effectively altered the index parameter by increasing their values for both the modes at cu, = cu^  .FiKurc 1. Varialion ol inodulaliDn index ol plus mode ( when A' > 2A' ) willi magnelK licld (0  -  o . ) and D -  ()2^S2^> m s e e ---- )liKiire 2. Vanaiioii ol modiilaiion index of minus mode ( when k > 2k ) with inapnclic field ( o), ) (O = o: . ) and O = 0 2382^  in’ sec' ,__ )(ii) When k <2k .aUnder this condition, the behaviour of modulation index for plus and minus modes are opposite m nature. Variation o fwith applied magnetic Held ( )  is shown in Figure 3 1 may be inferred from this figure that the amplitude of plusmoj^Figure 3. Variation of modulation index of plus mode ( when k -- Ik \ with magnetic field ( a)^  )IS out of phase with pump which shows demodulation pruicss and again at co^  = = 1.6 x 1 0 '^ sec”' , we find that thedemodulation is maximum. Figure 4 depicts the variaiior. olE~p~ I with magnetic field ( ) ,  which depicts that amplitudeof minus mode and pump amplitude are in phase; henu modulation occurs. Here the modulation of minus mode may be attributed to the sign of factor -  2k) under ^  ^<2k regime16 -%U— 6D=iy.23B19m*s'O«o0 10 2D X  40 SD0)^  (lO'^  sec”')Figure 4. Variation of modulation index of minus mode ( when  ^‘ with magnetic field ( ) ,Amplitude modulation and demodulation of electromagnetic wave etc 227The above discussion reveals that the amplitude modulation nd demodulation of an electromagnetic wave by an acoustic ; i^ c can easily be achieved in acousto-optic crystal. The carrier il lusion coefficient always increases the value of modulation/ cmodulaiion indices for both the modes around o),. »  0 )^  .It my be inferred that the diffusion altered the result favourably. Icncc. the consideration o f a diffusive crystal with acousto- ptic polarisation thus possibly offers an interesting area for ic purpose of investigations o f different modulational iitractions and one hopes to open a potential experimental )ol lor energy transmission and solid stale diagnostics in .ousio-optic diffusive crystal.cknowledgmentIK ot US (MPR) is thankful to the University Grants omniission, New Delhi, India for the award of Teacherlowslup lo him.■llTClUiVSI C H Max. J Aron.s and A B Langdon Ph\\\ Rev Lett 33 209(1074)[2] R Vazquez, F Vachss, R Neui;gaonkar and M Exbank / Opi Soc\ Am. B8 1932 (1991)[3] E Tervonen, A T Fnbcrg and J Turunen J Mod. Opi 40 625 (1993)[41 A Neogi, K P Maheshwari and M S Sodha J. Opt. Soc Am. Bll 597 (1994)[5] T F Volkov Plasma Physics and Problems oj Controlled Thermonuclear Reaction, Vol.4 (London.Pergamon) pi 14 (I960)[6 ] M S Sodha and C J Palumbo Can. J Phys. 42 1635 (1964)[7] C J K Virmani Plasma Physics 14 1047 (1972)[81 S S Mathur and S M Sagoo Can .1 Phys. 51 2461 (1973)[9] A Sen and P Kaw J PIm. D6 2091(1973)[10] Lushmorc - C N Davies Phys Fluids, 19 587 (1976)[11] MS Sodha and P K Kaw Bi: J Phys 16 1923 (1965)[121 V L Ginzbuig and A V Gurevich Soviet Phys. Uspekhi 3 115 (1960)[13] M Culolo ^at Bui Standards, USA Tech Nolc 2 211 (1964)[14] DR Anderson P/iv.v Rev A37 189 (1988)[15] P Varalharajah, J V Moloney, A C Newell and E M Wnghl J Opt Soc Am BIO 46 ( 1993)[ 16| P Varalharajah, A C Newell. J V Moloney and A B Aceves Phys. Rev A42 1767 (1990)[17] S Ghosh and M P Rishi Euro Phys J. D19 223 (2002)

Amplitude Modulation and Demodulation of Electromagnetic Wave in Magnetised Diffusive Semiconductors

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Amplitude Modulation and Demodulation of Electromagnetic Wave in Magnetised Diffusive Semiconductors

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