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by: Marlee Lehner


Marlee Lehner

GPA 3.68


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This 32 page Class Notes was uploaded by Marlee Lehner on Monday October 5, 2015. The Class Notes belongs to RLS 165 at California State University - Sacramento taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/218845/rls-165-california-state-university-sacramento in Recreation and Leisure Studies at California State University - Sacramento.

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Date Created: 10/05/15
Chapter 6 Photodetectors GreenAndGuldenEnergv eurnau HrAlpha Sular Flgure l Seetluna l SularEnergv speetrurn m nemwuu x Spaee Alr Mass Zero neutral 2 Photovoltate devlces or solar eells eonvert the rnerdent solar radlatlon energy rnto eleetneal energy minim 5 m r A hWrrrmtxn us Inerdent photons are absorbedto photogenerate eharge earners that pass through an external loadto do eleetneal work Earth 5 surface AMI 5 nan an m n u rr rra Whvdzrkzlhum The rntensrtv ofthe radlatlon ernrtted from the sun has a speetrurn Tmmmmmmmwmmdmm that resembles a black body radlatlon at a ternperature of about nunsrtv laws vrvelsngth slam the errth rnnnsphsre 6 000 K Wu ndunontrndrtthserrths sllrfac2AM15 v ndutnn uuehhouvndutnn rt ouuu K 15 shan ror eonprnsonthtter lll Mnller Samkonductovs vlolm our Anech lhnse press uoslon 1993 p In rru baa m Madman m SularEnergy Speetrum SularEnergy Speetrurn The aetual rntensrtv speetrurn on the earth39s surface depends on the absorpuon andseattenng tTeetofthe atmosphere The atrnosphere39s composmon pollutants alrbome parueulates and so on ath length through the atmosphere The earth39s atrnosphere absorbs and seatters the solar radlatlon dependmg on the wavelength Thus the spaee value AMU ls not avallable at the earth39s surface Lrght rntensrtv vanauon wth wavelength ls tvpreallv represented by mummy perumtwmlengthv called spectral mummy 11 All ofthese effects depend on the speetral vvavelength Indeed laser speetro opv and atrnosphene rnterferornetrv depends on tlus effect Imus the rntensrtv m a srnall rnterval 57h Integratron over the WM 593mm We the M1 WWI Note on the next gure the effeets of angle ofthe devlce wth respeet to the sun and dlffuse eloudv versus elear sky Thls total rntensrtv Iglves the total povver ow through a unrt area perpendlcular to the dlreetron othe sun Thls quanutv ls ealled solar eonstant or armass zero AMU radlatlon 1353 Wrn2 Figure 52 Dueet nuttee AMI Amoeba Tuudwaeme m a Hhmncnn emu effed unle areh ulrrhuenae gun he my xthhreth and th dz mcnxs quMEK AMI and mlseea nu 1rd abeweendu strnhearnaru uh hunz rs uh suhrhnmde a Sczmmg ndnces tle xmexs ymdgwes use he Ad lsednduuml law 0 Kuhn amtmmel more HAD Example 6 l l unfagels Sular energyeunvuslun So the spaee eapable systern would eost about 1 5 nnllllon dollars but wouldreeelyeeonyert more power by about afactor of4 The terrestnal lnstalled solar eell at 15 would eost about 6700 Obylously thls solar systern eannot rnateh the peak power requlrernents Storage battenes and energy transferto the power gnd add eost and eornplexlty The paybaek penod for a solar devlce ls between 3 and 30 years wlth 5 years consldered the eunent ayerage Flgure 4 Monocrystallne mwhmm he urnnu tor rum rrurenn Polycrystallne Flngu eleetmdes onthe surface of Saint eell redusethesenesressunse Ewwsu M zkmmllmmm Example l lmpageZS Sularenezgycunva39slm Suppose afamlly house ln a sunny geographl loeatlon eonsurnes a dally ayerage eleetneal power of 500 w Let the annual average solarlntenslty lneldent per day dayllght lntenslty averagedfor 24 hour day ls 6 kW hoursrn2 Thls ls about 7 hours of dreet sunllghtper day Lastly let the emeleney of the solar eell be about 15 Spaee borne solar eells aehleye about 30 ef clency at a eost o a out summonm2 The 15 emelent eell ls around 500rn2 What ls the requlred solar eell areato supply tlus requlred power7 m Energyper house lnsnlent sour energyperun trre gtlt merensy mullmanna w Pun zouusee way mquot m 15 13 M onnn Seetlon 6 2 Photovoltare Devlce Pnnelples Conslder a pn junctlon wlth a very narrow and more heavlly doped nrreglon The lllurnlnatlon ls through the Lhm nrslde The depleu on reglon w extends pnmanly lnto the prslde As ln any pn Junction there ls a bulltan fleld andyoltage Eu ssary eunent eolleeuon devlce strueture eornrnon y use Photovoltare Devlce Pnnclples A thln anure eetlon eoaung on the surfaee reduees re eetlons from the surfaee and allows more llghtto enter the demee EHPs generatedln the depleuon reglons are lmmedlately separated by the bulltrm eld to the bulk reglons where the eharges an external eunent For long wavelength photons only those EHPs ereated wlthln a nnln onty earner dlffuslon length othe depleuon reglon eontnbute to an external eunent Figure 5 5 EHFS EXPO Phutugenemted mma s within the vulumeLt W L gvensetu a phutucurrmtlph The 1 EHquot ahsurpuun cuef nent at themveiength urrnterest 1999 s o Knsnn Uptoelemovnc Prentice Hui Section 6 3 pn Junction Photovoltaic IV Characteristics Consider an ideal pn junction PV device connected to a resistive load Ltgm i r t K R r gt The voltage V and currentI above de ne the convention for the direction of positive current and vo tage Under short circuit conditions middle figure the only current in the circuit is the photocurrent Iph generated by the incident light KIntznsx 2y pn Junction Photovoltaic IV Characteristics The total current ow is now the sum ofthe photocurrent ccw and the load voltage induced current clockwise As the diode becomes forward biased the magnitude ofthe electric field in the depletion region decreases but does not vanish 39 n nor change directio The net current is always in the reverse bias direction V 7I I exp a u n Photovoltaic Device Principles Crystalline silicon has a bandgap of 11 eV which corresponds to a cutoff wavelength of about 1 1 pm The energy content of sunlight above quotm 11 p111 is about 25 o e to energy and is a limitation in first H39a r generation devices For short wavelengths surface recombination is a major parameter 3 Losses due to EHP recombination nn gmgmnns sun oweran near or at the surface can reach 40 mmmhqwnmmnmlm irther limiting the efficiency ofa solar cell Junction Photovoltaic IV Characteristics Consider an ideal pn junction PV device connected to a resistive load Light 639 i I K R r gt If a load R is now inserted as in the right figure a positive voltage V appears across the diode which forward biases the diode There is now minority carrier injection and the resulting diode current in H Id Figure 5 7 m Typical Ichharacteristics ofa 5r solar eeu The short circuit eunent is 11 andthe open circuitvoltage is V The Ichurves forpositzve eunent requires an external bias voltage Photovoltaic operation is always in the 1999 s o KaEp Oprmzltzcrmmc FrenticeHall pn Junction Photovoltaic IV Characteristics By the text s de nitions used for the solar cell the load resistor appears to be delivering power since the current is not in accordance to the power sign convention dilemma u u in 39 39 as negative resistance 177 R Thus we can nd a speci c R that solves for the VandI required The load line approach solves this problem graphically pn Junction Photovoltaic IV Characteristics Another approach is the solve the P VI equation and take the derivative for maximum power Let the ideality factor n 1 PIVrIpV VIn epr l LP dV 0IWIDCXP Now de ne the thermal voltage as V kBTe Vm 7 L Vi 7 i i xp7 1iVquot V xP V 139 In I 1M7 m V7 717 e V7 m r V V In V I see homework 11 u Problem 6 3 A solar cell driving aresistive load A solar cell ofarea A 4 cm2 in connected to drive a loadR Illumination 600 Wm2 behavior is shown in the gure Let the load R 20 O and the intensity change to 1 kwrn2 What are the current and voltage in the circuit The solar cell is now used under an illumination of 1 kwrn2 The short circuit current Is must be scaled by a factor of1000600 1 57 The gure shows the load line forR 20 O The corresponding current 1 22 5 mA Th v e voltage V 0 45 when P Halth Vin h mam Figure 68 mineraler mmnnm mwn mm 7 7 the malarial air tr 1 F lmrrtle hdt athnasnlarceldrmsaldeRhs the samevoltage rsthe solareell but the eurehtthmtghit is in the opposite direeoohto the eonvehoahthat cunem awsfmm hghto law tehoal bThz cunentl voltage Vih theeieutona canbe mini malmdlire eohstrosoah ponpisthe openohgpnnaV ne lasdllre lsfarR m m9 0 Karin apparent meme pn Junction Photovoltaic IV Characteristics Vm Vm 15 1 7 exp 7 1 I i n This last relationship can be solved by trial and error over the limited voltages typically 04 lt Vmax lt 06 for silicon ofa solar cell The current Iph will depend on the illumination and ID will be parameter for the particular pn junction solar ce 1 Since the open circuit voltage is the maximum voltage possible and short circuit current 15 is the maximum current possible the unachievable maximum power 15 DE 39Ihe llfactor is a measure ofhow close to the maximum power is a particular operating poin 1me I V 29 FF Problem6 3 A solar cell driving aresistive load What is the power delivered to the load 7 7 3 7 PM 7 IV 7 22 5x10 A045V7101mW Whatis the ef ciency ofthe solar cell in this circuit Pin Light IntensitySurface Area PM 1 000 sz m The ef ciency a is given by 00101 7 PM 00 x1002 5 g 04 Problem 5 4 Open Circuit voltage and illumination A solar cell under an illumination of loowhri2 Short circuit current LC 50 mA Open circuit voltage van 0 55 v What is It and vac when the light intensity is halved Example 5 3 2 showed We will assume are ideality constant h 1 Vessel9a nVrln LEW rufr Lm yz Jammy Intznsl 2y It Ira 50mg 25mA r Kg VM V lnj 20550 0259ln 0 5500180 53V l Figure 5 9 Back electrode RI law 5 o Kasap Opmelecmmxcs Prentice Hall Figure 5 11 Effect ofSeries and parallel resistance to are operau39rrg point mm The serles reslstance broaderrs the 17V curve and reduces the maxlmum available power and hence the overall efflclency othe solar cell The orample x 1039 mA Illumination is such that 1999 s o KaEp oproolomomr Frmuce Hall Section 6 4 Series Resistance and Equivalent Circuit Practical devices can deviate substantially from the ideal pn junction solar cell behavior considered so far li ht The nger electrodes introduce an effective series resistance Rs 39 quot 39 quotSmallthin L L for lul ulel 39 39 39 39 A fraction of the current can ow through the crystal surfaces edges of the device or through grain boundaries in polycrystalline devices This is represented as a shunt or parallel resistance Rp FigureGlO 1M Rr A I l Id In 3 RL 8 A Solar cell Load The equivalent circuit of a solar cell 1999 s o Kasap Optoelectramcs Prentice Hall Problem 5 5 Series Connected Solar Cells Consider two iderru39eal solar cells subject to the same illumirrau39or Iph 10 mA 5 x 10396 mA RS 20 O Ideality constantn 1 Find are maximum power that ear be delivered by two cells in series r u RS V I ZR VA Zlt r Thus are currentis V V I ZR allergy Velae we 1 e u o xp 2V thlem a Senes Cunneeteu Sular Cells Fmblem a a Senes Cunneeteu Sular Cells Cunsluertwu manual sular dls subjecnn the Emelllummahun lib 1U mA Cunsluertwu manual sular eells subjecttu the Emelllun39nnanun In In mA ln le mA la ZSXID mA 2 Emmy eunstantn l lumllty eunstant n Thus the vultage turthe twu eell eun gumuunls Frumthe gaphthemax puwa39ls 2H 5 mW l77mAanuv usav V2Vm 2gl Semun 5 TemperatureEffeds Semun Sular Cells Ma39a lals Dances andEf nennes Sm the rntnnsre eamer eoneentrauons anol denslty of states ls strongly temperature ole en olent the outpmvouage and emmmy The Workln solarphotovoltare oleereases wrth lncreaslng temperature eoneentrates on properly absorblng the rnerdentlrght Thls ghtmay be guroleolto the demos through opues anol anure etron eoatrngs surface geomemes ultze For example from the dlode current equatlon we can wrlte the lay r devmes are usedto create EHPS m the advantageous open erreurt voltage Vac as olepleuon reglon loeauon I K1 A In us we ean wnte the ehange m voltage requrreolto marntarn the am same eurrent as the temperature rnerease as denvauon m the tent wwpmymmm mt utrwnmrem may Tem m V evm 74 5 meV li 39 quot 39T quot Tr quot Tr Passrvatron ofsurface defects 330mgtry of mg 5mm Figure 614 mum Sular Cells Matmals Demees and Ef ciencies i mw Whlle the at platequot slllcon photovoltares olomrnate majority solar 39 energy olevrees sol eo eentratorPV and solarrthermalrelecm systems are maklng reeentgarns mnemnv ifmquotquotquot quot Coneentrator devlces rely on lrght whlch ls concentratedto a eentral reeerver uslng mrrrors orrefracuve optres m enamarr Coneentrators requlre duect solarrllumrnauon andthe opues or V MW mlnors must v nng the eourse othe day to traek the sun39s 39 trajectory Thls was a major stumblrng blockln the past However a key bene t of eoneentrator olevrees ls m reoluerng the physlcal slze othe reee er xpenslve part relauve to the arealn whlch the lrghtrs gathered unommrgsnmmsues armrevnr wemnmvsr enamel numuuumc unnur u Magus mu WanerYm new Ymk 1933 gure 3 l7 u 51 m nRuAnWmnmxtkPxHAW Sular One ijerlrMujave Cahrnrnta SEGS Preteetekramnhmennn Cahrerma Frrst generataon duecdy heated steam for the generator for powerm 1988 E65 7 so1arthermahe1eetme generatrng system stru m operataon E aAn B PALE Seeond generatron heate d molten salts then txansferredthe heat to a steam generator for power The parabohe re eetors heat ml whreh rs usedto generate steam for a eonventronal turbrne generator smce 1985 surhng Engmes Concentrator Photovoltaic Systems These are e1osed cycle regeneratrve gas engrnes Drsh eoneentrators by sarhng Engrne Systems R D MeCnnne11J Thanmsenmhttmat RenewableEnergy Lahnratnry Annnza Puhhe Semce speetrelah has tamed up wtth the Anzuna Puhhe Semee APS tn develup and depluy the rst grhennneeted enneentrater system that uLLhzes speetrelah39s GaInPGaAsGe mplerjunchun sular eeus Sntar Ceus Matmats Demees and Ef ciencies Coneentratorpv rehes on gathenng hght over some area and then foeusrng rt down onto aphotovoltare eeu This mndulexs Upa39aumal attheAFS Sular Te dee eAnzunaunder SEI mrehsTAR hulxtym 9 Am 2nn4 s Smce the net area densrty ofthe photovoltae matena1r m eh 39mcmcmmmnmsbem mural 51quot 1 smaller than for atrplatePV rts 15 eeonomreany possrble to use newer generatron hrgher emereney eeus reejuncnon eeu made by BoerngSpeetrolab In etatms emeteneres of39 n at 236 suns There are thermal agement rssues wrth these eoneentxator PV systems and eontanuedreseareh 15 addressrng thrs rssue Contanmztov Call on Cooling Plate Best Research Cell Ef ciencies Dye Solat Cell Swiss Federal Institute ofTechnology R D McCunneLl J Thempsen Neumel RanewableEnagy Labummry r e Sensitized Nano stalline Solar Cell YSC Dy cry D HELIOS pmlmype eteseup un me lakebed Augmt 18 mm Phutu Tum Tsehma NASA Dryden ngquesmmh Center SolarFlight 5w Federal Institute ofTechnology End of Chapter 6 Chapter 4 Stimulated Emission Devices LASERs Stimulated Emission and Photon Ampli cation When an electron at ahigher energy elevel transits down in energy to an unoccupied energy level it may emit a photon W E The electron can undergo the downward transition by itself quite spontaneously Spontaneous Emission In spontaneous emission the electron falls down in energy from level E2 to El and emits a photon of energy hu E2 7 E1 in arandom direction Thus a random photon is emitted This spontaneous process occurs at some rate which will be constant under thermal equilibrium It is important to note that these spontaneous energy level changes will always occur and the spontaneous emission of aphoton may result Section 41 Stimulated Emission and Photon Ampli cation electron in an atom can be excited from an energy level E1 to a higher energy level EZ by the absorption of a photon of energy h n E This absorption process requires that the electron change energy such that it moves from an allowed state to another allowed state If the change is from the valence band to the conduction band then the minimum energy is equal to the bandgap energy Stimulated Emission and Photon Ampli cation Another possibility is the electron can be induced to undergo the downward transition 52 kn In M M M30 in E This last transition is called stimulated emission 1 Stimulated Emiss10n M h m 4A W m I In stimulated emission an incoming photon of energy hv E2 7 El stimulates the whole emission process by inducing the electron at E2 to transit down to E1 Due to the coupling of the electric elds ofthe photon and the transitioning electron the emitted photon is in phare with the incoming ph on it39 t 439 39 itL L 39 39 39 quot ha 0 y the same energy hv E2 7 El Stimulated emission is the basis for obtaining photon ampli cation since one incoming photon results in two outgoing photons which are in p ase In an avalanche device the two outgoing photons interact again so that two more photons are emitted and so on Population Inversion To obtain stimulated emission the incoming photon should not be absorbed by another atom at E1 When we are considering a collection of atoms to amplify light we must have the majority of the atoms the energy level E2 Otherwise the photon is more likely to be absorbed rather than create a stimulated emission When there are more atoms at E2 than at El we have what is called a population inversion It should be apparent that with only two energy levels we can never achieve a population E2 gt El because in the steady state the incoming photon ux will cause as many upward excitations as downward stimulated emissions Optical Pumping 5 a in E m zI w 2 mim E1 in 1 mm U M hu I I II I untitth m In El db h EI7 m m y t J a A ZEI n a 1999 s o Kaap0ptbtzltzcrmmcs FrmuceHall Section 4 2 Stimulated Emission rate and Einstein Coefficients A use il LASER medium must have a higher efficiency of stimulated emission as compared to the efficiencies ofthe system in allowing spontaneous emission and absorption Consider a medium that has Nl atoms per unit volume with energy El and N2 atoms per unit volume with energy E The rate ofupward transitions from E1 to E2 by photon absorption will be proportional to the number of atoms N1 and also to the number of photons per unit volume with energy hu E2 7 El This number of photons per unit volume with energy ho is called the energy density in the radiation Optical Pumping Suppose that an external excitation causes the atoms in a system to become excited to some higher energy leve This process is called pumping Optical pumping is when the external source of excitation if incident photons The original ruby laser used a xenon ashlamp to provide this pumping external excitation energy See the picture on page 162 The energy to which the system is pumped is usually a short lived energy state and the atom rapidly decays to a nearby energy level that is long lived there is a lot of work involved in nding a system where oL39 39 oL IIYY L If e mkl H Either a spontaneous emission or other random photon can initiate the stimulated process with other atoms at this energy level Lasing Emission The emission from E2 to E1 in the previous figure is called the lasing emission By trapping nearly all of these photons in an optical cavity the intensity builds up in much the same way as we build up voltage oscillations in an electrical oscillator circuit What leaks out of the optical cavity is a highly coherent radiation at high intensity It is this coherency of awell defmed wavelength same energy same polarization and same direction that makes laser light distinctly different from random sources such as a lament light or LEDs Stimulated Emission Rate Thus the upward transition rate is R12 EMAMOW where BIZ39 I I 39 39 constant I Fimr in R coef ciem The phv term is the photon energy density per unit chqunn wniu 39 39 UJ puutuu per unit ulume with an energy ofhv Stimulated Emission Rate The rate of downward transitions from E2 to El involves both the spontaneous and stimulated emissions The spontaneous rate of downward transitions from E2 to El depends on the concentration of N2 atoms which are at the energy E The stimulated rate of downward transitions from E2 to El depends on both the concentration of N2 atoms which are at the energy E2 and the photon concentration phv with energy hv E2 E1 Thus the total downward transition rate is R21 spontaneous rate stimulated rate ANN2 321N2phv Where A21 B12 and B21 are called the Einstein coef cients Planck s Black Body Radiation In thermal equilibrium radiation from the atoms must give rise to an equilibrium photon energy density peqhv that is described by Planck s black body radiation distribution law 87rqu3 swig 71 who The above equation is for thermal equilibrium which is what a laser is NOT in during operation We will use the law to help us determine the coef cients only Stimulated Emission The ratio of stimulated emission to absorption is R21Stim BZINZPW Ruabwrp BizNi UtV N 1 Stimulated Emission Rate To nd the coef cients A21 spontaneous emission B12 absorption and B21 stimulated emission we will consider the medium under thermal equilibrium In equilibrium there is no net change with time in the populations at El and E2 thus R12 R I 39 39 L r T In thermal equilibrium at room temperature and above gt 3 ka Boltzmann statistics state Stimulated Emission Under thermal equilibrium R12 R21 which means BIZNIPUIV x4er2 HEMMOW Under these conditions it can be readily shown that B12 B21 and also A21 ism3 3 B21 0 Now consider the ratio of stimulated to spontaneous emission R21ltmmgt 821szva Ellsaw lm c3 3 WW R21Wquotquot A21 A21 A21 87mquot Stimulated Emission WW 3 3 WW WW N Knew my Known V There are two important conclusions from the last two slides For stimulated photon emission to exceed photon absorption we need to achieve population invernon that 15 NZ gt N For stimulated emission to far exceed spontaneous emission we must have a large photon concentration phv which is achieved by building an optical cavity to contain the photons Lastly recall that the laser is based on nonthermal equilibrium so the above results are qualitatively only Section 43 Optical Fiber Ampli ers A light signal that is traveling along an optical ber over a long 139 I II LU regenerate the light signal at certain intervals for long haul communications Classic ampli cation regenerating the optical signal by photodetection conversion to an electrical signal clean u and ampli cation and then conversion back from an electrical to light energy by a laser diode Is has become practical to amplify the signal directly by using an 39f optical amph ier EDFA A er optical pumping there ber has a long lived population inversion at V Incident photons at the 1550 nm wavelength will achieve stimulated emission as long as the pumping continues If the optical purnp fails this systems will see attenuation ofthe signal at the EDFA 53 an buUEI VZEI m The HeNe LASER The excitation of the He atom by an electron collision puts the excited He atom into a metastable long lasting state There are momentum arguments in the text but the result is that a large number of excited He atoms build up during the electrical discharge because they are not allowed by the quantum mechanics to simply decay back to the ground state When an excited He atom collides with a Ne atom it transfers its energy to the Ne atom by electronic resonance energy exchange since it has a state equal to the exited He electron state The collision excites the Ne and deexcites He down to the ground level energy Optical Fiber Amplifiers One practical optical ampli er is based on the erbium Eth ion doped ber ampli er EDFA A short stretch of rare earth dopants is fused to a single mode long distance optical ber The erbium Er3 ion implanted ber has the following energy levels Emmiks m mild six 5m Section 44 Gas Lasers The HeNe LASER With the HeNe Laser one has to confess that the actual explanation is 39 l 39 wena etuknowsuch L39 L states ofthe whole atom The actual stimulated emission occurs from the neon atoms The helium are used to excite the Ne atoms by atomic collisions states of the whole atom The text discusses the effect of exciting the outer shells of both the neon and helium atoms The important fact is that both can be excited to higher energies by the excitation of only one electron in the outermost shell The HeNe LASER With a large number of HeNe collisons in the gaseous discharge we end up with a large number of excited Ne atoms and apopulation inversion between the two outermost electron states of the Ne atorn H u m 1111mm vapuzcm m Her laser Her um um 511532 a mumsim mwwsumw axmnmm Example 44 1 Efficiency of the HeNe Laser A typical low power 5 mW HeNe laser tube operates at a dc voltage of 2000 V and carries a current of7 mA What is the efficiency of the laser Solution 511 4 WWW w 0 035 Input Electrical Power 7x10 A2000V Typically HeNe efficiencies are less than 01 What is important is the high concentration of coherent photons The 5 mW over a beam diameter of1 mm is 64 kW m39z Example 44 2 Laser Bean divergence Solution We can assume that the laser beam emanates like a lightcone as own above with an apex angle of 20 The angle 20 is then the total divergence ofthe beam Thus 20 1 mrad IfAr is the increase in the radius ofthe beam over a distance L then Ar 1 3 tan 73 Ar Ltan 10mtan510 rad 5mm The spot size is then 2w 2 Ar 1mm 25mm 11mm The Output Spectrum of a Gas Laser atom is moving towards the observer along the laser tube x axis the detected frequency is higher Since the atoms are in random motion the observer will detect arange offrequencies due to this Doppler effect The frequency or wavelength of the output radiation from a gas laser will have a linewidth Av v2 v1 Example 442 Laser Bean divergence The laser beam emerging fram a laser tube has a certain amount of divergence Atypical HeNe Laser has an output beam w39th diameter of 1 mm and a divergence of 1 mrad What is the diameter of the beam at a distance of 10 m Laser radiation Laser tube Section 45 The Output Spectrum ofa Gas Laser The output radiation from a gas laser is not one single welldefined wavelength corresponding to the lasing transition but covers a spectrum ofwavelengths with a central peak 39 39 39 i a direct result ofthe Doppler e ect The gas atomsmolecules are in random motion with an average kinetic energy of 32 kBT Thus when the a gas atom is moving away the observer detects a lower frequency Let vl the i ed quency v the frequency ofthe energy transition and velX the velocity ofthe gas atom presumed to be away from the observer vel V1Vu1 x c The Output Spectrum of a Gas Laser The velocities of a gas obey the Maxwell distribution Thus the stimulated emission wavelengths in the lasing medium exhibit a distribution about a central wavelength AU cvn For the Doppler broadened emission the lineshape is a Gaussian function The linewidth in terms of Full Width at Half Maximum FHWM is 2k ln 2 Am 2 MC Where M is the mass ofthe lasing atom or molecule optima Du at mitmg The Output Spectrum of a Gas Laser Consider an optical cavity of length L with parallel end mirrors 1 lt gt m 39w lt w i Stauanary EM Humans Mirmr Mirrar This style of optical cavity is called aFabryPerot optical resonator or etalon The re ections from the end mirrors of a laser give rise to traveling waves in opposite directions within the cavity These oppositely traveling waves interfere constructively to set up a standing wave The Output Spectrum of a Gas Laser For most gases the index ofrefract is very nearly n 1 When this is not the case the wavelength A must be modi ed to re ect the actual wavelength within the cavrty Or in other words do not use the free space wavelength inside a optical cavity unless you know that it applies Each success il constructive interference standing wave within the laser tube is called a cavity mode Allawed o scillauans c avny Mades m l b 4 The Output Spectrum of a Gas Laser The gas laser output thus has a relatively broad spectrum with peaks at certain quot lU ariuu c viy 39quotquot within the Doppler broadened optical gain curve Rum imenaty The net envelope of the output radiation is a Gaussian distribution The frequency width of an individual spike has a nite width due to the losses at the mirrors the Finesse of the cavity is nite and other nonidealities of the cavity The Output Spectrum of a Gas Laser Only standing waves with certain wavelengths however can be maintained within the optical cavity Any standing wave in the cavity must have an integer number of half wavelengths 7J2 that t into the cavity length L Where rn is an integer called the mode number of the standing wave The Output Spectrum of a Gas Laser Modes that exist along the cavity axis are called axial or longitudinal modes This is the only type ofmode that can exist when the end mirrors are at Any offaxis mode will walk offquot the mirror very quickly and not see constructive interference When the mirrors are not at other modes may exist An example is an optical cavity formed by confocal spherical mirrors Spherical mirror Wave ont Exarnple 451 Doppler Broadened Linewidth Calculate the Doppler broadened linewidths in terms of both frequency and wavelength for HeNe Laser with A 6328 nm The gas discharge temperature is 127 C 400 K Ne atomic mass 2 g mol391 Laser tube length 40 cm What is the linewidth in the output wavelength spectrum What is the mode number rn of the central wavelength What is the separation between two consecutive modes How many modes do you expect within the linewidth All of the optical gain curve gtP Equott Example 45 1 part 1 1 What is the linewidth in the output wavelength spectrum The central frequency VB is 5 3x10K 5 lb 532 gm 474x10 5124747512 The observed FWHM width of the frequencies AvlvZ is given by A 2V ml 132 WW 1 MHZ 39 MC 3 35x10 3x10 This last value is different by about 18 of that determined from the rms velocities of the gas which confirms that other processes are broadening the linewidth as well Example 45 1 part 2 2 What is the mode number m of the central wavelength 7 E 7 240m m A 5328x10 ucm 1254222 5 Since partial modes do not constructively interfere in the cavity the nearest full mode to the wavelength given is mu 12 222 Example 45 1 part 4 4 How many modes do you expect within the linewidth All of the optical gain curve The number of modes between the halfintensity points will depend on have the cavity modes and the optical gain curve ov l p mummy FWHMymm Numb4 unmme Smades depmdsm vw Mymaemmm m 1 mm 1mm 5 m lankmgamm 4mm mammmmm Mm w 0 may amulmym mam Example 451 part 1 1 What is the linewidth in the output wavelength spectrum The FWHM wavelength A All is Mum 151x109Hz 63 2 8m 74x10 1 202pm In problem 42 you are asked to find the minimum and maximum wavelengths corresponding to the extremes of the spectrum at the halfpower points Am A 7Aiu 532 am 0010mm 532 79899nm 1 Am in EAAH 532 8m 0010mm 532 8010mm Example 451 part 3 3 What is the separation between two consecutive modes The separation lm is the separation between two consecutive es m an m 1 5i qw s 2L mgsincemisaverylargenumber m 1 m terms of the cavity length and the central wavelen th Also since m ZLA we can find the separation ofmodes just in g 2 a 2 g 222 4532 8x1072m OSOIW m 2L 2 240x10 m in When the index of refraction is other than 1 we must include that in the equation 1 2 7 2rBL Example 451 part 4 4 How many modes do you expect within the linewidth All of the optical gain curve Without going into the specifics of the optical gain curve we can estimate the number of modes in the linewidth by A Mam Linewidth of spectrum A 2 02pm Separation oftwo modes Mquot 0 501pm 403 Thus we can expect 4 or maybe 5 modes within the linewidth of the output Example 45 1 part 4 4 How many modes do you expect within the linewidth All of the optical gain curve exact answer Am 632 80101nm Am 632 79899nm 1254229 1254221 1254222 1254223 1254224 1254225 63289125 6328 75 63289925 63279975 63279925 63279375 lt lt Nu Yes Yes Yes Yes Nu This table is similar to that in homework problem 4 2 By comparing of individual modes we can see the exact number of modes in linewidth In this case the number of modes 4 Optical Gain Coefficient g Consider an EM wave propagating in the medium along the x direction As it propagates its power energy ow per unit ime increases due to the greater stimulated emissions gain over losses spontaneous emissions and absorption ower increases as expgx where g is the optical gain per unit length and is called the optical gain coe lciem of the medium The gain coefficient g is defined as the fractional change in the light power or intensity per unit distance Optical Gain Coefficient g The difference between stimulated emission and absorption rates gives the net rate of change in the coherent photon concentration d Net iate of stimulated photon emission dN T NsziWW 7 M812phvN2 Ni BziJUW Where B12 B21 under thermal equilibrium We can now use this result for dehdt 71 N2 Ni BziPhV UNI g Section 46 Laser Oscillation Conditions Optical Gain Coefficient g Consider a general laser medium which has an optical gain for coherent radiation along some direction x 11 Zquot A a A lasa39medlum wtthan upuml gam b The upuml gam curve erthemenium The dashed tineis the appmmmale dmmuun in the ten i999 s o Kisip taoaln omc Pnntise rant Optical Gain Coefficient g Optical power P along x at any point in the cavity is proportional to the concentration of coherent photons Nph and their energy hv These coherent photons travel with a velocity cn where n is the refractive index of the cavity This in time 5t they travel a distance 6 x cn B t Thus the gain coefficient becomes gegi imt n P Ex N Ex N 55 N 5 n Optical Gain Coefficient g The emission and absorption processes are distributed in photon energy by Doppler broadening energy band spreading and other ocesses This means that the optical gain will re ect this distribution Optical Gain Coefficient g We can express phv in terms of Nph by noting that phv is the radiation energy density per unit frequency NP hv met Mu W we can write the optical gain coefficient in terms of photon concentrations and energies n n N B hv B nhv gm N2 JViBziPhVN M M Nz Ni 2 EN 5 NPhAvn CAVE The last equation gives the optical gain of the medium at the center frequency vu It takes a more rigorous derivation to nd the lineshape over the Av of a real laser Threshold Gain gh Under steady state conditions oscillations do not build up and do not die out Thus Pf must be the same as P Then there should be no optical power loss in the round trip and that the net round trip gain Gop 1 P G 7 1 for steady state Re ections at the faces 1 and 2 reduce the optical power since the re ectance R1 and R2 are less than one Threshold Gain gLh All the losses have to be made up by stimulated emissions in the optical cavity which is the optical gain in the medium As the wave propagates its power increases as Power Gain 0c eg The power Pf ofthe EM radiation a er one round trip ofpath length 2L is given Pf RRIRzegaike li Threshold Gain gh Consider an optical cavity with mirrors at the ends Re ecting surface 72 5mm slim Homes l J u E g E The cavity contains a laser medium so that lasing emissions build up to a steady state and we have continuous operation The optical cavity acts as an optical resonator Consider an EM wave with an initial optical power P starting at some point in the cavity and traveling in a round trip and arrive back at the starting point with a nal optical power Pf Threshold Gain gLh 233 P P my ere are other losses such as absorption and scattering during propagation in the medium The decrease in power is proportional to Power Loss 0c 2 7X Where 7 is the attenuation or loss coef cient ofthe medium 7 Represents all losses in the cavity and its walls except for light transmission losses through the end mirrors and absorption losses already accounted for by the gain coef cient g Threshold Gain gLh For steady state oscillations G Pg39P 1 must be satis ed The up value ofthe gain coef cient g that makes Pg39P 1 is called the threshold gain gm 7 iln 1 g 2L Rle The equation gives the optical gain needed in the medium to achieve a continuous wave lasing emission The necessary g1h has to be obtained by suitably pumping the medium so the N2 is suf ciently greater than N Threshold Gain gLh The threshold population inversion N2 7 N1 N2 7 N1 cAv A71 7 N2 m z gm m from equation 4 on page 176 Initially the medium must have again coefficient g greater than gh This allows the oscillations to buildup in the cavity until a steady state is reached when g gm The re ectance of the mirrors R1 and R2 are important in determining the threshold population inversion required as the control gh in shown before 7 Jriln 1 gwr 2L TR Threshold Gain gLh When the pumping rate exceeds the threshold value then N2 7 N remains clamped at N2 7 N1h because the value ofg must equal gm This above fact may be M 4mm difficult to accept But remember that we are considering a system that has specific energy configurations Pumpm with a large but limited KEMPquotWm number of available quantum states M M p Laugmmiymx M t M Thest mmn Additional pumping above that required for threshold increases the rate of stimulated transitions see B21 in equation 8 on pg 177 and hence increase the optical output power PU Exam le 46l Threshold 0 ulation p p p AM z gt Now consider a HeNe laser with wavelength 6328 nm Tube length L 50 cm Mirror Re ectances Rl 100 and R2 90 Linewi th A GHz Loss coefficient 7 005 m1 Spontaneous decay time constant 1 300 ns Index of refraction n 1 2 2 87m VUTWAV 62 The required gain is g nmn 1411554quot 4 1 K 1 2L 15R 250x10 2m 1109 Threshold Gain gLh It should be apparent that the laser device emitting coherent emissions is actually a laser oscillator Ni M M Pu M M p rm mom The figure to the right shows WNW 11stan the steady state output power PU and the population difference N2 7 N1 mm Thest M at Until the pump rate can bring N2 7 N to the threshold value N2 7 N1h there would be no coherent radiation output Example 461 Threshold population 8 quot2Vu273pA V Ath z 8 T Now consider aHeNe laser with wavelength 6328 nm Tube length L 50 cm Mirror Re ectances Rl 100 and R2 90 Linewidth Av 15 GHz Loss coefficient 7 005 m1 Spontaneous decay time constant 1 300 ns Index of refraction n 1 Calculate the threshold population inversion Solution The emission frequency is book is in error 5 105 N 4 74X10 HZ 3x v A 6328x103 Example 461 Threshold population Now consider aHeNe laser with wavelength 6328 nm Spontaneous decay time constant 1 300 ns Index of refraction n 1 smzvsw The required population inversion is AN z gm 6 2 2 l4 2 79 9 AN 0155m487 l 474gtlt10 3008x210 15gtlt10 Hz 3x10 4376x10 5m 3 Phase Condition and Laser Modes The discussion on threshold gain considered only the intensity inside the cavrty But the same round trip gain dialogue shows that there is a phase condition as well mama p surface 5 2 Steadystntz scillatmrs p The total phase change a er one round trip from E to Ef must be multiple of 27 Arimimp quot127 Phase Condition and Laser Modes These modes are controlled by length L of the optical cavity along its axis and are called longitudinal wa39al modes The analysis so far assumed the ideal case and m w assumed the wave inside the cavity was a perfect 3 plane wave All practical laser cavities have a nite W transverse size and o en use spherical mirrors to aid I alignment of the cavity m With spherical mirrors there can be offaxis selfreplicating rays such as a in the gure above The modes represent a particular electric eld pattern in the cavity that can replicate a er one round trip Mode Indexing These modal eld patterns can be described by three integers p q m And designated as TEMpqm 1 mm mm mm The integer m is the number of modes 3 1 I along the cavity axis x and is the usual 39 longitudinal mode number m is m V W usually large and not written i i 1 E 6 Thus we write the TEMpq descriptions m W W m where p and q describe the spatial distribution at the face of the exit re ector p is the number of nodes in the transverse y direction q is the number of nodes in the transverse z direction m is the number of modes along the x direction Phase Condition and Laser Modes A mmdimp m27I 1 2 2 quotlawman 2 n2L Since any multiple of 27 also satis es the phase condition we can rewrite the last equation with m21r where m is an integer 1 2 nk medium 2L m2r Now with a little more algebra and recalling A Zirk nkmm 2L m2r 2 n2L mk 2 2 L may quotindium n m L where m is the approximate number ofcavity modes 1m 2 n Phase Condition and Laser Modes The electric eld description of these modes are called transverse modes or transverse electric and magnetic modes TEAD mi i mi 1 1 i timings m i it Mr tit i m i E 39 1 m uni 39 I 39 V m rm 1 Each allowed mode corresponds to a distinct spatial eld distribution at a re ector Mode Indexing The TEMUU has an intensity distribution that is radially symmetric about the cavity axis and has a Gaussian intensity distribution across L quotquot Ithasthe lnweltt 439 439 L a highly desirable eld distribution in most applications mm mm mm m In this gure the x direction is coming straight at the observer The 39i39 direction is horizontal 1 ii 4 a m e to rightThe z direction is vertical down vii iii it to up w tit it mm mm mm m mm m Thus TEMm has one intensity reversal in the y direction two separate intensities Thus TEMEll has one intensity reversal in the z direction two separate intensities Section 47 Principle of the Laser Diode Consider a degenerater doped direct bandgap semiconductor pn junction P mm The Fermi level EFp in the pside is in the valence band EFn in the nside is in the conduction band All energy levels up to the Fermi level are assumed occupied by electrons In the absence ofan applied voltage the Fermi level is continuous across the diode EFp BF Principle of the Laser Diode The diode is now forward biased with an applied voltage V greater than the bandgap voltage eV gt Eg This applied voltage separates EFn and EFp by the applied voltage eV Since the diode is forward biased the potential barrier is reduced to almost zero The electron majority carriers are injected through the depletion region and become minority carriers in the ptside ofthe diode The holes have a similar result Thus we have a diode current due to the movement of both charge carriers Principle of the Laser Diode With some few relatively electrons in the valence band in the active region an incoming V photon with an energy EE 7 Ev suffers little 1 absorption Hales mVE Empty states So the incoming photon can stimulate an electron to fall down from EC to Ev The region where there is a population inversion and hence more stimulated emission than absorption has an optical gain The optical gain depends on the photon energy Principle of the Laser Diode The depletion region in such a pn junction is very narrow There is a builtin voltage VD that gives rise to apotential energy barrier eVU that prevents electrons in the CB of the ntside diffusing in the CB ofthe ptside There is similar potential energy barrier stopping hole diffusion from the ptside to Principle of the Laser Diode Electxms mCE HalesinVE Empty states Density ufstates This population inversion region is a layer along the metallurgicaljunction and is called the inversion layer or more commonly the 39ve region Principle of the Laser Diode Opuml gam En 7E Photons with energy between Egap and EFn r EFp cause stimulated emissions m t t I absorbed since there are no available E states in the system in the energy range 2 I 0 t 31 b n 1115 aPiment that the population inversion p E a 5 between energies near EE and those near Ev is achieved by the injection of carriers across the junction under a sufficiently large forward bias The pumping mechanism is the forward diode current and the pumping energy is supplied by the external voltage This is called injection pumping Principle of the Laser Diode In addition to population inversion we also need to have an optical cavity to implement laser oscillation Currant Aenve regun stimulated Emissrm regun A schematic illustration of a GaAs homojunctlon laser diode The eleaved surfaces act as re ecting mirrors m9 0 K1519 caymumm Renaudh Principle of the Laser Diode The required threshold gain is acumen 1 1 1 1 1 ln ln 2282 gm 7 2L 7 2L 01021 7 2L For the gas laser with mirror re ectances of 100 and 90 we had 7 iln L e i1n i e io 1054 g Vy 2L 5R2 7 Zr 09 7 2L Thus the semiconductor diode requires a considerable gain through pumping to achieve threshold Principle of the Laser Diode There are two critical diode currents First is the diode current that provides just f cient injection to lead to stimulated emission just balancing absorption This is called the transparency current IEns since there is no net photon absorption and the medium appears to be transparent Above ItEns there is optical gain When the diode current reaches Ih the gain has reached g gm By de nition then the cavity continues to support stimulated emission since all losses are covered Principle of the Laser Diode The pn junction uses the same direct bandgap semiconductor material throughout and hence has the name homojunction The ends ofthe crystal are cleaved to be at and optically polished to provide re ection and hence form an optical cavity For example the index of refraction for GaAs is about 36 so the re ectance is 2 z 2 R quot Z 36 1 3 031947 mm 3s1 4 s Principle of the Laser Diode The dependence of the optical gain ofthe medium on the wavelength of the radiation can be seen from the energy distribution of the electrons in the CB and the holes in the VB around the metallurgical junction Lasing radiation is obtained when the optical gain in the medium can overcome the photon losses from the cavrty Below the threshold current 111 the light from the device is due to spontaneous emission and not stimulated emission So below the threshold current 111 the light from the device is random and like an LED This is the basis for the superluminescent LEDs Principle of the Laser Diode The following gure shows the output light intensity as a rnction of diode current LED like below 111 then a er threshold a Laser Dpuzdewu39 Laser Typical mpm aphcal pawn vs made currentU characteristics and the canespandmg mam spectrum af alaser made m9 0 Km opnulumymsl Furlong Han Principle of the Laser Diode Note that the output frequency spectrum may depend on the diode current Later we will review mode hopping when the spectrum shi s suddenly 37mm Lee new Power Laser Typical mpm apncal pawn vs dude current shhssunsess she the canespandmg when spectrum af erase dude i 0 use Opymumm hum Ha Section 48 Heterostructure Laser Diodes The reduction of the threshold current Ih to a practical value ie Those not needing cryogenic cooling requires improving the rate of stimulated emission and improving the efficiency of the optical cavity The reduction of the threshold current Ih can be achieved by confining the injected electrons and holes to a narrow region around the junction Confining the carriers to a small region means that less current is needed to establish the necessary concentration of carriers for population inversion Secondly we can build a dielectric waveguide around the optical guide region to increase the photon concentration and hence the probability of stimulated emissions Heterostructure Laser Diodes The pGaAs region is a thin layer typically 01 r 02 pm It is the active layer in which lasing recombination takes place BomrFA Ar 39 quotrorArA A degenerate with EF in the valence band When a sufficiently large forward bias is applied E0 on nAlGaAs moves above EC 0 pGaAs w ich leads to a large injection of electrons in the CB on nAlGaAs in pGaAs Hnlzs in VB Principle of the Laser Diode The main problem with the homojunction laser diode is that the required threshold current is very lar e The current density Jh is too high for practical purposes low life ofthe device high heat low efficiencies Epudewu39 its Laser L Typical mpm aphcal pawn vs dude cunenlU characteristics and the canespandmg when spectrum af alaser dude m9 0 use opwllumymv Franck H41 Heterostructure Laser Diodes Thus we need both carrier confinement and photon confinement 213 duuble hetaustmcture drude has Wujun uns which are be een twu different bandgap semicunducturs GaAs and AlGaAs b Simpli ed enagy es GaAs lays Ha VB actw layth Refumve c Hrgqer bandgap deX l mammals have a ct Acme An 5 luwer refmmve e h ex a AlGaAs layers pruvlde lataal Dpuml cun nement Heterostructure Laser Diodes e A I the barrier AEC The barrier AEC Is due to the change in the bandgap which arises from the change in doping The small pGaAs active region allows for the concentration of injected electrons to be increased quickly even with moderate increases in forward current This is the carrier confinement requirement and thus the threshold current for population inversion is reduced Heterostruct39ure Laser Diodes E f A wider bandgap semiconductor generally has a lower refractive index AlGaAs has a lower refractive index higher bandgap than GaAs This change in the refractive index de nes an optical dielectric waveguide that con nes the photons to the active region of the optical cavity We now have reduced photon losses and increase photon concentration Recall that the photon con nement was to aid the optical resonance oscillation Light is still allowed to leak out through the AlGaAs pmquot i m m m An 5 am May mvsu ms mmenmumwlm DoubleHeterostructure Laser Diodes Without doubleheterostructure devices we would not have practical solid state lasers that can be operated continuously at room temperature mm m 5 Schematic dlmahm afthz m mumquot uf a dauble hetemjuncuan mp cantanlas nd m9 0 mm opwll cmamp new Ha Buried DoubleHeterostructure Laser Diodes The previous doubleheterostructure device did little to channel the photons laterally down the slab waveguide mm mth Sim Mamas m mm urn ma Wm M M mm m mmmmwn A modi ed device is called the buried doubleheterostructure The sides ofthe active area are also doped to reduce the index of refraction so the the photons are now guided down a box rather than a s a 3914 r Ipuwm c refractive index variation these diodes are called index guided Heterostruct39ure Laser Diodes Thus both carrier and optical con nement lead to a reduction in the threshold current density DoubleHeterostructure Laser Diodes 39Ihe doped layers are grown epitaxially on a crystalline substrate The term epitaxy greek quotepiquot quotabovequot and quottaxisquot quotin ordered manner describes an ordered crystalline growth on a single crystalline substrate As seen from the gure above many layers are used to form the slab waveguide and to allow the tailoring of current ow through the device In particular the stripe electrode down the top center ofthe device creates the current density down through the device Such current ow channeling is called a gain guided device Example 481 Modes in a laser and the optical cavity length Consider an AlGaAs based heterostructure laser diode Optical cavity length 200 pm Peak free space radiation wavelength 900 nm Index of refraction n 37 What is the mode integer m ofthe peak radiation t m i bmglkwmwm 2n 1 900x10 m Partial modes decay out so m 1644 Example 481 Modes in a laser and the optical cavity length Consider an AlGaAs based heterostructure laser diode Optical cavity length 200 p111 Peak free space radiation wavelength 900 nm Index ofrefraction n 37 What is the separation between modes in the cavity miL1EL 271 m 1an 2nL72nLm172nLmi 2m 2m 2m 712 m m1 mm1 m2m m2 ML ML 7 7 900xu m2 2 t 4 05473nm 2nL 23 7200x10 m Example 481 Modes in a laser and the optical cavity length Consider an AlGaAs based heterostructure laser diode Optical cavity length 200 p111 Peak free space radiation wavelength 900 nm Index ofrefraction n 37 Given optical gain vs All 6 nm How many modes are there within this bandwidth if the cavity shrinks to 20 p111 2 A 2 MW NLM5 473m 2nL 23 720x10 m A411 number ofmodes 67m 1 096 Mquot 5 473nm Number of modes 1 Laser Diode Characteristics The length L determines the longitudinal mode separation The width W and height H determine the transverse modes or lateral Moder If L 39 39 m 39 39 man only the lowest transverse mode TEMUU mode will exist This TEMUU mode however will have longitudinal modes whose separation depends on L The emerging laser beam exhibits divergence This is due to diffraction of the waves at the cavity ends The smallest aperture H in this gure causes the greatest diffraction Example 481 Modes in a laser and the optical cavity length Consider an AlGaAs based heterostructure laser diode Optical cavity length 200 pm Peak free space radiation wavelength 900 nm Index of refraction n 37 Given optical gain vs All 6 nm How many modes are there within this bandwidth In earlier examples we showed that the distribution can be important in the exact number of modes For this problem we will assume the modes are centered at the peak wavelength and evenly distributed le and right of peak number ofmodes M 6 Mquot 0 5473mm 10 96 Number of modes 10 Section 49 Laser Diode Characteristics The output spectrum from a laser diode LD depends on two factors the nature ofthe optical resonator used to build the laser oscillations and the optical gain curve lineshape of the active medium The optical resonator is essentially aFabryPerot cavity which can be assigned a length L width W and height H mutant mirmr whim Emmy Lenghl mum hmrtzdlaser beam Laser Diode Characteristics The actual modes that exist in the output spectrum will depend on the optical gain these modes experience The optical gain depends on on the optical resonator structure and the pumping current evel um 22 anth mmx an Mmfmwhldngza d m22m2 El n Uphulwwu39 m2 mums swam in mu mmu ksmmhspamm mm mm mmmmi Laser Diode Characteristics The laser diode s output characteristics also tend to be temperature sensitive PD mw n mm xn Outputaptrcalpuwervs dwdecummasthnem eremtzmpmms Th2 threshnldcummsh s m mm temperatures my 5 u K sPv rxkhmn Puma rm c 1 r increase 39 typically as the exponential of the absolute temperature Laser Diode Characteristics Between mode hops wavelength An increase slowly with the temperature due to the slight increase in the refractive index n and the cavity length with temperature yam mums mm b r 2n n n S zn n m m Cmmyu mml t Cmmnpumml Cl Highly stabilized laser diodes are usually marketed with thermoelectric coolers integrated into the diode package to control temperature Example 491 Laser output wavelength variations Consider an GaAs based laser diode Gi en dndtN 15 x 10394 K391 Emitted wavelength 870nm Estimate the change in the emitted wavelength per degree change in the temperature between mode hops 1m s w Li Mla m dT m dT dT m Putting the equation in terms of wavelength use Lm AmZn air an i 870 15x1041 3527amp de 2n dT T 37 K Laser Diode Characteristics The output spectrum also changes with temperature In the case ofa singlemode laser diode the peak emission wavelength AU exhibits jumps at certain temperatures mum 52 ma mum 3n n m m n on m Ewmpumlvl m Bunyan21 cw Peakwav enghvs use tmpera xe chummms s Made hapsrnthz gum speckum ufa mg made LD a Remnadmadg naps mdmm mum umpnm range afmtzresta 7 4 C c Outputspeckum rm amulumadeLD rm 0 may Wallznmpwxmcce a A jump corresponds to a mode hop in the output That is at the new operating temperature another mode il lls the laser oscillation conditions and a discrete change in the wavelength Laser Diode Characteristics A use il laser diode parameter is the rlope e ciency which determines optical power PD of the output coherent radiation in terms of the diode current above the threshold current Ih Pu Watts I 7 1 Amp 77Wz Where I is the diode current Highly stabilized laser diodes are usually marketed with thermoelectric coolers integrated into the diode package to control temperature Section 410 Steady State Rate Semiconductor Equations Consider a double heterostructure laser diode under forward bias The current carries the electrons into the active layer where they recombine with holes radiatively Let the length L the width W and the thickness d height H in the gure equal to heir rate of recombination y spontaneous and stimulated emission under steady state conditions The rate of electron injection into the active layer by the current I is b Steady State Rate Semiconductor Equations Rate of electron injection Rate of spontaneous Rate of stimulated 7 quotwand 5p I m r Cnmmtadeh Where nmlmed is the injected electron concentration Nph is the coherent photon concentration in the active layer 5p 15 the average time for spontaneous recombination C is a constant which depends on B The output light power PD is proportional to Nph Steady State Rate Semiconductor Equations If a is the total attenuation coef cient representing all these loss mechanisms the the power in a light wave in the absence of ampli cation decrease as exp tax This is equivalent to a decay in time since the velocity time distance x 4 in T n e L 2 where rP andnrefmctive index Cd 2 Threshold is reached when the stimulated emission just overcomes the spontaneous emission and the total loss mechanism in time rph 39Ihus The electron concentration at threshold n Cr Steady State Rate Semiconductor Equations Above threshold with the electron concentration clamped at nm 171 U C N d N 4 Jr BMW m n aquot n Ed h To nd the optical output power PU consider the following It takes At nLc seconds for photons to cross the laser cavity Only 2 Nph is moving towards one mirror at any instant steady state The light that escapes is 1 r R ofthe radiation Thus PD is NWcavity voiuArnexpnoton mergy 1 7 R ltdLWgtlth3gt 1 Tr l Inigo m LL lt1 c hcerW r R Rgt e ij J Laser Diode Equation Steady State Rate Semiconductor Equations Consider the coherent photon Nph in the cavity Under steady state Rate of coherent photon loss Rate of stimulated emissions N 1 Wannaan In Where rph is the average time for a photon to be lost from the cavity due to transmission through the endfaces scattering and absorption in the semiconductor Steady State Rate Semiconductor Equations When the current exceeds 11 the output optical power increases sharply with the current so we will let Nth 0 at11h This last assumption just sets an arbitrary level as zero for the convenience of counting 1 m nmedLW and J 1 Wed r Area I When the current exceeds the threshold current the excess carriers above nh recombine by stimulated emission The steady state electron concentration remains constant at nh though the rates of carrier injection and stimulated recombination have increased Section 411 Light Emitters for optical ber communications The type of light source suitable for optical communications depends not only on the communication distance but also on the bandwidth requirement For short haul applications ex 7 local area networks LEDs are impln to ive 39 have a longer lifetime and provide the necessary output power However the output spectrum for LEDs is much wider than that of a laser diode TET r39 ueuwim quot A A 439 A ber because the dispersion arising from the nite linewidth A ofthe output spectrum is not a major concern with these bers over the short haul links envisioned here Light Emitters for optical ber communications For long haul andor wide bandwidth communications laser diodes are invariably used because of their narrow linewidth and high output power The type of light source suitable for optical communications depends not only on the communication distance but also on the bandwidth requirement me Lunaad mmw m mum mm mum n Typicalaptwalpnwerautpmvs famdcumm an LED mmmma mme m Wanamm Note that the laser diode has a restricted current range where the light output is linear Section 4 12 Single Frequency Solid State Lasers Ideally the output spectrum from a laser device should be as narrow as possible The generally means that we have to allow only a signle mode to exist One method of ensuring only a single mode ofradiation is in the laser cavity is use frequency selective dielectric mirrors a the cleaved surfaces of the semiconductor The distributed Bragg re ector is a mirror that has been designed like a re ection type diffraction grating It has a periodic corrugated f m39 A m a dulumz mm b i DislnlnutedEngg n zcthDER rimming a Pmullyxe zcted mm at m camlganans humanism a Enema wave whenthz wavelzngth mm m Bragg sandman Re ected wava andE interfere caustth Wm mm A Single Frequency Solid State Lasers MM A q 2A n The Bragg wavelength equation has b n the index of refraction of the corrugated material An integer q1 23 known as the diffraction order A is the corrugation period spacing The distributed Bragg re ector DBR has a high re ectance around AB but low re ectance away from AB The result is that only a particular FabryPerot cavity mode within the optical gain curve that is close to la can lase and exist in the output Light Emitters for optical ber communications The laser diode is the clear winner when linewidth must be narrow It is also the winner for another important parameter rise time The speed response ofan emitter is generally described by a rise time If the driving current is applied suddenly as a step input to the diode the rise time is the time it takes for the light output to rise from 10 to 90 ofthe nal value ALI Laser quot bandwidths are required wiuc Single Frequency Solid State Lasers Intuitively partial re ections ofwaves from the corrugations interfere constru ive y 0 give a re ected wave only when the wavelen corresponds to twice the corrugation periodicity A A 90150quot A I Two partially re ected wavegsuch as A and B have an optical path difference of 2A where A is the corrugation period This 2A is called a Bragg wavelength AB and is given by the condition for inphase interference q 2A n Distributed Feedback Laser In the distributed feedback DFB laser there is a corrugated layer called the guiding layer next to the active layer A Comgzted m r cng by Ame by The cavity radiation spreads from the active layer to the guiding layer These corrugations in the refractive index act as optical feedback over the length of the cavity by producing partial re ections Thus optical feedback is distributed over the cavity length The optical 39 39 39 to both 39 39 f L r L each L 39 and the le and right traveling waves inside the cavity Distributed Feedback Laser The allnwedlquot e artlv atthe Dld are symmetrically placed about 2113 t i3 I 1WXE2nLm1 1kmquot b I 1 0 Am In practice either inevitable asymmetry introduced by the fabrication process or intentional asymmetry lead to only one of the modes pearing CleavedCoupled Cavity C3 Laser T quotff setof 39 quot anal r CavityMudes lnL 111D 39 A 1mm LandD 4 This restriction is possible modes in the combined cavity and the wide separation between modes results in a single mode operation Example 4121 DFB Laser Consider a DFB laser that has Corrugation period A 022 p111 Grating length L 400 Bragg effective index of refraction n 35 Assume a rst order grating this is q 1 Calculate the mode wavelengths Solution 42 2 2 aquot i m1154ymi 154W 1 154 0847 1 m m m 23 5400m M For m 0 we have 1quot 154ym0847nm0115391ym and 1540851m CleavedCoupled Cavity C3 Laser In the cleavedcoupled cavity device two different laser optical cavities L andD are coup e 2 gt lt Dgt The two lasers are pumped by different currents Only those waves that can exist in both cavities are now allowed because the system has been coupled 03W Mum In L Example 4121 DFB Laser Consider a DFB laser that has Corrugation period A 022 p111 Grating length L 400 Bragg effective index of refraction n 35 Assume a rst order grating this is q 1 Calculate the Bragg wavelength Solution 2 2An 7 2022tm35 q 1 q52AgtAB 154tm 71 Example 4121 DFB Laser Consider a DFB laser that has Corrugation period A 022 p111 Grating length L 400 pm Bragg effective index of refraction n 35 Assume a rst order grating this is q 1 Calculate the mode separation Solution The separation ofthe modes is the difference ofthe two Mquot 1 54085m1715391m1 75 In practice only one ofthese modes will appear as the output Section 413 Quantum Well Devices A typical quantum well device has an ultra thin typically less than 50 nm wide narrow bandgap semiconductor such as GaAs sandwiched between two wider bandgap semiconductors such as AlGaAs The two semiconductors should be lattice lattice parameter a Lattice defects due to mismatch of crystal dimensions are thus mi imal Quantum Well Devices The energy of an electron in this three dimensional potential well of size 11 Dy and D2 is given y 2 2 h2n2 2 2 E EC 2 8md SmaDy SmaDl Where n ny and n2 are quantum number with values 1 2 3 The potential barrier height is defined with respect to the arbitrary energy leve EC Since the dimensions Dy and D2 are some much greater than d the minimum energy is almost entirely found from term with n and d Quantum Well Devices Under current injection the electron concentration at El increases rapidly and hence population inversion occurs quickly without the need for a large current to bring in a great number of electrons Stimulated transitions of electrons lead to a lasing emission Quantum Well Devices At the interface between the semiconductors at d in the figure EE and Ev are discontinuous This forms a potential barrier and conduction band electrons in the thin GaAs layer are confined in the x direction of the figure 39Ihis confinement is so small that we can treat the electron as in a one dimensional potential energy well in the xdirection which is free in Quantum Well Devices The holes in the valence band are also confined by the quantum well Thus this system can be considered as a gas of electrons in a two dimensional space constrained in the third dimension 7 x in this case Thus we have a system with a large number of states in a very small region Under forward bias electrons are injected in the thin GaAs region which serves as the active layer 39Ihese injected electrons readily populated the large number of available states likewise there are a large number of available states in the valence band for the holes Quantum Well Devices r There are two distinct advantages of this structure The threshold current for population inversion and hence lasing emission is markedly reduced in comparison to that for bulk semiconductors Secondly since the majority ofthe electrons are at or very near to E1 and the holes are at or near El the range of emitted photon energies is very close to E17 El Consequently the spread in the wavelength the linewidth in the utput spectrum is substantially narrower than that in bulk semiconductor lasers Multiple Quantum Well Devices The advantages of the single quantum well structure can be extended to a larger volume of the crystal by using multiple quantum wells In MQW lasers the structure has alternating ultrathin layers of wide and narrow bandgap semiconductors MM hyu hm lays 2 5r 2 Amulhple quantum we Mom smch Elemms are injectedsz fewstd Current mm active layers mm are quantum wens 19w 0 Km walunmp Pram Ha Example 4131 A GaAs quantum well Consider a GaAs quantum well Effective mass of a conduction electron 007mE Calculate the first two electron energy levels wrt Ec for quantum well thickness d 10 nm Solution E 7 EC 7 2 2 n 8 6062 x10 2 n2Joules my 80 079 11x10 10gtlt10 7 8 6062x10 2 7 79 nzeV 0 053721n2 1 602x10 So E1 00537 eV and E2 02149 eV Example 4131 A GaAs quantum well Consider a GaAs quantum well Effective mass of a conduction electron 007mE Effective mass of a valance band hole 050me What is the wavelength of emission of the SQW versus bulk GaAs Solution For bulk GaAs with Eg 142 eV 734 8 Eg hv hc3 AEWg73g3nm 1 Eg 1421602gtlt1039 For the SQW also with Eg 142 eV 55251x10 3x10X lawn kc 49 7nm EgEE 14200537000751602x10 Multiple Quantum Well Devices E s quoth quot h The smaller bandgap layers are the active i E EEE layers where electron confinement and lasing trasition take place The wider bandgap layers are the barrier layers Though the optical gain curve is narrow it is not necessarily single mode The number of modes depends on the individual widths ofthe quantum wells Example 4131 A GaAs quantum well Consider a GaAs quantum well Effective mass of a conduction electron 007mE Effective mass of a valance band hole 050me What is the hole energy wrt EV Solution EV r n2 1 205 x10 2 n2Joules 7 my 7 80 509 11x1o 10x1o92 7 s 6062x107 1 502x10w So El 0007521 eV n eV 7 521x101 ng Section 4 14 Vertical Cavity Surface Emitting Lasers VCSELs A vertical cavity surface emitting laser has the optical cavity axis along the direction of current ow rather than perpendicular to current ow as in conventional laser diodes The active region length is very short compared with the lateral dimensions so that the radiation emerges from the surface of the cavity rather than its e e The re ectors at the ends of the cavity are dielectric mirrors made from alternating high and low refractive index quarterwave thick multilayers Vertical Cavity Surface Emitting Lasers VCSELs Since the wave is re ected because of periodic variation in the refractive index as in a grating the dielectric mirror is essentially a distributed Bragg re ector High re ectance end mirrors are needed because the short cavity length L reduces the optical gain There may be 20 r 30 layers in the dielectric mirrors to obtain the required re ectance N99 Section 415 Optical Laser Ampli ers A semiconductor laser structure can also be used as an optical ampli er that ampli es light waves passing through its active region Pimp meat sigiil am 9 sigiili ARAmiimecam AR ceiling a vaelmg wave ampli er a FabryrFerut ampli er The wavelength of radiation to be ampli ed must fall within the optical gain bandwidth ofthe laser Optical Laser Ampli ers The FabryPerot laser ampli er is operated below the threshold current for lasing oscillations My piniil miiiiii pimil miiiiii a FabryrFerut amph a The active region has an optical gain but is not suf cient to sustain a selflasing output The wavelengths closest to optical gain bandwidth receive the most increase in intensity but other wavelengths are ampli ed as well Vertical Cavity Surface Emitting Lasers VCSELs One of the principle advantages of this structure is that they can be arrayed to construct a matrix emitter use ll in optical interconnects Optical Laser Ampli ers the ua elin rquot 39 is pumpcu the mirrors have antire ection coatings so the optical cavity does not act as an ef cient resonator Pimp mien sigiil am ceiling a vaelmg wave amph a Light input is ampli ed by the stimulated emissions and leaves the optical cavity at higher intensity Typically such ampli ers are buried heterostructure devices and have optical gains of around 20 dB Section 416 Holography This section will not be covered It is an interesting if very brief introduction into holography End of Chapter 4


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