光电子学第4章(lpl.ppt

1. Introduction,2. Spontaneous and Stimulated Emission,3. The laser structure: the optical cavity (光学谐振腔),4. The laser below and above threshold and static output properties,5. Advanced structures: tailoring electronic structure,6. Advanced structures: tailoring the cavity,Chapter4 Laser Diode: Static Properties,1. Introduction,The main advantage of the LED:,simplicity of the fabrication process,LED is an incoherent light source.,The key drawbacks of the LED :,small output power (several 10mW) the broad spectrum of the emitted light the difficulty in pushing the modulation bandwidth above 1 GHz,LED is an incoherent light source.,LASER DIODE e-h recombination in a high quality optical cavity,LED,Spectral output is broad,Temporal response is limited by spontaneous emission,Use an optical cavity to enhance emission of certain photon states,Use stimulated emission to enhance e-h recombination rates,Improvements,LD is a coherent light source, which can overcome the limits of LED .,the output power of LD is up to 3000W the linewidth of LD is two orders of magnitude narrower than that of LED the modulation bandwidth of LD approaches 50 GHz,The stimulated emission process provides narrow spectral linewidth of the photon output, provides coherent photons, and offers high speed performance. Thus, the key difference between the LED and the laser diode arises from difference between spontaneous and simulated emission.,2. Spontaneous and Stimulated Emission,Assumed two energy grades,basic state energy grade at the top of valence band,stimulated state energy grade at the bottom of conduction band,Stimulated Absorption (受激吸收 ),Spontaneous Emission (自发辐射),Stimulated Emission (受激辐射),Spontaneous emission:,random process emitting incoherent photons,Stimulated emission:,emitting coherent photons (same phase as the photons causing the emission),(same in energy; different in phase and direction),When semiconductor stimulated by photons with the stimulated radiation and the absorption both may occur.,Which is dominant?,At equilibrium state:,the number of particles at E1:,Reversed distribution of particles (粒子分布反转),the number of particles at E2:,At non-equilibrium state by carriers injected,the occupation probabilities:,When semiconductor stimulated by photons with the stimulated radiation and the absorption both may occur.,The stimulated radiation efficiency,The absorption efficiency,distribution of particles reversed,Other stimulating methods :,Stimulated by electron beam Stimulated by light Stimulated by impact ionization,Stimulating methods of semiconductor laser:,Stimulated by P-n junction current injected,How to realize the reversed distribution of particles?,Essential condition for reversed distribution of particles:,high injection, heavy doped,is not given accurately by the Boltzman statistics,To use the Joyce-Dixon approximation for,3. The laser structure: the optical cavity (光学谐振腔),Optical cavity,Feedback (gain),Select mode,Important cavities used for solid state lasers:,Fabry-Perot cavity (FP腔),Cavity for distributed feedback lasers containing periodic gratings (含周期光栅的分布反馈式腔),Surface emitting laser cavities containing specially designed reflectors (含特殊反射器的表面发射腔),A typical F-P laser structure,I. Optical cavity,The basic parts of laser:,P-N junction two parallel mirrored surfaces perpendicular to PNJ electrode and heat sink,Resonant condition:,q: an integer; L: cavity length; light wavelength,Optical cavity is a resonant cavity (共振腔),frequency of optical wave,The frequency separation of the resonant modes:,a longitudinal mode (纵模),The active region in which e-h pairs are recombining may only occupy a small fraction of the optical cavity.,The optical confinement factor (光波限制因子),The optical confinement factor (光波限制因子),F(z): electric field representing the optical wave in the z-direction,Bulk laser : If d=1m,Quantum well laser :,Major processes to produce lasing:,Spontaneous radiation,Stimulated radiation,Select mode,Amplify,Lasing,Photons generatted by spontaneous radiation stimulate new photons emitting;,The distribution of particles is reversed by excitation, such as carriers injected,The laser structure is designed to create an optical cavity which can guide the photons generated.,Example 4.1,Solution:,Condition: GaAs LD,Calculation: the frequency separation of the resonant modes,The frequency separation is given by,The energy separation of the modes is,. Optical absorption, Loss and Gain (光吸收，损耗和增益),i) Absorption coefficient,Before the distribution of particles reversed,net absorption,The photon flux,When,net stimulated radiation,Gain coefficient,The photon flux,ii) Gain coefficient,at small injection , g0,at injection increasing, g0,G: cavity gain,material gain,iii) Loss and threshold condition of gain (增益阈值条件),Major parts of loss :,(1) Photon loss because of absorption of the photons in the cladding regions and contacts of the laser;,Photon loss due to the photons emerging from the cavity,Threhold condition:,( reflection coefficient ),Gain and loss are account,Example 4. 2,Solution :,Condition: GaAs FP laser cavity ,Calculation: cavity length L at,Homework: 4.1, 4.3,4. the laser below and above threshold and static output properties,The laser below and above threshold,When I is small there is no buildup of photon in the cavity.,When I increases to threshold, the photon number start to build up in the cavity.,When I increases further, stimulated emission occurs and dominates.,Consider the interaction of the photons and the electrons via the rate equations,a. Rate equation(s) of photon (速率方程(组),Rate of change of photon density = Stimulated emission cavity loss rate +Spontaneous emission,The laser above threshold:,2D rate equation:,is the spontaneous emission factor which represents the fraction of total spontaneous emission photons that are emitted into a particular mode.,( for FP cavities ),is the photon population per unit area in the mode m ;,Stimulated emission rate (受激辐射率),Here, is the refractive index,Photon loss rate by cavity loss (腔损耗率),is photon time in the cavity,Spontaneous emission rate (自发辐射率),Rate equation for the photon density :,b. Rate equation for the carrier density,Here, is the area carrier density,is the nonradiative part of the current density,For the steady state:,These two coupled equations are solved by iterative (self-consistent) method 迭代(自洽)法 .,Assumptions in performing calculations,iv) Gain compression effects (增益压缩效应) are ignored,ii) is uniform in space,i) and are uniform over the cavity length;,iii) and is independent of current injection,is close to the maximum gain energy,and are the energy and wavelength corresponding to the peak in the gain curve;,Select mode,F-P cavity,Gain spectrum,several longitudinal modes,Current injection,The main peak starts to dominate.,The other modes become weak.,below threshold,Several important observations must be made regarding the solution of the steady state rate equations.,For the steady state:,The carrier density in the active region,Photon density,2) The total output photon density,3) The spontaneous emission factor,by designing special cavities,However,The peak mode of emission shifts with J,4) Gain coefficient: g,The total current is given by:,5) Radiative current density,Non-radiative current density,Radiative current density,The Auger rate can be written as RAuger = Fn3 Where F is Auger coefficient.,Two source of the non-radiative current,Defect (traps) related e-h recombination,Auger recombination,It is proportional to the defect density and is usually quite low for lasers based on mature technologies,depends upon intrinsic bandstructure of the active material,How to calculate the threshold current density ?,Threshold condition of gain,Threshold condition of injected carrier density,Threshold current density,Here, is the width of the active region of the laser, F is the Auger coefficient,ii) The static output properties,(1) Output versus injected current,(2) Efficiencies of semiconductor laser,a) Internal quantum efficiency,b) External quantum efficiency,c) Differential quantum efficiency,d) Power conversion efficiency,V is the biased voltage of laser, is total series resistance .,(3) Laser modes,a) Longitudinal modes (纵模),b) Transverse mode (横模),The distribution of optical fields perpendicular transmission direction,the efficiency coupled to fiber or other devices,(4) Temperature dependence,a) Temperature dependence of the threshold current,Effects:,Reasons:,Experience equation,b) Temperature dependence of the emission frequency,Effects:,Reasons:,c) Temperature dependence of efficiencies,Example 4.4,Calculation :,Solution :,Condition: GaAs LD at 300K ,Example 4.6,Solution :,Condition : GaAs LD ,Calculation : photon lifetime,The loss coefficient for the photon is,This represents the inverse distance traveled by the photon before it is either absorbed or emitted from the cavity. The lifetime is therefore (v=velocity of light),5. Advanced structures: tailoring electronic structure,Important design issues :,Low threshold current; high modulation bandwidth; narrow emission linewidth; particular application (long wavelength, short wavelength),ADVANCED LASER STRUCTURES,. Single heterostructure lasers (单异质结LD),Characteristics：,iii) Simple fabrication,ii) Unsuitable to work at continuous method at roomtemperature (RT),at pulse method,i) Unsystematic optical wave guide (非对称光波导) at active region,. Double Heterostructure Lasers (双异质结LD),Advantages:,i) Systematic optical wave guide to increase the injection efficiency and to reduce leakage current; ii) Suitable to work at RT continuously.,. Quantum Well Lasers (量子阱LD),i) The physical basic for QW,Structure and scheme of energy band,Quantum Size Effect (量子尺寸效应),Quantum Well (量子阱),Total energy,ii) The electronic state in QW,The motion in z-direction (perpendicular to HTJ) is confined; the motion in xoy plane is free .,quasi-2D electronic gas (准二维电子气),Schrdinger equation for the electron states,Confining potential,Wave function,Energy of electron,Here , is the crosswise energy is the energy at z-direction,Schrdinger equation,Total energy,ii) QW LD,a) Interband Radiation,Comparison between QW-LD and bulk-LD,b) The choice of dw,c) Optical confinement,Separate Confinement Heterostructure SCH (分离限制异质结构),Graded Index SCH (梯度折射率分离限制异质结构),d) The advantages of QW LD,(1) Tunability of emission wavelength,(2) Low,(3) High,. Strained Quantum Well Lasers (应变量子阱),lattice dismatching,strain at defects,dramatic influence on the optical properties,tensile strain (拉伸应变),compressive strain (压缩应变),lattice matching (晶格匹配),The effect of strain on the bandedges (with reference to the conduction band),. Quantum Wire and Quantum Dot Lasers,2D quantum well N(E): step-up distribution (台阶状),1D quantum wire N(E): sawtooth distribution (锯齿状),0D quantum dot N(E): -function distribution ( 函数分布),3D bulk material N(E) (抛物线型),quantum well,quantum wire,quantum dot,Sub-2D Systems for Lasers,High material gain at low injection,Greater ease in polarization tunability,Extremely difficult fabrication technology,Serious problems in achieving high fill factor and high optical confinement,Serious challenges in charge injection from contactscarrier thermalization problems,Advantages,Challenges,6. Advanced structures: Tailoring the cavity,. FabryPerot Cavity,i) Issues in FP Cavity,Fabrication: cleaving a semiconductor wafer along the cleavage planes (解理面),Typical data: reflective coefficience R0.30.4 length of cavity L150 m1mm frequency separation,Narrow stripe . single transverse mode Wide stripe . multiple transverse modes,Strong transverse confinement can be achieved by two approaches :,(1) Gain guide cavities (增益导引型光腔),(2) Index guide cavities (折射率导引型光腔),ii) Gain Guide Cavities (GGC),Stripe Geometry Laser,Metal,Metal,p.213,(1) Effects to be considered :,Gain guided confinement :,gain within stripe width is higher,Anti-guided effect :,carrier concentration within stripe width is high,Leakage loss :,confinement effect is weak,(2) The disadvantages for GGC,higher multi-modes output linewidth larger kink occurred in P-J curve,iii) In