PHYSICS OF OPTOELECTRONICS
CONTENTS CHAPTER BASIC COMPONENTS AND THE ROLE OF FEEDBACK BASIC PROPERTIES OF LASERS WAVELENGTH AND ENERGY DIRECTIONALITY MONOCHROMATICITY AND BRIGHTNESS COHERENCE TIME AND COHERENCE LENGTH INTRODUCTION TO EMITTER CONSTRUCTION IN-PLANE AND EDGE-EMITTING LASERS VCSEL BURIED WAVEGUIDE LASER LATERAL INJECTION LASER THE LIGHT EMITTING DIODE SEMICONDUCTOR LASER AMPLIFIER GAS LASER THE SOLID STATE LASER INTRODUCTION TO MATTER AND BONDS CLASSIFICATION OF MATTER BONDING AND THE PERIODIC TABLE INTRODUCTION TO BANDS AND TRANSITIONS INTUITIVE ORIGIN OF BANDS INDIRECT BANDS, LIGHT AND HEAVY HOLE BANDS INTRODUCTION TO TRANSITIONS INTRODUCTION TO BAND EDGE DIAGRAMS BANDGAP STATES AND DEFECTS RECOMBINATION MECHANISMS INTRODUCTION TO THE PN JUNCTION FOR THE LASER DIODE JUNCTION TECHNOLOGY BAND-EDGE DIAGRAMS AND THE PN JUNCTION NONEQUILIBRIUM STATISTICS INTRODUCTION TO LIGHT AND OPTICS PARTICLE-WAVE NATURE OF LIGHT CLASSICAL METHOD OF CONTROLLING LIGHT THE RIDGE WAVEGUIDE THE CONFINEMENT FACTOR INTRODUCTION TO NOISE IN OPTOELECTRONIC COMPONENTS BRIEF ESSAY ON NOISE FOR SYSTEMS JOHNSON NOISE LOW FREQUENCY NOISE THE ORIGIN OF SHOT NOISE THE MAGNITUDE OF THE SHOT NOISE INTRODUCTION TO NOISE IN OPTICS REVIEW EXERCISES 110 FURTHER READING CHAPTER INTRODUCTION TO THE RATE EQUATIONS THE SIMPLEST RATE EQUATIONS OPTICAL CONFINEMENT FACTOR TOTAL CARRIER AND PHOTON RATE THE PUMP TERM AND THE INTERNAL QUANTUM EFFICIENCY RECOMBINATION TERMS SPONTANEOUS EMISSION TERM THE OPTICAL LOSS TERM STIMULATED EMISSION—ABSORPTION AND GAIN TEMPORAL GAIN SINGLE PASS GAIN MATERIAL GAIN MATERIAL TRANSPARENCY INTRODUCTION TO THE ENERGY DEPENDENCE OF GAIN THE PHENOMENOLOGICAL RATE EQUATIONS THE POWER-CURRENT CURVES PHOTON DENSITY VERSUS PUMP-CURRENT NUMBER DENSITY COMMENT ON THE THRESHOLD DENSITY POWER VERSUS CURRENT POWER VERSUS VOLTAGE SOME COMMENTS ON GAIN RELATIONS FOR CAVITY LIFETIME, REFLECTANCE AND INTERNAL LOSS INTERNAL RELATIONS EXTERNAL RELATIONS MODULATION BANDWIDTH INTRODUCTION TO THE RESPONSE FUNCTION AND BANDWIDTH SMALL SIGNAL ANALYSIS INTRODUCTION TO RIN AND THE WEINER–KHINTCHINE THEOREM BASIC DEFINITION OF RELATIVE NOISE INTENSITY BASIC ASSUMPTIONS THE FLUCTUATION-DISSIPATION THEOREM DEFINITION OF RELATIVE INTENSITY NOISE AS A CORRELATION THE WEINER–KHINTCHINE THEOREM ALTERNATE DERIVATIONS OF THE WEINER–KHINTCHINE FORMULA LANGEVIN NOISE TERMS ALTERNATE DEFINITIONS FOR RIN RELATIVE INTENSITY NOISE FOR THE SEMICONDUCTOR LASER RATE EQUATIONS WITH LANGEVIN NOISE SOURCES AND THE SPECTRAL DENSITY LANGEVIN–NOISE CORRELATION THE RELATIVE INTENSITY NOISE FURTHER READING A BRIEF REVIEW OF MAXWELL’S EQUATIONS AND THE CONSTITUENT RELATIONS DISCUSSION OF MAXWELL’S EQUATIONS AND RELATED QUANTITIES RELATION BETWEEN ELECTRIC AND MAGNETIC FIELDS IN VACUUM RELATION BETWEEN ELECTRIC AND MAGNETIC FIELDS IN DIELECTRICS GENERAL FORM OF THE COMPLEX TRAVELING WAVE THE WAVE EQUATION DERIVATION OF THE WAVE EQUATION THE COMPLEX WAVE VECTOR DEFINITIONS FOR COMPLEX INDEX, PERMITTIVITY AND WAVE VECTOR THE MEANING OF KN APPROXIMATE EXPRESSION FOR THE WAVE VECTOR APPROXIMATE EXPRESSIONS FOR THE REFRACTIVE INDEX AND PERMITTIVITY THE SUSCEPTIBILITY AND THE PUMP BOUNDARY CONDITIONS FOR THE ELECTRIC AND MAGNETIC FIELDS ELECTRIC FIELD PERPENDICULAR TO AN INTERFACE ELECTRIC FIELDS PARALLEL TO THE SURFACE THE BOUNDARY CONDITIONS FOR THE GENERAL ELECTRIC FIELD THE TANGENTIAL MAGNETIC FIELD MAGNETIC FIELD PERPENDICULAR TO THE INTERFACE (WITHOUT MAGNETIZATION) ARBITRARY MAGNETIC FIELD GENERAL RELATIONS AND SUMMARY LAW OF REFLECTION, SNELL’S LAW AND THE REFLECTIVITY THE BOUNDARY CONDITIONS THE LAW OF REFLECTION FRESNEL REFLECTIVITY AND TRANSMISSIVITY FOR TE FIELDS THE TM FIELDS GRAPH OF THE REFLECTIVITY VERSUS ANGLE THE POYNTING VECTOR INTRODUCTION TO POWER TRANSPORT FOR REAL FIELDS POWER TRANSPORT AND ENERGY STORAGE MECHANISMS POYNTING VECTOR FOR COMPLEX FIELDS POWER FLOW ACROSS A BOUNDARY ELECTROMAGNETIC SCATTERING AND TRANSFER MATRIX THEORY INTRODUCTION TO SCATTERING THEORY THE POWER-AMPLITUDES REFLECTION AND TRANSMISSION COEFFICIENTS SCATTERING MATRICES THE TRANSFER MATRIX EXAMPLES USING SCATTERING AND TRANSFER MATRICES THE FABRY-PEROT LASER IMPLICATIONS OF THE TRANSFER MATRIX FOR THE FABRY-PEROT LASER LONGITUDINAL MODES AND THE THRESHOLD CONDITION LINE NARROWING INTRODUCTION TO WAVEGUIDES BASIC CONSTRUCTION INTRODUCTION TO EM WAVES FOR WAVEGUIDING THE TRIANGLE RELATION THE CUT-OFF CONDITION FROM GEOMETRIC OPTICS THE WAVEGUIDE REFRACTIVE INDEX PHYSICAL OPTICS APPROACH TO WAVEGUIDING THE WAVE EQUATIONS THE GENERAL SOLUTIONS REVIEW THE BOUNDARY CONDITIONS THE SOLUTIONS AN EXPRESSION FOR CUT-OFF 310 DISPERSION IN WAVEGUIDES THE DISPERSION DIAGRAM A FORMULA FOR DISPERSION BANDWIDTH LIMITATIONS 311 THE DISPLACEMENT CURRENT AND PHOTOCONDUCTION DISPLACEMENT CURRENT THE POWER RELATION VOLTAGE INDUCED BY MOVING CHARGE 312 REVIEW EXERCISES 313 FURTHER READING VECTOR AND HILBERT SPACES DEFINITION OF VECTOR SPACE INNER PRODUCT, NORM, AND METRIC HILBERT SPACE DIRAC NOTATION AND EUCLIDEAN VECTOR SPACES KETS, BRAS, AND BRACKETS FOR EUCLIDEAN SPACE BASIS, COMPLETENESS, AND CLOSURE FOR EUCLIDEAN SPACE THE EUCLIDEAN DUAL VECTOR SPACE INNER PRODUCT AND NORM HILBERT SPACE OF FUNCTIONS WITH DISCRETE BASIS VECTORS THE CONTINUOUS BASIS SET OF FUNCTIONS PROJECTING FUNCTIONS INTO COORDINATE SPACE THE SINE BASIS SET THE COSINE BASIS SET THE FOURIER SERIES BASIS SET THE FOURIER TRANSFORM THE GRAHM-SCHMIDT ORTHONORMALIZATION PROCEDURE LINEAR OPERATORS AND MATRIX REPRESENTATIONS DEFINITION OF A LINEAR OPERATOR AND MATRICES A MATRIX EQUATION COMPOSITION OF OPERATORS INTRODUCTION TO THE INVERSE OF AN OPERATOR DETERMINANT TRACE THE TRANSPOSE AND HERMITIAN CONJUGATE OF A MATRIX BASIS VECTOR EXPANSION OF A LINEAR OPERATOR THE HILBERT SPACE OF LINEAR OPERATORS CONTENTS 4510 A NOTE ON MATRICES AN ALGEBRA OF OPERATORS AND COMMUTATORS OPERATORS AND MATRICES IN TENSOR PRODUCT SPACE TENSOR PRODUCT SPACES OPERATORS MATRICES OF DIRECT PRODUCT OPERATORS THE MATRIX REPRESENTATION OF BASIS VECTORS FOR DIRECT PRODUCT SPACE UNITARY OPERATORS AND SIMILARITY TRANSFORMATIONS ORTHOGONAL ROTATION MATRICES UNITARY TRANSFORMATIONS VISUALIZING UNITARY TRANSFORMATIONS SIMILARITY TRANSFORMATIONS TRACE AND DETERMINANT HERMITIAN OPERATORS AND THE EIGENVECTOR EQUATION ADJOINT, SELF-ADJOINT AND HERMITIAN OPERATORS ADJOINT AND SELF-ADJOINT MATRICES EIGENVECTORS AND EIGENVALUES FOR HERMITIAN OPERATORS THE HEISENBERG UNCERTAINTY RELATION 410 A RELATION BETWEEN UNITARY AND HERMITIAN OPERATORS 411 TRANSLATION OPERATORS THE EXPONENTIAL FORM OF THE TRANSLATION OPERATOR TRANSLATION OF THE POSITION OPERATOR TRANSLATION OF THE POSITION-COORDINATE KET EXAMPLE USING THE DIRAC DELTA FUNCTION 412 FUNCTIONS IN ROTATED COORDINATES ROTATING FUNCTIONS THE ROTATION OPERATOR 413 DYADIC NOTATION 414 MINKOWSKI SPACE 415 REVIEW EXERCISES 416 FURTHER READING INTRODUCTION TO GENERALIZED COORDINATES CONSTRAINTS GENERALIZED COORDINATES PHASE SPACE COORDINATES INTRODUCTION TO THE LAGRANGIAN AND THE HAMILTONIAN LAGRANGE’S EQUATION FROM A VARIATIONAL PRINCIPLE THE HAMILTONIAN HAMILTON’S CANONICAL EQUATIONS CLASSICAL COMMUTATION RELATIONS CLASSICAL FIELD THEORY CONCEPTS FOR THE LAGRANGIAN AND HAMILTONIAN DENSITY THE LAGRANGE DENSITY FOR 1-D WAVE MOTION SCHRODINGER EQUATION FROM A LAGRANGIAN LINEAR ALGEBRA AND THE QUANTUM THEORY OBSERVABLES AND HERMITIAN OPERATORS THE EIGENSTATES THE MEANING OF SUPERPOSITION OF BASIS STATES AND THE PROBABILITY INTERPRETATION PROBABILITY INTERPRETATION THE AVERAGE AND VARIANCE MOTION OF THE WAVE FUNCTION COLLAPSE OF THE WAVE FUNCTION NONCOMMUTING OPERATORS AND THE HEISENBERG UNCERTAINTY RELATION COMPLETE SETS OF OBSERVABLES BASIC OPERATORS OF QUANTUM MECHANICS SUMMARY OF ELEMENTARY FACTS OPERATORS, EIGENVECTORS AND EIGENVALUES THE MOMENTUM OPERATOR DEVELOPING THE HAMILTONIAN OPERATOR AND THE SCHRODINGER WAVE EQUATION INFINITELY DEEP QUANTUM WELL THE HARMONIC OSCILLATOR INTRODUCTION TO THE CLASSICAL AND QUANTUM HARMONIC OSCILLATORS THE HAMILTONIAN FOR THE QUANTUM HARMONIC OSCILLATOR INTRODUCTION TO THE OPERATOR SOLUTION OF THE HARMONIC OSCILLATOR LADDER OPERATORS IN THE HAMILTONIAN PROPERTIES OF THE RAISING AND LOWERING OPERATORS THE ENERGY EIGENVALUES THE ENERGY EIGENFUNCTIONS QUANTUM MECHANICAL REPRESENTATIONS DISCUSSION OF THE SCHRODINGER, HEISENBERG AND INTERACTION REPRESENTATIONS THE SCHRODINGER REPRESENTATION RATE OF CHANGE OF THE AVERAGE OF AN OPERATOR IN THE SCHRODINGER PICTURE EHRENFEST’S THEOREM FOR THE SCHRODINGER REPRESENTATION THE HEISENBERG REPRESENTATION THE HEISENBERG EQUATION NEWTON’S SECOND LAW FROM THE HEISENBERG REPRESENTATION THE INTERACTION REPRESENTATION 510 TIME DEPENDENT PERTURBATION THEORY PHYSICAL CONCEPT TIME DEPENDENT PERTURBATION THEORY FORMALISM IN THE SCHRODINGER PICTURE TIME DEPENDENT PERTURBATION THEORY IN THE INTERACTION REPRESENTATION AN EVOLUTION OPERATOR IN THE INTERACTION REPRESENTATION 511 DENSITY OPERATOR INTRODUCTION TO THE DENSITY OPERATOR THE DENSITY OPERATOR AND THE BASIS EXPANSION ENSEMBLE AND QUANTUM MECHANICAL AVERAGES LOSS OF COHERENCE SOME PROPERTIES 512 REVIEW EXERCISES CONTENTS 513 FURTHER READING A BRIEF OVERVIEW OF THE QUANTUM THEORY OF ELECTROMAGNETIC FIELDS THE CLASSICAL VECTOR POTENTIAL AND GAUGES RELATION BETWEEN THE ELECTROMAGNETIC FIELDS AND THE POTENTIAL FUNCTIONS THE FIELDS IN A SOURCE-FREE REGION OF SPACE GAUGE TRANSFORMATIONS COULOMB GAUGE LORENTZ GAUGE THE PLANE WAVE EXPANSION OF THE VECTOR POTENTIAL AND THE FIELDS BOUNDARY CONDITIONS THE PLANE WAVE EXPANSION THE FIELDS SPATIAL-TEMPORAL MODES THE QUANTUM FIELDS THE QUANTIZED VECTOR POTENTIAL QUANTIZING THE ELECTRIC AND MAGNETIC FIELDS OTHER BASIS SETS EM FIELDS WITH QUADRATURE OPERATORS AN ALTERNATE SET OF QUADRATURE OPERATORS PHASE ROTATION OPERATOR FOR THE QUANTIZED ELECTRIC FIELD TROUBLE WITH AMPLITUDE AND PHASE OPERATORS THE OPERATOR FOR THE POYNTING VECTOR THE QUANTUM FREE-FIELD HAMILTON AND EM FIELDS THE CLASSICAL FREE-FIELD HAMILTONIAN THE QUANTUM MECHANICAL FREE-FIELD HAMILTONIAN THE EM HAMILTONIAN IN TERMS OF THE QUADRATURE OPERATORS THE SCHRODINGER EQUATION FOR THE EM FIELD INTRODUCTION TO FOCK STATES THE FABRY–PEROT RESONATOR AS AN EXAMPLE CREATION AND ANNIHILATION OPERATORS COMPARISON BETWEEN CREATION–ANNIHILATION AND LADDER OPERATORS INTRODUCTION TO THE FERMION FOCK STATES FOCK STATES AS EIGENSTATES OF THE EM HAMILTONIAN COORDINATE REPRESENTATION OF BOSON WAVEFUNCTIONS FOCK STATES AS ENERGY EIGENSTATES SCHRODINGER AND INTERACTION REPRESENTATION INTERPRETATION OF FOCK STATES THE ELECTRIC FIELD FOR THE FOCK STATE INTERPRETATION OF THE COORDINATE REPRESENTATION OF FOCK STATES COMPARISON BETWEEN THE ELECTRON AND EM HARMONIC OSCILLATOR AN UNCERTAINTY RELATION BETWEEN THE QUADRATURES FLUCTUATIONS OF THE ELECTRIC AND MAGNETIC FIELDS IN FOCK STATES INTRODUCTION TO EM COHERENT STATES THE ELECTRIC FIELD IN THE COHERENT STATE AVERAGE ELECTRIC FIELD IN THE COHERENT STATE NORMALIZED QUADRATURE OPERATORS AND THE WIGNER PLOT INTRODUCTION TO THE COHERENT STATE AS A DISPLACED VACUUM IN PHASE SPACE INTRODUCTION TO THE NATURE OF QUANTUM NOISE IN THE COHERENT STATE COMMENTS ON THE THEORY 610 DEFINITION AND STATISTICS OF COHERENT STATES THE COHERENT STATE IN THE FOCK BASIS SET THE POISSON DISTRIBUTION THE AVERAGE AND VARIANCE OF THE PHOTON NUMBER SIGNAL-TO-NOISE RATIO POISSON DISTRIBUTION FROM A BINOMIAL DISTRIBUTION THE SCHRODINGER REPRESENTATION OF THE COHERENT STATE 611 COHERENT STATES AS DISPLACED VACUUM STATES THE DISPLACEMENT OPERATOR PROPERTIES OF THE DISPLACEMENT OPERATOR THE COORDINATE REPRESENTATION OF A COHERENT STATE 612 QUASI-ORTHONORMALITY, CLOSURE AND TRACE FOR COHERENT STATES THE SET OF COHERENT-STATE VECTORS NORMALIZATION QUASI-ORTHOGONALITY CLOSURE COHERENT STATE EXPANSION OF A FOCK STATE OVER-COMPLETENESS OF COHERENT STATES TRACE OF AN OPERATOR USING COHERENT STATES 613 FIELD FLUCTUATIONS IN THE COHERENT STATE THE QUADRATURE UNCERTAINTY RELATION FOR COHERENT STATES COMPARISON OF VARIANCE FOR COHERENT AND FOCK STATES 614 INTRODUCTION TO SQUEEZED STATES 615 THE SQUEEZING OPERATOR AND SQUEEZED STATES DEFINITION OF THE SQUEEZING OPERATOR DEFINITION OF THE SQUEEZED STATE THE SQUEEZED CREATION AND ANNIHILATION OPERATORS THE SQUEEZED EM QUADRATURE OPERATORS VARIANCE OF THE EM QUADRATURE COORDINATE REPRESENTATION OF SQUEEZED STATES 616 SOME STATISTICS FOR SQUEEZED STATES THE AVERAGE ELECTRIC FIELD IN A SQUEEZED COHERENT STATE THE VARIANCE OF THE ELECTRIC FIELD IN A SQUEEZED COHERENT STATE THE AVERAGE OF THE HAMILTONIAN IN A SQUEEZED COHERENT STATE PHOTON STATISTICS FOR THE SQUEEZED STATE 617 THE WIGNER DISTRIBUTION THE WIGNER FORMULA AND AN EXAMPLE DERIVATION OF THE WIGNER FORMULA EXAMPLE OF THE WIGNER FUNCTION 618 MEASURING THE NOISE IN SQUEEZED STATES CONTENTS 619 REVIEW EXERCISES 620 FURTHER READING INTRODUCTION TO THE QUANTUM MECHANICAL DIPOLE MOMENT COMPARISON OF THE CLASSICAL AND QUANTUM MECHANICAL DIPOLE THE QUANTUM MECHANICAL DIPOLE MOMENT A COMMENT ON VISUALIZING AN OSCILLATING ELECTRON IN A HARMONIC POTENTIAL INTRODUCTION TO OPTICAL TRANSITIONS THE EM INTERACTION POTENTIAL THE INTEGRAL FOR THE PROBABILITY AMPLITUDE ROTATING WAVE APPROXIMATION ABSORPTION EMISSION DISCUSSION OF THE RESULTS FERMI’S GOLDEN RULE DEFINITION OF THE DENSITY OF STATES EQUATIONS FOR FERMI’S GOLDEN RULE INTRODUCTION TO LASER GAIN INTRODUCTION TO THE ELECTROMAGNETIC LAGRANGIAN AND FIELD EQUATIONS A SUMMARY OF RESULTS AND NOTATION THE EM LAGRANGIAN AND HAMILTONIAN 4-VECTOR FORM OF MAXWELL’S EQUATIONS FROM THE LAGRANGIAN 3-VECTOR FORM OF MAXWELL’S EQUATIONS THE CLASSICAL HAMILTONIAN FOR FIELDS, PARTICLES AND INTERACTIONS THE EM HAMILTONIAN DENSITY THE CANONICAL FIELD MOMENTUM EVALUATING THE HAMILTONIAN DENSITY THE FIELD AND INTERACTION HAMILTONIAN THE HAMILTONIAN FOR FIELDS, PARTICLES AND THEIR INTERACTIONS DISCUSSION THE QUANTUM HAMILTONIAN FOR THE MATTER–LIGHT INTERACTION DISCUSSION OF THE CLASSICAL INTERACTION ENERGY SCHRODINGER’S EQUATION WITH THE MATTER–LIGHT INTERACTION THE ORIGIN OF THE DIPOLE OPERATOR THE SEMICLASSICAL FORM OF THE INTERACTION HAMILTONIAN STIMULATED AND SPONTANEOUS EMISSION USING FOCK STATES RESTATEMENT OF FERMI’S GOLDEN RULE THE DIPOLE APPROXIMATION CALCULATE MATRIX ELEMENTS STIMULATED AND SPONTANEOUS EMISSION INTRODUCTION TO MATTER AND LIGHT AS SYSTEMS THE COMPLETE SYSTEM INTRODUCTION TO HOMOGENEOUS BROADENING LIOUVILLE EQUATION FOR THE DENSITY OPERATOR THE LIOUVILLE EQUATION USING THE FULL HAMILTONIAN THE LIOUVILLE EQUATION USING A PHENOMENOLOGICAL RELAXATION TERM 710 THE LIOUVILLE EQUATION FOR THE DENSITY MATRIX WITH RELAXATION 7101 PRELIMINARIES CONTENTS 7102 ASSUMPTIONS FOR THE DENSITY MATRIX 7103 LIOUVILLE’S EQUATION FOR THE DENSITY MATRIX WITHOUT THERMAL EQUILIBRIUM 7104 THE LIOUVILLE EQUATION FOR THE DENSITY MATRIX WITH THERMAL EQUILIBRIUM 7105 THE DEPHASING TIME 7106 THE CARRIER RELAXATION TIME 711 A SOLUTION TO THE LIOUVILLE EQUATION FOR THE DENSITY MATRIX 7111 EVALUATING THE COMMUTATOR 7112 TWO INDEPENDENT EQUATIONS 7113 THE OPTICAL BLOCH EQUATIONS 7114 THE SOLUTIONS 712 GAIN, ABSORPTION AND INDEX FOR INDEPENDENT TWO LEVEL ATOMS 7121 THE QUANTUM POLARIZATION AND THE POLARIZATION ENVELOPE FUNCTIONS 7122 THE QUANTUM POLARIZATION AND MACROSCOPIC QUANTITIES 7123 COMPARING THE CLASSICAL AND QUANTUM MECHANICAL POLARIZATION 7124 THE NATURAL LINE SHAPE FUNCTION 7125 QUANTUM MECHANICAL GAIN 7126 DISCUSSION OF RESULTS 7127 COMMENTS ON SATURATION POWER AND INTENSITY 713 BROADENING MECHANISMS 7131 HOMOGENEOUS BROADENING 7132 INHOMOGENEOUS BROADENING 7133 HOLE BURNING 714 INTRODUCTION TO JAYNES-CUMMINGS’ MODEL 7141 THE PAULI OPERATORS 7142 THE ATOMIC HAMILTONIAN 7143 THE FREE-FIELD HAMILTONIAN 7144 THE INTERACTION HAMILTONIAN 7145 ATOMIC AND INTERACTION HAMILTONIANS USING FERMION OPERATORS 7146 THE FULL HAMILTONIAN 715 THE INTERACTION REPRESENTATION FOR THE JAYNES-CUMMINGS’ MODEL 7151 ATOMIC CREATION AND ANNIHILATION OPERATORS 7152 THE BOSON CREATION AND ANNIHILATION OPERATORS 7153 INTERACTION REPRESENTATION OF THE SUBSYSTEM DENSITY OPERATORS 7154 THE INTERACTION REPRESENTATION OF THE DIRECT-PRODUCT DENSITY OPERATOR 7155 RATE EQUATION FOR THE DENSITY OPERATOR IN THE INTERACTION REPRESENTATION 716 THE MASTER EQUATION 7161 THE SYSTEM 7162 MULTIPLE RESERVOIRS 7163 DYNAMICS AND THE PERTURBATION EXPANSION 7164 THE LANGEVIN DISPLACEMENT TERM 7165 RESERVOIR CORRELATION TIME AND THE COURSE GRAIN DERIVATIVE 7166 THE RELAXATION TERM 7167 THE PAULI MASTER EQUATION 717 QUANTUM MECHANICAL FLUCTUATION-DISSIPATION THEOREM 7171 SOME INTRODUCTORY COMMENTS CONTENTS 7172 QUANTUM MECHANICAL FLUCTUATION DISSIPATION THEOREM 7173 THE AVERAGE OF THE LANGEVIN NOISE TERM 7174 DAMPING OF THE SMALL SYSTEM 718 REVIEW EXERCISES 719 FURTHER READING EFFECTIVE MASS, DENSITY OF STATES AND THE FERMI DISTRIBUTION EFFECTIVE MASS INTRODUCTION TO BOUNDARY CONDITIONS THE FIXED ENDPOINT BOUNDARY CONDITIONS THE PERIODIC BOUNDARY CONDITION THE DENSITY OF K-STATES THE ELECTRON DENSITY OF ENERGY STATES FOR A 2-D CRYSTAL OVERLAPPING BANDS DENSITY OF STATES FROM FIXED-ENDPOINT BOUNDARY CONDITIONS CHANGING SUMMATIONS TO INTEGRALS 8110 A BRIEF REVIEW OF THE FERMI-DIRAC DISTRIBUTION 8111 THE QUASI-FERMI LEVELS THE BLOCH WAVE FUNCTION FREE ELECTRON MODEL THE NEARLY FREE ELECTRON MODEL INTRODUCTION TO THE BLOCH WAVE FUNCTION ORTHONORMALITY RELATION FOR THE BLOCH WAVE FUNCTIONS THE EFFECTIVE MASS EQUATION DENSITY OF STATES FOR NANOSTRUCTURES ENVELOPE FUNCTION APPROXIMATION SUMMARY OF SOLUTION TO THE SCHRODINGER WAVE EQUATION FOR THE QUANTUM WELL DENSITY OF ENERGY STATES FOR THE QUANTUM WELL THE DENSITY OF ENERGY STATES FOR THE QUANTUM WIRE THE QUANTUM BOX THE REDUCED DENSITY OF STATES AND QUASI-FERMI LEVELS THE REDUCED DENSITY OF STATES QUANTUM WELL REDUCED DENSITY OF STATES THE QUASI-FERMI LEVELS FERMI’S GOLDEN RULE FOR SEMICONDUCTOR DEVICES VECTOR POTENTIAL FORM OF THE INTERACTION THE MATRIX ELEMENTS FOR THE HOMOJUNCTION DEVICES THE QUANTUM WELL SYSTEM FERMI’S GOLDEN RULE AND SEMICONDUCTOR GAIN HOMOJUNCTION EMITTERS AND DETECTORS THE GAIN FOR QUANTUM WELL MATERIALS GAIN FOR QUANTUM DOT MATERIALS EXAMPLE OF A HOMOJUNCTION 2-D LASER WITH UNEQUAL BAND MASSES THE LIOUVILLE EQUATION AND SEMICONDUCTOR GAIN HOMOJUNCTION DEVICES QUANTUM WELL MATERIAL QUANTUM DOT MATERIAL CONTENTS PICTORIAL REPRESENTATION OF THE STIMULATED EMISSION PROCESS AN INCIDENT WAVE (LEFT) INDUCES THE ELECTRON TO MAKE A TRANSITION TO A LOWER ENERGY LEVEL THEREBY PRODUCING A SECOND WAVE (RIGHT)