PRINCIPLES OF LASERS AND OPTICS
CONTENTS 1 SCALAR WAVE EQUATIONS AND DIFFRACTION OF LASER RADIATION 1 1 INTRODUCTION 1 2 THE SCALAR WAVE EQUATION THE SOLUTION OF THE SCALAR WAVE EQUATION BY GREEN’S FUNCTION – KIRCHHOFF’S DIFFRACTION FORMULA 1 3 1 THE GENERAL GREEN’S FUNCTION G GREEN’S FUNCTION, G 1, FOR U KNOWN ON A PLANAR APERTURE GREEN’S FUNCTION FOR ?U KNOWN ON A PLANAR APERTURE, G THE EXPRESSION FOR KIRCHHOFF’S INTEGRAL IN ENGINEERING ANALYSIS 1 3 5 FRESNEL AND FRAUNHOFER DIFFRACTION 1 4 APPLICATIONS OF THE ANALYSIS OF TEM WAVES 1 4 1 FAR ?ELD DIFFRACTION PATTERN OF AN APERTURE FRAUNHOFER DIFFRACTION IN THE FOCAL PLANE OF A LENS THE LENS AS A TRANSFORMATION ELEMENT INTEGRAL EQUATION FOR OPTICAL RESONATORS SUPERPOSITION THEORY AND OTHER MATHEMATICAL TECHNIQUES DERIVED FROM KIRCHHOFF’S DIFFRACTION FORMULA REFERENCES GAUSSIAN MODES IN OPTICAL LASER CAVITIES AND GAUSSIAN BEAM OPTICS MODES IN CONFOCAL CAVITIES THE SIMPLI?ED INTEGRAL EQUATION FOR CONFOCAL CAVITIES ANALYTICAL SOLUTIONS OF THE MODES IN CONFOCAL CAVITIES PROPERTIES OF RESONANT MODES IN CONFOCAL CAVITIES RADIATION ?ELDS INSIDE AND OUTSIDE THE CAVITY FAR ?ELD PATTERN OF THE TEM MODES GENERAL EXPRESSION FOR THE TEMLM MODES EXAMPLE ILLUSTRATING THE PROPERTIES OF CONFOCAL CAVITY MODES MODES IN NON-CONFOCAL CAVITIES FORMATION OF A NEW CAVITY FOR KNOWN MODES OF CONFOCAL RESONATORS FINDING THE VIRTUAL EQUIVALENT CONFOCAL RESONATOR FOR A GIVEN SET OF RE?ECTORS FORMAL PROCEDURE TO ?ND THE RESONANT MODES IN NON-CONFOCAL CAVITIES EXAMPLE OF RESONANT MODES IN A NON-CONFOCAL CAVITY GAUSSIAN BEAM SOLUTION OF THE VECTOR WAVE EQUATION PROPAGATION AND TRANSFORMATION OF GAUSSIAN BEAMS (THE ABCD MATRIX) PHYSICAL MEANING OF THE TERMS IN THE GAUSSIAN BEAM EXPRESSION DESCRIPTION OF GAUSSIAN BEAM PROPAGATION BY MATRIX TRANSFORMATION EXAMPLE OF A GAUSSIAN BEAM PASSING THROUGH A LENS EXAMPLE OF A GAUSSIAN BEAM PASSING THROUGH A SPATIAL ?LTER EXAMPLE OF A GAUSSIAN BEAM PASSING THROUGH A PRISM EXAMPLE OF FOCUSING A GAUSSIAN BEAM EXAMPLE OF GAUSSIAN MODE MATCHING MODES IN COMPLEX CAVITIES EXAMPLE OF THE RESONANCE MODE IN A RING CAVITY GUIDED WAVE MODES AND THEIR PROPAGATION ASYMMETRIC PLANAR WAVEGUIDES TE AND TM MODES IN PLANAR WAVEGUIDES TE PLANAR WAVEGUIDE MODES TE PLANAR GUIDED WAVE MODES TE PLANAR GUIDED WAVE MODES IN A SYMMETRICAL WAVEGUIDE CUT-OFF CONDITION FOR TE PLANAR GUIDED WAVE MODES PROPERTIES OF TE PLANAR GUIDED WAVE MODES TE PLANAR SUBSTRATE MODES TE PLANAR AIR MODES TM PLANAR WAVEGUIDE MODES TM PLANAR GUIDED WAVE MODES TM PLANAR GUIDED WAVE MODES IN A SYMMETRICAL WAVEGUIDE CUT-OFF CONDITION FOR TM PLANAR GUIDED WAVE MODES PROPERTIES OF TM PLANAR GUIDED WAVE MODES TM PLANAR SUBSTRATE MODES TM PLANAR AIR MODES GENERALIZED PROPERTIES OF GUIDED WAVE MODES IN PLANAR WAVEGUIDES AND APPLICATIONS PLANAR GUIDED WAVES PROPAGATING IN OTHER DIRECTIONS IN THE YZ PLANE HELMHOLTZ EQUATION FOR THE GENERALIZED GUIDED WAVE MODES IN PLANAR WAVEGUIDES APPLICATIONS OF GENERALIZED GUIDED WAVES IN PLANAR WAVEGUIDES RECTANGULAR CHANNEL WAVEGUIDES AND EFFECTIVE INDEX ANALYSIS EXAMPLE FOR THE EFFECTIVE INDEX METHOD PROPERTIES OF CHANNEL GUIDED WAVE MODES PHASED ARRAY CHANNEL WAVEGUIDE DEMULTIPLEXER IN WDM SYSTEMS GUIDED WAVE MODES IN SINGLE-MODE ROUND OPTICAL ?BERS GUIDED WAVE SOLUTIONS OF MAXWELL’S EQUATIONS PROPERTIES OF THE GUIDED WAVE MODES PROPERTIES OF OPTICAL ?BERS CLADDING MODES EXCITATION OF GUIDED WAVE MODES GUIDED WAVE INTERACTIONS AND PHOTONIC DEVICES PERTURBATION ANALYSIS FIELDS AND MODES IN A GENERALIZED WAVEGUIDE SIMPLE APPLICATION OF THE PERTURBATION ANALYSIS COUPLING OF MODES IN THE SAME WAVEGUIDE, THE GRATING ?LTER AND THE ACOUSTO-OPTICAL DE?ECTOR GRATING ?LTER IN A SINGLE-MODE WAVEGUIDE ACOUSTO-OPTICAL DE?ECTOR, FREQUENCY SHIFTER, SCANNER AND ANALYZER PROPAGATION OF MODES IN PARALLEL WAVEGUIDES – THE COUPLED MODES AND THE SUPER-MODES MODES IN TWO UNCOUPLED PARALLEL WAVEGUIDES ANALYSIS OF TWO COUPLED WAVEGUIDES BASED ON MODES OF INDIVIDUAL WAVEGUIDES THE DIRECTIONAL COUPLER, VIEWED AS COUPLED INDIVIDUAL WAVEGUIDE MODES DIRECTIONAL COUPLING, VIEWED AS PROPAGATION OF SUPER-MODES SUPER-MODES OF TWO COUPLED NON-IDENTICAL WAVEGUIDES PROPAGATION OF SUPER-MODES IN ADIABATIC BRANCHING WAVEGUIDES AND THE MACH–ZEHNDER INTERFEROMETER ADIABATIC Y-BRANCH TRANSITION SUPER-MODE ANALYSIS OF WAVE PROPAGATION IN A SYMMETRIC Y-BRANCH ANALYSIS OF WAVE PROPAGATION IN AN ASYMMETRIC Y-BRANCH MACH–ZEHNDER INTERFEROMETER PROPAGATION IN MULTIMODE WAVEGUIDES AND MULTIMODE INTERFERENCE COUPLERS MACROSCOPIC PROPERTIES OF MATERIALS FROM STIMULATED EMISSION AND ABSORPTION BRIEF REVIEW OF BASIC QUANTUM MECHANICS BRIEF SUMMARY OF THE ELEMENTARY PRINCIPLES OF QUANTUM MECHANICS EXPECTATION VALUE SUMMARY OF ENERGY EIGEN VALUES AND ENERGY STATES SUMMARY OF THE MATRIX REPRESENTATION TIME DEPENDENT PERTURBATION ANALYSIS OF ? AND THE INDUCED TRANSITION PROBABILITY TIME DEPENDENT PERTURBATION FORMULATION ELECTRIC AND MAGNETIC DIPOLE AND ELECTRIC QUADRUPOLE APPROXIMATIONS PERTURBATION ANALYSIS FOR AN ELECTROMAGNETIC ?ELD WITH HARMONIC TIME VARIATION INDUCED TRANSITION PROBABILITY BETWEEN TWO ENERGY EIGEN STATES MACROSCOPIC SUSCEPTIBILTY AND THE DENSITY MATRIX POLARIZATION AND THE DENSITY MATRIX EQUATION OF MOTION OF THE DENSITY MATRIX ELEMENTS SOLUTIONS FOR THE DENSITY MATRIX ELEMENTS SUSCEPTIBILITY SIGNI?CANCE OF THE SUSCEPTIBILITY COMPARISON OF THE ANALYSIS OF ? WITH THE QUANTUM MECHANICAL ANALYSIS OF INDUCED TRANSITIONS HOMOGENEOUSLY AND INHOMOGENEOUSLY BROADENED TRANSITIONS HOMOGENEOUSLY BROADENED LINES AND THEIR SATURATION INHOMOGENEOUSLY BROADENED LINES AND THEIR SATURATION SOLID STATE AND GAS LASER AMPLI?ER AND OSCILLATOR RATE EQUATION AND POPULATION INVERSION THRESHOLD CONDITION FOR LASER OSCILLATION POWER AND OPTIMUM COUPLING FOR CW LASER OSCILLATORS WITH HOMOGENEOUS BROADENED LINES STEADY STATE OSCILLATION IN INHOMOGENEOUSLY BROADENED LINES Q-SWITCHED LASERS MODE LOCKED LASER OSCILLATORS MODE LOCKING IN LASERS WITH AN INHOMOGENEOUSLY BROADENED LINE MODE LOCKING IN LASERS WITH A HOMOGENEOUSLY BROADENED LINE PASSIVE MODE LOCKING LASER AMPLI?ERS SPONTANEOUS EMISSION NOISE IN LASERS SPONTANEOUS EMISSION: THE EINSTEIN APPROACH SPONTANEOUS EMISSION NOISE IN LASER AMPLI?ERS SPONTANEOUS EMISSION IN LASER OSCILLATORS THE LINE WIDTH OF LASER OSCILLATION RELATIVE INTENSITY NOISE OF LASER OSCILLATORS