Laser basicsOptics, Eugene Hecht, Chpt. 13;Optical resonator tutorial: Laser oscillationLaser is oscillator•Like servo with positive feedback •Greater than unity gainRuby laser exampleLaser turn-on and gain saturationLaser gain and lossesGain decreases as output power increases• Saturation Fabry-Perot cavity for feedback•High reflectivity mirrors•Low loss per round trip•Must remember resonance conditions–round trip path is multiple of l •High reflectivity Fabry-Perot cavity•Boundary conditions–field is zero on mirrors•Multiple wavelengths possible–agrees with resonance conditionsLaser longitudinal modesClassical mechanics analogMulti-mode laserFabry-Perot boundary conditionsMultiple resonant frequencies Single longitudinal mode lasers•Insert etalon into cavity•Use low reflectivity etalon–low loss Laser transverse modes•Wave equation looks like harmonic oscillator•Ex: E = E e -iwt•Separate out z dependence •Solutions for x and y are Hermite polynomialsFrequencies of transverse modesTransverse laser modes Single transverse mode lasers•Put aperture in laser•Create loss for higher order modesMulti-longitudinal Multi-transverse&long. Single mode Gaussian beams•Zero order mode is Gaussian•Intensity profile:•beam waist: w0•confocal parameter: z•far from waist•divergence angle Gaussian propagation Power distribution in Gaussian•Intensity distribution:•Experimentally to measure full width at half maximum (FWHM) diameter•Relation is dFWHM = w 2 ln2 ~ 1.4 w•Define average intensity•Iavg = 4 P / (p d2FWHM)•Overestimates peak: I0 = Iavg/1.4 Resonator options•Best known -- planar, concentric, confocal•Confocal unique–mirror alignment not critical–position is critical–transverse mode frequencies identicalTypes of resonatorsSpecial cases 。