Laser oscillation Laser is oscillator Ruby laser example Laser is oscillator Like servo with positive feedback Greater than unity gain Laser gain and losses Laser turn-on and gain saturation Gain 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

Laser longitudinal modes Classical mechanics analog High reflectivity Fabry-Perot cavity Boundary conditions field is zero on mirrors Multiple wavelengths possible agrees with resonance conditions Fabry-Perot boundary conditions Multi-mode laser Multiple 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 polynomials Transverse laser modes Frequencies of transverse modes

Single transverse mode lasers Put aperture in laser Create loss for higher order modes Multi-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 identical Special cases Types of resonators