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Laser basics
Optics, Eugene Hecht, Chpt. 13;Optical resonator tutorial:
http://www.dewtronics.com/tutorials/lasers/leot/
Laser oscillationLaser is oscillator• Like servo with positive feedback • Greater than unity gain
Ruby laser example
Laser turn-on and gain saturation
Laser gain and losses
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
• High reflectivity Fabry-Perot cavity• Boundary conditions
– field is zero on mirrors• Multiple wavelengths possible
– agrees with resonance conditions
Laser longitudinal modesClassical mechanics analog
Multi-mode laser
Fabry-Perot boundary conditions
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 -it
• Separate out z dependence
• Solutions for x and y are Hermite polynomials
Frequencies of transverse modes
Transverse laser modes
02
2
EcnE
02
2
xmk
dtxd
02 22
2
2
2
2
2
2
Ek
cn
yE
xE
zEik
zE
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
22 /20
wreII
2
20
0 1
wzww
2
0wzR
0wzw
00
637.02ww
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 / ( d2
FWHM)
• Overestimates peak: I0 = Iavg/1.4
22 /20
wreII
Resonator options• Best known -- planar, concentric, confocal• Confocal unique
– mirror alignment not critical– position is critical– transverse mode frequencies identical
Types of resonators
Special cases
