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Laser basics
Optics, Eugene Hecht, Chpt. 13;
Optical resonator tutorial:
http://www.dewtronics.com/tutorials/lasers/leot/
Laser oscillation
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
Ruby laser example
Fabry-Perot cavity for feedback
• High reflectivity mirrors
• Low loss per round trip
• Must remember resonance conditions
– round trip path is multiple of l
Classical mechanics analog
Laser longitudinal modes
• 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
 nw 
 E 
 E0
 c 
2
d 2x k
 x0
dt 2 m
2
• Separate out z dependence
2

 2E
E   2 E  2 E   wn 
 2  2ik
  2  2     k 2  E  0
 c 

z  x
y
 z


• Solutions for x and y are Hermite polynomials
Frequencies of transverse modes
Transverse laser 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: I  I e 2 r 2 / w2
0
• beam waist: w0
 lz 
w  w0 1   2 
 w0 
2
• confocal parameter: z
w02
zR 
l
• far from waist
w
lz
w0
• divergence angle
2l
l

 0.637
w0
w0
Gaussian propagation
Power distribution in Gaussian
•
•
•
•
•
•
2 r 2 / w2
Intensity distribution: I  I 0e
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 / ( 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
Types of resonators
Special cases