1. Lasers work by stimulating emission of photons within an optical cavity, achieving gain through stimulated emission. 2. The optical cavity contains two highly reflective mirrors, forming a Fabry-Perot cavity, which provides feedback through multiple reflections satisfying resonance conditions. 3. Lasers can operate in multiple longitudinal and transverse modes simultaneously, but single modes are preferred, achieved through additional elements that introduce controlled loss for other modes.

1. Laser basics
Optics, Eugene Hecht, Chpt. 13;
Optical resonator tutorial:
http://www.dewtronics.com/tutorials/lasers/leot/

2. Laser oscillation
Laser 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

3. Fabry-Perot cavity for feedback
• High reflectivity mirrors
• Low loss per round trip
• Must remember resonance conditions
– round trip path is multiple of l

4. • High reflectivity Fabry-Perot cavity
• Boundary conditions
– field is zero on mirrors
• Multiple wavelengths possible
– agrees with resonance conditions
Laser longitudinal modes
Classical mechanics analog
Multi-mode laser
Fabry-Perot boundary conditions
Multiple resonant frequencies

5. Single longitudinal mode lasers
• Insert etalon into cavity
• Use low reflectivity etalon
– low loss

6. 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
Frequencies of transverse modes
Transverse laser modes
0
2
2








 E
c
n
E
w
0
2
2

 x
m
k
dt
x
d
0
2 2
2
2
2
2
2
2
2




































E
k
c
n
y
E
x
E
z
E
ik
z
E w

7. Single transverse mode lasers
• Put aperture in laser
• Create loss for higher order modes
Multi-longitudinal Multi-transverse&long. Single mode

8. Gaussian beams
• Zero order mode is Gaussian
• Intensity profile:
• beam waist: w0
• confocal parameter: z
• far from waist
• divergence angle
2
2
/
2
0
w
r
e
I
I 

2
2
0
0 1 









w
z
w
w

l
l
 2
0
w
zR 
0
w
z
w

l

0
0
637
.
0
2
w
w
l

l



Gaussian propagation

9. 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
2
2
/
2
0
w
r
e
I
I 


10. 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