激光原理英文
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– field is zero on mirrors
• Multiple wavelengths possible
– agrees with resonance conditions
Classical mechanics analog
Fabry-Perot boundary conditions
Multi-mode laser
Resonator options
• Best known -- planar, concentric, confocal • Confocal unique
– mirror alignment not critical – position is critical – transverse mode frequencies identical
Laser basics
Optics, Eugene Hecht, Chpt. 13; Optical reser oscillation
Laser is oscillator • Like servo with positive feedback • Greater than unity gain
Laser gain and losses
Ruby laser example
Laser turn-on and gain saturation
Gain decreases as output power increases • Saturation
Fabry-Perot cavity for feedback
lz w02
• confocal parameter: z
zR
w
2 0
l
• far from waist
w lz w0
• divergence angle
2l 0.637l
w0
w0
Gaussian propagation
Power distribution in Gaussian
•
Intensity distribution:
Multi-longitudinal Multi-transverse&long. Single mode
Gaussian beams
• Zero order mode is Gaussian
• •
Intensity profile:
I
I e2r2/w2 0
beam waist: w0
2
w w0
1
Multiple resonant frequencies
Single longitudinal mode lasers
• Insert etalon into cavity • Use low reflectivity etalon
– low loss
Laser transverse modes
• 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
Special cases
Types of resonators
I
I e2r2/w2 0
• 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
• Wave equation looks like harmonic oscillator
•
Ex: E = E e -iwt
2E
nw2
E0
d2x dt2
k m
x
0
c
• Separate out z dependence
2 zE 22ik E z 2 xE 2 2 yE 2 w c n 2k2 E0
• High reflectivity mirrors • Low loss per round trip • Must remember resonance conditions
– round trip path is multiple of l
Laser longitudinal modes
• High reflectivity Fabry-Perot cavity • Boundary conditions
• Multiple wavelengths possible
– agrees with resonance conditions
Classical mechanics analog
Fabry-Perot boundary conditions
Multi-mode laser
Resonator options
• Best known -- planar, concentric, confocal • Confocal unique
– mirror alignment not critical – position is critical – transverse mode frequencies identical
Laser basics
Optics, Eugene Hecht, Chpt. 13; Optical reser oscillation
Laser is oscillator • Like servo with positive feedback • Greater than unity gain
Laser gain and losses
Ruby laser example
Laser turn-on and gain saturation
Gain decreases as output power increases • Saturation
Fabry-Perot cavity for feedback
lz w02
• confocal parameter: z
zR
w
2 0
l
• far from waist
w lz w0
• divergence angle
2l 0.637l
w0
w0
Gaussian propagation
Power distribution in Gaussian
•
Intensity distribution:
Multi-longitudinal Multi-transverse&long. Single mode
Gaussian beams
• Zero order mode is Gaussian
• •
Intensity profile:
I
I e2r2/w2 0
beam waist: w0
2
w w0
1
Multiple resonant frequencies
Single longitudinal mode lasers
• Insert etalon into cavity • Use low reflectivity etalon
– low loss
Laser transverse modes
• 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
Special cases
Types of resonators
I
I e2r2/w2 0
• 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
• Wave equation looks like harmonic oscillator
•
Ex: E = E e -iwt
2E
nw2
E0
d2x dt2
k m
x
0
c
• Separate out z dependence
2 zE 22ik E z 2 xE 2 2 yE 2 w c n 2k2 E0
• High reflectivity mirrors • Low loss per round trip • Must remember resonance conditions
– round trip path is multiple of l
Laser longitudinal modes
• High reflectivity Fabry-Perot cavity • Boundary conditions