Contents

Part 1 Fundamentals of light-matter interaction 
1.1 
Fundamentals of the semiclassical laser theory 
V.A. Lopota, H. Weber ............................................... 3

1.1.1 
The laser oscillator ...................................................... 3

1.1.2 
The electromagnetic .eld................................................. 5

1.1.2.1 
Maxwells equations ..................................................... 5

1.1.2.2 
Homogeneous, isotropic, linear dielectrics................................... 6

1.1.2.2.1 
The plane wave ......................................................... 7

1.1.2.2.2 
The spherical wave ...................................................... 8

1.1.2.2.3 
The slowly varying envelope (SVE) approximation........................... 9

1.1.2.2.4 
The SVE-approximation for di.raction..................................... 9

1.1.2.3 
Propagation in doped media .............................................. 10

1.1.3 
Interaction with two-level systems ......................................... 11

1.1.3.1 
The two-level system .................................................... 11

1.1.3.2 
The dipole approximation ................................................ 12

1.1.3.2.1 
Inversion density and polarization ......................................... 12

1.1.3.2.2 
The interaction with a monochromatic .eld................................. 14

1.1.3.3 
The MaxwellBloch equations............................................. 15

1.1.3.3.1 
Decay time T1 of the upper level (energy relaxation) ......................... 15

1.1.3.3.1.1 
Spontaneous emission.................................................... 15

1.1.3.3.1.2 
Interaction with the host material ......................................... 15

1.1.3.3.1.3 
Pumping process ........................................................ 16

1.1.3.3.2 
Decay time T2 of the polarization (entropy relaxation) ....................... 16

1.1.4 
Steady-state solutions.................................................... 17

1.1.4.1 
Inversion density and polarization ......................................... 17

1.1.4.2 
Small-signal solutions .................................................... 19

1.1.4.3 
Strong-signal solutions ................................................... 19

1.1.5 
Adiabatic equations ..................................................... 20

1.1.5.1 
Rate equations.......................................................... 20

1.1.5.2 
Thermodynamic considerations............................................ 21

1.1.5.3 
Pumping schemes and complete rate equations .............................. 22

1.1.5.3.1 
The three-level system ................................................... 23

1.1.5.3.2 
The four-level system .................................................... 24

1.1.5.4 
Adiabatic pulse ampli.cation ............................................. 25

1.1.5.5 
Rate equations for steady-state laser oscillators.............................. 26

1.1.6 
Line shape and line broadening ........................................... 26

1.1.6.1 
Normalized shape functions............................................... 27

1.1.6.1.1 
Lorentzian line shape .................................................... 27

1.1.6.1.2 
Gaussian line shape...................................................... 27

1.1.6.1.3	
Normalization of line shapes .............................................. 27

1.1.6.2	
Mechanisms of line broadening ............................................ 28

1.1.6.2.1	
Spontaneous emission.................................................... 28

1.1.6.2.2	
Doppler broadening...................................................... 28

1.1.6.2.3	
Collision or pressure broadening........................................... 28

1.1.6.2.4	
Saturation broadening ................................................... 29

1.1.6.3	
Types of broadening ..................................................... 29

1.1.6.3.1	
Homogeneous broadening................................................. 29

1.1.6.3.2	
Inhomogeneous broadening ............................................... 30

1.1.6.4	
Time constants ......................................................... 31

1.1.7	
Coherent interaction ..................................................... 31

1.1.7.1	
The Feynman representation of interaction ................................. 32

1.1.7.2	
Constant local electric .eld ............................................... 33

1.1.7.3	
Propagation of resonant coherent pulses.................................... 34

1.1.7.3.1	
Steady-state propagation of np-pulses...................................... 35

1.1.7.3.1.1	
2p-pulse in a loss-free medium ............................................ 35

1.1.7.3.1.2	
p-pulse in an amplifying medium.......................................... 36

1.1.7.3.2	
Superradiance .......................................................... 37

1.1.8	
Notations .............................................................. 37


X	Contents 
References for 1.1 ....................................................... 40

Part 2 Radiometry 
2.1	
De.nition and measurement of radiometric quantities 

B. 
Wende, J. Fischer ................................................. 45

2.1.1	
Introduction ............................................................ 45

2.1.2	
De.nition of radiometric quantities ........................................ 45

2.1.3	
Radiometric standards ................................................... 47

2.1.3.1	
Primary standards....................................................... 47

2.1.3.2	
Secondary standards..................................................... 48

2.1.4	
Outlook  State of the art and trends ...................................... 50



References for 2.1 ....................................................... 51

2.2	
Beam characterization 
B. 
Eppich	............................................................. 53

2.2.1	
Introduction ............................................................ 53

2.2.2	
The Wigner distribution ................................................. 53

2.2.3	
The second-order moments of the Wigner distribution........................ 55

2.2.4	
The second-order moments and related physical properties.................... 56

2.2.4.1	
Near .eld .............................................................. 56

2.2.4.2	
Far .eld................................................................ 58

2.2.4.3	
Phase paraboloid and twist ............................................... 59

2.2.4.4	
Invariants .............................................................. 60

2.2.4.5	
Propagation of beam widths and beam propagation ratios .................... 60

2.2.5	
Beam classi.cation ...................................................... 61

2.2.5.1	
Stigmatic beams ........................................................ 62

2.2.5.2	
Simple astigmatic beams ................................................. 63

2.2.5.3	
General astigmatic beams ................................................ 64

2.2.5.4	
Pseudo-symmetric beams................................................. 64

2.2.5.5	
Intrinsic astigmatism and beam conversion ................................. 65

2.2.6	
Measurement procedures ................................................. 66

2.2.7	
Beam positional stability ................................................. 67

2.2.7.1	
Absolute .uctuations .................................................... 67

2.2.7.2	
Relative .uctuations..................................................... 69

2.2.7.3	
E.ective long-term beam widths .......................................... 69



References for 2.2 ....................................................... 70

Part 3 Linear optics 
3.1	
Linear optics 


R. 
G
uther ............................................................ 73

3.1.1 
Wave equations ......................................................... 73

3.1.2 
Polarization ............................................................ 75

3.1.3 
Solutions of the wave equation in free space................................. 78

3.1.3.1 
Wave equation .......................................................... 78

3.1.3.1.1 
Monochromatic plane wave ............................................... 78

3.1.3.1.2 
Cylindrical vector wave .................................................. 78

3.1.3.1.3 
Spherical vector wave .................................................... 78

3.1.3.2 
Helmholtz equation...................................................... 79

3.1.3.2.1 
Plane wave ............................................................. 79

3.1.3.2.2 
Cylindrical wave ........................................................ 79

3.1.3.2.3 
Spherical wave .......................................................... 79

3.1.3.2.4 
Di.raction-free beams.................................................... 79

3.1.3.2.4.1 
Di.raction-free Bessel beams.............................................. 79

3.1.3.2.4.2 
Real Bessel beams....................................................... 80

3.1.3.2.4.3 
Vectorial Bessel beams ................................................... 80

3.1.3.3 
Solutions of the slowly varying envelope equation............................ 80

3.1.3.3.1 
Gauss-Hermite beams (rectangular symmetry) .............................. 81

3.1.3.3.2 
Gauss-Laguerre beams (circular symmetry) ................................. 83

3.1.3.3.3 
Cross-sectional shapes of the Gaussian modes ............................... 83

3.1.4 
Di.raction.............................................................. 84

3.1.4.1 
Vector theory of di.raction ............................................... 85

3.1.4.2 
Scalar di.raction theory.................................................. 85

3.1.4.3 
Time-dependent di.raction theory......................................... 89

3.1.4.4 
Fraunhofer di.raction patterns............................................ 89

3.1.4.4.1 
Rectangular aperture with dimensions 2a 2b .............................. 89

3.1.4.4.2 
Circular aperture with radius a ........................................... 90

3.1.4.4.2.1 
Applications ............................................................ 92

3.1.4.4.3 
Gratings ............................................................... 92

3.1.4.5 
Fresnels di.raction .gures ............................................... 93

3.1.4.5.1 
Fresnels di.raction on a slit .............................................. 93

3.1.4.5.2 
Fresnels di.raction through lens systems (paraxial di.raction)................ 94

3.1.4.6 
Fourier optics and di.ractive optics........................................ 94

3.1.5 
Optical materials........................................................ 95

3.1.5.1 
Dielectric media......................................................... 96

3.1.5.2 
Optical glasses .......................................................... 97

3.1.5.3	
Dispersion characteristics for short-pulse propagation ........................ 97

3.1.5.4	
Optics of metals and semiconductors....................................... 98

3.1.5.5	
Fresnels formulae ....................................................... 98

3.1.5.6	
Special cases of refraction ................................................101

nand 
3.1.5.6.1	Two dielectric isotropic homogeneous media (n. are real) ...............101

3.1.5.6.2	
Variation of the angle of incidence.........................................101

3.1.5.6.2.1	
External re.ection (n<n)...............................................101

3.1.5.6.2.2	
Internal re.ection (n>n) ...............................................101

3.1.5.6.3	
Re.ection at media with complex refractive index 



Contents	XI 
XII	Contents 

n=1 and 
(Case n=n. +ik) ...........................................103

3.1.5.7	
Crystal optics...........................................................104

3.1.5.7.1	
Classi.cation ...........................................................104

3.1.5.7.2	
Birefringence (example: uniaxial crystals)...................................106

3.1.5.8	
Photonic crystals........................................................107

3.1.5.9	
Negative-refractive-index materials ........................................108

3.1.5.10	
References to data of linear optics .........................................108

3.1.6	
Geometrical optics.......................................................108

3.1.6.1	
Gaussian imaging (paraxial range).........................................108

3.1.6.1.1	
Single spherical interface .................................................109

3.1.6.1.2	
Imaging with a thick lens.................................................110

3.1.6.2	
Gaussian matrix (ABCD-matrix, ray-transfer matrix) formalism for paraxial
optics..................................................................111

3.1.6.2.1	
Simple interfaces and optical elements with rotational symmetry ..............112

3.1.6.2.2	
Non-symmetrical optical systems ..........................................112

3.1.6.2.3	
Properties of a system ...................................................112

3.1.6.2.4	
General parabolic systems without rotational symmetry ......................112

3.1.6.2.5	
General astigmatic system................................................116

3.1.6.2.6	
Symplectic optical system ................................................116

3.1.6.2.7	
Misalignments ..........................................................116

3.1.6.3	
Lens aberrations ........................................................117

3.1.7	
Beam propagation in optical systems ......................................120

3.1.7.1	
Beam classi.cation ......................................................120

3.1.7.2	
Gaussian beam: complex q-parameter and its ABCD-transformation............120

3.1.7.2.1	
Stigmatic and simple astigmatic beams.....................................120

3.1.7.2.1.1	
Fundamental Mode ......................................................120

3.1.7.2.1.2	
Higher-order Hermite-Gaussian beams in simple astigmatic beams .............123

3.1.7.2.2	
General astigmatic beam .................................................123

3.1.7.3	
Waist transformation ....................................................124

3.1.7.3.1	
General system (fundamental mode) .......................................124

3.1.7.3.2	
Thin lens (fundamental mode) ............................................124

3.1.7.4	
Collins integral..........................................................126

3.1.7.4.1	
Two-dimensional propagation .............................................126

3.1.7.4.2	
Three-dimensional propagation............................................127

3.1.7.5	
Gaussian beams in optical systems with stops, aberrations, and waveguide
coupling................................................................127

3.1.7.5.1	
Field distributions in the waist region of Gaussian beams including stops and
wave aberrations by optical system ........................................127

3.1.7.5.2	
Mode matching for beam coupling into waveguides ..........................128

3.1.7.5.3	
Free-space coupling of Gaussian modes.....................................128

3.1.7.5.4	
Laser .ber coupling......................................................129


References for 3.1 .......................................................131

Contents	XIII 
Part 4 Nonlinear optics 
4.1	
Frequency conversion in crystals 
G.G. Gurzadyan ......................................................141

4.1.1	
Introduction ............................................................141

4.1.1.1	
Symbols and abbreviations ...............................................141

4.1.1.1.1	
Symbols................................................................141

4.1.1.1.2	
Abbreviations...........................................................142

4.1.1.1.3	
Crystals................................................................142

4.1.1.2	
Historical layout ........................................................143

4.1.2	
Fundamentals...........................................................144

4.1.2.1	
Three-wave interactions ..................................................144

4.1.2.2	
Uniaxial crystals ........................................................145

4.1.2.3	
Biaxial crystals .........................................................145

4.1.2.4	
E.ective nonlinearity ....................................................147

4.1.2.5	
Frequency conversion e.ciency............................................151

4.1.2.5.1	
General approach .......................................................151

4.1.2.5.2	
Plane-wave .xed-.eld approximation.......................................152

4.1.2.5.3	
SHG in nonlinear regime (fundamental wave depletion) ....................154

4.1.3	
Selection of data ........................................................154

4.1.4	
Harmonic generation (second, third, fourth, .fth, and sixth) ..................156

4.1.5	
Sum frequency generation ................................................167

4.1.6	
Di.erence frequency generation ...........................................172

4.1.7	
Optical parametric oscillation.............................................176

4.1.8	
Picosecond continuum generation..........................................186


References for 4.1 .......................................................187

4.2	
Frequency conversion in gases and liquids 
C.R. Vidal ............................................................205

4.2.1	
Fundamentals of nonlinear optics in gases and liquids ........................205

4.2.1.1	
Linear and nonlinear susceptibilities .......................................205

4.2.1.2	
Third-order nonlinear susceptibilities.......................................206

4.2.1.3	
Fundamental equations of nonlinear optics..................................207

4.2.1.4	
Small-signal limit........................................................207

4.2.1.5	
Phase-matching condition ................................................208

4.2.2	
Frequency conversion in gases.............................................209

4.2.2.1	
Metal-vapor inert gas mixtures............................................209

4.2.2.2	
Mixtures of di.erent metal vapors .........................................209

4.2.2.3	
Mixtures of gaseous media................................................209


References for 4.2 .......................................................212

4.3	
Stimulated scattering 
A. 
Laubereau .........................................................217

4.3.1	
Introduction ............................................................217

4.3.1.1	
Spontaneous scattering processes ..........................................217

4.3.1.2	
Relationship between stimulated Stokes scattering and spontaneous scattering ..219

4.3.2	
General properties of stimulated scattering .................................219

4.3.2.1	
Exponential gain by stimulated Stokes scattering ............................219

4.3.2.2	
Experimental observation.................................................220

4.3.2.2.1	
Generator setup.........................................................220

4.3.2.2.2	
Oscillator setup .........................................................220

4.3.2.2.3	
Stimulated ampli.cation setup ............................................221

4.3.2.3	
Four-wave interactions ...................................................221

4.3.2.3.1	
Third-order nonlinear susceptibility........................................221

4.3.2.3.2	
Stokesanti-Stokes coupling...............................................222

4.3.2.3.3	
Higher-order Stokes and anti-Stokes emission ...............................222

4.3.2.4	
Transient stimulated scattering............................................222

4.3.3	
Individual scattering processes ............................................223

4.3.3.1	
Stimulated Raman scattering (SRS) .......................................223

4.3.3.2	
Stimulated Brillouin scattering (SBS) and stimulated thermal Brillouin
scattering (STBS) .......................................................227

4.3.3.3	
Stimulated Rayleigh scattering processes, SRLS, STRS, and SRWS ............228


XIV	Contents 
References for 4.3 .......................................................232

4.4	
Phase conjugation 
H.J. Eichler, A. Hermerschmidt, O. Mehl ............................235

4.4.1	
Introduction ............................................................235

4.4.2	
Basic mathematical description ...........................................236

4.4.3	
Phase conjugation by degenerate four-wave mixing ..........................236

4.4.4	
Self-pumped phase conjugation............................................237

4.4.5	
Applications of SBS phase conjugation .....................................240

4.4.6	
Photorefraction .........................................................242


References for 4.4 .......................................................245

Index ............................................................................247


