- •Preface
- •Contents
- •1.1 Fundamentals of the semiclassical laser theory
- •1.1.1 The laser oscillator
- •1.1.2.2 Homogeneous, isotropic, linear dielectrics
- •1.1.2.2.1 The plane wave
- •1.1.2.2.2 The spherical wave
- •1.1.2.2.3 The slowly varying envelope (SVE) approximation
- •1.1.2.3 Propagation in doped media
- •1.1.3 Interaction with two-level systems
- •1.1.3.1 The two-level system
- •1.1.3.2 The dipole approximation
- •1.1.3.2.1 Inversion density and polarization
- •1.1.3.3.1 Decay time T1 of the upper level (energy relaxation)
- •1.1.3.3.1.1 Spontaneous emission
- •1.1.3.3.1.2 Interaction with the host material
- •1.1.3.3.1.3 Pumping process
- •1.1.3.3.2 Decay time T2 of the polarization (entropy relaxation)
- •1.1.4 Steady-state solutions
- •1.1.4.1 Inversion density and polarization
- •1.1.4.2 Small-signal solutions
- •1.1.4.3 Strong-signal solutions
- •1.1.5 Adiabatic equations
- •1.1.5.1 Rate equations
- •1.1.5.2 Thermodynamic considerations
- •1.1.5.3 Pumping schemes and complete rate equations
- •1.1.5.3.1 The three-level system
- •1.1.5.3.2 The four-level system
- •1.1.5.5 Rate equations for steady-state laser oscillators
- •1.1.6 Line shape and line broadening
- •1.1.6.1 Normalized shape functions
- •1.1.6.1.1 Lorentzian line shape
- •1.1.6.1.2 Gaussian line shape
- •1.1.6.1.3 Normalization of line shapes
- •1.1.6.2 Mechanisms of line broadening
- •1.1.6.2.1 Spontaneous emission
- •1.1.6.2.2 Doppler broadening
- •1.1.6.2.3 Collision or pressure broadening
- •1.1.6.2.4 Saturation broadening
- •1.1.6.3 Types of broadening
- •1.1.6.3.1 Homogeneous broadening
- •1.1.6.3.2 Inhomogeneous broadening
- •1.1.6.4 Time constants
- •1.1.7 Coherent interaction
- •1.1.7.1 The Feynman representation of interaction
- •1.1.7.3 Propagation of resonant coherent pulses
- •1.1.7.3.2 Superradiance
- •1.1.8 Notations
- •References for 1.1
- •2.1.1 Introduction
- •2.1.3 Radiometric standards
- •2.1.3.1 Primary standards
- •2.1.3.2 Secondary standards
- •References for 2.1
- •2.2 Beam characterization
- •2.2.1 Introduction
- •2.2.2 The Wigner distribution
- •2.2.3 The second-order moments of the Wigner distribution
- •2.2.4 The second-order moments and related physical properties
- •2.2.4.3 Phase paraboloid and twist
- •2.2.4.4 Invariants
- •2.2.4.5 Propagation of beam widths and beam propagation ratios
- •2.2.5.1 Stigmatic beams
- •2.2.5.2 Simple astigmatic beams
- •2.2.5.3 General astigmatic beams
- •2.2.5.4 Pseudo-symmetric beams
- •2.2.5.5 Intrinsic astigmatism and beam conversion
- •2.2.6 Measurement procedures
- •2.2.7 Beam positional stability
- •References for 2.2
- •3 Linear optics
- •3.1 Linear optics
- •3.1.1 Wave equations
- •3.1.2 Polarization
- •3.1.3 Solutions of the wave equation in free space
- •3.1.3.1 Wave equation
- •3.1.3.1.1 Monochromatic plane wave
- •3.1.3.1.2 Cylindrical vector wave
- •3.1.3.1.3 Spherical vector wave
- •3.1.3.2 Helmholtz equation
- •3.1.3.2.1 Plane wave
- •3.1.3.2.2 Cylindrical wave
- •3.1.3.2.3 Spherical wave
- •3.1.3.2.4.2 Real Bessel beams
- •3.1.3.2.4.3 Vectorial Bessel beams
- •3.1.3.3 Solutions of the slowly varying envelope equation
- •3.1.3.3.1 Gauss-Hermite beams (rectangular symmetry)
- •3.1.3.3.2 Gauss-Laguerre beams (circular symmetry)
- •3.1.3.3.3 Cross-sectional shapes of the Gaussian modes
- •3.1.4.4.2 Circular aperture with radius a
- •3.1.4.4.2.1 Applications
- •3.1.4.4.3 Gratings
- •3.1.5 Optical materials
- •3.1.5.1 Dielectric media
- •3.1.5.2 Optical glasses
- •3.1.5.3 Dispersion characteristics for short-pulse propagation
- •3.1.5.4 Optics of metals and semiconductors
- •3.1.5.6 Special cases of refraction
- •3.1.5.6.2 Variation of the angle of incidence
- •3.1.5.7 Crystal optics
- •3.1.5.7.2 Birefringence (example: uniaxial crystals)
- •3.1.5.8 Photonic crystals
- •3.1.5.9 Negative-refractive-index materials
- •3.1.5.10 References to data of linear optics
- •3.1.6 Geometrical optics
- •3.1.6.1 Gaussian imaging (paraxial range)
- •3.1.6.1.1 Single spherical interface
- •3.1.6.1.2 Imaging with a thick lens
- •3.1.6.2.1 Simple interfaces and optical elements with rotational symmetry
- •3.1.6.2.2 Non-symmetrical optical systems
- •3.1.6.2.3 Properties of a system
- •3.1.6.2.4 General parabolic systems without rotational symmetry
- •3.1.6.2.5 General astigmatic system
- •3.1.6.2.6 Symplectic optical system
- •3.1.6.2.7 Misalignments
- •3.1.6.3 Lens aberrations
- •3.1.7 Beam propagation in optical systems
- •3.1.7.2.1 Stigmatic and simple astigmatic beams
- •3.1.7.2.1.1 Fundamental Mode
- •3.1.7.2.1.2 Higher-order Hermite-Gaussian beams in simple astigmatic beams
- •3.1.7.2.2 General astigmatic beam
- •3.1.7.3 Waist transformation
- •3.1.7.3.1 General system (fundamental mode)
- •3.1.7.3.2 Thin lens (fundamental mode)
- •3.1.7.4 Collins integral
- •3.1.7.4.1 Two-dimensional propagation
- •3.1.7.4.2 Three-dimensional propagation
- •3.1.7.5 Gaussian beams in optical systems with stops, aberrations, and waveguide coupling
- •3.1.7.5.1 Field distributions in the waist region of Gaussian beams including stops and wave aberrations by optical system
- •3.1.7.5.2 Mode matching for beam coupling into waveguides
- •3.1.7.5.3 Free-space coupling of Gaussian modes
- •References for 3.1
- •4.1 Frequency conversion in crystals
- •4.1.1 Introduction
- •4.1.1.1 Symbols and abbreviations
- •4.1.1.1.1 Symbols
- •4.1.1.1.2 Abbreviations
- •4.1.1.1.3 Crystals
- •4.1.1.2 Historical layout
- •4.1.2 Fundamentals
- •4.1.2.1 Three-wave interactions
- •4.1.2.2 Uniaxial crystals
- •4.1.2.3 Biaxial crystals
- •4.1.2.5.1 General approach
- •4.1.3 Selection of data
- •4.1.5 Sum frequency generation
- •4.1.7 Optical parametric oscillation
- •4.1.8 Picosecond continuum generation
- •References for 4.1
- •4.2 Frequency conversion in gases and liquids
- •4.2.1 Fundamentals of nonlinear optics in gases and liquids
- •4.2.1.1 Linear and nonlinear susceptibilities
- •4.2.1.2 Third-order nonlinear susceptibilities
- •4.2.1.3 Fundamental equations of nonlinear optics
- •4.2.1.4 Small-signal limit
- •4.2.1.5 Phase-matching condition
- •4.2.2 Frequency conversion in gases
- •4.2.2.1 Metal-vapor inert gas mixtures
- •4.2.2.3 Mixtures of gaseous media
- •References for 4.2
- •4.3 Stimulated scattering
- •4.3.1 Introduction
- •4.3.1.1 Spontaneous scattering processes
- •4.3.1.2 Relationship between stimulated Stokes scattering and spontaneous scattering
- •4.3.2 General properties of stimulated scattering
- •4.3.2.1 Exponential gain by stimulated Stokes scattering
- •4.3.2.2 Experimental observation
- •4.3.2.2.1 Generator setup
- •4.3.2.2.2 Oscillator setup
- •4.3.2.3 Four-wave interactions
- •4.3.2.3.1 Third-order nonlinear susceptibility
- •4.3.2.3.3 Higher-order Stokes and anti-Stokes emission
- •4.3.2.4 Transient stimulated scattering
- •4.3.3 Individual scattering processes
- •4.3.3.1 Stimulated Raman scattering (SRS)
- •4.3.3.2 Stimulated Brillouin scattering (SBS) and stimulated thermal Brillouin scattering (STBS)
- •4.3.3.3 Stimulated Rayleigh scattering processes, SRLS, STRS, and SRWS
- •References for 4.3
- •4.4 Phase conjugation
- •4.4.1 Introduction
- •4.4.2 Basic mathematical description
- •4.4.3 Phase conjugation by degenerate four-wave mixing
- •4.4.4 Self-pumped phase conjugation
- •4.4.5 Applications of SBS phase conjugation
- •4.4.6 Photorefraction
- •References for 4.4
Ref. p. 187] |
4.1 Frequency conversion in crystals |
141 |
|
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4.1Frequency conversion in crystals
G.G. Gurzadyan
4.1.1 Introduction
4.1.1.1 Symbols and abbreviations
4.1.1.1.1 Symbols |
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|
η |
conversion e ciency |
||
η (energy) |
energy conversion e ciency |
||
η (power) |
power conversion e ciency |
||
η (quantum) |
quantum conversion e ciency |
||
τp, τ |
pulse duration |
|
|
α |
angle between interacting beams |
||
∆ λ |
wavelength bandwidth |
||
∆ ν |
frequency bandwidth |
||
∆ θ |
angular bandwidth |
||
E |
energy |
|
|
f |
laser pulse repetition rate |
||
I0 |
pump intensity |
||
Ithr |
threshold intensity |
||
ϕpm |
phase-matching angle in the XY plane from X axis |
||
L |
crystal length |
|
|
λ |
wavelength |
|
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n |
refractive index |
||
no |
ordinary refractive index |
||
ne |
extraordinary refractive index |
||
ν |
wave number, frequency |
||
P |
power |
|
|
θpm |
phase-matching angle from Z axis |
||
ρ |
birefringence (walk-o ) angle |
||
T , Tpm |
crystal temperature |
||
Type I |
o + o → e |
or |
e + e → o |
Type II |
o + e → e |
or |
o + e → o |
ooe |
o + o → e |
or |
e → o + o |
eeo |
e + e → o |
or |
o → e + e |
eoe |
e + o → e |
or |
e → e + o |
oeo |
o + e → o |
or |
o → e + o |
Landolt-B¨ornstein
New Series VIII/1A1
142 |
4.1.1 Introduction |
[Ref. p. 187 |
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4.1.1.1.2 Abbreviations
av cw DFG
DROPO ERR FIHG FOHG ICDFG ICSHG IR
mid IR NC NCSHG OPA OPO SFG SH SHG SIHG
SP OPO SROPO SRS THG TROPO TWOPO UV
4.1.1.1.3 Crystals
Chemical formula
Ag3AsS3
AgGaS2
AgGaSe2
Ag3SbS3
Ba2NaNb5O15 β−BaB2O4 CdGeAs2 CdSe
CsB3O5 CsH2AsO4 CsLiB6O10 C6H6N2O3 C8H8O3
C10H11N3O6 C10H13N3O3
C11H14N2O3
CsD2AsO4 GaSe
average continuous wave
di erence frequency generation doubly resonant OPO
external ring resonator fifth harmonic generation fourth harmonic generation
intracavity di erence frequency generation intracavity second harmonic generation infrared
middle infrared noncollinear
noncollinear second harmonic generation optical parametric amplifier
optical parametric oscillator sum frequency generation second harmonic
second harmonic generation sixth harmonic generation synchronously pumped OPO singly resonant OPO stimulated Raman scattering third harmonic generation triply resonant OPO traveling-wave OPO ultraviolet
Symbol |
Crystal name |
|
Proustite |
|
Silver Thiogallate |
|
Silver Gallium Selenide |
|
Pyrargyrite |
|
Barium Sodium Niobate (Banana) |
BBO |
Beta-Barium Borate |
|
Cadmium Germanium Arsenide |
|
Cadmium Selenide |
CBO |
Cesium Borate |
CDA |
Cesium Dihydrogen Arsenate |
CLBO |
Cesium Lithium Borate |
POM |
3-Methyl-4-Nitro-Pyridine-1-Oxide |
MHBA |
4-Hydroxy-3-Methoxy-Benzaldehyde (Vanillin) |
MAP |
Methyl N-(2,4-Dinitrophenyl)-L-Alaninate |
DAN |
N-[2-(Dimethylamino)-5-Nitrophenyl]-Acetamide |
NPP |
N-(4-Nitrophenyl)-(L)-Propinol |
DCDA |
Cesium Dideuterium Arsenate |
|
Gallium Selenide |
Landolt-B¨ornstein
New Series VIII/1A1