- •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 |
143 |
|
|
|
HgGa2S4
α−HIO3
KB5O8 4D2O
KB5O8 4H2O
KD2AsO4
KD2PO4
KH2PO4
KNbO3
KTiOAsO4
KTiOPO4
LiB3O5
LiCOOH H2O
LiIO3
LiNbO3
LiNbO3:MgO
(NH2)2CO
NH4H2AsO4
NH4H2PO4
NO2C6H4NH2
RbH2AsO4
RbH2PO4
RbTiOAsO4
Te
Tl3AsSe3
ZnGeP2
|
Mercury Thiogallate |
|
α−Iodic Acid |
DKB5 |
Potassium Pentaborate Tetradeuterate |
KB5 |
Potassium Pentaborate Tetrahydrate |
DKDA |
Potassium Dideuterium Arsenate |
DKDP |
Potassium Dideuterium Phosphate |
KDP |
Potassium Dihydrogen Phosphate |
|
Potassium Niobate |
KTA |
Potassium Titanyl Arsenate |
KTP |
Potassium Titanyl Phosphate |
LBO |
Lithium Triborate |
LFM |
Lithium Fomate |
|
Lithium Iodate |
|
Lithium Niobate |
|
Mg:O-doped Lithium Niobate |
|
Urea |
ADA |
Ammonium Dihydrogen Arsenate |
ADP |
Ammonium Dihydrogen Phosphate |
mNA |
meta-Nitroaniline |
RDA |
Rubidium Dihydrogen Arsenate |
RDP |
Rubidium Dihydrogen Phosphate |
RTA |
Rubidium Titanyl Arsenate |
|
Tellurium |
|
Thallium Arsenic Selenide |
|
Zinc Germanium Phosphide |
4.1.1.2 Historical layout
The pioneering work of Franken et al. [61Fra] on second harmonic generation of ruby laser radiation in quartz and invention of the phase-matching concept [62Gio, 62Mak] generated a new direction in the freshly born field of nonlinear optics: frequency conversion in crystals. Sum frequency generation by mixing the outputs of two ruby lasers in quartz was already realized in 1962 [62Mil, 62Bas]. Zernike and Berman [65Zer] were the first to demonstrate di erence frequency mixing. Optical parametric oscillation was experimentally realized in 1965 by Giordmaine and Miller [65Gio]. First monographs on nonlinear optics by Akhmanov and Khokhlov [64Akh] and Bloembergen [65Blo] greatly stimulated development of the nonlinear frequency converters. At present the conversion of laser radiation in nonlinear crystals is a powerful method for generating widely tunable radiation in the ultraviolet, visible, near, mid, and far IR regions.
For theoretical and experimental details of nonlinear frequency conversions in crystals, see monographs by Zernike and Midwinter [73Zer], Danelyus, Piskarskas et al. [83Dan], Dmitriev and Tarasov [87Dmi], Shen [84She], Handbook of nonlinear optical crystals (by Dmitriev, Gurzadyan, Nikogosyan) [91Dmi, 99Dmi], Handbook of nonlinear optics (by Sutherland ) [96Sut]. For frequency conversion of femtosecond laser pulses, see also [88Akh]. For linear and nonlinear optical properties of the crystals, see [77Nik, 79Kur, 84Jer, 87Nik, 87Che, 96Sut, 99Dmi, 00Cha, 00Sas]. For related nonlinear phenomena, see [96Sut]. For the historical perspective of the nonlinear frequency conversion over the first forty years, see [00Bye]. In the following section, Sect. 4.1.2, we present some basic equations which may be useful for simple calculations of frequency converters.
Landolt-B¨ornstein
New Series VIII/1A1