- •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. 212] |
4.2 Frequency conversion in gases and liquids |
209 |
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4.2.2 Frequency conversion in gases
The following conditions have to be met for large conversion e ciencies:
1.a large nonlinear susceptibility χ(3)T which may be enhanced by a proper two-photon resonance,
2.large column densities with a proper phase matching,
3.small optical depths for the incident and generated waves to avoid reabsorption.
4.2.2.1 Metal-vapor inert gas mixtures
Metal-vapor inert gas mixtures are generally generated in concentric heat pipes because for e cient frequency mixing the phase matching can be accurately and independently adjusted through the partial pressures in the heat pipe [71Vid, 87Vid, 96Vid].
Tables of the multi-wave mixing experiments in di erent gaseous nonlinear media are arranged according to the elements, Table 4.2.1. For every element the wavelength is given together with the method of generation. The method of generation is indicated where (ω1 + ω1)Res + ω2 , for example, indicates a two-photon resonance of ω1 in the particular atomic or molecular medium and the additional wave ω2 can make the resulting radiation tunable.
4.2.2.2 Mixtures of di erent metal vapors
The modified concentric heat pipe [71Vid, 87Vid, 96Vid] is used for phase matching with small partial pressures avoiding strong homogeneous broadening.
In Table 4.2.2 mixtures of di erent metal vapors are listed.
4.2.2.3 Mixtures of gaseous media
For λ > 106 nm one prefers gas cells with lithium fluoride windows [87Vid]. For λ < 106 nm one should use either pulsed nozzle beams [87Bet] without windows or gas cells with a fast shutter [85Bon].
In Table 4.2.3 mixtures of gaseous media are given.
Landolt-B¨ornstein
New Series VIII/1A1
210 |
4.2.2 Frequency conversion in gases |
[Ref. p. 212 |
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Table 4.2.1. Metal-vapor inert gas mixtures.
Vapor |
Wavelength [nm] |
Method |
Ref. |
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Na |
354.7 |
3 · ω1 |
[75Blo1, 75Blo2, 76Oha] |
Na |
330.5 |
(ω1 + ω1)Res + ω2 |
[74Blo] |
Na |
268 (cw) |
(ω1 + ω2)Res + ω3 |
[84Bol] |
Na |
231 |
(ω1 + ω2)Res + ω3 |
[76Bjo] |
Na |
151.4 |
7 · ω1 |
[77Gro2, 79Mit] |
Na |
117.7 |
9 · ω1 |
[77Gro1, 79Mit] |
Rb |
354.7 |
3 · ω1 |
[71You, 75Blo1, 76Pue, |
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76Oha] |
Cs |
213.4 |
(ω1 + ω1)Res + ω1 |
[74Leu, 75War] |
Be |
121–123 |
(ω1 + ω1)Res + ω2 |
[79Mah] |
Mg |
173.5 |
2 · ω1 + ω1 + ω1 |
[85Hut] |
Mg |
140–160 |
(ω1 + ω1)Res + ω2 |
[76Wal, 80Jun, 96Ste] |
Mg |
143.6 (cw) |
(ω1 + ω1)Res + ω1 |
[83Tim] |
Mg |
115, 121.2, 127 |
(ω1 + ω1)Res + ω2 |
[81Car, 85Car] |
Mg |
121–129 |
(ω1 + ω1)Res + ω2 |
[78McK] |
Mg+ |
123.6 |
(ω1 + ω1)Res + ω2 |
[85Leb] |
Ca+ |
200 |
3 · ω1 |
[76Fer] |
Ca |
127.8 |
(ω1 + ω1)Res + ω2 |
[75Sor] |
Zn |
106–140 |
(ω1 + ω1)Res + ω2 |
[82Jam] |
Cd |
118.2, 152, 177.3 |
(ω1 + ω1)Res + ω2; 3 · ω1 |
[72Kun] |
Cd |
128.7–135.3 |
(ω1 + ω1)Res + ω2 |
[84Miy] |
Cd |
145.3–171.1 |
(ω1 + ω1)Res − ω2 |
[86Miy] |
Sr |
155.3, 166.7, 169.7, 173.5, 183.5 (cw) |
(ω1 + ω2)Res + ω3 |
[90Nol1] |
Sr |
184.6, 185.7, 192.0, 195.8, 208.8, 217.9 (cw) |
(ω1 + ω2)Res + ω3 |
[90Nol1] |
Sr |
171.2, 168.3, 169.7, 190 (cw) |
(ω1 + ω2)Res + ω3 |
[77Bjo, 78Fre] |
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(ω1 + ω1)Res + ω2 |
[90Nol2] |
Ca |
153.0, 159.5, 161.3, 163.3, 167.0 (cw) |
(ω1 + ω2)Res + ω3 |
[90Nol1] |
Ca |
169.7, 170.9, 172.3, 173.1, 176.9 (cw) |
(ω1 + ω2)Res + ω3 |
[90Nol1] |
Zn |
134.5–141.6 (cw) |
(ω1 + ω2)Res + ω3 |
[90Nol1] |
Cd |
138.1–140.3 |
(ω1 + ω1)Res + ω2 |
[88Sch] |
Sr |
177.8–195.7 |
(ω1 + ω1)Res + ω2 |
[74Hod, 75Sor, 76Sor] |
Sr |
165–166 |
(ω1 + ω2)Res + ω3 |
[78Eco] |
Sr |
192.3 |
(ω1 + ω1)Res + ω1 |
[80Pue, 81Egg] |
Sr |
171.2 |
(ω1 + ω1)Res + ω2 |
[80Eco] |
Ba |
190–200 |
(ω1 + ω1)Res + ω2 |
[80Hei] |
Hg |
109–196 |
(ω1 + ω1)Res ± ω2 |
[83Hil2] |
Hg |
184.9, 143.5, 140.1, 130.7, 125.9, 125.0 |
(ω1 + ω1)Res ± ω2 |
[81Bok] |
Hg |
125.1, 183.3, 208.5 |
(ω1 + ω1)Res ± ω2 |
[81Tom] |
Hg |
124.7–125.5, 122.8–123.5, 117.4–122 |
(ω1 + ω1)Res + ω2 |
[82Mah, 82Tom] |
Hg |
120.3 |
(ω1 + ω1)Res + ω2 |
[76Hsu] |
Hg |
87.5–105, 99.1–126.8 |
(ω1 + ω1)Res + ω2 |
[85Her, 83Hil2] |
Hg |
89.6 |
(ω1 + ω1)Res + ω1 |
[78Sla] |
Hg |
132–185 |
(ω1 + ω1)Res + ω2 |
[86Hil2] |
Tl |
195.1 |
(ω1 + ω1)Res + ω1 |
[75Wan] |
Eu, Yb |
185.5, 194 |
(ω1 + ω1)Res + ω2 |
[75Sor, 76Sor] |
Table 4.2.2. Mixtures of di erent metal vapors.
Mixture |
Wavelength [nm] |
Method |
Ref. |
|
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|
|
Na + K |
2–25 µm |
(ω1 − ω2)Res − ω3 |
[74Wyn] |
Na + Mg |
354.7 |
3 · ω1 |
[75Blo2] |
Landolt-B¨ornstein
New Series VIII/1A1
Ref. p. 212] |
4.2 Frequency conversion in gases and liquids |
211 |
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Table 4.2.3. Mixtures of gaseous media. |
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Gas |
Wavelength [nm] |
Method |
Ref. |
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He, Ne, Ar, Kr, Xe |
231.4 |
3 |
· ω1 |
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[67New, 69War] |
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He |
53.2 |
5 |
· ω1 |
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[76Rei, 77Rei, |
77She, |
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· ω1 |
|
78Rei2, 78Rei1] |
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He |
38 |
7 |
; 5 · ω1; 7 · ω1 |
[77Rei, 78Rei2] |
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He |
82.8, 50, 35.5 |
3 |
· ω1 |
[83Bok] |
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He, Ne |
106.4 |
(ω1 + ω1)Res + ω2 |
[78Rei2] |
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He, Ne |
88.7 |
3 |
· ω1 |
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[78Rei2, 78Rei1] |
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He, Ne |
76, 70.9, 62.6, 59.1 |
4 |
· ω1 ± ω2 |
[77She, 78Rei2] |
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He, Xe |
49.7, 35.5 |
5 |
· ω1; 7 · ω1 |
[83Bok] |
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Ne |
53.2, 118.2 |
5 |
· ω1; (ω1 + ω1)Res + ω2 |
[76Rei, 77She, 78Rei2] |
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Ne |
72.05–73.58, 74.3–74.36 |
3 |
· ω1 |
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[84Hil] |
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Ar |
120.4 |
(ω1 + ω1)Res + 3 · ω1 |
[80Din] |
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Ar |
85.7–87.0, 97.4–104.8 |
3 |
· ω1 |
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[83Hil3, 83Mar] |
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Ar |
106.7 |
(ω1 + ω1)Res + ω1 |
[82Mil] |
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Ar |
102.6–102.8 |
3 |
· ω1 |
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[79Rei, 80Rei] |
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Ar, Kr |
61.6, 53.2 |
5 |
· ω1 |
|
[78Rei2, 81Rei] |
|
Ar |
57 |
(ω1 + ω1)Res + ω1 |
[76Hut] |
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Kr |
131.2, 92.3, 92.8, 94.2 |
(ω1 + ω1)Res ± ω2 |
[85Bon] |
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Kr |
121.6 |
3 |
· ω1 |
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[81Hil, 80Lan, 81Bat] |
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Kr |
123.6 |
(ω1 + ω1)Res + ω1 |
[82Mil] |
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Kr |
112.4, 120.3–123.6 |
(ω1 + ω1)Res + ω2 |
[79Cot1, 79Cot2] |
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Kr |
131.2 |
(ω1 + ω1)Res − ω2 |
[85Bon] |
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Kr |
72.5–83.5; 127–180 |
(ω1 + ω1)Res ± ω2 |
[87Hil] |
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Kr |
121–200 |
(ω1 + ω1)Res − ω2 |
[90Mar] |
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Kr, Xe |
71–92 |
(ω1 + ω1)Res + ω2 |
[89Miy] |
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Kr, Xe |
110–210 |
(ω1 + ω1)Res ± ω2 |
[82Hil] |
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Xe |
84.6–109.5, 155–220 |
(ω1 + ω1)Res ± ω2 |
[82Hil, 82Hag, 83Hil1] |
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Xe |
155 |
(ω1 + ω1)Res − ω2 |
[83Hut] |
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Xe |
147 |
(ω1 + ω1)Res + ω1 |
[82Mil] |
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Xe |
140.3–146.9 |
3 |
· ω1; (ω1 + ω1)Res + ω2 |
[81Hil, 83Val] |
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Xe |
74.8, 75, 75.2 |
(ω1 + ω1)Res + ω1 |
[82Mui] |
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Xe |
125.4, 125.9, 126.1 |
(ω1 + ω1)Res − ω2 |
[82Mui] |
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Xe |
101.5, 101.8, 13.0 |
(ω1 + ω1)Res + ω2 |
[82Mui] |
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Xe |
163.1–194.6 |
(ω1 + ω1)Res ± ω2 |
[74Kun] |
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Xe |
118.2 |
3 |
· ω1 |
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[83Kun, 76Kun, 82Gan, |
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· ω1 |
|
83Bok] |
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Ar, Kr, Xe, CO, N2 |
72; 90.4–102.5 |
3 |
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[87Pag] |
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Ne, Ar, Kr, Xe, Hg |
60–200 |
(ω1 + ω1)Res ± ω2 |
[86Hil1] |
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Ar, Xe, CO |
74.2, 80.4, 95.1, 98.2, 100.1, |
ω1 + ω1 + ω2; 3 · ω1 |
[89Cro] |
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116.5, 117.8, 123.6 |
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Landolt-B¨ornstein
New Series VIII/1A1