Optical quadrupole sum-frequency generation in sodium vapor. [Spin-orbit splitting]

Technical Report · Sun May 01 04:00:00 EDT 1977

OSTI ID:7220718

Bethune, D S

It is shown that second order nonlinear optical processes such as sum and difference generation can be observed in isotropic media, despite the fact that such processes are forbidden in the dipole approximation. A theoretical treatment of quadrupole sum and difference frequency generation is given, which includes the effects of spin-orbit splitting. The symmetry of the vapor is used to derive the form of the quadrupole susceptibility tensor, and the quadrupole moment tensor is then expressed as a scalar susceptibility multiplied by a tensor constructed directly from the input field polarization vectors. The expression shows that two noncollinear beams must be used. The effect of applying a magnetic field is derived. Expressions for phase matching and output power are found. In sodium vapor one observed quadrupole sum frequency generation (QSFG) of ultraviolet light. The output radiation showed very sharp resonant enhancement when ..omega../sub 1/ + ..omega../sub 2/ was tuned near the 3s ..-->.. 4d quadrupole allowed transition of Na. The experimental results generally confirm the theoretical predictions. Deviations of the data from the simple theory can be satisfactorily accounted for by the effects of two photon saturation, induced index of refraction changes and single and multi-photon absorption. It is also shown that by applying a D.C. electric field to the sodium vapor, interference effects between QSFG and D.C. induced, third-order sum-frequency generation may be observed, allowing an accurate determination of quadrupole matrix elements relative to dipole matrix elements of atoms. This technique is used to measure the value of the 3s to 4d quadrupole transition moment of Na. The result is (3s/zz/2/4d) = (2.2 +- 0.4) a/sub 0//sup 2/. Finally, the generalization of the dipole forbidden susceptibilities to the case of quadrupole pumped processes is discussed, with difference frequency generation in Cs vapor considered as an example.

• Research Organization: California Univ., Berkeley (USA). Lawrence Berkeley Lab.
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7220718
• Report Number(s): LBL-6264
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ALKALI METALS
COUPLING
ELECTROMAGNETIC RADIATION
ELEMENTS
ENERGY-LEVEL TRANSITIONS
FLUIDS
FREQUENCY DEPENDENCE
GASES
INTERFERENCE
INTERMEDIATE COUPLING
ISOTROPY
L-S COUPLING
MAGNETIC FIELDS
MAGNETIC PROPERTIES
MAGNETIC SUSCEPTIBILITY
MATRIX ELEMENTS
METALS
MULTIPOLES
NONLINEAR PROBLEMS
OPTICAL PROPERTIES
PHYSICAL PROPERTIES
QUADRUPOLE MOMENTS
QUADRUPOLES
RADIATIONS
SODIUM
SYMMETRY
TENSORS
ULTRAVIOLET RADIATION
VAPORS