We report measurements of the degree of linear polarization of scattered light as a function of excitation frequency near the Doppler-broadened
NaD2 resonance line. For resonant excitation of the
D2 line, the hyperfine interaction strongly depolarizes the emitted light due to precession of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ prior to spontaneous emission. However, as the laser frequency is tuned away from resonance, the polarization degree sharply rises to the level predicted using a simple
JMJ basis, i.e., neglecting any coupling of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ with the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$. Roughly speaking, there is a transition from
F selection rules ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$) for resonant excitation to
J selection rules for off-resonant excitation. We present a rigorous calculation of the polarization degree with the use of multipole moments of the density matrix which agrees quantitatively with our data and also predicts complicated interference structure when Doppler broadening is negligible. We show that this structure may shift peaks observed in precision laser-spectroscopy experiments. For Doppler-broadened transitions we discuss a simplified approach (based on an approximation to the Voigt profile) which treats separately the contributions of resonant and off-resonant scattering.
The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.
The effect of foreign gases upon the fluorescence of sodium vapor excited by the second line of the principal series has been investigated. The gases used were helium, nitrogen, and hydrogen and the intensities of both the 3303A line and the
D light were observed. From the variation in intensity of the 3303A line as gas is added it is concluded that the presence of an inert gas has no appreciable effect upon the relative transition probabilities in the
32P state of sodium. With nitrogen or hydrogen as the added gas the
D light intensity variation followed that of the 3303A line very closely but with helium a marked increase in intensity was produced by the first gas added with a decrease at higher pressures. This increase was explained as due to a transfer of sodium atoms from the
32P to the
32D state by collisions, thus increasing the number of atoms which radiate the
D light. In addition to this increase in number the collisional transfers produced an increased "Doppler width" in the
D light which persisted up to pressures well over 100 mm of helium and caused a decreased absorption of the fluorescence light. The bearing of this work on the difference in the intensity ratio of the ${2}^{2}S\ensuremath{-}{3}^{2}P$ and ${1}^{2}S\ensuremath{-}{3}^{2}P$ transitions as reported by Weiss for an arc and by Christensen and Rollefson in fluorescence is discussed. It is concluded on the basis of experimental evidence that any explanation of the difference which depends upon multiplicity of the
32P state is incorrect. An explanation of this difference based upon the assumption that the life period of an excited atom varies inversely as the transition probability of the radiation emitted is presented. It is shown that recent work on the life periods of atoms in the
23S1 state of mercury at least partially supports this assumption. A new type of sodium arc with increased intensity and stability of operation is described.
An equation has been developed for the polarization, and the angle of maximum polarization of resonance radiation as observed along a magnetic field perpendicular to the electric vector and the direction of propagation of the incident beam. Explicit application has been made to the polarization and the angle for the line $^{1}S_{0}\ensuremath{-}^{1}P_{1}$ for various values of the ratio of the hyperfine separation constant to the natural breadth of the levels, for a nuclear moment of \textonehalf{}. It was noted here that the form of the curves might differ widely from that to be expected from classical considerations. The polarization, and the angle of maximum polarization for the sodium D lines, for several values of the same ratio, were computed and compared with experimental observations. Thus a range of possible values of
A was determined, which is not in disagreement with previous figures, and a value for $\ensuremath{\tau}$ established which agrees well with that calculated from optical dispersion data.
The close-coupled theory of atomic collisions in the presence of a radiation field may be used to calculate the distribution of final atomic states which results from absorption of polarized light during a collision. The theory applies equally well to optical collisions (line broadening) and to radiative collisions (laser-induced collisional energy transfer). For an optical collision the detuning $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\infty}}$ is restricted to be larger than either the Rabi frequency or the widths due to natural, Doppler, or pressure broadening. The radiation field is assumed to be weak enough that the transition probabilities are linear in field intensity. The molecular picture is emphasized in which the wave function is expanded in a basis of field-free molecular states and the Hamiltonian is blocked in accordance with molecular quantum numbers. The quantities needed to predict experimental observables are reduced radiative scattering
S-matrix elements ${s}_{\ensuremath{\omega}}$ in the asymptotic Hund's case-(e) representation. The theory of product orientation and alignment is equivalent to that which has been developed for molecular photodissociation. It requires coherent sums of ${s}_{\ensuremath{\omega}}$ matrix elements from different transition branches, that is, for
P-,
Q-, and
R-type transitions corresponding to changes of -1, 0, and +1 in total molecular angular momentum. On the other hand, the total absorption coefficient and the branching ratio to different final fine-structure states irrespective of orientation or alignment depend on incoherent sums of the same matrix elements.