Spatial symmetries inherent to tight focus optical beams are applied to control the field phase generated at interfaces in nonlinear optical processes. We use these symmetries to obtain a background-free pure Raman spectrum in coherent anti-Stokes Raman scattering spectroscopy from a resonant medium forming a transverse interface with a nonresonant medium. We demonstrate that the nonresonant medium acts as a local oscillator with which the Raman spectrum is measured in heterodyne detection. This method is relevant to remove the nonresonant background in other third-order resonant processes excited with focused beams.
A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid
Pr3+: La
F3 at 1.6 K utilizing the
Pr3+ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the
Pr3+: La
F3 hyperfine splittings where the optical heterodyne signals are shot-noise limited. The
Pr3+ nuclear quadrupole parameters are obtained for the
3H4 and
1D2 states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the
3H4 and
1D2 hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.
Raman heterodyne detection of nuclear magnetic resonance is a sensitive technique for optical detection of an NMR transition, which is driven by a resonant radio-frequency field. The observed signal is linear in the transition matrix elements of the magnetic resonance transition and two optical transitions. This linearity is the reason that signal contributions from different sites or different rf transitions can interfere, in many cases destructively. In this article, we discuss such an interference effect, which appears to have been overlooked in the past. It occurs between signal contributions that originate from the same magnetic resonance transition of atoms with different positions within the inhomogeneously broadened optical resonance line. These atoms contribute to the coherent Raman scattering through different scattering paths, which involve optical transitions to different nuclear spin states of the same electronic state. We show that the interference between all possible scattering paths leads to complete signal cancellation, if the atoms that are involved in the different scattering paths are equally polarized. To study the effect and to eliminate the interference, we used a pump-and-probe technique with two laser beams. With two independent laser frequencies, it becomes possible to separate the individual scattering paths. We calculate the dependence of the signal on the frequency of both laser beams as well as on the radio frequency and compare the results to experimental data from
Pr3+:
YAlO3. Our results show that the interference reduces the signal amplitude of the conventional Raman heterodyne experiment but can be eliminated in the new experiment.
Raman oscillation, frequency upconversion, and Raman amplification can be achieved in a second-order nonlinear medium at the phonon-polariton resonance. By beating two optical fields, a second-order nonlinear polarization is generated inside the medium. Such a polarization induces a spatially uniform nonpropagating electric field at the beat frequency, which in turn mixes with the input optical field at the lower frequency to generate or amplify the anti-Stokes optical field. Raman oscillation can be efficiently reached for the copropagating configuration. In comparison, efficient frequency upconversion and large amplifications are achievable for the counterpropagating configuration. These Raman processes can be used to effectively remove transverse-optical phonons before decaying to lower-frequency phonons, achieve laser cooling, and significantly enhance coherent anti-Stokes Raman scattering. The counterpropagating configuration offers advantages for amplifying extremely weak signals.
Laser and microwave fields can be mixed in paramagnetic samples in a coherent Raman process. The radiation scattered in the forward direction contains frequency components at the sum and difference frequency. We consider the details of this scattering process in a static magnetic field, where two types of signals appear: magnetic-resonance transitions give rise to signals at fixed magnetic fields, independent of the laser frequency. Another set of resonances is determined by the optical transition frequencies. These resonances are particularly prominent in samples with narrow optical absorption lines. We derive a comprehensive theory that describes both contributions and compare it with experimental data from the R lines of ruby.
Saturation effects in coherent anti-Stokes Raman scattering (CARS) spectroscopy are discussed. The discussion is limited to Raman-resonant CARS (${\ensuremath{\omega}}_{l}\ensuremath{-}{\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{21}$, where ${\ensuremath{\omega}}_{l,s}$ are the frequencies of the pump fields with powers
Pl,s, and ${\ensuremath{\omega}}_{21}$ is the frequency of the Raman transition $|1〉\ensuremath{\rightarrow}|2〉$) with the possible addition of a one-photon resonance (${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$ is the frequency of the electronic transition $|1〉\ensuremath{\rightarrow}|3〉$). For these cases we show that the CARS polarization
pCARS is proportional to the off-diagonal density-matrix element ${\ensuremath{\rho}}_{21}$. In order to determine ${\ensuremath{\rho}}_{21}$, we use Laplace transforms to solve the Bloch equations for the effective two-level system
∣1〉 and
∣2〉 when ${\ensuremath{\omega}}_{l}$ is far from resonance, or for the three-level system
∣1〉,∣2〉, and
∣3〉, when ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$. The steady-state expression for
pCARS in the former case gives ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}{P}_{s}^{\frac{1}{2}}$ at low powers and ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{0}{P}_{s}^{\frac{\ensuremath{-}1}{2}}$ at high powers. In the three-level system, we show that when the pressure is low and at least one field is weak, the slow time dependence of ${\ensuremath{\rho}}_{21}$ must be considered. When one field is strong and the other weak, the CARS spectrum is Stark split. When
Pl is high, for example, ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{0}{P}_{s}^{\frac{1}{2}}$ for ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}$ and ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{({P}_{l}{P}_{s})}^{\frac{1}{2}}$ when ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}\ifmmode\pm\else\textpm\fi{}{V}_{13}$ where
V13 is the one-photon Rabi frequency for the $|1〉\ensuremath{\rightarrow}|3〉$ transition. The Wilcox-Lamb approximation is used to reduce the three-level Bloch equations to rate equations containing one- and two-photon terms. When the fields are so weak that both one- and two-photon terms are small compared to the decay terms, the usual expression for
pCARS is reproduced. If only the direct two-photon processes are important, the effective-two-system results are reproduced. When both fields are intense and nearly resonant, the steady state is rapidly achieved. The results for the case where one field is much stronger than the other are essentially the same as those for one strong and one weak field. When the fields are of comparable strength, ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{\frac{1}{2}}{P}_{s}^{0}$ for ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$ and ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}$, and the CARS spectrum is split into five components.