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Journal of the Optical Society of America B

Electronic coherent anti-Stokes Raman spectroscopy in CeF_3

David Piehler

Published Sep 1, 1991• 7 citations
Publisher

Abstract

The coherent anti-Stokes Raman spectroscopy (CARS) of electronic states of the Ce3+ ion in a CeF3 crystal at 3.8 K is reported. CARS resonances involving the ground state of the 2F5/2 manifold and the Stark components of the 2F7/2 manifold at 2161 and 2239 cm−1 have been detected. Measurements were made with both visible (λ1 ≈ 476 nm, λ2 = 532 nm) and near-ultraviolet (λ1 = 355 nm, λ2 ≈ 385 nm) lasers. The enhancement of the third-order susceptibility owing to the electronic transitions, |χ(3)R/χ(3)NR|max, is as great as 4.8. This represents an order-of-magnitude increase over that in singly resonant electronic CARS experiments in other rare-earth crystals. The CARS data also yielded accurate measurements of the Ce3+ electronic Raman cross sections. In the visible region, σzz(2161 cm−1) = (5.0 ± 1.1) × 10−30 cm2 and σzz(2239 cm−1) = (1.9 ± 0.7) × 10−30 cm2. One could calculate both the absolute magnitude and the dispersion of |χ(3)R|max by modeling the virtual intermediate states as a single degenerate 5d state at 45 000 cm−1.

DOI
10.1364/josab.8.001889

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Physical Review A•Jun 1, 1990•15 citations

Saturation effects in coherent anti-Stokes Raman scattering

A. D. Wilson‐Gordon, R. Klimovsky-Barid, Harry Friedmann

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 ${P}_{l,s}$, 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 ${\mathcal{p}}_{\mathrm{CARS}}$ 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 ${\mathcal{p}}_{\mathrm{CARS}}$ 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 ${P}_{l}$ 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 ${V}_{13}$ 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 ${\mathcal{p}}_{\mathrm{CARS}}$ 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.

Physical Review A•Mar 1, 1982•39 citations

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Time-resolved, electronically resonant, coherent anti-Stokes Raman scattering is used to prepare and interrogate vibronic coherences of molecular iodine in matrix Ar. Coherences that involve evolution on the excited B(3Π0u) state, first- and third-order coherences, decay in less than one vibrational period (τ<300 fs). In contrast, as many as 200 vibrational periods of motion can be observed for Raman-prepared wave packets consisting of zero-phonon vibrational superpositions on the ground electronic state (second-order coherence). Packets consisting of v=4, 5 and v=3, 4, 5 on the X(1Σg) state decay with a half-life of 10±1 ps at 31 K, allowing a more accurate measure of vibrational level spacings and decoherence time than has been possible in frequency domain. The harmonic frequency of the molecule is reduced by 1.5 cm−1 (0.7%) in the matrix. The lack of recurrence in the excited electronic state ensures that the resonant anti-Stokes scattering arises only from the negative momentum component of the Raman packet. This momentum filter, which should be ubiquitous in condensed media, leads to a signal with deeper modulation than in the gas phase.

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The effects of pump field intensity are investigated for resonant coherent anti-Stokes Raman spectroscopy (CARS) in inhomogeneously broadened media. It is shown that the CARS line, although Doppler broadened for low intensity, is narrowed to its natural linewidth as intensity is increased and that higher order selectively saturating processes become dominant. Splitting effects are also discussed. Analog results are found for "double electronic resonances."

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Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering

G. S. Agarwal, Surendra Singh

The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of ${T}_{1}$ or ${T}_{2}$. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.

Physical Review A•Jun 1, 1982•46 citations
The coherent anti-Stokes Raman spectroscopy (CARS) of electronic states of the Ce3+ ion in a CeF3 crystal at 3.8 K is reported. CARS resonances involving the ground state of the 2F5/2 manifold and the Stark components of the 2F7/2 manifold at 2161 and 2239 cm−1 have been detected. Measurements were made with both visible (λ1 ≈ 476 nm, λ2 = 532 nm) and near-ultraviolet (λ1 = 355 nm, λ2 ≈ 385 nm) lasers. The enhancement of the third-order susceptibility owing to the electronic transitions, |χ(3)R/χ(3)NR|max, is as great as 4.8. This represents an order-of-magnitude increase over that in singly resonant electronic CARS experiments in other rare-earth crystals. The CARS data also yielded accurate measurements of the Ce3+ electronic Raman cross sections. In the visible region, σzz(2161 cm−1) = (5.0 ± 1.1) × 10−30 cm2 and σzz(2239 cm−1) = (1.9 ± 0.7) × 10−30 cm2. One could calculate both the absolute magnitude and the dispersion of |χ(3)R|max by modeling the virtual intermediate states as a single degenerate 5d state at 45 000 cm−1.
We have measured coherent anti-Stokes Raman spectra between crystal-field levels of the 2^{2}2F5/2{\mathit{F}}_{5/2}F5/2​ and 2^{2}2F7/2{\mathit{F}}_{7/2}F7/2​ manifolds of the Ce3+{\mathrm{Ce}}^{3+}Ce3+ ion diluted in LuPO4{\mathrm{LuPO}}_{4}LuPO4​ at \ensuremath{\sim}10 K. The anti-Stokes signal is nearly resonant with the lowest crystal-field level of the 5d1{\mathit{d}}^{1}d1 configuration of Ce3+{\mathrm{Ce}}^{3+}Ce3+ at 30 460 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. For a LuPO4{\mathrm{LuPO}}_{4}LuPO4​ crystal doped with 0.06 mol % Ce3+{\mathrm{Ce}}^{3+}Ce3+, we found enhancements of the third-order susceptibility \ensuremath{\Vert}${\mathrm{\ensuremath{\chi}}}^{(3)\mathrm{R}}$/${\mathrm{\ensuremath{\chi}}}^{(3)\mathrm{NR}}$\ensuremath{\Vert} as high as 11.6. This enhancement is over 20 times larger than that seen previously in singly resonant experiments with pure rare-earth crystals.
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{P}_{l,s}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{\mathcal{p}}_{\mathrm{CARS}}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〉|1〉∣1〉 and ∣2〉|2〉∣2〉 when ${\ensuremath{\omega}}_{l}$ is far from resonance, or for the three-level system ∣1〉,∣2〉|1〉,|2〉∣1〉,∣2〉, and ∣3〉|3〉∣3〉, when ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$. The steady-state expression for pCARS{\mathcal{p}}_{\mathrm{CARS}}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{P}_{l}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{V}_{13}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{\mathcal{p}}_{\mathrm{CARS}}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.
The saturation threshold of a probe pulse in an ultrafast electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman spectroscopy (CARS) configuration is calculated. We demonstrate that while the underdamping condition is a sufficient condition for saturation of ERE-CARS with the long-pulse excitations, a transient gain must be achieved to saturate the ERE-CARS signal for the ultrafast probe regime. We identify that the area under the probe pulse can be used as a definitive parameter to determine the criterion for a saturation threshold for ultrafast ERE-CARS. From a simplified analytical solution and a detailed numerical calculation based on density-matrix equations, the saturation threshold of ERE-CARS is compared for a wide range of probe-pulse durations from the 10-ns to the 10-fs regime. The theory explains both qualitatively and quantitatively the saturation thresholds of resonant transitions and also gives a predictive capability for other pulse duration regimes. The presented criterion for the saturation threshold will be useful in establishing the design parameters for ultrafast ERE-CARS.
Time-resolved, electronically resonant, coherent anti-Stokes Raman scattering is used to prepare and interrogate vibronic coherences of molecular iodine in matrix Ar. Coherences that involve evolution on the excited B(3Π0u) state, first- and third-order coherences, decay in less than one vibrational period (τ<300 fs). In contrast, as many as 200 vibrational periods of motion can be observed for Raman-prepared wave packets consisting of zero-phonon vibrational superpositions on the ground electronic state (second-order coherence). Packets consisting of v=4, 5 and v=3, 4, 5 on the X(1Σg) state decay with a half-life of 10±1 ps at 31 K, allowing a more accurate measure of vibrational level spacings and decoherence time than has been possible in frequency domain. The harmonic frequency of the molecule is reduced by 1.5 cm−1 (0.7%) in the matrix. The lack of recurrence in the excited electronic state ensures that the resonant anti-Stokes scattering arises only from the negative momentum component of the Raman packet. This momentum filter, which should be ubiquitous in condensed media, leads to a signal with deeper modulation than in the gas phase.
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.