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Doubly-resonant two-photon-absorption-induced four-wave mixing in Tb(OH)₃and LiTbF₄

David A. Ender

Published Jan 1, 1982• 1 citation

Abstract

Doubly-resonant two-photon-absorption-induced four-wave mixing has been observed for the first time in a rare earth insulator.The generation of the nonlinear signal exhibits strong intermediate and two-photon resonances in crystalline Tb (OH)3 and LiTbF4 This provides a novel method for high resolution measurements of intermediate 4f^n configurations and excited configurations of rare earth ions.The intermediate resonance showed spectral line narrowing up to ten times narrower than the corresponding inhomogeneously broadened absorption.In LiTbF4, laser-limited line widths were obtained and in Tb(OH)3, a homogeneous limit corresponding to T2 = 50 psec may have been reached.The qualitative behavior of the narrowing is explained by the dispersion of the anamalous index of refraction and its effect on phase matching.Direct measurement of the anamalous dispersion was made to test the model.Results indicate nonlinear contributions to the refractive index may have been present.The two-photon resonance in Tb(OH)3 was measured to be a 230 cm^-1 wide crystal field component of the broad 4f^n 5d excited configuration.Thus high resolution UV spectroscopy with tunable visible lasers is demonstrated.Applications are discussed including the extraction of homogeneous line widths from inhomogeneously broadened spectra, coherent transient measurements, and UV and VUV spectrosocpy.The latter uses different selection rules than linear absorption methods and allows study of transitions between excited states.DOUBLY-RESONANT TWO-PHOTON-AB^ORPTION-INDUCED EOUR-WAVB MIXPNQ IN, .T b .(DR) 3 . .

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Doubly-resonant two-photon-absorption-induced four-wave mixing has been observed for the first time in a rare earth insulator.The generation of the nonlinear signal exhibits strong intermediate and two-photon resonances in crystalline Tb (OH)3 and LiTbF4 This provides a novel method for high resolution measurements of intermediate 4f^n configurations and excited configurations of rare earth ions.The intermediate resonance showed spectral line narrowing up to ten times narrower than the corresponding inhomogeneously broadened absorption.In LiTbF4, laser-limited line widths were obtained and in Tb(OH)3, a homogeneous limit corresponding to T2 = 50 psec may have been reached.The qualitative behavior of the narrowing is explained by the dispersion of the anamalous index of refraction and its effect on phase matching.Direct measurement of the anamalous dispersion was made to test the model.Results indicate nonlinear contributions to the refractive index may have been present.The two-photon resonance in Tb(OH)3 was measured to be a 230 cm^-1 wide crystal field component of the broad 4f^n 5d excited configuration.Thus high resolution UV spectroscopy with tunable visible lasers is demonstrated.Applications are discussed including the extraction of homogeneous line widths from inhomogeneously broadened spectra, coherent transient measurements, and UV and VUV spectrosocpy.The latter uses different selection rules than linear absorption methods and allows study of transitions between excited states.DOUBLY-RESONANT TWO-PHOTON-AB^ORPTION-INDUCED EOUR-WAVB MIXPNQ IN, .T b .(DR) 3 . .

We report the first observation of intermediate state enhancement of four wave mixing induced by two photon absorption in rare earth insulators. Coherent generation of ω4=ω1+ω2−ω3 exhibits strong intermediate state resonances when ω1 sweeps through a single photon transition to the 5D4 states arising from the 4f8 ground configuration of Tb3+ while (ω1+ω2) is simultaneously resonant with an allowed transition to the excited 4f75d configuration. Measurements are presented for Tb(OH)3 and LiTbF4.

Coherent nonlinear optical generation of ω4=ω+ω2−ω3 exhibits strong sharp intermediate (ω1) and two‐photon (ω1+ω2) resonances in crystalline Tb(OH)3 and LiTbF4, providing a novel method for high resolution coherent measurements of both excited electronic configurations and intermediate 4 fn states of rare earth ions. New regions of the UV and VUV are thus made accessible to existing tuneable visible and near ultravisible lasers. Selection of sharp features from broad overlapping absorptions, line narrowing due to phase matching selectivity, and coherent transient applications are discussed.

A new technique for overcoming inhomogeneous broadening in condensed matter is reported. Phase-matchinginduced frequency selectivity associated with multiresonant four-wave mixing is explored in detail for the first time to our knowledge and shown to give laser-limited linewidths that are more than 10 times narrower than the inhomogeneous width of an intermediate resonance in LiTbF (4). The anomalous dispersion associated with the resonance. was also measured, and model calculations suggest that significantly greater narrowing is feasible.

We have observed kilohertz and sub-kilohertz resonance structures in RF-optical double resonance experiments of rare-earth-doped solids, when the frequency of the RF field is scanned across the hyperfine transitions while monitoring the resonant optical absorption of a CW laser. The effect is observed only when the laser spectral width is broad compared to the hyperfine structure. The observed line widths are apparently free of the inhomogeneous widths of hyperfine levels and the line shape has peculiar double peak structure. The effect is modelled with a resonance involving three atomic levels interacting with three electromagnetic fields, two optical and one RF, in a triangular or “delta’ configuration. While the ordinary optical-RF two-field resonance is limited by spin inhomogeneous width, the simultaneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyperfine transition.

We explain the utility of third-order nonlinear susceptibility, χ (3) (ω 2 ; ±ω 1 ,

{\mp}\omega_{1}

, ω 2 ), for the observation of resonances with homogeneous widths from inhomogeneously broadened distributions in three-level systems related to Raman or two-photon allowed electronic transitions. The line narrowing and high resolution capabilities are demonstrated theoretically using a model for inhomogeneous distributions of transitions in which we regard an absorption spectrum as the composition of some inhomogeneously broadened substructures. The experimental methods to separate a signal having frequency ω 2 from ingoing beam at the same frequency are outlined.

Resonant enhancement by a factor of over 20 of direct two-photon absorption from the ground state

^{7}\mathrm{F}_{6}

to the excited state

^{5}\mathrm{G}_{6}

of the 4

{f}^{8}

configuration of the

{\mathrm{Tb}}^{3+}

ion at 40 200 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ has been observed in time-resolved experiments with two separate pulsed lasers. The results provide clear evidence for resonant enhancement of two-photon absorption in rare-earth compounds and imply a similar enhancement for Raman scattering and nonlinear-optical mixing. Two separate contributions to the direct transition moment were observed. When a single laser frequency was used, the intermediate states which made the largest contribution were from excited configurations of opposite parity; those intermediate states were far from resonance. Detailed two-frequency experiments showed, however, that near a single photon

^{7}\mathrm{F}_{6}

${\mathrm{\ensuremath{-}}}^{5}$

{\mathrm{D}}_{4}

resonance, a much stronger contribution arose from the 4

{f}^{8}

configuration

^{5}\mathrm{D}_{4}

intermediate state. Two-photon absorption was clearly isolated from two-step (incoherent) excitation by varying the timing of two separately triggered lasers.