Journal of Applied Physics

Enhancement of third-order susceptibility due to electronic transitions in rare-earth ions

Michael L. Shand

Published Mar 1, 1981• 8 citations

Abstract

Three-wave mixing experiments demonstrate resonance enhancement of the third-order susceptibility due to electronic transitions in rare-earth ions. The position, width, and strength of eight resonances in the 2100–2500-cm−1 range in terbium aluminum garnet (TbAlG) are determined. These resonances are due to 7F5→7F6 intermanifold transitions of terbium. In addition, the nonresonant susceptibility has been measured for TbAlG : xNRxxxx = (12.4±2.5)×10−14 m3/J and xNRxyyx = (3.8±0.8)×10−14 m3/J.

DOI: 10.1063/1.329784

Related papers

Nonradiative Transitions Between Levels of Trivalent Rare-earth Ions in Yttrium-Aluminum Garnet Crystals

Georgii M. Zverev, G. Ya. Kolodnyǐ, А. М. Онищенко

Journal of Experimental and Theoretical PhysicsJan 1, 197111 citations

Nondegenerate Four Wave Mixing in Rare-Earth Doped Fiber Under the Influence of Coherent Population Trapping

Guo Yang, Ming Hai, Liu Fang-Xin +1 more

Chinese Physics LettersApr 1, 20000 citations

Negative refraction in terbium at ultraviolet frequencies

Zachary Noel Buckholtz, Deniz D. Yavuz

Optics LettersAug 10, 20204 citations

Interconfigurational two-photon transitions in Nd^3+:Y_3Al_5O_12

Swapan Kumar Gayen, Bin Qing Xie

Journal of the Optical Society of America BJun 1, 19938 citations

Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Stefan Kröll, E. Y. Xu, M. K. Kim +2 more

Physical review. B, Condensed matterJun 1, 199033 citations

Observation of sub-kilohertz resonance in Rf-Optical double resonance experiment in rare earth ions in solids

M. K. Kim, Byoung Seung HAM, Philip Hemmer +1 more

Journal of Modern OpticsAug 15, 20003 citations

Journal of Applied Physics

Enhancement of third-order susceptibility due to electronic transitions in rare-earth ions

Michael L. Shand

Published Mar 1, 1981• 8 citations

Publisher

Abstract

DOI: 10.1063/1.329784

Related papers

Nonradiative Transitions Between Levels of Trivalent Rare-earth Ions in Yttrium-Aluminum Garnet Crystals

Georgii M. Zverev, G. Ya. Kolodnyǐ, А. М. Онищенко

Journal of Experimental and Theoretical PhysicsJan 1, 197111 citations

Nondegenerate Four Wave Mixing in Rare-Earth Doped Fiber Under the Influence of Coherent Population Trapping

Guo Yang, Ming Hai, Liu Fang-Xin +1 more

By applying a strong coupling field between a lower state and the upper state of an allowed transition to ground, an enhancement of nondegenerate four wave mixing (NDFWM) with a resonantly enhanced third-order nonlinear susceptibility in a rare-earth doped fiber can be obtained. We have derived an expression for the third-order nonlinear susceptibility using quantum theory and discussed the conversion efficiency for NDFWM. The theoretical result shows that the conversion efficiency has a maximum value while the third-order nonlinear susceptibility shows constructive interference at the Rabi frequency Ω 23 = ±√Γ 2 Γ 3 . On account of phase-mismatch, the frequency conversion efficiency has a maximum value over a certain small range of frequency separation (such as 0 < Δ f < 30 GHz at the wavelength λ c = 1.55 μm), and the frequency conversion range increases with increase of the third-order nonlinear susceptibility.By applying a strong coupling field between a lower state and the upper state of an allowed transition to ground, an enhancement of nondegenerate four wave mixing (NDFWM) with a resonantly enhanced third-order nonlinear susceptibility in a rare-earth doped fiber can be obtained. We have derived an expression for the third-order nonlinear susceptibility using quantum theory and discussed the conversion efficiency for NDFWM. The theoretical result shows that the conversion efficiency has a maximum value while the third-order nonlinear susceptibility shows constructive interference at the Rabi frequency Ω 23 = ±√Γ 2 Γ 3 . On account of phase-mismatch, the frequency conversion efficiency has a maximum value over a certain small range of frequency separation (such as 0 < Δ f < 30 GHz at the wavelength λ c = 1.55 μm), and the frequency conversion range increases with increase of the third-order nonlinear susceptibility.

Chinese Physics LettersApr 1, 20000 citations

Negative refraction in terbium at ultraviolet frequencies

Zachary Noel Buckholtz, Deniz D. Yavuz

One of the key challenges in the development of negative index metamaterials is creating a sufficiently strong magnetic response in the material. Rare-earth ions can contain a strong optical magnetic response even in the ultraviolet region of the spectrum, which can be enhanced using magneto-electric cross-coupling. Using energies, transition strengths, and linewidths from atomic structure software, along with realistic inhomogeneous broadenings and densities in a solid, we simulate a negative index scheme using a terbium crystal at a wavelength of 282 nm.One of the key challenges in the development of negative index metamaterials is creating a sufficiently strong magnetic response in the material. Rare-earth ions can contain a strong optical magnetic response even in the ultraviolet region of the spectrum, which can be enhanced using magneto-electric cross-coupling. Using energies, transition strengths, and linewidths from atomic structure software, along with realistic inhomogeneous broadenings and densities in a solid, we simulate a negative index scheme using a terbium crystal at a wavelength of 282 nm.

Optics LettersAug 10, 20204 citations

Interconfigurational two-photon transitions in Nd^3+:Y_3Al_5O_12

Swapan Kumar Gayen, Bin Qing Xie

Resonantly enhanced, near-ultraviolet 4f3 → 4f25d two-photon transitions have been observed in trivalent neodymium-doped yttrium aluminum garnet (Nd3+:Y3Al5O12). The two-photon excitation spectra over the 40 400–46 730 cm−1 transition energy range are characterized by sharp resonance peaks on a slowly varying background caused by nonresonant transitions. The peak two-photon cross section involving the 2P1/2 resonant intermediate state is 9 × 10−51 cm4 s, and the integrated cross section is 2.2 × 10−38 cm4.Resonantly enhanced, near-ultraviolet 4f3 → 4f25d two-photon transitions have been observed in trivalent neodymium-doped yttrium aluminum garnet (Nd3+:Y3Al5O12). The two-photon excitation spectra over the 40 400–46 730 cm−1 transition energy range are characterized by sharp resonance peaks on a slowly varying background caused by nonresonant transitions. The peak two-photon cross section involving the 2P1/2 resonant intermediate state is 9 × 10−51 cm4 s, and the integrated cross section is 2.2 × 10−38 cm4.

Journal of the Optical Society of America BJun 1, 19938 citations

Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Stefan Kröll, E. Y. Xu, M. K. Kim +2 more

Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$ ${\mathrm{\ensuremath{-}}}^{3}$ ${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$ :YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$ ${\mathrm{\ensuremath{-}}}^{1}$ ${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ , and $^{7}\mathrm{F}_{0}$ ${\mathrm{\ensuremath{-}}}^{5}$ ${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$ :YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{3}$${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$:YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$, and $^{7}\mathrm{F}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$:${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.

Physical review. B, Condensed matterJun 1, 199033 citations

Observation of sub-kilohertz resonance in Rf-Optical double resonance experiment in rare earth ions in solids

M. K. Kim, Byoung Seung HAM, Philip Hemmer +1 more

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 ® eld is scanned across the hyper® ne transitions while monitoring the resonant optical absorption of a CW laser. The ea ect is observed only when the laser spectral width is broad compared to the hyper® ne structure. The observed line widths are apparently free of the inhomogeneous widths of hyper® ne levels and the line shape has peculiar double peak structure. The ea ect is modelled with a resonance involving three atomic levels interacting with three electromagnetic ® elds, two optical and one RF, in a triangular ordelta' con® guration. While the ordinary optical- RF two-® eld resonance is limited by spin inhomogeneous width, the simul- taneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyper® ne transition. We have observed a peculiarly narrow resonance structure in the course of optical-RF double resonance experiment of rare earth ions in solids. The reso- nance is characterized by a sharp doublepeak structure in the absorption spectrum as the RF frequency is scanned across the hyper® ne transition, with the few kilohertz width of the transparency hole at least an order of magnitude narrower than the spin inhomogeneous width. The ea ect is evident only when the laser bandwidth is larger than the hyper® ne level splittings. A theoretical model is presented based on the assumption that the optical ® elds of a noisy laser simul- taneously couples an optically excited state with two hyper® ne levels of the ground state, which in turn are acted on by the RF ® eld. A quantum interference ea ect among the three coupled transitions creates sharp fringes in the frequency domain that are not averaged out by ensemble average over the inhomogeneousbroadening of the optical or spin transitions. The model is found to be consistent with the main features of the experimental observations. Various quantum interference ea ects in atomic transitions have recently been research topics of great interest, because of the rich and often counter-intuitiveWe 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 ® eld is scanned across the hyper® ne transitions while monitoring the resonant optical absorption of a CW laser. The ea ect is observed only when the laser spectral width is broad compared to the hyper® ne structure. The observed line widths are apparently free of the inhomogeneous widths of hyper® ne levels and the line shape has peculiar double peak structure. The ea ect is modelled with a resonance involving three atomic levels interacting with three electromagnetic ® elds, two optical and one RF, in a triangular ordelta' con® guration. While the ordinary optical- RF two-® eld resonance is limited by spin inhomogeneous width, the simul- taneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyper® ne transition. We have observed a peculiarly narrow resonance structure in the course of optical-RF double resonance experiment of rare earth ions in solids. The reso- nance is characterized by a sharp doublepeak structure in the absorption spectrum as the RF frequency is scanned across the hyper® ne transition, with the few kilohertz width of the transparency hole at least an order of magnitude narrower than the spin inhomogeneous width. The ea ect is evident only when the laser bandwidth is larger than the hyper® ne level splittings. A theoretical model is presented based on the assumption that the optical ® elds of a noisy laser simul- taneously couples an optically excited state with two hyper® ne levels of the ground state, which in turn are acted on by the RF ® eld. A quantum interference ea ect among the three coupled transitions creates sharp fringes in the frequency domain that are not averaged out by ensemble average over the inhomogeneousbroadening of the optical or spin transitions. The model is found to be consistent with the main features of the experimental observations. Various quantum interference ea ects in atomic transitions have recently been research topics of great interest, because of the rich and often counter-intuitive

Journal of Modern OpticsAug 15, 20003 citations

Photon-echo-relaxation measurements made on the

^{3}\mathrm{H}_{4}

${\mathrm{\ensuremath{-}}}^{3}$

{\mathrm{P}}_{0}

transition of 0.01 at. %

{\mathrm{Pr}}^{3+}

:YAG (where YAG represents yttrium aluminum garnet),

^{3}\mathrm{H}_{4}

${\mathrm{\ensuremath{-}}}^{1}$

{\mathrm{D}}_{2}

transition in 0.1 at. %

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

, and

^{7}\mathrm{F}_{0}

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

{\mathrm{D}}_{0}

transition in 0.25 at. %

{\mathrm{Eu}}^{3+}

{\mathrm{YAlO}}_{3}

show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in

{\mathrm{Pr}}^{3+}

:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring

{\mathrm{Pr}}^{3+}

ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.