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Physical Review Letters

Ultranarrow Nonlinear Optical Resonances in Solids

Duncan G. Steel, Stephen Colby Rand

Published Nov 18, 1985• 50 citations
Publisher

Abstract

Using a method for nonlinear laser spectroscopy which eliminates the effects of laser jitter in nearly degenerate four-wave mixing, we present the first direct measurement of the ground-state relaxation rate of optically excited ${\mathrm{Cr}}^{3+}$ ions in Cr: YAl${\mathrm{O}}_{3}$. The Lorentzian linewidth of the emission resonance is 9.8 Hz (FWHM). The mechanism of ground-state relaxation is established to be fluorescent decay of the $^{2}E$ metastable level.

DOI
10.1103/physrevlett.55.2285

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•Jan 1, 1971•0 citations
Using a method for nonlinear laser spectroscopy which eliminates the effects of laser jitter in nearly degenerate four-wave mixing, we present the first direct measurement of the ground-state relaxation rate of optically excited Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions in Cr: YAlO3{\mathrm{O}}_{3}O3​. The Lorentzian linewidth of the emission resonance is 9.8 Hz (FWHM). The mechanism of ground-state relaxation is established to be fluorescent decay of the 2E^{2}E2E metastable level.
We have performed nondegenerate four-wave mixing measurements on Cr(3+) ions in three crystals: BeAl(2)O(4), Gd(3)Sc(2)Ga(3)O(12), and LaMgAl(11)O(19). Two laser beams of the same frequency were used to resonantly pump one of the absorption bands of Cr(3+), and probe beams with three different wavelengths ranging from 442 to 1064 nm were used to generate a signal from the laser-induced population grating. The observed four-wave mixing signal strength was found to increase as the wavelength of the probe beam was decreased. A model was utilized to explain these results based on the change in polarizability of the Cr(3+) ions when they are in the metastable state versus the ground state, and it was found that the dispersion effects can be described by a single-oscillator model with the lowest-energy charge-transfer transition of Cr(3+) making the dominant contribution to the signal.
The nonlinear effect in Cr+3 doped crystals has been studied by populating the excited metastable level 2E through the 4T2 absorption band due to its higher absorption cross section compared with the R lines. The excited state 2E has a complex susceptibility different from that of the ground state so the material susceptibility changes in proportion to the excited state population.1 However, when the laser is sintonized near one of the R lines (the direct transitions between the ground and excited states), we must also consider the effect of this resonant interaction on the nonlinearity.
We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105-\AA{} zero-phonon transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\leftrightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$ of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in a YAlO3{\mathrm{O}}_{3}O3​ crystal at 2\ifmmode^\circ\else\textdegree\fi{} K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction VVV between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened $2\ensuremath{\leftrightarrow}3$ transition. Ground- and excited-state gyromagnetic ratios ${\ensuremath{\gamma}}_{i}(i=X,Y,Z)$ and the interactions VVV are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for 141Pr3+^{141}\mathrm{Pr}^{3+}141Pr3+ which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of \ensuremath{\sim} 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed.
We explore the potential of direct spectroscopy of ultranarrow optical transitions of atoms localized in an optical cavity. In contrast to stabilization against a reference cavity, which is the approach currently used for the most highly stabilized lasers, stabilization against an atomic transition does not suffer from Brownian thermal noise. Spectroscopy of ultranarrow optical transitions in a cavity operates in a very highly saturated regime in which nonlinear effects such as bistability play an important role. From the universal behavior of the Jaynes-Cummings model with dissipation, we derive the fundamental limits for laser stabilization using direct spectroscopy of ultranarrow atomic lines. We find that, with current lattice clock experiments, laser linewidths of about 1 mHz can be achieved in principle, and the ultimate limitations of this technique are at the 1 $\ensuremath{\mu}$Hz level.
Techniques for the measurement of non-radiative decay rates between the optically excited states in solid-state laser materials are described. Two crystals have been investigated, ruby (Cr3+:Al2O3) and Sm2+:CaF2. A review of the spectroscopy of these materials is presented with particular emphasis on aspects relevant to non-radiative decay. An experiment is described using a second harmonic Nd3+ Nd:glass Q-switched laser to pump ruby crystals. Limiting non-radiative relaxation times were derived from the rise of fluorescence. Rubies varying in concentration between 0.05% and 0.4% were studied over a range of temperatures, 77 -> 7000 K. 4T2 -> 2E(E + 2A), 4T2 -> 2T1 (Eb) and 4T2 -> 2T1 (2A + Ea) non-radiative relaxations were all found to be <4ns in good agreement with the experimental results of other workers. Two experiments employing a ruby laser to pump Sm2+ :CaF2 are described. The first used a Q-switched laser and, apart from some improvements was similar to the ruby experiment. An upper limit of 4f5 5d pump -> metastable non-radiative decay of 2ns was found for Sm2+:CaF2, The fluorescence decay constant at 295 K was also measured to be 63ns. The second experiment employed a mode-locked laser and the Sm2+:CaF2 non-radiative decay time was <0.5ns. A new effect - provisionally called 'surface emission' - discovered during the ruby measurements, has been examined in detail and the results of this investigation are presented. A phase-shift technique for the measurement of non-radiative decay times is examined in detail. A pilot experiment using a self-mode-locked He-Ne laser at 633 nm to pump Sm2+:CaF2 is described. The non-radiative relaxation time found by this method was <33ps. Suggestions for improved experiments, both pulsed and phase-shifts, are made and the application of the techniques to other materials is discussed.