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Physical Review Letters

Discrimination of Resonant and Nonresonant Contributions to the Nonlinear Refraction Spectroscopy of Ion-Doped Solids

S.M. Lima, T. Catunda

Published Dec 14, 2007• 26 citations
Publisher

Abstract

Nonlinear refraction spectroscopy measurements were performed in resonance with absorption lines in Nd3+ and Cr3+ doped crystals. The observed line shapes can be explained by the interference of resonant and nonresonant contributions to the nonlinear refractive index. These effects were fully discriminated using a pump and probe configuration, in which a dispersive line shape was observed on the top of a plateau that was attributed to the polarizability difference between excited and ground states (Deltaalpha). A theoretical model was used to obtain Deltaalpha from the experimental data, and the results are in agreement with several previous experiments. Slow and fast light propagation are also discussed.

DOI
10.1103/physrevlett.99.243902

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Optics Letters•Nov 1, 1990•25 citations
Nonlinear refraction spectroscopy measurements were performed in resonance with absorption lines in Nd3+ and Cr3+ doped crystals. The observed line shapes can be explained by the interference of resonant and nonresonant contributions to the nonlinear refractive index. These effects were fully discriminated using a pump and probe configuration, in which a dispersive line shape was observed on the top of a plateau that was attributed to the polarizability difference between excited and ground states (Deltaalpha). A theoretical model was used to obtain Deltaalpha from the experimental data, and the results are in agreement with several previous experiments. Slow and fast light propagation are also discussed.
This work intends to distinguish resonant and nonresonant contributions to the nonlinear refractive index in ion doped solids using a two-color nonlinear technique. In this experiment, the alexandrite metastable excited state (/sup 2/E) is populated via the /sup 4/T/sub 2/ absorption band using a 514 nm pump beam (Ar/sup +/ laser), while the refractive index change is probed by a tunable dye laser, in resonance with the R lines (from ground to metastable transition at /spl lambda/ /spl sim/ 680 nm). The absorption spectrum with the two characteristic R lines is also shown just for comparison of the spectra. Observations reveal that an absorption saturation signal follows the linear absorption spectrum.
The refractive index of most ion-doped materials increases with the excited state population. This effect was studied in many laser materials, particularly those doped with Cr3+ and rare earth ions, using several techniques, such as interferometry, wave mixing, and Z-scans. This refractive index variation is athermal (has an electronic origin) and is associated with the difference in the polarizabilites of the Cr3+ ion in its excited and ground states, Δαp. The Cr3+ optical transitions in the visible domain are electric-dipole forbidden, and they have low oscillator strengths. Therefore, the major contribution to Δαp has been assigned to allowed transitions to charge transfer bands (CTBs) in the UV with strengths ∼3 orders of magnitude higher. Although this CTB model qualitatively explains the main observations, it was never quantitatively tested. In order to further investigate the physical origin of Δαp in Cr3+-doped crystals, excited state absorption (ESA) and Z-scan measurements were thus performed in Cr:Al2O3 (ruby) and Cr:GSGG. Cr:GSGG was selected because of the proximity of its E2 and T24 emitting levels, and thus the possibility to explore the role of the spin selection rule in the ESA spectra and the resulting variations in polarizability by comparing low and room temperature data, which were never reported before. On the other hand, Cr:Al2O3 (ruby) was selected because it is the only crystal for which it is possible to obtain CTB absorption data from both ground and excited states, and thus for which it is possible to check the CTB model more accurately. Thanks to these more accurate and more complete data, we came to the first conclusion that the spin selection rule does not play any significant role in the variation of the polarizability with the E2–T24 energy mismatch. We also discovered that using the CTB model in the case of ruby would lead to a negative Δαp value, which is contrary to all refractive index variation (including Z-scan) measurements.
The mechanism for refractive-index changes that accompany changes in population during pumping and amplification of an optical beam is studied in a Nd:YAG laser crystal by both resonant four-wave mixing and interferometric techniques. It is found that these refractive-index changes (connected with the difference in polarizability of excited and unexcited Nd3+ ions) have two components: a small noninertial component that accompanies an amplified optical pulse and the major changes that are intensified with a delay time of ∼3 µs. The latter effect is explained by population (or depopulation) of a higher-lying energy level 2(F2)5/2 of the 4f electron shell of Nd3+ ions, which has large polarizability in near-IR and visible light. The real part of the nonlinear optical resonant susceptibility of the inverted Nd:YAG caused by the refractive-index changes is also discussed.
Absence of full knowledge on resonant susceptibility (RS) of laser crystals leads to underestimation of different nonlinear optical effects (such as holorgraphic grating formation and others) which are very important for understanding the complicated laser dynamics and construction of new laser architectures. In the majority of previous experiments the resonant wave mixings (using nonlinearity of saturation of the working transition) in inverted Nd:YAG are explained by the gain grating (GG) formation (sec. for example. [1]). On the other hand, it is well known, that pumped and unpumped laser crystals have different refractive indexes due to difference in polarizability of excited and unexcited Nd3 ions [2,3]. However. various investigation methods provide different values of the polarizability difference varying from 4.10−3nm3 [2] to 9.10−4 nm3 [3] for the well-studied Nd-dopcd materials.
The degenerate-multiwave-mixing spectroscopy of alexandrite at 77 K using a pulsed dye laser in resonance with the R1m{\mathit{R}}_{1\mathit{m}}R1m​ line was studied in this work. Unusual asymmetric line shapes that can be explained by an interference effect between resonant and nonresonant contributions of the media susceptibility were observed. The resonant effect is caused by the saturation of the two-level system susceptibility and the nonresonant contribution comes from the linear polarizability difference between excited and ground states. The present work shows an observation of this kind of interference phenomena in degenerate-wave-mixing experiments. Furthermore, we note that it is an observation of saturation line splitting in degenerate wave mixing in a narrow line in solids.
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.