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Journal of the Optical Society of America B

Accurate determination of saturation parameters for Cr^4+-doped solid-state saturable absorbers

Alphan Sennaroğlu, Umıt Demırbas, Sarper Özharar, Fatih Yaman

Published Feb 1, 2006• 43 citations

Abstract

We describe a systematic, rigorous procedure for the determination of the optical absorption saturation parameters for Cr4+:YAG and Cr4+:forsterite crystals at 1064 nm. A rate-equation approach was used to analyze the cw and pulsed transmission data of several crystals by accounting for the transverse as well as longitudinal variation of the beam intensity, saturation effects, and excited-state absorption. Use of an iterative procedure whereby the cw and pulsed data were simultaneously analyzed led to a considerable reduction in the error for the determination of cross sections. The average value of the absorption cross section sigmaa and the normalized excited-state absorption cross section fp=sigmaesa/sigmaa were determined to be 6.13×10−19 cm2 and 0.45, respectively, for Cr4+:forsterite and 19.6×10−19 cm2 and 0.06, respectively, for Cr4+:YAG. Detailed comparison was also made with previous saturation measurements in the literature. Our results further show that lumped models based on the thin-length approximation should be used with caution in the determination of cross sections, especially when the pump beam is tightly focused inside the absorber.

DOI: 10.1364/josab.23.000241

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We describe a systematic, rigorous procedure for the determination of the optical absorption saturation parameters for Cr4+:YAG and Cr4+:forsterite crystals at 1064 nm. A rate-equation approach was used to analyze the cw and pulsed transmission data of several crystals by accounting for the transverse as well as longitudinal variation of the beam intensity, saturation effects, and excited-state absorption. Use of an iterative procedure whereby the cw and pulsed data were simultaneously analyzed led to a considerable reduction in the error for the determination of cross sections. The average value of the absorption cross section sigmaa and the normalized excited-state absorption cross section fp=sigmaesa/sigmaa were determined to be 6.13×10−19 cm2 and 0.45, respectively, for Cr4+:forsterite and 19.6×10−19 cm2 and 0.06, respectively, for Cr4+:YAG. Detailed comparison was also made with previous saturation measurements in the literature. Our results further show that lumped models based on the thin-length approximation should be used with caution in the determination of cross sections, especially when the pump beam is tightly focused inside the absorber.

We studied both experimentally and theoretically the transmission and polarization characteristics of a Cr4+ : YAG saturable absorber crystal as a function of the intensity and polarization state of an incident laser beam. We found that a birefringent absorption behaviour is induced and we show that the experimental results are well described by a full numerical model which includes excited-state absorption as well as a ground-state cross-absorption term. By using pump-probe measurements we show that a finite cross-saturation of the absorption is achieved along the crystal axes orthogonal to the polarization of the optical radiation. No induced refractive index birefringence is observed.

An experimental study of saturable absorption and excited-state absorption (ESA) in several inorganic saturable absorbers, Cr/sup 4+/:YAG, Cr/sup 4+/:GGG, and Cr/sup 4+/:YSGG, is presented. We provide the theoretical background of absorption characteristics in saturable absorbers that exhibit ESA, with some new results: approximate analytical solutions are proposed for the optical transmission in the case of a slow absorber, and for various light intensity conditions of spatially or temporally Gaussian beams in fast and slow absorbers. Experimentally, partial bleaching of the first excited state itself could be observed in Cr/sup 4+/:YAG at /spl lambda/=1064 nm, yielding the higher excited-state lifetime as /spl tau/*=(0.55/spl plusmn/0.1) ns. The regular transmission bleaching curve was measured in Cr/sup 4+/:GGG, for the first time in this material, yielding /spl sigma//sub ga/=(58/spl plusmn/5)/spl times/10/sup -1/ cm/sup 2/, and /spl sigma/e/sub s/=(13/spl plusmn/2)/spl times/10/sup -19/ cm/sup 2/ at /spl lambda/=1064 nm, ESA spectra were measured for the three materials between /spl sim/700 and 900 nm. All three exhibit crossing between saturable absorption at longer wavelengths and inverse saturable absorption at shorter wavelengths.

A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.

Polarization dependence of saturable absorption in Cr4+:YAG was investigated. We theoretically proposed its general analytical formula expressed in terms of the intensity and the polarization angle of the pump beam. We also derive transmission formulas for specific incident surfaces of (100)-, (110)-, and (111)-planes. In order to prove our model, we examined the polarization dependence in the transmittance of (110)-cut Cr4+:YAG. With the consideration of pump depletion in Cr4+:YAG, we succeeded to explain the polarization dependence that is consistent with past spectroscopic parameters of Cr4+:YAG.

The gain dynamics of photoexcited chromium-doped forsterite (Cr4+:Mg2SiO4) were measured by means of a pulsed excite-and-probe technique. The nonradiative relaxation time within the 3T2 vibronic state was determined by measuring the change in the induced gain of the probe pulse as a function of the pumpprobe delay. A 30 ps, 1.064 m pulse from a mode-locked Nd:YAG laser was split into two beams. The first beam provided the pump pulse to populate the 3T2 manifold. The other beam was focused in a calcite crystal to generate a 1.2 m probe pulse by means of stimulated Raman scattering. The transient gain was determined from the measured ratio of the transmitted probe intensity for unpumped and pumped cases as a function of the pumpprobe delay. The rise time (time for growth of the gain from 10% to 90%) was calculated to be 50 ps. A rate-equation analysis of population in the various states was used to extract a value for the vibrational relaxation time from the experimental data under the assumption of Gaussian pump and probe pulses. The best fit to the experimental data of gain as a function of time yields a value of 10 5 ps for the intra-3T2-state vibrational relaxation time.