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Journal of the Optical Society of America B

Nondegenerate two-wave mixing in Cr^3+:Er^3+:YAlO_3

André G. Skirtach, David J. Simkin, Simon A. Boothroyd

Published Mar 1, 1996• 9 citations
Publisher

Abstract

We present the results of nondegenerate two-wave mixing measurements in Cr−3:YAlO3 and in Cr−3: Er−3:YAlO3 in which the induced index change arises from the population of the 2E excited state of the chromium. The presence of erbium ions alters the 2E-level lifetime and quenches the chromium nonlinearity. We interpret our results in terms of a model in which different lifetimes are assigned to the chromium ions. Chromium ions close enough to an erbium ion to experience quenching by nonradiative energy transfer have lifetimes that are shorter than chromium ions that are not affected by energy transfer.

DOI
10.1364/josab.13.000546

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Investigation of non-linear energy transfer dynamics of erbium in yttrium aluminum garnet (Conference Presentation)

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Yttrium Aluminum Garnet (YAG) crystals doped with Erbium have posed an interesting position in the field of rare earth solid state lasers as they possess the property of self-saturation, in which the upper energy level in a laser has a much shorter lifetime than that of the lower level.The non-linear energy transfer dynamics of Er:YAG are modeled under high resonant pump conditions. Specifically the multi-photon effect known as excited state absorption (ESA) is modeled by measuring the cross section in a single crystal Er:YAG sample utilizing a pump and probe technique. The measured ESA cross section is then included in the rate equation modeling that has typically been ignored such an effect when modeling the non-linear ion to ion interactions. By pumping with selective resonant pumps, the interaction dynamics of the upper and the lower laser levels in the Erbium ion reveal the contributions of the non-linear energy transfer mechanisms towards the populations of the levels respectively. This thesis work shows the added accuracy of the rate equation modeling by its inclusion of the measured ESA cross-section and its effect on the population evolution in the Er:YAG system. The model will be tested with measurements made with select Er:YAG crystals being pumped by combinations of resonant infra-red lasers with a chopper spinning at a rate on the order of magnitude of the lower lasing level lifetime.

SPIE Solid State Lasers: Technology and Devices•Mar 13, 2019•0 citations
We present the results of nondegenerate two-wave mixing measurements in Cr−3:YAlO3 and in Cr−3: Er−3:YAlO3 in which the induced index change arises from the population of the 2E excited state of the chromium. The presence of erbium ions alters the 2E-level lifetime and quenches the chromium nonlinearity. We interpret our results in terms of a model in which different lifetimes are assigned to the chromium ions. Chromium ions close enough to an erbium ion to experience quenching by nonradiative energy transfer have lifetimes that are shorter than chromium ions that are not affected by energy transfer.
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.
Yttrium Aluminum Garnet (YAG, Y_3 〖Al〗_5 O_12) crystals doped with Erbium have posed an interesting position in the field of rare earth solid state lasers as they possess the property of self-saturation, in which the upper energy level in a laser has a much shorter lifetime than that of the lower level. This is the case of the 2.94μm transition in Er:YAG. That property at first seems to make this material unfit for use as a laser gain medium, however further research into these classes of rare earth materials revealed interesting non-liner energy transfer mechanisms that allow it to be a useful mid wave infra-red (MWIR) coherent source in the continuous wave (CW) and pulsed regimes. This came to fruition due to decades of modeling and spectroscopic research investigating the non-linear energy transfer mechanisms of excited state absorption (ESA), energy transfer up-conversion (ETU), and cross relaxation (XR). These effects show up in the rise and fall times of the levels observed through fluorescence. Resulting in the non-exponential rise and fall characteristics and having a squared or even cubed relation to the population. The population evolution for each of the lasing levels is now affected by ions recycling energy and in turn cause the lifetimes of the levels to “effectively” change to a point where simple linear models do not adequately describe the system and its performance. The non-linear energy transfer dynamics of Er:YAG are modeled under high resonant pump conditions. By pumping with selective resonant pumps, the interaction dynamics of the (_ ^4)I_(11/2) and the (_ ^4)I_(13/2) levels in the Erbium ion reveal the contributions from generally ignored non-linear energy transfer mechanisms. Specifically, the multi-photon effect known as excited state absorption (ESA) is modeled by measuring and characterizing the cross section in single crystal Er:YAG samples utilizing a pump and probe technique coupled with transient fluorescence measurements. The measured ESA cross section is then included in the rate equation modeling.
The solution of the nondegenerate two-wave-mixing problem in an absorptive Kerr medium including the contribution from nonlinear absorption is obtained for the first time to our knowledge. This solution enables us to analyze the influence of nonlinear absorption on the two-wave-mixing gain and account for previously unexplained results reported for ruby and Cr3+:YAlO3. The effect of nonlinear absorption of a pump beam on the gain of a probe beam is shown to be minimized when incident intensities of the interacting beams are equal. The intensity dependence of the two-wave-mixing gain for dispersive (ruby and Cr3+:YAlO3) media and the gain measurements for absorptive (fluorescein-doped glass) media are also in agreement with the new theory.
An analysis is made of some processes that occur under conditions of accumulation of population inversion due to the 4 I 13/2 – 4 I 15/2 resonant transition in Er 3+ ions in ytterbium–erbium (Yb–Er) glasses of various compositions. Methods of measuring the parameters of direct and reverse excitation energy transfer between Er 3+ and Yb 3+ ions are also studied. It is found that, under certain conditions achieved in practice, appreciable bleaching of the medium should be observed at the frequency of the pump radiation, particularly under conditions of high-intensity reverse transfer of excitation energy from Er 3+ to Yb 3+ ions. This is typical of glasses having a low rate of intracenter relaxation of Er 3+ ions. It is also shown that nonsteady-state rate equations that assume a linear relationship between the rate of interionic transfer and the ground state population of the acceptor consistently describe the energy characteristics of the excitation processes of Yb–Er glasses. In this case, it is not necessary to introduce in the calculation model additional excitation losses that increase nonlinearly with the pump radiation.
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.
Yttrium Aluminum Garnet (YAG) crystals doped with Erbium have posed an interesting position in the field of rare earth solid state lasers as they possess the property of self-saturation, in which the upper energy level in a laser has a much shorter lifetime than that of the lower level.The non-linear energy transfer dynamics of Er:YAG are modeled under high resonant pump conditions. Specifically the multi-photon effect known as excited state absorption (ESA) is modeled by measuring the cross section in a single crystal Er:YAG sample utilizing a pump and probe technique. The measured ESA cross section is then included in the rate equation modeling that has typically been ignored such an effect when modeling the non-linear ion to ion interactions. By pumping with selective resonant pumps, the interaction dynamics of the upper and the lower laser levels in the Erbium ion reveal the contributions of the non-linear energy transfer mechanisms towards the populations of the levels respectively. This thesis work shows the added accuracy of the rate equation modeling by its inclusion of the measured ESA cross-section and its effect on the population evolution in the Er:YAG system. The model will be tested with measurements made with select Er:YAG crystals being pumped by combinations of resonant infra-red lasers with a chopper spinning at a rate on the order of magnitude of the lower lasing level lifetime.