Аннотация:Crystalline and glass Nd-doped laser media are widely used to produce and amplify high-peak-power picosecond and short nanosecond pulses. Most often, laser action occurs between the Stark sublevels of the 7F3/2→4I11/2 transition, which is usually addressed as a classical 4-level scheme. However, when amplifying pulses with duration comparable to or shorter than the lifetime of the lower laser level, the aspiring to implement the most energetically favorable amplification regime closed to saturation, can meet so-called "bottleneck" effect [1]. Population accumulates at the lower laser level during the pulse amplification and tends to be equalized with the upper level population. As a result, the medium becomes more optically transparent and the gain drops. In turn, sufficiently rapid relaxation of the lower laser level population, contributes to the partial recovery of the population difference and, respectively, to the amplifying ability of the medium. Thus, the detailed description of short pulse amplification represents a substantially non-stationary task depending on specific parameters of the amplifying medium. Here we focus on the lower level relaxation.Based on the available data on the lower laser level lifetimes in various Nd-doped crystalline and glass matrices, one can conclude that the values differ quite significantly. For example, in the cases of widely used popular media such as Nd:YAG, Nd:YLF, Nd:glass etc. the values range from near 100 ps to over 10 ns [1]. These important nuances should be taken into account when developing advanced energy-effective laser systems. Two-pass amplifying schemes are the mportant structural components of many linear laser amplifying systems providing operation near the saturation condition and representing optimal solution from the point of view of pump conversion efficiency. They offer near uniform complete exhaustion of population inversion along the entire length of the pumped laser medium [2]. This seemingly obvious statement may not be entirely correct if to neglect the terminal laser level population relaxation conditions. Thus, the value of the lifetime of the lower laser level should be adequately taken into account when creating efficient, especially two-pass, schemes for amplifying picosecond and short nanosecond pulses. However, reference information on this matter is often only approximate, and the data from the most systematic studies [1] upon closer examination appear to be the result of indirect measurements. Previously, we proposed and implemented experimentally an approach for direct measurement the dynamics of partial gain recovery of a probe pulse following the saturating one with a variable delay in Nd:YAG amplifier [3,4]. The performed analysis showed that the lifetime of the lower level is at least no more than 100 ps. Further refinement and obtaining a lower estimation value require more detailed measurements, saturating and probe pulses better time reference, as well as adequate modeling of the gain under the partial saturation and the accompanying lower level population relaxation. We develop these approaches in the present work. The experiments are performed with a picosecond laser delivering 40 ps pulses of several mJ energy, split into saturating and probe channels with orthogonal polarizations and with a relative time shift by means of an optical delay line. In the case of Nd:YAG, a significant complicating factor is the closeness of the values of the relaxation time being studied and the duration of the laser pulses employed in the scheme. Based on the experimental data and calculations, we came to a more accurate estimation 60±20 ps of the lower level relaxation time in Nd:YAG.We modified a widely used model of laser pulse amplification [5] by introducing corrections that take into account the finite value of the relaxation rate of the lower laser level. This approach allowed possibility of accurate and adequate analysis of practical schemes for two-pass side- and end-pumped picosecond pulse amplifiers. Also, it looks attractive when applied to short nanosecond amplifier schemes on Nd:glass. [1] C. Bibeau, S.A. Payne, H.T. Powell. J. Opt. Soc. Am. B 12(10) 1981-1992 (1995).[2] V.B. Morozov, A.N. Olenin, D.V. Yakovlev. ALT 2024, Vladivostok, Book of Abstracts, 135 (2024).[3] V.B. Morozov, A.N. Olenin, D.V. Yakovlev. ALT 2023, Samara, Book of Abstracts, LS-0-14 (2023).[4] V.B. Morozov, A.N. Olenin, D.V. Yakovlev. ICLO 2024, IEEE Photonics Society, 17 (2024).[5] L.M.Frantz, J.S.Nodvik. J. Appl. Phys. 34(8) 2346-2349 (1963)
