ИСТИНА

In this paper we propose simple and visual approach for analysis of mode composition and beam quality evaluation at longitudinal pumping accompanied by axially symmetric aberrational thermal lens. It directly relates to diode end-pumping which is widely used in laser systems due to compactness and reliability. It provides efficient amplification of lowest cavity mode and, as a result, output beam excellent spatial quality. At the same time, focused pump beam usually produces essentially inhomogeneous intensity distribution in radial direction inside active medium. This results in aberrational component of thermal lens formation and in essentially inhomogeneous amplification profile even at low pump powers. With pump power increasing, growing up aberrations leads to laser beam quality degrading and falling down of output power. In some cases, it is suitable to consider aberrations as a mechanism of additional diffraction losses for lowest Gaussian mode of resonator without aberrations [1,2]. It allows defining stable laser operation condition [2]. Such approach thought contains definite internal contradiction since mode of resonator with aberrational lens principally is not Gaussian. Universal way of aberrations accounting and finding resonator modes is Fox-Li method [3]. However, it does not provide visual presentation of resonator mode composition and its dependence on aberrational lens parameters. We present here an approach for finding modes of resonator with aberrational thermal lens in axially symmetric case on the basis of field decomposition into Laguerre-Gaussian beams. Aberrational thermal lens works as a phase screen redistributing energy between different order components. Field roundtrip through resonator is described by action of a linear operator on vector with coordinates equal to decomposition coefficients. Each operator eigenvector defines some resonator mode and consists of decomposition coefficients set, which depends on specific form of aberrational lens, and each eigenvalue defines roundtrip losses and phase shifts for corresponding mode. Width of “embedded” Laguerre-Gaussian beams may be found on the basis of mode field distribution [4]. Coefficients set of “embedded” beams gives visual presentation of mode structure and clearly characterizes space quality of laser output. Results for typical resonator with aberrational thermally induced power depending lens will be presented. Radially inhomogeneous amplification in steady-state may be incorporated into roundtrip operator that makes it possible to find field distribution in this case. Profiled amplification influence on mode structure of resonator with aberrational lens is analyzed. Performance of pulsed end-diode-pumped laser will be examined on the basis of proposed approach. Using pulsed pump regime usually implies energy accumulation during the pump pulse and subsequent fast amplification of pico- or nanosecond radiation pulse. Round trip amplification in this case usually is much higher than in cw lasers. Therefore relation between transversal sizes of pumped region in active medium and of laser mode affects not only pump power transfer efficiency, but the laser mode profile too. On the basis of modeling results, we propose optimization criterion for efficient generation of high-quality beam in end-diode-pumped picosecond laser with aberrational thermal lens. [1] J.Bourderionnet, A.Brignon, J.-P.Huignard, R. Frey, Influence of aberrations on fundamental mode of high power rod solid-state lasers, Opt. Commun., 204, 299-310 (2002); [2] V.B. Morozov, A.N. Olenin, V.G. Tunkin, D.V. Yakovlev, Operation conditions for a picosecond laser with an aberration thermal lens under longitudinal pulsed diode pumping, Quant. Electron., 41, 508-514 (2011); [3] A.G. Fox, T. Li, Resonant modes in a maser interferometer, Bell Syst. Tech. J., 40, 453-488 (1961); [4] A. Siegman, “How to (Maybe) Measure Laser Beam Quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues p. MQ1 (OSA, 1998).