IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 5, MAY2004 499 Reduction of Thermally Induced Lenses in Nd:YAG With Low Temperatures Hansjürg Glur, Raphael Lavi, and Thomas Graf Abstract—At high pump powers, Nd:YAG lasers suffer from thermally induced optical effects such as graded-index lenses, bire- fringence, and bi-focusing. Due to more favorable material prop- erties at low temperatures, the thermal lenses are significantly re- duced by cryogenic cooling. In the present study, we measured the thermal lens in a Nd:YAG rod to be reduced by more than an order of magnitude when cooled with liquid nitrogen. Index Terms—Nd:YAG lasers, thermal effects. I. INTRODUCTION A T HIGH PUMP powers, Nd:YAG lasers suffer from ther- mally induced optical effects such as graded-index lenses, birefringence, bi-focusing, and higher order optical aberrations as well as stress-induced damage of the crystal. The (ideal spher- ical) thermal lens limits the power range over which a resonator supports stable laser oscillation [1], whereas the spherical aber- rations cause diffraction losses [2] that significantly limit the laser performance at high powers. The ultimate power limit is finally given by the stress fracture of the laser material. The key parameters for these thermally induced effects in the laser ma- terials are the heat conductivity , the expansion coefficient , the thermal dispersion , and the photoelastic coefficients . An improved heat conductivity is beneficial for all of the abovementioned effects. However, for a significant reduction of the thermally induced optical distortions, it is also important to have small values for , , and . It is well known that the heat conductivity is improved at lower temperatures but the behavior of and of YAG at cryogenic temperatures still requires more detailed research. Recent investigations [3], [4] led to two different models for the temperature dependence of and . One of the two models predicts that the thermal dispersion reaches a value of exactly 0 K at a temper- ature of about 80 K, which would mean that the graded-index lens would completely vanish in an Nd:YAG laser rod that is properly cooled with liquid nitrogen. As this has, to the best of our knowledge, not yet been observed experimentally, to inves- tigate the behavior of the thermal effects at cryogenic cooling in more detail we performed a series of experiments that are sum- marized in the following. Based on our experimental results, it was possible to determine which of the two proposed models for the temperature dependence of the expansion coefficient and the Manuscript received June 24, 2003; revised January 13, 2004. H. Glur and T. Graf are with the Institute of Applied Physics, University of Bern, Bern, Switzerland. R. Lavi is with the Nonlinear Optics Group, Electro-Optics Division, Soreq NRC, Yavne 81800, Israel. Digital Object Identifier 10.1109/JQE.2004.826448 thermal dispersion is more accurate in the temperature range be- tween 80 K and room temperature. Although all (higher order) optical aberrations are affected by the abovementioned material properties, we restrict our discussion to the dioptric power of the thermally induced lenses, since it gives already enough informa- tion on the behavior of the investigated material parameters. A. Thermal Lenses There are three effects that contribute to the dioptric power of the thermally induced lens (1) where is due to the thermal dispersion, is caused by thermal expansion, and is due to the thermally induced strain. In an end-pumped laser rod, the three contributions are given by [5] (2) (3) (4) with (5) where is the incident pump power, is the absorbed pump power, and is the pump spot radius. The other quantities are listed in Table I. Inserting (2)–(4) into (1), we obtain (6) hence (7) The quantity depends only on the material properties and the geometry and is referred to as specific dioptric power. Under the condition that every mode with a radius smaller than is oscillating, the maximum absorbed pump power range for stable oscillation of any symmetric laser resonator without apertures smaller than the gain region is given by [1] (8) 0018-9197/04$20.00 © 2004 IEEE