Simulation of Thermal Effects in Totally and Partially Pumped Solid-State Laser Rod with Side-Pumping Structure

In this work, a steady-state heat transfer equation in a side-pumped Nd:YAG laser rod was solved numerically using finite element method (FEA). The resulting temperature and stress distributions were calculated under the condition of totally and partially direct side pumping structures with LASCAD software. From the result of simulation, we compare between the different pumping lengths, and mainly indicate the effect of pumping lengths on the temperature distribution, stress, displacement and the optical path difference (OPD). Keyword: Thermal Effects, Side-Pumping Structure, pump Uniformity. خضملا ةبلصلا ةلاحلا رزیل ملقل ةیرارحلا تاریثأتلا ةاكاحم ُایئزجو ًایلك بناجلا نم ةــــــــــــصلاـخلا رز#یل م#لقل ًایددع ةرارحلا لاقتنا ةلداعم لحل ةدودحملا رصانعلا ةقیرط مادختسا مت لمعلا اذھ يف مویمید#نلا دویاد#لا رز#یل مادخت#ساب ب#ناجلا ن#م خ#ضملاو كا#ی . م#ت د#قل ةرار#حلا تا#جرد تا#عیزوت با#سح او رز#یللا م#لق ى#لع ةد#لوتملا تادا#ھجلا ًا#یئزجو ًا#یلك ةر#شابم ةرو#صب خ#ضملاو جما#نرب مادخت#ساب میم#صت رز#یللا فیوا#جت ل#یلحتو (LASCAD) . ا#ھیلع لو#صحلا م#ت ي#تلا جئا#تنلا للا#خ ن#م , ت#مت لا ة#نراقم نی#ب ا لاوط ریثأ#ت ى#لا ةرا#شلاا متو ةمدختسملا خضلا #جرد ع#یزوت ةرار#حلا تا , تادا#ھجلاا , ةد#لوتملا ة#حازلاا ریثأت كلذكو لوط يرصبلا راسملا قرف ىلع خضلا . INTRODUCTION iode pumped solid-state lasers have many obvious advantages over the traditional lamp-pumped solid-state lasers, especially in the aspect of overcoming the thermally induced problems. Thermal effect is still one of the major problems for the application and commercialization of high-power DPSS lasers. Strong thermal effects caused by the deposited heat in laser crystals introduce complications, that is, the laser crystal is greatly influenced by the heat induced; it limits the maximum pump power and makes its resonator unstable [1]. Subsequent cooling of the crystal medium with the associated thermal gradient would lead to a thermally-induced change of refractive index. D Eng. & Tech. Journal , Vol.32,Part (A), No.3, 2014 Simulation of Thermal Effects in Totally and Partially Pumped Solid-State Laser Rod with Side-Pumping Structure 609 Many noticeable efforts for managing and reducing thermal effects under various types of pumping geometries are found in [2-6]. In this work, thermal problems in a totally and partially side-pumped Nd: YAG laser rod under super-Gaussian pumping profile was modeled using finite element method with the LASCAD software package. PUMP LIGHT DISTRIBUTION IN LASER ROD Diode laser arrays with a maximum CW output power of 90W at the center wavelength of 808nm were selected to side pump an Nd: YAG rod of 3mm in diameter, and 33mm in length. In the simulation process, 9 diode arrays, which are arranged in 3 groups around the rod was used. Each group contains 3 diodes that illuminate the rod symmetrically from 3 sides. The length of the diodes are (11mm) for totally pumping structure and (10 mm) and (9mm) for partially side pumping structure as shown in Figure (1). Figure (1) Cross section of laser crystal with side-pumping geometry. For totally side pumping structure, the first group extends from z=0 mm to z=11 mm, the second from z=11 mm to z= 22 mm, and the third from z=22 mm to z=33 mm, while for partially pumping structure, two pumped length has been used (30mm) and (27mm) respectively. For (30mm) the first group extends from z=1.5 mm to z=11.5 mm, the second from z=11.5 mm to z= 21.5 mm, and the third from z=21.5 mm to z=31.5 mm. while for (27mm) the first group extends from z=3 mm to z=12 mm, the second from z=12 mm to z= 21 mm, and the third from z=21 mm to z=30 mm. The origin z=0 is located at the center of the left end face of the rod. The groups are offset with respect to each other by an angle of 360/2m, where m is the number of bars around the rod. The laser beam emitted from a linear diode array can be described with a Gaussian beam [7]. The main characteristics are that it is generally with a slow axis divergence ( ) // θ full angle of o o 12 10 − and a fast axis divergence ( ) ⊥ θ full angle Eng. & Tech. Journal , Vol.32,Part (A), No.3, 2014 Simulation of Thermal Effects in Totally and Partially Pumped Solid-State Laser Rod with Side-Pumping Structure 610 of o o 40 35 − . Since, the pumping energy distribution in the cross-section of the rod is more important for side pumping; so we can neglect the divergence in the direction of the slow axis and assumes that the fast axis pump profile of the diodes is superGaussian with exponent 4. The diodes illuminate the rod through a flow tube with inner diameter of 5 mm and outer diameter 7 mm. The pump light is reflected by a reflector concentric with the rod whose distance from the rod is 4 mm. Numerical Model to Calculate Temperature Distribution The following equation governs the temperature distribution in steady-state heat problems [8]: ( ) ( ) K X Q X T − = ∇ 2 ... (1) Where: Q(X) is the distribution of heat power density in (W/m), K is the thermal conductivity in (W/m.K), and T(X) is the temperature distribution of the laser rod in (K) with a water cooling procedure. The boundary conditions at the end and side surfaces of the rod are given by [9,10]