A first-order formula for calculations of the direction cosines of the rays refracted by Risley prisms was derived. The formula was obtained by representing the deviation of the ray passing through a prism by the product of rotation matrices, and using the series expansion of the product. It can be applied to the system of an arbitrary number of prisms or a combination of Risley prisms. Related errors were discussed and some numerical calculations were made and compared with the exact solutions using the refraction equation. The scan patterns of a single Risley prism or a combination of two Risley prisms calculated using the generalized first-order formula are in good agreement with the exact solutions.
We evaluated characteristics of various shapes of reflector to get uniform and efficient pumping of Nd:YAG rod
even with single-side pumping geometry using commercial software ZEMAX and LASCAD. The combined application
of the software enabled us to evaluate numerically the laser performance and absorbed pump diode profile. We tried
various shape of reflector such as semi-circular, square, elliptical reflectors, and cusp-shape, to get uniform pumping. In
the calculation, water flows inside the cooling tube which surrounds the Nd:YAG rod. For further improvement a planarconcave
window was placed in front of the diode to enlarge pump beam divergence angle. Through several trial and
error, we found optimal pumping chamber configuration for single-side pumping, which gives reasonably uniform and
efficient pumping of Nd:YAG rod. The output power and pulsewidth of Q-switched laser output were optimized by
varying the laser cavity length and the output coupler reflectivity.