We predict theoretically that it is possible to stabilize the steady state in multimode, intracavity doubled, diode pumped Nd:YAG (neodymium-doped yttrium aluminum garnet) lasers using two output signals, namely, the sum intensities of the infrared laser modes polarized in two different orthogonal directions (X and Y) and one feedback input parameter, the pump rate. The stabilization is possible for arbitrarily large numbers of modes polarized in the X and Y direction. Different strategies of stabilization based on proportional feedback, derivative control, and their combination are discussed. The analytical and numerical results of the linear control theory are illustrated with numerical simulations of the underlying nonlinear differential equations. We show that one can maintain the stable steady state of the laser output for an arbitrarily large pump rate by taking advantage of a tracking procedure.
We suggest a quantitatively correct procedure for reducing the spatial degrees of freedom of the space-dependent rate equations of a multimode laser that describe the dynamics of the population inversion of the active medium and the mode intensities of the standing waves in the laser cavity. The key idea of that reduction is to take advantage of the small value of the parameter that defines the ratio between the population inversion decay rate and the cavity decay rate. We generalize the reduction procedure for the case of an intracavity frequency doubled laser. Frequency conversion performed by an optically nonlinear crystal placed inside the laser cavity may cause a pronounced instability in the laser performance, leading to chaotic oscillations of the output intensity. Based on the reduced equations, we analyze the dynamical properties of the system as well as the problem of stabilizing the steady state. The numerical analysis is performed considering the specific system of a Nd:YAG (neodymium-doped yttrium aluminum garnet) laser with an intracavity KTP (potassium titanyl phosphate) crystal.
Mask topography contributes diffraction-induced phase near edges, affecting the through-focus intensity variation and hence the process window at the wafer. We analyze the impact of edge diffraction on projection printing directly with experiments on an aerial image measurement system (AIMS). We show here that topographic effects change with illumination angle and can be quantified using through-focus intensity measurements. Offaxis incidence influences not just defocus image behavior (as for normal incidence), but also the at-focus intensity at wafer. Moreover, with oblique illumination, mask diffraction varies for left-facing and right-facing sidewalls, the nature of the asymmetry being polarization dependent. The image degradation due the polarization parallel to the sidewall (TE) is seen to be stronger, owing to the interplay of mask topography and pupil filtering in the imaging system. This translates to a CD variation of 2% between the two polarizations, even at focus. A simple thin-mask boundary layer model that treats each sidewall independently is shown to be able to approximate mask topography induced diffraction for both polarizations with 5-10nm wide boundary layers.
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