Recently attention is focused on the quasi-phase-matched self-frequency-conversion (SFC) laser generations in rare-earth doped optical superlattice crystals

mainly because of their ability to generate multicolor lasers across the visible portion of the spectrum through a single crystal. We present a general model for quasi-phase-matched SFC lasers in rare-earth doped optical superlattice crystals by combining quasi-phase-matching (QPM) theory and the self-sum-frequency mixing (or self-frequency-doubling) laser patterns. The new model takes into account the TEM

00

distribution of Gaussian beams with loose focusing

absorption and coupling of pump beams

and effects of imperfect periodical structures. Two types of errors:(1) random period errors and (2) linearly tapered period errors in the periodicity of these structures are analyzed to find their effects on the value of equivalent effective nonlinear coefficient and on the tuning curves of normalized conversion efficiency. Finally the model is applied to simulate the SFC laser properties in a Nd

3+

doped aperiodically poled lithium niobate crystal. The calculated results

especially the threshold

the total visible laser output power and spectrum of relative laser intensity in the visible

agree well with the experiment

which indicates the validity of this model. Most significantly

the model presented explains and verifies the simultaneous laser generation of multiple visible wavelengths (686

605

542

482

441 and 372nm) from a single crystal.