Effect of spatial variation of the duty cycle in transverse second-harmonic generation

Transverse second-harmonic generation, in which the emission angles of the second harmonic are determined by the spatial modulation of the quadratic nonlinearity, has important applications in nonlinear optical imaging, holography, and beam shaping. Here we study the role of the local duty cycle of the nonlinearity on the light intensity distribution in transverse second-harmonic generation, taking the generation of perfect vortices in periodically poled ferroelectric crystal as an example. We show, theoretically and experimentally, that spatial variations of the nonlinearity modulation must be accompanied by the corresponding changes of the width of inverted ferroelectric domains, to ensure uniformity of the light intensity distribution in the generated second harmonic. This work provides a fundamental way to achieve high-quality transverse second-harmonic generation and, hence, opens more possibilities in applications based on harmonic generation and its control.