Transverse Inhomogeneous Carrier-Envelope Phase Distribution of Idler Generated through Difference-Frequency-Generation

The transverse inhomogeneous carrier-envelope phase (CEP) distribution of idler generated through difference-frequency-generation (DFG) in quadratic nonlinear crystals is theoretically studied. In practical CEP stabilized DFG setups, the pump and the signal are usually Gaussian beams with non-uniform intensity distribution. Since the idler CEP is dependent on gain, this non-uniform intensity distribution leads to inhomogeneous gain across the aperture of the idler beam, resulting in a varying transverse idler CEP. Simulation results show that in practical settings, in the high-gain regime, transverse inhomogeneous CEP can be much smaller compared with π/2. However, when gain on the propagation axis reaches saturation, CEP difference can well exceed π/2.