Simultaneous Matching of Phase and Amplitude for Spontaneous Parametric Down-conversion in Semiconductor Waveguides

We propose a non-uniform modulation of $\chi^{(2)}_{xyz}$ to significantly enhance photon pair generation efficiency via spontaneous parametric down-conversion in modal phase-matched semiconductor waveguides. This approach enables amplitude-matching in the transverse direction while preserving the phase-matching along the waveguide propagation axis. Our analysis predicts a tenfold efficiency increase in comparison to the most efficient non-modulated waveguide, and up to 13 orders of magnitude efficiency enhancements relative to solely phase-matched waveguides. Furthermore, we explore the implementation of a highly efficient compact twin-photon source, tunable across the communication band, using an amplitude- and phase-matched structure.