Modal approach to quantum temporal imaging

We consider the problem of quantum temporal imaging in the case where the time lens is implemented by a sum frequency generation nonlinear process, in particular when the device is operated in high conversion efficiency regimes. In the general case where the time lens also presents a finite aperture and a nonperfect phase matching, the relevant figures of merit, as for example the temporal resolution, do not have an explicit expression. As a consequence, the performances of the imaging scheme are difficult to assess. We show that this problem can be solved for conversion efficiencies up to 80% in terms of the eigenmodes of the imaging scheme, approximated by chirped Gauss-Hermite functions, and we show how its relevant figures of merit can be extracted from the modal description of the imaging scheme. As a consequence, we obtain criteria allowing one to design imaging schemes with high efficiencies.