A 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 close to 100% conversion efficiency. In the general case where the time lens also presents a finite aperture and a non-perfect 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 imaging scheme are difficult to assess. Having a reliable estimation of these figures of merits is particularly important because they can be significantly different from the regime of low conversion efficiency usually considered in classical temporal imaging. We show that this problem can be approached in terms of the eigenmodes of the imaging scheme 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 to design imaging schemes with close to unity efficiencies.