Gain-induced spectral non-degeneracy in type-II parametric down-conversion

Abstract

We demonstrate the novel effect of gain-induced spectral shifts in the type-II parametric down-conversion (PDC) process, which results in a transition from degenerate to non-degenerate PDC with increasing parametric gain. This effect, originating from the second-order dispersion terms, significantly alters the properties of PDC in the high-gain regime, where it leads to increased distinguishability of the generated photon pairs. The effect is established by evaluating a rigorous theoretical model, which is based on solving a system of coupled integro-differential equations for monochromatic operators. The widely used spatially-averaged approximate model fails to reproduce this important effect.

Figures (12)

• Figure 1: The scheme of the (a) low-gain and (b) high-gain regime of type-II PDC. Signal (s) and idler (i) fields belong to the orthogonal polarizations. (c,d) The spectra of the generated signal (dashed) and idler (solid) fields for (c) low and (d) high gain, respectively.
• Figure 2: (a,b) The dependence of the RSD on the total number of generated photons (parametric gain) for a set of waveguides with randomly chosen dispersion in the case of (a) $\Delta k_2=0$ and (b) $\Delta k_2\neq0$. Each line presents a fixed waveguide. (c) The distribution of the RSD (color bar) in the characteristic time space ($\tau_1/\tau$, $\tau_2/\tau$) for the fixed number of generated photons $N=10$. Each dot presents a fixed waveguide. The diamond and triangle correspond to examples Ex1 and Ex2 shown in (d, e) and (f, g), respectively. (d, f) The low-gain regime with ($N \approx10^{-5}$), (e, g) the high-gain regime with ($N\approx10^{7}$). The star corresponds to the random waveguide in Fig. \ref{['evol']} of the SM sec. \ref{['evo_section']}. In Figs. (d-g) and below for similar figures, the red diagonal lines indicate the FWHM of the pump spectral function $S(\Omega_s+\Omega_i)$. The black solid lines represent the isolines of the wavevector mismatch $\Delta k$ [1/$\mu m$].
• Figure 3: Normalized JSI for (a,b) WG0, (c,d) WG1, and (e,f) WG2 in the case of (a,c,e) low-gain and (b,d,f) high-gain regimes with the total number of generated photons $N\approx10^{-5}$ and $N\approx10^5$, respectively.
• Figure 4: FWHM of the idler (solid) and signal (dashed) spectra as a function of the number of generated photons for (a) WG0 and WG1 and (b) WG2. RM corresponds to the rigorous model and AM to the spatially-averaged model.
• Figure 5: Relative spectral distance for WG2 as a function of the pump pulse duration. Different colors correspond to different numbers of generated photons N. Note that the blue and orange lines almost coincide.