Experimental investigation of the effect of dispersion on squeezing generation in a synchronously pumped optical parametric oscillator

Abstract

An experimental investigation of intracavity dispersion effects in a synchronously pumped optical parametric oscillator (SPOPO) is presented. A flexible setup combining spectral and phase shaping of both pump and local oscillator fields with frequency-resolved balanced homodyne detection is employed to examine how intracavity dispersion influences squeezing. Different cavity configurations with varying finesse and dispersion conditions are studied, and the squeezing is measured as a function of pump power and local oscillator bandwidth. Contrary to expectations based on existing theoretical models, the measured squeezing levels remain essentially unchanged as dispersion varies. To account for these observations, a modeling approach is introduced in which intracavity dispersion is described as an effective spectral filtering occurring at the stage of SPOPO supermode generation. Within this framework, the filtering is incorporated directly into the interaction Hamiltonian of the nonlinear process. This perspective establishes a consistent experimental benchmark for the study of dispersion in SPOPOs and underscores the importance of spectral filtering in the interpretation of multimode squeezing experiments.

Figures (11)

• Figure 1: Scheme of the combs involved in the SPDC process. The pump comb (green), centered around $2\omega_0$, generates the quantum-state comb (red) centered at $\omega_0$. The comb of the SPDC photons is then projected onto the cavity comb (gray). In the absence of dispersion (a), the quantum-state comb and the cavity comb coincide. In the presence of dispersion (b), a detuning $\delta\omega_j$ arises between the cavity and quantum-state teeth according to Equation \ref{['eq:dispshift']}, leading to a spectral cut (notice that the cavity teeth are shifted to right with respect to SPDC teeth). The dashed line is the original spectrum for comparison.
• Figure 2: Assessment of the impact of the dispersive phase contribution $\Phi(\omega)$ under the experimental parameters of this work. Top: FWHM in the temporal domain obtained from the Fourier transform of the full cavity response $f(\omega)$ (blue) and of the amplitude term $A(\omega)$ alone (orange), as a function of the GDD. Bottom: relative difference in the temporal width between the two cases (green). At a GDD of 900fs, neglecting the phase term introduces an error below 5%, and in all cases the deviation remains below 8%, quantitatively validating the amplitude-only approximation.
• Figure 3: Top: temporal duration $\tau_s$ of the fundamental supermode as a function of intracavity dispersion $\mathrm{GDD}$, calculated from the unfiltered matrix $L_{m,n}$ (blue) and from the filtered matrix $L'_{m,n}$ (orange). Bottom: corresponding parameter $K$ for the two models. The cavity finesse is $\mathcal{F} = 75$.
• Figure 4: Simulations for no intracavity dispersion. Top: calculated squeezing and anti-squeezing levels $\sigma_\mathrm{sq}^2$ at SPOPO output for the first 30 supermodes $k$ at $P=0.3$. Middle: projections $\left|M_k\right|^2$ onto symmetric LOs with FWHM bandwidths of 1nm, 2nm, and 3nm. Bottom: projections for antisymmetric LOs with the same bandwidths. Simulations assume $R_\mathrm{oc}=0.95$ and $\mathrm{GDD}=0fs\squared$. Note that modes up to high orders contribute to the total squeezing level at SPOPO output. It is also clear that the projection onto the LO extends to higher order modes by reducing LO spectral width, or by using an antisymmetrical LO.
• Figure 5: Simulations for 900fs of intracavity dispersion. Top: calculated squeezing and anti-squeezing levels $\sigma_\mathrm{sq}^2$ at SPOPO output for the first 30 supermodes $k$ at $P=0.3$. Middle: projections $\left|M_k\right|^2$ onto symmetric LOs with FWHM bandwidths of 1nm, 2nm, and 3nm. Bottom: projections for antisymmetric LOs with the same bandwidths. Simulations assume $R_\mathrm{oc}=0.95$ and $\mathrm{GDD}=900fs\squared$. Note that only the first few modes contribute to the total squeezing level at SPOPO output, as the variance of higher order modes approaches the shot noise level. Also in this case, the projection onto the LO extends to higher order modes by reducing LO spectral width, or by using an antisymmetrical LO.