Dispersion in nonlinear interferometry: implications for optical coherence tomography with undetected photons

Nonlinear SU(1,1) quantum interferometers based on non-degenerate optical parametric down-conversion exhibit strong unbalanced group velocity dispersion (GVD). This feature is intrinsic to this type of interferometer as correlated photons of vastly different frequencies propagate through a dispersive nonlinear crystal; consequently, the dispersion arises from the source itself. The resulting GVD degrades the axial point-spread function (PSF) in optical coherence tomography (OCT) with undetected photons; and physical compensation is less straightforward, in particular for non-degenerate broadband regimes due to the limited number of suitable materials. In this contribution, we analyze dispersion in bulk nonlinear interferometry and describe its implications for OCT imaging. Aspects of hardware compensation are addressed, and a novel empirical numerical method of compensation is proposed. The approach is based on the extraction of the phase component directly from the time-domain modality (high precision linearized quantum Fourier transform infrared spectrometer) and its injection into the mid-IR spectral-domain OCT signals (central wavelength of around 3770 nm) before the Fourier transform. The proposed method is compared with an alternative numerical technique. The results demonstrate a 2.2-fold improvement in axial resolution and outperform the alternative correction method in overall imaging performance.

💡 Research Summary

This paper investigates the intrinsic group‑velocity dispersion (GVD) that arises in nonlinear SU(1,1) quantum interferometers based on non‑degenerate spontaneous parametric down‑conversion (SPDC) and its detrimental impact on optical coherence tomography (OCT) performed with undetected photons. In a typical configuration a monochromatic pump (660 nm) traverses a periodically poled KTP crystal, generating broadband, highly non‑degenerate signal–idler photon pairs. Because energy conservation forces ωp = ωs + ωi, the signal (near‑IR) and idler (mid‑IR, ≈ 3.7 µm) travel at different group velocities and experience opposite signs of GVD inside the same crystal. Consequently the collective phase term Δφ = φp − φs − φi that governs the interference pattern contains a zero‑order offset, a first‑order group‑delay mismatch Δτ, and a second‑order term Γ(2) = k″s zs + k″i zi. Unlike classical OCT, where only the differential GVD between reference and sample arms must be compensated, here the effective GVD is the sum of the signal and idler contributions, and it is largely dictated by the crystal itself. For KTP the idler band exhibits a strong negative GVD that dominates, broadening the axial point‑spread function and degrading resolution.

Physical dispersion compensation is problematic because the two interferometer arms operate at different wavelengths; inserting the same bulk material in both arms does not balance the dispersion. The authors therefore propose a numerical compensation scheme that exploits the duality between the time‑domain bi‑photon coherence function and the complex spectrum, as expressed by the Wiener–Khinchin theorem. A high‑precision linearized quantum Fourier‑transform infrared spectrometer (QFTIR) is used to directly measure the phase φi(ωi) of the idler photons in the same interferometer. This phase is then injected into the mid‑IR spectral‑domain OCT interferograms before the Fourier transform: each spectral point is multiplied by exp