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Journal of Physics Photonics

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

Ivan Zorin, Paul Gattinger

Published Mar 1, 2026• 1 citation
Publisher

Abstract

Abstract 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 in optical coherence tomography (OCT) with undetected photons; and physical compensation is not 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-infrared spectral-domain OCT signals (central wavelength of around 3770 nm) before the Fourier transform. The proposed method is evaluated using alternative numerical techniques as baseline references. The results demonstrate a 2.2-fold improvement in axial resolution in representative measurements.

DOI
10.1088/2515-7647/ae536e

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Abstract 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 in optical coherence tomography (OCT) with undetected photons; and physical compensation is not 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-infrared spectral-domain OCT signals (central wavelength of around 3770 nm) before the Fourier transform. The proposed method is evaluated using alternative numerical techniques as baseline references. The results demonstrate a 2.2-fold improvement in axial resolution in representative measurements.
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.
Mid-infrared (mid-IR) light scatters much less than shorter wavelengths, allowing greatly enhanced penetration depths for optical imaging techniques such as optical coherence tomography (OCT). However, both detection and broadband sources in the mid-IR are technologically challenging. Interfering entangled photons in a nonlinear interferometer enables sensing with undetected photons, making mid-IR sources and detectors obsolete. Here we implement mid-IR frequency-domain OCT based on ultra-broadband entangled photon pairs spanning from 3.3 to 4.3 µm. We demonstrate 10 µm axial and 20 µm lateral resolution 2D and 3D imaging of strongly scattering ceramic and paint samples. By intrinsically being limited only by shot noise, we observe times more sensitivity per integration time and power of the probe light. Together with the vastly reduced footprint and technical complexity, our technique can outperform conventional approaches with classical mid-IR light sources.
Using spectrally correlated photon pairs instead of classical laser light and coincidence detection instead of light intensity detection, Quantum Optical Coherence Tomography (Q-OCT) outperforms classical OCT in several experimental terms. It provides twice better axial resolution with the same spectral bandwidth and it is immune to even-order chromatic dispersion, including Group Velocity Dispersion responsible for the bulk of axial resolution degradation in the OCT images. Q-OCT has been performed in the time domain configuration, where one line of the two-dimensional image is acquired by axially translating the mirror in the interferometer's reference arm and measuring the coincidence rate of photons arriving at two single-photon-sensitive detectors. Although successful at producing resolution-doubled and dispersion-cancelled images, it is still relatively slow and cannot compete with its classical counterpart. Here, we experimentally demonstrate Q-OCT in a much faster Fourier-domain configuration, theoretically proposed in 2020, where the reference mirror is fixed and the joint spectrum is acquired by inserting long fibre spools in front of the detectors. We propose two joint spectrum pre-processing algorithms, aimed at compensating resolution-degrading effects within the setup. While the first one targets fibre spool dispersion, an effect specific to this configuration, the other one removes the effects leading to the weakening of even-order dispersion cancellation, the latter impossible to be mitigated in the time-domain alternative. Being additionally contrasted with both the time-domain approach and the conventional OCT in terms of axial resolution, imaging range and multilayer-object imaging, Fourier-domain Q-OCT is shown to be a significant step forward towards a practical and competitive solution in the OCT arena.
We report Fourier-domain Quantum Optical Coherence Tomography employing a photon pair source covering a very broad wavelength range spanning from around 1350 to 1750 nm. With nearly 180 nm full width at half maximum, it enables high axial resolution of 2.7 μm, most commonly achieved only in classical OCT working at a much shorter wavelength of 800 nm. The light of such considerable bandwidth is especially vulnerable to axial-resolution-degrading effects of chromatic dispersion, and although the even-order dispersion - responsible for the bulk of resolution degradation - is inherently cancelled, the odd-order dispersion becomes non-negligible, with the third-order-dispersion effects already observed in various Quantum OCT setups. We introduce a dimensionless parameter χ₃, dependent on the photon pair source and medium parameters, facilitating prediction of the appearance of these image-distorting dispersion effects. Also, we show that this issue - impossible to be removed in time-domain Quantum OCT - is easily mitigated in its Fourier-domain configuration by mere post-processing of a joint spectrum, resulting in the high axial resolution being maintained throughout most of the imaging depth, here approx. 0.35 mm. Finally, we show that the imaging depth can be extended to 0.7 mm if the fibre spools - central to the joint spectral detection - are extended from 5 km to 10 km, however at the expense of a longer acquisition time.