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

TL;DR

This work addresses intrinsic net dispersion in nonlinear SU(1,1) interferometers used for OCT with undetected photons, where the bi-photon propagation through the dispersive crystal degrades axial resolution. It develops a dispersion framework based on the collective phase $\Delta\varphi(\omega_s,\omega_p)=\varphi_p-\varphi_s-\varphi_i$ and the effective GVD term $\Gamma^{(2)}=k_s^{(2)}z_s+k_i^{(2)}z_i$, demonstrating that the net dispersion cannot be mitigated by simple arm matching. The authors introduce a novel empirical compensation method that leverages QFTIR phase retrieval from time-domain interferograms, injecting the recovered phase into spectral-domain OCT data; this is complemented by a physical compensator in the idler arm. Experimentally, they achieve a 2.2× enhancement in axial resolution and improved B-scans for high-scatter samples using mid-IR OCT with undetected photons and low probing power, highlighting practical routes toward dispersion-engineered, mid-IR OCT systems and potential extensions to classical OCT.

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 (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.

Figures (7)

• Figure 1: Principles of nonlinear interferometry and sensing with undetected photons: (a) Simplified schematic of a nonlinear interferometer (base OCT unit) employing a non-degenerate SPDC source (a $\chi^{(2)}$ crystal pumped by a monochromatic laser). DM1 forms the reference (signal and pump) and sample (idler) arms. Interference is detected in the signal channel (signal photons are reflected by DM2) by a grating spectrometer. The interference pattern is governed by the amplitude and phase response experienced by the idler photons. (b) Spectral interferogram measured in the frequency domain.
• Figure 2: Group velocity dispersion of KTP crystal 10.1063/1.1375802 derived in the wavelengths $\lambda = 2\pi c/{\omega}$; signal and idler spectral ranges (660 nm pump, poling period of KTP $\Lambda$=20.45 µ m) are indicated in orange and red respectively; signal and idler have equal bandwidth in frequency domain (determined by the energy conservation rule $\omega_p=\omega_s+\omega_i$) and scale nonlinearly when displayed in wavelengths.
• Figure 3: Spectral-domain OCT with undetected photons based on nonlinear low-gain SU(1,1) interferometer: 500 mW pump laser (660 nm), Lens - achromatic doublet (silicon and germanium) lens, $\chi^{(2)}$ crystal - ppKTP (periodically poled potassium titanyl phosphate, $\Lambda = 20.45$ µ m, $l=2.55$ mm), OPM - off-axis parabolic mirror, DM - dichroic mirror, CM - cold mirror.
• Figure 4: Time-domain interferogram recorded with a single point detector during simultaneous scanning of phases of signal and pump photons ($\varphi_p-\varphi_s$); raw signal of the QFTIR modality, contains amplitude as well as phase information.
• Figure 5: Three-dimensional representation of the QFTIR-retrieved complex spectrum, with amplitude and phase shown as projections; the phase encodes the uncompensated nonlinear dispersion.