Seeded SU(1,1) interferometry for Fourier-domain optical coherence tomography

Abstract: We demonstrate Fourier-domain optical coherence tomography (FD-OCT) based on a seeded SU(1,1) interferometer. Multilayer objects are probed with broadband light centered at 1550nm, while depth-resolved 3D images are reconstructed from photon flux measurements centered at 810nm. We show that, in the low parametric-gain regime, seeding increases the photon flux, enabling volumetric imaging with a spectrometer rather than single-photon detectors. Our analysis further shows that, under the conditions considered, seeding provides a more effective route to sensitivity enhancement than increasing the parametric gain.

• The paper presents the first experimental demonstration of a seeded SU(1,1) interferometer for Fourier-domain Optical Coherence Tomography (FD-OCT), showing 10X flux enhancement and real-time imaging with a conventional spectrometer
• Improvement of reflectivity-estimation precision using seeded low-gain operation versus unseeded high-gain, indicating that increased parametric gain saturates sensitivity and has no advantage over seeding.
• Theoretical analysis predicts that at a higher gain, increasing the seed power of the system still improves precision.

Overview

This paper reports an experimental demonstration of Fourier-domain optical coherence tomography (FD-OCT) based on a seeded Yurke-type SU(1,1) interferometer operating in the low parametric gain regime. The system probes multilayer samples with broadband idler light centered at 1550 nm while reconstructing depth-resolved, three-dimensional images from signal photon flux measurements at 810 nm. The central contributions are twofold: first, seeding a low-gain nonlinear interferometer raises the photon flux sufficiently to replace single-photon detection with a conventional spectrometer; second, a theoretical analysis shows that, under the conditions considered, increasing the seed power provides strictly better sensitivity in reflectivity estimation than increasing the parametric gain of an unseeded interferometer, whose sensitivity saturates at high gain.

Experimental implementation

The interferometer is built around a 1 mm periodically poled lithium niobate (PPLN) crystal pumped by a narrowband CW laser at 532 nm (linewidth 5 MHz) focused to a waist of 75 μm. Type-0 non-degenerate spontaneous parametric down-conversion (SPDC) generates signal photons at 810 nm and idler photons at 1550 nm. The pump and signal arms are retro-reflected into the crystal for the second parametric interaction, while the idler arm illuminates the sample, which is mounted on translation stages for axial and transverse scanning. The focused spot size at the sample plane is approximately 18.5 μm.

Using the standard expression for CW-pumped parametric gain, the authors estimate $G_{CW} \sim 7 \times 10^{-5}$ for their operating conditions (3.5 mW pump power, $\chi^{(2)} = 14$ pm/V), confirming operation deep in the low-gain regime where unseeded photon fluxes mandate single-photon counting modules (SPCMs) behind a monochromator, with FPGA-based acquisition.

The key modification is injection of a broadband superluminescent diode (SLD) seed at 1550 nm (40 nm bandwidth, set by filter F1) into the idler path. The seed spectrum overlaps strongly with the SPDC idler spectrum, so the combined field retains a smooth Gaussian-like profile by the Gaussian product theorem. With seeding, the stimulated flux at the output port is large enough that the output signal spectrum can be recorded directly with a spectrometer (resolution 0.36 nm), enabling real-time spectral interferogram acquisition for Fourier-domain reconstruction.

Correct FD-OCT operation requires the total group delay between arms to satisfy

$$\frac{\lambda_s^2}{\Delta\lambda_s} \ll \Delta L + N_g L \ll \frac{\lambda_s^2}{\delta\lambda_s},$$

which in this setup translates to $40~\mu\text{m} \ll \Delta L + N_g L \ll 1.72$ mm. Notably, the intrinsic group-index mismatch across the crystal ($N_g L = 77.6~\mu$m) already exceeds the lower bound, so fringe density is guaranteed by construction and alignment reduces to keeping the total delay below the upper bound.

Axial and volumetric imaging results

Axial scans (A-scans) were obtained by recording two spectra with a relative phase shift of π and subtracting them to suppress DC and autocorrelation terms, followed by resampling in wavenumber and Fourier transformation. A sensitivity-decay (roll-off) correction, calibrated empirically with a mirror scan and fitted to a Gaussian-sinc envelope, was applied to all scans to equalize amplitudes across depth.

Three glass samples were characterized: two single-layer slides with nominal thicknesses of 172 μm and 146 μm, and a three-layer stack of two glass plates separated by a 173 μm air gap. The reconstructed A-scans show the expected two peaks per glass layer (four peaks for the multilayer stack), with layer thicknesses extracted via $\Delta z = 2 n_g d$ ($n_g \approx 1.5$) in good agreement with manufacturer specifications. This validates axial sectioning of weakly reflecting transparent media — uncoated glass reflects only ~4% per interface at 1550 nm — using spectrometer-based detection rather than photon counting.

Volumetric imaging was demonstrated on a 170 μm glass slide bearing a 300 nm aluminum pattern on its top surface, fabricated by maskless optical lithography and sputter deposition. Raster scanning with 0.2 mm transverse steps and stacking A-scans yields a full 3D reconstruction: the aluminum pattern (≈97% reflectivity at 1550 nm) appears as a high-contrast feature at the front surface, while the back surface appears as a weaker peak at $z \approx 180~\mu$m, with the pattern visible in negative contrast there. The contrast ratio between metallic and dielectric interfaces is preserved throughout the reconstruction, confirming that seeding does not degrade the OCT axial response.

Photon flux enhancement from seeding

A direct comparison of seeded versus unseeded operation was performed with a silver mirror sample at fixed pump power (9.2 mW) and a very modest seed power of only 12 μW, with acquisition times ranging from 100 ms to 1 s. The seeded configuration yields approximately one order of magnitude higher detected photon flux than the unseeded configuration at all acquisition times, and the mirror position is retrievable from the A-scan already at the shortest integration time (100 ms), whereas the unseeded configuration requires substantially longer acquisitions to reach comparable visibility. The practical implication is significant: even microwatt-level seeding converts a photon-counting experiment requiring long integrations into a spectrometer-based measurement compatible with real-time imaging.

Sensitivity comparison: seeding versus high gain

The paper's principal analytical result concerns the precision of estimating the sample reflectivity $R_i$ from measurements of the output signal photon number, derived within the single-mode approximation including sample, signal-path, and detection losses. The precision follows error propagation,

$$\sigma^2 = \frac{\mathrm{Var}(N_{s_2})}{\left[\partial \langle N_{s_2}\rangle / \partial R_i\right]^2},$$

with the optimal operating phase found to be $\chi^{(2)} = 14$0. Two strategies are compared:

• Seeded low-gain operation: holding the gain fixed at $\chi^{(2)} = 14$1 and increasing the seed amplitude. For $\chi^{(2)} = 14$2, the sensitivity scales as $\chi^{(2)} = 14$3, i.e., it improves without bound as the seed flux increases.
• Unseeded high-gain operation: increasing the mean pump power of a pulsed source (gain related to the CW value by $\chi^{(2)} = 14$4, where $\chi^{(2)} = 14$5 is the duty cycle). For $\chi^{(2)} = 14$6, the sensitivity saturates at a constant value independent of further gain increase.

The comparison shows that seeding dominates: at any given idler flux probing the sample, the seeded configuration achieves better estimation precision, and only seeding yields continuously improving sensitivity. Increasing parametric gain alone saturates because the variance grows commensurately with the signal once gain dominates over the coherent displacement. This is a strong claim: it implies that the high-gain regime, despite its potential for sub-shot-noise scaling in idealized lossless settings, offers no sensitivity benefit over seeding under the lossy conditions modeled here — consistent with prior findings that losses restrict quantum advantages in SU(1,1) interferometry to selected parameter regions. Practically, the seeded route also requires only CW lasers delivering up to tens of milliwatts, whereas reaching comparable idler fluxes in the high-gain regime demands pulsed sources with peak-power enhancement factors on the order of $\chi^{(2)} = 14$7 relative to equivalent CW pumping.

Two caveats attach to this analysis. It relies on the single-mode approximation, and the sensitivity model assumes specific values of the sample and signal-arm reflectivities ($\chi^{(2)} = 14$8, $\chi^{(2)} = 14$9, $$\frac{\lambda_s^2}{\Delta\lambda_s} \ll \Delta L + N_g L \ll \frac{\lambda_s^2}{\delta\lambda_s},$$0); the saturation behavior of the unseeded high-gain curve and the relative advantage of seeding may shift for other loss configurations. Additionally, the analysis addresses reflectivity estimation rather than full phase-sensing metrology, so it does not by itself settle whether seeded schemes retain an advantage for Heisenberg-limited phase estimation in the presence of realistic losses.

Limitations and open questions

The demonstrated imaging performance remains modest relative to state-of-the-art classical OCT: the axial resolution is set by the 17.4 nm signal bandwidth, the transverse resolution by the ~18.5 μm focus, and acquisition involves mechanical raster scanning. The sensitivity advantage of seeding is established theoretically within a single-mode, fixed-loss model rather than measured directly against a high-gain implementation in the same apparatus. The paper also leaves open the question of what the optimal configuration is for high-resolution, short-acquisition-time OCT combining both transverse and longitudinal performance, and how unknown experimental losses modify the conditions under which any beyond-shot-noise advantage of high-gain operation could be realized.

Conclusion

This work demonstrates that a seeded SU(1,1) interferometer in the low parametric gain regime constitutes a viable platform for FD-OCT with spectrometer-based detection, decoupling the probe wavelength (1550 nm) from the detection wavelength (810 nm) while avoiding single-photon detectors. Seeding with as little as 12 μW increases the detected flux by roughly an order of magnitude and enables volumetric imaging of weakly reflecting multilayer samples. Analytically, the paper establishes that, under the considered loss model, increasing seed power monotonically improves reflectivity-estimation sensitivity whereas increasing parametric gain saturates, positioning seeded low-gain operation as both the simpler and the more sensitive route among the configurations compared.