Pablo Yepiz-Graciano, Alí Michel Angulo Martínez, Dorilian Lopez-Mago, Hector Cruz-Ramirez, Alfred B. U’Ren, "Spectrally resolved Hong–Ou–Mandel interferometry for quantum-optical coherence tomography," Photonics Res. 8, 1023 (2020)

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- Photonics Research
- Vol. 8, Issue 6, 1023 (2020)

Fig. 1. (a) Simulation of frequency-delay interferogram r c ( τ , Ω ) . (b) Result of integrating the interferogram over Ω , yielding the HOM interferogram. (c) Result of integrating the interferogram over τ , yielding a HOM-like dip in the frequency variable Ω . (d) Fourier transform of (a), so as to yield the time-domain interferogram r ˜ c ( τ , T ) . (e) Evaluation of r ˜ c ( τ , T ) at T = 0 , yielding the HOM interferogram. (f) Evaluation of r ˜ c ( τ , T ) at τ = − 1 ps . (g) Function A ( Ω ) . (h) Function B ( Ω ) .

Fig. 2. (a) Frequency-delay interferogram r c ( τ , Ω ) for two-interface sample (borosilicate coverslip of 170 μm thickness). (b) Result of integrating the interferogram over Ω , yielding the HOM interferogram. (c) Fourier transform of (a) yielding the time-domain interferogram r ˜ c ( τ , T ) .

Fig. 3. (a) and (d) Simulation of the temporal-domain interferogram | r ˜ c ( τ , T ) | for a three-layer sample (intermediate layer at 40% of the sample thickness, in addition to the two extremal interfaces); in (a) we show the case of an SPDC source centered at 775 nm with a narrowband pump (0.1 nm), while in (d) we increase the pump bandwidth to 10 nm. (b) and (e) Evaluation of | r ˜ c ( τ , T ) | at τ 0 = − 1.7 ps ; while (b) corresponds to a narrow pump bandwidth (0.1 nm), (e) shows the effect of increasing the bandwidth to 10 nm. (c) and (f) HOM interferogram resulting for the above two cases; (c) for a narrow pump bandwidth (0.1 nm) and (f) for a pump bandwidth of 10 nm.

Fig. 4. Experimental setup. Ti:Sa, titanium–sapphire laser; TC, temperature controller; L, plano-convex spherical lens; PPLN, periodically poled lithium niobate nonlinear crystal; SF, set of bandpass and long-pass filters; MPC, manual fiber polarization controller; PMC, polarization-maintaining optical circulator; FC, compensating fiber; S, sample; RM, reference mirror; BS, beamsplitter; FSs, fiber spools; TDC, time-to-digital converter; APD, avalanche photodetectors.

Fig. 5. (a) Experimental measurement of the delay-frequency interferogram r c ( τ , Ω ) , for a single-layer sample (plain mirror). (b) Result of integrating the interferogram over Ω , yielding the HOM interferogram. (c) Result of integrating the interferogram over τ , yielding a HOM-like dip in the frequency variable Ω . (d) Numerical Fourier transform of (a), yielding the time-domain interferogram | r ˜ c ( τ , T ) | . (e) Evaluation of | r ˜ c ( τ , T ) | at T = 0 , yielding the HOM interferogram. (f) Evaluation of | r ˜ c ( τ , T ) | at τ = − 1 ps .

Fig. 6. Reconstruction procedure for the functions A ( Ω ) and B ( Ω ) , from which we can compute the HOM interferogram through Eq. (6 ). (a) Evaluation of the delay-frequency interferogram r c ( τ , Ω ) at τ = − 1 ps . (b) Numerical Fourier transform of (a), yielding | r ˜ c ( τ 0 , T ) | with τ 0 = − 1 ps . (c) and (d) Peaks 1 and 2 isolated from | r ˜ c ( τ 0 , T ) | by restricting the T variable to the two windows indicated in panel (b). (e) Function A ( Ω ) obtained as the inverse Fourier transform of peak 1. (f) Function B ( Ω ) obtained as the inverse Fourier transform of peak 2, multiplied by the phase exp ( i Ω τ 0 ) ; both amplitude and phase are shown.

Fig. 7. Reconstructed HOM dip (red line) and conventional HOM dip obtained through scanning the delay with non-frequency-resolved coincidence counting (black dots).

Fig. 8. (a) Experimental measurement of the delay-frequency interferogram r c ( τ , Ω ) for a two-layer sample (borosilicate glass coverslip of 170 μm thickness). (b) Result of integrating the interferogram over Ω , yielding the QOCT interferogram. (c) Numerical Fourier transform of (a), yielding the time-domain interferogram | r ˜ c ( τ , T ) | .

Fig. 9. Reconstruction of the sample morphology and QOCT interferogram for a two-layer sample (borosilicate glass coverslip of 170 μm thickness). (a) Experimental measurement of the function r c ( τ 0 , Ω ) at a fixed delay τ 0 = − 0.363 ps . (b) Numerical Fourier transform of (a), yielding | r ˜ c ( τ 0 , T ) | ; here we have labeled five of the resulting peaks with the numbers 1–5. (c) Reconstructed QOCT interferogram (red line) and conventional delay-scanning, non-spectrally resolved HOM measurement (black points).

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