Time-resolved photon counting plays an indispensable role in precision metrology in both classical and quantum regimes. Therein, time-correlated single-photon counting (TCSPC) [1] has been the key enabling technology for applications such as fluorescence lifetime microscopy [2], time-gated Raman spectroscopy [3], photon counting time-of-flight (ToF) 3D imaging [4], light-in-flight imaging [5], and computational diffuse optical tomography [6]. For all these applications, one of the most important figures of merit is the single-photon timing resolution (SPTR, also referred to as photon counting timing jitter). The TCSPC SPTR is limited by the available single-photon detectors. For example, photomultiplier tubes typically provide an SPTR larger than 100 ps [7]. Meanwhile, superconducting nanowire single-photon detectors have superior SPTR in the sub-10-ps range [8,9]. However, cryogenic cooling significantly increases the system complexity. Single-photon avalanche diodes (SPADs) operate at moderate temperature, which makes them a popular choice for various applications mentioned above. Nevertheless, their SPTR is still limited to tens-of-picoseconds level [10]. On the other hand, orders-of-magnitude enhancement on SPTR is required for many challenging applications such as the study of ultrafast fluorescent decay dynamics [11,12].

In this Letter, we demonstrate a time-magnified TCSPC (TM-TCSPC) that achieves an ultrashort SPTR of 550 fs using an off-the-shelf single-photon detector. The key component is a quantum temporal magnifier using a low-noise high-efficiency fiber parametric time lens [13,14] based on four-wave mixing Bragg scattering (FWM-BS) [15–17]. A temporal magnification of 130 with a 97% photon conversion efficiency has been achieved while maintaining the quantum coherence of the signal under test (SUT). Detection sensitivity of ${-}{{95}}\;{\rm{dBm}}$ (0.03 photons per pulse), limited by the spontaneous Raman scattering noise, is possible and allows efficient processing and characterization of quantum-level SUT. The TM-TCSPC can resolve ultrashort pulses with a 130-fs pulse width difference at a 22-fs accuracy. When applied to photon counting ToF 3D imaging, the TM-TCSPC greatly suppresses the range walk error (RWE) that limits all photon counting ToF 3D imaging systems by 99.2% (130 times) and thus provides high depth measurement accuracy and precision of 26 µm and 3 µm, respectively. The TM-TCSPC is a promising solution for photon counting at the femtosecond regime that will benefit various research fields such as fluorescence lifetime microscopy, time-gated Raman spectroscopy, light-in-flight imaging, and computational diffuse optical tomography.

The schematic diagram is shown in Fig. 1. In conventional TCSPC (upper row of Fig. 1), the start–stop time between the excitation pulse and the emission photon is registered and logged by the TCSPC timing electronics. Provided the probability of registering more than one photon per cycle is low, the TCSPC timing histogram depicts the time-resolved intensity profile of the SUT at the quantum level. Depending on the choice of single-photon detectors, the TCSPC time resolution is in the range of 10–100 ps. In the TM-TCSPC system (lower row of Fig. 1), the quantum-level SUT is first temporally magnified before being characterized by the subsequent TCSPC system. The SPTR of the TM-TCSPC is thus significantly improved by the temporal magnification ratio to the femtosecond regime. To implement the temporal magnifier that preserves the SUT quantum coherence, a fiber parametric time lens based on FWM-BS is developed. FWM-BS is advantageous for quantum applications due to its noiseless nature and near-unity conversion efficiency [17,18]. Moreover, the flexibility of choosing the pump wavelength also enables processing quantum-level SUT over a large wavelength range [19].

 

Fig. 1. Schematic diagram of TM-TCSPC.

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The experimental setup is shown in Fig. 2. The fiber parametric time lens was implemented using a spool of 30-m highly nonlinear fiber (HNLF) and two optical pumps. First, a swept pump was generated by chirping a 100-MHz mode-locked erbium-doped fiber laser (MLFL, Menlosystems C-Fiber) through 680-m single-mode fiber to obtain a pump dispersion of ${-}{15.12}\;{\rm{p}}{{\rm{s}}^2}.$ It was then bandpass filtered at 1540 nm at a bandwidth of 14 nm and subsequently amplified by an erbium-doped fiber amplifier (EDFA). The swept pump pulse duration is stretched to 165 ps, defining the aperture of the time lens. At the same time, a quasi-continuous-wave (CW) pump was generated from a tunable laser source (TLS, Santec TSL 710) operating at 1558 nm. An amplitude modulator synchronized with the swept pump modulated the CW TLS into 360-ps pulses, which was then amplified by two EDFAs as the quasi-CW pump. A 0.7-nm bandwidth filter was deployed between the two EDFAs to suppress the amplified spontaneous emission noise. The two pumps were then combined through a wavelength-division multiplexer (WDM) and temporally overlapped using an optical tunable delay line. The SUT was a sub-picosecond pulse with 5-nm bandwidth at 1255 nm obtained through supercontinuum generation of the same MLFL, and it was thus optically synchronized with the two pumps. The SUT then propagated through 200-m of dispersion compensating fiber (DCF), which provided an input dispersion of ${{15}}\;{\rm{p}}{{\rm{s}}^2}$. Finally, the pumps and the SUT were combined using an O/C band WDM and then launched together into the 30-m HNLF with a nonlinear coefficient $\gamma = {{24}}\;({{\rm{W}}^{- 1}}\;{\rm{k}}{{\rm{m}}^{- 1}})$ and a zero-dispersion wavelength of 1395 nm. The pumps and the HNLF formed a time lens, which induced quadratic phase modulation onto the SUT through FWM-BS. The peak power of the swept pump (${{\rm{P}}_1}$) and the quasi-CW pump (${{\rm{P}}_2}$) were adjusted such that ${{\rm{P}}_1} = {{\rm{P}}_2}$, and (${{\rm{P}}_1} + {{\rm{P}}_2}$)·$\gamma \cdot {{\rm L}} = \pi$ in the HNLF to achieve the highest conversion efficiency [15]. After the time lens, a narrowband idler generated through FWM-BS was filtered out before it propagated through two DCF modules that provide a total output dispersion of $1958\; {\rm ps}^2$. Overall, the system functions as a temporal magnifier, and the output is a temporally magnified SUT, which would then be characterized by the subsequent TCSPC system that consisted of a near-infrared SPAD (MPD, PDM-IR) and timing electronics (PicoQuant, Hydraharp 400) (see Supplement 1 Section 1 for detailed setup). From the quantum perspective, the temporal magnifier reduces the frequency uncertainty of the SUT photons and consequently stretches the single-photon temporal wave function. Detailed quantum theory of temporal magnification for both classical and nonclassical lights has been developed in [20].

 

Fig. 2. Experimental setup of the temporal magnifier using a fiber parametric time lens based on FWM-BS.

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Fig. 3. Optical spectra of FWM-BS at (a) the pump and (b) the signal bands. A conversion efficiency of 97% was achieved.

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The corresponding optical spectrum is shown in Fig. 3. As shown in Fig. 3(a), the pumps consisted of a 14-nm swept pump centering at 1540 nm and a quasi-CW pump at 1558 nm. The spectral modulations of the swept pump are inherited from the spectrum of the MLFL. After passing through the HNLF, some inevitable parasitic FWM processes happened between the two pumps. However, their influence was negligible because the conversion efficiency is less than 0.1% and they are spectrally separated from the SUT. As shown in Fig. 3(b), when the two pumps were turned on, the 5-nm signal at 1255 nm was converted to a narrowband idler at 1244 nm with a close-to-unity conversion efficiency. Comparing with the initial signal, more than 16-dB signal depletion was achieved. Similar to the pump side, some parasitic FWM could be observed. However, they only consisted of 0.76% of the original signal power. Therefore, 97% of the signal was efficiently converted to the narrowband idler, and the efficiency could be further improved toward unity by optimizing the spectral flatness of the swept pump. It is worth noticing that such close-to-unity conversion efficiency is critical for noiseless magnification of photons with nonclassical features such as anti-bunching [21]. A free-space grating monochromator was used to filter out the 1244-nm idler with a 100-dB extinction ratio.

In the TCSPC that characterizes the temporally magnified SUT, the SPAD was operated at gated mode with a gate-on time of 5 ns and a gate frequency of 25 MHz synchronized with the SUT. The hold-off time for the SPAD was set to 5 μs to suppress afterpulsing. Under such settings, the dark count was found to be 6000/s. The input to the SPAD was then attenuated properly such that the maximum detection probability per gate was 1% to minimize the pile-up effect. Therefore, the maximum counting rate was about 110,000/s. Overall, the performance of the TM-TCSPC is summarized in Fig. 4. Figure 4(a) shows the TM-TCSPC timing histograms obtained with different start–stop times. The FWM-BS conversion efficiency gradually rolled off as the start–stop time increases and the 10-dB record length was measured to be 30 ps. It consisted of only 18% of the available 165-ps aperture of the time lens owing to the restriction of phase matching. Therefore, the record length can be further expanded by using HNLF with a lower dispersion slope. A zoom-in plot of the central histogram in (a) is shown in the inset of Fig. 4(b) and the red dashed trace is the Gaussian fitting. A full width at half-maximum of 123 ps is obtained from the fitting. Figure 4(b) plots the magnified start–stop time with respect to the start–stop time within the 30-ps record length, showing a linear relationship with a slope of 130 that is the temporal magnification ratio. To demonstrate the potential of TM-TCSPC in ultrafast fluorescence lifetime measurement, we analyzed its capability to resolve small pulse width changes of about 130 fs (see Supplement 1 Section 2). SUTs with four different pulse widths were first calibrated with a background-free second-harmonic generation intensity autocorrelator (AC) and then measured using the TM-TCSPC [Fig. S2(b) and S2(c), respectively]. An instrument response function of 550 fs was obtained by deconvolving the TM-TCSPC histogram with the AC-measured pulse width under Gaussian approximation, which was regarded as the SPTR of the TM-TCSPC system (see Supplement 1 Section 2 for details). Figure 4(c) plots the TM-TCSPC-measured pulse widths (red stars) overlaid with the AC-calibrated pulse widths (black stars). Evidently, the TM-TCSPC can accurately differentiate all four SUTs with different pulse widths and an rms error of only 22 fs is observed.

 

Fig. 4. Characterization of TM-TCSPC. (a) Measured output photon counting histograms as the input pulse is delayed. (b) Temporal shifting of the histogram peak as a function of input time extracted from (a), featuring a magnification ratio of 130. Inset: zoom-in of the central histogram in (a) showing a full width at half-maximum of 123 ps. (c) Measurement deviations between autocorrelation and TM-TCSPC.

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At zero start–stop time, the sensitivity of the system was also characterized and the minimum measurable SUT power was ${-}{{67}}\;{\rm{dBm}}$, corresponding to about 20 photons per pulse. The sensitivity is currently limited by the SPAD dark count and the large insertion loss of the output DCF modules (32 dB). To estimate the sensitivity when the DCF module is replaced by low-loss chirped fiber Bragg grating (CFBG) in the future, the output DCF module was removed and a detection sensitivity of ${-}{{95}}\;{\rm{dBm}}$ (0.03 photons per pulse) was measured, allowing efficient processing and characterization of quantum-level SUT. The difference between the 28-dB sensitivity enhancement and the 32-dB DCF module loss was attributed to spontaneous Raman noise that became the new sensitivity limit when the insertion loss is optimized. By further suppressing the spontaneous Raman noise and minimizing the connection loss through optimized splicing, the sensitivity penalty of TM-TCSPC compared to conventional TCSPC is expected to be less than 3 dB [18].

 

Fig. 5. Demonstration of ToF 3D imaging. (a) Photograph of the sample. (b) 3D image obtained using TM-TCSPC. (c) 3D image obtained using conventional TCSPC. (d) Comparison of the height profiles with TM-TCSPC (red trace) and conventional TCSPC (black trace) along the white dashed line.

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Finally, a proof-of-principle photon counting ToF 3D imaging [22,23] was demonstrated to further highlight the benefit of sub-picosecond time resolution of TM-TCSPC, where its 550-fs SPTR is translated to 82-µm depth resolutions in air. As shown in Fig. 5(a), the imaging sample consisted of four small pieces of glass with different heights glued onto a glass slide, which was then sputtered with chromium coating to eliminate multi-surface reflection. The heights of the four glass pieces were independently characterized to be 520 µm (upper left), 400 µm (upper right), 990 µm (lower left), and 180 µm (lower right) using spectral-domain optical coherence tomography (SD-OCT) [24].

To acquire the ToF 3D image, the sample was put under a low-resolution confocal microscope with the TM-TCSPC attached to the return signal port. Each timing histogram was denoised by a low-pass filter before its peak was located and translated from time to depth (see Supplement 1 Section 3). The resulting ToF 3D image is shown in Fig. 5(b). The heights of all four glass pieces were differentiated even with only 120-µm height difference between the upper two glass pieces. The measured heights were 565 µm (upper left), 382 µm (upper right), 1010 µm (lower left), and 182 µm (lower right), which matched well with the SD-OCT calibration results. The measurement accuracy, defined as the rms error between TM-TCSPC measurement and SD-OCT calibration, is calculated to be 26 µm. In addition, the TM-TCSPC featured high measurement precision. As shown in the red trace of Fig. 5(d), the height measurement along the white dashed line shows a standard deviation of only 3 µm. As a comparison, the ToF 3D image obtained using conventional TCSPC is shown in Fig. 5(c) and the height variation along the same line as that in Fig. 5(b) is shown as the black trace in Fig. 5(d). Evidently, TM-TCSPC offers orders-of-magnitude higher measurement precision and accuracy over conventional TCSPC. More significantly, conventional TCSPC image shows much more evident cross talk between depth and intensity information [see Supplement 1 Fig. S3(a) for reference]. Specifically shown in Fig. 5(d), the measured height of the bottom right glass piece has a large error of 350 µm and the glass edges were even measured to exhibit negative heights that were unphysical. Such cross talk stems from the photon pile-up effect in SPAD and is referred to as RWE in photon counting ToF 3D imaging systems [25]. As shown in Supplement 1 Section 4, a 15-ps RWE was observed when the detection probability increased from 0.1% to 1%, a range typically used for TCSPC. Such a phenomenon is detrimental for high-resolution ToF 3D imaging because it not only results in millimeter-scale depth error but also severely limits the intensity dynamic range. While RWE still exists in the TM-TCSPC, it is significantly suppressed by 99.2% (130 times) thanks to the selective temporal magnification of the depth-induced timing. As a result, the RWE is reduced to 19 µm, which is in good agreement with the 26-µm measurement accuracy shown in Fig. 5. Here the total detected photon number is kept the same when comparing the TM-TCSPC with conventional TCSPC images. It represents the maximum advantage of TM-TCSPC when the system insertion loss is optimized to less than 3 dB.

It is worth mentioning that alternative techniques such as femtosecond upconversion [11,26] and photon counting streak camera (PCSC) [12,27] can also provide SPTR in the sub-picosecond regime. While femtosecond upconversion offers an unrivaled resolution (${\lt}{{100}}\;{\rm{fs}}$), the use of ultrashort optical gating significantly lowers the photon efficiency rendering it not suitable for applications in photon starved conditions. PCSC does not suffer from the low photon efficiency, but its tens-of-milliseconds image readout time strictly limits the overall photon count rate unless multiplexing in the spatial or spectral domain is utilized [27]. Thus, PCSC is more suitable for applications with high photon flux at low-speed excitation. In addition, PCSC has a limited resolvable point (record length/SPRT) around 100 that is inherently limited by the attainable pixel number. While the TM-TCSPC demonstrated in this Letter achieves a similar value, it is not fundamentally limited and over 30,000 resolvable points can be achieved by further optimizing the time-lens implementation [28]. By increasing the pump bandwidth and pump dispersion, an extended record length of $ {\gt} 10\; {\rm ns}$ has been demonstrated at sub-picosecond resolution [28]. The record length can be further scaled by orders of magnitude without sacrificing SPTR using asynchronously optical sampling [29] for an even wider range of applications.

In conclusion, we have demonstrated a TM-TCSPC that enables photon counting at the femtosecond regime. Using a temporal magnification ratio of 130, 550 fs SPTR has been achieved, enabling resolving 130-fs pulse width difference at a 22-fs accuracy. By replacing the DCF modules in the current system with a low-loss CFBG, detection sensitivity of ${-}{{95}}\;{\rm{dBm}}$ (0.03 photons per pulse), limited only by the spontaneous Raman scattering noise, can be achieved. A 97% conversion efficiency has been achieved in the time lens and the optimal photon efficiency of the whole system is expected to be higher than 50%. Therefore, TM-TCSPC is a promising solution for high-resolution photon counting in photon starved conditions, benefiting various research fields including low-light fluorescence lifetime microscopy, time-gated Raman spectroscopy, light-in-flight imaging, and computational diffuse optical tomography. In addition, when applied to photon counting ToF 3D imaging, the TM-TCSPC greatly suppresses the RWE that limits all photon counting ToF 3D imaging systems by 99.2% (130 times) and thus provides high depth measurement accuracy and precision of 26 µm and 3 µm, respectively. By improving the time-lens implementation, the record length can be extended to more than 10 ns without sacrificing the sub-picosecond SPTR. In combination with computer vision [30], TM-TCSPC-based ToF 3D imaging will enable human face recognition even when the object is beyond line-of-sight [31,32].