1. Introduction

Superconducting nanowire single photon detectors (SNSPDs) are a new subfield of photon detectors proposed by Gol’tsman in 2001 [1] and play a vital role in various applications, including quantum computation [2], quantum key distribution technology [3], satellite communications [4] and imaging [5], due to their superior characteristics, such as high system detection efficiency (SDE) [6,7], short recovery time [8], low dark count rate and low timing jitter [9]. Among all these prominent features, SDE is the most important characteristic, which is proportional to the optical absorptance of the ultrathin superconducting film. Researchers have explored many ways to improve the SDE and have demonstrated significant achievements. The most acknowledged way is to apply meandering-type nanowire patterns when designing superconducting film chips, with an optical cavity and anti-reflection coating [10] integrated to enhance the photon confinement in the nanowire region. In addition, SNSPDs integrated with waveguides [11] and nanoantennae [12] have also been proposed for seeking better performance and applications of SNSPDs.

Due to the anisotropic nature of the periodically arranged meander nanowires, the SDE of SNSPD shows a strong dependence on the polarization states of the incident photons. The polarization feature of SNSPD is vital in quantum optical experiments and applications requiring high detection efficiency and low polarization dependency. To reduce the polarization sensitivity induced by the grating structure of the nanowire, various schemes have been proposed [13–17]. While effort is almost fully focused on the device design for perfect detector performance, the measurement tactic of the optical response of SNSPD seems to be stagnant. Note that since single-mode optical fibers are in general slightly birefringent due to stresses and manufacturing imperfections, the polarization state at the detector end may differ significantly from the polarization state prepared at the input end of the device’s delivery fiber in an unknown manner. This creates a difficulty for aligning the polarization of the received photon being parallel or perpendicular to the nanowire direction of the SNSPD. To overcome this difficulty and measure the polarization-dependent SDE, one common approach is with the help of a paddle polarization controller [18], which is a manual operation and suffers from many uncertainties. Another common approach is sweeping the polarization states of the input light over the whole Poincaré sphere [6] to find the maximum SDE_max and minimum SDE_min. However, over hundreds of sweeping points are generally needed [19] for accurate SDE characterization at only one wavelength. This leads to significant consumption of measurement time, especially in spectral characterization covering a broadband wavelength range [20].

In this paper, we propose an alternative method for measuring the polarization-dependent SDEs of SNSPDs, which we term as the four-state polarization algorithm (FSPA). By employing a computational scheme inspired by the computational spectrometer developed recently [21], it is shown theoretically that by preparing incident photons with four specific polarization states and measuring the four corresponding SDEs, the maximum and minimum detection efficiencies of SNSPDs can be computed, even if the birefringent property of the delivery fiber is not known. Experimental results confirm that the SDE spectra obtained using the FSPA method agree well with the spectra obtained from the traditional method (i.e., sweeping hundreds of points on the Poincaré sphere) and the simulated absorptance spectra (with the effect of quantum efficiency being considered). The proposed method is therefore a promising candidate for fast and accurate characterization of the optical performance of SNSPDs.

2. Concept and methods

2.1 Measurement setup and theory model

We first briefly introduce the optical measurement setup before elaborating on the FSPA method. As shown in Fig. 1, the whole measurement configuration consists of two main compositions, the optical part in the green dashed box and the electrical section in the blue dashed box. The red line denotes the optical fiber, while the black line represents the coaxial cable. A continuous-wave (CW) laser (Keysight N7778C) spans a wavelength range from 1490 nm to 1640 nm, and the generated light is directed into a polarization synthesizer (Keysight N7786B). The polarization synthesizer enables us to prepare the polarization of the input photon with arbitrary states. An attenuator A₁ functions as a first-stage attenuator and is followed by a fiber-coupled beam splitter with a splitting ratio of 50:50. One branch of the splitter connects to a power meter PM₁ (Thorlabs PM320E) and monitors the real-time optical power incident onto the SNSPD, while the other branch is directed toward the second attenuator A₂. With proper settings, the light is attenuated to the single-photon level and sent to the fiber-connected SNSPD. Note that before we take the measurement, the splitting ratio between PM₂ and PM₁ was calibrated over the whole spectra. Thus, the dispersion effect of the measurement system is eliminated.

 

Fig. 1. Schematics of the polarization-dependent SDE measurement setup.

Download Full Size | PDF

Inspired by the computational spectrometer developed recently [21], here we attempt to measure the two eigen-absorptances of SNSPDs using a polarization related computational scheme. Consider the case where the polarization synthesizer outputs a light field with two orthogonal components E_x and E_yexp(iφ_△), where E_x and E_y denote the amplitude of the two polarization components and φ_△ denotes the phase difference between them. Dictated by the square law of intensity detection, the absorptance of the SNSPD can be in general expressed as an interferometric quadrature form:

It follows that A_max and A_min are computable, if a, b and c can be determined using some sort of measurements.

Note that in Eq. (1), E_x, E_y and φ_△ can be adjusted at will by programming the polarization synthesizer. Taking advantage of this fact, one can simply choose: E_x = 1, E_y = 0 (horizontally polarization), E_x = 0, E_y = 1 (vertically polarization), E_x =${{\sqrt 2 } / 2}$, E_y =${{\sqrt 2 } / 2}$, φ_△= 0 (45° oblique linearly polarization) and E_x =${{\sqrt 2 } / 2}$, E_y =${{\sqrt 2 } / 2}$, φ_△ = π/2 (circularly polarization). Substituting the above parameters into Eq. (1), one ends up with:

Equation (4) shows that the maximum absorptance A_max and minimum absorptance A_min can be computed from measurements that involve only four special points on the Poincaré sphere. We note here that for the case of a regular SNSPD, which contains only one absorptive layer, i.e. the nanowire meander, we have A_max = A_TE and A_min = A_TM. A discussion on a more general case that involving multiple absorptive layers can be found in Supplement 1. Also, we note that the four special polarization states proposed here are not the only choice for measuring A_max and A_min. In other word, one can also choose a different set of four-polarization states to complete the absorptance measurement, as long as a, b and c can be uniquely determined from measurements of Eq. (1).

2.2 Device fabrication

SNSPD was fabricated on the substrate of a distributed Bragg reflector (DBR), as shown in Fig. 2(a). The DBR consists of 13.5 pairs of alternative SiO₂ and Ta₂O₅, on top of which the NbN thin film was deposited by sputtering. The gold conduct was then fabricated by lift-off processes. The meandering nanowire pattern was written by electron beam lithography. After development, the nanowire pattern is transferred to the NbN film by reactive ion etching process. Finally, a deep silicon etch step was implemented to obtain the key-hole for self-aligning SNSPD [22]. Figure 2(b) presents the typical scanning electron microscopy (SEM) image of the meandering nanowire, with a nanowire width of 65 ± 2 nm and a pitch of ∼160 nm. The active area of the nanowire is a circle with a diameter of 16 µm. The zoomed SEM images in the right panel of Fig. 2(b) indicate that the fabricated nanowires feature a good uniformity.

 

Fig. 2. (a) Schematic of the NbN nanowire fabricated on a DBR substrate. Light is directly coupled to the nanowire region by self-aligning coupling approach. (b) SEM image of the fabricated SNSPD. The nanowire shows a uniform width of 65 ± 2 nm and a pitch of ∼160 nm. (c) Measured SDE (scatters) and sigmoid fitting curve (lines) for TE (red) and TM (blue) polarized wave as a function of normalized bias current at a wavelength of 1550 nm. DCR is indicated by the black dots referring to the right y-axis. (d) Timing jitter of SNSPD at three different bias currents of the measured SNSPD.

Download Full Size | PDF

Figure 2(c) shows the measured SDE of SNSPD as a function of the normalized bias current at a wavelength of 1550 nm. The red and blue scatters indicate the response for TE- and TM-polarized light while the red and blue lines show the sigmoid-curve fittings of the corresponding photon-responses. The dark count rate (DCR) is presented by the black dots, referring to the right y-axis of Fig. 2(c). The DCR is less than 100 when I_b is less than 0.85 I_c, where I_c indicates the critical current. The SDE of SNSPD for TE- and TM- polarized photon at I_b = 0.85 I_c is 60% and 13.5%, respectively. Figure 2(d) shows the typical timing jitter of the fabricated SNSPD, with full width at half maximums (FWHMs) of 170 ps, 146 ps, 124 ps for the histogram, at a bias current of I_b = 0.76 I_c, 0.85 I_c, and 0.93 I_c, respectively. The inset of Fig. 2(d) shows the photon-response pulse waveforms recorded with a high-speed oscilloscope at a working current of 5.5 µA. The pulse peak is ∼100 mV in total, and fits well with the exponential decay function, with a pulse-decay time of ∼40 ns.

3. Results and discussion

Using the FSPA method summarized in Eq. (4), the maximum (TE) and minimum (TM) SDEs of the fabricated SNSPD are measured. The results are presented in Fig. 3(a) as a function of wavelength for cases of three different bias currents. The blue, orange and magenta circles represent the SDE spectra of the TE-polarized photons, while the green, violet and cyan squares represent the SDE spectra of the TM-polarized photons. The difference in the SDE spectra at different biases is caused by the change of quantum efficiency, since the detector is not operated at the saturation regime. To validate the proposed FSPA method, Fig. 3(b) compares the spectra obtained by the FSPA with the spectra obtained by the Poincaré sphere scan approach. The orange and violet symbols denote the SDE for TE and TM polarized light measured by the FSPA approach at a bias current of 0.85 I_c, and the light blue triangles denote the SDE measured by sweeping 100 points on the Poincaré sphere. The 100 points are chosen to be evenly distributed on the Poincaré sphere. Two observations can be made from Fig. 3(b). First of all, the unfilled portion of the blue area indicates that 100 sampling points on the Poincaré sphere are insufficient to precisely measure the SDE. Secondly and most importantly, A_TE and A_TM obtained by the FSPA method agree well with the maximum and minimum bounds obtained by sweeping points on the Poincaré sphere, suggesting a validation of the FSPA approach.

 

Fig. 3. (a) Measured SDE as a function of wavelength for cases of three different bias currents by means of FSPA. (b) Comparison of the SDE spectra obtained by FSPA and sweeping 100 points on the Poincaré sphere at I_b = 0.85 I_c. The measurement uncertainty of SDE by means of FSPA is determined as σ_SDE,max = ± 3.13% and σ_SDE,min = ± 3.19% (see Supplement 1).

Download Full Size | PDF

We next provide a further validation of the FSPA by comparing the absorption spectra obtained from the FSPA with the absorption spectra obtained from numerical simulations. For this purpose, the quantum efficiency (QE) needs to be determined and excluded from the measured SDE. We determine the QEs by measuring SDEs as a function of the bias current and normalizing them by the saturated value of their current-related sigmoid-curve fittings [23]. Since literature studies reveal [24,25] that the quantum efficiency depends on the polarization state of the incident photons, QEs for both TE and TM cases are measured (deduced). The results are shown in Fig. 4(a) and 4(b) as a function of the bias current for cases of several different photon wavelength, where the dotted lines correspond to the measured (deduced) data and the solid lines correspond to their sigmoid-curve fittings.

 

Fig. 4. QE as a function of bias current at different wavelengths for TE (a) and TM (b) polarized photons. (c) The sigmoid-curve extracted (scatters) and power-law fitted (lines) QEs. (d) Deduced absorptance as a function of wavelength at different bias currents.

Download Full Size | PDF

Based on the above results, QEs at three different I_b (0.93 I_c, 0.85 I_c and 0.76 I_c) are plotted as a function of wavelength in Fig. 4(c), where the scatters denote the measured (deduced) QEs and lines denote their wavelength-related power law fittings [26]. The absorptance of the fabricated SNSPD is then obtained by dividing the measured SDE spectra with respect to the QE spectra, i.e. Figure 4(c). The results are presented in Fig. 4(d), where the blue, orange and magenta scatters represent the measured (deduced) absorption spectra of the TE-polarized photons, and the green, violet and cyan dots represent the measured (deduced) absorption spectra of the TM-polarized photons. We note that with the effect of quantum efficiency being excluded, the three absorption spectra at different bias currents coincide well with each other, suggesting that the removal of QE is successful.

The simulated absorption spectrum is also shown in Fig. 4(d) using the red lines for TE polarization and blue lines for TM polarization. In our numerical simulation, the DBR substrate is set to be 13.5 pairs of alternative SiO₂ and Ta₂O₅, with each layer have a quarter-wavelength (at 1550 nm) thickness. The dielectric constants of SiO₂ and Ta₂O₅ are assumed to be 2.08 and 4.33, respectively. The thickness of the ultrathin NbN film is 5.5 nm, and the linewidth of the nanowire is 65 nm with a pitch of 160 nm. The dielectric constant of NbN is -5 + 45i (i.e. n_NbN = 4.49 + 5.01i) and is assumed to be constant in the wavelength range from 1490 nm to 1640 nm [27]. Note that to better account for the real situation, we also assume that there exists an airgap between the detector and the fiber end facet (shown in Fig. 2(a)) [18]. In our simulation, the airgap of the SNSPD is chosen as 7.68 µm. Excellent agreement between the measured and simulated absorptance spectra can be identified, suggesting a further validation of the FSPA.

4. Conclusion

In conclusion, we have proposed a four-state polarization algorithm for measuring polarization-dependent SDEs, which requires only four polarization state-related measurements at a given wavelength. The experimental results of the SDE spectra obtained using the FSPA method agree well with the spectra obtained using the traditional method (i.e., sweeping hundreds of points on the Poincaré sphere). The simulated absorptance spectra also coincide well with the measured spectra when the effect of quantum efficiency has been considered. The proposed measurement method is fast and accurate, and is expected to be a useful tool for characterizing the optical performance of SNSPDs.