Rotational diffusion measurements using polarization-dependent fluorescence correlation spectroscopy based on superconducting nanowire single-photon detector

Johtaro Yamamoto; Makoto Oura; Taro Yamashita; Shigehito Miki; Takashi Jin; Tokuko Haraguchi; Yasushi Hiraoka; Hirotaka Terai; Masataka Kinjo

doi:10.1364/OE.23.032633

1. Introduction

Fluorescence correlation spectroscopy (FCS), a type of fluctuation spectroscopy, is often used to investigate biomolecule dynamics [1–3]. FCS is used to analyze fluorescence intensity fluctuations due to the diffusion of fluorescent target molecules. The measurements obtained facilitate determination of the translational diffusion coefficient and the concentrations of fluorescence-tagged target molecules within a cell. The molecular size, weight, and shape of the target molecules can also be estimated via additional analyses. FCS also facilitates analysis of molecular interactions, because a complex comprising the target molecule and other large molecules has a smaller diffusion coefficient than that of the free target molecules. However, measurements of translational diffusion coefficients are less sensitive to changes in molecular volume because the translational diffusion coefficient is inversely proportional to the cube root of the volume of the target molecule. To date, using FCS to analyze small changes in volume, such as oligomerization and aggregation of proteins, has been difficult.

In 1974, Ehrenberg and Rigler proposed a polarization-dependent FCS method called pol-FCS [4]. In pol-FCS, the relaxation time of the fluctuating fluorescence intensity of a polarized fluorescence signal is first obtained via correlation-function analysis. The rotational diffusion coefficient can then be calculated from the relaxation time. However, because the rotational diffusion coefficient is inversely proportional to the volume of the target molecules, pol-FCS has a higher sensitivity to molecular size than conventional FCS, in which the obtained translational diffusion coefficient is inversely proportional to the radius of the target molecules. Consequently, pol-FCS has been expected as a new tool for measurement of small changes in volume such as dimerization of proteins or formation of small aggregation of particles.

However, the relaxation time of biomolecular rotational diffusion is usually in the sub-microsecond range, which is comparable to the time range of the after-pulse noise of photo detectors, such as avalanche photodiodes (APDs). Dual-channel detection and cross-correlation analyses of fluorescence are therefore essential in order to eliminate the after-pulse effect [5–7]. In experiments, the fluorescence is usually separated into two paths, and detected by two different photo detectors. Because there is no correlation between the after-pulses generated by two different detectors, the after-pulse component is eliminated, and a reliable measurement can be obtained. However, adjusting the optical alignment is difficult owing to an increase in optical elements and a decrease in the signal-to-noise ratio due to the halved photon number detected by each detector. Consequently, photon detectors free of after-pulse noise, and a pol-FCS system based on a single-photon detector are strongly desired.

We recently reported on an FCS system that uses a detector based on a new concept—a visible-wavelength superconducting nanowire single-photon detector (VW-SSPD) [8]. After-pulse-free detection of VW-SSPD, which in VW-SSPDs constitutes a significant advantage over conventional APDs, was demonstrated in the FCS system. In the present study, a new and simple pol-FCS system based on single-channel detection—a single-channel pol-FCS (SC-pol-FCS)—was developed and used to perform rotational diffusion coefficient measurements. In this paper, we compare our system with the conventional dual-channel detection-based pol-FCS (dual-channel pol-FCS; DC-pol-FCS) and demonstrate the feasibility of the SC-pol-FCS with VW-SSPD.

2. Setup of the pol-FCS system

The experimental setup of the pol-FCS is shown in Fig. 1. The direction of the optical axis is signified by the z axis and its perpendicular direction by the x and y axes. To provide excitation, an Ar⁺ laser with wavelength 488 nm (IMA101010B0S004, Melles Griot, USA) was expanded and guided to the excitation light port of an inverted microscope (Axiovert 100 TV, Carl Zeiss, Germany). The laser was polarized in the x direction by the polarizer, reflected by the dichroic mirror (FT580, Carl Zeiss, Germany), and tightly focused by an objective lens (C-Apochromat x40, NA = 1.2, Carl Zeiss, Germany) to the fluorescent solution samples. The laser power was in the range 2.8–8.7 μW in the focal plane of the objective lens. Emitted fluorescence was corrected via the same objective lens and passed through the dichroic mirror to an emission filter (BLP01-488R-25, Semrock, USA). The fluorescence was separated into two directions according to its polarization, using an analyzer and a beam splitter. The fluoresced light was coupled to multimode optical fibers possessing a core diameter of 62.5 μm and detected by two different detectors (VW-SSPDs [9] or APDs (SPCM-CD3017 and SPCM-AQR-15-FC, PerkinElmer, Canada)). The laser power was calibrated such as to avoid overly strong light being incident on the detectors. Confocal detection was obtained using the end face of the optical fiber core that acted as a pinhole. Two fluorescent intensity signals were recorded, and auto-correlation functions (ACFs) and the cross-correlation function (CCF) were computed via a digital correlator (ALV-5000/FAST, ALV-GmbH, Germany). Five 10-s measurements were conducted and averaged.

Fig. 1 Optical setup: Pol, polarizer. DM, dichroic mirror. Obj., objective lens. Em., emission filter. M, mirror. Ana., analyzer. BS, beam splitter. L, lens. MF, multimode fiber.

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In the pol-FCS system, measurements were performed in four different polarization states, as represented by the three letters shown in Table 1 (specifically, “X,” “N,” and “Y”). The direction of the transparent polarization pass through polarizer and analyzer, and the usedbeam splitter, which is non-polarized beam splitter (NPBS) or polarized beam splitter (PBS), in each condition name are summarized. The split ratio of the NPBS was 50:50, and that is independent of the polarization of the fluorescence. “X” and “Y” respectively represent x-polarization and y-polarization, and “N” means “not polarized.” The first letter of the polarization state signifies the polarization direction of the excited light. The second and third letters are assigned to the polarized direction of the fluorescence detected by detectors 1 and 2, respectively. For example, “XXY” signifies that the fluorescent sample is excited by the x-polarized light, and the fluorescence polarized in the x- and y-directions are detected by the two detectors D₁ and D₂, shown in Fig. 1, respectively. Similarly, “XX-” signifies that the sample is excited by the x-polarized light, and the only fluorescence polarized in the x direction is detected only by detector D₁. In the SC-pol-FCS, the NPBS was not essential; however, the NPBS was used in all the configurations of SC-pol-FCS to equalize the optical condition to the DC-pol-FCS. With the polarized excitation light and the analyzer, the detected fluorescence intensity fluctuates because of the rotational diffusion of the fluorescent molecules in addition to the translational diffusion because fluorophores have dipole moment of electric transition for absorption and emission. In other words, the excitation and emission efficiency of fluorophores is dependent on the polarization direction. Kask et al. [10] and Widengren et al. [11] assert that the rotational diffusion term can be separated from the translational diffusion term. The CCF G_n_,_m of the fluorescence intensity signal I detected by detector n and m is defined as

G_{n, m} (τ) = \frac{〈 I_{n} (t) \cdot I_{m} (t + τ) 〉}{〈 I_{n} (t) 〉 〈 I_{m} (t) 〉} - 1 = G_{D} (τ) \cdot G_{R} (τ),

G_{D} (τ) = \frac{1}{N} [f_{1} {(1 + \frac{τ}{τ_{D 1}})}^{- 1} {(1 + \frac{τ}{s^{2} τ_{D 1}})}^{- 1 / 2} + (1 - f_{1}) {(1 + \frac{τ}{τ_{D 2}})}^{- 1} {(1 + \frac{τ}{s^{2} τ_{D 2}})}^{- 1 / 2}],

G_{R} (τ) = 1 + f_{R} \exp (- \frac{τ}{τ_{R}}),

where, G_D and G_R are the translational diffusion component and the rotational diffusion component of the CCF, respectively. G_D has two components for translational diffusion (translational diffusion time) with relaxation times τ_D₁ and τ_D₂, and f₁ is a fraction of τ_D₁. N is the average number of target molecules inside the confocal volume. s is the aspect ratio, i.e., the ratio of the radii of the longer axis to the shorter axis of the confocal volume of the system, called the structure parameter. τ_R and f_R are the relaxation times of the rotational diffusion (rotational diffusion time) and a fraction of the rotational diffusion component, respectively. The rotational diffusion coefficient D_R can be obtained via the equation

D_{R} = 1 / (6 τ_{R})

in accordance with a first order approximation of the D_R for anisotropic particles presented by Aragon and Pecora [12], indicating that the rotational diffusion time is independent of any optical configuration such as the size of the confocal volume. In a case where n = m, the correlation function becomes the ACF. The ACFs were evaluated for the case of SC-pol-FCS. Because the Qrods have no triplet state [13], the triplet term of ACF and CCF was neglected. Nonlinear global fitting analyses were conducted using the software Origin Pro 9.1J (OriginLab Corp., USA) to extract the parameters from the correlation functions acquired on the samples. In the fitting analysis, the rotational diffusion time was shared for all the polarization conditions because the rotational diffusion time of all polarization conditions should be identical.

Table 1. The polarization condition and its optical configurations.

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3. Sample preparation

CdSe/CdS (core/shell) Qrod, a kind of quantum dot with a rod-like shape [14–16] and a peak emission wavelength of 650 nm, was prepared and used as a sample in the pol-FCS experiment because such a semiconductive nanowire was previously reported as a possible sample of the pol-FCS [6]. The transmission electron microscope (TEM) image of CdSe/CdS Qrods was taken using the Hitachi HF2000 (Hitachi High-technologies, Japan) at 200 kV. Samples were prepared by dropping 2 μL of a chloroform solution of the Qrods onto a carbon-coated copper grid and letting it stand overnight to evaporate the solvent. The TEM image of the Qrod and its size distribution are shown in Figs. 2(a) and 2(b), respectively; the size was determined using the TEM image and the software ImageJ 1.48v [17]. The mean diameter and the length of the Qrod were 7.60 ± 5.24 nm (mean ± standard deviation) and 22.18 ± 5.61 nm, respectively. The mean aspect ratio was 2.78 ± 1.44. The theoretically predicted rotational diffusion coefficient was 18.0 × 10⁴ s⁻¹ using the Broersma’s relations for such an object [18, 19]. In the pol-FCS experiment, the Qrod was diluted to a concentration of 10 nM in a phosphate buffered saline solution. We found that the Qrod was well-dispersed and contained few aggregated Qrods in solution by following experiments.

Fig. 2 Size distribution of the Qrod. (a) TEM image of the Qrod; the scale-bar length is 20 nm. (b) Histogram of the diameter and length of the Qrod; n = 48.

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4. Results and discussions

4.1 Conventional DC-pol-FCS measurements

The averaged correlation functions of Qrod (10 nM) obtained using the DC-pol-FCS system, in which CCFs were analyzed using two detectors, APDs and VW-SSPDs, are shown in Fig. 3. Their normalized correlation functions $G' (τ) = N \cdot G (τ)$ are shown in Figs. 3(c) and 3(d), respectively. The correlation curves were fitted using Eq. (1), and all the measurements repeated three times to verify reproducibility. The results are summarized in Table 2. Pol., CR, and CPM mean the polarization condition defined in Table 1, the count rate of the fluorescence photons, and the count rate per single molecule (QR), respectively. χ² is the chi-squared error per degree of freedom of the fitting. All values are shown by mean ± standard deviation (n = 3). The τ_R was shared among all the polarization conditions in each data set. Only one χ² value was obtained via the global fitting. In the measurements, there were few strong spikes or pulses due to the aggregated Qrods crossing the measurement volume in fluorescence signals, indicating that the Qrods were well-dispersed and contained few aggregations. In the CCFs for DC-pol-FCS, there were no components for the dead time of the detectors, after-pulsing, or any other noises originating from the detectors. This is due to the fact that no correlations exist between the two independent detectors [5, 6]. As a result, the valid CCFs in the entire time range of the hardware correlator were obtained.

Fig. 3 Results of DC-pol-FCS. A sample of 100 nM Qrod was considered here. (a) and (b) are the typical CCFs and the residuals of fitting obtained by the APDs and VW-SSPDs, respectively. The symbols represent experimentally obtained CCFs, while the red solid lines show the fitted theoretical CCF curves. (c) and (d) show the CCFs normalized by the number of particles detected by the APDs and VW-SSPDs, respectively. The solid lines are the averaged CCFs and the shaded areas show the standard deviations (n = 3).

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Table 2. Results of global nonlinear fitting.

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The amplitudes of the CCFs in each polarization state, which are related to the mean number of fluoresced particles inside the confocal volume, were different for each APD and VW-SSPDs as shown in Figs. 3(a) and 3(b) despite the fact that the same sample was used for each measurement. In addition, the diffusion times were also different. This difference may be the result of a slight change in the measurement volume generated by the optical condition associated with a change in polarization states because we manually exchanged the optical elements—the beam splitters and the analyzer—which could cause slight changes in the accuracy of the optical setup. The Pearson correlation coefficient between the number of molecules N, which is proportional to the confocal volume, and the translational diffusion time τ_D₁, which is proportional to the squared radius of the shorter axis of the confocal volume, was 0.73. This supports the supposition that the change in the translational diffusion time was caused by the slight change in the confocal volume. This problem can be rectified byintroducing an automation system to exchange optical elements and an auto-adjustment system.

The exponential decay of the CCFs in the time range of several hundred nanoseconds to several microseconds, due to the rotational diffusion of the Qrod, is shown in Figs. 3(c) and 3(d). The rotational diffusion coefficients, as calculated using the rotational diffusion times shown in Table 2, were comparable to the theoretical coefficients 18.0 × 10⁴ s⁻¹. The relatively large deviation in Fig. 3(d) resulted from the shortage of the detected photon (count rate of the fluorescence photon), as shown in Table 2. Possible reasons for the shortage in the photon count rate include optical coupling loss between the SSPD and FCS systems and the polarization dependencies of the detectors. These possible reasons will be clarified in further investigations. Two different values were obtained via nonlinear fitting of Eq. (1) to the data for the translational diffusion time. The ratio τ_D₂/τ_D₁, which corresponds to the diffusion coefficient ratio, was found to be approximately 10. Although there were no large aggregations of Qrod and the size distribution of Qrod was single peak, the reason of two diffusion species may be caused from weak biding and/or dispersion of Qrod. The reason why there were two diffusion species is not clear, yet. However as one of the possible explanation, the fast component, τ_D₁, and slow component, τ_D₂, may be characterized by the diffusion coefficient in the direction perpendicular to the long axis of the molecule $D_{⊥}$ and parallel to the axis $D_{/ /}$ , respectively. The ratio $D_{⊥} / D_{/ /}$ should be 2.0 according to the hydrodynamic stick model [20], or should be equal to the aspect ratio of the diffusing object according to the ellipsoid model [19]. However, the results of the Qrod experiment do not appear to accord with these two theories. The shape of the Qrod is definitely not stick or ellipsoid, which in turn might reflect the structure and hydrodynamics of Qrod.

4.2 SC-pol-FCS measurements

The average correlation functions obtained using SC-pol-FCS are shown in Fig. 4. The ACF was analyzed using only a single APD detector in Figs. 4(a), 4(c), and 4(e) and a single VW-SSPD detector in Figs. 4(b), 4(d), and 4(f). The full view of the ACFs is shown in Figs. 4(a) and 4(b), and the enlarged view of the ACFs is shown in Figs. 4(c) and 4(d). The normalized correlation functions, $G' (τ)$ , of these ACFs are shown in Figs. 4(e) and 4(f). The fitted parameters are summarized in Table 2. The difference in amplitudes of the ACFs, or particle numbers, may be as a result of a change in the operating conditions, as illustrated in Fig. 3.

Fig. 4 Results of the SC-pol-FCS experiment. A 100 nM Qrod sample was considered. (a) and (b) are the experimentally obtained typical ACFs measured using the APDs and VW-SSPDs, respectively. (c) and (d) are the same ACFs as (a) and (b) but in the different y scale and the residuals of fitting. The symbols represent the experimentally obtained ACFs, and the solid red lines show the fitted theoretical CCF curves. (e) and (f) are the CCFs normalized by the particle numbers detected by the APDs and the VW-SSPDs, respectively. The solid lines are the averaged CCFs and the shaded areas show the standard deviations (n = 3).

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In Figs. 4(a) and 4(b), the values of the ACFs were < −1 in the time range of several tens of nanoseconds (10⁻⁸ s) to several hundred nanoseconds (10⁻⁷ s). This negative correlation is due to the dead time of the detectors [7, 8]. Dead time is the time interval following a photon detection event during which the APD or VW-SSPD is not sensitive. The dead time of the APD and the VW-SSPD were approximately 40 and 100 ns, respectively. This longer dead time of the VW-SSPD is one of the drawbacks of the current VW-SSPD. In Fig. 4(a), a sharp peak due to after-pulse noise in the APD at several tens of nanoseconds is shown. Note that this component could not be separated from the rotational diffusion measurement. On the other hand, measurements obtained by the VW-SSPD shown in Fig. 4(b) had no strong peak due to after-pulse noise because of its inherent structural design [8]. In addition, evident polarization dependence on the amplitude of the ACFs was observed when using the VW-SSPD, and this result of the VW-SSPD experiments demonstrated the feasibility of the SC-pol-FCS method.

The obtained rotational diffusion time and the fraction of the rotational diffusion component are compared in Fig. 5. The rotational diffusion times of all polarization conditions were the same level, as shown in Fig. 5(a), and there were no significant differences. However, relatively large errors were observed in the APD single condition as shown in Fig. 5(b), whereas the results of APD cross were reliable. In particular, in the measurement of “XYY,” the result of APD single was significantly different from that of APD cross. This suggests that the unavoidable after-pulse components were mixed into the rotational diffusion component in the case of APD single, but not in the case of APD cross. In contrast, the results of SSPD single agree well with the APD cross and SSPD cross owing to the after-pulse-free detection of the SSPD.

Fig. 5 Fitted parameters of the rotational diffusion components. (a) Comparison of the relaxation time of the rotational diffusion component: according to the student t-test there were no significant differences between the APD cross and each condition. (b) Comparison of the fraction of the rotational diffusion component: according to the student t-test there were no significant difference between the APD cross and each condition in each polarization condition except between the APD cross and the APD single in the XYY condition. The error bars show the standard deviations. * p = 0.020 < 0.05. n = 3.

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5. Conclusions

This paper reported on the feasibility of the SC-pol-FCS system, which was previously difficult to realize owing to the high efficiency but large after-pulse components of photon detectors such as APDs. The system was realized using a VW-SSPD as a detector, as it does not produce after-pulse noise. This feature is a result of its inherent design principle. The optical setup of the SC-pol-FCS is simpler than that of the conventional DC-pol-FCS and optical efficiency is improved as a result of a less complex arrangement of the optical elements. Furthermore, the simple optics of the SC-pol-FCS system are easy to install in the FCS and laser microscope systems, including commercialized microscope systems based on single-channel detection, because only existing photon detectors need to be exchanged with VW-SSPDs.

The VW-SSPD has the great advantage of after-pulse-free detection; however, the dead time of the VW-SSPD is longer than that of the APD. In the future, a faster rotational diffusion analysis of small molecules such as proteins will be achieved by improving the dead time of VW-SSPDs. This will allow for rotational diffusion measurements of proteins in living cells with high sensitivity.

Acknowledgments

This work was supported by grants from the Japan Science and Technology Agency (JST) (to YH and HT), the Japan Agency for Medical Research and Development (AMED) (to YH and HT) and partially supported by JSPS KAKENHI Grant Number 26870007 (to JY).

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System	Condition name	Polarizer direction	Analyzer direction	Beam Splitter
DC-pol-FCS	XNN	X	Not used	NPBS
(Conventional)	XXX	X	X	NPBS
	XYY	X	Y	NPBS
	XXY	X	Not used	PBS
SC-pol-FCS	XN-	X	Not used	NPBS
(Proposed)	XX-	X	X	NPBS
	XY-	X	Y	NPBS

System	Pol.	CR (kHz)		N		CPM (kHz)			f₁	τ_D₁ (ms)		τ_D₂ (ms)
APD	XNN	898 ± 26		4.65 ± 0.52		195 ± 25			0.56 ± 0.16	0.73 ± 0.23		8.9 ± 4.7
cross	XXX	149 ± 4		6.03 ± 2.40		28.3 ± 13.8			0.41 ± 0.11	0.45 ± 0.21		9.0 ± 5.0
	XYY	308 ± 9		3.74 ± 0.08		82.4 ± 1.2			0.39 ± 0.13	0.50 ± 0.20		5.3 ± 2.2
	XXY	1,242 ± 6		5.67 ± 0.37		220 ± 20			0.45 ± 0.18	0.64 ± 0.30		5.7 ± 2.3
SSPD	XNN	333 ± 3		3.57 ± 0.08		93.3 ± 2.5			0.44 ± 0.16	0.49 ± 0.19		3.9 ± 1.1
cross	XXX	80 ± 3		2.41 ± 0.20		33.2 ± 3.4			0.23 ± 0.09	0.29 ± 0.14		3.6 ± 0.8
	XYY	102 ± 6		2.17 ± 0.15		47.2 ± 5.8			0.30 ± 0.17	0.28 ± 0.23		3.0 ± 1.3
	XXY	387 ± 7		5.07 ± 0.14		76.4 ± 2.7			0.39 ± 0.23	0.53 ± 0.35		4.6 ± 2.2
APD	XN-	591 ± 18		4.44 ± 0.97		138 ± 37			0.35 ± 0.15	0.46 ± 0.21		4.8 ± 0.9
single	XX-	48 ± 2		2.77 ± 0.36		17.7 ± 2.3			0.35 ± 0.17	0.36 ± 0.15		3.3 ± 1.2
	XY-	188 ± 3		4.30 ± 0.19		44.0 ± 2.6			0.35 ± 0.01	0.44 ± 0.03		4.4 ± 0.3
SSPD	XN-	221 ± 4		3.43 ± 0.12		64.5 ± 1.7			0.27 ± 0.12	0.31 ± 0.13		2.5 ± 0.5
single	XX-	83 ± 6		2.84 ± 0.22		29.4 ± 3.8			0.36 ± 0.12	0.38 ± 0.18		3.6 ± 1.1
	XY-	61 ± 3		2.40 ± 0.03		25.5 ± 1.1			0.29 ± 0.08	0.34 ± 0.10		2.8 ± 0.4

System	Pol.		f_R				τ_R (μs)				D_R ( × 10⁴ s⁻¹)		χ² ( × 10⁻⁶)
APD	XNN		0.087 ± 0.009		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
cross	XXX		0.27 ± 0.02				1.6 ± 0.5				11 ± 1		19.6 ± 1.3
	XYY		0.12 ± 0.01
	XXY		−0.053 ± 0.004
SSPD	XNN		0.086 ± 0.009		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
cross	XXX		0.33 ± 0.04				1.2 ± 0.1				11 ± 1		59.1 ± 16.6
	XYY		0.10 ± 0.04
	XXY		−0.051 ± 0.003
APD	XN-		0.076 ± 0.032		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
single	XX-		0.47 ± 0.18				1.4 ± 0.5				12 ± 4		9.1 ± 0.8
	XY-		0.16 ± 0.02
SSPD	XN-		0.082 ± 0.008		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
single	XX-		0.26 ± 0.03				2.0 ± 0.3				8.5 ± 1.2		10.1 ± 0.8
	XY-		0.10 ± 0.01

System	Condition name	Polarizer direction	Analyzer direction	Beam Splitter
DC-pol-FCS	XNN	X	Not used	NPBS
(Conventional)	XXX	X	X	NPBS
	XYY	X	Y	NPBS
	XXY	X	Not used	PBS
SC-pol-FCS	XN-	X	Not used	NPBS
(Proposed)	XX-	X	X	NPBS
	XY-	X	Y	NPBS

System	Pol.	CR (kHz)		N		CPM (kHz)			f₁	τ_D₁ (ms)		τ_D₂ (ms)
APD	XNN	898 ± 26		4.65 ± 0.52		195 ± 25			0.56 ± 0.16	0.73 ± 0.23		8.9 ± 4.7
cross	XXX	149 ± 4		6.03 ± 2.40		28.3 ± 13.8			0.41 ± 0.11	0.45 ± 0.21		9.0 ± 5.0
	XYY	308 ± 9		3.74 ± 0.08		82.4 ± 1.2			0.39 ± 0.13	0.50 ± 0.20		5.3 ± 2.2
	XXY	1,242 ± 6		5.67 ± 0.37		220 ± 20			0.45 ± 0.18	0.64 ± 0.30		5.7 ± 2.3
SSPD	XNN	333 ± 3		3.57 ± 0.08		93.3 ± 2.5			0.44 ± 0.16	0.49 ± 0.19		3.9 ± 1.1
cross	XXX	80 ± 3		2.41 ± 0.20		33.2 ± 3.4			0.23 ± 0.09	0.29 ± 0.14		3.6 ± 0.8
	XYY	102 ± 6		2.17 ± 0.15		47.2 ± 5.8			0.30 ± 0.17	0.28 ± 0.23		3.0 ± 1.3
	XXY	387 ± 7		5.07 ± 0.14		76.4 ± 2.7			0.39 ± 0.23	0.53 ± 0.35		4.6 ± 2.2
APD	XN-	591 ± 18		4.44 ± 0.97		138 ± 37			0.35 ± 0.15	0.46 ± 0.21		4.8 ± 0.9
single	XX-	48 ± 2		2.77 ± 0.36		17.7 ± 2.3			0.35 ± 0.17	0.36 ± 0.15		3.3 ± 1.2
	XY-	188 ± 3		4.30 ± 0.19		44.0 ± 2.6			0.35 ± 0.01	0.44 ± 0.03		4.4 ± 0.3
SSPD	XN-	221 ± 4		3.43 ± 0.12		64.5 ± 1.7			0.27 ± 0.12	0.31 ± 0.13		2.5 ± 0.5
single	XX-	83 ± 6		2.84 ± 0.22		29.4 ± 3.8			0.36 ± 0.12	0.38 ± 0.18		3.6 ± 1.1
	XY-	61 ± 3		2.40 ± 0.03		25.5 ± 1.1			0.29 ± 0.08	0.34 ± 0.10		2.8 ± 0.4

System	Pol.		f_R				τ_R (μs)				D_R ( × 10⁴ s⁻¹)		χ² ( × 10⁻⁶)
APD	XNN		0.087 ± 0.009		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
cross	XXX		0.27 ± 0.02				1.6 ± 0.5				11 ± 1		19.6 ± 1.3
	XYY		0.12 ± 0.01
	XXY		−0.053 ± 0.004
SSPD	XNN		0.086 ± 0.009		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
cross	XXX		0.33 ± 0.04				1.2 ± 0.1				11 ± 1		59.1 ± 16.6
	XYY		0.10 ± 0.04
	XXY		−0.051 ± 0.003
APD	XN-		0.076 ± 0.032		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
single	XX-		0.47 ± 0.18				1.4 ± 0.5				12 ± 4		9.1 ± 0.8
	XY-		0.16 ± 0.02
SSPD	XN-		0.082 ± 0.008		$\begin{array}{l} \end{array}}$			$\begin{array}{l} \end{array}}$				$\begin{array}{l} \end{array}}$
single	XX-		0.26 ± 0.03				2.0 ± 0.3				8.5 ± 1.2		10.1 ± 0.8
	XY-		0.10 ± 0.01

Rotational diffusion measurements using polarization-dependent fluorescence correlation spectroscopy based on superconducting nanowire single-photon detector

Abstract

1. Introduction

2. Setup of the pol-FCS system

3. Sample preparation

4. Results and discussions

4.1 Conventional DC-pol-FCS measurements

4.2 SC-pol-FCS measurements

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Tables (2)

Equations (3)

Optics Express