1. Introduction

Optical parametric generators (OPGs) using unseeded parametric down-conversion (PDC) are powerful tools for optical microscopy and spectroscopy. A key feature of OPGs is that the wavelengths of the emitted signal and idler beam pair can be tuned over a wide range from the visible to infrared regions [1–3]. In addition, OPGs have the advantages of being compact, potentially low cost, and easy to operate, since cavity and seed light sources are not used [4]. Thus, OPGs might serve as promising alternatives or new choices to existing light sources in a wide range of applications. Specifically, there is growing interest in the use of OPGs as laser sources in nonlinear microscopy imaging in biology and medicine.

Importantly, the PDC process can also enhance nonlinear optical effects in both the low-gain (spontaneous) and high-gain regimes. Time-frequency entanglement generated in the low-gain regime significantly increases the two-photon excitation rate [5,6]. This enables the observation of two-photon signals with an ultralow excitation power and minimizes perturbations from the imaging system. Experimentally, entangled two-photon absorption has been demonstrated for samples such as atomic gases [7] and organic molecules [8–20]. Recently, quantum enhanced entangled two-photon microscopy of breast cancer cells was demonstrated by extremely low excitation intensity [21]. Unfortunately, the weak light intensity under these conditions necessitates an extremely long image acquisition time, making it practically incompatible with most bioimaging research aimed at capturing fast phenomena.

Although the benefit of entanglement is lost when the gain is increased beyond the spontaneous PDC regime [22], PDC light has another feature that enhances nonlinear interactions. PDC generates larger intensity fluctuations than the coherent state of light, and the time scale of the fluctuations from unseeded PDC is typically on the order of sub-picoseconds and femtoseconds due to the broad spectrum [23,24]. These large, ultrafast fluctuations induce an instantaneous increase in the intensity of the pulsed light, as shown in Fig. 1. In other words, it causes bunching of light on an ultrashort timescale, increasing the efficiency of nonlinear interactions compared with coherent light with the same pulse energy. The bunching effect is very important in practical use because it is produced in PDC light even in the high-gain region, raising the possibility that it can be utilized in nonlinear microscopy imaging in biology and medicine.

 

Fig. 1. Representation of ultrafast intensity fluctuations in a pulse. The solid and dotted curves show the pulse with and without ultrafast intensity fluctuations. The maximum instantaneous intensity is increased due to the fluctuations while the pulse energy is unchanged.

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The enhancement by light bunching can be quantified by a second-order autocorrelation function, $g^{(2)}(\tau )$, at zero delay $(\tau = 0)$. This is related to the enhancement factor for two-photon excitation and second-harmonic generation processes [25]. For high-gain PDC, $g^{(2)}(0)$ for the signal and idler beam pair can be up to 3, which means it is three times more efficient [26,27]. In the case of the signal or idler alone, $g^{(2)}(0) = 2$ can be realized, as for thermal sources.

In recent years, experimental research on nonlinear effects based on the bunching effects of light have been carried out with the aim of applying them to nonlinear imaging and spectroscopy. Enhanced two-photon excited fluorescence (TPEF) in fluorophore solutions by bunching has been demonstrated using super-luminescence diodes [28] and OPGs [29]. Furthermore, OPGs have been experimentally shown to be useful in improving depth observations in two-photon microscopy [30] and achieving simultaneous high resolution in time and frequency, space and wavevector in two-photon spectroscopy [31]. Although the usefulness of bunching in nonlinear optical measurements has been experimentally demonstrated, nonlinear optical imaging of biological samples using intense PDC pulses with calibrated $g^{(2)}$ values has not been realized. In fact, to date, few attempts have been made to develop potential implementations of such optical effects for biological imaging, despite the increasing use of nonlinear microscopy techniques in biology and medicine, and the resulting need for further improvements in these techniques.

Here, we report the evaluation of $g^{(2)}(\tau )$ for intense PDC pulses and enhanced two-photon fluorescence from green fluorescent proteins (GFP) by bunching on an ultrashort timescale. We construct a pulsed OPG that emits intense pulses with an instantaneous intensity of about 1 kW. The wavelength of the emitted light is tuned to around 927 nm so that the two-photon absorption of GFP is maximized [32]. We confirm that the ultrafast intensity fluctuations in a pulse enhances the two-photon fluorescence from a GFP solution by a factor of $g^{(2)}(0) \sim 1.9$. We also show that two-photon fluorescence imaging of a GFP-expressing mouse brain can be readily implemented using PDC light with $g^{(2)}(0) \sim 1.9$. This study demonstrates the benefit of bunching effect at the high-laser power regime that is sufficient for the practical two-photon excitation microscopy observation of biological samples.

2. Results and discussion

2.1 Evaluation of optical parametric generator

The setup of the OPG is shown in Fig. 2(a). The light source to pump the PDC is a $Q$-switched laser emitting light pulses at a wavelength of 532 nm with a 3.4-ns full width at half maximum (FWHM) and a 7.1-kHz repetition rate (Cobolt, Tor). The pump laser is focused with a beam waist diameter of 350 $\mu$m on a 25-mm long periodically poled LiNbO$_3$ (PPLN) crystal (HC Photonics, SHVIS-SB-25).

 

Fig. 2. Characterization of optical parametric generator. (a) Experimental setup. (b) Temperature tuning curve for the signal and idler wavelengths. The filled and empty circles indicate the experimental data for the signal and idler, respectively. The calculated curve (solid) is based on the Sellmeier equation. The inset shows the spectrum obtained at a PPLN temperature of 120 $^{\circ }$C. (c) Pump power dependence of the average signal power. The solid curve is an exponential fitting curve for a pump power $\leq 250$ mW. The inset shows the pulse shape for the signal obtained by averaging over multiple pulses.

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The wavelengths of the signal and idler beams can be controlled by changing the phase-matching condition of the nonlinear medium. To do this, we adjust the temperature of the PPLN mounted in a PID controlled oven (Conversion, PV40 and OC3) [Fig. 2(b)]. Our OPG is capable of emitting wavelengths from $876$ to $1354$ nm, which is in good agreement with the numerical curves calculated based on the Sellmeier equation [33]. In the following experiments, the wavelength of the signal beam is adjusted to around $\lambda _{\mathrm {2PA}} =$ 927 nm, which is the peak wavelength for two-photon absorption by GFP [32]. The FWHM for the signal at $927$ nm is about 5 nm (see the inset of Fig. 2(b)). The idler and pump beams propagating collinearly with the signal beam from the PPLN are removed using a short-pass filter (Edmund, 64-330) and long-pass filters (Edmund, 62-978 and 86-062).

Figure 2(c) shows the pump-power dependence of the average output power for the signal beam at $927$ nm. The maximum average output power reaches 20 mW for an average pump power of 384 mW. The corresponding peak intensity of the signal pulses was estimated to be about 1 kW by measuring the pulse waveform using a photodetector (Newport, model 1444). Note that ultrafast fluctuations on the subpicosecond to femtosecond time scale cannot be observed in this measurement due to the slow response time of the detector. When the average pump power exceeds 300 mW, the output signal power deviates from the exponential curve depicted by the solid curve in Fig. 2(c). This indicates that pump depletion occurs during the PDC process due to the high conversion efficiency [34].

2.2 Evaluation of enhanced TPEF from GFP solution

$g^{(2)}$ can be determined by autocorrelation measurements using a two-photon absorption process [35]. An important feature of our method is that we measure TPEF from GFP solutions to determine two-photon absorption. In contrast, a semiconductor-based two-photon absorption detector was used in pioneering work [35] and other experiments [36–38]. Our method based on TPEF detection allows us to directly link the $g^{(2)}$ value to the enhancement factor for fluorescence from the GFP [29], enabling us to evaluate the potential benefit of photon bunching on biological imaging.

The experimental setup for measuring $g^{(2)}(\tau )$ is shown in Fig. 3(a). The signal from the OPG is incident on a Michelson interferometer. The mirror on one arm is placed on a moving stage equipped with a DC servomotor actuator and PZT actuator (Thorlabs, MTS50-Z8 & NF15AP25). Their actuators are used to tune and modulate $\tau$. The output from the Michelson interferometer is focused by an objective lens (Mitutoyo Plan Apo NIR B $20\times$, NA $0.40$) onto a GFP in a phosphate-buffered saline (PBS) solution with a concentration of 10 $\mu$M. The TPEF from the GFP reflected by the dichroic mirror (Semrock, FF705-DIO01-25X36) is collected by an electron-multiplying charge-coupled device (EMCCD) camera (Princeton Instruments, ProEM-HS 512BX3-G). Fluorescence filters (Edmund, 84-743, 84-708) are placed in front of the EMCCD camera.

 

Fig. 3. Evaluation of enhanced TPEF from GFP. (a) Experimental setup for measuring $g^{(2)}(\tau )$. (b) TPEF measured by randomly modulating the optical pass length and slightly varying its offset using the PZT actuator. In the inset, the offset is shifted without random modulation around $\tau = 0$. (c) Experimentally observed $g^{(2)}(\tau )$.

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The TPEF obtained using the setup in Fig. 3(a) can be expressed by the following [35,39]:

In order to accurately estimate $g^{(2)}(0)$, we smooth the high-frequency components by rapidly modulating $\tau$ using the PZT actuator while obtaining data. This technique works robustly even if the optical path length is unstable. In previous studies [23,24,35], these terms were numerically filtered out by post-processing of the experimental data.

The appropriate modulation amplitude that smooths only the high-frequency components is determined experimentally. The inset in Fig. 3(b) shows the case for a varying offset without rapid modulation of $\tau$. In this case, the TPEF counts vary periodically, which corresponds to the high-frequency component in Eq. (1). Since the high-frequency components are smoothed out by modulating $\tau$, the normalized TPEF converges to $1+ 2 G_2(\tau )$ as the modulation amplitude is increased. In the main figure of Fig. 3(b), random noise modulation is applied to the PZT actuator during data collection, and the inset figure with zero modulation amplitude corresponds to a horizontal axis position of $0$ in the main figure. The noise bandwidth of the applied random modulation is set to 100 Hz, which produces noise sufficiently faster than the acquired time of 1 s for one data point, to average out the high-frequency components. Variations in the TPEF decrease with increasing modulation amplitude of the random noise, and the variations are suppressed for a modulation amplitude of about $3.5$ fs or more. This means that $S_{\mathrm {LPF}}(\tau )$ can be obtained by applying a modulation amplitude of more than 3.5 fs.

Figure 3(c) shows $g^{(2)}(\tau )$ experimentally determined from the observed $S_{\mathrm {LPF}}(\tau )$ with a random modulation amplitude of 6.7 fs, where the horizontal axis ($\tau$) is varied using a DC servo motor. $g^{(2)}(0)$ = $1.85 \pm 0.03$ is achieved, which means the TPEF from GFP is enhanced by a factor of about 1.9 compared with the coherent state of light ($g^{(2)} = 1$). The time scale of the fluctuations corresponding to the full width at $g^{(2)}(\tau ) = (g^{(2)}(0)-1)/2+1$ is 260 fs, which is much shorter than the nanosecond pulse envelope width shown in the inset of Fig. 2(c).

In order to confirm the repeatability of the $g^{(2)}(0)$ value, we remeasured the same data set as in Fig. 3(c) after five hours. The result yields $g^{(2)}(0)$ = $1.85 \pm 0.04$, indicating that the magnitude of $g^{(2)}(0)$ is temporally stable.

Our observed value of $g^{(2)}(0) = 1.85$ is slightly smaller than the value of $g^{(2)}(0) = 2$ achievable by thermal sources. A possible cause of this decrease in $g^{(2)}(0)$ is pump depletion in the PDC process, as observed in Fig. 1(c). In fact, although the method of evaluating $g^{(2)}(0)$ differs from our method, it was experimentally observed that $g^{(2)}(0)$ for the PDC light is decreased by the interplay between the pump beam and PDC light in the pump depletion regime [40]. In addition, $g^{(2)}(0)=2$ with a time resolution in the femtosecond range scale was observed for signal or idler beam in the undepleted pump regime [23].

One of the other factors that lowers $g^{(2)}(0)$ is the imperfect mode matching between separated beams in the Michelson interferometer. However, the effect of imperfections in the Michelson interferometer is expected to be negligibly small. This is because we have observed $g^{(2)}(0) =2.0$ for frequency degenerate parametric down-conversion in the undepleted pump regime by using similar optical setup [29], and this result is well reproduced by the theoretical prediction even without considering such imperfections.

The OPG can be driven in the undepleted pump region by reducing the pump power to about 250 mW, as shown in Fig. 1(c). In that case, even though $g^{(2)}(0) = 2$ can be achieved, the output power from the OPG is reduced by about an order of magnitude or more. On the other hand, if the conversion efficiency of the PDC is increased too much, there is concern that $g^{(2)}(0)$ will decrease even more due to pump depletion. Therefore, to increase the signal-to-noise ratio in two-photon excitation imaging, it is important to achieve the permissible irradiation intensity at low conversion efficiency. In actual experiments, the conversion efficiency can be tuned by adjusting the waist size of the pump beam in the nonlinear crystal.

2.3 Two-photon imaging of GFP in brain tissue

Finally, we implement two-photon imaging of GFP in a sample of mouse brain tissue to show that our OPG source emits sufficient intensity to obtain two-photon images. Figure 4(a) shows the experimental setup for implementing two-photon imaging. The signal beam is focused onto sliced brain tissue by an objective lens. When acquiring images, a Galvo scanner (Thorlabs, GVS012) is used to sweep the focus position in the $x$ and $y$ directions simultaneously. The spot size of the signal beam for excitation is $R_{\mathrm {waist}} \sim 3$ $\mu$m. This relatively large spot is likely due to the unoptimized input beam diameter to the objective. TPEF emitted from the brain tissue is collected by the same objective lens and then detected by the EMCCD camera after being reflected by the dichroic mirror. Figure 4(b) shows a test image of TPEF taken for 10 seconds with Rhodamine B solution placed as a sample, where the sweep frequency in the $x$ direction is set to $100$ Hz, whereas the $y$ direction is swept slowly ($1$ Hz). The field of view is about 400 $\mu$m $\times$ 400 $\mu$m.

In order to achieve the TPEF enhancement proportional to $g^{(2)}(0)$, the TPEF emission must not be saturated, i.e., TPEF intensity changes proportional to the square of the excitation light power. To confirm this, we acquired two-photon images as a function of the signal beam power. The left image in Fig. 5(a) shows the typical two-photon image of GFP in brain tissue, with an acquisition time per image of 10 s. In this image, the average power of the irradiated signal beam is about $P$ = $17$ mW, and the corresponding peak intensity is $I_P = P/(\pi (R_{\mathrm {waist}})^2 (\tau _p f)) = 3$ GW/cm$^2$, where $\tau _p$ is the pulse width and $f$ is the pulse repetition rate. The total counts in the region of interest in the acquired image are plotted as a function of signal beam power, as shown in the right graph of Fig. 5(a). The experimental data in red circles are in good agreement with the quadratic function (solid curve). This means that the TPEF emission is not saturated. In Fig. 3(c), the enhancement factor in TPEF by bunching is calibrated using GFP solution. Thus, it is reasonable to consider that the TPEF from GFP in brain tissue is also enhanced by 1.9-fold. A more direct way to demonstrate signal enhancement in TPEF image is to perform the $g^{(2)}$ measurement in Fig. 3 using GFP in brain tissue. However, in that case, the enhancement effect cannot be accurately evaluated because of the severe fading.

 

Fig. 4. Two-photon imaging system using a signal beam. (a) Experimental setup for two-photon imaging. (b) Test image of TPEF from Rhodamine B solution acquired using the imaging system in (a).

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Fig. 5. Observation of GFP in mouse brain tissue using a signal beam. (a) Typical two-photon image (left). The total counts in the region of interest in the acquired image are plotted as a function of signal beam power (right). (b) Three different fields of view.

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Our imaging performed in seconds is comparable to currently used two-photon imaging [41]. As shown in Fig. 5(b), the acquired images shows complex patterns of blood vessels where enhanced GFP proteins are enriched, with high contrast over a wide imaging area. This clearly demonstrates that our OPG source emits enough high power to realize TPEF microscopy imaging of biological samples. To date, this type of TPEF imaging in biology has been performed using commercially available femtosecond lasers, which are very expensive and hard to handle. On the other hand, OPGs have unique advantages, including low cost, wide wavelength tunability, and enhancement by photon bunching demonstrated in this study. The results obtained in this study encourage OPGs to become a new option as a light source for two-photon biological imaging.

Light sources with pulse widths longer than femtoseconds are important in terms of reducing photodamage. In two-photon excitation microscopy with ultrashort laser pulses, the damage caused by instantaneous intensity is sometimes more severe than that caused by mean power. In fact, the typically used mean power of a few tens of milliwatts hardly changes the temperature of the water [42], the main component of living organisms. In other words, depending on the sample, it would be possible to achieve a high signal-to-noise ratio by using lasers with longer pulse widths than femtoseconds. In fact, in Ref. [43], the signal-to-noise ratio is improved by splitting single femtosecond pulse into multiple dense femtosecond pulses. This operation increases the effective pulse width. In addition, the pulse repetition rate is also important parameter. The mode-locked lasers used in typical two-photon microscopes have a repetition rate of about 80 MHz. However, it has been shown that using the excitation laser with a repetition rate lower than the inverse of the metastable state lifetime of the samples can reduce photodamage and increase fluorescence [44]. The above studies indicate that ultrashort pulses with high peak power and high repetition rate are not the only optimal tools for implementing two-photon excitation microscopy. The nanosecond or sub-nanosecond pumped OPGs are the possible choice to reduce the pulse repetition rate and increase the pulse width.

The primary objective of this study is to validate the effectiveness of photon bunching in two-photon microscopy, and thus the experimental setup was designed for this purpose. In the future, it is important to compare the performance with conventional two-photon excitation microscopy by improving the objective lens, detector, and scanning method. Photon bunching demonstrated here is the effect related to the temporal degrees of freedom of light. Therefore, even three-dimensional observation using the OPG light source can, in principle, be expected to achieve the same level of depth resolution as conventional two-photon microscopy systems.

3. Conclusion

In conclusion, we have demonstrated enhanced TPEF from GFP in solution by ultrafast fluctuations in intense pulse using wavelength-tunable OPG and its applicability for biological imaging. The enhancement factor for the TPEF was calibrated by autocorrelation measurements on ultrafast time scales, and was found to be about 1.9 times higher than when coherent light was used. Our experimental results suggest that the effect of bunching is beneficial even with the intense pulses used in nonlinear spectroscopy and imaging. Our study also shows that calibration of $g^{(2)}$ is very important for quantitative evaluation in such applications.