Nanometer scale light penetration depths of halide perovskite (HP) set an intrinsic limit on the performance improvement of optoelectronic devices. Here, we show that two-photon excitation can overcome this limit by markedly increasing the light penetration depth and significantly enhance photon recycling. Through a comparison study between one-photon and two-photon excitations by femtosecond laser pulses in a CsPbBr3 nanosheet, our results demonstrate that two-photon excitation can increase photocarrier transport distance by about 900 nm, which is even comparable to the photocarrier diffusion length. Our work provides substantial insights into the photon recycling of HP induced by nonlinear optical excitations, which can benefit the performance optimization of advanced optoelectronic devices.

Halide perovskite (HP) possesses appealing optoelectronic properties, such as high exciton binding energy,1,2 large optical absorption coefficients,3–5 tunable bandgaps,6,7 long carrier diffusion lengths,8,9 and high defect tolerance.10 Strong light–matter interactions and facile fabrications enable HPs to be an ideal material to construct advanced optoelectronic devices, such as solar cells,11 light-emitting diodes,12 photo-detectors,13 and micro-lasers.14,15 Among these devices, fundamental photocarrier transport properties are important for overall device performance. By optimizing intrinsic material properties and designing rational device structures, the efficiencies of these devices have been significantly improved so far.16,17

Despite these means, nontrivial physical processes of light–matter interactions, such as the photon recycling effect, can further promote device performances.18–21 The photon recycling effect is a dynamical process where photons emitted by luminescent materials are reabsorbed during photon propagation paths, which will keep exciting the luminescent materials and spatiotemporally recycling photons. From the viewpoint of energy transport, photon recycling can not only elongate the lifetime of photocarriers but also increase their transport distance. Both intrinsic performance (such as photocarrier diffusion length) and extrinsic performance (luminescent efficiency) can be boosted by the photon recycling effect, which has attracted a lot of attention in previous studies.22–25 

However, when light with photon energies larger than HP optical bandgaps incidents on a HP device with a thin-film structure, the light energy will be absorbed by the HP through one-photon absorption (OPA). As a consequence, the light fluence will exponentially attenuate as a function of propagation distance, according to the Beer–Lambert law. In this scenario, large optical absorption coefficients of HP point to nanometer scale light penetration depth, which will inevitably limit the photon recycling efficiency and overall device performances. Being different, nonlinear optical excitations, such as two-photon absorption (TPA), are expected to significantly increase the light penetration depth and enhance the photon recycling.26–28 As the nonlinear optical properties of HP have been rapidly advancing,29 two-photon excitations can serve as a promising means to lift up device performances and develop new device functionalities.30–32 Unfortunately, the photon recycling of HP under two-photon excitation has been rarely explored so far.

Here, we comprehensively study the photon recycling effect with a CsPbBr3 perovskite nanosheet under one-photon and two-photon excitations utilizing femtosecond lasers. Through comparison measurements of one-photon luminesce (OPF) and two-photon luminesce (TPF), it turns out that TPA can enhance the lateral photon-recycling distance by about 900 nm. This indicates that photon recycling induced by TPA can significantly increase the effective carrier diffusion length. Our results provide insights into the nonlinear optical photon recycling effect that will benefit the rational design of optoelectronic devices with improved performances and new functionalities.

To reveal the difference in photon recycling induced by OPA and TPA, we designed a scheme of experiments by employing a home-built microscope, as shown in Fig. 1, that can simultaneously measure PL spectra and capture PL microscopic images. A femtosecond laser is tightly focused on the CsPbBr3 nanosheet by an objective lens (OB) with a numerical aperture (NA) of 0.4. Photoluminescence of the CsPbBr3 nanosheet is recollected by the same OB and then sent to a spectrometer and a CMOS camera, respectively. The physical schemes of the photon recycling processes are further depicted by the cartoons in Fig. 1. The bandgap of CsPbBr3 is about 2.38 eV. When a femtosecond laser of 400 nm excites the CsPbBr3 nanosheet, OPF will be induced, as indicated in Fig. 1(a). Emitted photons inside the CsPbBr3 nanosheet will undergo a recycling process of re-absorption and re-emission. Along the lateral direction of femtosecond laser propagation, the interplay between carrier diffusion and photon recycling will increase the photocarrier transport distance. However, along the axial direction, as CsPbBr3 has a large one-photon absorption coefficient of about 0.008 nm−1, the penetration depth of the 400 nm femtosecond laser is only about 125 nm3. As a consequence, most of the bulk region cannot be excited. To completely excite the CsPbBr3 nanosheet along the axial direction, a femtosecond laser of 800 nm can be deployed. As shown in Fig. 1(b), photon recycling is expected to be enhanced. As a benefit, the photocarrier transport distance will be increased. Interestingly, since the femtosecond laser is a Gaussian beam, such enhancement of photon recycling can be observed by measuring the lateral sizes of OPF and TPF microscopic images.

FIG. 1.

Schematic illustration of proposed experimental schemes. Photon recycling dynamics of a perovskite thin-film when excited by 400 nm (a) and 800 nm (b) femtosecond laser pulses. SM: Spectrometer, OB: Objective lens, CMOS: Complementary metal oxide semiconductor camera.

FIG. 1.

Schematic illustration of proposed experimental schemes. Photon recycling dynamics of a perovskite thin-film when excited by 400 nm (a) and 800 nm (b) femtosecond laser pulses. SM: Spectrometer, OB: Objective lens, CMOS: Complementary metal oxide semiconductor camera.

Close modal

Single-crystal CsPbBr3 samples have been fabricated on a glass substrate by a method reported in previous work.4 A CsPbBr3 nanosheet with a lateral size of about 30 × 50 μm2 was selected for experimental measurements. Figure 2(a) shows an optical microscopic image of the nanosheet, the thickness of which has been measured to be about 762 nm by a scanning profiler. We point out that the thickness of the nanosheet is sufficiently larger than the optical penetration depth of a 400 nm femtosecond laser (about 125 nm) and smaller than the spatial coherence length of a femtosecond laser pulse, which will facilitate the effective observation of the photon recycling effect. The optical absorptance and PL spectrum of the nanosheet are presented in Fig. 2(b). The Stokes shift between the optical absorption peak at 510 nm and the PL peak at 535 nm is about 25 nm, which is consistent with previous reports.4 It is clear that the short wavelength part of the PL spectrum overlaps with the optical absorption edge, leading to a predominant photon recycling process. The OPF spectra of the nanosheet measured under different 400 nm femtosecond laser powers are presented in Fig. 2(c). By taking the integral of measured OPF spectra, spectrum intensities as a function of 400 nm femtosecond laser powers are further depicted in Fig. 2(e). The solid green curve is a linear fitting. In a similar fashion, TPF spectra of the nanosheet under various 800 nm femtosecond laser powers are presented in Fig. 2(d). By taking the integral of measured TPF spectra, spectrum intensities as a function of 800 nm femtosecond laser powers are further plotted in Fig. 2(f). Since the TPA is a third-order nonlinear optical process, the spectra intensity of TPF is expected to be proportional to the square of the excitation laser intensity, according to nonlinear optical theory. Hence, a square function has been used to fit the spectra intensities in Fig. 2(f). The fitting curve (solid green line) matches very well with experimental data points, which validates the nature of TPF.

FIG. 2.

(a) Optical microscopic image of the CsPbBr3 nanosheet sample with a scalebar of 10 μm. Thickness is measured to be about 762 nm. (b) PL spectrum (green) and optical absorptance spectrum (black) of the CsPbBr3 nanosheet. (c) OPF spectra of the CsPbBr3 nanosheet as a function of 400 nm excitation power. (d) TPF spectra of the CsPbBr3 nanosheet as a function of 800 nm excitation power. 400 and 800 nm excitation power dependence of (e) OPF and (f) TPF intensity. Solid green curves are fittings.

FIG. 2.

(a) Optical microscopic image of the CsPbBr3 nanosheet sample with a scalebar of 10 μm. Thickness is measured to be about 762 nm. (b) PL spectrum (green) and optical absorptance spectrum (black) of the CsPbBr3 nanosheet. (c) OPF spectra of the CsPbBr3 nanosheet as a function of 400 nm excitation power. (d) TPF spectra of the CsPbBr3 nanosheet as a function of 800 nm excitation power. 400 and 800 nm excitation power dependence of (e) OPF and (f) TPF intensity. Solid green curves are fittings.

Close modal

Simultaneously captured lateral spectra images by the CMOS camera have been presented in Fig. 3. In our measurements, we confirmed that the gray values of the CMOS camera were below saturation. By focusing the 400 nm femtosecond laser on the glass substrate, the microscopic images of the 400 nm femtosecond laser focal spots are illustrated in the upper panel of Fig. 3(a). To capture the microscopic images of OPF from the nanosheet, we laterally moved the 400 nm femtosecond laser focal spot and placed a long-pass filter before the CMOS camera to eliminate the 400 nm components. As shown in the lower panel of Fig. 3(a), the intensity of observed OPF microscopic images increases as the power of the 400 nm femtosecond laser increases from 10 to 20 μW. More importantly, it is clear that the lateral sizes of green spots (OPF) become much larger than those of purple spots (400 nm femtosecond laser) due to the interplay between photocarrier diffusion and photon recycling. For comparison, imaging results for TPF have been presented in Fig. 3(b). To capture the microscopic images of TPF from the nanosheet, we laterally moved the 800 nm femtosecond laser focal spot and placed a short-pass filter before the CMOS camera to eliminate the 800 nm components. As shown in the lower panel of Fig. 3(b), the intensity of observed OPF microscopic images increases as the power of the 800 nm femtosecond laser increases from 5 to 10 mW. It is straightforward to see that the lateral sizes of green spots (TPF) become much larger than those of red spots (800 nm femtosecond laser), arising from the interplay between photocarrier diffusion and photon recycling. Considering that the initial and final states of transition electrons for OPA are exactly the same as those of TPA, and the photocarrier diffusion coefficient of the CsPbBr3 nanosheet is an intrinsic physical parameter of photocarrier diffusion, it can be reasonably expected that enlargements of fluence spots contributed by photocarrier diffusion length are comparable. Hence, it should be emphasized that the spot size differences between OPF and TPF should be caused by the mediated photon recycling of different penetration depths along the axial direction of excitation lasers.

FIG. 3.

(a) Spot images of 400 nm femtosecond laser focused on the glass substrate with powers of 10–20 μW and corresponding OPF spot images as the 400 nm femtosecond laser was focused on the CsPbBr3 nanosheet. (b) Spot images of 800 nm femtosecond laser focused on the glass substrate with powers of 5–10 mW and corresponding TPF spot images as the 800 nm femtosecond laser was focused on the CsPbBr3 nanosheet.

FIG. 3.

(a) Spot images of 400 nm femtosecond laser focused on the glass substrate with powers of 10–20 μW and corresponding OPF spot images as the 400 nm femtosecond laser was focused on the CsPbBr3 nanosheet. (b) Spot images of 800 nm femtosecond laser focused on the glass substrate with powers of 5–10 mW and corresponding TPF spot images as the 800 nm femtosecond laser was focused on the CsPbBr3 nanosheet.

Close modal

Last but not least, we investigate the tailored photon recycling in the CsPbBr3 nanosheet by quantitatively analyzing the spatial distributions of OPF and TPF microscopic images. Two examples of image analysis have been presented in Figs. 4(a) and 4(b). To be specific, Fig. 4(a) is obtained by microscopic images of Fig. 3(a) when the power of the 400 nm femtosecond laser was 10 μW. The pixel size of microscopic images has been calibrated with a standard microlithography plate. A Gaussian function has been utilized to fit the full width at half maximum (FWHM) of 400 nm and corresponding OPF focal spots. The fitted FWHM of the 400 nm femtosecond laser spot is about 1.8 μm, while the fitted FHWM of the corresponding OPF focal spot increases to about 6.0 μm. A similar fitting example for TPF has been given in Fig. 4(b), where the power of an 800 nm femtosecond laser was 5 mW. The fitted FWHM of the 800 nm femtosecond laser spot is about 2.2 μm, while the fitted FHWM of the corresponding TPF focal spot increases to about 8.2 μm. Accordingly, we fitted all microscopic images and fitted FWHM as a function of femtosecond laser power, as plotted in Fig. 4(c). The FWHM of all microscopic images is independent of femtosecond laser power, indicating that excitation laser powers were low enough to avoid the photocarrier saturation effect. Measured FWHM can be well-fitted through linear functions, as shown by the solid lines in Fig. 4(c), which validate the high quality of our experiments. In addition, we can evaluate the additional distance of photon recycling by using two-photon excitation. Effective distances of photocarrier transport along the lateral direction induced by OPA and TPA can be obtained by (FWHMOPF-FWHM400nm)/2 and (FWHMTPF-FWHM800nm)/2, which are plotted by blue and red triangles as a function of femtosecond laser powers in Fig. 4(d). Obviously, the average distances of photocarrier transport induced by TPA (about 3.0 μm) are larger (marked by the magneta arrows) compared to OPA (2.1 μm). Hence, the additional distance contributed by photon recycling through TPA is about 900 nm, which is comparable to the photocarrier diffusion length in HPs.8,9 These results suggest that two-photon excitations can significantly enhance the photon recycling effect in HPs and robustly increase the effective photocarrier transport distance. For optoelectronic devices constructed by HPs, our results can provide important insights to lift up the device’s performance through two-photon excitations. For example, the optical gain of light-pumped HP micro-lasers is expected to increase if using two-photon excitation. The light energy conversion efficiency of HP tandem solar cells can be improved by increased gain layer thickness enabled by two-photon excitation.

FIG. 4.

(a) Spatial distribution of 400 nm femtosecond laser spot (blue) and OPF spot (green) when the 400 nm femtosecond laser power was fixed at 10 μW. (b) Spatial distribution of the 800 nm femtosecond laser spot (red) and TPF spot (green) when the 800 nm femtosecond laser power was fixed at 5 mW. (c) Spot FWHM of the 400 nm/800 nm femtosecond laser and OPF/TPF as a function of excitation power. (d) Photocarrier transport distances of photon cycling for one-photon (blue) and two-photon (red) excitations.

FIG. 4.

(a) Spatial distribution of 400 nm femtosecond laser spot (blue) and OPF spot (green) when the 400 nm femtosecond laser power was fixed at 10 μW. (b) Spatial distribution of the 800 nm femtosecond laser spot (red) and TPF spot (green) when the 800 nm femtosecond laser power was fixed at 5 mW. (c) Spot FWHM of the 400 nm/800 nm femtosecond laser and OPF/TPF as a function of excitation power. (d) Photocarrier transport distances of photon cycling for one-photon (blue) and two-photon (red) excitations.

Close modal

In conclusion, we have performed a comparison study between one-photon and two-photon excitations with femtosecond laser pulses by experimentally measuring the spectra and spatial distributions of OPF and TPF. Our results demonstrate that two-photon excitations of a CsPbBr3 nanosheet markedly enhance the photon recycling effect, which can not only improve the lighting efficiency but also significantly increase the effective distance of photocarrier transport. Excitingly, TPA enhanced photon recycling leads to an increased photocarrier transport distance of about 900 nm, which is comparable to photocarrier diffusion length in HPs. Our work provides substantial insights into the photon recycling of HP induced by nonlinear optical excitations, which can benefit the design and construction of optoelectronic devices with improved performances.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61904082, 61704024, 61875089, and 62175114), the Natural Science Foundation of Jiangsu Province (Grant No. BK20190765), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 19KJB510039), and the Startup Foundation for Introducing Talent of NUIST (Grant No. 2018r042). The authors thank Dr. Yizhi Zhu for providing the CsPbBr3 sample.

The authors have no conflicts to disclose.

Yuanyuan Li: Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Project administration (lead); Supervision (equal); Writing – review & editing (equal). Jiaxin Xie: Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Yu Sun: Software (supporting); Validation (supporting). He Zhang: Resources (supporting); Software (supporting); Validation (supporting). Chuansheng Xia: Resources (supporting); Software (supporting); Validation (supporting). Min Wang: Software (supporting); Validation (supporting). Tianjie Wang: Software (supporting); Validation (supporting). Jianhua Chang: Project administration (supporting); Validation (supporting). Qiannan Cui: Conceptualization (lead); Formal analysis (lead); Funding acquisition (equal); Project administration (equal); Supervision (lead); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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