Abstract

Photoelectronic performance of organic–inorganic hybrid perovskites has been investigated extensively. Advancement in optoelectronic characterization and application of this group of materials in solar cells, light-emitting diodes, and lasers has been pushed forward rapidly. However, nonlinear optical properties for applications in optical logic devices have not been exploited. Moreover, long-lived excitons and charges limit the response speed of such materials and further construction of ultrafast devices. In this work, we make use of the high third-order optical nonlinearity of $({{\rm CH}_3}{{\rm NH}_3}){{\rm PbBr}_3}$ single crystals and develop a femtosecond optical switch (OS) based on strong two-photon processes through absorbing one pump and one probe photon. The fascinating band structure, with a steep edge at 2.22 eV between the transmission and strong absorption bands, endows single crystals of $({{\rm CH}_3}{{\rm NH}_3}){{\rm PbBr}_3}$ with perfect characteristics for two-photon optical switching in the near infrared. An on–off ratio of the probe pulses of about 90% and a speed faster than 400 fs have been achieved for this OS device. To the best of our knowledge, such high efficiency has not been realized for an ultrafast OS with any other materials and devices. Moreover, this is a first exploration, to our best knowledge, of the third-order optical nonlinearity of organic–inorganic hybrid halide perovskites for application in ultrafast optical logic devices with high reliability and low threshold in the near infrared.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Organic–inorganic hybrid perovskite materials have evolved as excellent candidates for solar cells [15], light-emitting diodes [610], and lasing devices [1115] and attracted research interests in their physichemical, photophysical, and optoelectronic performances [16]. High-efficiency solar cells are the most fascinating applications of this group of materials, where a power conversion efficiency larger than 20% has been reported extensively [1719]. Studies on the interplay between excitons and charges are the most important part of the research work on the photoelectronics in hybrid halide perovskites [2023], which lay the fundamentals for the development of optoelectronic devices. In particular, ultrafast spectroscopy [24] is an effective tool for investigating electronic dynamics to reveal mechanisms for the generation and transport of charge carriers [2527].

Although optoelectronic performance of hybrid halide perovskites has been deeply investigated, optical nonlinear properties of these materials, in particular, their third-order optical nonlinearities [28,29], have not been exploited for optical logic devices so far. Enhancement of ${n_2}$ was studied in two-dimensional organic–inorganic lead iodide perovskites [30] and strong two-photon absorption was observed in Mn-doped ${{\rm CsPbCl}_3}$ perovskite nanocrystals [31]. Two-photon excitation induced lasing [32] and amplified spontaneous emission [33] have been studied in perovskite microcubes and nanocrystals, respectively.

Single crystals [3436] of this category of materials possess multifold advantages as compared with their thin-film and micro-/nano-crystalline counterparts, which may include low trap-state densities, long diffusion length of charge carriers, and high-quality molecular arrangement over a large thickness due to the long-range ordering of the lattices. Apparently, high-quality single crystals may facilitate efficient nonlinear optical interactions with long effective lengths. In this work, we report discoveries of efficient two-photon absorption processes in $({{\rm CH}_3}{{\rm NH}_3}){{\rm PbBr}_3}$ ($\rm MAPbBr_{3}$) single crystals and exploration of a two-photon optical switch with ultrafast speeds and high on–off ratios. Such functionalization of this kind of perovskite single crystals is based on the steep band edge at about 2.2 eV, which provides a perfect channel for two-photon absorption processes in the near infrared.

2. METHODS

A. Synthesis of (${{\rm CH}_3}{{\rm NH}_3}$) ${{\rm PbBr}_3}$ Single Crystals

The synthesis of ${{\rm MAPbBr}_3}$ single crystals is based on a modified inverse temperature crystallization method similar to a previous report [36]. The crystal growth begins with the ${{\rm MAPbBr}_3}$ powders, which are prepared by reacting methylamine (${{\rm CH}_3}{{\rm NH}_2}$, 40 wt.% in water, AR), lead (II) acetate trihydrate (${\rm Pb}{({\rm Ac})_2}\cdot{{\rm 3H}_2}{\rm O}$, AR) with a molar ratio of about 1.1 : 1 and a slight surplus of ${{\rm CH}_3}{{\rm NH}_2}$ to avoid the production of lead (II) bromide in the concentric hydrobromic acid (HBr, 40 wt.% in water, AR). The ${{\rm MAPbBr}_3}$ powders are then dissolved in ${\rm N},{\rm N}$-dimethylformamide (DMF, ${\ge} {99.9}\%$, Aladdin) to obtain precursor solutions (0.375 g/mL). The solution is filtered using a polytetrafluoroethylene filter with 0.2 µm pore size (Whatman), stabilized with appropriate reagents, and placed on a hot plate preheated to 90°C for crystallization. At the finish of the growth, the single crystal is taken out of the solution with care, washed with antisolvent, wiped with laboratory tissues, and stored in a glove box filled with Ar.

B. Spectroscopic Measurements

The steady-state absorption spectrum is measured by an Agilent 8253 UV-Vis spectrometer. A combined light source of a deuterium and a halogen lamp supplies broadband illumination. The absorption spectrum can be measured in the spectral range from 190 to 1000 nm.

For ultrafast spectroscopy, a Ti:sapphire amplifier supplies femtosecond pulses with a center wavelength of 800 nm, pulse length of about 150 fs, repetition rate of 1 kHz, and pulse energy of 1 mJ, which are sent to a commercialized transient absorption (TA) spectroscopic system. This system has been described in our previous reports on ultrafast photophysical investigations on metal oxides [24]. A portion of the 800-nm pulses is focused into a cuvette containing heavy water with a thickness of 3 mm to produce a supercontinuum spectrum extending from about 340 to 1200 nm, which is used as the probe in the TA measurement. The rest of the 800-nm pulses are used as the pump with variable pump fluence. The pump beam is focused by a curved mirror with metal coating into the sample with a diameter of about 4 mm, whereas the probe beam is also reflectively focused by a metal-coated concave mirror into a spot with a diameter smaller than 300 µm on the sample in the center of the pump spot. The delay of the pump pulses with respect to the probe is adjusted by a linear translation stage with a resolution of 1 fs and a range of more than 1 ns. The three-dimensional TA data are acquired by $\Delta {\rm A}$ as a function of wavelength and time delay, so that broadband TA spectra with dynamics at each resolved wavelength are measured simultaneously at one scan over the delay line.

3. RESULTS AND DISCUSSION

A. Principles and Design of 2PA Optical Switching

Figure 1 shows the design of the femtosecond optical switch (OS) system using a ${{\rm MAPbBr}_3}$ single crystal. Figure 1(a) depicts the experimental setup for femtosecond pump–probe measurement. The output from a Ti:sapphire laser amplifier supplied pump pulses at 800 nm (1.55 eV) with a pulse length of about 150 fs and a repetition rate of 1 kHz. The maximum pulse energy was 1 mJ; however, we used only a small portion (1–20 µJ) as the pump for the OS experiments. Another portion of the 1.55-eV pulses was focused into a 3-mm-thick cuvette of heavy water to produce supercontinuum pulses extending from about 340 to 1200 nm, which were employed as the probe. The efficiency of the OS effect is dependent on the strength of the 2PA process. Fig. S1 shows the two-photon absorption behavior of the ${{\rm MAPbBr}_3}$ single crystal, which is plotted by the absorption ratio in percentage as a function of the pump pulse energy and exhibits a three-stage variation. In stage 1, the 2PA process is still weak, so that reflection and scattering of light dominates the “absorption” curve. A threshold effect can be observed with stage 2, and a much larger slope of the variation implies dominant 2PA processes, which start at a threshold pulse energy of about 300 nJ, corresponding to a pump fluence of about ${2.4}\;\unicode{x00B5} {{\rm J/cm}^2}$, as for the pump beam having a diameter of about 4 mm. The saturation effect appears in stage 3. Thus, we can estimate a 2PA cross-section of roughly ${\sigma _2} = {3.63} \times {{10}^{3\:}}{\rm GM}$ (${1}\;{\rm GM} = {{10}^{- 50}}\;{{\rm cm}^4}{\rm \cdot {\rm s}}/{\rm photon}$) at 800 nm for the femtosecond laser pulses employed in the experiments. Although this cross-section value is smaller than that reported for microcrystals [37], it is larger than that reported for single crystal ${{\rm MAPbBr}_3}$ [38,39]. Such a large 2PA cross-section supports the high-efficiency ultrafast optical switch in this work.

 figure: Fig. 1.

Fig. 1. (a) Pump–probe scheme for the optical switching process. 150-fs pump pulses at ${E_P} = {1.55}\;{\rm eV}$ have a pulse energy as low as 1 µJ. Supercontinuum pulses with a photon energy ${E_D}$ sent to overlap the pump inside the single crystal have a total pulse energy of less than 1 nJ. The output of the probe pulses was switched on and off with a modulation depth as large as 90%. Inset: photograph of the $({{\rm CH}_3}{{\rm NH}_3}){{\rm PbBr}_3}$ single crystal with a thickness of about 1 mm. (b) Absorption spectrum of the single crystal characterized by optical extinction (ABS) in optical density (OD) as a function of photon energy (E). (c) Energy level diagram explaining the two-photon absorption optical switching (2PA OS) mechanisms. The 2PA-OS process is highlighted by a yellow-filled triangle. (d) Simplified illustration of the optical switching process through 2PA of one pump and one probe photon (${h}{\nu _{{\rm pump}}} + { h}{\nu _{{\rm probe}}}$), resulting in nearly no transmission of the probe photon during the overlap between the pump and probe pulses.

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A photograph of a ${{\rm MAPbBr}_3}$ single crystal is included in Fig. 1(a) in the right-bottom corner, which has a dimension of roughly ${5.5} \times {5.5} \times {1}\;{{\rm mm}^3}$ and exhibits excellent homogeneity. Therefore, the OS process was achieved for an interaction length of about 1 mm in the single crystal between the pump and probe pulses. Figure 1(b) shows the steady-state absorption spectrum of the single crystal having a thickness of about 1 mm. Strong absorption with an optical extinction larger than 2.5 OD (optical density) or a transmission reduction of more than 99.7% can be observed for photon energies larger than 2.22 eV, which implies nearly total absorption of the incident light. However, nearly total transmission is observed for photon energies smaller than 2.16 eV, implying a steep rising edge of the absorption spectrum at about 2.2 eV. Thus, the single crystal has nearly no single-photon absorption (1PA) of pump pulses at 1.55 eV, whereas strong 2PA can be achieved for probe photon energies larger than 0.67 eV through absorbing one pump and one probe photon with $h{\nu _{{\rm pump}}} + h{\nu _{{\rm probe}}} \,{\gt} {2.22}\;{\rm eV}$. This is a perfect scheme for 2PA OS and lays the basis for the OS design in this work.

Figure 1(c) shows an energy-level diagram of the single crystal, which is aligned with the 1PA spectrum in Fig. 1(b). The ground-state molecules at ${E_1}$ with a density of states of ${N_1}$ are excited by absorbing two pump photons (${1.55}\;{\rm eV} \times {2}$) to the excitation bands, where ${h}{\nu _{{\rm pump}}}\; \lt \;{E_2} - {E_1}\; \lt \;{2} \times {h}{\nu _{{\rm pump}}}$, populating the lower edge of the excitation band at ${E_2}$ and resulting in a population density of ${N_2}$. Transitions from ${E_2}$ to ${E_1}$ induced photoluminescence (PL) in the green, as shown in Fig. S2. Interestingly, single- and two-photon excitation at 400 and 800 nm, respectively, induced much different PL spectra, which are centered at 544 and 562 nm, respectively. The corresponding spectral bandwidth at FWHM is about ${25}\sim{26}\;{\rm nm}$ for both spectra. Although the re-absorption process through 2PA may partially explain such observations, our experimental results show further that even with excitation by continuous-wave (CW) lasers at 405 and 473 nm, the variation of the PL spectrum with excitation wavelength can still be observed, as shown in the newly modified Fig. S2. Apparently, the two-photon-excitation induced re-absorption cannot be the only responsible physics. Some more important mechanisms need to be disclosed, which requires more extensive investigations. Excitons populated on ${E_2}$ may be further excited by the pump pulses to higher-lying states, bleaching the exciton absorption or dissociating into charges [40,41]. Long-lived excitons and charges are responsible for the slow process of the TA dynamics, as described in Fig. 2.

 figure: Fig. 2.

Fig. 2. (a) TA spectra measured at delays of 0, 0.4, 0.55, 1.2, 1.75, 4.5, and 10 ps. Inset: TA dynamics at 787.2 and 815.4 nm. (b) TA dynamics at 800-nm pump and 815.4-nm probe with a pump fluence of ${55}\;\unicode{x00B5} {{\rm J/cm}^2}$. Inset: more detailed view of the optical switching signal, showing an on–off ratio of 933 mOD or 89% modulation on transmission rate and a speed faster than 400 fs at FWHM.

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The high density of states on the excitation band with a large bandwidth results in extremely strong 2PA from ${E_1}$ to ${E_2}$ or ${E_m}$ through ${h}{\nu _{{\rm pump}}} + {h}{\nu _{{\rm probe}}}$, as shown in Fig. 1(c) and highlighted by a yellow triangle, where ${h}{\nu _{{\rm probe}}}$ may extend in a broad spectral range above 0.67 eV. Figure 1(d) presents a simplified illustration of the OS process, where a probe pulse is incident into the single crystal and interacts with the “waiting” pump pulse; they work together to accomplish the 2PA process. As a result, the majority of the probe pulse energy is absorbed, and a very small portion may pass through the single crystal, which can be taken as a logic process of signal “off.” Since the 2PA process takes place only within the overlap between the femtosecond pump and probe pulses, it leads to an OS process as fast as the cross-correlation of the interaction pulses.

B. Two-Photon Optical Switching with an ${\sim}{90}\%$ On–Off Ratio

1. High-Efficiency High-Contrast Optical Switching

Femtosecond TA spectroscopy was employed to investigate the OS performance of the ${{\rm MAPbBr}_3}$ single crystal, as described in Section 2. The pump beam was sent via a delay line to the single-crystal sample, where a curved mirror was used to control the spot size of the pump on the sample surface. In all of the measurements in this work, the pump beam has a diameter of about 4 mm on the front surface of the sample. An attenuator before the sample was used to adjust the pump fluence. The probe beam was focused by a curved mirror into a spot of about 300 µm in diameter on the surface of the single-crystal sample, which overlapped with the center area of the pump spot.

Figure 2(a) presents TA spectra at different delays. Strong TA signals can be observed in the spectral range from 750 to 850 nm, which last for only a few hundreds of femtoseconds. The pump pulses destroyed the completeness of the TA spectrum at the center wavelength of 800 nm, producing two peaks at about 790 and 820 nm. This can be understood by considering the mechanisms as follows. The fundamental spectrum at 800 nm is still the strongest component in the supercontinuum. To ensure sufficient intensity at other spectral positions, the intensity at 800 nm has to be saturated, which results in strong nonlinear modulation on the TA spectrum, explaining the doublet structure in the TA spectrum. Meanwhile, the probe and pump have the same spectrum and same polarization at about 800 nm, and interference between them may also modulate strongly the corresponding TA spectrum. These mechanisms also explain the variation of the doublet TA spectrum at a time delay of 1.2 ps, as shown in Fig. 2(a) by the blue curve, as highlighted by a yellow triangle.

Furthermore, it is understandable that the strength of 2PA also depends on the intensity of the probe pulses; therefore, the TA spectra in Fig. 2(a) are also dependent on the spectrum of the supercontinuum generation, as shown in Fig. S3. The doublet structure with two peaks in the supercontinuum spectrum basically agree with that in the TA. Due to the low resolution of the spectrometers, the peak shifts slightly at different delays. The TA spectrum remains nearly constant after a delay longer than 1 ps, as shown in Fig. 2(a), implying long-lived exciton absorption. The inset in Fig. 2(a) shows TA dynamics at two spectral peaks of 787.2 and 815.4 nm. Clearly, the dynamics at both wavelengths evolve into two stages: a fast process with extremely strong TA and a slow one as a weak tail of the whole dynamics curve. The fast one results from a 2PA process through absorbing one pump and one probe photon [24,42], which is equivalent to a cross-correlation between the pump and probe pulses. This cross-correlation performance can be roughly verified by the experimental result in Fig. S4, where a pump–probe measurement was carried out on a piece of quartz. Since no excitonic excitations and transitions may take place in quartz when pumped at 800 nm, the ultrafast process is basically the cross-correlation between the pump and probe pulses. The full width at half maximum is about 220 fs for this dynamic curve, implying a pulse length of 150–160 fs. This also indicates nearly transform-limited pump and probe pulses. The slow dynamics in Fig. 2(a) result from absorption by the excitons, which supplies a precise measurement on the lifetime of the excitons. Obviously, the fast TA dynamics can be used as OS of the probe pulses, which is the key mechanism of this work.

Figure 2(b) supplies a more detailed analysis of the TA dynamics at about 1.52 eV (815.4 nm), where a most efficient OS process is observed. A very fast OS signal and a slow-decay dynamics constitute the whole OS process. However, the slow process is negligibly small and can be nearly leveled with the background. A pump pulse energy of 7 µJ, corresponding to a pump fluence of ${55}\;\unicode{x00B5}{{\rm J/cm}^2}$, was employed in the excitation, and a peak amplitude of 933 mOD was achieved, corresponding to a modulation of about 89% on the transmission and implying that nearly 90% of the probe pulse energy was absorbed through a two-photon process. The switching process finishes the on–off operation within 400 fs at FWHM with a high contrast of ${993}:{55\approx 18}:{1}$. The roughly symmetric shape of the switching signal confirms a cross-correlation-like interaction between the pump and probe pulses in the 2PA process, agreeing well with our proposed mechanism for such an ultrafast OS device. Such a high efficiency has not yet been reported for a femtosecond OS device. The slow process has a lifetime of more than 100 ps, corresponding to the exciton absorption dynamics as mentioned above.

 figure: Fig. 3.

Fig. 3. (a) TA dynamics at 815.4 nm (1.52 eV) at different pump fluences. (b) Pump fluence dependence of the fast TA process at a delay of 400 fs [highlighted by a red triangle in (a)]. (c) Pump fluence dependence of the slow TA process at a delay of 600 ps [blue triangle in (a)].

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2. Pump-Fluence-Dependent OS Performance

Figure 3 shows the TA dynamics at 787.2 nm or 1.57 eV for varied pump fluences. With increasing the pump fluence, the OS signal increases dramatically and exhibits different fast and slow dynamic stages, as shown in Fig. 3(a). Figures 3(b) and 3(c) show the variation of the measured TA values at $\tau = {400}\;{\rm fs}$ [red triangle in Fig. 3(a)] and $\tau = {600}\;{\rm ps}$ [blue triangle in Fig. 3(a)], respectively, with the increase in pump fluence, corresponding to the fast and slow TA processes. To understand the involved photoelectronic processes, we need to model the pump–probe dynamics using rate equations. According to the energy-level diagram in Fig. 1(c), we formulate the following differential equations:

$$\frac{{d{N_2}}}{{dt}} = {\sigma _2}{N_1}I_P^2 - \frac{{{N_2}}}{{{\tau _2}}} - {\sigma _E}{N_2}{I_P} + \frac{{{N_m}}}{{{\tau _m}}},$$
$$\frac{{d{N_1}}}{{dt}} = - {\sigma _2}{N_1}I_P^2 + \frac{{{N_2}}}{{{\tau _2}}},$$
$$\frac{{d{N_m}}}{{dt}} = {\sigma _E}{N_2}{I_P} - \frac{{{N_m}}}{{{\tau _m}}},$$
$${N_0} = {N_1} + {N_2} + {N_m},$$
where ${N_1}$, ${N_2}$, and ${N_m}$ are the population density on energy levels of ${E_1}$, ${E_2}$, and ${E_m}$, respectively; ${\tau _2}$ and ${\tau _m}$ are the exciton lifetimes on ${E_2}$ and ${E_m}$, respectively; ${\sigma _1}$ and ${\sigma _2}$ are, respectively, the single- and two-photon absorption cross-sections for the ground-state molecules on ${E_1}$; ${\sigma _E}$ is the excitonic absorption cross-section on ${E_2}$; ${N_0}$ is the total molecular density; ${I_P}$ is the intensity of the pump pulses. Assuming that ${\tau _m}$ is so short that the population on ${E_m}$ transits immediately back to ${E_2}$, we have roughly ${N_m} = 0$. Furthermore, it is reasonable to assume square pulses for both the pump and probe with ${I_P}(t) = {I_P}$ for ${0} \le t \le {\tau _P}$ and ${I_P}(t) = 0$ for $t\; \lt \;0$ and $t \gt {\tau _P}$. Additionally, the experimental results indicate ${\tau _2} \gg {\tau _P}$ and ${\tau _2} \gg {\tau _m}$. We can understand that the pump and probe pulses have an overlap for a time duration of ${2}{\tau_{P}}$ for square pulses.

Solving Eqs. (1)–(4) for ${0} \le \;{t}\; \le {2}{\tau _{P}}$, we obtain

$${N_2}(t ) = \frac{B}{A}\left({1 - {e^{- At}}} \right),$$
with ${ A} = {{\sigma}_2}I_P^2 + \frac{1}{{{\tau _2}}}$ and ${B} = {{\sigma}_2}{N_0}I_P^2$, and
$${N_1}(t ) = {N_0} - {N_2}(t ).$$

However, charge generation is an efficient process for such single crystals, where excitons dissociate efficiently into charges through further excitation by the pump pulses. Therefore, the expression for ${N_2}(t)$ has to be modified as

$${N_2}(t ) \approx \frac{B}{A}\left({1 - {e^{- At}}} \right)\left({1 - \alpha {\sigma _E}{I_P}} \right) \approx {{\sigma}_2}{N_0}I_P^2t\!\left({1 - \alpha {\sigma _E}{I_P}} \right),$$
where $\alpha$ is the dissociation ratio of the excitons after further excitation by the pump pulse. Without such a modification, neither of the pump-fluence dependence performances in Figs. 3(b) and 3(c) can be fitted using the solutions to the rate equations. This verifies convincingly the existence of efficient charge separation through the sequential processes of two-photon excitation of the ground-state molecules and further excitation of the excitons by the pump pulses.

Thus, ${N_1}(t)$ can be rewritten as

$${N_1}(t ) = {N_0}(1 - {\sigma _2}I_P^2t + \alpha {\sigma _2}{\sigma _E}I_P^3t).$$

Considering that the fast dynamics indicated by the downward red triangle in Fig. 2 are mainly a 2PA process through absorbing one pump and one probe photon during the temporal overlap between them, the corresponding TA is depicted by

$$\Delta{{A}_f} \propto {{\sigma}_2}{N_1}(t ){I_P}{I_d} = {\sigma _2}{N_0}(1 - {\sigma _2}I_P^2t + \alpha {\sigma _2}{\sigma _E}I_P^3t){I_P}{I_d}.$$

If we assume that the peak of $\Delta {A_f}$ appears at a time delay of ${\tau _f}$ with ${0} \le {\tau _f}\; \le {2}{\tau _{\:P}}$, the peak TA value can be expressed as

$$\Delta {A_f} \propto {\sigma _2}{N_0}{I_d}{I_P} - \sigma _2^2{N_0}{\tau _f}{I_d}I_P^3 + \alpha \sigma _2^2{\sigma _E}{N_0}{\tau _f}{I_d}I_P^4,$$
which is a fourth-order polynomial of ${I_P}$ without terms of $I_P^2$ and can be used to fit the measurement data in Fig. 3(b). A perfect agreement in the fitting using a function of ${y} = {{A}_0} + {B_1}x - {B_2}{x^3} + {B_3}{x^4}$, with ${A_0}$, ${B_1}$, ${B_2}$, and ${B_3}$ defined as positive values, as shown by the red curve in Fig. 3(b), implies correct revealing of the photophysical mechanisms.

The slow process for ${ t}\; \gt \;{2}{\tau _P}$ can be attributed mainly to the exciton absorption, where the pump pulse does not take any effect or we have ${I_P} = {0}$. Solving Eqs. (1)–(4) for ${t}\; \gt \;{2}{\tau _P}$, we obtain

$$\begin{split}{N_2}(t ) &\approx {N_2}\!\left({2{\tau _P}} \right){e^{- \frac{t}{{{\tau _2}}}}} \\[-3pt] &\approx 2{{\sigma}_2}{N_0}I_P^2{\tau _P}\!\left({1 - \alpha {\sigma _E}{I_P}} \right){e^{- \frac{t}{{{\tau _2}}}}} \\[-3pt] &= 2\!\left({{{\sigma}_2}{N_0}{\tau _P}I_P^2 - \alpha {{\sigma}_2}{\sigma _E}{N_0}{\tau _P}I_P^3} \right){e^{- \frac{t}{{{\tau _2}}}}}.\end{split}$$

Therefore, the slow TA dynamics at a specific time delay of $\Delta \tau \gg {2}{\tau _{P}}$ can be evaluated by

$$\begin{split}&\Delta{A_s}\!\left({\Delta\tau} \right) \propto {\sigma _E}{N_2}\!\left({\Delta\tau} \right){I_d}\\& \approx 2\!\left({{{\sigma}_2}{\sigma _E}{N_0}{\tau _P}{I_d}I_P^2 - \alpha {{\sigma}_2}\sigma _E^2{N_0}{\tau _P}{I_d}I_P^3} \right){e^{- \frac{{\Delta\tau}}{{{\tau _2}}}}},\end{split}$$
which is a third-order polynomial without the first-order term. Fitting the measurement data in Fig. 3(c) using a function of ${y} = {{A}_0} + {B_1}{x^2} - {B_2}{x^3}$, we also achieve perfect agreement, implying precise determination of the photophysical mechanisms.

It needs to be noted that the charge separation term with ${\sigma _E}$ is indispensable for both fittings in Figs. 3(b) and 3(c), which can be taken not only as an indication of efficient charge generation through sequential excitation by femtosecond laser pulses, but also as a possibly precise evaluation on the charge generation efficiency. More specifically, the value of α may be determined with resolved ${\sigma _E}$ and ${\sigma _2}$ through data fitting by our concise modeling in Eqs. (1)–(12). This needs more detailed investigations on the two-photon band structures but is out of the scope of this work.

According to Eq. (12), we have

$$\partial\Delta{A_s}\!\left({\Delta\tau} \right)/\partial{I_P} \propto 2{\sigma _2}{\sigma _E}{N_0}{\tau _P}{I_d}{I_P}\!\left({1 - 1.5\alpha {\sigma _E}{I_P}} \right)\!.$$

Clearly, if the value of $1.5\alpha {\sigma _E}{I_P}$ is smaller than one, we have $\partial{A_s}/\partial{I_P}\gt 0$, which is reasonable and is always satisfied for our employed pump intensity, since ${\sigma _E}{I_P}$ is an extremely small value, compared with one. Therefore, the amplitude of the TA dynamics of the slow process increases quickly with the pump intensity. As shown in Figs. 3(b) and 3(c), the increasing rate of $\Delta {{A}_s}$ is larger than that of $\Delta {{A}\!{_f}}$; therefore, the contrast of the OS signal is reduced with increasing the pump fluence. Thus, a lower pump pulse energy is preferred for achieving a high signal contrast. In the measurement result in Fig. S5, we employ a pump pulse energy of only 1 µJ, and the TA dynamics with a probe pulse at 815.4 nm (1.52 eV) show a signal contrast larger than 52:1, which is much larger than that measured using a pump pulse energy of 7 µJ [Fig. 2(b)]. Even at such a low pump pulse energy, the amplitude of the OS signal can reach 438.3 mOD, corresponding to an on–off ratio of about 64%, which is already much higher than that required for practical applications in optical logic circuits. This also implies that pulse energies on the order of nanojoules will be high enough to achieve efficient operation of such an optical switch.

In fact, for the 2PA process, the probe intensity also contributes to the OS signals. This can be understood by the definition in Eq. (9) and by a comparison between the TA spectra in Fig. 2(a) and the supercontinuum spectrum in Fig. S3. An OS signal was measured at 1032 nm, as shown in Fig. S6, where the supercontinuum spectrum has extremely low intensity; the amplitude of the OS signal was reduced to only 2.7 mOD. Nevertheless, a clear 2PA OS signal with a speed of about 400 fs can still be observed with excellent contrast. This not only verifies the dependence of OS signals on the probe intensity, but also confirms the 2PA nature of the OS process through absorbing one pump (800 nm, 1.55 eV) and one probe photon (e.g. 1032 nm, 1.20 eV).

Furthermore, the single crystal employed in this research exhibits high stability and a high damage threshold. During the whole investigation, we did not notice any degradation in either the material or the nonlinear optical performance. The OS device worked with a constant performance and repeatable properties for all of the experiments. Furthermore, even with a 1-mm thickness, we did not observe a large chirp in the OS signals, which ensures a femtosecond on–off speed. Additionally, since the OS signal is in fact a cross-correlation between the pump and probe pulses, it overcomes the slow excitonic response in the materials, and the speed of the OS device is dependent solely on the pulse length. Thus, if we reduce the pulse length further, we can reach an even much higher switching speed with this OS device.

C. Responsible Mechanisms for the Contrast of OS Signals

High-contrast signals are important for the reliability and practical application of OS devices. It is clearly understandable that high-contrast femtosecond OS signals require strong ultrafast 2PA dynamics and the subsequent weak exciton absorption process. Mechanisms based on different photoelectronic processes and different optical designs need to be understood to optimize the signal contrast.

1. Polarization Dependence

Figure 4(a) shows the measurements on the TA dynamics at a probe photon at 815.4 nm in different configurations of the polarization directions of the pump and probe pulses, as well as the orientations of the single crystal. A pump fluence of about ${31.9}\;\unicode{x00B5}{{\rm J/cm}^2}$ is used in this group of measurement results. Clearly, the OS process has little dependence on the orientation of the single crystal; however, it depends strongly on the polarization relationship between the pump and probe pulses. Strong OS signals can be observed only when the pump and probe pulses are polarized in the same direction, where a signal intensity ratio of 4.8 can be resolved, as highlighted for the fast TA dynamics in Fig. 4(a). The 2PA process requires identical polarizations of the two absorbed photons, which can be taken as a selection rule for the two-photon absorption by the employed single crystals. The third-order nonlinearity based on dipolar transitions from the ground to two-photon energy levels facilitates the most efficient 2PA process for the same polarizations of the involved photons.

 figure: Fig. 4.

Fig. 4. (a) TA dynamics at a probe wavelength of 815.4 nm (photon energy of 1.52 eV) measured with different configurations of polarization directions of the pump and probe pulses, and orientation of the ${{\rm MAPbBr}_3}$ single crystal: “$//$” pump polarized parallel to the probe, “$\bot$” pump perpendicular to the probe, “${\rm V}$” crystal oriented vertically, “${\rm H}$” crystal oriented horizontally. (b) TA spectra measured at a time delay of 10 ps for a pump wavelength of 400 (red) and 800 nm (green), corresponding to single- and two-photon pumps, respectively. The dark area (red${+}$green) corresponds to the overlap between the two spectra. Blue arrows indicate the discrepancy on the band edges. Black and red triangles indicate probe wavelengths at 787.2 and 815.4 nm, respectively. (c) Comparison between single- (400 nm, open circles) and two-photon (800 nm, solid lines) pumped TA dynamics at probe wavelengths of 787.2 (black) and 815.4 nm (red) for a time delay larger than 10 ps, implying pure exciton absorption processes. Insets: evaluation on the decay dynamics in different time ranges for resolving the lifetimes of the involved exciton-absorption processes.

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The optical switch performance has little dependence on the orientation of the single crystal, which can be observed as a small difference between the fast TA dynamics, as designated by ${\delta}$ in Fig. 4(a). Such influences by the crystal orientation can be observed more clearly for the slow process, as shown in Fig. S7, where all the TA dynamic curves in Fig. 4(a) are normalized and only the slow process is displayed. The two-photon excitation at 800 nm (1.55 eV) produces more excitons or induces more efficient exciton generation at the horizontal orientation (${\rm H}$) than at the vertical (${\rm V}$), as highlighted in Fig. S7, explaining the difference defined by $\Delta$ in Fig. S7. The larger difference (${4}\Delta$) between ${\rm H}$ and ${\rm V}$ orientations for the orthogonally polarized pump and probe pulses than for the parallel is due to the rescaling during the normalization operation. However, we did not find any anisotropy between the lattice constants in the plane of the optical window, where we measured a lattice constant of 0.59335 nm at room temperature for our synthesized single crystal, as confirmed by the x-ray diffraction spectrum in Fig. S8. The weak polarization dependence of the 2PA performance of ${\rm MAPbBr3}$ was also investigated and confirmed in [39]. Therefore, we have to attribute the small difference in the slow TA dynamics to the possible orientation-dependent defects on the surface of or inside the crystal, which might come into the interaction area as the crystal is rotated. This did not have much effect on the contrast of the OS signals.

2. Two-Photon Excitons Favoring High-Contrast OS Signals

The unique feature of the two-photon pumped excitonic processes, as compared with single-photon pumping, endows the single crystals with extremely strong two-photon absorption and extremely weak exciton absorption, which favors the enhancement of the contrast of the two-photon OS signals. Figure 4(b) compares the measurements of single- (light green) and two-photon (light red) pumped TA spectra at a time delay of 10 ps, implying pure exciton absorption processes. The dark-color area shows the overlap of the two spectra. These two spectra basically reflect the density of states of the 1PA and 2PA bands.

For single-photon pumping at 400 nm, we include only the exciton absorption spectrum in Fig. 4(b), where the bleaching of the ground-state absorption is not included for clear comparison with the two-photon spectrum. The full TA spectra at different pump fluences are presented in Fig. S9. An emission spectrum (green filled) is included in Fig. S9 as a reference, which is the TA spectrum at a delay before the overlap between the pump and probe pulses and exhibits a negative TA signal. Due to the disturbance by this emission spectrum, the bleaching and the exciton absorption spectra are strongly modulated where the TA signals did not increase monotonically with increasing the pump fluence, as highlighted by the curved arrows in Fig. S9. However, outside the emission band, the TA spectrum increases with increasing the pump fluence at wavelengths longer than 700 nm, as indicated by the upward arrows.

Looking at the TA spectra in Fig. 4(b), we may find that there is a large discrepancy between single- and two-photon spectra, in particular at the band edges, as highlighted by the blue arrows. The visibility of the discrepancy is reduced at the longer-wavelength end, which is due to the cut-off of the probe white-light spectrum at about 850 nm. Therefore, we have to consider different excitonic bands for single- and two-photon excitation, which is confirmed not only by the PL spectra in Fig. S2, but more convincingly by the TA dynamics in Fig. 4(c), where the dynamics curves are plotted at a delay larger than 2 ps, so that there is no temporal overlap with the pump pulses. Furthermore, the two-photon pumped dynamics (solid black and red curves for 787.2 and 815.4 nm, respectively) have been rescaled to fit the tails of the single-photon dynamics (black and red open circles for 787.2 and 815.4 nm, respectively). The two wavelengths are indicated by the black and red triangles in Fig. 4(b). The single-photon dynamics has to be fitted by three lifetimes: ${\tau _1}{\approx 10}\;{\rm ps}$, ${\tau _2}{\approx 247}\;{\rm ps}$, and ${\tau _3} \gt {1.7}\;{\rm ns}$. However, the two-photon dynamics exhibit only one lifetime ${\tau _3}$. The insets in Fig. 4(c) show exponential decay fittings to different segments of the dynamic curve, as guided by the lines in magenta. For time delays longer than 400 ps, the single- and two-photon pumped TA dynamics are basically overlapped, corresponding to a decay lifetime of ${\tau _3} \gt {1.7}\;{\rm ns}$. Compared with the single-photon excitonic dynamics, the two-photon exciton absorption dynamics by a flat curve with a slow variation and a single long lifetime not only maintain the high contrast, but also favor the high stability of the two-photon OS signals.

It needs to be noted that there are sharp peaks or steep edges in the single- and two-photon TA spectra in Fig. 4(b). However, they are not simply noisy jumps; instead, they reflect basically the true variation of the intensity of the OS signal with wavelength. One of the reasons is the limitation by the equipment settings, where the spectral resolution was set as 6 nm, allowing high resolution in the time delay. The smoothness of the TA spectrum was thus reduced. Such an observation is more obvious with the single-photon-pumped TA spectrum. Another reason is that a very low pump fluence was employed for single-photon pumping to avoid possible two-photon processes, so that the signal noise was indeed increased. However, this noise level is much lower than the variation amplitude in the TA spectrum in Fig. 4(b), which can be verified by the measurement results in Fig. S10. TA dynamics are presented at 735.8, 758.7, 764.4, and 770 nm in Fig. S10b, which are located at the most serious jumps in the spectrum, as indicated by triangles in different colors in Fig. S10a. Clearly, the amplitude in the TA dynamics basically agrees with the variation in the TA spectrum.

5. CONCLUSION

The two-photon OS effect is discovered in ${{\rm MAPbBr}_3}$ single crystals with an on–off ratio of about 90%, a speed faster than 400 fs, and a contrast higher than 18:1 at a pump pulse energy of only 7 µJ. A higher contrast of 52:1 has been reached for a relatively lower pump pulse energy of 1 µJ, at which an on–off ratio of about 64% has been achieved. This implies possible further reduction of the threshold pulse energy even to the orders of nanojoules. Large third-order optical nonlinearity of such materials is the photophysical basis that enables strong simultaneous absorption of the pump and probe pulses around 1.55 eV during their temporal overlap. Strong absorption of photons at energies higher than 2.22 eV and high transmission of photons at lower energies with a steep band edge make ${{\rm MAPbBr}_3}$ single crystals perfect candidates for two-photon OS in the near infrared. This category of OS devices with high stability and high compactness not only extends application of the hybrid halide perovskites, but also exploits new approaches for optical logic devices working in optical communication bands.

Funding

National Natural Science Foundation of China (61735002, 12074020, 11674015, 51988101); Beijing Municipal Commission of Education (KZ202010005002).

Disclosures

The authors declare no conflicts of interest.

Author Contributions Xinping Zhang designed this research, did the data processing and analysis, formulated the presentations and theoretical modeling, and wrote this paper. Meng Wang carried out the femtosecond pump–probe and steady-state spectroscopic measurements. Lin Ma synthesized the single crystal and supplied the structural parameters. Yulan Fu, Jinxin Guo, He Ma, and Yiwei Zhang helped with the operation and maintenance of the femtosecond laser system and with the pump–probe experiments. Zhengguang Yan and Xiaodong Han supervised the materials preparation and supplied the (CH3NH3)PbBr3 single crystals.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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References

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  16. G. C. Xing, N. Mathews, S. Sun, S. S. Lim, Y. M. Lam, M. Gratzel, S. Mhaisalkar, and T. C. Sum, “Long-range balanced electron- and hole-transport lengths in organic-inorganic CH3NH3PbI3,” Science 342, 344–347 (2013).
    [Crossref]
  17. W. S. Yang, B. W. Park, E. H. Jung, N. J. Jeon, Y. C. Kim, D. U. Lee, S. S. Shin, J. Seo, E. K. Kim, J. H. Noh, and S. I. Seok, “Iodide management in formamidinium-lead-halide–based perovskite layers for efficient solar cells,” Science 356, 1376–1379 (2017).
    [Crossref]
  18. N. Arora, M. I. Dar, A. Hinderhofer, N. Pellet, F. Schreiber, S. M. Zakeeruddin, and M. Grätzel, “Perovskite solar cells with CuSCN hole extraction layers yield stabilized efficiencies greater than 20%,” Science 358, 768–771 (2017).
    [Crossref]
  19. O. Ergen, S. M. Gilbert, T. Pham, S. J. Turner, M. T. Z. Tan, M. A. Worsley, and A. Zettl, “Graded bandgap perovskite solar cells,” Nat. Mater. 16, 522–525 (2017).
    [Crossref]
  20. V. D’Innocenzo, G. Grancini, M. J. P. Alcocer, A. R. S. Kandada, S. D. Stranks, M. M. Lee, G. Lanzani, H. J. Snaith, and A. Petrozza, “Excitons versus free charges in organo-lead tri-halide perovskites,” Nat. Commun. 5, 3586 (2014).
    [Crossref]
  21. M. Saba, M. Cadelano, D. Marongiu, F. Chen, V. Sarritzu, N. Sestu, C. Figus, M. Aresti, R. Piras, and A. G. Lehmann, “Correlated electron-hole plasma in organometal perovskites,” Nat. Commun. 5, 5049 (2014).
    [Crossref]
  22. J. S. Manser and P. V. Kamat, “Band filling with free charge carriers in organometal halide perovskites,” Nat. Photonics 8, 737–743 (2014).
    [Crossref]
  23. H. H. Fang, R. Raissa, M. Abdu-Aguye, S. Adjokatse, G. R. Blake, J. Even, and M. A. Loi, “Photophysics of organic-inorganic hybrid lead iodide perovskite single crystals,” Adv. Funct. Mater. 25, 2378−2385 (2015).
    [Crossref]
  24. X. P. Zhang, F. W. Tang, M. Wang, W. B. Zhan, H. X. Hu, Y. R. Li, R. H. Friend, and X. Y. Song, “Femtosecond visualization of oxygen vacancies in metal oxides,” Sci. Adv. 6, eaax9427 (2020).
    [Crossref]
  25. G. Grancini, A. R. S. Kandada, J. M. Frost, A. J. Barker, M. De Bastiani, M. Gandini, S. Marras, G. Lanzani, A. Walsh, and A. Petrozza, “Role of microstructure in the electron–hole interaction of hybrid lead halide perovskites,” Nat. Photonics 9, 695–702 (2015).
    [Crossref]
  26. J. S. Manser, J. A. Christians, and P. V. Kamat, “Intriguing optoelectronic properties of metal halide perovskites,” Chem. Rev. 116, 12956−13008 (2016).
    [Crossref]
  27. W. D. Xu, J. A. McLeod, Y. G. Yang, Y. M. Wang, Z. W. Wu, S. Bai, Z. C. Yuan, T. Song, Y. S. Wang, J. J. Si, R. B. Wang, X. Y. Gao, X. P. Zhang, L. J. Liu, and B. Q. Sun, “Iodomethane-mediated organometal halide perovskite with record photoluminescence lifetime,” ACS Appl. Mater. Interfaces 8, 23181–23189 (2016).
    [Crossref]
  28. T. Kondo, S. Iwamoto, S. Hayase, K. Tanaka, J. Ishi, M. Mizuno, K. Ema, and R. Ito, “Resonant third-order optical nonlinearity in the layered perovskite-type material (C6H13NH3)2PbI4,” Solid State Commun. 105, 503–506 (1998).
    [Crossref]
  29. J. Xu, X. Li, J. Xiong, C. Yuan, S. Semin, T. Rasing, and X. H. Bu, “Halide perovskites for nonlinear optics,” Adv. Mater. 31, 1806736 (2018).
    [Crossref]
  30. F. O. Saouma, C. C. Stoumpos, J. Wong, M. G. Kanatzidis, and J. I. Jang, “Selective enhancement of optical nonlinearity in two-dimensional organic-inorganic lead iodide perovskites,” Nat. Commun. 8, 742 (2017).
    [Crossref]
  31. T. C. He, J. Z. Li, C. Ren, S. Y. Xiao, Y. W. Li, R. Chen, and X. D. Lin, “Strong two-photon absorption of Mn-doped CsPbCl3 perovskite nanocrystals,” Appl. Phys. Lett. 111, 211105 (2017).
    [Crossref]
  32. Z. P. Hu, Z. Z. Liu, Y. Bian, D. J. Liu, X. S. Tang, W. Hu, Z. G. Zang, M. Zhou, L. D. Sun, J. X. Tang, Y. Q. Li, J. Du, and Y. X. Leng, “Robust cesium lead halide perovskite microcubes for frequency upconversion lasing,” Adv. Opt. Mater. 5, 1700419 (2017).
    [Crossref]
  33. S. Y. Liu, X. H. Fang, Y. M. Wang, and X. P. Zhang, “Two-photon pumped amplified spontaneous emission based on all-inorganic perovskite nanocrystals embedded with gold nanorods,” Opt. Mater. 81, 55–58 (2018).
    [Crossref]
  34. D. Shi, V. Adinolfi, R. Comin, M. Yuan, E. Alarousu, A. Buin, Y. Chen, S. Hoogland, A. Rothenberger, K. Katsiev, Y. Losovyj, X. Zhang, P. A. Dowben, O. F. Mohammed, E. H. Sargent, and O. M. Bakr, “Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals,” Science 347, 519–522 (2015).
    [Crossref]
  35. T. Baikie, Y. Fang, J. M. Kadro, M. Schreyer, F. Wei, S. G. Mhaisalkar, M. Graetzeld, and T. J. White, “Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solid-state sensitised solar cell applications,” J. Mater. Chem. A 1, 5628 (2013).
    [Crossref]
  36. K. H. Wang, L. C. Li, M. Shellalah, and K. W. Sun, “Structural and photophysical properties of methylammonium lead tribromide (MAPbBr3) single crystals,” Sci. Rep. 7, 13643 (2017).
    [Crossref]
  37. W. Zhang, L. Peng, J. Liu, A. W. Tang, J. S. Hu, J. N. Yao, and Y. S. Zhao, “Controlling the cavity structures of two-photon-pumped perovskite microlasers,” Adv. Mater. 28, 4040–4046 (2016).
    [Crossref]
  38. T. C. Wei, S. Mokkapati, T. Y. Li, C. H. Lin, G. R. Lin, C. Jagadish, and J. H. He, “Nonlinear absorption applications of CH3NH3PbBr3 perovskite crystals,” Adv. Funct. Mater. 28, 1707175 (2018).
    [Crossref]
  39. G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9, 9340–9346 (2015).
    [Crossref]
  40. C. Silva, A. S. Dhoot, D. M. Russell, M. A. Stevens, A. C. Arias, J. D. MacKenzie, N. C. Greenham, R. H. Friend, S. Setayesh, and K. Müllen, “Efficient exciton dissociation via two-step photoexcitation in polymeric semiconductors,” Phys. Rev. B 64, 125211 (2001).
    [Crossref]
  41. X. P. Zhang, Y. J. Xia, R. H. Friend, and C. Silva, “Sequential absorption processes in two-photon-excitation transient absorption spectroscopy in a semiconductor polymer,” Phys. Rev. B 73, 245201 (2006).
    [Crossref]
  42. Y. Pang, M. Samoc, and P. N. Prasad, “Third-order nonlinearity and two-photon-induced molecular dynamics: femtosecond time-resolved transient absorption, Kerr gate, and degenerate four-wave mixing studies in poly (p-phenylene vinylene)/sol-gel silica film,” J. Chem. Phys. 94, 5282 (1991).
    [Crossref]

2020 (5)

H. Z. Lu, Y. H. Liu, P. Ahlawat, A. Mishra, W. R. Tress, F. T. Eickemeyer, Y. G. Yang, F. Fu, Z. W. Wang, C. E. Avalos, B. I. Carlsen, A. Agarwalla, X. Zhang, X. G. Li, Y. Q. Zhan, S. M. Zakeeruddin, L. Emsley, U. Rothlisberger, L. R. Zheng, A. Hagfeldt, and M. Grätzel, “Vapor-assisted deposition of highly efficient, stable black-phase FAPbI3 perovskite solar cells,” Science 370, eabb8985 (2020).
[Crossref]

X. C. Li and J. Cao, “Porphyrin/phthalocyanine meatal complexes as modifiers for efficient perovskite solar cells,” Sci. Bull. 65(20), 1688–1690 (2020).
[Crossref]

C. Huang, C. Zhang, S. Xiao, Y. Wang, Y. Fan, Y. Liu, N. Zhang, G. Qu, H. Ji, J. Han, L. Ge, Y. Kivshar, and Q. Song, “Ultrafast control of vortex microlasers,” Science 367, 1018–1021 (2020).
[Crossref]

C. Zou, Y. Liu, D. S. Ginger, and L. Y. Lin, “Suppressing efficiency roll-off at high current densities for ultra-bright green perovskite light-emitting diodes,” ACS Nano 14, 6076−6086 (2020).
[Crossref]

X. P. Zhang, F. W. Tang, M. Wang, W. B. Zhan, H. X. Hu, Y. R. Li, R. H. Friend, and X. Y. Song, “Femtosecond visualization of oxygen vacancies in metal oxides,” Sci. Adv. 6, eaax9427 (2020).
[Crossref]

2019 (3)

A. Zhizhchenko, S. Syubaev, A. Berestennikov, A. V. Yulin, A. Porfirev, A. Pushkarev, I. Shishkin, K. Golokhvast, A. A. Bogdanov, A. A. Zakhidov, A. A. Kuchmizhak, Y. S. Kivshar, and S. V. Makarov, “Single-mode lasing from imprinted halide-perovskite microdisks,” ACS Nano 13, 4140–4147 (2019).
[Crossref]

N. Zhang, Y. B. Fan, K. Y. Wang, Z. Y. Gu, Y. H. Wang, L. Ge, S. M. Xiao, and Q. H. Song, “All-optical control of lead halide perovskite microlasers,” Nat. Commun. 10, 1770 (2019).
[Crossref]

E. H. Jung, N. J. Jeon, E. Y. Park, C. S. Moon, T. J. Shin, T. Y. Yang, J. H. Noh, and J. Seo, “Efficient, stable and scalable perovskite solar cells using poly(3-hexylthiophene),” Nature 567, 511–515 (2019).
[Crossref]

2018 (5)

D. Luo, W. Yang, Z. Wang, A. Sadhanala, Q. Hu, R. Su, R. Shivanna, G. F. Trindade, J. F. Watts, Z. Xu, T. Liu, K. Chen, F. Ye, P. Wu, L. Zhao, J. Wu, Y. Tu, Y. Zhang, X. Yang, W. Zhang, R. H. Friend, Q. Gong, H. J. Snaith, and R. Zhu, “Enhanced photovoltage for inverted planar heterojunction perovskite solar cells,” Science 360, 1442–1446 (2018).
[Crossref]

X. L. Yang, X. W. Zhang, J. X. Deng, Z. Chu, Q. Jiang, J. H. Meng, P. Y. Wang, L. Q. Zhang, Z. G. Yin, and J. B. You, “Efficient green light-emitting diodes based on quasi-two-dimensional composition and phase engineered perovskite with surface passivation,” Nat. Commun. 9, 570 (2018).
[Crossref]

J. Xu, X. Li, J. Xiong, C. Yuan, S. Semin, T. Rasing, and X. H. Bu, “Halide perovskites for nonlinear optics,” Adv. Mater. 31, 1806736 (2018).
[Crossref]

S. Y. Liu, X. H. Fang, Y. M. Wang, and X. P. Zhang, “Two-photon pumped amplified spontaneous emission based on all-inorganic perovskite nanocrystals embedded with gold nanorods,” Opt. Mater. 81, 55–58 (2018).
[Crossref]

T. C. Wei, S. Mokkapati, T. Y. Li, C. H. Lin, G. R. Lin, C. Jagadish, and J. H. He, “Nonlinear absorption applications of CH3NH3PbBr3 perovskite crystals,” Adv. Funct. Mater. 28, 1707175 (2018).
[Crossref]

2017 (7)

K. H. Wang, L. C. Li, M. Shellalah, and K. W. Sun, “Structural and photophysical properties of methylammonium lead tribromide (MAPbBr3) single crystals,” Sci. Rep. 7, 13643 (2017).
[Crossref]

F. O. Saouma, C. C. Stoumpos, J. Wong, M. G. Kanatzidis, and J. I. Jang, “Selective enhancement of optical nonlinearity in two-dimensional organic-inorganic lead iodide perovskites,” Nat. Commun. 8, 742 (2017).
[Crossref]

T. C. He, J. Z. Li, C. Ren, S. Y. Xiao, Y. W. Li, R. Chen, and X. D. Lin, “Strong two-photon absorption of Mn-doped CsPbCl3 perovskite nanocrystals,” Appl. Phys. Lett. 111, 211105 (2017).
[Crossref]

Z. P. Hu, Z. Z. Liu, Y. Bian, D. J. Liu, X. S. Tang, W. Hu, Z. G. Zang, M. Zhou, L. D. Sun, J. X. Tang, Y. Q. Li, J. Du, and Y. X. Leng, “Robust cesium lead halide perovskite microcubes for frequency upconversion lasing,” Adv. Opt. Mater. 5, 1700419 (2017).
[Crossref]

W. S. Yang, B. W. Park, E. H. Jung, N. J. Jeon, Y. C. Kim, D. U. Lee, S. S. Shin, J. Seo, E. K. Kim, J. H. Noh, and S. I. Seok, “Iodide management in formamidinium-lead-halide–based perovskite layers for efficient solar cells,” Science 356, 1376–1379 (2017).
[Crossref]

N. Arora, M. I. Dar, A. Hinderhofer, N. Pellet, F. Schreiber, S. M. Zakeeruddin, and M. Grätzel, “Perovskite solar cells with CuSCN hole extraction layers yield stabilized efficiencies greater than 20%,” Science 358, 768–771 (2017).
[Crossref]

O. Ergen, S. M. Gilbert, T. Pham, S. J. Turner, M. T. Z. Tan, M. A. Worsley, and A. Zettl, “Graded bandgap perovskite solar cells,” Nat. Mater. 16, 522–525 (2017).
[Crossref]

2016 (4)

H. M. Zhu, Y. P. Fu, F. Meng, X. X. Wu, Z. Z. Gong, Q. Ding, M. V. Gustafsson, M. T. Trinh, S. Jin, and X. Y. Zhu, “Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors,” Nat. Mater. 14, 636–642 (2016).
[Crossref]

J. S. Manser, J. A. Christians, and P. V. Kamat, “Intriguing optoelectronic properties of metal halide perovskites,” Chem. Rev. 116, 12956−13008 (2016).
[Crossref]

W. D. Xu, J. A. McLeod, Y. G. Yang, Y. M. Wang, Z. W. Wu, S. Bai, Z. C. Yuan, T. Song, Y. S. Wang, J. J. Si, R. B. Wang, X. Y. Gao, X. P. Zhang, L. J. Liu, and B. Q. Sun, “Iodomethane-mediated organometal halide perovskite with record photoluminescence lifetime,” ACS Appl. Mater. Interfaces 8, 23181–23189 (2016).
[Crossref]

W. Zhang, L. Peng, J. Liu, A. W. Tang, J. S. Hu, J. N. Yao, and Y. S. Zhao, “Controlling the cavity structures of two-photon-pumped perovskite microlasers,” Adv. Mater. 28, 4040–4046 (2016).
[Crossref]

2015 (8)

D. Shi, V. Adinolfi, R. Comin, M. Yuan, E. Alarousu, A. Buin, Y. Chen, S. Hoogland, A. Rothenberger, K. Katsiev, Y. Losovyj, X. Zhang, P. A. Dowben, O. F. Mohammed, E. H. Sargent, and O. M. Bakr, “Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals,” Science 347, 519–522 (2015).
[Crossref]

G. Walters, B. R. Sutherland, S. Hoogland, D. Shi, R. Comin, D. P. Sellan, O. M. Bakr, and E. H. Sargent, “Two-photon absorption in organometallic bromide perovskites,” ACS Nano 9, 9340–9346 (2015).
[Crossref]

G. Grancini, A. R. S. Kandada, J. M. Frost, A. J. Barker, M. De Bastiani, M. Gandini, S. Marras, G. Lanzani, A. Walsh, and A. Petrozza, “Role of microstructure in the electron–hole interaction of hybrid lead halide perovskites,” Nat. Photonics 9, 695–702 (2015).
[Crossref]

D. W. de Quilettes, S. M. Vorpahl, S. D. Stranks, H. Nagaoka, G. E. Eperon, M. E. Ziffer, H. J. Snaith, and D. S. Ginger, “Impact of microstructure on local carrier lifetime in perovskite solar cells,” Science 348, 683–686 (2015).
[Crossref]

H. H. Fang, R. Raissa, M. Abdu-Aguye, S. Adjokatse, G. R. Blake, J. Even, and M. A. Loi, “Photophysics of organic-inorganic hybrid lead iodide perovskite single crystals,” Adv. Funct. Mater. 25, 2378−2385 (2015).
[Crossref]

J. P. Wang, N. N. Wang, Y. Z. Jin, J. J. Si, Z. K. Tan, H. Du, L. Cheng, X. L. Dai, S. Bai, H. P. He, Z. Z. Ye, M. L. Lai, R. H. Friend, and W. Huang, “Interfacial control toward efficient and low-voltage perovskite light-emitting diodes,” Adv. Mater. 27, 2311–2316 (2015).
[Crossref]

R. L. Z. Hoye, M. R. Chua, K. P. Musselman, G. R. Li, M. L. Lai, Z. K. Tan, N. C. Greenham, J. L. MacManus-Driscoll, R. H. Friend, and D. Credgington, “Enhanced performance in fluorene-free organometal halide perovskite light-emitting diodes using tunable, low electron affinity oxide electron injectors,” Adv. Mater. 27, 1414–1419 (2015).
[Crossref]

S. D. Stranks and H. J. Snaith, “Metal-halide perovskites for photovoltaic and light-emitting devices,” Nat. Nanotechnol. 10, 391–402 (2015).
[Crossref]

2014 (4)

G. C. Xing, N. Mathews, S. S. Lim, N. Yantara, X. F. Liu, D. Sabba, M. Grätzel, S. Mhaisalkar, and T. C. Sum, “Low-temperature solution-processed wavelength-tunable perovskites for lasing,” Nat. Mater. 13, 476–480 (2014).
[Crossref]

V. D’Innocenzo, G. Grancini, M. J. P. Alcocer, A. R. S. Kandada, S. D. Stranks, M. M. Lee, G. Lanzani, H. J. Snaith, and A. Petrozza, “Excitons versus free charges in organo-lead tri-halide perovskites,” Nat. Commun. 5, 3586 (2014).
[Crossref]

M. Saba, M. Cadelano, D. Marongiu, F. Chen, V. Sarritzu, N. Sestu, C. Figus, M. Aresti, R. Piras, and A. G. Lehmann, “Correlated electron-hole plasma in organometal perovskites,” Nat. Commun. 5, 5049 (2014).
[Crossref]

J. S. Manser and P. V. Kamat, “Band filling with free charge carriers in organometal halide perovskites,” Nat. Photonics 8, 737–743 (2014).
[Crossref]

2013 (2)

G. C. Xing, N. Mathews, S. Sun, S. S. Lim, Y. M. Lam, M. Gratzel, S. Mhaisalkar, and T. C. Sum, “Long-range balanced electron- and hole-transport lengths in organic-inorganic CH3NH3PbI3,” Science 342, 344–347 (2013).
[Crossref]

T. Baikie, Y. Fang, J. M. Kadro, M. Schreyer, F. Wei, S. G. Mhaisalkar, M. Graetzeld, and T. J. White, “Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solid-state sensitised solar cell applications,” J. Mater. Chem. A 1, 5628 (2013).
[Crossref]

2006 (1)

X. P. Zhang, Y. J. Xia, R. H. Friend, and C. Silva, “Sequential absorption processes in two-photon-excitation transient absorption spectroscopy in a semiconductor polymer,” Phys. Rev. B 73, 245201 (2006).
[Crossref]

2001 (1)

C. Silva, A. S. Dhoot, D. M. Russell, M. A. Stevens, A. C. Arias, J. D. MacKenzie, N. C. Greenham, R. H. Friend, S. Setayesh, and K. Müllen, “Efficient exciton dissociation via two-step photoexcitation in polymeric semiconductors,” Phys. Rev. B 64, 125211 (2001).
[Crossref]

1998 (1)

T. Kondo, S. Iwamoto, S. Hayase, K. Tanaka, J. Ishi, M. Mizuno, K. Ema, and R. Ito, “Resonant third-order optical nonlinearity in the layered perovskite-type material (C6H13NH3)2PbI4,” Solid State Commun. 105, 503–506 (1998).
[Crossref]

1991 (1)

Y. Pang, M. Samoc, and P. N. Prasad, “Third-order nonlinearity and two-photon-induced molecular dynamics: femtosecond time-resolved transient absorption, Kerr gate, and degenerate four-wave mixing studies in poly (p-phenylene vinylene)/sol-gel silica film,” J. Chem. Phys. 94, 5282 (1991).
[Crossref]

Abdu-Aguye, M.

H. H. Fang, R. Raissa, M. Abdu-Aguye, S. Adjokatse, G. R. Blake, J. Even, and M. A. Loi, “Photophysics of organic-inorganic hybrid lead iodide perovskite single crystals,” Adv. Funct. Mater. 25, 2378−2385 (2015).
[Crossref]

Adinolfi, V.

D. Shi, V. Adinolfi, R. Comin, M. Yuan, E. Alarousu, A. Buin, Y. Chen, S. Hoogland, A. Rothenberger, K. Katsiev, Y. Losovyj, X. Zhang, P. A. Dowben, O. F. Mohammed, E. H. Sargent, and O. M. Bakr, “Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals,” Science 347, 519–522 (2015).
[Crossref]

Adjokatse, S.

H. H. Fang, R. Raissa, M. Abdu-Aguye, S. Adjokatse, G. R. Blake, J. Even, and M. A. Loi, “Photophysics of organic-inorganic hybrid lead iodide perovskite single crystals,” Adv. Funct. Mater. 25, 2378−2385 (2015).
[Crossref]

Agarwalla, A.

H. Z. Lu, Y. H. Liu, P. Ahlawat, A. Mishra, W. R. Tress, F. T. Eickemeyer, Y. G. Yang, F. Fu, Z. W. Wang, C. E. Avalos, B. I. Carlsen, A. Agarwalla, X. Zhang, X. G. Li, Y. Q. Zhan, S. M. Zakeeruddin, L. Emsley, U. Rothlisberger, L. R. Zheng, A. Hagfeldt, and M. Grätzel, “Vapor-assisted deposition of highly efficient, stable black-phase FAPbI3 perovskite solar cells,” Science 370, eabb8985 (2020).
[Crossref]

Ahlawat, P.

H. Z. Lu, Y. H. Liu, P. Ahlawat, A. Mishra, W. R. Tress, F. T. Eickemeyer, Y. G. Yang, F. Fu, Z. W. Wang, C. E. Avalos, B. I. Carlsen, A. Agarwalla, X. Zhang, X. G. Li, Y. Q. Zhan, S. M. Zakeeruddin, L. Emsley, U. Rothlisberger, L. R. Zheng, A. Hagfeldt, and M. Grätzel, “Vapor-assisted deposition of highly efficient, stable black-phase FAPbI3 perovskite solar cells,” Science 370, eabb8985 (2020).
[Crossref]

Alarousu, E.

D. Shi, V. Adinolfi, R. Comin, M. Yuan, E. Alarousu, A. Buin, Y. Chen, S. Hoogland, A. Rothenberger, K. Katsiev, Y. Losovyj, X. Zhang, P. A. Dowben, O. F. Mohammed, E. H. Sargent, and O. M. Bakr, “Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals,” Science 347, 519–522 (2015).
[Crossref]

Alcocer, M. J. P.

V. D’Innocenzo, G. Grancini, M. J. P. Alcocer, A. R. S. Kandada, S. D. Stranks, M. M. Lee, G. Lanzani, H. J. Snaith, and A. Petrozza, “Excitons versus free charges in organo-lead tri-halide perovskites,” Nat. Commun. 5, 3586 (2014).
[Crossref]

Aresti, M.

M. Saba, M. Cadelano, D. Marongiu, F. Chen, V. Sarritzu, N. Sestu, C. Figus, M. Aresti, R. Piras, and A. G. Lehmann, “Correlated electron-hole plasma in organometal perovskites,” Nat. Commun. 5, 5049 (2014).
[Crossref]

Arias, A. C.

C. Silva, A. S. Dhoot, D. M. Russell, M. A. Stevens, A. C. Arias, J. D. MacKenzie, N. C. Greenham, R. H. Friend, S. Setayesh, and K. Müllen, “Efficient exciton dissociation via two-step photoexcitation in polymeric semiconductors,” Phys. Rev. B 64, 125211 (2001).
[Crossref]

Arora, N.

N. Arora, M. I. Dar, A. Hinderhofer, N. Pellet, F. Schreiber, S. M. Zakeeruddin, and M. Grätzel, “Perovskite solar cells with CuSCN hole extraction layers yield stabilized efficiencies greater than 20%,” Science 358, 768–771 (2017).
[Crossref]

Avalos, C. E.

H. Z. Lu, Y. H. Liu, P. Ahlawat, A. Mishra, W. R. Tress, F. T. Eickemeyer, Y. G. Yang, F. Fu, Z. W. Wang, C. E. Avalos, B. I. Carlsen, A. Agarwalla, X. Zhang, X. G. Li, Y. Q. Zhan, S. M. Zakeeruddin, L. Emsley, U. Rothlisberger, L. R. Zheng, A. Hagfeldt, and M. Grätzel, “Vapor-assisted deposition of highly efficient, stable black-phase FAPbI3 perovskite solar cells,” Science 370, eabb8985 (2020).
[Crossref]

Bai, S.

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ACS Appl. Mater. Interfaces (1)

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Supplementary Material (1)

NameDescription
» Supplement 1       Supporting information

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (4)

Fig. 1.
Fig. 1. (a) Pump–probe scheme for the optical switching process. 150-fs pump pulses at ${E_P} = {1.55}\;{\rm eV}$ have a pulse energy as low as 1 µJ. Supercontinuum pulses with a photon energy ${E_D}$ sent to overlap the pump inside the single crystal have a total pulse energy of less than 1 nJ. The output of the probe pulses was switched on and off with a modulation depth as large as 90%. Inset: photograph of the $({{\rm CH}_3}{{\rm NH}_3}){{\rm PbBr}_3}$ single crystal with a thickness of about 1 mm. (b) Absorption spectrum of the single crystal characterized by optical extinction (ABS) in optical density (OD) as a function of photon energy (E). (c) Energy level diagram explaining the two-photon absorption optical switching (2PA OS) mechanisms. The 2PA-OS process is highlighted by a yellow-filled triangle. (d) Simplified illustration of the optical switching process through 2PA of one pump and one probe photon ( ${h}{\nu _{{\rm pump}}} + { h}{\nu _{{\rm probe}}}$ ), resulting in nearly no transmission of the probe photon during the overlap between the pump and probe pulses.
Fig. 2.
Fig. 2. (a) TA spectra measured at delays of 0, 0.4, 0.55, 1.2, 1.75, 4.5, and 10 ps. Inset: TA dynamics at 787.2 and 815.4 nm. (b) TA dynamics at 800-nm pump and 815.4-nm probe with a pump fluence of ${55}\;\unicode{x00B5} {{\rm J/cm}^2}$ . Inset: more detailed view of the optical switching signal, showing an on–off ratio of 933 mOD or 89% modulation on transmission rate and a speed faster than 400 fs at FWHM.
Fig. 3.
Fig. 3. (a) TA dynamics at 815.4 nm (1.52 eV) at different pump fluences. (b) Pump fluence dependence of the fast TA process at a delay of 400 fs [highlighted by a red triangle in (a)]. (c) Pump fluence dependence of the slow TA process at a delay of 600 ps [blue triangle in (a)].
Fig. 4.
Fig. 4. (a) TA dynamics at a probe wavelength of 815.4 nm (photon energy of 1.52 eV) measured with different configurations of polarization directions of the pump and probe pulses, and orientation of the ${{\rm MAPbBr}_3}$ single crystal: “ $//$ ” pump polarized parallel to the probe, “ $\bot$ ” pump perpendicular to the probe, “ ${\rm V}$ ” crystal oriented vertically, “ ${\rm H}$ ” crystal oriented horizontally. (b) TA spectra measured at a time delay of 10 ps for a pump wavelength of 400 (red) and 800 nm (green), corresponding to single- and two-photon pumps, respectively. The dark area (red ${+}$ green) corresponds to the overlap between the two spectra. Blue arrows indicate the discrepancy on the band edges. Black and red triangles indicate probe wavelengths at 787.2 and 815.4 nm, respectively. (c) Comparison between single- (400 nm, open circles) and two-photon (800 nm, solid lines) pumped TA dynamics at probe wavelengths of 787.2 (black) and 815.4 nm (red) for a time delay larger than 10 ps, implying pure exciton absorption processes. Insets: evaluation on the decay dynamics in different time ranges for resolving the lifetimes of the involved exciton-absorption processes.

Equations (13)

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d N 2 d t = σ 2 N 1 I P 2 N 2 τ 2 σ E N 2 I P + N m τ m ,
d N 1 d t = σ 2 N 1 I P 2 + N 2 τ 2 ,
d N m d t = σ E N 2 I P N m τ m ,
N 0 = N 1 + N 2 + N m ,
N 2 ( t ) = B A ( 1 e A t ) ,
N 1 ( t ) = N 0 N 2 ( t ) .
N 2 ( t ) B A ( 1 e A t ) ( 1 α σ E I P ) σ 2 N 0 I P 2 t ( 1 α σ E I P ) ,
N 1 ( t ) = N 0 ( 1 σ 2 I P 2 t + α σ 2 σ E I P 3 t ) .
Δ A f σ 2 N 1 ( t ) I P I d = σ 2 N 0 ( 1 σ 2 I P 2 t + α σ 2 σ E I P 3 t ) I P I d .
Δ A f σ 2 N 0 I d I P σ 2 2 N 0 τ f I d I P 3 + α σ 2 2 σ E N 0 τ f I d I P 4 ,
N 2 ( t ) N 2 ( 2 τ P ) e t τ 2 2 σ 2 N 0 I P 2 τ P ( 1 α σ E I P ) e t τ 2 = 2 ( σ 2 N 0 τ P I P 2 α σ 2 σ E N 0 τ P I P 3 ) e t τ 2 .
Δ A s ( Δ τ ) σ E N 2 ( Δ τ ) I d 2 ( σ 2 σ E N 0 τ P I d I P 2 α σ 2 σ E 2 N 0 τ P I d I P 3 ) e Δ τ τ 2 ,
Δ A s ( Δ τ ) / I P 2 σ 2 σ E N 0 τ P I d I P ( 1 1.5 α σ E I P ) .

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