Giant five-photon absorption from multidimensional core-shell halide perovskite colloidal nanocrystals

Multiphoton absorption processes enable many technologically important applications, such as in vivo imaging, photodynamic therapy and optical limiting, and so on. Specifically, higher-order nonlinear absorption such as five-photon absorption offers significant advantages of greater spatial confinement, increased penetration depth, reduced autofluorescence, enhanced sensitivity and improved resolution over lower orders in bioimaging. Organic chromophores and conventional semiconductor nanocrystals are leaders in two-/three-photon absorption applications, but face considerable challenges from their small five-photon action cross-sections. Herein, we reveal that the family of halide perovskite colloidal nanocrystals transcend these constraints with highly efficient five-photon-excited upconversion fluorescence—unprecedented for semiconductor nanocrystals. Amazingly, their multidimensional type I (both conduction and valence band edges of core lie within bandgap of shell) core–shell (three-dimensional methylammonium lead bromide/two-dimensional octylammonium lead bromide) perovskite nanocrystals exhibit five-photon action cross-sections that are at least 9 orders larger than state-of-the-art specially designed organic molecules. Importantly, this family of halide perovskite nanocrystals may enable fresh approaches for next-generation multiphoton imaging applications.

The almost flat open-aperture Z-scan curve of the toluene under the same excitation condition (contained in 1-mm-thick cuvette, laser excitation at 800 nm with peak intensity of ~ 35.0 GW cm -2 ) is also shown in (d).

Supplementary Figure 5 | Experimental setup for MEPL measurements.
The excitation wavelengths were varied from 675 nm to 2300 nm to investigate two-, three-, four-and five-photon absorption excited PL. OPA, LP and SP are abbreviations for optical parametric amplifier, long-pass filter and short-pass filter. For excitation wavelengths smaller than 800 nm, a notch filter at 800 nm was utilized to block off the light at undesired wavelengths. For excitation wavelengths larger than 800 nm, an appropriate long-pass filter (at 750 nm or at 1500 nm) was applied to filter out light at unwanted wavelengths. A short-pass filter at 650 nm was applied to filter out the excitation laser beam from the signal.  a, d, g, j, m, p, s, v, y) Measured two-dimensional FROG traces of the laser pulses. x axis represents the delay time and y axis corresponds to the wavelength. The right side is the scale bar characterizing the normalized magnitude of the FROG signal; (b, e, h, k, n, q, t, w, z) The corresponding temporal distributions; (c, f, i, l, o, r, x, aa) The corresponding spectral distributions; (ab) Summarized Ch^2 and R^2 of the Gaussian function fitting to laser pulse temporal distribution at all wavelengths. Both the negligible Ch^2 and the very close to unity R^2 demonstrates the good fitting thus indicating the Gaussian temporal distribution of the laser pulses; (ac) Summarized Ch^2 and R^2 of the Gaussian function fitting to spectral distribution at all wavelengths with similar negligible Ch^2 and very close to unity R^2, demonstrating the good fitting thus the Gaussian spectral distribution of the laser pulses, which is in agreement with (ab); (ad) Summary of the measured pulse-widths of the laser pulses at all wavelengths; (ae) Relation between the measured spectral bandwidths and temporal pulse-widths, together with the fitting with the time-bandwidth relation of Fourier-transform-limited pulses:  FWHM = (A  K / c)  (( 0 ) 2 /  FWHM ). Figure 16 | Spectral bandwidth measurements of the laser beam at wavelength range 675-1700 nm by a visible monochromator coupled with silicon CCD and infrared monochromator coupled with liquid-nitrogen-cooled InGaAs infrared detector, together with the pulse derivation. (a-q) Measured optical spectra at the wavelengths range from 675 nm to 1700nm; (r) Summarized Ch^2 and R^2 of the Gaussian function fitting to laser pulse spectral distribution at wavelengths 675-1700 nm. Both the negligible Ch^2 and the very close to unity R^2 demonstrate the good fitting, thus indicating the Gaussian spectral distribution of the laser pulses; (s) Comparison of the acquired spectral bandwidths at 700-1100 nm by spectrometer with that obtained from the FROG measurements, indicating high consistency with variation less than 5%; (t) Summary of the measured spectral bandwidths at 675-1700 nm and the comparison of the derived pulse-widths at wavelengths of 675 & 1200 -1700 nm based on the pulse-width-bandwidth relation of Fourier-transform-limited pulses with the measured pulse-widths at 700-1100 nm by FROG, revealing the pulse widths at wavelength range 675 -1700 nm are in the range of (50.6  5.1) -(62.9  6.3) fs, with variation smaller than 25%, consistent with the specification of the OperA-Solo OPA.

Supplementary
Supplementary Figure 17 | Knife-edge scans along the x-and y-directions of the cross-sectional plane of the laser beam for characterizing the spatial distributions of the laser beam and measuring its beam radius. (a-x) Measured knife-edge scans curves along the x-and y-directions at the excitation wavelengths range from 675 nm to 2300nm, together with the Gaussian distribution fitting; (y,z) Summarized Ch^2 and R^2 of the Gaussian fitting to laser spatial distributions along both x-and y-directions at wavelengths 675-2300 nm. Both the negligible Ch^2 and the very close to unity R^2 demonstrate the good fitting thus indicating the Gaussian spatial distribution of the laser beam at both x-and y-directions ; (aa) Summary of the measured laser beam radii along both x-and y-directions at 675-2300 nm. The high consistency of the measured laser beam radii in x-direction with that measured in y-direction at all wavelengths with variation less than 6 %, further validating that the two-dimension spatial profiles of the laser beams in the cross-sectional plane follow the Gaussian distributions.

Absorption and photoluminescence (PL) by one-photon excitation
The one-photon absorption (1PA) and one-photon-excited PL spectra of the MAPbBr 3 , The absolute photoluminescence quantum yields (PLQYs) of the perovskite NCs were measured using an Ocean-optics USB4000 spectrometer with a BaSO 4 -coated integrating sphere excited by a laser beam at 400 nm. The PLQY of MAPbBr 3 NCs was measured to be ~84%; while the PLQY of the core-shell MAPbBr 3 /(OA) 2 PbBr 4 NCs was ~92%. Its increased PLQY and the enhanced stability (retaining a 60% PLQY after two months) is attributed to the effective surface passivation and efficient carrier confinement provided by the shell, as detailed in Ref [3]. The PLQY of CsPbBr 3 NCs was determined to be ~ 55%, which is close to the reported value in the literature 2 .

Structural characterization
Representative Although the (100) and (200) peak intensity is lower for the MAPbBr 3 /(OA) 2 PbBr 4 NCs compared to MAPbBr 3 NCs, the relative intensity difference and peak positions remains unchanged.

Photo electron spectroscopy in air (PESA) measurements for MAPbBr 3 and (OA) 2 PbBr 4 thin films
Photo electron spectroscopy in air (PESA) measurements on MAPbBr 3 and (OA) 2 PbBr 4 thin films were performed to estimate the valance band maximum (VBM) alignment between the core and shell in the core-shell MAPbBr 3 /(OA) 2 PbBr 4 NCs, and to avoid the influence from the organic ligands on surface of NCs films. A Riken Keiki AC-2 PESA spectrometer was utilized to perform the PESA measurements with a power setting of 800 nW and a power number of 0.5 as shown in Supplementary Fig. 1f, the PESA results of MAPbBr 3 and (OA) 2 PbBr 4 thin films reveals their VBM at -5.62 eV and -6.00 eV, respectively. Together with the bandgap values determined from the 1PA spectra in Supplementary Fig. 1and in the reference 4-5 , a type-I conduction and valence band-edge alignment between the core and shell in the core-shell MAPbBr 3 /(OA) 2 PbBr 4 NCs is expected, as shown in Fig. 1ain the main text.

Theoretical calculations to determine the conduction and valence band-edge alignment in core-shell perovskite NCs
We employed the all-electron-like projector augmented wave (PAW) method 9  The detailed calculation method can be found in ref. 13. In Supplementary Fig. 2

Femtosecond laser specifications from manufacturer's data sheets
The excitation laser pulses applied in our measurements were generated by an optical parametric  Figure S3 shows the acquired two-dimensional FROG traces, temporal distributions and spectral distributions of the laser pulses in the wavelength range 700 -1100nm. Supplementary Figures 15a, d,  The laser pulses at 800 nm was from the Libra Ti:Sapphire Amplifier, whereas the laser pulses at other wavelengths were generated by the OperA-Solo OPA.
As shown in Supplementary Fig. 15 Hence, the variation in the pulse-widths at different wavelengths in the range 700 -1100nm will not lead to variation of the order of the measured 5PA cross-sections in the lead bromide perovskite NCs.
In addition, Supplementary Fig. 15ae demonstrated that the measured spectral bandwidths and temporal pulse-widths followed the time-bandwidth relation of Fourier-transform-limited pulses ( FWHM = (A  K / c) 14 , a typical characteristic of ultrashort laser pulses generated by mode-locked lasers. c is the speed of light in vacuum, K is a constant depending only on the pulse shape and equals to 0.441 for Gaussian temporal distribution, A is a scaling factor called time-transform-limit factor. From the best fit to the experimental results, A was determined to be about 1.27, as indicated in Supplementary Fig. 15ae.

Direct characterization of the spectral distributions and indirect characterization of the temporal distributions of the applied femtosecond laser beams at 675 -1700 nm utilizing a visible monochromator coupled with a CCD and an infrared monochromator coupled with a liquid-nitrogen-cooled InGaAs infrared detector
Unfortunately, due to limited available wavelength range of our FROG set-up, we could not perform direct measurements on the pulse-widths of utilized laser pulses at wavelengths beyond the range of 700 -1100nm (i.e., 675 and 1200-2300 nm). Based on the above verified pulse-width-bandwidth relation of The acquired optical spectra of the laser pulses at wavelength range 675 -1700 nm were displayed in Supplementary Fig. 16. Supplementary Figs 16a-q displayed the measured optical spectra at the wavelengths range from 675 -1700 nm, respectively. The negligible Ch^2 and the very close to unity R^2 at all wavelengths summarized in Supplementary Fig. 16r demonstrates the good Gaussian fitting, revealing the Gaussian spectral distribution of the laser pulses at these wavelengths. This is highly consistent with the results acquired from FROG measurements and indicates Gaussian temporal distributions at the wavelength range 675 -1700 nm, beyond the one obtained from FROG results. Due to the limitation of our experimental set-up, we could not directly measure the optical spectra at wavelength range 1800 -2300 nm.
However, since the laser pulses at wavelength range 1700 -2300 nm belong to the same idler part of the OperA Solo output, laser pulses at wavelength range 1800 -2300 nm are expected to possess similar Gaussian temporal and spectral distributions as at 1700 nm.
Supplementary Figure 16s displayed the comparison between the acquired spectral bandwidths at 700 -1100 nm by spectrometer and that obtained from the FROG measurements. The acquired spectral bandwidths at different wavelengths were summarized in Supplementary Fig. 16t. Moreover, the high consistency between the measured knife-edge scans in the x direction and y direction at all wavelengths manifested in Supplementary Figs 17a-x reveals the two-dimension Gaussian spatial distribution of the laser beams in the cross-section plane. Supplementary Fig. 17aa summarized the acquired laser beam radiuses along both x and y directions at all wavelengths. The measured laser beam radii in x-direction at all wavelengths are in good agreement with the ones measured by in y-direction with variation less than 6 %, further demonstrating that the two-dimension spatial profiles of the laser beams in the cross-sectional plane follow the Gaussian distribution. Hence, the knife edge beam scans along both the xand y-directions of cross-sectional plane of laser beams at different wavelengths validate that spatial profiles of the applied laser beams followed the Gaussian distribution.
In addition, as in Supplementary Fig. 17aa, the laser beam radius at all wavelengths are in range of (1.8

Supplementary Notes
Open-aperture Z-scan measurements for quantifying 2PA cross-sections ( 2 ) at 800 nm and 3PA

cross-sections ( 3 ) at 1050 and 1100 nm
Open-aperture Z-scan measurements 20 were conducted to quantify the  2 values (at 800 nm) of  Table   1), indicating that the Z-scan measurements in current work were appropriately conducted. On the other hand, the estimated  2 value of the CsPbBr 3 NCs at 800 nm here is about one order larger than another published value 1 (Supplementary Table 1). A plausible origin of the difference in the obtained  2 values might be the sample diversity utilized in the different measurements, as illustrated in Ref. [2]. Taking account of both the volume and the local field effects, the elucidated  2 value of the MAPbBr 3 NCs, is about three-orders of magnitude larger than the result corresponding to the recently reported 2PA coefficient of bulk MAPbBr 3 crystal 23 ( 2 corresponding to the bulk MAPbBr 3 crystal is derived based on the formula in ref. [24], with = 2.38 and = 25.5 are dielectric constants of toluene and MAPbBr 3 25 , respectively.).
Such large enhancement results from the quantum confinement effect, which has been well-documented in conventional semiconductor NCs 26,27 . Moreover, the shell coating with (OA) 2 PbBr 4 has further enhanced the mJ cm -2 further justify that MPA is responsible for the fluorescence excitation at infrared wavelengths in these NCs. Supplementary Figure 6d and Figure 1c in main text schematically illustrate the corresponding frequency-upconverted PL processes from simultaneous 2-, 3-, 4-and 5PA excitation via virtual energy levels. Photographs of frequency-upconverted PL from the NCs collected at 800, 1200, 1600, 2100 nm displayed in Supplementary Fig. 11 provide more direct evidence for the occurrence of MEPL processes. As in Supplementary Fig. 11, the core-shell MAPbBr 3 /(OA) 2 36,37 . Since there have been no report on the five-photon absorption in R6G, we only provide a qualitatively direct comparison on the five-photon excited PL photos. The unedited photos (taken with the same camera and the same exposure) displayed in Supplementary Fig. 12 show the five-photon excited PL from MAPbBr 3 /(OA) 2 PbBr 4 NCs in toluene as compared to R6G in methanol at 2100 nm femtosecond laser excitation. As in Supplementary Fig. 12, under the applied excitation conditions, no five-photon excited PL was observed from the R6G in methonal and no upconversion PL signal could be detected with our visible monochromator (Acton, Spectra Pro 2750i) coupled with CCD. In contrast, relatively bright five-photon excited PL was excited under the same experimental conditions at 2100 nm, validating the much superior five-photon absorption properties of our MAPbBr 3 /(OA) 2 PbBr 4 NCs than R6G. Moreover, R6G exhibits one-photon absorption peak at around 525nm and 2100 nm is the boundary wavelength for R6G where an admixture of contributions from both the 4PA and 5PA processes is possible. This further confirms the outstanding 5PA properties of the MAPbBr 3 /(OA) 2 PbBr 4 NCs.
Comparison between the MEPL from MAPbBr 3 , MAPbBr 3 /(OA) 2 PbBr 4 and CsPbBr 3 NCs under the same excitation fluence at 800, 1200, 1600 and 2100 nm displayed in Supplementary Fig. 7 clearly indicates the much larger MEPL in the core-shell MAPbBr 3 /(OA) 2 PbBr 4 NCs than the core-only MAPbBr 3 NCs, consistent with photos shown in Supplementary Fig. 11. CsPbBr 3 NCs with lower PLQY and smaller concentration display MEPL with similar amplitude to MAPbBr 3 NCs as presented in Supplementary Fig. 7 (under the same irradiation fluence), in accordance with photos in Supplementary Fig. 11 and demonstrating its larger MPA cross-sections. The normalized one-photon excited PL spectra and MEPL spectra of the NCs are displayed in Supplementary Fig. 10, for comparison. As illustrated, the MEPL spectra are on the red side of the one-photon excited PL. Such red-shift of the MEPL spectra with respect to one-photon counterpart has been well reported in traditional semiconductor NCs 38 and can be ascribed to the reabsorption effect and size inhomogeneity 39,40 .
We applied the MEPL measurements on the MAPbBr 3 , MAPbBr 3 /(OA) 2 PbBr 4 and CsPbBr 3 NCs at wavelengths ranging from 675 to 2300nm using the measured  2 values at 800 nm as a standard to determine their MPA cross-sections ( n ), thus acquiring the MPA spectra. Through integrating f n given by . w 0 is related to the incident laser beam waist before focal lens ′ by 41 ( ′ ), which is related to the laser wavelength  0 . f is the focal length, n is the refractive index of the air n  1. Taking account of the fact that NCs contained in 2-mm-thick quartz cuvettes were placed 3.5 cm away from focal point of the lens (beam waists at the sample point are dependent on the excitation wavelengths) and considering the spatial and temporal profiles of the laser pulses are Gaussian functions, the MEPL signal F n (n = 2, 3, 4, and 5) for 2PA, 3PA, 4PA and 5PA processes can be derived as: A similar experimental set-up to that of multi-photon excited photoluminescence measurements was utilized for the time-resolved PL measurements. Instead of using the CCD for PL detection, the one-photon-excited and multi-photon-excited PL emission were acquired by a Optronis Optoscope streak camera system, which possesses an ultimate temporal resolution of ~10 ps. Importantly, comparison between the one-photon excited PL decay traces in MAPbBr 3 and MAPbBr 3 /(OA) 2 PbBr 4 NCs displayed in