(271j) Formalized Statistical Determination of Electronic Transition Alignments in Nanomaterials from Back Focal Plane Imaging for Improved Accuracy and Precision

Next-generation photonic devices require unprecedented control and understanding of optoelectronic properties of photonic materials. Increasingly, the need to finely control the emission of fluorescent materials and understand their optoelectronic behavior on a quantum level demands more accurate and precise characterization of the transition dipole moment (orientation of the average electron transition) for nanomaterials, especially with new-wave materials such as cesium lead halide nanocrystals, which show remarkable transition dipole moment tunability and extraordinary quantum optic phenomena [1], [2]. Knowing this transition dipole moment angle and its associated uncertainty is of paramount importance for optoelectronic devices; for example, the potential external quantum efficiency of an LED changes from 25.8% to 31.7% for transition dipole moment angles of 35.26° and 14°, respectively [2]. This work provides new statistical methods to improve the precision and accuracy of transition dipole moment measurements and provides a new framework for transient momentum-resolved imaging to allow decoupling of the radiative lifetimes of each component vector of the transition dipole moment.

Back focal plane imaging, also known as momentum imaging, involves focusing the back focal plane of an infinity-corrected objective onto an image sensor, enabling direct observation of the light emission intensity as a function of angle. This angular emission pattern can then be used to extract the average electronic transition dipole moment [3], [4]. While this approach has been used in literature [2], [5], [6], most reports neglect to describe the accuracy and precision to which the angular emission spectrum can be fit to the transition dipole moment angle. The observed angular emission pattern with back focal plane imaging has an inherent uncertainty with respect to the accuracy of the fit transition dipole moment angle [7]. In this work, we show that because the angular emission at momentum vectors do not vary linearly with the transition dipole moment angle, traditional fitting methods do not guarantee best-fit results or accurate standard errors. We apply improved statistical methods to characterize the goodness of fit for calculating the transition dipole moment angle from angular emission data and guidelines to calculate the confidence intervals of a given fit. We demonstrate how the uncertainty is broadened when various additional parameters of the fit are unknown, such as in films of unknown refractive index and thickness [8].

Using these capabilities, we show microscopy and statistical methods that improve the accuracy and precision of transition dipole moment angle observations from angular emission data. Finally, we present a method for performing time-resolved back focal plane imaging, allowing direct measurement of the radiative lifetimes of each component of the transition dipole moment by measuring the back focal plane image transiently using a time-resolved photoluminescence setup. Through this work, we aim to support existing research on photonic materials, both for understanding the transition dipole moment of fluorescent emitters and for the design of high-efficiency, next-generation optoelectronic devices.

References:

[1] M. J. Jurow et al., “Tunable Anisotropic Photon Emission from Self-Organized CsPbBr3 Perovskite Nanocrystals,” Nano Lett., vol. 17, no. 7, pp. 4534–4540, Jul. 2017, doi: 10.1021/acs.nanolett.7b02147.

[2] M. J. Jurow et al., “Manipulating the Transition Dipole Moment of CsPbBr3 Perovskite Nanocrystals for Superior Optical Properties,” Nano Lett., vol. 19, no. 4, pp. 2489–2496, Apr. 2019, doi: 10.1021/acs.nanolett.9b00122.

[3] J. A. Kurvits, M. Jiang, and R. Zia, “Comparative analysis of imaging configurations and objectives for Fourier microscopy,” JOSA A, vol. 32, no. 11, pp. 2082–2092, Nov. 2015, doi: 10.1364/JOSAA.32.002082.

[4] M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” JOSA B, vol. 21, no. 6, pp. 1210–1215, Jun. 2004, doi: 10.1364/JOSAB.21.001210.

[5] Y. Gao, M. C. Weidman, and W. A. Tisdale, “CdSe Nanoplatelet Films with Controlled Orientation of their Transition Dipole Moment,” Nano Lett., vol. 17, no. 6, pp. 3837–3843, Jun. 2017, doi: 10.1021/acs.nanolett.7b01237.

[6] J. A. Schuller et al., “Orientation of luminescent excitons in layered nanomaterials,” Nat. Nanotechnol., vol. 8, no. 4, pp. 271–276, Apr. 2013, doi: 10.1038/nnano.2013.20.

[7] T. T. Lin, “Analysis of the Transition Dipole Moment Orientation from Nanoparticles,” UCLA, 2021. Accessed: Mar. 26, 2024. [Online]. Available: https://escholarship.org/uc/item/84r7j6hg

[8] W. H. Press, Ed., Numerical recipes in C. Book: C version / William H. Press, Reprinted. Cambridge: Cambridge Univ. Pr, 1991.

Figure 1: a. Schematic of transition dipole moment as a function of nanocrystal size. b-e. Back focal plane image as a function of transition dipole moment angle (14°, 35.26°, 70°, 85°). f. Back focal plane image fit to experimental data using the minimum method. g. Back focal plane image fit to experimental data using the minimum method with weighting.