From 357568e1fb77afed9dfa203e62da237bf7ce51b3 Mon Sep 17 00:00:00 2001 From: Blaise Thompson Date: Mon, 9 Apr 2018 00:24:18 -0500 Subject: 2018-04-09 00:24 --- PbSe_global_analysis/introduction.tex | 50 +++++++++++++++++++++++++++++++++++ 1 file changed, 50 insertions(+) create mode 100644 PbSe_global_analysis/introduction.tex (limited to 'PbSe_global_analysis/introduction.tex') diff --git a/PbSe_global_analysis/introduction.tex b/PbSe_global_analysis/introduction.tex new file mode 100644 index 0000000..4fd37cb --- /dev/null +++ b/PbSe_global_analysis/introduction.tex @@ -0,0 +1,50 @@ +Lead chalcogenide nanocrystals are among the simplest manifestations of quantum confinement\cite{Wise2000} and provide a foundation for the rational design of nano-engineered photovoltaic materials. +The time and frequency resolution capabilities of the different types of ultrafast pump-probe methods have provided the most detailed understanding of quantum dot (QD) photophysics. +Transient absorption (TA) studies have dominated the literature. +In a typical TA experiment, the pump pulse induces a change in the transmission of the medium that is measured by a subsequent probe pulse. +The change in transmission is described by the change in the dissipative (imaginary) part of the complex refractive index, which is linked to the dynamics and structure of photoexcited species. +TA does not provide information on the real-valued refractive index changes. +Although the real component is less important for photovoltaic performance, it is an equal indicator of underlying structure and dynamics. +In practice, having both real and imaginary components is often helpful. +For example, the fully-phased response is crucial for correctly interpreting spectroscopy when interfaces are important, which is common in evaluation of materials.\cite{Price2015,Yang2015,Yang2017} +The real and imaginary responses are directly related by the Kramers-Kronig relation, but it is experimentally difficult to measure the ultrafast response over the range of frequencies required for a Hilbert transform. +Interferometric methods, such as two-dimensional eletronic spectroscopy (2DES), can resolve both components, but they are demanding methods and not commonly used. +% note that they often use TA to phase spectra + +Transient grating (TG) is a pump-probe method closely related to TA. +Figures \ref{fig:tg_vs_ta} illustrates both methods. +In TG, two pulsed and independently tunable excitation fields, $E_1$ and $E_2$, are incident on a sample. +The TG experiment modulates the optical properties of the sample by creating a population grating from the interference between the two crossed beams, $E_2$ and $E_{2^\prime}$. +The grating diffracts the $E_1$ probe field into a new direction defined by the phase matching condition $\vec{k}_{\text{sig}} = \vec{k}_1 - \vec{k}_2 + \vec{k}_{2^\prime}$. +In contrast, the TA experiment creates a spatially uniform excited population, but temporally modulates the ground and excited state populations with a chopper. +TA can be seen as a special case of a TG experiment in which the grating fringes +become infinitely spaced ($\vec{k}_2-\vec{k}_{2^\prime} \rightarrow \vec{0}$) +and, instead of being diffracted, the nonlinear field overlaps and interferes with the probe beam. +% BJT: we might consider introducing TA first, since it is more familiar + +\begin{figure} + \includegraphics[width=\linewidth]{"tg vs ta"} + \caption{The similarities between transient grating and transient absorption measurements. + Both signals are derived from creating a population difference in the sample. + (a) A transient grating experiment crosses two pump beams of the same optical frequency ($E_2$, $E_{2^\prime}$) to create an intensity grating roughly perpendicular to the direction of propagation. + (b) The intensity grating consequently spatially modulates the balance of ground state and excited state in the sample. + The probe beam ($E_1$) is diffracted, and the diffracted intensity is measured. + In transient absorption (c), the probe creates a monolithic population difference, which changes the attenuation the probe beam experiences through the sample. + (d) The pump is modulated by a chopper, which facilitates measurement of the population difference.} + \label{fig:tg_vs_ta} +\end{figure} + +Like TA, TG does not fully characterize the non-linear response. +Both imaginary and real parts of the refractive index spatially modulate in the TG experiment. +The diffracted probe is sensitive only to the total grating contrast (the response \textit{amplitude}), and not the phase relationships of the grating. +Since both techniques are sensitive to different components of the non-linear response, however, the combination of both TA and TG can solve the fully-phased response. +%A local oscillator beam can act as a phase-sensitive reference and is often used to provide that resolution in time-domain techniques. +%In this paper, we demonstrate that one can discern the complete, fully-phased optically-induced refractive from frequency domain techniques. + +Here we report the results of dual 2DTA-2DTG experiments of PbSe quantum dots at the 1S exciton transition. +We explore the three-dimensional experimental space of pump color, probe color, and population delay time. +We define the important experimental factors that must be taken into account for accurate comparison of the two methods. +We show that both methods exhibit reproducible spectra across different batches of different exciton sizes. +Finally, we show that the methods can be used to construct a phased third-order response spectrum. Both experiments can be reproduced via simulations using the standard theory of PbSe excitons. +Interestingly, the combined information reveals broadband contributions to the quantum dots non-linearity, barely distinguishable with transient absorption spectra alone. +This work demonstrates TG and TA serve as complementary methods for the study of exciton structure and dynamics. -- cgit v1.2.3