From 357568e1fb77afed9dfa203e62da237bf7ce51b3 Mon Sep 17 00:00:00 2001
From: Blaise Thompson <blaise@untzag.com>
Date: Mon, 9 Apr 2018 00:24:18 -0500
Subject: 2018-04-09 00:24

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+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.
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