Multi-dimensional Spectroscopy: A brief intro

Alexander,

Some days I call myself a spectroscopist—a scientist whose primary tool is light. When I think of light, I think of it as an electromagnetic wave—I’ll call it an electric field from now on. In lab I use electric fields to tickle samples. But I don’t just use one field, I use many fields. In my lab these fields are laser beams.

I would like to give you a sweeping overview of what my lab does. To do this, I first need to give you a bit of perspective/context. I expect this post to merely whet your appetite. In the future I plan to write about more specialized topics which have to do with my research (like your request of explaining detection strategies: homodyne vs. heterodyne, or how you can do frequency or time domain measurements).

In days of old the predominant type of spectroscopy was vanilla absorption/reflection/transmission spectroscopy. Light from a source, like a tungsten lamp, is shone on a sample. The amount of light both incident on the sample and reflected off of (transmitted through) the sample is quantified. A mathematical metric is then used to define the reflectance (transmittance) spectrum. Different colors of light interact differently with the same sample. So, a spectrum of intensity vs. incident color can give information about a sample. In general chemistry labs which I have taught, students use absorption spectroscopy to find the concentration of metal ions in solutions, and monitor the progression of a reaction. It is fun to note that the human eye works by observing the light transmitted and reflected off of surfaces and then spectrally resolving that light to give us information about our surroundings. In other words, the human eye/brain uses vanilla absorption/reflection/transmission spectroscopy to interrogate the world.

My lab specializes in multi-dimensional spectroscopy. This is in contrast to 1-dimensional spectroscopy like the spectroscopy outlined in the previous paragraph. There are many ways for a spectroscopy to colloquially be called multi-dimensional, but the most common definition requires the spectroscopy to entail the usage of at least two different colors of electric fields. These interrogating fields can be scanned in their color. Information is then represented as 2D plots of color_1 vs. color_2 with some measured intensity as a z-axis which is generally represented as a heat map. There is another way for a spectroscopy to be multi-dimensional. You can have multiple electric fields which are pulses in time (they can be the same color). You can then change the amount of time present between each pulse. Information is then represented as 2D plots of color vs. delay_time with some measured intensity as a z-axis which is generally represented as a heat map. My lab uses both of these types tricks to do our spectroscopies.

Alexander, I presume you are currently furious with me! I have introduced complexity without telling you why. Why should I go through the effort of having multiple colors of laser pulses and then change their time delays? The traditional answer: because the world is so complex and interesting that vanilla 1D spectroscopy can’t begin to tell us everything about a sample. A more nuanced answer divides the rational into multiple categories.

Some people do multi-dimensional spectroscopy because the extra dimensionality allows them to understand the ground state[footnote: By the ground state, I mean the unexcited and not perturbed system] of complex systems which have 1D spectra which are impossible to interpret due to “spectral congestion”. Spectral congestion is just a fancy word for a system having lots of things giving response at a particular color so that you don’t know what individual things are giving you response. Multi-dimensional spectroscopy can then allow someone to quantify an individual component’s response by providing additional spectral selectivity (the mechanism for how this works is interesting, important, and of no consequence currently). When people want to use spectroscopy to understand the ground state of a system, they are generally interested in the structure of the ground state or the amount of a component in a sample.

Other people do multi-dimensional spectroscopy because they want to know what the excited state(s) of a system looks like. They use the first (or more) electric field(s) to build an excited state and the second (or more) electric field(s) to interrogate the newly created excited state. The spectroscopist can then ask the simple question of “what is the spectra of the excited state?” This can give information about the structure of the excited state, but the spectroscopist can also ask how the spectra of the excited state changes as a function of time.

My group does multi-dimensional spectroscopy for both of the outlined reasons. We also do spectroscopies which entail accomplishing three plus dimensioned scans were we scan pump color, probe color, and the time delay between them (and even more dimensions). Broadly, I am interested in how certain semiconductors respond to having light shined on them. If I am interested in what happens the direct instant after excitation then I need to use a spectroscopy of the first type—I need to know the electronic structure of the semiconductor. Conversely, if I am interested in thinking about how charge flows through a semiconductor as function of time, this is a question the second type of spectroscopy can answer.

In general, as a spectroscopy becomes more intricate, it can be used to unravel more complicated puzzles. This is a direct analog to what you know about multi-dimensional NMR. Scientists build intricate pulse sequences to hash out certain solvent effects on particular atoms in a sample. Optical spectroscopists build time orderings, phase-matchings, and frequencies of electric fields to work in an ensemble to hash out a complicated puzzle.

I would like to offer a word of caution. I don’t want you (or others) to think “simple” or “old” measurements like 1D absorbance are not useful or interesting. A wealth of information is buried in an absorbance spectrum. Moreover, it is not trivial to get a good absorbance spectrum on non-traditional samples like semiconductor thin-films (what I work with). Single-dimension and multi-dimensioned spectroscopies all give important and complementary information about a sample. They are all tools in the scientist’s toolbox that she can use to unravel a complex system.

I hope you have had a wonderful start to a prime year.

Darien