Quantum Optics III: Raman Spectroscopy

Let’s start by talking about molecules. We can think of them as being built of tiny balls attached to each other by tiny springs:


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Molecules vibrate at certain frequencies determined by their spring strength and structure.

When I talked about lasers, I told you that light interacted with atoms via absorption, stimulated emission, or spontaneous emission. Unintentionally, I totally neglected to mention scattering. Scattering is an entirely different beast, and if you’ve taken a quantum mechanics class that covers scattering, you know those problems are pretty much the worst. But we’ll make it through this lesson easily, promise.


There is elastic (also called Rayleigh) scattering, where the photon simply changes directions without losing energy, and there is inelastic scattering. Raman scattering is inelastic: the scattered photons have different energies than the incident photons.


So a photon acts like wave, yes? And you probably know that the energy of a photon, E, is related to its frequency, f, by the simple relationship:

E=hf (1)

Where h is Planck’s constant (=6.626E-34 J*s). I don’t like these variables so we’re going to divide h by 2π and multiply f by 2π to get angular frequency and write:

E=ħω (2)

So much better.


Here comes some math... after the mixed response from last week's blog, I'm going to spoiler the math and you can read the derivation if you want (it's just simple algebra this week, so try!) or you can just take the final result at face value.

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Then with the help of trig, we can simplify this to:

μ=C1*cos(ωvib*t)+C2*{cos((ω0-ωvib)*t)+cos((ω0+ωvib)*t)} (8)

with more C's we don't care much about...


So we see that there are 3 cosine terms with 3 different frequencies. ω0 is just the frequency of the electric field; this corresponds to Rayleigh scattering. The photon just bounces back with the same energy it started with.

There are also 2 shifted frequencies, these correspond to Raman scattering. The blue shifted term (ω0+ωvib) is called anti-Stokes scattering and the red shifted (ω0-ωvib) is called Stokes scattering.


You can also think of this in terms of the Doppler Effect, the thing that causes the frequency of sound to change as something is traveling toward and away from you. The molecule oscillates toward and away from your light source, causing the shifts in the observed frequencies.


So that’s what Raman scattering is. The scattered light can be detected using a CCD hooked up to a spectrometer, and we’ll get something like this:


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Pretty complicated, huh? People who want a Ph.D. in molecular dynamics or quantum chemistry can calculate spectra like this by having a very good understanding of the molecular structure. I am not one of these people, so don’t ask how, haha. Theory combined with experiments performed over the course of several decades has allowed us to build a pretty decent database of what each of these peaks is for.


Raman spectra are essentially molecular signatures. Every molecule vibrates in a very unique way, and by looking at the Raman spectrum we can say exactly what molecule we’re looking at. Raman spectroscopy is a method that compliments techniques such as mass spectroscopy, NMR, fluorescence spectroscopy, etc. The advantage of Raman is its sensitivity, robustness, and the fact that it is non-invasive and non-destructive. We use low enough powers that we can look at sensitive living cells without compromising their health. You can’t do NMR or MS on a biological cell and keep everything intact. You could do fluorescence, but then you have to add dyes to the cell that can affect its behavior or even kill it.


There are lots and lots of variations of Raman spectroscopy, each have their own advantage. The stuff explained above is spontaneous Raman scattering. We shine light on a sample and some (actually, very few) molecules will Raman scatter light back at us.

My favorite variation is CARS (coherent anti-Stokes Raman scattering). We use 3 femtosecond pulsed lasers. 2 of them “prepare” the sample. The wavelengths are chosen carefully so that they get all of the molecules in a sample to vibrate together, then the 3rd pulse “probes” the sample to see what’s going on, and the signal we receive comes from manyyy of the molecules. This signal is many orders of magnitude larger than that from spontaneous Raman,


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Even better is something called FAST-CARS. It’s extremely tricky to do experimentally, but the basic idea is this:

CARS uses 2 laser pulses to prepare the sample. This is pretty good, but there are usually a lot of vibrational modes in big molecules, and CARS will only excite a few of them. FAST CARS (femtosecond adaptive spectroscopic techniques via CARS) uses laser pulses to “sing a melody” to the molecules. If the musical notes are resonant with the vibrational “notes” of the molecule, they will sing back in unison. This creates a very big signal that is easy to detect in fractions of a microsecond. This is what our lab used to detect anthrax: click!.


Raman can be used in microscopy as well; we scan the lasers across a sample and collect a spectrum for every pixel and can create images like this:

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The applications of Raman spectroscopy are limitless. Every day we’re developing better methods for enhancing the Raman signal and making cheaper and smaller systems so you can do Raman anywhere and everywhere. We have a handheld Raman spectrometer that my boss likes taking to his ranch to shine at crops to evaluate plant health. Biomedical researchers use Raman in endoscope form to look for cancer. It’s a beautifully powerful technique that will only improve with time.