FPALM & SFS

Light acts like waves, similar to the waves in the ocean that we see at the beach. Waves posses a certain height (amplitude), with a certain number crashing on the shore every minute (frequency), and all moving at a characteristic speed across the water (the wave speed). The distance between waves is called the wavelength - waves close together (short wavelength) carry more energy than ones far apart (long wavelength). Light shares these properties - the wave speed of a light wave is simply the speed of light and different speeds of light exhibit different colors.

Historically, spectroscopy referred to the use of visible light that had been scatt prism

ered or absorbed according to it's wavelength; this was often achieved through the use of a prism (shown at right). In modern times spectroscopy has evolved to become one of the principle experimental techniques for determining the electronic structure of atoms. Sum Frequency Spectroscopy is one of several spectroscopic techniques that provide information about molecules, and their characteristics, within a sample.

Spectrometry data produce a vibrational spectra of different groups in a molecule, which equate to characteristic frequencies. Thus, the molecules in a sample can be identified by examining their vibrational spectrum and referring to a table of characteristic frequencies and intensities (below).

Infra-red spectrums, like the one above, are produced by shining a range of infra-red frequencies through a sample of an organic compound - some of the frequencies will be absorbed and others will transmit through the sample; these transmitted frequencies are read by the spectrometer and provide important information about the bonds in the compound.

In Sum Frequency Spectroscopy, a sample is exposed to 2 beams of light with known frequencies. The sample then emits light at the sum of those two frequencies, hence the name of the technique. SFS is unique from other forms of spectroscopy in that it can target a single plane within the sample and obtain the vibrational spectra of molecules from that specific interface (rather than passing through the sample as other spectroscopic techniques do).

Michael Stenner & Chris Lockheardt of MITRE.org explain linear optics and how non-linear optics differs:

The concept of linear vs. nonlinear is a mathematical one. Simply put, an effect is called linear if the response varies linearly with the input. For example, sales tax is a linear function of the amount spent. If you buy twice as much stuff, you pay twice as much tax. By contrast, income tax is nonlinear; if your income doubles, you pay more than twice as much tax. Social Security tax is also nonlinear, but in the other direction; as your income increases, your Social Security tax eventually saturates, meaning that it stops increasing. Often, nonlinear systems have a domain in which they are effectively linear, like Social Security below the tax cap.

For optical systems, the mathematical relationship in question is usually between the electric field of the light and a material's polarization—the amount that the electrons are moved around by the light. The polarization is important because as the light acts on matter and creates this polarization, matter acts back on the light. This interaction is responsible for all major optical effects, including reflection, refraction, and absorption. To behave linearly basically means that any light output from an interaction can be described as a multiple of the light input. A multiple smaller than one means absorption, larger than one means amplification, and a complex multiple means a change of phase.

When the polarization of light behaves nonlinearly with the incoming electric field, it can make for dramatic changes in the wavelength of the light. While wavelength-changing may sound mundane, the resulting effects can be profound. For example, the lasers used in green laser pointers naturally produce invisible infrared light. But by using "frequency doubling crystals" that operate on NLO principles, the lasers can efficiently convert that invisible infrared light into the green beam you observe.

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In linear optics light may be deflected but it's frequency (wavelength) remains unchanged, something un-true for non-linear optics.

Non-pulsed lasers, referred to as continuous, produce a steady output of low intensity energy. However, in the pulsed mode of operation, the output of a laser alternates between 'on' and 'off' periods. The aim is to deposit as much energy as possible at a given place in as short a time as possible. These pulses of energy occur MANY MANY times per unit time.

For instance: Pulsed lasers used in SFS output 10⁸ watts in 10^-15 second (100 femptosecond) bursts. What is a femptosecond, well it's one quadrillionth, or one billionth of one millionth of a second! A femtosecond is to a second, what a second is to about 420 million years!!!

This is important for a technique such as SFS where the probability of sum frequency occurring is incredibly low, to the order of 10^-35 to 10^-45. The more times we can expose the sample to high energy pulses, the better our chance of attaining the sum frequency emission... and producing an informative spectrum.