Cooperation is key:
Super-charging nonlinear optical processes

Nonlinear Optics: semiclassical picture

The broad category that encompasses much of my research is called Nonlinear Optics. Let me first break this title down - the study of optics, in general, is the study of light and its interaction with the world around us. Examples of everyday optical elements include lenses (like in glasses), mirrors, and prisms. The aformentioned optical elements all make use of linear optical effects - that is, the materials that make up the elements respond in a way that is just proprotional to the incident light. A useful example of something that has a linear response is a spring: the farther you stretch a spring, the harder it is to continue stretching it - this is because the response of the spring is linearly proportional to the distance that it is stretched.

Examples of linear optical processes
Diffraction (aperture)
Reflection (mirror)
Refraction (lens)
Dispersion (prism)

In the context of optics, this analogy follows straightfowardly - the atoms that make up matter can be thought of as masses on a spring. The heavy, positively-charged nucleus of the atom is like the fixed end of the spring, and the light, negatively-charged electron is like moveable end of the spring. When light, which is made up of a combination of electric and magnetic fields that vary sinusoidally in time, is incident on an atom, it acts to push/pull the electron toward/away from the nucleus. In the regime of linear optics, just like in the case of the spring, the amount that the electron is pulled or pushed is just proportional to the strength of the electric field of the light. This gives rise to oscillatory motion of the electron that occurs at exactly the same frequency of the light wave that is driving it. Because the color of light is just a description of the frequency at which the electromagnetic wave oscillates, this means that the color of the light radiated by the atom will be exactly the same as the incident light. Thus, linear optical elements can modify some of the characteristics of an incident light beam (like the direction of propagation for a mirror or shape for a lens), but the color of the light remains unchanged.


Example of nonlinear optical process
Image showing second harmonic generation (SHG) - red light interacts with the crystal to give rise to purple light. In this process, two red photons effectively combine to give rise to one purple photon.

Now, to go beyond linear interactions, we can again return to the spring analogy. There is a point (known as the yield point) after which the spring no longer stretches an amount that varies linearly with the applied force. Any response such as this that is not proportional to the applied cause is called a nonlinear response. Therefore, nonlinear optics refers to any situation where a beam of light causes an atom to respond in a nonlinear way. One example of a nonlinear optical response is one in which the light of one color (or frequency) is incident upon an atom, which then oscillates at a different frequency and gives rise to light of a different color (see the above picture).