To understand what nonlinear optics is, we first need to consider linear optics. Linear optics relates to all optical phenomena in which
the energy (or color) of the radiation does not change. The momentum of the photons is allowed to change, that is - the direction of propagation.
Here we can consider diffraction, refraction and reflection. For all of these, the light field that is generated in a material has an amplitude which
is proportional to the amplitude of the exciting radiation. We say that the generated light field is linearly dependent on the exciting light.
Now, in general nature is nonlinear. The assumption in linear optics that the generated field is linearly dependent on the exciting field is only an approximation.
There are always some other terms (new colors) that are being excited with a nonlinear dependence on the excitation. However, normally these terms are very weak such that the
approximation for linear optics is justified. With the advent of the laser these nonlinear terms could be made strong enough to be observed and used.
Another important difference from linear optics is that in linear optics
we always assume that different light beams do not interact - they can pass through each other in vacuum and within some material without the one changing the other. This is no longer true
in nonlinear optics, where different light beams can be "mixed" - changing each other and other generated radiation inside the material.
In regular nonlinear optics the exciting radiation is strong enough to generate significant nonlinear effects. Still,
if we compare the amount of force this radiation exerts on the electrons inside a material, they are quite small compared to the binding forces these electrons are subject to
by the protons of the material. Thus, we regard the nonlinear terms as some small perturbation of the overall linear response.
In extreme nonlinear optics the exciting radiation is much stronger than in regular nonlinear optics. The forces exerted by the radiation are as strong as the binding forces acting on the electrons.
Because of that, extreme nonlinear optics is a violent interaction - destroying the material that excites new radiation components. So, in
experiments of extreme nonlinear optics, the medium needs to be replenished all the time. However, what we gain from such an extreme nonlinear optics
is the ability to combine together hundreds of photons of the exciting radiation to generate X-ray laser light! Also, the physics is
quite interesting.
Ultrafast optics deals with the generation, manipulation and applications of laser pulses whose time duration is on the order of 1E-15 seconds (femtoseconds). Such short pulses are interesting due to two main reasons. The first, the energy of the laser pulse is constrained within a very short period which leads to very high peak intensities, so that nonlinear optics and extreme nonlinear optics phenomena are ubiquitous in ultrafast optics. The second interest is due to the fact that chemical reactions occur on femtosecond time scales and so ultrafast optics can be used to measure and control such reactions in real time. Furthermore, in the last decade ultrafast optics gave rise to even shorter laser pulses measuring in 1E-18 seconds (attoseconds), which is the natural time scale in which an electron evolves within an atom or a molecule, and so real time measurements and control of electronic processes were finally made possible. Electronic processes are important as they are responsible for the physics that governs our life - all of chemistry and biology is electronic in nature.
Nanophotnics deals with the interaction of light with matter on sub-wavelength scales. A major thrust of this field is the construction of optically-engineered devices, fabricated with nanometer resolution. Metallic nano-structures are known to facilitate a phenomenon known as nano-focusing: the focusing of electric fields into nanometric volumes. This extreme focusing leads to very large enhancements in the intensities of light fields, which makes it a very useful tool for nonlinear optics.