Dear Aamir

Consider you have a system (atomic, molecular or periodic). It has electron density, a cloud of negative charge. This density can be polarized (may deform from an initial state) under the incidence of an electric field, let's say, if your system is between a pair of plate electrodes with opposite charge.

The total polarization P(E) for this system, as a function of the incident electric field, can be described as 

P(E) = m0 + alpha*E + beta*E^2 + gamma*E^3 + ...

where m0 is the ground state dipole (the intrinsic polarization of your system in the absence of an external field)

Alpha is the polarizability (or linear response) of your system to the incident field.

Beta and gamma are the first and second hyperpolarizabilities, i. e. the quadratic and cubic response of your system to the external field... and so on.

These coefficients are unique for every system, and highly polarizable electron density may display a strong nonlinear response. Conjugated pi systems, push-pull compounds, quadrupolar and octupolar molecules are some examples.

Of course... response may be large (and useful) if the incoming field is very intense, too!

If your field comes from a laser, you probably will use short laser pulses. In very short pulses, the associated electric field can be strong enough to manifest even in systems with small hyperpolarizabilities.

Hope this helps.

Best regards

Mauricio

Dear Aamir! If You wont to look nonlinear interaction of light with some  substances ask your friends who has Q-switch Nd3+- laser to  make with You following experiments (or one of them):

1) Take a short focusing lens and  direct to it laser beam. Without lens beam pass free and You see nothing. With lens You will see creation of bright white point-like discharge that result due to many photon absorption and air ionization. It is eye observed impressive experiment from nonlinear optics.

2) Second  eye observed experiment  You can do if You take small sized crystal powder of dye- Brilliant green and locate it between 2 glass  plates so to direct on it laser beam. When unseen Nd-laser beam 1064nm illuminate spot on dyes the spot will emit green light 532nm in all directions because small dye  crystals are  oriented randomly and every one generate  second harmonic of  incident light. But You must be quite careful against accidental reflected beam of very intensive light from Nd-laser in your eyes. I send  You my  old work with similar  experiments to find efficient substances  for  second harmonic generation. If You make less intensity of Your laser no one  of described results You will observe.

It would be enough for You at the start. And I wish You any success.

Article Second harmonic generation of a neodymium laser by crystalli...

in the presence of low intensity excitation molecules/atoms interact to the photons individually and the optical properties will depends on the material characteristics. this is what we will study in the linear optics. when the excited intensity is high intensity (means it is sufficient to change the dielectric constant ) then the molecules simultaneously interact with more than one photon and therefore the optical properties not only on material but also they are depends on the incident light intensity and this study comes under nonlinear optics.

for precise answer I can give the definition of nonlinear optics is

Def: At sufficient high intensity light-matter interaction, the optical response of the material to the interacting optical field depends in the nonlinear manner on optical field and it is called as nonlinear optical phenomenon. 

there are so many nonlinear phenomena are there like harmonic generation, non linearity in absorption, refraction and scattering etc. what kind of kind of nonlinear phenomenon we are observing in a material is depends on the material and laser intrinsic properties.

for more understand you can read this book

Sutherland, R.L., 2003. Handbook of nonlinear optics. CRC press.

nonlinear processes

Optical Kerr effect, intensity dependent refractive index (a effect)

Self-focusing, an effect due to the Optical Kerr effect (and possibly higher order nonlinearities) caused by the spatial variation in the intensity creating a spatial variation in the refractive index

Kerr-lens modelocking (KLM), the use of Self-focusing as a mechanism to mode lock laser.

Self-phase modulation (SPM), an effect due to the Optical Kerr effect (and possibly higher order nonlinearities) caused by the temporal variation in the intensity creating a temporal variation in the refractive index

Optical solitons, An equilibrium solution for either an optical pulse (temporal soliton) or Spatial mode (spatial soliton) that does not change during propagation due to a balance between dispersion and the Kerr effect (e.g. Self-phase modulation for temporal and Self-focusing for spatial solitons).

Cross-phase modulation (XPM) where one wavelength of light can affect the phase of another wavelength of light through the optical Kerr effect.

Four-wave mixing (FWM), can also arise from other nonlinearities

Cross-polarized wave generation (XPW), a effect in which a wave with polarization vector perpendicular to the input one is generated

Modulational instability

Raman amplification Optical phase conjugation

Stimulated Brillouin scattering, interaction of photons with acoustic phonons

Multi-photon absorption, simultaneous absorption of two or more photons, transferring the energy to a single electron

Multiple photoionisation, near-simultaneous removal of many bound electrons by one photon

Chaos in Optical Systems

Related processes

In these processes, the medium has a linear response to the light, but the properties of the medium are affected by other causes:

Pockels effect, the refractive index is affected by a static electric field; used in electro-optic modulators;

Acousto-optics, the refractive index is affected by acoustic waves (ultrasound); used in acousto-optic modulators.

Raman scattering, interaction of photons with optical phonons;

for more understand you can read this book

Nonlinear Optical Properties of Materials

Authors: Ganeev, Rashid A.

Non-linear properties is indeed a rather broad definition. In general, on quantum level it means that polarization in the material depends on electric (or electromagnetic) field to a power greater than one.

P=X1*E+X2*E^2+X3*E^3+.....

Here P is polarization and coefficients X1, X2 ... are polarizabilities of diferent  orders

For instance the very refractive index is a result of LINEAR polarizability (X1), namely the polarization generated in the material by external EM field to the first power.

Second harmonic generation (SHG) is a second order process (depends on X2). Keeping in mind that P and E are vectors, it is easy to see that only materials with no inversion symmetry can posses X2. 

X3 is responsible for Four-Wave-Mixing processes as: nonlinear refractive index, Kerr effect, coherent Raman and  coherent Rayleigh scatterings,  third harmonic generation and many other exciting effects (i.e. self phase modulation, soliton formation, etc). Since there are little constrains on symmetry of particles, the X3 is in many cases the dominant nonlinearity in the system (unless special crystals are used for high X2).

So the very top level answer to your question is the "he cause/origin of non linearity or non linear behavior in materials" is the structure of quantum states and symmetry of the system, but that is a good answer to about anything :)

There is a great book by R. Boyed giving a comprehensive view on nonliner optics. Another, less reader friendly book is by S. Mukamel, I would recommend reading these two to get somewhat more familiar with the topic.

(also good one is by Shen Y. R.)

Good Luck

thanks