dependence of Intensity on penetration of light
In general, when light penetrates a material (water for example) its intensity decreases exponentially with increasing depth. This process is known as attenuation or absorption. The severity of attenuation differs with the wavelength of electromagnetic radiation. In the region of visible light, the red part of the spectrum attenuates more rapidly than the shorter-wavelength blue part.

But what you are asking about is a non-linear optical property known under the name: Saturable absorption It is a property of materials where the absorption of light decreases with increasing light intensity. At sufficiently high incident light intensity, atoms in the ground state of a saturable absorber material become excited into an upper energy state at such a rate that there is insufficient time for them to decay back to the ground state before the ground state becomes depleted, and the absorption subsequently saturates. The material becomes transparent at that wavelength. Saturable absorbers are useful in laser cavities.

Another kind  of non-linear materials is known under the name "optical power limiting materials". In these materials the absorption of light increases with intensity such that beyond a certain input intensity the output intensity approaches a constant value. Such a material can be used to limit the amount of optical power entering a system. This can be used to protect expensive or sensitive equipment such as sensors, can be used in protective goggles, or can be used to control noise in laser beams.

For more details, please see: http://en.wikipedia.org/wiki/Saturable_absorption
and http://en.wikipedia.org/wiki/Two-photon_absorption