According to the previous handout provided by ESA Echos in Space Course. The cross-polarization principle of SAR imaging says there’s an option to transmit vertically polarized echos and receive horizontally polarized echos or vice versa. Is it possible that vertically polarized light can be reflected horizontally polarized

The polarization referes to the direction of the electric field of a light wave which is to be one direction. The unpolarized light interacts with a material in various ways such as reflection, scattering, refraction. and each of which can transform an unpolarized light into a vertically or horizontally polarized light with respect to the plane of the material. In co-polarization SAR images, there are certain features that appear VV vertically sent and vertically received images , and other features only appear in HH horizontally sent horizontally received images. Then why the need for cross-polarization systems VH, HV. How can a radar antenna that is adjusted to a vertical polarization axis receive hortizontally polarized reflected echos? How is it even possible for the direction of the electric field to change 45 degrees upon interaction with a certain material.If possible, how come if the surface is rough and depolarizes incident light (or if a bulk media is turbid and scatters light), cross-polarization measurements can quantify how much depolarization is happening? Does light repolarization from H to V or vice versa, indicate the nature of the geometry of the scatterer material?

Edit by @ABraun: I removed the handout because of copyright reasons, please register to access it:

The target interacts with the radar pulse and affects the polarisation of the backscattered pulse. For example volume scattering in vegetation canopies frequently produces relatively strong cross-polarised returns even if only co-polarised pulses were transmitted by the radar.

I do appreciate your response
Does the scattering mechanism affect the polarization of the back scattered light ?
Does the back scattering cross-section of either co-pol. or cross-pol. give any clues about the nature of the scatterer material, geometry, roughness, or its the intrinsic properties such as humidity, moisture salinity or medium density? If so, how?

The short answer is: yes.

I’m afraid you will have to study active microwave remote sensing at some depth as there are no simple answers to your question.