In Radar concept the SAR-Synthetic Aperture radar performs as side-looking to collect information, why it is not downlooking? There are down-looking radar also. So what are the differences between them
A radar measures the time of arrival of the backscattered signal to infer the distance between the target and the platform (satellite, aircraft, whatever). If two targets are at the same distance from the platform, one on the left and one on the right because the platform is looking down, then their signals will arrive at the same time, making them impossible to distinguish. Looking sideways removes this ambiguity. Look at this figure from the Center for Space Research of the University of Texas (there is also a text explanation in the link).
Both down-looking and side looking radar look down.
Down-looking radar illuminates terrain forward and below the aircraft to detect targets on or near the ground. Stationary targets would be lost among the ground clutter, but moving targets on or near the ground can be separated by their doppler shift. Software eliminates the background clutter and leaves only small objects with a doppler shift displayed on the screen. These objects will be vehicles or low flying aircraft, which is what the fighter pilot is looking for.
Side-looking radar scans a wide swathe of land below and to one side of the aircraft, usually for mapping purposes, rather like side-scan sonar maps the ocean floor.