If the amplitude distribution is given how can we calculate the total energy?
If the field amplitude is known, then get the intensityfrom |E(x,y)^2|. Now, you need to integrate this over x and y, times dx dy, to have the power transferred. Energy is this power integrated over time (if stable then simply maultiplied by time). If you relate to pulses then their energy content is the integration over time. Can also be obtai ned from dividing average power by the pulse frequency rate...
Power=0.9E/t, where E is the energy recorded by energy meter and t is pulse duration of the laser beam.
Dear Yariv Shamir
Thank you for your answer. I have a doubt about the units of the intensity that we can calculate using field amplitude. is it power/m2 or power/Sr ( power per unit solid angle)?
It is W/m2, otherwise integration over dx dy would not yield power, but rather power times area - meaningless. The W/str is a partial measure of irradiance (lacks the area in the denominator), not sure what can be yielded out of this...
Note: in your problem, a field was given, i.e. I assume E=Volt/meter. applying |E|2 yields W/m2...