Problem 4: (15 marks) Here we consider a Gaussian beam. We define the total power P(z) carried by a Gaussian beam at pos

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Problem 4 15 Marks Here We Consider A Gaussian Beam We Define The Total Power P Z Carried By A Gaussian Beam At Pos 1 (130.66 KiB) Viewed 29 times

Problem 4: (15 marks) Here we consider a Gaussian beam. We define the total power P(z) carried by a Gaussian beam at position z along the direction of propagation by the integral of the intensity I over a transverse plane, i.e. P(z) = SS dAI (p, z), transverse plane where dA denotes an infinitesimal surface element. We use the polar coordinates (p,0) for the transverse plane. 1) Recall the expression of the intensity of a Gaussian beam. 2) Expressing the infinitesimal surface element dA in polar coordinates, show that the total power (4) can be written as P(z) = 2π + f dpp1(p, z). (5) 3) Compute P(z).