Figure A.1: Illustrating the E and B fields and the k vector of a plane electromagnetic wave.
In this section we study some general properties of plane electromagnetic waves,
illustrated in Figure A.1. Substituting Eq. (A.10a) into the first Maxwell equation, Eq.
(A.1a), yields
where we used the notation E 0 = (E x , 0 , E y , 0 , E z,0 ). In a similar manner, by substituting Eq.
(A.10b) into the first Maxwell equation, Eq. (A.1c), we obtain
Thus, neither the electric nor the magnetic fields have components in the propagation
direction but only components perpendicular to the propagation direction (the x and y
directions in our case).
Without loss of generality we now assume that the electric field only has an x
component, E 0 = (E x , 0 , 0 0). Substituting this electric field into the left-hand side of the
second Maxwell equation, Eq. (A.1b), yields
The right-hand side of Eq. (A.1b) yields
In this section we study some general properties of plane electromagnetic waves,
illustrated in Figure A.1. Substituting Eq. (A.10a) into the first Maxwell equation, Eq.
(A.1a), yields
where we used the notation E 0 = (E x , 0 , E y , 0 , E z,0 ). In a similar manner, by substituting Eq.
(A.10b) into the first Maxwell equation, Eq. (A.1c), we obtain
Thus, neither the electric nor the magnetic fields have components in the propagation
direction but only components perpendicular to the propagation direction (the x and y
directions in our case).
Without loss of generality we now assume that the electric field only has an x
component, E 0 = (E x , 0 , 0 0). Substituting this electric field into the left-hand side of the
second Maxwell equation, Eq. (A.1b), yields
The right-hand side of Eq. (A.1b) yields