What is a wave? The one-dimensional wave equation
What is a wave? The one-dimensional wave equation
What is a wave? The one-dimensional wave equation
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2/3/14Waves using complex amplitudesWe can let the amplitude be complex:Where the constant stuff <strong>is</strong> separated from the rapidly changing stuff.€E(x,t) = E 0exp[i(kx − ωt − θ)]E(x,t) = [ E 0exp(−iθ) ]exp[i(kx − ωt)]<strong>The</strong> resulting "complex amplitude”:<strong>is</strong> constant in th<strong>is</strong> case (as E 0 and θ are constant), which implies that themedium in which the <strong>wave</strong> <strong>is</strong> propagating <strong>is</strong> nonabsorbing.€[ E 0exp(−iθ) ]<strong>What</strong> happens to the <strong>wave</strong> amplitude upon interaction with matter?Vector fieldsHowever, light <strong>is</strong> a 3D vector field.A 3D vector field assigns a 3D vector (i.e., an arrow having bothdirection and length) to each point in 3D space.A light <strong>wave</strong> has both electric and magnetic 3D vector fields:And it can propagate in any direction, and point in any direction in space.9
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