Monochromatic wave

A monochromatic wave (word origin of monochromatic light , i.e. with a single frequency ) is a wave whose deflection at a fixed point in an inertial system can be described by the function

${\displaystyle V(t)=A\cdot \cos(\omega t-\phi )}$

With

• A is the amplitude
• t the time
• ω is the angular frequency
• Φ the initial phase .

In the case of transverse waves , one has such a function with a corresponding angular frequency for each polarization component.

Complex notation

In optics and electrical engineering , waves are often represented in the complex notation :

${\displaystyle V(t)=\Re ({\underline {V}}(t))}$

The deflection is understood as the real part of the associated analytical signal.This is a complex number that describes for  t from 0 to a circle around the origin of the coordinate system with radius  A : ${\displaystyle V(t)}$ ${\displaystyle \Re }$ ${\displaystyle {\underline {V}}(t).}$ ${\displaystyle {\frac {2\pi }{\omega }}}$

${\displaystyle {\underline {V}}(t)\equiv A\cdot e^{-i(\omega t-\phi )}}$

With

• the Euler's number ${\displaystyle e}$
• the imaginary unit ${\displaystyle i.}$