Relationships between various responses of the electromagnetic field

Relationships between Various Responses of the Electromagnetic Field 

In this section we will explore some general relationships between the various responses of an electromagnetic field. First of all we will start from a relationship between the quadrature and inphase components of the field. For example, representing the complex amplitude of the electric field as being the sum of two components  

there is a relationship between the inphase and quadrature components of the spectrum. Let us examine this in more detail. We will make use of a solution in the form Me where M is a complex amplitude of the spectrum. In obtaining an actual sinusoidal solution one should take the imaginary part of this expression  

If the solution contains the complex amplitude term from the physical point of view this means that there is a phase shift and thus the field can be represented as being the sum of the quadrature (Q) and the inphase (In) components. We will have  

Using the conventional symbols for representing a complex variable we can write M as  

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