text: According to Beer–Lambert law, the intensity of an electromagnetic wave inside a material falls off exponentially from the surface as
  If  denotes the penetration depth, we have 
  Penetration depth is one term that describes the decay of electromagnetic waves inside of a material. The above definition refers to the depth  at which the intensity or power of the field decays to 1/e of its surface value. In many contexts one is concentrating on the field quantities themselves: the electric and magnetic fields in the case of electromagnetic waves. Since the power of a wave in a particular medium is proportional to the square of a field quantity, one may speak of a penetration depth at which the magnitude of the electric (or magnetic) field has decayed to 1/e of its surface value, and at which point the power of the wave has thereby decreased to  or about 13% of its surface value:
  Note that  is identical to the skin depth, the latter term usually applying to metals in reference to the decay of electrical currents (which follow the decay in the electric or magnetic field due to a plane wave incident on a bulk conductor). The attenuation constant   is also identical to the (negative) real part of the propagation constant, which may also be referred to as  using a notation inconsistent with the above use. When referencing a source one must always be careful to note whether a number such as  or  refers to the decay of the field itself, or of the intensity (power) associated with that field. It can also be ambiguous as to whether a positive number describes attenuation (reduction of the field) or gain; this is usually obvious from the context.